136 - Core-Log Integration

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Core-Log Integration

Geological Society Special Publications Series Editors." A. J. FLEET A. C. MORTON A. M. ROBERTS

GEOLOGICAL SOCIETY SPECIAL PUBLICATION NO. 136

Core-Log Integration EDITED BY

P. K. H A R V E Y & M. A. L O V E L L University of Leicester, UK

1998 Published by The Geological Society London

THE GEOLOGICAL SOCIETY The Society was founded in 1807 as The Geological Society of London and is the oldest geological society in the world. It received its Royal Charter in 1825 for the purpose of 'investigating the mineral structure of the Earth'. The Society is Britain's national society for geology with a membership of around 8500. It has countrywide coverage and approximately 1500 members reside overseas. The Society is responsible for all aspects of the geological sciences including professional matters. The Society has its own publishing house, which produces the Society's international journals, books and maps, and which acts as the European distributor for publications of the American Association of Petroleum Geologists, SEPM and the Geological Society of America. Fellowship is open to those holding a recognized honours degree in geology or cognate subject and who have at least two years' relevant postgraduate experience, or who have not less than six years' relevant experience in geology or a cognate subject. A Fellow who has not less than five years' relevant postgraduate experience in the practice of geology may apply for validation and, subject to approval, may be able to use the designatory letters C Geol (Chartered Geologist). Further information about the Society is available from the Membership Manager, The Geological Society, Burlington House, Piccadilly, London WIV 0JU, UK. The Society is a Registered Charity, No. 210161.

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First published 1998

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Contents Preface

vii

Measurement, sealing and calibration BRISTOW, C. S. & WILLIAMSON,B. J. Spectral gamma ray logs: core to log calibration, facies analysis and correlation problems in the Southern North Sea

CORBETT,P. W. M., JENSEN,J. L. & SORBIE, K. S. A review of up-scaling and cross-scaling issues in core and log data interpretation and prediction DUNCAN,A. R., DEAN,G. & COLLIE,D. A. L. Quantitative density measurements from X-ray radiometry 17

HARVEY,P. K., BREWER,T. S., LOVELL,M. A. & KERR,S. A. The estimation of modal mineralogy: a problem of accuracy in core-log calibration

25

LOVELL,M. A., HARVEY,P. K., JACKSON,P. D., BREWER,T. S. WILLIAMSON,G. & WILLIAMS,C. G. Interpretation of core and log data-integration or calibration?

39

RAMSEY,M. H., WATKINS,P. J. & SAMS,M. S. Estimation of measurement uncertainty for in situ borehole determinations using a geochemical logging tool

53

Physical and chemical properties

AHMADI,Z. M. & COE, A. L. Methods for simulating natural gamma ray and density wireline logs from measurements on outcrop exposures and samples: examples from the Upper Jurassic, England

65

HERRON,M. M. & HERRON,S. L. Quantitative lithology: open and cased hole application derived from integrated core chemistry and mineralogy database

81

KINGDON, A., ROGERS, S. F., EVANS, C. J. (~¢ BRERETON, N. R. The comparison of core and geophysical log measurements obtained in the Nirex investigation of the Sellafield region

97

LAUER-LEREDDE,C., PEZARD,P. A., TOURON,F. & DEKEYSER,I. Forward modelling of the physical properties of oceanic sediments: constraints from core and logs, with palaeoclimatic implications

115

WADGE,G., BENAOUDA,D., FERRIER,G., WHITMARSH,R. B., ROTHWELL, R. G. & MACLEOD, C. Lithological classification within ODP holes using neural networks trained from integrated core-log data

129

Petrophysical relationships BASTOS, A. C., DILLON, L. D., VASQUEZ,G. F. & SOARES,J. A. Core-derived acoustic, porosity & permeability correlations for computation pseudo-logs

14I

DENICOL, P. S. & JING, X. D. Effects of water salinity, saturation and clay content on the complex resistivity of sandstone samples

147

SAMWORTH, J. R. Complementary functions reveal data hidden in your logs

159

SHAKEEL, A. & KING, M. S. Acoustic wave anisotropy in sandstones with systems of aligned cracks

173

vi

CONTENTS

WIDARSONO,B., MARSDEN,J. R. & KING, M. S. In situ stress prediction using differential strain analysis and ultrasonic shear-wave splitting

185

WORDEN, R. H. Dolomite cement distribution in a sandstone from core and wireline data: the Triassic fluvial Chaunoy Formation, Paris Basin

197

WORTHINGTON,P. F. Conjunctive interpretation of core and log data through association of the effective and total porosity models

213

Xu, S. & WHITE, R. Permeability prediction in anisotropic shaly formations

225

Integration of core and borehole images GOODALL,T. M., Me~LLER,N. K. & RONNINGSLAND,T. M. The integration of electrical image logs with core data for improved sedimentologicaI interpretation

237

HALLER,D. & PORTURAS,F. How to characterize fractures in reservoirs using borehole and core images: case studies

249

JACKSON,P. D., HARVEY,P. K., LOVELL,M. A., GUNN, D. A., WILLIAMS,C. G. & FLINT, R. C. Measurement scale and formation heterogeneity: effects on the integration of resistivity data

261

LOFTS, J. C. & BRISTOW,J. F. Aspects of core-log integration: an approach using high resolution images

273

MAJOR, C. O., PIRMEZ, C., GOLDBERG, D. & LEG 166 SCIENTIFICPARTY High-resolution core-log integration techniques: examples from the Ocean Drilling Program

285

Applications and case studies AYADI M., PEZARD, P. A., LAVERNE, C. & BRONNER, G. Multi-scalar structure at DSDP/ODP Site 504, Costa Rica Rift, I: stratigraphy of eruptive products and accretion processes

297

AYADI, M., PEZARD, P. A., BRONNER, G., TARTAROTTI, P. & LAVERNE, C. Multi-scalar structure at DSDP/ODP Site 504, Costa Rica Rift, III: faulting and fluid circulation. Constraints from integration of FMS images, geophysical logs and core data

311

BARCLAY,S. A. & WORDEN, R. H. Quartz cement volumes across oil-water contacts in oil fields from petrography and wireline logs: preliminary results from the Magnus Field, Northern North Sea

327

BREWER,T. S., HARVEY,P. K., LOVELL,M. A., HAGGAS,S. WILLIAMSON,G. & PEZARD, P. A. Ocean floor volcanism: constraints from the integration of core and downhole logging measurements

341

BOCKER, C. J., DELIUS, H., WOHLENBERG,J. • LEG 163 SHIPBOARDSCIENTIFICPARTY. Physical signature of basaltic volcanics drilled on the northeast Atlantic volcanic rifted margins

363

GONq:ALVES,C. A. & EWERT, L. Development of the Cote d'Ivoire-Ghana transform margin: evidence from the integration of core and wireline log data

375

TARTAROTTI, P., AYADI, M., PEZARD, P. A., LAVERNE, C. & DE LAROUZII~RE,F. D. Multi-scalar structure at DSDP/ODP Site 504, Costa Rica Rift, II: fracturing and alteration. An integrated study from core, downhole measurements and borehole wall images

391

Index

413

Preface Core and log measurements provide crucial information about subsurface formations. Their usage, either for integration or calibration, is complicated by the different measurement methods employed, different volumes of formation analysed, and in turn, the heterogeneity of the formations. While the problems of comparing core and log data are only too well known, the way in which these data can be most efficiently combined is not at all clear in most cases. In recent years there has been increased interest in this problem both in industry and academia, due in part to developments in technology which offer access to new types of information, and in the case of industry, pressure for improved reservoir models and hydrocarbon recovery. The application of new numerical methods for analysing and modelling core and log data, the availability of core scanning facilities, and novel core measurements in both two and three dimensions, currently provide a framework for the development of new and exciting approaches to core-log integration. This Special Publication addresses some of the problems of core-log integration encountered by scientists and engineers from both industry and academia. The diverse nature of the contributions in this volume are an expression of the value and need to understand core and log measurements, and the way in which they can be combined to maximum effect. Contributions range geologically from hydrocarbon-bearing sediments in the North Sea to the volcanic rocks that form the upper part of the oceanic crust. In order to constrain this diversity for presentation the volume has been divided into five sections and starts with 'Measurement, scaling and calibration', 6 papers concerned purely with aspects of core and,or log measurements themselves including cross-correlation, upscaling, measurement uncertainty and accuracy. Subsequent sections include (2) 'Physical and chemical p r o p e r t i e s ' - 5 papers, (3) 'Petrophysical relationships'-8 papers, (4) 'Integration of core and borehole i m a g e s ' - 5 papers and (5) 'Applications and case s t u d i e s ' - 7 papers. All papers were submitted in response to an open call for contributions so, within the constraints of work loads and other factors, may be considered to represent a fair snapshot of recent developments in Core-Log Integration. The volume arises from a meeting of the Borehole Research Group of the Geological Society and the London Petrophysical Society (London Chapter of the Society of Professional Well Log Analysts) held in London in September 1996. The editors are particularly grateful to Gail Williamson both for the organization of the meeting and for persistence in coaxing authors, reviewers, and editors; also to Jo Cooke at the Geological Society Publishing House for her continuous support in the production of this volume. We also wish to thank all those who undertook the often arduous job of reviewing the manuscripts, and without whose help this volume would have been that much poorer. Peter K. Harvey & Michael A. Lovell Leicester University

Spectral gamma ray logs: core to log calibration, facies analysis and correlation problems in the Southern North Sea C. S. B R I S T O W 1 & B. J. W I L L I A M S O N 2

1Research School of Geological and Geophysical Sciences, Birbeck College and UCL, Gower Street, London WC1E 6BT 2 Present address." Department of Mineralogy, The Natural History Museum, Cromwell Road, London S W7 5BD Abstract: The aim of this study is to test the usefulness of spectral gamma ray logs in subsurface correlation, lithofacies description and the interpretation of depositional environments of Namurian and Dinantian sandstones in the southern North Sea. Lithofacies and depositional environments were identified from core descriptions and compared with spectral gamma ray logs from thirteen boreholes. The results show that lithofacies and sedimentary environments can be discriminated within single wells. However, there is too much variation between wells to make an unequivocal assessment of depositional environment on the basis of spectral gamma ray logs alone. Comparison of stratigraphically correlated sandstones shows that variations between wells are often greater than variations between lithofacies. The differences between correlated sandstones using spectral gamma ray logs are largely attributed to changes in the logging environment, mainly mud characteristics, borehole quality and contractor. In addition, the occurrence of negative numbers for uranium and potassium in some wells indicates that the algorithm used to calculate elemental concentrations may be in error. For sandstones with a low total gamma ray response, small errors associated with tool calibration and data processing make a comparatively large difference to results, which has made detailed correlation of sandstones untenable. The most significant problem is the correction factor for potassium in KC1 drilling mud.

G a m m a ray logs are an essential tool for subsurface correlation and gamma ray log curve shapes or signatures are often used as the basis for interpreting ancient sedimentary environments (Selley 1978; Cant 1992). The spectral gamma ray tool measures radiation produced by the radioactive decay of naturally occurring radioactive elements. The most common naturally occurring radioactive elements in sedimentary rocks are potassium, thorium and uranium. As each of these elements decay they give off gamma radiation of a particular energy measured in MeV (millions of electron volts). The principle energies for each element are 1.46 MeV for potassium, 0.68MeV for thorium, and 1.12 and 0.98 MeV for uranium (Desbrandes 1985). The radiation from potassium (K 40) is a single energy while uranium and thorium have a series of isotopes producing radiation with a range of energies which overlap (Rider 1986). In addition, Compton scattering leads to a reduction in energy and the total gamma radiation is a complex spectrum. The spectral gamma ray tool samples the spectrum around specific energy levels, 1.46MeV for potassium, 1.76MeV for uranium and 2.62 MeV for thorium (Rider 1986;

Dresser Atlas 1992). These measured values are then recalculated to estimate the proportions of potassium, thorium and uranium, expressed as percentages or API units. Spectral gamma ray data recorded from outcrop have been used for correlation and to define sediment facies in Upper Carboniferous deltaic sediments (Myers & Bristow 1989; Davies & Elliot 1995). Spectral gamma ray data have also been used to characterize marine bands in the Upper Carboniferous (Archard & Trice 1990; Leeder et al. 1990). In this study we have attempted to apply the methodology of Myers & Bristow (1989) to Carboniferous rocks in the Southern North Sea. We have examined spectral gamma ray logs from thirteen wells in the Southern North Sea (Wells 1-13). Sedimentary logs of core were available for seven of the boreholes and stratigraphic information showed that two sandstone units 'A' and 'B' could be correlated between three and six of the wells, respectively. Unfortunately due to confidentiality agreements we are unable to identify the wells in question or the names of the correlated units. G a m m a ray logs are affected by hole conditions, in particular an oversized hole can lead to

BRISTOW,C. S. & WILLIAMSON,B. J. 1998. Spectral gamma ray logs: core to log calibration, facies analysis and correlation problems in the Southern North Sea In. HARVEY,P. K. • LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 1-7

2

C.S. BRISTOW & B. J. WILLIAMSON

a decrease in gamma ray response. To provide some control on data quality, gamma ray measurements were plotted against caliper data. Another common borehole effect is the use of KC1 in drilling mud. The potassium in the drilling mud produces an increase in absolute values of potassium on the spectral gamma ray log. This is supposed to be corrected in the processing and we have assumed that the contractors have made the right corrections to the data. However, there appears to have been no correction for variations in mud chemistry down hole. Of the thirteen wells that we have examined, ten were logged by one contractor and the remaining three were logged by a second contractor (Table 1). Seven of the wells were drilled using an oil based mud, five were drilled using a water based KCI mud and one was drilled with a salt saturated polymer. Table 1. Summary of well characteristics

Well number

Logging contractor

Drilling mud

Correlated sandstone A

1

1

KC1

2 3 4 5 6 7 8 9

1 1 2 2 1 ! 1 1

Oil KC1 Oil Oil Oil KC1 Oil Oil

A

A B

10

1

KC1

B

11 12 13

2 1 1

polymer KC1 Oil

B B B

Methods

A simple seven category lithofacies scheme was adopted for the cored wells with classification on the basis of lithology and sedimentary structures: cross-stratified sandstones, silty sandstones, s a n d y siltstones, claystones, coal, limestones and rooted beds. After depth matching of core and log and corrections for core to log slip, depth intervals for each lithofacies were defined. Lithological boundaries were picked at the shoulder of gamma ray curves to take account of readings which 'smear' across bed boundaries. The gamma ray log data were then assigned a lithofacies classification on the basis of core descriptions. Where core log depths were metric and the wireline log data in feet, the data were recalculated to metric units. For several of the wells, potassium values were given in deci. % rather than as percentages. As deci. % units give

good separation of curves on log plots, all potassium values were converted to deci. %. Having reduced the log data to cored depth intervals, element data and element ratios were plotted for each well on cross plots and logs, and between wells on cross plots and box plots. Observations

Potassium-thorium cross plots discriminate lithofacies Cross plots of potassium against thorium, thorium against uranium and potassium against uranium were produced for each cored well. The cross plots provide an easy to read display of the range of measurements from each well by facies and for comparing each facies between wells. The cross plot of potassium against thorium from Well 1 (Fig. 1) is a typical example; It shows limestones with very little gamma radiation clustered in the lower left-hand corner of the plot with cross-stratified sandstones in a field around 0.01 deci % potassium and 10ppm thorium. Finer grained lithologies, silty sandstones, sandy siltstones and claystones are less well discriminated but all show relatively high potassium and thorium. One intriguing feature of this plot (Fig. 1) is the negative values for potassium in the limestones. Negative values for potassium are very small, less that 0.005 deci %, and were only found in Well 1; however, negative values for uranium were found in wells 2, 6 and 7. The negative values indicate a problem with the algorithm used by the contractor to calculate elemental concentrations. Other wells such as Well 5 (Fig. 2) show clear discrimination between lithofacies although the absolute values are different from those in Well 1. Cross-stratified sandstones generally contain slightly less potassium and less thorium, most claystones have relatively high values of potassium but a few have almost no potassium. Changes within lithofacies for a particular well could be due to differences in the detrital composition and diagenetic history of the claystones. However, low values may also be encountered where the gamma ray response is averaged across a bed boundary. The resolution of a gamma ray tool is typically about 3 0 4 0 cm depending on the speed that the tool was run (Rider 1986) and where the sampling interval coincides with a bed boundary the measurement will not represent either lithology, but a mixture of two different lithologies. Another possible source of error is in the core to log calibration where reconstruction of a core may lead to small offsets in the core to log slip.

SPECTRAL GAMMA RAY LOG CORRELATION PROBLEMS

3

Fig. 1. Potassium and thorium cross plot for Well 1 showing good discrimination of lithofacies with limestones in the lower left corner and fine-grained claystone and siltstones in the top right.

Fig. 2. Potassium and thorium cross plot for Well 5 showing good discrimination of lithofacies. The lithofacies have similar relative values to those in Welt 1 (Fig. 1) although absolute values for each lithofacies are slightly different.

Comparison of correlated sandstones On Fig. 3, which shows cross plots of crossstratified sandstones from all seven cored wells, the data for individual wells form distinct clusters. The differences within wells is less than the differences between wells, which suggests some systematic changes between wells. Geologic factors such as a change in provenance or

diagenesis are unlikely to produce such a clear systematic difference. Other possible explanations are that the sandstones were deposited in different deltaic environments: mouth bar, distributary channel or shoreface; or that the sandstones are stratigraphically different and have different detrital sources or different diagenetic histories. One way of testing these hypotheses is to examine the character of correlated sandstones.

4

C.S. BRISTOW & B. J. WILLIAMSON

Fig. 3. Cross plots of cross-stratified sandstones between wells showing a loose grouping of all the data in the lower left hand corner of the cross plot. Measurements from individual wells tend to be tightly grouped and the difference between wells appears to be greater than the differences within a well.

Fig. 4. Cross plot of potassium against thorium for the correlated sandstone Unit A shows the same sandstone in three different wells plotting in slightly different areas, note the lack of overlap between wells with lower potassium values in Well 1 which was drilled with a KC1 mud. Unit A. This has been correlated stratigraphically between three wells. The cross plot of potassium against t h o r i u m (Fig. 4) shows the same sandstone in three different wells plotting in slightly different areas. There is almost no overlap between the three data sets and although the trends appear to be similar in each well, there is a clear difference in the absolute values. Some

variation between wells could be due to lateral facies changes, but these are unlikely to have produced the observed shift in absolute values. The similar shape of the trends combined with their differences in absolute values indicates a systematic change between wells which we attribute to changes in the borehole environment. The factors most likely to affect the logs are caving, the use of different drilling fluids, and

SPECTRAL GAMMA RAY LOG CORRELATION PROBLEMS

5

Fig. 5. Cross plot of potassium against thorium for Unit B showing a consistent trend in the data for Wells 9, 10, 12 and 13. Well 11 appears to lie off trend with significantly higher potassium and thorium content which can be attributed to an error in the correction factor for KCI in the drilling mud..

Unit B.

Fig. 6. Box plot of total gamma for sandstones and claystones. Claystones usually have higher total gamma than sandstones although there is some overlap in Wells 3 and 6. The lower than usual values in these claystones may be due to deposition in an interdistributary bay rather than a prodelta environment. variations in the procedures of different logging contractors. There is very little difference in caliper data between wells and no evidence for significant caving, which leaves two possible e x p l a n a t i o n s for the differences observed. Firstly, Well 1 was drilled with water based mud, while Wells 4 and 8 were drilled with an oil based mud. Secondly, Wells 1 and 8 were logged by a different contractor to Well 4. Reduced values for potassium in Well 1 are most likely to be due to an over-correction for potassium in the KC1 drilling mud.

The cross plot of potassium against thorium for Unit B (Fig. 5) shows a consistent trend in the data for Wells 9, 10, 12 and 13, although there is an offset between the wells largely due to differences in the amount of thorium. Well 11 has a flatter trend with significantly higher potassium and a wider range in thorium. Assuming that the original correlation is correct, is there any simple explanation for the difference? Wells 9 and 13 were drilled with an oil based mud, Wells 10 and 12 were drilled with a water based mud and Well 11 was drilled with a salt saturated polymer (221 ppmK). It would appear most likely that the correction factor for potassium in the mud has left a residual of enhanced potassium values. One might wonder why the other Wells (10 and 12), with water based mud and relatively high KC1 contents, lie on a trend with Wells 9 and 13? The answer may be that Wells 9, 10, 12 and 13 were all logged by a different contractor to Well 11. It would appear therefore that the choice of logging contractor can have a significant effect on results.

Box plots show differences between wells Box plots have been used for a comparison of total gamma ray values for cross-stratified sandstones and claystones between wells, using lithofacies defined from core. Each plot (including boxes and whiskers) shows the spread of observations about the median. The box repre-

6

C.S. BRISTOW & B. J. WILLIAMSON

Fig. 7. Cross plot of K/Th against K/U for three correlated sandstones (Unit A) shows lower potassium values and an exceptionally good correlation of thorium and uranium in Well I which are attributed to correction factors which have over-compensated for KC1 in the drilling mud.

sents 50% of measurements about the median, the whiskers extend to the minimum and maximum data values. Median values for cross-stratified sandstones are generally 50 API units or less, although they do vary between wells (Fig. 6). Total gamma ray response for sandstones is almost always less than the total gamma ray response for claystones, where the median value is close to 100 API units, although there is some overlap in Wells 3 and 6 where the claystones have lower total gamma ray response than the other claystones. There is no obvious reason for the lower total gamma ray response in these two wells. Well 3 was drilled with a water based mud, but so were Wells 1 and 7, while Well 6 was drilled with an oil based mud as were Wells 2, 4 and 5. Wells 3 and 6 are from broadly similar stratigraphic units but Wells 5 and 7 are from the same Group. One possible explanation is that the claystones in Wells 3 and 6 were deposited in slightly different environments. The core logs indicate a prodelta environment for claystones in Wells 1, 2, 4, and 7 and an interdistributary bay environment for claystones in Wells 3, 6 and 5. Re-examination of the core logs indicates that the claystones in Well 5, originally attributed to an interdistributary bay, are significantly thicker than other interdistributary bay deposits and could be re-interpreted as prodelta deposits. If this is the case, then the total gamma ray response is discriminating between sedimentary environments, not just between lithofacies.

Eliminating inter well differences using ratio plots Element ratio vs element ratio plots were generated to eliminate the systematic variations in gamma ray tool response between wells (usually due to varying well conditions) which may have been inadequately compensated for in logging company calibration procedures. The plot of K/Th ratio against K/U ratio for Unit A (Fig. 7) shows that measurements from Wells 4 and 8 overlap while measurements from Well 1 are clearly lying on a different trend. Wells 4 and 8 were both drilled with an oil based mud while Well 1 was drilled with a water based mud containing KC1. The K/Th cross plot (Fig. 4) shows low potassium values for Well 1, and the ratio plot (Fig. 7) shows an offset due to low potassium values. In addition, Fig. 7 shows an exceptionally good correlation between thorium and uranium. We suspect that the correction factor applied to compensate for KC1 mud in Well 1, has over-compensated for potassium and also affected the measurements of thorium and uranium.

Conclusions Lithofacies for Carboniferous deltaic sequences from the Southern N o r t h Sea have been identified from core descriptions and compared with spectral gamma ray logs. The results show

SPECTRAL GAMMA RAY LOG CORRELATION PROBLEMS that lithofacies can be discriminated within single wells. However, comparison of correlated sandstones shows that variations between wells are greater than variations within wells. There is too much variation between wells to make an unequivocal assessment of lithofacies and depositional environment on the basis of spectral gamma ray logs alone. The differences between wells are attributed to changes in logging environment, mainly mud characteristics, borehole quality and different logging companies which have made detailed correlations impossible. For sandstones showing low total gamma ray response, small errors associated with calibrations and correction factors will make a comparatively large difference to results. In three wells, negative values for uranium were noted and in one well negative values for potassium were found which suggests a problem with the algorithm used to calculate elemental concentrations. Cross plots of correlated sandstones indicate that correction factors for KC1 in drilling muds are not always successful, and there appears to be a difference between the results achieved by different contractors in this respect. Corrections for KC1 appear to be based on a single value for each well although mud chemistry will almost certainly change down hole. More detailed tool calibration is required before subsurface correlations and facies analysis can be reliably made using spectral gamma ray response alone. The influence of downhole environment could be further tested by comparing the geochemical composition of core with gamma ray response. In the meantime avoid trying to read too much from spectral gamma ray response where KC1 mud is involved. The authors thank Mobil North Sea for funding this work and for permission to publish the results. The manuscript has been improved by the comments of J. S. Schweitzer and P. Corbett.

7

References ARCHARD, G. & TRICE, R. 1990. A preliminary investigation into the spectral radiation of the Upper Carboniferous marine bands and its stratigraphic application. Newsletters on Stratigraphy, 21, 167-173. CANT, D. J. 1992. Subsurface facies analysis. In: WALKER R. G. • JAMES, N. P. (eds)Facies Models, Geological Association of Canada, pp. 27-45. DAVIES, S. J. 8~ ELLIOT, T. 1995. Spectral gamma ray characterisation of high resolution sequence stratigraphy: examples from upper Carboniferous fluvio~leltaic systems, County Clare, Ireland. In: HOWELL, J. A. 8z AITKEN, J. F. (eds) High

Resolution Sequence Stratigraphy: Innovations and Applications. Geological Society Special Publications No. 104, pp. 25-35. DESBRANDES, R. 1985. Encyclopedia of well logging. Institut Francais du Petrole, Graham and Trotman Ltd, London. DRESSER ATLAS. 1982. Well logging and interpretation techniques (3rd edition). Dresser Industries Inc., USA. LEEDER, M. R., RAISWELL,R., AL-BIATTY,H., MCMAHON, A. & HARDMAN, M. 1990. Carboniferous stratigraphy, sedimentation and correlation of well 48/3-3 in the southern North Sea Basin: integrated use of palynology, natural gamma/ sonic logs and carbon/sulphur geochemistry. Journal of the Geological Society, London, 147, pp. 287-300. MYERS, K. J & BRISTOW, C. S. 1989. Detailed sedimentology and gamma ray log characteristics of a Namurian deltaic succession II: Gamma ray logging. In: WHATELEY,M. K. C. & PICKERING,K. T. (eds) Deltas." Sites and Traps for Fossil Fuels, Geological Society Special Publications No. 41, pp. 81-88. RIDER, M. H. 1986. The Geological Interpretation of Well Logs, Blackie Halsted Press, Glasgow. SELLEY, R. C. 1978. Concepts and methods of subsurface facies analysis. American Association of Petroleum Geologists, Continuing Education Short Notes 9.

A review of up-scaling and cross-scaling issues in core and log data interpretation and prediction P. W. M. C O R B E T T , J. L. J E N S E N 1 & K. S. S O R B I E

Department of Petroleum Engineering Heriot-Watt University, Edinburgh, EH14 4AS, UK 1 Present address." University o f Alaska at Fairbanks, Alaska Abstract: In a heterogeneous geological formation, each rock petrophysical property (e.g., permeability, porosity, and electrical conductivity) reflects the heterogeneity and varies in a manner related to the underlying changes in fabric (grainsize, mineralogy, lamination, wettability, etc.). However, measurements, both laboratory and downhole, are made at certain volume scales dictated by the size of the core plug used or the wireline log resolution. The comparison of core and log data needs to account for both the scale and physics of the particular measurements and how these relate to the underlying scale of the geological heterogeneity of the formation. In this review, these two fundamental issues are addressed as follows: (a) measurement scale and how it relates to the 'true' or 'required' petrophysical properties of the formation is defined as 'up-scaling'; (b) measurement physics and how we relate the physics of one measurement (e.g. permeability) to that of another (e.g. density, electrical, or acoustic properties) is termed 'cross-scaling'. We illustrate how these two issues arise in the comparison and prediction of permeability using several published studies. We also outline an approach to petrophysical measurement reconciliation termed 'genetic petrophysics'. This combines all three elements--measurement scale, measurement physics, and geology--to provide an integrated and robust model. We illustrate this approach for permeability to provide fit-for-purpose models of anisotropy in the near-well region of a reservoir. It has been appreciated for some time that there is a problem of scale in reservoir engineering (e.g. Warren et al. 1961; Haldorsen 1986). The volume of a reservoir under production greatly exceeds the volume of rock recovered from cores or investigated by wireline logs. There are many efforts underway to improve the modelling of reservoirs, which particularly address the extrapolation from the sparse core-log data to the interwell volumes. Computer flow models of reservoirs involve grid blocks that are by necessity large, relative to the investigation volumes of core or logs. Therefore engineers have to integrate the core and log data for use in simulation models in a process loosely referred to as 'up-scaling'. Permeability is a particular property of interest and several techniques have been developed for its up-scaling, e.g. power averaging, renormalization, and pseudo-isation. The aim of up-scaling is to estimate the 'effective' or equivalent properties at the chosen volume scale, e.g. grid blocks. The adjectives 'effective' and 'pseudo' are often used interchangeably in the petroleum literature to denote an up-scaled property, but there is a subtle difference. The former attempts to be intrinsic to the rock/fluid system and aims to be independent of boundary conditions,

including time. The latter, on the other hand, applies on some coarse grid as a replacement of a fine grid domain, but it may change radically if the boundary conditions are changed. It will emerge from our discussion that we are frequently talking about pseudo properties when we refer to core-log data integration. The petrophysical community have appreciated for some time that there are also scaleup problems in making comparisons between core and log data (e.g. Knutson et al. 1961). However, historical practice relied on the sampling of cores with plug-size measurements at one-foot spacing (Fig. l a). These were then compared directly with the log measurements, recorded at half-foot intervals. Shifts between core depths and log depths accounted for the offset (if present) between the core and log. Occasionally, a primitive up-scaling technique using a running average ( 1 : 2 : 1 weighting) was used for the plug data prior to comparing with the log data. Although the scale discrepancies were often appreciated, there was not much else that could be done. The development of high resolution petrophysical measurements in the laboratory (probe permeameter) and downhole (image logs) has presented new opportunities to address the scale

CORBETT,P. W. M. JENSEN, J. L. & SORBIE,K. S. 1998. A review of up-scaling and cross-scaling issues in core and log data interpretation and prediction In: HARVEY,P. K. • LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 9-16

10

P . W . M . CORBETT E T AL.

Fig. 1. A comparison between (a) the traditional core plug and logging tool scales of measurement and sample spacing and, (b) the new opportunities provided by closely spaced probe data and high resolution logging tools. Both schemes are shown schematically against a core interval with a missing section. In (b) there is more scope for identifying small scale heterogeneities and less sensitivity to missing core material. Depth matching is also improved.

issues between core and log measurements. These high resolution measurements image the geology far more effectively than the conventional, low resolution devices. Indeed, image logs were developed specifically to image the geology in the subsurface, potentially replacing the need for core data. With data at high sampling densities and small volumes of measurement, the comparison between logs and cores becomes more tractable (Fig. lb) and therefore gives us a feasible approach to corelog scaling. Since the laboratory probe permeameter measures a different physics (gas flow rate) to a subsurface image log (acoustic reflection or electrical conductivity) with different boundary conditions, there are also cross-scaling relationships (see below) that must be considered in addition to volume scale and sampling density effects. In this paper, we illustrate the cross-scaling and up-scaling of permeability between core and wireline logs for subsurface prediction of permeability. Larger scale dynamic data are used to justify the methods presented. Having reviewed the method, we discuss the implications for other properties and outline a new approach to petrophysics--genetic petrophysics--which is

Fig. 2. A comparison between (a) Up-scaling and (b) Cross-scaling. Numbers refer to approximate volumes in cubic metres. Refer to the text for definition of these terms. being developed. This approach is tied directly to the needs of reservoir modeUers and offers a way of integrating data and procedures from the original geological conceptual model, through the petrophysical data acquisition, the up-scaling/cross-scaling, and the construction of the numerical reservoir simulation model.

Definitions In this paper, we define the terms up-scaling and cross-scaling as follows (Fig. 2): Up-scaling: The determination of an effective (or pseudo) property at a scale larger than that of the original measurement. An example would be using the arithmetic average of a set of layer permeabilities as an estimator of the horizontal permeability of the composite layered media (Jensen et al. 1997, pp. 137139). Comparing probe to plug to well test permeabilities is an up-scaling problem (Corbett et al. 1996a). The issue of measurement scale for the same petrophysical property is the process of upscaling. Reservoir engineers are familiar with the up-scaling of permeability for reservoir simulation. Cross-scaling is a much less familiar concept and may be defined as follows: Cross-scaling: The determination of a relationship between two different physical prop-

A REVIEW OF UP-SCALING AND CROSS-SCALING

11

erties. Using regression to summarize the relationship between porosity and permeability for a suite of core plugs is a simple example. Comparing compressional wave transit time with porosity is a cross-scaling procedure. Cross-scaling provides the relationship--if there is one--between measurements of different petrophysical properties, at different measurement volume scales which are affected by the (different again) underlying volume scale of the geological heterogeneity. This clearly concerns the transfer of information on a certain required property via a more 'easy-to-measure' surrogate. The scales at which these transfers take place are critical to assessing the appropriateness--or inappropriateness--of the surrogate property. The definition of these terms helps us distinguish the impact of geology (largely up-scaling) from the physics (largely cross-scaling) in a more systematic fashion. These concepts are useful in the comparison of core and log data. In the next two sections, we look first at the cross-scaling of permeability and resistivity at compatible scales. These data are then up-scaled for comparison with larger scale dynamic data. Together these case studies show that cross-scaling and upscaling of permeability can be achieved in practice.

Fig. 3. Measurement of properties in the laboratory at similar volume scales with a resistivity probe (above) and permeability probe (below). Refer to Jackson et al. (1994) for more details.

Case studies We consider three examples of the cross-scaling between permeability and resistivity which have been carried out and which have been reported in the literature.

Fig. 4. Correlation between resistivity (shown a formation resistivy factor= measured resistivity/brine resistivity) against probe permeability for a slab of Lochabriggs Sandstone.

Laboratory study Jackson et al. (1994) measured permeability and resistivity with probe devices for an aeolian sample that was saturated with brine in the laboratory (Fig. 3). The resistivity probe was carefully designed to investigate a volume similar to that of a steady state probe permeameter and both volumes were comparable to the sample's scale of sedimentary variation. A strong relationship was observed (Fig. 4) and this can be related to the fundamental physical control.

As-Sarah study Ball et al. (1997) carried out a probe permeameter study on a fluvial sandstone. They found that averaged probe data (at 10cm spacing) correlated reasonably well with microresistivity

(Fig. 5a) and provided the basis of a permeability predictor which was a considerable improvement over methods based on the density log and core plugs (Fig. 5b).

Morecambe Bay study Thomas et al. (1996, 1997) undertook a detailed probe study over a fluvial interval for which resistivity images had also been acquired. They found a strong correlation between the probe permeability and microscanner resistivity (Fig. 6). In all of these cases, an empirical relationship existed and was reflected in the measurements at similar scales. Such relationships could reflect an underlying physical relationship, explained by an existing analytical model (e.g. Biot's and the C a r m a n - K o z e n y models) or might provide

12

P.W.M. CORBETT E T AL.

Fig. 5. Correlation between (a) probe permeability (averaged over a 30 cm window) and micro-spherically focussed log (MSFL) resistivity and (b) plug permeability and wireline density for an interval of PUC-B Reservoir. Refer to Ball et al. (1997) for more details. insight into the need for new petrophysical analysis.

Cross-scaling permeability and resistivity In the three studies just mentioned, the relationship is driven by the effects of pore geometry and porosity upon both the hydraulic and electrical conductivities. Several workers (e.g. Doyen 1988; Katz and Thompson 1987) have shown that both transport properties depend on a characteristic pore size in the rock. The form of that dependency differs for hydraulic and electrical conductivity, thus making the hydraulic--electrical relationship strength dependent also upon the level of rock heterogeneity. In a homogeneous sample, one characteristic length and its mutual effects upon both permeability and conductivity will give rise to a strong electrical-hydraulic relationship. Heterogeneity, however, will diminish the relationship strength because different portions of a sample will have differing characteristic sizes. This explains why data at the lamination scale (e.g. Jackson et al.

Fig. 6. Comparison between probe permeability, formation image and FMI resistance for an interval of Sherwood Sandstone. Refer to Thomas et al. 0996, 1997) for more details. 1994; Thomas et al. 1996) show very strong resistivity-permeability relations, while laminaset measurements (Ball et al. 1997) exhibit a weaker, though still useful, relationship. In all cases, the effects of geological variation were mitigated by chosing similar measurement volumes.

Up-scaling permeability In two of the cases presented above, the permeability was up-scaled for comparison with some larger scale dynamic data. In the As-Sarah study, the permeability predictor developed from the microresistivity was used to predict permeability in the uncored sections of several wells. With a continuous permeability log, the cumulative permeabilitythickness product, the transmissivity, was compared with a production log spinner survey. A good comparison was found supporting the appropriateness of the predictor (Fig. 7). This predictor continues to form the basis for permeability models in the field (von Winterfeld, pers. comm.).

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In the Morecambe Bay study, the up-scaling of both horizontal (kh) and vertical (kv) permeability were required for comparison with a borehole pressure measurement. The horizontal permeability was up-scaled by taking the arithmetic average of the probe data, the vertical permeability by taking the harmonic average (Thomas et al. 1996, 1997). The up-scaled

properties (effective kv/kh ratio) compared well with a larger-scale dynamic measurement (Fig. 8). The importance of the geology in the upscaling is well illustrated in two ways in this second study. Firstly, the abrupt decline in vertical permeability (i.e. increase in anisotropy) occurs at the bed length scale which, for these stacked fluvial channels, represents several feet. The image log picks out the geological features associated with bedding and this can be exploited to produce improved prediction of formation anisotropy. Secondly, there is an assumption, supported by geological analysis of similar beds in outcrop, that the layers or beds observed at the wellbore extend well beyond the volume of investigation of the dynamic measurement. This is in contrast to the anisotropy shown by plug scale measurements which is notably poor in estimating effective kv/kh at larger scales. Averaging plug scale kv/kh ratios is also an inappropriate up-scaling method for this parameter, which is very sensitive to scale changes (Corbett et al. 1996b, Cowan 7 Bradney 1997). The comparison of up-scaled permeability (probe, plug, or wireline) with the well test can provide additional corroboration of permeability predictors. For these larger scales, the effects of the organization of the geology (i.e. sedimentary structure) can also be important. This level of up-scaling is beyond the scope of this review (refer to Corbett et al., 1996a). Nonetheless, it is important to note that up-scaling from core to log must be tied with a consistent geological framework to the scales of well tests and full field numerical grid blocks.

14

P.W. M. CORBETT E T AL.

Plug permeability - density log cross-scaling revisited We can revisit the As-Sarah example to compare the probe-microresistivity method with the plugdensity method for permeability prediction 9 This will reveal the nature of improvements provided to the petrophysicist by the smaller scale measurements 9 It seems ironic that solutions to the up-scaling problem have been facilitated (i.e. they are more accurate, not necessarily faster) by having more 'smaller' scale petrophysical measurements. This irony, however, overlooks the role of the geology in the scaling process: smaller-scale measurements are often more easily interpreted in their geological context 9 The geology provides information regarding the volume and shape of each event, allowing analysts to make inferences about the validity and frequency of the value in the unsampled regions 9 If we examine the porosity-permeability relationship (Fig. 9) for the As-Sarah reservoir, we see that it is very weak. The lack of relationship is due to a number of factors-variable grain size and sorting in the fluvial sediments, patchy rhizocretionary cements, plug orientation with respect to heterogeneities, and others. Weak porosity-permeability relationships in fluvial reservoirs are often observed (Brayshaw et al. 1996). The cross-scaling relationship, in this case, is strongly obscured by the geological heterogeneity--a smaller or larger volume scale is suggested or separation of the grain size classes (Hogg et al. 1996). Any porosity-permeability relationship from these data will be associated with a high degree of uncertainty if used to predict permeability 9 On the (weak) assumption that porosity and permeability are related, the wireline density derived porosity might be used to predict permeability. The density log has a volume of investigation that is larger than the small scale (lamination) textural features that control permeability. In this example, it also proved very difficult to depth match the plug data with the log data, the probe data were more useful in this respect. The 'true' variation in permeability shown by the probe did not correlate well with the poor resolution of the density log. Any permeability predictor based on the latter will eliminate a scale of heterogeneity that may be important to the sweep efficiency of the reservoir. The up-scaling of permeability, if this method had been followed, would result in a more uniform reservoir permeability field, which may have been inappropriate for modelling oil recovery 9

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Genetic petrophysics The Morecambe Bay example shows the power (for prediction) of scale-compatible cross-scaling and geologically-assisted up-scaling. Fig. 8 shows that the effective property (in this case, k v / k h ) varies at certain geological length scales. There is a significant and abrupt change at the bed scale (4ft) and the bedset scale (12ft). Above the bedset scale, there appears to be less variability in the estimates and close agreement with the Modular Dynamic Tool (MDT) response. While the cost implications of MDT versus image log have to be considered, image log based predictors, calibrated by MDT measurements at carefully selected intervals, hold potential for improved anisotropy estimates in the future. Anisotropy in sediments is strongly affected by bedding, so it is only appropriate that a predictor based on a log that 'sees' the bedding will be better than estimates from small volume, plug measurements. The length scales (i.e. the geological architecture) provide important guidance for the petrophysicist--the length scales for combining or comparing appropriate measurements and also the length scales to be avoided for sampling intervals. Sampling close to the frequency of the data (volume or wavelength) is a notoriously poor procedure in geophysical measurements. Unfortunately, the 1-inch plug size and 1-foot sampling interval are close to the Nyquist frequency of lamina and beds!

A REVIEW OF UP-SCALING AND CROSS-SCALING Smaller scale measurements mean more data and more work in reducing, summarizing, and integrating the data. In that respect, their development is not welcome in the time- and personnel-challenged climate demanded by industry. However, the very fact that there are representative elements within reservoirs (e.g. stratal elements, genetic units, architectural elements) can also be exploited. The fundamental rock measurements can be targetted on these representative elements. The effective properties (or even pseudos) can then be determined--by simulation or measurement for these elements (Corbett et al. 1992; Ringrose et al. 1993; Pickup et al. 1995; Huang et al. 1995). The modelling of these elements--geobodies in G O C A D - - c a n then be accompanied by the appropriate petrophysics--genetic petrophysics. This method involves a more selective use of petrophysical measurement which is intended to be more costeffective. Indeed, a genetic petrophysics approach which explicitly recognizes and solves the cross-scaling problem may be the only successful route to true data integration.

Conclusions Cross-scaling between petrophysical properties is best achieved when the scales and density of measurements are comparable. Up-scaling of petrophysical properties benefits when the geological architecture is accounted for. Probe data and image logs can be jointly used to predict permeability (horizontal and vertical in the subsurface), demonstrating that consistent-volume cross-scaling and geologically-constrained up-scaling can be effective. The tools, understanding, and techniques are now available for the development of a more geologically-based petrophysics m e t h o d - - w h i c h we refer to as genetic petrophysics--that is fit for the purposes of reservoir modelling. It is understood that improved modelling prepares the way for improved oil recovery--the ultimate motivation behind this work. The authors acknowledge the support of Wintershall and British Gas in the studies discussed above. They also wish to acknowledge the support of EPSRC and industrial co-sponsors (Amerada Hess, Amoco, BHP Petroleum, British Gas, Chevron, Fina, Saga, Schlumberger, Shell, Statoil, Texaco) for continued work in this area under the PEGASUS project. The authors also acknowledge the contributions of the various authors of the case studies from which this overview has been drawn L. Ball, J. Lewis, S. Thomas, D. Bowen and M. Jackson. Their insights while working with the data have helped to formulate and illustrate these concepts.

15

References BALL, L. D., CORBETT,P. W. M., JENSEN,J. L. & LEWIS, J. M. 1997. The role of geology in the behavior and choice of permeability predictors. SPE Formation Evaluation, 12, 32-39. BRAYSHAW,A. C., DAVIES,G. W. • CORBETT,P. W. M. 1996. Depositional controls on primary permeability and porosity at the bedform scale in fluvial reservoir sandstones. In CARLING, P. A. & DAWSON, M. R. (eds) Advances influvial dynamics and stratigraphy, John Wiley & Sons, 373-394. CORBETT, P. W. M., RINGROSE,P. S., JENSEN, J. L. & SORBIE,K. S. 1992. Laminated clastic reservoirs-The interplay of capillary pressure and sedimentary architecture. SPE 24699. Proceedings of the 67th SPE Annual Technical Conference and Exhibition, October, Washington, 365-376. --, PINISETTI, M., TORO-RIVERA, M. & STEWART, G. 1996a. The comparison of plug and well test permeabilities, Dialog, 4-8. --, GOOD, T., JENSEN, J. L., LEWIS, J. J. M., PICKUP, G., RINGROSE, P. S. & SORBIE, K. S. 1996b. Reservoir description in the 1990s: A perspective from the flow simulation through layercake parasequence flow units. In: GLENNIE, K. & HURST, A. (eds), AD 1995: N W Europe's Hydrocarbon Industry, Geological Society, London, 169-178. COWAN, G. & BRADNEY,J. 1997. Regional diagenetic controls on reservoir properties in the Millom accumulation: implications for field development. In: MEADOWS,N. S., TRUEBLOOD,S. P., HARDMAN, M. & COWAN,G. (eds) Petroleum Geology of the Irish Sea and Adjacent Areas. Geological Society, London, Special Publications, 124, 373-386. DOYEN, P. M. 1988. Permeability, conductivity, and pore geometry of sandstone. Journal of Geophysical Research, 93, 7729-7740. HALDORSEN, H. H. 1986. Simulator parameter assignment and the problem of scale in reservoir engineering. In: LAKE, L. W. & CARROLL, H. B. (eds), Reservoir Characterisation, Academic Press, Orlando. HOGG, A. J. C., MITCHELL,A. W. & YOUNG, S. 1996. Predicting well productivity from grain size analysis and logging while drilling. Petroleum Geoscience, 2, 1-15. HUANG, Y. RINGROSE, P. S. & SORBIE, K. S. 1995. Capillary trapping mechanisms in water-wet laminated rocks. SPE Reservoir Engineering, 10, 287-292. JACKSON,M. A., BOWEN,D. G., JENSEN,J. L. & TODD, A. C. 1994. Resistivity and permeability mapping at the lamina scale. Proceedings of the International Symposium of the Society of Core Analysts, Stavanger, 12-14 Sept., paper SCA-9415, 163-172. JENSEN, J. L., LAKE, L. W., CORBETT, P. W. M. & GOGGIN, D. J. 1997. Statistics for Petroleum Engineers and Geoscientists, Prentice-Hall, New Jersey. KATZ, A. J. & THOMPSON, A. H. 1987. Prediction of rock electrical conductivity from mercury injec-

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tion measurements. Journal of Geophysical Research, 92, 599-607. KNUTSON, C. F., CONLEY, F. R., BOHOR, B. F. & TIMKO, D. J. 1961. Characterization of the San Miguel Sandstone by a coordinated logging and coring program. Journal of Petroleum Technology, 13, 425-432. PICKUP, G. E., RINGROSE, P. S., CORBETT, P. W. M., JENSEN, J. L. ~; SORBIE, K. S. 1995. Geology, g e o m e t r y , and effective flow. Petroleum Geoscience, 1, 37-42. RIN~ROSE, P. S., SORBIE, K. S., CORBETT, P. W. M. & JENSEN, J. L. 1993. Immiscible flow behaviour in laminated and cross-bedded sandstones. Journal of Petroleum Science and Engineering, 9, 103-124. THOMAS, S. D., CORBETT, P. W. M. & JENSEN, J. L. 1997. Permeability anisotropy estimation within the Sherwood Sandstone, Morecambe Bay Gas

Field: a numerical approach using probe permeametry. In: OAKMAN, C. D., MARTIN, J. H. CORBETT, P. W. M. (eds) Coresfrom the Northwest European Hydrocarbon Province." An illustration of geological applications from exploration to development. Geological Society, London, 197-203. & JENSEN,J. L. 1996. Permeability and permeability anisotropy characterization in the near well-bore: a numerical model using probe permeability and formation micro-resistivity data, Transactions of The Society of Professional Well Log Analysts Thirty-Seventh Annual Logging Symposium, New Orleans, 16-19 June, paper JJJ. WARREN,J. E., SK1BA,F. F. & PRICE, H. S. 1961. An evaluation of the significance of permeability measurements. Journal of Petroleum Technology, 13, 739-744. -

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Quantitative density measurements from X-ray radiometry A. R. D U N C A N 2, G. D E A N 1 & D. A. L. C O L L I E 2

t Amerada Hess Limited, 33 Grosvenor Place, London, S W 1 X 7HY, UK 2 Robertson Research International Limited, Unit 7, Wellheads Crescent, Wellheads Industrial Estate, Dyce, Aberdeen, AB21 7GA, UK Abstract: Qualitative linear X-ray scanning has an established role in the non-destructive imaging of both slabbed and whole core and has been routinely used in visual assessment and quality control of material being subjected to other physical measurements. Since core may be observed in real time, whole core can be oriented to maximum dip prior to slabbing, especially useful where core has been resin-stabilized within an outer liner. Linear scanning is also useful in the observation of heterogeneous lithologies; the features observed are distinguished by their penetrabilities to X-rays. As a result, the linear scanner produces an image which reflects the density variation in the section analysed. A joint project carried out by Robertson Research International Limited and Amerada Hess Limited on 108ft of heterogeneous sediments has shown that the digital X-ray penetrability values ('luminance') can be extracted in order to produce a surface density variation log. X-ray luminance values show a linear relationship with the downhole Formation Density Log and may, therefore, provide an accurate tool for the correlation of core density with log density.

Qualitative linear X-ray scanning already has an established role in non-destructive imaging of both slabbed and whole core and has been routinely used in visual assessment and quality control of material being subjected to other physical measurements (for example Algeo et al. 1994; Rigsby et al. 1994). Since core may be observed in real time, whole core can be oriented to maximum dip prior to plugging or slabbing, especially useful where the core has been resinstabilized within fibreglass, pvc or aluminium liners. This ability to examine interactively, in detail and non-destructively, the 3-D nature of the internal structure of the core material is particularly important. Linear scanning is therefore useful in the observation of both heterogeneous and apparently homogenous lithologies and the following features are commonly characterized: (a) bedding features and sedimentary structures; (b) bioturbation (ichnofacies analysis), especially in slabbed sections; (c) identification of remnant structure (not readily visible to the naked eye) which has been obscured by bioturbation; (d) natural and coring-induced fractures and shears (cemented/uncemented/open); (e) cement distribution; (f) small scale grain size variation; (g) assessment of resin competence in preserved and/or sleeved core. These features are distinguished by their

different penetrabilities to X-rays. As a result the linear scanner produces an image which reflects the density variation in the section analysed (Tolansky 1961). A project carried out on 108ft of heterogeneous sediments (Duncan et al. 1996) has shown that a digital measure of the X-ray penetrability values ('luminance') can be extracted in order to produce a surface density variation log. These X-ray luminance values may yield data at close and equally spaced points producing a log with significant advantages over the data from conventional core analysis (where sample spacing may be irregular, widely spaced and lithologically chosen, or where Gamma Ray response may be poor). Such data can be compared directly with the wireline logs and it is found that the X-ray luminance values show a linear relationship with the downhole Formation Density Log (FDL). The X-ray luminance data may therefore provide an accurate tool for the correlation of core density with log density. Database

The Scott partner group provided access to a range of core and associated materials: (a) 108ft of lithologically/mineralogically variable sediments (resinated archive slabs); (b) wireline logs for the analysed interval including the appropriate FDL traces; (c) the sedimentological composite log;

DUNCAN, A. R., DEAN, G. & COLLIE,D. A. L. 1998. Quantitative density measurements from X-ray radiometry In. HARVEY,P. K. & LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 17-24

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A. R. DUNCAN ET AL.

18

(d) petrographic data for the seven thin section samples which fall within the analysed interval; (e) core analysis data (porosity, permeability and grain density) for the analysed interval.

Brief description of cores Section A The analysed interval commences within relatively 'clean', blocky, medium grained sandstones. These sandstones are assigned to the Piper Formation Depositional Unit 4c and are interpreted to be shoreface sandstones, possibly representing gully fill within an upper delta front system. At a depth of 6 ft below top of section these deposits are underlain by variably argillaceous sandstones with sandy, argillaceous siltstone interbeds. The sandstones are generally fine grained and are frequently apparently structureless or faintly laminated. Current ripples and burrows are locally observed. Bioturbation is more commonly observed in the finer grained units, some units are micaceous and locally contain carbonaceous material. Nodular calcareous cement is observed at approximately 36 ft below top of section. These lower deposits are assigned to Piper Formation Depositional Unit 4b and are interpreted to belong to an offshore transition zone. They are believed to be the deposits from turbidite flows in the lower delta front to pro-delta. Thin section analysis indicates that the predominant cement is quartz (8-11.5%) with relatively minor calcite (13.5%). Authigenic clays are dominated by kaolinite (0-3 %).

Section B The sediments within Section B are also assigned to Piper Formation Depositional Unit 4b and similarly consist of relatively clean, fine grained sandstones interbedded with siltier, argillaceous sediments which are moderately to highly bioturbated. The finer material is frequently micaceous and carbonaceous debris is locally recorded. Some of the coarser units show development of calcareous cement which is locally nodular. Thin section analysis indicates that the predominant cement is calcite (4-40%) with subordinate quartz (1-12%). No authigenic clays are recorded from the two samples analysed.

Section C The sediments analysed from Section C are

again assigned to Piper Formation Depositional Unit 4b. They also consist of interbedded fine or very fine grained sandstones and silty, argillaceous deposits. The modal grain size of the sandstones is seen to decrease towards the lower part of the analysed section. Pervasive calcareous and dolomitic, nodular cements are locally common. Thin section analysis indicates that the predominant cement is dolomite (42.5-48%) with subordinate calcite (3.5-5%) and minor quartz (0.5-2%). Authigenic kaolinite accounts for only 0.5%.

Methodology Production of the X-ray scan images A schematic representation of the scanning system is shown in Fig. 1. Although the imaging system has been developed to operate with core material of various forms and dimensions, the present investigations employed 3 ft resinated archive slabs for the imaging and quantitative density measurements. This presents a thickness of rock material for analysis which is relatively constant, both across the core diameter and along its length, and for which the 3-D inhomogeneities are reduced. In this way, differences in the core thickness and variability due to the curvature of the core are reduced and interpretation can be simplified to essentially 2-D. The X-rays passing through the rock create an inverted image of the material on an electronic image intensifier. This visible image of the X-ray field is picked up by a CCD camera and subsequently digitized. This image may be viewed in real time (i.e. the 'live' image on screen moves as the rock is transported along the gantry) and approximately 6-7in of core are observed at any one time within the camera image frame. These frames may be enhanced by a dedicated image processing computer and can be combined to produce a composite image of the 3 ft section. After positioning the core, each 'live' frame is frozen and a digital filter, which enhances the edge and structure information, is used to sharpen the image. Once the optimum image has been captured it is electronically transferred to a PC computer terminal and stored as a TIFF format file. Overlaps of approximately lin between neighbouring frames are used in order to ensure the optimum matching in the composite. The individual images are manipulated on the PC, using conventional image processing software, to produce the composite image, which is similarly stored in TIFF format. 'Hard

QUANTITATIVE X-RAY DENSIMETRY

19

Fig. 1. Schematic of X-ray scanner system. copy' images are produced using a grey scale printer matching the resolution of the digitized images. To further ensure accurate and straightforward matching of each frame to form the 3 ft composite image, a steel mesh with a grid of V2in is placed alongside each resin slab as it is inserted into the scanner. This is especially useful in sections of the core which appear structureless and homogenous. The steel mesh is positioned to avoid obscuration of the core and its image may optionally remain on the composite image for scaling and quality control purposes. Where no rock is present the image appears to be very bright (white). This is due to saturation or 'burn out' within the image intensifier, caused by the higher intensity of X-rays where there is little core material present to block them. This 'burn-out' of the image artificially increases the intensifier output in closely neighbouring areas, resulting in the surrounding rock appearing 'bleached'. In order to avoid the possible misinterpretation of the X-ray intensity in these areas, disks and/or strips of lead shielding approximating the density of the resinated slab material are placed into plug holes, and other significant gaps.

Production of the quantitative X-ray density data The digital images which are obtained from the scanner are composed of pixels of varying grey scale (0 to 255). The grey scale can be read, in

real time, at any given point across the image. Thus, by taking regularly spaced readings, a profile of the variation in the grey scale can be produced. These data (referred to as luminance values) indicates the penetrability of the rock material to X-rays and are, therefore, related to the density of the rock (Tolansky 1961). Higher luminance values represent greater penetration of the rock by the X-rays and, therefore, lower density. Conversely, lower luminance represents areas of rock with higher density and therefore greater X-ray 'stopping ability'. The luminance values (which vary between approximately 60 and 200 for typical core material) are, therefore, inversely related to the rock density. Despite the high quality of the imaging system used in the capture of the information, each of the images contains an astigmatic error. This means that there is an apparent density variation between the centre of the image compared with the edges. While this does not significantly effect the visual interpretation of the images; it is undesirable in the point luminance data. To eliminate this error, therefore, the luminance measurements are recorded from a fixed point within the X-ray field. The luminance profile is obtained by moving the rock (using the scanner transport mechanism) and recording the values at the known fixed point within the field of view. Measurements may be recorded at any required spacing; with 1 92 in spacing being used in the current project. The luminance measurements are made using a 'live' image, from which the background

20

A. R. DUNCAN E T AL.

Fig. 2. Example X-ray image frame. The included grid is of '/2 in mesh.

Fig. 3. (a) Correlation plot of luminance values from slabbed material and bulk density data from wireline logs. Core depth to log depth correction is shown schematically by tie lines. (b) Luminance data after depth correction to log depth; with wireline bulk density data overlaid. Arbitrary luminance and density scales. Luminance: solid line, Density: dashed line.

QUANTITATIVE X-RAY DENSIMETRY

21

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Fig. 4. Cross plot of luminance values from slabbed material and bulk density values derived from wireline logs. Luminance values shown both uncorrected and corrected for variations in thickness of core material. 'noise' is reduced by using a moving average filter (i.e. each measurement is made on an image comprising the average of 20 scans of the stationary rock). This is done automatically, and in 'pseudo real time', using the image processing computer. Measurements of the thickness of the slab at each luminance recording point are noted. In addition, luminance values for an aluminium block 'standard' placed at the top and base of each 3ft section are measured. Where necessary the scanner controls can be adjusted prior to scanning to ensure that the observed luminance from these calibration standards remains consistent. These data, along with the luminance values are entered into a spreadsheet and stored on the PC for subsequent analysis

Description of X-ray images Figure 2 presents a single frame showing the Xray image at the point 'F' marked on Fig. 3. The bright, irregular lines represent core breaks which are likely to be coring induced. The core breaks are locally bedding-parallel. This frame displays very clearly a partially cemented fracture running subvertically through the core. The contrast produced by variations in the core material density allows detailed examination of these and other features. A conventional core analysis plug hole, with included masking, is shown, as is the '/2 in alignment grid.

Discussion The luminance values indicate the penetrability of the rock material to X-rays and are, therefore, related to the density of the rock. Higher luminance values represent greater penetration of the rock by the X-rays and, therefore, lower density. Conversely, lower luminance represents areas of rock with higher density and therefore greater 'stopping ability' of the X-radiation. The luminance values are, therefore, inversely related to the rock density. A comparison of this luminance data, representing density, with traditional wireline log density measurements is presented in Figs 3(a and b). Figure 3(a) shows the correlation of the luminance data with the FDL trace. The tie lines indicate the core to log depth shifts appropriate for this core material. Clearly excellent correlation between the luminance profile and wireline log is observed, with Fig. 3(b) showing the luminance data depth shifted and superimposed on the FDL trace. The luminance values are smoothed (using a simple 5 point moving average filter) but are otherwise unprocessed. A cross plot of luminance against bulk density (from the wireline log) is shown in Fig. 4. Luminance values are shown both uncorrected and corrected for slab thickness variations. The correction is performed assuming a simple reciprocal relationship between thickness and luminance value: this is considered to adequately

22

A. R. DUNCAN E T AL.

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Fig. 6. Cross plot of luminance values and bulk density values, both from analysis of selected core plugs, Data differentiated by lithological unit. (Independent plug set).

describe the interaction of the X-rays with the bulk material over the relatively small observed variation in both luminance and thickness. This thickness c o r r e c t i o n is seen to h a v e little significance in the final correlation of the logs.

Detailed conventional core analysis and sedimentological analysis has been carried out on the core sections analysed for this project; this data has been c o m p a r e d with the luminance data measured from the slabbed section close to the

QUANTITATIVE X-RAY DENSIMETRY plug locations. Figure 5 shows, for example, a cross plot of porosity of the CCA plug samples against the luminance values. Again the linear relationship between luminance and this key physical property is well defined. As further confirmation of these relationships, X-ray luminance values were measured for an independent and varied collection of conventional core analysis plug samples whose physical and geological properties are well established (Duncan 1993). Figure 6 shows the bulk density for these samples plotted against luminance; the strong linear relationship is again confirmed. These data are further differentiated by lithology and while it is interesting to speculate on the relationship between lithology and luminance, this dataset is considered too sparse to prompt any reliable conclusion. Interestingly, and as a positive demonstration of the utility of these X-ray densimetry measurements, the original core to wireline shifts for the slabbed core sections were taken to be: Wireline Log Depth equals Core Depth + six feet. Comparison of the quantitative FDL (log) and luminance measurements, however, indicates that a core to wireline correction of eight feet (downhole) for section A is more appropriate. A shift of six feet for Sections B and C is confirmed by comparison of the density and luminance traces. These revised depth shifts have been applied to the luminance data presented in Fig. 3(b). While the sections analysed for this project were chosen in part for their known variation in sedimentological structure, the success of this correlation technique in its most basic form without any significant data processing clearly demonstrates the potential of these measurements. It is believed that refinement of the processing could yield considerable additional data which, coupled to the non-destructive nature of the methods, the ability to analyse material within opaque liners and the speed of data capture, makes the technique of very considerable importance.

Development Technically, the performance of the scanner is excellent. Quantitative investigations of the physical performance of the scanner, for example of the effects of variations in X-ray power output or the influence of 'burn-out' around unshielded plug holes etc., could potentially lead to direct calibration of the luminance values in terms of physical properties of the core material. Improvements in the operating procedures, in

23

the loading of the core material and, in particular, in the automated capture of the image and luminance data could allow higher throughput; enabling greater data sampling densities and potentially more detailed data processing and analysis. Perhaps of greatest interest is the elimination of the optical distortion error in the individual image frames. While the necessary geometry of the scanner is a major contributory factor to this error, it is believed that image processing may yield a significant and reliable reduction. By viewing the image of a homogenous standard (such as an aluminium block of similar size to the core section), it is possible to store the variations in the image due to this error in digital form. By 'deconvolving' the standard image obtained in this way from the images of the scanned rock it may be possible to provide a much flatter response from the imaging system. This intermediate processing would allow an accurate digital representation of the density of the core across the full image to be produced. Instead of collecting data at specific points, it would then be possible to map the density variation of the rock slab in two dimensions. This would provide, not only a more accurate log for comparison with downhole logs, but also allow the density variation to be plotted as a three-dimensional map, potentially highlighting more subtle variations in the core structure. Initial work carried out is encouraging.

Conclusion Linear X-ray scanning has an established role in non-destructive imaging of core, with the variation in image reflecting the density variation in the core section. The techniques described here allow not only the qualitative X-ray image to be produced, but also quantitative luminance values to be extracted. These correlate very well with physical core properties, for example bulk density and porosity, derived from wireline or conventional core analysis techniques. These luminance values thus provide a valuable core to log correlation tool which may be of particular value where traditional Gamma Ray or Core Analysis techniques are unavailable or relatively unreliable due to poor response or sparse data. The possibility of improving the operating procedures, in particular the sampling interval and processing methods, as well as ultimately providing full density maps of the core section promise to yield even greater benefits, and confirm the importance of X-ray imaging as a core analysis tool.

24

A . R . DUNCAN ET AL.

We gratefully acknowledge the permission to publish this material granted by the Scott partner group: Amerada Hess Limited, Amoco (UK) Exploration, Deminex (UK) Oil and Gas, Enterprise Oil, Kerr McGee Oil (UK), Superior Oil (UK) and Premier Pict Petroleum. Our thanks goes to F. Matheson at Robertson Research Int. Ltd who diligently and expeditiously undertook the preparation and measurements of the core material analysed during this project.

References ALGEO, T. J., PHILLIPS,M., JAM1NSKI,J. & FENWlCK,M. 1994. High resolution X-radiography of laminated sediment cores. Journal of Sedimentary Research A: Sedimentary Petrology and Processes, A64, 665-668.

DUNCAN, A. R., 1993. A sedimentological, petrographic and reservoir geological study of the Devonian age, old red sandstone of Gamrie Bay, Grampian Region. M.Sc. Thesis, University of Aberdeen. DUNCAN, A. R., MATHESON,F. E., & COLLIE, D. A. L. 1996. Quantitative X-ray density imaging of selected cores. Robertson Research International Ltd Project Report No D213 for Amerada Hess Ltd. RIGSBY, C. A., ZIERENBERG,R. A. & BAKER, P. A. 1994. Sedimentary and diagenetic structures and textures in turbiditic and hemiturbiditic strata as revealed by whole-core X-radiography; Middle Valley, northern Juan de Fuca Ridge. Proceedings, Scientific Results, ODP leg 139, 105-111. TOLANSKY, S. 1961. Introduction to Atomic Physics. Longmans.

The estimation of modal mineralogy: a problem of accuracy in core-log calibration P. K. H A R V E Y , 1 T. S. B R E W E R , 1 M. A. L O V E L L 1 & S. A. K E R R 2

1Borehole Research, Department o f Geology, University of Leicester, Leicester, LE1 7RH, UK 2 British Petroleum, Chertsey Road, Sunbury-on-Thames. Middlesex, TW16 7LN, UK

Abstract: In the case study described here the quantitative modal mineralogy of a number of core samples was determined with the objective of using these modes to calibrate geochemical logs. Modal estimates were obtained for the core samples by quantitative X-ray diffraction, infrared spectroscopy, point counting of thin sections, and indirectly by calculation from a complete chemical analysis of the samples. In the case of calculated modes, three different algorithms were applied. A by-product of this particularly complete dataset is the possibility of evaluating the most accurate method of modal analysis, and although no certain conclusion is reached on this point the analysis of these data does demonstrate the difficulty of obtaining accurate modal estimates. The core samples, taken at regular intervals through a sand, sandy-shale sequence, capped by a carbonate unit, have a mineralogy which, although dominated by quartz, includes feldspars, carbonates, and clays (illite, kaolinite) together with minor phases. There was generally good agreement between methods in the estimation of quartz, total carbonate, albite, kaolinite, total clay and pyrite. The results for illite and K-feldspar were poor, a reflection of their relatively low concentrations (< 10%), and problems of compositional co-linearity in the calculated modes.

A useful way of presenting data from geochemical logging tools is to transform the raw oxide curves into mineralogy logs. In a recent exercise aimed at calibrating geochemical logs in a UK borehole a number of core samples (103) were taken and analysed extensively in the laboratory for both chemistry and mineralogy, to provide a database to support the log calibration. For all 103 core plugs quantitative mineralogy was determined by X-ray diffraction at the British Petroleum laboratories in Sunbury and by infrared spectroscopy (MINERALOG) at Core Laboratories. In addition a petrographic examination was carried out, and a minimal point count made (200 points per thin section) on approximately half the samples to provide approximate modal data. All core plugs were also chemiclly analysed by X-Ray Assay Laboratories (XRAL) in Ottawa for all major and all potentially significant trace elements (a total of 69 elements per sample). From the chemical data, estimates of the modal mineralogy were calculated using a selection of different algorithms. Together these analyses result in a range of modal estimates and the purpose of this contribution is to compare these estimates in an attempt to evaluate the accuracy of the different methods. Apart from the petrographic work, all

measurements were made on aliquots of the same crushed and thoroughly homogenized rock powder for each sample. There is, therefore, essentially no scaling problem involved to explain variations in the modal estimates, and a minimal problem of sub-sampling from the rock powder.

Background Through the use of pulsed neutron devices, direct activtion of the formation by appropriate isotopes, and the natural gamma spectra it is possible to obtain an almost complete, and continuous log of the major element chemistry of a formation. These techniques were pioneered by Schlumberger (Hertzog & Plasek 1979; Hertzog et al. 1987a, 1987b, 1989; Galford et al. 1988; Rupp et al. 1989) with their Geochemical Logging Tool (GLT) offering measurements of Si, A1, Ti, Fe, Ca, K, S, the minor elements Gd, Th, and U, together with H and C1. Other tools are now available (Wyatt & Jacobson et al. 1993; Odom et al. 1994; Jacobson & Wyatt 1996, Herron & Herron 1998). Transformation of the major elements into the more conventional oxide form gives virtually complete major element oxide analysis at each measured depth interval,

HARVEY,P. K., BREWER,T. S., LOVELL,M. A. & KERR, S. A. 1998. The estimation of modal mineralogy: a problem of accuracy in core-log calibration In. HARVEY,P. K. & LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 25-38

25

26

P. K. HARVEY E T AL.

typically every 15cm, down the borehole. One approach to the interpretation of the resulting geochemical logs is their conversion into computed mineral assemblages, the so called 'chemical modes' of Wright and Doherty (1970). The resulting mineralogy logs are valuable in their own right but may be used in addition with a suitable rock classification filter to produce lithological logs (Herron 1988), or estimation of other formation properties such as matrix (grain) density, porosity, Cation Exchange Capacity (Chapman et al. 1987; Herron 1987b; Herron & Grau 1987), thermal conductivity (Dove & Williams 1988), heat flow (Anderson & Dove 1988), photoelectric factor, Pe (Kerr et al. 1992), magnetic susceptibility (Harvey et al. 1997), fluid saturation (Hastings 1988), neutron capture cross-section (Herron 1987b), and, indirectly and probably only in formationspecific situations, permeability (Herron 1987a). The transformation of a rock's elemental composition to mineral assemblages has been the subject of many contributions. Igneous petrologists have long employed the C.I.P.W. norm (Cross et al. 1903), and similar ideas have been extended to metamorphic rocks with Niggli's normative procedures (Burri 1964). In calculating norms there is no requirement that the mineral assemblage used is that which actually occurs in a rock, and as such the C.I.P.W. norm, for example, was developed originally for purposes of classification and employed a strict and standard list of 'possible'. minerals. However, for the purposes to which geochemically derived mineralogy logs might be put (lithological analysis, basin modelling, petrophysical estimation) it is necessary to estimate the percentage of the minerals that are actually present in the rock. The latter is the 'mode' of the rock which is conventionally determined directly by micrometric analysis (point counting of a thin section) or spectral methods such as Xray diffraction or infrared spectroscopy (Harville & Freeman 1988; Adam et al. 1989; Matteson & Herron 1993). The alternative approach is to compute the mode from a complete chemical analysis. Numerous authors have offered specific solutions to this inversion problem including modified normative schemes (Imbrie & Poldervaart 1959; Nicholls 1962; Pearson 1978), graphical models (Miesch 1962; Fuh 1973) and a variety of numerical models including least squares minimization, linear programming and genetic algorithms (Wright & Doherty 1970; Albarede & Provost 1976; Fang et al. 1996), while others have considered the strategy and associated practical problems of performing the inversion

on a routine basis (Herron 1986; Harvey et al. 1990; Harvey & Lovell 1992; Harvey et al. 1992; Lofts et al. 1994, 1995b). For the case study described here a particularly complete dataset is available consisting of conventional (physical) modal mineral measurements, together with comprehensive chemical analyses from which calculated modes could be obtained. It is the particularly complete nature of these data which justifies a comparison between physical and calculated methods of modal analysis, and the opportunity to make some comment on the accuracy of modes. Using natural samples (borehole core plugs) in this case, however, precludes any definite means by which one method can be chosen as 'more accurate' than another, unless a particular mode is 'obviously' wrong. As a first order assumption, however, it is likely that if two or more unrelated methods of estimation give essentially the same result then they are probably close to the true value. This level of uncertainty arises because all methods of modal estimation can give seriously erroneous results sometimes, and for some minerals; it is not simply a question of calibration and precision (repeat measurement error). With the spectral techniques particular problems arise from spectral overlap and poor resolution at the lower concentrations. With computed modes it is the choice of the correct mineral assemblage, the correct 'composition' and possible problems of compositional colinearity which are important. Modes are usually obtained by micrometric analysis (point counting of a thin section) and as such are usually expressed in volume percent of the optically identified minerals. In contrast, a set of modal proportions may be calculated, to give 'norms', by assuming an ideal or theoretical suite of minerals, and the compositions for those minerals. From these data some sort of fit may be found that partitions the mineral compositions within the initial rock analysis. Norms are usually expressed in weight percentages, and have found very wide application, particularly in igneous petrology, for characterization and classification. In these applications comparison between rocks is made with a common set of (chosen) minerals, unlike the mode, which reflects the actual minerals present. Normative mineralogy logs may be useful in the early stages of an investigation but are no substitute for the estimation of the actual mineral percentages present if attempts are to be made later to generate, for instance, a grain density log. In this report the attempt is made to calculate chemical modes, or the mineral proportions of the actual minerals present in the sample.

THE ESTIMATION OF MODAL MINERALOGY

27

Table 1. Mineralogy of the core samples. Technique Silica Feldspars Carbonates

Clays/Micas

Minor phases

Quartz Albite K-feldspar Calcite Ankerite Dolomite Siderite Muscovite Illite Smectite Kaolinite Chlorite Zircon Barite Pyrite Apatite

XRD

MINERALOG

Petrography

* * * * *

* * * *

* * * *

* *

* * * *

* * *

* * *

*

* *

* * * * * *

* mineral detected in at least one of the core samples. Anhydrite and chlorite were not detected in any of the samples by the infrared (MINERALOG) technique. See report for further comments.

Mineralogy of the core samples The mineralogy of the core samples derived from a combination of XRD, infrared (MINERALOG) and petrographic information is summarized in Table 1, and also shown as a downhole mineralogy log in Fig. 1. The 100 metre sequence consists of clastics covered by some 8 m of limestone. For purposes of description the section can be divided into five units: (Unit 1) (360-368 re)virtually pure calcite limestone; (Unit 2) (368-382m) quartz rich (60-65%) section with sub-equal quantities of feldspar (both albite and K-feldspar) and clays. Both kaolinite and illite (the latter generally in excess) are present; (Unit 3) (382-397m) quartz-carbonate dominant lithology with quartz in excess, and sub-equal proportions of kaolinite and illite; (Unit 4) (397-430 m) Very inhomogeneous section with 40 to 70% quartz, no significant carbonate, and clay concentrations up to c.30%; kaolinite generally in excess of illite. Locally high concentrations of pyrite (included with 'minor' minerals in Figure 1). ( U n i t 5) ( 4 3 0 - 4 6 0 m ) R e l a t i v e l y u n i f o r m quartz-rich (70-80%) section with minor feldspar, about 15% clay, some two-thirds of which is kaolinite, with a few percent of minor minerals. Of the possible carbonate phases calcite,

dolomite and siderite are clearly distinguishable petrographically in stained thin sections and are quantified as those species in the infrared ( M I N E R A L O G ) results. In the X R D analyses, ankerite (a Ca, Mg, Fe carbonate) is quantified in place of dolomite, so that the two spectral techniques are not estimating the same carbonate species. The carbonates occurring in Units 2 and 3 are dominantly dolomite or ankerite, with minor amounts of siderite, while the limestone unit at the top of the logged section (Unit 1) is a virtually pure calcite limestone. For the clay and other phyllosilicate minerals, kaolinite and chlorite are measured together in the X R D analyses. Chlorite was only seen in thin section in occasional grains and was not detected in the infrared figures. For this study chlorite is considered to be absent. Muscovite and illite are also determined together by XRD. Occasional distinct flakes of white mica are present in a number of sections but in no case would these make up more than a fraction of one percent of the rock. While white mica (assumed to be muscovite) is known to be present in a very small amount in some samples it was not detected by infrared spectroscopy, and is virtually impossible to calculate with any reliability due to a strong compositional colinearity with K-feldspar, illite and kaolinite which are present in significant proportions. Included amongst the minor phases which occur in at least some of the samples are zircon, barite, apatite and pyrite, all of which have been identified petrographically. Of these, only pyrite occurs locally in sufficient quantity to be identified and measured by both X R D and

28

P.K. HARVEY E T AL.

Fig. 1. Computed mineralogy log (Model A) for the section under study and showing the stratigraphic units discussed in the text. For clarity only, the major mineral groups are shown. The depth scale in arbitary. infrared. Of the other three minerals barite was detected by infrared, but both apatite and zircon were too low for the spectral methods.

Numerical modelling of the core sample mineralogy The estimation of a modal mineral assemblage from the chemical analysis of a sample requires the minerals in the assemblage to be chosen, and the compositions of those minerals to be defined. Given this information there are a variety of solution methods and strategies that can be employed to solve for the mode (Harvey et al. 1990, 1992; Lofts et al. 1994; Fang et al. 1996). For the modelling of the samples described here, the main minerals are quartz, feldspars (albite, K-feldspar), carbonates (calcite, dolomite, siderite), clays (kaolinite, illite) and the minor phases (zircon, barite, apatite, pyrite).

From the mineral data above, all the observed mineral assemblages can be established, and these, minor phases excluded, are summarized in Table 2; in all a total of thirteen different assemblages. From the chemical viewpoint the following components are available for modelling: SiO2, A1203, TiO2, Fe203, MgO, CaO, Na20, K20, MnO, P205, S, CO 2 and H 2 0 + , expressed in weight percent, together with Ba and Zr which were reported in parts per million. No other 'minor' elements are in sufficient concentration to be expected to form discrete mineral phases, or significantly alter the modal estimates of other mineral phases in which they might occur as trace lattice components. Zr and Ba are considered to occur only in zircon and barite, respectively. In addition, amongst the oxide components P205 almost certainly occurs at significant levels only in

29

THE ESTIMATION OF MODAL MINERALOGY

Table 2.

Observed mineral assemblages in the core samples (excluding minor phases).

Assemblage

l

2

3

4

5

6

7

8

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10

11

12

Silica Feldspars

* * * *

* *

* * * *

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* *

* * * *

* * *

* * * * *

* * * *

13

*

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* *

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* *

*

* mineral detected in at least one of the core samples. Anhydrite and chlorite were not detected in any of the samples by the infrared (MINERALOG) technique. See report for further comments. + dolomite or ankerite. See text for explanation. apatite which has been identified petrographically. TiO2 poses a problem, and in the first instance is best calculated as rutile, though there is no evidence that this mineral actually occurs in any of the samples. TiO2 may also be present in one of the clay phases, and this problem is discussed later where there is good evidence that it actually occurs in different minerals in different parts of the section. Sulphur is assumed to be present only as a component of pyrite. Other minerals, such as gypsum or anhydrite are possibilities, though there is no evidence for any sulphates being present, and pyrite is the only identified sulphide. Manganese, which is only present at a very low level (maximum 0.75% MnO, 90% of measurements less than 0.18% MnO), was a d d e d to iron (as FeO) for purposes of computation. Manganese often substitutes for iron, and the significant correlation (at a = 0.05; r = 0.58) between the two elements in these data is consistent with this occurring here. Removing MnO leaves a total of 14 possible mineral phases and 15 chemical components to consider. Of the several strategies employed in the modelling of the mineral assemblages in this case history three simple methods are presented here. In each case the data were pre-processed to remove the minor phases rutile, apatite, barite, zircon and pyrite which were calculated out of each core analysis assuming ideal stoichiometric compositions. Provided the chemical analyses of the core samples are accurate this procedure gives excellent estimates for these minerals which cannot be matched by any direct measurement. Although treated here as a minor phase, pyrite does reach significant concentrations in a few samples; the variation in pyrite downhole is shown in Fig. 2, and is discussed later. With extraction of these minor minerals TiO2,

BaO, ZrO2, S and P205 were removed from the data matrix leaving SiO2, A1203, FeO, MgO, CaO, Na20, K20, CO2 and H 2 0 + to be distributed, as appropriate, between the important remaining mineral phases: quartz, albite, Kfeldspar, calcite, dolomite, siderite, kaolinite, illite and possibly smectite. The simultaneous estimation of all these minerals together would constitute a fully determined system for methods of inversion involving the solution of systems of equations.

Strategies for extraction of the main mineral phases: Models A, B, C To remove complications related to methods of solution a simple unconstrained and unweighted least squares method has been used throughout (Harvey, et al. 1990) for inverting the different models. One consequence of the lack of constraint is that mineral proportions may be negative, implying an insufficiency of a combination of elements with respect to a 'perfect' solution. Such negative estimates, while impossible, offer a guide to the fact that either the modelled assemblage is wrong, or one or more of the mineral compositions are in error. Clearly, such a solution is unacceptable. One approach, then, is to model a given composition with all likely minerals, and to reject those minerals which turn out negative. This is the basis of Model A, described below. Another approach is to model each given composition to all the mineral assemblages which are known to occur in the section (Table 2), and chose the best fit as the appropriate solution. This is the basis of Model B. For Model C the mineral assemblage obtained from the X R D analysis was taken as correct, and the given composition fitted to that assemblage. This latter approach, in principle,

P. K. HARVEY ET AL.

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removes the 'guesswork' out of the choice of mineral assemblage. M o d e l A. minerals

iterative removal o f n e g a t i v e

Solutions with negative compositions imply that there is an inconsistency in the postulated mineral compositions (as stated above) and a simple means of overcoming this is by removing the mineral from the analysis. Wholesale removal of all negative minerals in one pass,

however, cannot be justified because of the complex interaction of phases in a least squares model. With little or no formal justification one procedure we have found very effective is to remove the most negative phase and re-solve the system. If negative phases still occur the procedure is repeated until all phases are positive. The procedure is illustrated in Table 3 for sample K78. The least squares fit using all nine minerals is good but dolomite is slightly negative (a) at --0.21. Removing dolomite as one of the phases sends calcite slightly negative

31

THE ESTIMATION OF MODAL MINERALOGY

Table 3. Example of the successive removal of negativephasesfor sample K78. a Quartz Albite K-feldspar Calcite Dolomite Siderite Kaolinite Illite Smectite Std. Err.

79.81 0.21 5.42 0.01 -0.21 0.22 12.13 0.00 1.29 0.011

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MINERALOG

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(a) unconstrained and unweighted least squares model. (b) as (a) but with dolomite (negative proportion) excluded. (c) as (b) but with calcite removed to give a fully positive solution. Corresponding XRD (X-ray diffraction) and Mlog (MINERALOG) estimates are given for comparison. (XRD includes 2% pyrite, Mlog 1%). Std. Err.: standard error (see text for calculation). (b). In a final stage calcite in removed (c) to give the final estimate. The mineralogical pseudo-log shown in Fig. 1 was produced using this model. For completion in Fig. 1, the trace minerals were added and the Model A derived mineralogy normalized to make the assemblages sum to 100%. The standard error given in Table 3 is a measure of the fit of the core and mineral chemistry and is computed between the original (input) chemistry, and the composition backcalculated from the derived (output) mineralogy (Harvey et al. 1990).

For each core sample a list of the minerals present had already been identified by X R D , petrography or infrared analysis. For this model the X R D mineral assemblage was chosen for each sample and then fitted accordingly. Poor fits, often with negative mineral estimates, identify a real incompatibility between the rock and mineral chemistry assuming that the phases are correctly identified by the XRD.

Model B. choice o f known mineral assemblages

Comparison of measured and calculated estimates of mineralogy

Thirteen possible parageneses for the core samples have been identified, within limits of detection, from the X R D , petrographic and infrared data. These are summarized in Table 2. Most assemblages contain five or six phases; only one (assemblage 3) contains over six (7), so that the number of minerals is generally at least two less than the number of chemical components. The procedure was to fit each sample to each of these possible assemblages. The optimum assemblage was then chosen using the following criteria:

Figs 2 through 4 summarize the variation in measured (XRD & M I N E R A L O G ) and computed (Models A & B) values for quartz, feldspars and pyrite (Fig. 2), carbonates (Fig. 3), and the clays (Fig. 4). A more detailed comparison may be made by examination of Table 4 which shows the correlations between all models and the physically derived measurements. In Table 4, based on 103 core samples, correlations > 0.19 are different from zero at a significance level of 0.05, and > 0.25, at a level of 0.01. For quartz, the best correlation is between Model A and the infrared ( M I N E R A L O G ) data; the relationship is linear (Fig. 5) and close to the 1:1 line. The agreement between the two is particularly good in the lower half of the section (Units 4 & 5), though in the upper part, below the limestone cap, the computed quartz estimates are almost consistently lower. Regression analysis of this relationship gives a slope of

(a) in virtually all cases this procedure yields a selection of potentially acceptable (nonnegative) assemblages; the one with the smallest standard error is then chosen; (b) but, if all possibilities gave at least one negative mineral proportion the assemblage with the smallest absolute negative sum was chosen.

Model C: fit to the individual mineral assemblage for each core sample

32

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1.03 and standard error of 2.36% quartz after removal of four outlying points. In view of this excellent relationship is of note that the correlation for quartz between the X R D and the infrared is slightly lower with the X R D measurements being generally higher than the infrared, often by several percent. Overall for quartz, all models perform reasonably well and show similar patterns of variation. It is not at all clear which set of data is correct! Of the feldspars, both albite and potashfeldspar are present in small quantities. Albite is virtually restricted to Units 2 and 3, with

estimates averaging between 7% and 9% for Models A and B, respectively. The infrared figures agree at 7.4%; the X R D average is lower at 2.6%. The highest linear correlation is again shown between Model A and the MINERALOG, and it is likely that these methods are giving close to the true result. For the calculated modes the albite concentration is constrained by the sodium concentration, and in the absence of any other sodium bearing mineral, an accurate estimate should be expected. With albite occurring in concentrations below 10% there are problems of sensitivity and detection limit with

THE ESTIMATION OF MODAL MINERALOGY

33

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Fig. 1. Maps showing the main structural features of the Wessex Basin (after Whittaker 1985) and the location of boreholes and Upper Jurassic exposures. (a) Boreholes in the Weald Sub-basin and position of Fig. l(b). (b) Details of the location of boreholes and outcrops in the Dorset area. between Weymouth and Swanage, which is at the edge of the Central Channel Sub-basin. Boreholes Encombe 1 (SY 9446 7785), 98/11-1 (SZ 1187 8386) and 98/11-3 (SZ 1329 8459) are on the up-thrown northern edge of the Central Channel Sub-basin, and borehole 98/11-4 (SZ 1187 8084) is in the Central Channel Sub-basin. Winterbourne Kingston 1 (SY 8470 9796) borehole is in the Dorset Sub-basin and Marchwood 1 (SU 3991 1118) is in the Mere Sub-basin. All of the other boreholes mentioned are from the Weald Sub-basin, a moderately deep graben in the eastern part of the Wessex Basin (Fig. 1). The Oxfordian Stage is represented in the lower part by mudstones of the Upper Oxford Clay Formation and in the upper part by the

Corallian Group, a complex succession of shallow-marine siliciclastics and carbonates which show marked lateral and vertical variation. The Kimmeridgian Stage (sensu anglico) of Dorset is represented by interbedded organicrich and organic-poor mudstones, with a few thin beds of fine-grained sandstone near the base and the top. These mudstones and sandstones comprise the Kimmeridge Clay Formation, and are generally of wide lateral extent. They can be correlated across the Wessex Basin and into the Wash area and Humberside using outcrops, wireline logs and borehole cores (Gallois & Cox 1974; Cox & Gallois 1981; Penn et al. 1986; Melnyk et al. 1994, 1995). The Portlandian Stage is represented by marine silty and clay-rich

CORRELATION OF WIRELINE LOGS WITH OUTCROP dolomites deposited in a moderate water-depth (Portland Sand Formation) overlain by a shallow and non-marine carbonate ramp system which comprises the Portland Stone Formation and Lulworth Beds (Coe 1996).

Field and laboratory methods for reproducing wireline log trends g a m m a ray logging

Two types of wireline gamma ray sondes exist, the conventional one which records the total natural radiation, and the spectral gamma ray sonde which separately records gamma rays emitted from 4~ 232Th or 238U and their decay products (Serra 1984). The main uses of gamma ray logs are: (i) as an indicator of lithology; (ii) to correlate the wireline signatures between boreholes; (iii) to correlate separate wireline runs within one borehole. The fact that the gamma ray tool is run in all boreholes makes it the key wireline tool for any attempt to make correlations between outcrop and the subsurface. Field gamma ray logs can be constructed using hand-held portable gamma ray spectrometers, which were originally developed and used for uranium ore exploration (Adams & Gasperini 1970). Following the lead of Ettensohn et al. (1979), total gamma ray logs have subsequently been used for surface to subsurface correlation of sedimentary strata (Chamberlain 1984; Cowan & Myers 1988; Slatt et al. 1992; Van Buchem et al. 1992). More recently, portable gamma ray spectrometers have also been used to study the distribution of K, U and Th in sedimentary rocks, and as a tool for stratigraphical correlation between rock exposures (Dypvik & Eriksen 1983; Myers & Bristow 1989; Davies & Elliott 1996; Hesselbo 1996; Parkinson 1996; Bessa & Hesselbo 1997). Previous spectral gamma ray studies on the Upper Kimmeridge Clay Formation in Dorset have been completed by Myers (1987) and Myers & Wignall (1987), who took spectral gamma ray measurements using an Exploranium GR256 on the wave-cut platforms. They utilized these data for a sedimentological and stratigraphical interpretation of organic-rich mudstones. Talwar et al. (1992) completed a study of the gamma ray spectrometry of the Corallian Beds (Oxfordian) at Bran Point,

67

Dorset using a Scintrex Scintillation Counter (SCC) spectrometer. There are two problems with the work of Talwar et al. (1992). Firstly, they appear to have used an exceedingly short sampling time of only 3-6 s, which would result in significant errors; a count time of greater than 60 s for sedimentary rocks is usual (Lovborg & Mose 1987; Parkinson 1996). Secondly, their correlation with two boreholes from the North Dorset and Wiltshire area show little similarity because the lower two-thirds of the Oxfordian strata examined in the boreholes is older than any of the rocks which they illustrate from Bran Point, and thirdly they did not take into account any of the unconformities in the Oxfordian succession (Coe 1992, 1995). Gamma ray logging field procedure. Two portable gamma ray spectrometers have been used and compared in the work reported here: a geoMetrics GR310 (manufactured 1980) and an Exploranium GR320 (manufactured 1996). Both tools use thallium-doped sodium iodide detector crystals. The Exploranium GR320 was calibrated in Toronto by Exploranium Ltd (Canada) and the geoMetrics GR310 was calibrated on the calibration pads at the British Geological Survey, Keyworth. A value for background radiation was measured 2 km offshore from Swanage, Dorset for each tool at the same time (Fig. 1). Detailed explanation of the calibration of portable gamma ray spectrometers is provided by Lovborg (1984) and Lovborg & Mose (1987). The geoMetrics GR310 provides separate measurements of either total gamma ray count, or diagnostic gamma radiation for either K, or U, or Th, and only allows count times of 1, 10, 100 and 1000s to be chosen. Source, detector and recorder are all housed in one unit 9 cm x 18 cm x 28 cm, weighing 3.4 kg. There are several advantages of the Exploranium GR320 for this type of stratigraphical study. Total counts and counts in the K, U and Th fields are all recorded during one counting period the length of which can be set by the user anywhere in the range 1 to 9999 s. The instrument carries out automatic gain stabilization, unlike the geoMetrics GR310 which has to be calibrated by the user. Automatic gain stabilization is important because portable spectrometers are prone to tool drift due to changes in temperature and humidity. The fact that the Exploranium GR320 stabilizes itself at regular intervals saves time and reduces the risk of errors due to incorrect manual stabilization. The inbuilt computer chip allows the spectra to be displayed and the amount of K, U and Th to be

68

Z.M. AHMADI & A. L. COE

a)

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Mass of effective sample = 49 kg assuming a density of 2.8 g/cm3 )ept~ =

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Cliff face Borehole Fig, 2. Sampled volume for a portable gamma ray spectrometer compared to a wireline gamma ray sonde. (a) Dimensions of the sampled volume for a portable spectrometer (modified from Lovborg et al. 1971). (b) Typical orientation and position of the sampled volume for the portable gamma ray spectrometer as used in this study. (c) Spherical sampled volume for a wireline gamma ray sonde in a borehole. This depends on the speed at which the tool is drawn up the hole, as well as the density of the rocks, but typically has a radius of 30 cm (Rider 1991). The sampled volume tends to a more ellipsoidal shape when the tool is drawn up the borehole faster.

calculated directly. The only disadvantage to this instrument compared with the geoMetrics GR310 is that it is bulkier and heavier. This spectrometer comprises two parts, a detector (11.4x39.4cm) and a recording/processing unit (24 x 10 x 25 cm) which have a combined weight of 8.4 kg. The effective sampling region of portable gamma ray spectrometers is shown in Fig. 2a. The dimensions in the figure are only approximate because the density value used by Lovbor~ et al. (1971) to calculate them was 2.8gcm-which is about 0.3-0.5 gcm 3 higher than most of

the sedimentary rocks in this study. Rocks with lower density and the same amount of natural radiation would result in a slightly larger effective sampling region. The most precise absolute values for a particular bed of greater than about 14cm in thickness are obtained by placing the tool on top of a flat bedding surface of at least 1 m diameter. Similar measurements made on beds with a thickness of less than 14 cm will obviously include some component of the underlying bed or beds. The aim of this study, however, was to compare the general trends of field gamma ray logs with wireline data. Therefore the detector was placed perpendicular to bedding (Fig. 2b) so that measurements made on all beds less than about 84cm thick will have been influenced by adjacent beds, as is the case in wireline logging (Fig. 2c). Where possible, all readings were taken on a relatively flat section of the cliff face, avoiding irregularities such as overhangs and corners to ensure that the same volume of rock contributed to each reading. Readings were only taken where the tool could be used at least 1 m above the base of the cliff, thus avoiding errors due to gamma ray contribution from rocks on the beach. Count times of 100s for the geoMetrics GR310 and 200 s for the Exploranium GR320 were used in this study. This resulted in theoretical tool precision errors of < 2.5% and < 1.5%, respectively, for the total count reading. Parkinson (1996) showed that, in practice, departures of measurement geometry from a true plane far outweigh instrument precision as a source of experimental error. In this study, it was found that readings taken along 20m of a bed vary by up to 7% for both the geoMetrics GR310 and the Exploranium GR320. This is probably due to slight lithological variations as well as differences in the volume of the effective sample size due to small undulations in the cliff face. A longer count time was used for the Exploranium GR320 because spectral data were also recorded. Radioactive decay of natural elements is a r a n d o m process, so shorter sampling periods give a greater statistical error. Specifically, the percentage statistical error varies with the number of counts collected: the higher the count, the more accurate the measurement. For typical needs, 1000 counts (3% error) is accurate enough (geoMetrics GR310,

Fig. 3. Composite field gamma ray log for the Upper Jurassic succession exposed between Furzy Cliff and St. Alban's Head, Dorset, measured using the geoMetrics GR310 portable gamma ray spectrometer, plotted against the wireline gamma ray log from borehole 98/11-4 (SZ 1187 8084). Gaps in the composite field log are due to lack of exposure or non-accessibility of the section with a portable gamma ray tool. See Fig. 1 for location of borehole and outcrop sections.

CORRELATION OF WIREEINE LOGS WITH OUTCROP

69

70

Z . M . A H M A D I & A. L. COE

CORRELATION OF WIRELINE LOGS WITH OUTCROP Operating Manual; Lovborg 1984). A longer count time had to be used for the Exploranium GR320 because it takes longer to record sufficient gamma ray counts in the K, Th and U windows than it does for the total gamma ray measurement. The spectral data recorded with the Exploranium GR320 are not discussed further in this paper. The measurement procedure used for both spectrometers was to take a reading once in every bed of less than 50 cm thick and every 3050cm in beds greater than 50cm thick. The geoMetrics GR310 was used to record total gamma ray readings throughout the best Upper Jurassic exposures in Dorset, resulting in 1124 total gamma ray readings with an average sample interval of 45cm over 503m (Fig. 3). Part of the Kimmeridge Clay Formation was selected to compare the results from the two spectrometers. Full spectral gamma ray data were thus recorded with the Exploranium GR320 at 824 sample points over 251 m of the Kimmeridge Clay Formation (average sample interval 30cm; Fig. 4). The average sampling distance of 30-45 cm is within the limits of the effective sampled volume for each spectrometer (84cm; Fig. 2; Lovborg et al. 1971) and each consecutive reading overlaps the previous reading resulting in a moving average, thus making it comparable with the wireline gamma ray tool as it is pulled slowly up the borehole.

Density logging Wireline density logs record the bulk density of rocks, by emitting gamma rays into the formation and recording the number of back-scattered gamma rays at a fixed distance from the source. The bulk density is a function of the density of the matrix and the density of the fluids in the pore space. Therefore any attempt to construct a field density log with the same character and resolution as the wireline density log has to take into account the density of the matrix and the density of the pore fluid. The vertical resolution for older single-detector tools is 40 cm and for more modern two-detector tools is 25 cm (Serra 1984).

Density logging laboratory procedure. Fresh rock samples of smaller than 3.1 cmx3.1 cmx3.7cm

71

representative of the majority of the beds in the Upper Oxford Clay F o r m a t i o n , Corallian Group and Upper Kimmeridge Clay Formation were collected for density analysis. These amounted to 116 samples over 90m of the Upper Oxford Clay Formation and Corallian Group (Fig. 5) and 260 samples over 280m of the Kimmeridge Clay Formation (Fig. 6). All the samples were dried in an oven at a temperature of less than 35~ prior to the measurements being taken. A Ruska Universal Porometer (model 1051-801) was then used to measure the volume and grain density of the samples. The density of each sample was then calculated using a single typical fluid density value of 1.06gcm -3 for pore fluids present within Upper Jurassic rocks of the Wessex Basin; this actual value was recorded at Palmers Wood 3 borehole (TQ 3655 5255) in the Weald Basin (pers. comm. P. Rowe). The raw density curves on Figs 5 and 6 show the density values calculated from the actual samples measured. To obtain the box curve, two further procedures were applied. Firstly, beds from which no samples had been obtained were assigned an average density typical for that particular lithology, calculated from the measured samples collected nearby. Secondly, the same density value was assigned to the whole thickness of the bed. It was noted that the sandstones of the Nothe Grit Formation and the Bencliff Grit Member (top of the Redcliff Formation) had lower density values than those seen on the wireline density logs. This was interpreted to be due to higher porosities of these rocks at outcrop than in the subsurface, resulting from dissolution of calcite cement. The density values of these beds were therefore corrected as follows: their average porosity in the subsurface was estimated by plotting typical density and sonic values on porosity evaluation log interpretation charts (Atlas Wireline Services 1985; Schlumberger 1994). The additional, secondary dissolution porosity that was calculated to be present in the rock samples was multiplied by the difference between the density of calcite and the pore fluid and added to the calculated total density for the samples. The box curve was then filtered using the Atlas Wireline Services field acquisition filter (Atlas Wireline Services 1992). This is an eleven point, Gaus-

Fig. 4. Comparison of the field gamma ray logs measured using the Exploranium GR320 and the geoMetrics GR310 portable gamma ray spectrometers, for that part of the Kimmeridge Clay Formation exposed between Hobarrow Bay and Chapman's Pool, Dorset (SY 896 790-SY 955 771). For detailed sedimentological and stratigraphical log of the section, for the definition of the bed group numbers which have partly been derived from the literature and for formalization of the following beds; Clavell's Hard Stone Band, Little Stone Band and Pectinatus Nodules, see Coe (1992). See Fig. 1 for location of outcrop sections.

72

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sian-weighted, moving-average filter. The total filter length used was 1.1 m. This results in a filtered field density curve with similar character and resolution to a wireline density log (Figs 5 and 6).

Surface to subsurface correlation

Upper Jurassic composite field gamma ray log The field gamma ray data from nine different locations along the Dorset coast were combined to produce a composite field gamma ray log for the Upper Jurassic strata of Dorset (Fig. 3). Comparison with the wireline gamma ray data from borehole 98/11-4, which are plotted at the same scale, show that the same general trends and wireline log patterns are present in both sets of data throughout the Upper Jurassic interval. Clearly distinguishable in both log signatures are the overall trends of decreasing and increasing response which are interpreted as representing long-term facies changes controlled by relative changes in sea-level (Coe 1992). For instance, the overall upwards decrease in gamma ray values for the pallasioides Zone of the Kimmeridgian to the anguiformis Zone in the Portlandian reflects the change from marine mudstones to carbonates interpreted as a long-term lowering of relative sea-level (Coe 1992, 1996). The one notable difference is that the Lower Kimmeridge Clay (baylei to autissiodorensis zones) is thicker in borehole 98/11-4 than in the outcrop section. This is due to the fact that the measurements for the Lower Kimmeridge Clay were made on exposures situated on the footwall of the Central Channel Sub-basin, where the succession is apparently complete but thinner.

Comparison of the geoMetrics GR310 and the Exploranium GR320 Figure 4 shows a comparison of the total gamma ray measurements taken with the two spectrometers over part of the Kimmeridge Clay Formation. The decreasing and increasing trends, amplitude of variation, and the shape of the peaks and troughs correlate very well. The main difference between the two signatures is the higher resolution of the Exploranium GR320 log, which results from the 30 cm average sample interval compared to a 45 cm average sample interval for the geoMetrics GR310. The correlation coefficient between the two field gamma ray logs over 245 m of the

Kimmeridge Clay Formation is 0.7 (Fig. 4) . This was calculated using Corpac, a signal correlation computer program (Globex Consulting Services, Ltd 1992) which is based on a simple mathematical inverse method to correlate two time series (in this case depth series) described by Martinson et al. (1982). The reason the correlation coefficient is not higher is because the Exploranium GR320 log has higher resolution, and because of the gaps in the data. Higher correlation coefficients are obtained if the two logs are correlated over shorter intervals which contain no gaps in the data.

Correlation of field and wireline gamma ray logs Upper Oxford Clay and Corallian Beds. The field gamma ray log shows, from the base, an overall upwards decreasing and then increasing trend in the gamma ray values, as do the logs in boreholes 98/11-4 and 98/11-3, reflecting the change in lithology from mudstones to sandstones and limestones, and then back to mudstones and iron-rich sandstones (Fig. 7). The Nothe Grit Formation is a better defined gamma ray low in boreholes 98/11-4 and 98/11-3 than in the field gamma ray log, probably because the sands are cleaner in the boreholes and the clays of the overlying Redcliff Formation contain a high percentage of carbonate in the outcrop section. Three prominent gamma ray peaks in the Osmington Oolite Formation can be seen on both the field gamma ray log and in 98/11-4 (Fig. 7). Over a wider geographical area the Corallian Beds are lithologically very variable, being comprised of shallow-marine sandstones and limestones. Sequence stratigraphical interpretation of the wireline logs using the number and character of the cycles does permit a correlation to be made across the Wessex Basin; however, the lateral lithological variability makes correlation based purely on the wireline log character difficult. Kimmeridge Clay Formation. The similarity between the field gamma ray logs produced by the two different spectrometers and the wireline gamma ray log from Encombe 1 borehole (approximately 1 km inland from the outcrops) is shown in Fig. 8. The data acquired using the smaller sample interval with the Exploranium GR320 spectrometer produces a higher resolution curve, despite the fact that the sampling interval is about one third of the effective sampling diameter of the tool (Fig. 2). Using the methodology for calculating correlation

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coefficients described above, the correlation coefficient for the Exploranium GR320 field gamma ray log and the wireline log from the Encombe 1 borehole is 0.92, but it is only 0.82 for the geoMetrics GR310 field gamma ray log and the wireline log. Figure 9 shows the similarity between the geoMetrics GR310 field gamma ray log and wireline gamma ray logs from boreholes up to 170 km away (Fig. 1). There are several particularly prominent features, including the two gamma ray lows with a low amplitude of variation seen in the Collendean Farm (TQ 2480 4429) and Ashdown 1 (TQ 5005 3035) boreholes in the hudlestoni and wheatleyensis zones, which are often referred to as the 'Kimmeridge limestones' (Hancock & Mithen 1987). At outcrop, these two gamma ray lows with a low amplitude of variation are prominent thick homogeneous calcareous mudstone units (middle and upper part of bed 40 and the lower part of bed 44; Fig. 4). The two gamma ray lows in Collendean Farm 1 and Ashdown 1 (Figs 1 and 9) are probably more enhanced than those in 98/11-4 and the field gamma ray log because the sediments have an even higher calcium carbonate content. A higher quartz sand content is discounted because the lithology over the same intervals in the nearby Warlingham borehole (TQ 3476 5719) comprises argillaceous limestones and calcareous mudstones (Worssam et al. 1971). Prominent gamma ray lows on the field gamma ray log like those in the middle of autissiodorensis Zone, at the base of elegans Zone and near the top of scitilus Zone, are carbonate-rich cemented horizons. Similar sharp gamma ray lows in 98/11-4 and Collendean Farm 1 probably also relate to calcareous cemented horizons.

Correlation of field and wireline density logs Upper Oxford Clay and Corallian Beds. Production of an outcrop density log over this interval of mixed siliciclastics and carbonates is more problematic than that for the Kimmeridge Clay Formation. Processing of the data in a similar manner to that of the Kimmeridge Clay Formation resulted in a filtered density curve with very little variation. However, further processing of the data to take into account dissolved carbonate cement at outcrop, as described above, resulted in a curve which is more similar to the borehole density logs. The general trends seen on the filtered density log (Fig. 5) show a positive correlation with the wireline density from Marchwood 1 borehole

and to a certain extent with borehole 98/11-1. The Winterbourne Kingston 1 borehole density log is more difficult to correlate in the lower part due to the lack of variation on the large scale. Fig. 5 also shows the marked lateral and vertical variation of the Oxfordian strata between the wireline logs of 98/11-1, Marchwood 1 and Winterbourne Kingston 1. One notable example of this is the differences seen between the three wells for the density of the Nothe Grit Formation (or its equivalent) and the Osmington Oolite Formation.

Kimmeridge Clay Formation. Figure 6 shows the comparison between the processed field density log for the Dorset coast (filtered density log of Fig. 6) against the nearby Encombe 1 borehole, and the Bletchingley 1 (TQ 3622 4772) and Detention 1 (TQ 7478 4020) boreholes in the Weald Basin. The general trends and the character of all of these logs is remarkably similar. The four high peaks which straddle the pectinatus to hudlestoni zonal boundary in both the outcrop density log and Encombe 1 log represent more carbonate-rich cementstone beds. The distinctive increase in density seen in all the logs at the top of the lower third of the hudlestoni Zone represents at outcrop a change from interbedded organic-rich and organic-poor mudstones to a thick calcareous mudstone (Coe 1992). Similar lithological changes are interpreted to occur in the borehole sections. Conclusions (1) The geoMetrics GR310 and Exploranium GR320 gamma ray spectrometers can both be used to produce field gamma ray logs which are comparable with borehole gamma ray wireline logs. Whilst the newer Exploranium GR320 is more accurate and can be used to gather spectral data more quickly, the older geoMetrics GR310 does produce excellent data with repeatable and comparable gamma ray trends. The most comparable signal between hand-held spectrometers and wireline log tools is produced by using the hand-held spectrometer perpendicular to the bedding with a sample interval of 30 cm or less. Field gamma ray logs produced for the Kimmeridge Clay Formation can be used to positively correlate, often down to the bed (typically < l m ) but at least down to the bed group scale (typically 10 in), with wireline gamma ray data from nearby boreholes. Larger gamma ray features can also be correlated with boreholes as far as 170km

CORRELATION OF WIRELINE LOGS WITH OUTCROP away in the Weald Sub-basin. Field gamma ray and wireline gamma ray data for the Oxfordian show similar trends but complex local lithological heterogeneity may be misleading. The concepts of sequence stratigraphy (i.e. recognition of the metre to tens of metre scale cycles) considerably aid in making the correlation. This is because the interpretation relies on the recognition of wireline log trends rather than correlating similar lithologies, and requires identification of stratigraphic gaps and condensed intervals. (2) Small rock samples from outcrop can be used to produce a field density log. Some processing of the data is required to produce a signal which is directly comparable with the wireline tool. The method could easily be applied to small rock samples from core or washed cuttings. Excellent results comparable with the wireline signature were obtained for a thick succession of interbedded organic-rich and organic-poor mudstones and cementstones (Kimmeridge Clay Formation). Where the lithology varies more widely and shallowmarine sandstones and limestones (e.g. Corallian Beds) are present, it is necessary to take into account the differences in porosity between the borehole and outcrop section and apply a further correction factor to the outcrop density data. (3) The measurement and processing of the physical characteristics of rock exposures to produce a wireline log signature is invaluable in the understanding of boreholes where core is not available. The data can be readily used to supplement and enhance conventional litho- and bio- stratigraphical correlations between boreholes, and boreholes and outcrop. Z. Ahmadi was supported by a Durham University Research Studentship and an AAPG-PESGB Grantsin-Aid grant for field and laboratory studies. We thank Charlotte Martin and Toby Harrold for their assistance in the field, and Brian Turner for the loan of his geoMetrics GR310 gamma ray spectrometer. The Exploranium GR320 was purchased from a grant awarded to A. L. Coe from the Open University Research Development Fund. M. Oates of British Gas provided the wireline and biostratigraphical data from boreholes 98/11-1, 98/11-3 and 98/11-4, and H. Bailey of the British Geological Survey provided the wireline data for the onshore boreholes in the Wessex Basin. We would particularly like to thank N. Goulty for his constructive comments during the preparation of this paper and two anonymous referees are thanked for reviewing this paper.

79

References ADAMS, J. A. S. & GASPERINI, P. 1970. Gamma ray spectrometry of rocks, Elsevier, Holland. ATLAS WIREL1NE SERVICES. 1985. Log Interpretation Charts. Western Atlas International, Inc. ATLAS WIRELINE SERVICES. 1992. WDS advanced log evaluation - documentation. Western Atlas International, Inc. BESSA, J. L. & HESSELBO, S. P. 1997. Gamma ray character and correlation of the Lower Lias, SW Britain. Proceedings of the Geologists' Association, 108, 113-129. CHAMBERLAIN,A. K. 1984. Surface gamma ray logs: a correlation tool for frontier areas. American Association of Petroleum Geologists Bulletin, 68, 1040-1043. COE, A. L. 1992. Unconformities within the Upper Jurassic of the Wessex Basin, Southern England, DPhil Thesis, University of Oxford. 1995. A comparison of the Oxfordian successions of Dorset, Oxfordshire, and Yorkshire. In: TAYLOR, P. D. (ed.) Field Geology of the British Jurassic. Geological Society, London, 151-172. 1996. Unconformities within the Portlandian Stage of the Wessex Basin and their sequencestratigraphical significance. In: HESSELBO,S. P. & PARKINSON, D. N. (eds) Sequence Stratigraphy in British Geology, Geological Society Special Publications No. 103, 109 143. COWAN, D. R. & MYERS, K. T. 1988. Surface gamma ray logs: A correlation tool for frontier areas: Discussion. American Association of Petroleum Geologists Bulletin, 72, 634-636. Cox, B. M. & GALLOIS,R. W. 1981. The stratigraphy of the Kimmeridge Clay of the Dorset type area and its correlation with some other Kimmeridgian sequences. Report of the Institute of Geological Sciences, 80/4. DAVIES, S. J. & ELLIOTT,T. 1996. Spectral gamma ray characterisation of high resolution sequence stratigraphy: examples from Upper Carboniferous fluvio~leltaic systems, County Clare, Ireland. In: HOWELL, J. A. & AITKEN, J. F. (eds) High Resolution Sequence Stratigraphy." innovations and applications, Geological Society Special Publications No. 104, 25-35. DYPVIK, H. & ERIKSEN, D. O. 1983. Natural radioactivity of clastic sediments and the contributions of U, Th and K. Journal of Petroleum Geology, 5, 4094 16. ETTENSOHN, F. R., FULTON, L. P. & KEPFERLE, R. C. 1979. Use of scintillometer and gamma ray logs for correlation and stratigraphy in homogeneous black shales. Geological Society of America Bulletin, part II, 90, 828-849. GALLOIS,R. W. 8z Cox, B. M. 1974. Stratigraphy of the Upper Kimmeridge Clay of the Wash area. Bulletin of Geological Survey of Great Britain, 47, 1-16. HANCOCK,F. R. P. & MITHEN,D. P. 1987. The geology of the Humbly Grove Oilfield, Hampshire, UK. In: BROOKS, J. & GLENNIE, K. (eds) Petroleum Geology of North West Europe, Graham & Trot-

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Z . M . AHMADI & A. L. COL

man, 161-170. HESSELBO, S. P. 1996. Spectral gamma ray logs in relation to clay mineralogy and sequence stratigraphy, Cenozoic of the Atlantic Margin, offshore New Jersey. In: MOUNTAIN, G. S, MILLER, K. G, BLUM, P., POAG, C. W. & TWlCHELL, D. C. (eds) Proceedings of the Ocean Drilling Program Scientific Results, 150. LOVBORG, L. 1984. The calibration of portable and airborne gamma ray spectrometers - theoo', problems and facilities, Report Riso-M-2456, Riso National Laboratory, Denmark. & MOSE, E. 1987. Counting statistics in radioelement assaying with a portable spectrometer. Geophysics, 52, 555-563. , WOLLENBERG,H., SORENSEN,P. & HANSEN, J. 1971. Field determination of uranium and thorium by gamma ray spectrometry, exemplified by measurements in the llimaussaq alkaline intrusion, South Greenland. Economic Geology, 66, 368-384. MARTINSON,D. G., MENKE,W. & STOFFA,P. 1982. An inverse approach to signal correlation. Journal of Geophysical Research, 87, 4807~4818. MELNYK, D. H., SMITH, D. G. & AMIRI-GARROUSSl,K. 1994. Filtering and frequency mapping as tools in subsurface cyclostratigraphy, with examples from the Wessex Basin, UK. In: DE BOER, P. L. & SMITH, D. G. (eds) Orbital Jorcing and cyclic sedimentary sequences, International Association of Sedimentologists, Special Publications 19, 35 46. , ATHERSUCH,J., AINSWORTH,N. & BRITTON, P. D. 1995. Measuring the dispersion of ostracod and foraminifera extinction events in the subsurface Kimmeridge Clay and Portland beds, Upper Jurassic, United Kingdom. In: MANN, K. O., LANE, H. R. & SCHOLLE,P. A., Graphic correlation, Society of Economic Paleontologists and Mineralogists, Special Publications, 53, 185-203. MYERS, K. J. 1987. Onshore-outcrop gamma ray spectrometry as a tool in sedimentological studies. PhD thesis, University of London. - - & BRISTOW,C. S. 1989. Detailed sedimentology and gamma ray log characteristics of a Namurian deltaic succession II: gamma ray logging. In: WHATELEY, M. K. G. & PICKERING,K. T. (eds), Deltas." Sites and traps for jbssil fuels, Geological Society Special Publications, 41, 81-88. & W1ONALL, P. B. 1987. Understanding Jurassic organic-rich mudrocks new concepts

using gamma ray spectrometry and palaeoecology: examples from the Kimmeridge Clay of Dorset and the Jet Rock of Yorkshire. In: LE~GETT, J. K. & ZUFFA, G. G. (eds) Marine Clastic Sedimentology - concepts and case studies, Graham & Trotman, London, 172-189. PARKINSON,D. N. 1996. Gamma ray spectrometry as a tool for stratigraphical interpretation: examples from the western European Lower Jurassic. In: HESSELBO, S. P. & PARKINSON, O. N. (eds) Sequence Stratigraphy in British Geology, Geological Society Special Publications, 103, 231-255. PENN, I. E., Cox, B. M. & GALLOIS, R. W. 1986. Towards precision in stratigraphy: geophysical log correlation of Upper Jurassic (including Callovian) strata of the Eastern England Shelf. Journal of the Geological Society, London, 143, 381-410. RIDER, M. H. 1991. The geological interpretation of well logs. Whittles Publishing, Caithness. SCHLUMBEROER 1994. Log Interpretation Charts. Schlumberger Wireline & Testing, Houston, Texas. SERRA, O. 1984. Fundamentals qf well-log interpretation 1. The acquisition of logging data. Developments in Petroleum Science 15A. Elsevier, Holland. SLATT, R. M., JORDAN. D. W., D'AGOSTINO, A. E. & GILLESPIE, R. H. 1992. Outcrop gamma ray logging to improve understanding of subsurface well log correlation. In." HURST, A., GR1FFITHS, C. M. & WORTHINGTON, P. F. (eds) Geological Applications of Wireline Logs H, Geological Society Special Publications, 65, 3-19. TALWAR, A. D., HENDERSON, A. S. & HART, M. B. 1992. Simple gamma ray response of the Upper Jurassic from the Dorset coast - a preliminary investigation using the scintillometer profile technique. Proceedings of the Ussher Society, 8, 70-72. VAN BUCHEM,F. S. P., MELNYK,D. H. & McCAvE, [. N. 1992. Chemical cyclicity and correlation of Lower Lias mudstones using gamma ray logs, Yorkshire, UK. Journal of the Geological Society, London, 149, 991-1002. WmTTAKER, A. (ed.) 1985. Atlas of Onshore Sedimentary Basins in England and Wales: Post-Carboniferous Tectonics and Stratigraphy. Blackie, Glasgow. WORSSAM, B. C., IVIMEY-COOK, H. C. 1971. The stratigraphy of the Geological Survey Borehole at Warlingham, Surrey. Bulletin of the Geological Survey of Great Britain, 36, 1-146.

Quantitative lithology: open and cased hole application derived from integrated core chemistry and mineralogy database M. M. H E R R O N & S. L. H E R R O N Schlumberger-Doll Research, Old Quarry Road, Ridgefield, C T 06877-4108, USA

Abstract: A new quantitative lithology interpretation is based on elemental concentrations of silicon, iron, calcium and sulfur available from logs. The lithology interpretation is founded on an integrated chemistry-mineralogy core database comprising over 400 samples from many wells of predominantly sand and shaly sand composition located on four continents. The lithological components include 'clay', which is the sum of all clay minerals; 'carbonate', which is the sum of calcite and dolomite; "anhydrite', which is the sum of anhydrite plus gypsum; and 'sand' or 'quartz-feldspa~mica', which is the remainder of the formation essentially constituting the sand fraction. The new interpretation demonstrates that the elements aluminium alone or a combination of silicon, calcium, and iron provide a much more accurate estimation of clay than either gamma ray or its individual components potassium, thorium and uranium. Calcium alone or calcium and magnesium are used to determine carbonate concentrations. Calcium and sulfur can be used to estimate the anhydrite fraction. Having estimated the total clay, carbonate, and anhydrite fractions, the remainder of the formation is assumed to be composed quartz, feldspar, and mica minerals. Examples of the new lithology interpretation are provided for core data and also for geochemical log data from both open and cased hole environments.

The accurate determination of formation lithology from common geophysical logs is hindered by a lack of sensitivity coupled with nonunique responses to the minerals that reside in sedimentary rocks. The interpretation of lithology for the purpose of wireline petrophysical evaluation or geological characterization primarily consists of estimating fractions of shale, sand, and carbonate. Nuclear logs, either gamma ray, photoelectric factor, and/or a combination of neutron and density are the most commonly used logs for lithology interpretation, A desire for improved accuracy in Ethological description led to the introduction of several generations of nuclear spectroscopy logs. Recent developments in open and cased hole logging have made it possible to obtain accurate concentration logs for the elements silicon, calcium, iron, sulfur, titanium, and gadolinium at relatively low cost and high logging speeds (Herron 1995). A new lithological interpretation has been developed to capitalize on these new logging capabilities. It is founded on an extensive database of core chemistry and mineralogy. The new interpretation provides quantitative estimates of: total clay, which is the sum of all clay minerals; carbonate, which is the sum of calcite and dolomite; anhydrite, which is the sum of anhydrite plus gypsum; and quartz-feldsparmica (Q F-M), which is the remainder of the formation essentially constituting the sand frac-

tion. The clay, carbonate, and quartz-feldsparmica portions of this interpretation have been presented previously (Herron & Herron 1996). This paper provides a brief introduction to the new geochemical logging capabilities in both open and cased holes and a detailed examination of the new core-based interpretation.

Elemental concentration logs The recently developed technique to estimate elemental concentrations from a single, inducedneutron gamma ray spectrometer (Herron 1995) is an adaptation of a geochemical oxides closure model already employed in the computation of elemental concentrations from multiple nuclear sondes (Hertzog et al. 1987; Schweitzer et al. 1988; Grau & Schweitzer 1989; Grau et al. 1989). The most significant modifications are: (1) the elimination of aluminium and potassium as necessary inputs to the geochemical closure model, thus considerably reducing the number of wireline sondes necessary to produce elemental concentrations of potassium; (2) a change in the elemental associations of iron. Figure 1 presents examples of elemental concentration logs from the new processing using data

HERRON, M. M. & HERRON,S. L. 1998. Quantitative lithology: open and cased hole application derived from integrated core chemistry and mineralogy database. In. HARVEY,P. K. & LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 81-95

81

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from an open hole Elemental Capture Spectroscopy (ECS; Mark of Schlumberger) sonde. This is a nuclear spectroscopy device which uses a standard AmBe source and a BGO detector. It is combinable and can log at up to 540 m hr -l (1800 fthr-~). Chemical concentrations measured on

core samples are shown for comparison. Two points should be made when examining the data. The first is that since the uncorrected prompt capture yield for iron contains gamma rays from both Fe and A1, the log Fe should be approximately equal to Fe+0.14A1. Accordingly, the

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core points plotted for c o m p a r i s o n are Fe+0.14A1. The second point is that the log concentrations agree well with core data. A second example is provided from a cased hole Reservoir Saturation Tool (RST; Mark of Schlumberger) log acquired from a well in Venezuela (Fig. 2). This example is processed using new elemental standards to derive the far detector capture yields (Roscoe et al. 1995), and corrections are made for casing and a 3.8cm cement annulus. The results show good agreement between log concentrations and the sparse core data.

tion coupled plasma mass spectrometry, for whole rock elemental concentrations of silicon (Si), aluminium (A1), iron (Fe), calcium (Ca), magnesium (Mg), sodium (Na), potassium (K), phosphorus (P), titanium (Ti), manganese (Mn) and chromium (Cr), expressed as oxides, plus Loss on Ignition (LOI) representing total volatiles, H20 +, H 2 0 , sulfur (S), organic carbon, thorium (Th), uranium (U), gadolinium (Gd) and boron (B). A synthetic core gamma ray (GR) computed from core chemistry using the gamma ray response is given by equation (1) G R = 4 T h + 8 U + 16 K

Core database The development of the new quantitative lithology interpretation begins with a core database that contains chemistry and mineralogy measurements on over 400 core plug samples from numerous wells on four continents. The wells are diverse in age and geographic location, but all are predominantly sands and shaly sands. To analyse the samples, rocks were crushed and split with a microsplitter into chemistry and mineralogy fractions. The chemistry fraction was analysed at X-Ray Assay Laboratories using XRay fluorescence, neutron activation and induc-

(1)

where Th and U concentrations are in ppm and K concentrations are in wt% (Ellis 1987). The mineralogy fraction was analysed using a new Fourier Transform-Infrared (FT-IR) procedure which simultaneously analyses the mid-IR and far-IR frequencies. The mid-IR procedure was described in Matteson & Herron (1993). Since that time the number of mineral standards has been increased to 26 with approximately the same level of accuracy (better than +2 wt %). The mineral standard set includes quartz, albite, anorthite, K-feldspar, muscovite, biotite, kaolinite, illite, smectite, chlorite, glauconite, calcite,

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dolomite, siderite, ankerite, magnesite, aragonite, gypsum, anhydrite, hematite, barite and opal. Total clay is the sum of kaolinite, illite, smectite, chlorite and glauconite. Although there are significant amounts of mica, another layered silicate, they are not included in the total clay fraction. At high clay concentrations there is sometimes interference between illite and mica phases. Exploring elemental relationships

The most complex aspect of the new lithology interpretation is the computation of the clay mineral fraction. In the logging world, clay, or more often volume of shale, is most frequently estimated from the gamma ray log. However, there are many type of clay minerals with widely differing compositions and log responses, so shale estimates often carry large uncertainties. The estimation is further degraded by the many non-clay minerals which contribute significantly to the gamma ray.

Gamma ray and clay With the core database, it is possible to evaluate the relationship between total clay determined by FT-IR and the computed gamma ray on a

porosity-free basis, as recently advocated by K a t a h a r a (1995). The relationship for core samples from 12 data sets is presented in Fig. 3. A line connecting the origin with 100% clay and 250 API is included for visual reference. As expected, gamma ray content generally increases as clay content increases. However, there are a number of characteristics in the clay-gamma ray plots that highlight the weaknesses inherent in this approach; many of these have been recently discussed by Bhuyan & Passey (1994) and Hurst & Milodowski (1994). The first major feature is the large range of slopes in the gamma ray versus clay plots which demonstrates the necessity for local calibration. For example, in Well 1, a linear trend predicts a maximum gamma ray value of about 100 API for the pure clay end member, whereas Well 2 would predict 500 API. For Well 12, a pure clay would have a gamma ray of only about 150 API. In several wells, either the data or an extrapolation of the data to zero clay indicate a near zero minimum gamma ray, but Well 4 has a minimum gamma ray of 30 API, and in Well 12 an extrapolation points to 70 API for minimum gamma ray. The difference between evaluating these plots and using only log data is that with core calibration the amount of clay is known, and it is possible to accurately extrapolate to

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2.5 5 Potassium wt% o o

9

ee

9 9 e~po

d.'t' t

lb

Aluminumwt*/,

20

0

100

i

5 10 Uranium ppm

k,..'

100, ,

~~'

0

1 2 Titanium wt*/, ....

0

5 Gadolinium

0

20

10

. 9 00

u." 0

"4.

25 Silicon wt%

50

~ 0

15 Iron wt%

30

Calcium wt%

40

Fig. 6. Comparison of individual chemical elements that can be measured by logging against total clay for Well 6. A1 shows a strong positive correlation. The anticorrelation with Si is significantly perturbed by carbonates.

86

M.M. HERRON & S. L. HERRON

comparison of clay with aluminium. In Well 3, aluminium displays a strong relationship with total clay. The remaining elements in this figure are some that can be obtained by prompt thermal neutron capture spectroscopy logging devices. The two elements remaining in the second row of the figure are titanium and gadolinium. These elements are commonly enriched in shales, but they show only a loose correlation with total clay. The third row holds the key to a new technique for estimating clay. It begins with silicon, which is a major constituent of rock forming minerals. Although silicon is commonly associated with quartz, it is actually the second most abundant element after oxygen in both sandstones and shales. Because it is a major element, its abundance is not affected by trace minerals, and concentrations form a smooth continuum between high silicon sandstones and medium silicon shales. For reference, quartz has 46.8 wt% silicon. The next element is iron, which has numerous associations, including heavy minerals such as siderite, pyrite, hematite, and magnetite and the clay minerals illite, chlorite, glauconite and some smectites. High concentrations of the heavy iron minerals can interrupt the smooth relationship between silicon and clay content. The final element is calcium which is mainly associated with the carbonate minerals calcite and dolomite. The low calcium concentrations indicate the absence of carbonate minerals in Well 3. The same type of comparison between total clay and elemental concentrations is presented in Fig. 5 for Well 5. For this well, none of the individual elements (Th, U and K) contributing Seeking an elemental alternative to natural gamma ray is any better correlated with clay than is total gamma ray. In contrast, One goal of this study is to identify an aluminium again shows a tight correlation with alternative, less subjective approach to determining clay content using elemental data available clay content. Silicon again shows a strong from nuclear spectroscopy logging devices. The negative correlation with clay, but there are two data points which clearly deviate from the technology exists to measure elemental concenmajor trend. These two samples contain 13 and trations from natural radioactivity (Th, U and 38 wt% siderite (FeCO3) as reflected by the two K), neutron activation (AI), and capture gamma high iron points. As in Well 3, the near absence ray spectroscopy (Si, Ca, Fe, Ti, Gd and S). of calcium reflects the absence of calcite and Figure 4 shows a comparison of clay content with all available logging elements (except sulfur) dolomite. A final example of the element-clay comparfor Well 3. The three components of natural gamma ray; Th, U, and K, are presented in the isons is presented in Fig. 6 for Well 6. In this first row. Thorium and uranium show wide well, thorium and potassium exhibit positive scatter and little correlation with clay. In this correlations with clay, but the degree of scatter well, potassium shows a strong correlation with precludes the use of these elements for accurate clay, but examination of data from four other clay prediction, especially at low clay contents. Aluminium again shows a strong positive correwells in the field reveals that this correlation breaks down entirely in sands containing less lation with clay. Silicon again shows a negative correlation with clay, but the impact of carbothan 25% clay. The second row of Fig. 4 begins with a nate minerals on the silicon--clay curve is much

zero clay. With only log data, one must choose a minimum and maximum gamma ray value without knowing the correspondence to real clay concentrations, and the picture is further complicated by porosity variations. For Well 11, the minimum gamma ray value observed on the log is about the same as the 50 API minimum computed for the core data. This value would normally be assigned to zero clay instead of the actual 25 wt% clay. Clearly, such a log interpretation would severely under-estimate the clay content in the well. The second dominant feature in Fig. 3 is the scatter in the data, particularly in Wells 1-10. In these wells, even if the observed correlation between gamma ray and clay were known, the scatter in the data would produce an uncertainty of as much as +20 wt% clay or more. For Wells 3, 5, 7 and 9, at levels of about 20% clay, observed gamma ray values span almost the full range from clean sand to shale. The relative error is particularly large in sands. A third and less common feature is that some wells exhibit a small dynamic range in gamma ray while clay content varies considerably. This is notable in Well 12 which is a typical offshore Gulf of Mexico example. It is also true in Wells 4 and 11. In spite of the problems outlined above, it would be possible to make good clay predictions in Wells 2, 11 and 12 if detailed and accurate core data were available. Without such a calibration, it is doubtful that the picks for GRmax and GRmi n from the log data would match the core calibration parameters.

QUANTITATIVE LITHOLOGY

100

a

w

87

r

Well I

.="/

Well5o

/

_~ s o

100 Well6

o/

-./ .

/

; Y

100

I Well9 /

Well8

/

.'.s/

Well1 2 ~

.

Aluminum wt%

00

Alumi10num wt%

20 0

10 ' 20 0 Aluminumwt%

Alumi1()num wt%

20

Fig. 7. Aluminium versus total clay for all 12 wells. The correlation with total clay is much tighter for aluminium

than for GR. In addition, the slopes are about the same and most wells show a near-zero offset.

more obvious 9There are many samples with high calcium reflecting calcite concentrations that range from 0 to 85 wt%. This mineral assemblage produces a ternary composition diagram in the silicon-clay plot with the vertices representing pure carbonate, clean sand, and shale. Summarizing the observations in Figs 4 through 6, it appears that aluminium is the best single elemental indicator of clay. Silicon shows a complementary anti-correlation to clay content, but the simple linear relationship between silicon and clay is distorted by carbonate minerals. The carbonate content is chemically represented by calcium and/or iron. These trends are typical of those observed in the other data sets. Having observed the strong relationship between aluminium and clay, it is useful to examine the data for all 12 wells, as shown in Fig. 7. In 10 of the 12 wells, the slope of the aluminium-clay plot is nearly constant. In 9 of the 12 wells, the intercept of the aluminium-clay linear relationship is essentially zero. Comparison between Fig. 7 and Fig. 3 shows that aluminium is a much better clay estimator than gamma ray in most wells. This is true even when a porosity-free core calibration is available for gamma ray, and it is especially true in the sands 9

The improvement of aluminium over gamma ray is marginal in Well 8, but it is significant for the cleanest sands. In Wells 11 and 12, the aluminium and gamma ray are comparable clay indicators if the core calibration is known. However, a log interpreter who equates the minimum gamma ray response with zero clay introduces a 20 to 25 wt% error in the clay estimation. Aluminium has an even more striking relationship with the sum of clay plus mica. This is demonstrated in Fig. 8. Improvements in the correlation with aluminium are most notable in Wells 7 and 8, and the effects are most obvious in the shales. The lines drawn in Fig. 8 represent a slope of 6.4 and the relationship for the first 10 wells has a correlation coefficient of 0.98. It is possible that some of the differences between Figs 7 and 8 are due to analytical interference between illite and mica phases in shales 9 The decision to include or exclude mica from the clay fraction depends on the application. Since micas do not contribute significantly to clay counterion conductivity, they are not generally included in saturation interpretation. On the other hand, like clays, micas can be detrimental to formation productivity. There are several reasons for the strong

88

M.M. HERRON & S. L. HERRON 100

5c

I~ +

100

....

~; + 50 /

,/,

tO |

lOO

/

~ 50 0

Well1 /

Well1 0 /

lO |

Aluminum wt%

20 0

Well 12

/ 1'0

Aluminum

wt% 20 0

1'0

Aluminum

wt% 20 0

,

10

Aluminum

.......

wt% 20

Fig. 8. Aluminium versus total clay +mica for all 12 wells shows an even tighter and more universal relationship than aluminium versus clay.

correlation between aluminium and total clay mineral content. Clays are aluminosilicates; aluminium is a major element in and an integral part of the chemical composition of virtually all clays. This is very different from the case of thorium and uranium which occur at trace (ppm) levels and are not structural components of the clays. Of course, the clay-A1 relationship is a simplified picture and is not expected to be perfect. Different clay minerals have different A1 concentrations and there are important nonclay minerals that contain aluminium.

Relationship between AI and Si, Ca, Mg and Fe Although aluminium is the best element for clay estimation, its measurement in a borehole is accomplished by induced neutron activation and currently requires a chemical source, two gamma ray spectrometers, and an independent measurement of formation capture cross-section, making it an expensive measurement. Fortunately, an alternative exists due to the complementary relationship between aluminium and the elements silicon, calcium, magnesium and iron. This relationship is illustrated in Fig. 9, which combines elemental data from all 12 data sets

into three plots. For samples containing more than 2 wt% organic carbon, the elemental data must be normalized to an organic-free matrix or else they will perturb the linear relationship. Earlier, Figs 4 to 6 showed that as clay increases, silicon decreases. Therefore, as aluminium increases, silicon decreases. In Fig. 9a, silicon is converted to SiO2 (by multiplying by 2.139) and subtracted from 100. Now, we see that as AI increases, 100-SiO2 also increases. In this presentation, carbonate minerals drive the data toward A1 of zero and ( 1 0 0 - SiO2) values of 100 wt%. We can use concentrations of Ca and Mg to compensate for the presence of calcite (CaCO3) and dolomite (CaMg(CO3)2). Fig. 9b shows that concentrations of A1 vary linearly when plotted against 1 0 0 - S i O 2 - CaCO3 - MgCO3 concentrations and that the additional terms remove almost all of the disturbance of that major trend. The few remaining outliers are predominantly siderite or pyrite, and they can be removed as 1.99Fe where the coefficient of 1.99 is optimized on these data. The trend in Fig. 9c can be used to estimate the aluminium concentration from A1 = 0.34(100 - SiO2 - CaCO3 MgCO3-1.99Fe),

(2)

.r

89

QUANTITATIVE LITHOLOGY

20[a

I' b

o 'ot

C

/

;

~

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06

5"0

100

100 - Si02

0

00

50

100

100 - Si02- CaCOzMgC03

0

O Q

50

100

100 - Si02- CaCOsMgCOs- 1.99Fe

Fig.

9. Aluminium is estimated from the other major elements in sedimentary rocks. (a) A1 vs 100-SIO2 shows a clear trend that is disturbed primarily by carbonates. (b) A1 vs 100 SiO2-siderite and dolomite shows a very tight trend that is disturbed only by siderite and pyrite rich samples. (c) When the high-Fe minerals are corrected for, A1 can be estimated from Si, Ca and Fe.

2~ We"' / "10I f ~< 0 U ;

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o

,

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IlU'

2O

E < e

00

|

|

10 20 0 10 20 10 20 0 10 20 0 Aluminum Emulator Aluminum Emulator AluminumE m u l a t o r Aluminum Emulator

Fig. 10. Aluminium estimated from Si, Ca, Mg and Fe closely matches measured aluminium in all 12 wells. which produces estimates of A1 with a correlation coefficient of 0.99 and a standard error of 0.6 wt% A1. Figure 10 presents a comparison of measured A1 concentrations with those estimated from equation (2) for each of the 12 wells. Clearly, this is a robust means of estimating A1 from Si, Ca, Mg and Fe.

Quantitative lithology The strong correlation between aluminium and clay provides the cornerstone of the lithology

interpretation. This relationship can be quantified to estimate clay, and the elements calcium, magnesium, and sulfur can be used to estimate the other major mineralogical components. The mineralogical fractions defined here are different from the lithologies commonly used in log interpretation. The main difference is that a clay fraction rather than a shale fraction is computed. According to Bhuyan & Passey (1994), shales commonly have about 60 wt% clay minerals and 40 wt% Q - F - M . Using this ratio, a rock with 60 wt% clay is 100 wt% shale. The other difference

90

M. M. HERRON & S. L. HERRON 100 .........

.,

]Well 1

,~

/

01r ol00[Well5 " /

Well 4

Well 6

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o /

./

./

jwey.

IWe"7/

Iwe"

0[/r

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50 100 Estimated Clay

50 1O0 0 Estimated Clay

50 1O0 Estimated Clay

Fig. 11. Clay estimated from Si, Ca, Mg and Fe plotted against total clay for all 12 wells is a near duplicate of Fig. 7.

is that the values determined here are all on porosity-free (or matrix) basis, and they are weight rather than volume fractions.

minimum of 1.3 for Well 10. If we solve for clay plus mica (Fig. 8) instead of clay, we obtain the following equation:

Estimating clay

Clay + Mica = 2.20(100- SiO2-

The two major points from the preceding section are that A1 correlates well with clay content and that aluminium concentrations can be estimated from Si, Ca, Mg and Fe. The next logical step is to estimate clay content from Si, Ca, Mg and Fe using the form of equation (2). The problem is set up to determine clay content by optimizing the slope. Samples from Wells 11 and 12 are excluded from the optimization because, as seen in Fig. 7, the relationship between aluminium and clay differs significantly from the relationships observed in Wells 1 through 10. The new clay algorithm is: Clay = 1.67(100 - SiO2 - CaCO3 M g C O 3 - 1.99Fe),

(3)

which has a correlation coefficient of 0.94 and a standard error of 6.9 wt% clay. The slope of 1.67 obtained here is representative of the combined datasets. Slopes optimized on individual datasets range from a maximum of 2.0 for Well 1 to a

C a C O 3 - M g C O 3 - 1.99Fe),

(4)

with a correlation coefficient of 0.97 and a standard error of 6.5 wt%. Figure 11 presents measured clay content and estimates from equation (3) for all 12 wells. The estimated clay concentrations are in good agreement with the measured values for Wells 1-7, 9 and 10. They are almost the same as the estimates from aluminium shown in Fig. 7. For most of the first ten wells, the clay estimates portrayed in Fig. 11 constitute an improvement over those attainable from gamma ray. The scatter in the estimate is drastically reduced, particularly at the low clay concentrations where clay estimation is most critical. This is especially clear in Wells 1-7 and 9 and 10. In Well 8, the estimate of clay shows a less spectacular effect relative to gamma ray, but it does offer slight improvement in the clean sands. In this well, an estimate of clay plus mica would clearly be superior to gamma ray estimates. Equation (3) is a general algorithm for

QUANTITATIVE LITHOLOGY

91

estimating clay from elemental data. It has broad applicability and does not require picks of minimum and maximum values. Unlike neut r o n - d e n s i t y separation, equation 3 is not affected by the presence of light hydrocarbons or gas. Although the slope would vary if optimized on individual datasets, the overall slope of 1.67 in equation (3) produces a good clay estimate. For Wells 11 and 12 the clay estimated from equation (3) agrees with the measured clay in the cleanest samples but under-estimates the clay content of the shales. The cleanest samples in these two wells have 20 and 28 wt% clay, and it is not obvious which way the data would trend in cleaner rocks. This is the same trend observed for these two wells in the comparison of aluminium versus clay. The problem with the interpretation of clay from A1 or from Si, Ca and Fe in Wells 11 and 12 is basically the same as the problem with interpreting gamma ray. Inherent in both interpretation schemes is the presumption that nonclay minerals do not interfere. For most wells, this is true for aluminium. However, Wells 11 and 12 are characterized by feldspar-rich sands. This is true to a lesser degree for Well 4. In fact, for all three of these wells, there is an anticorrelation between clay and non-clay aluminosilicates (feldspars plus micas). The high feldspar content of the sands can be either authigenic as in Well 11 or detrital as in Well 12. In spite of vast geological differences, Wells 11 and 12 show similar patterns in terms of aluminium vs clay. This suggests that a common algorithm might exist to interpret clay content in these wells, and if so, it might be broadly applicable to feldspar- or mica-rich sands. The relationship determined by least absolute error optimization on the combined Well 11 and Well 12 datasets is:

feldspathic sands, so the application of equation (5) requires some external knowledge.

Clay2 = -20.8 + 3.1 (100 - SiO2 -

Here, the non-zero offset of - 7 . 5 wt% accounts for the small calcium contribution from plagioclase feldspar in sandstones, and the offset and

C a C O 3 - M g C O 3 - 1.99Fe)

(5)

This differs from equation (4) by modifying the slope and introducing an intercept. The results for Wells 11 and 12 are compared to measured clay in Fig. 12. Data from Well 4, which also has moderately feldspar-rich sandstones, are included as different symbols; this well was not included in the optimization. Equation (5) for feldspar-rich sandstones gives reasonable results for clay contents in the reservoir rocks despite the fact that these wells are from very different geological environments. Using the geochemical data alone, it is not possible to identify such

loo ;g/

~, 5

50

0 ~0

50 1 oo Estimated Clay2

Fig. 12. Clay estimated from equation (5) for feldsparrich sands and shales vs measured clay for Wells 11 and l 2 (o) and Well 4 (+). Estimating carbonate The second c o m p o n e n t in this lithological description is the carbonate fraction. The carbonate fraction will be determined from calcium, but first we need to consider the calcium concentration which we obtain from log data. Pure calcite (CaCO3) formations have Ca concentrations of 40 wt%, and this concentration is accurately reflected by log data. A complication arises in dolomites (CaMg(CO3)2) because magnesium has not normally been detected by spectroscopy logs. As a result, the log calcium concentration in a pure dolomite is also 40 wt% (see Hertzog et al. 1987 and Roscoe et al. 1995 for detecting Mg from logs). This is equivalent to saying that the Ca detected by logs equals C a + 1.455Mg, an expression that equals 40 wt% in either pure calcite or dolomite. Using the core data base, calcite plus dolomite concentrations were optimized as a function of (Ca + 1.455 Mg) to produce equation (6): Calcite + Dolomite - 7.5 + 2.69(Ca + 1.455Mg). =

(6)

/ ,/ o

o 50 1 oo Estimated Calcite + Dolomite

Fig. 13. Calcite plus dolomite estimated from equation (6) vs measured calcite plus dolomite for all twelve wells.

92

M.M. HERRON & S. L. HERRON

oo[

o

so

0

0 50 100 0 50 100 E~imated Clay wt% Estimated Carbonate wt%

0 50 100 Estimated Q-F-M wt%

Fig. 14. Comparison of estimated and measured quantities of clay, carbonate, and quartz-feldspar-mica on samples from all 12 wells.

slope (2.69) are balances to provide the correct answer in pure carbonate. The carbonate estimate from equation (6) closely approximates the sum of calcite plus dolomite from all 12 wells (Fig. 13) with a correlation coefficient of 0.98. A distinction of calcite from dolomite is possible with the inclusion of magnesium (Hertzog et al. 1987; Roscoe et al. 1995).

Estimating quartz-feldspar-mica The third component of the new lithological description is the sand fraction composed primarily of quartz, feldspars and micas ( Q - F M). This fraction is determined by subtracting the clay and carbonate fractions from 100 wt%. Figure 14 shows the estimated and measured concentrations of clay, carbonate, and quartzfeldspar-mica for all 12 wells. In the reservoir rocks, where clay content is less than 30 wt%, the agreement between measured and estimated concentrations is remarkably good for all components. In the shales, particularly where clay exceeds 50 wt%, the interpretation tends to under-estimate clay and over-estimate Q - F - M . Obviously, the clay algorithm could be optimized to give more accurate estimates in shales. The carbonate estimates are good over the entire dynamic range.

Estimating anhydrite This three component lithological description is easily modified to accommodate formations containing significant amounts of anhydrite or gypsum. The anhydrite estimate precedes the carbonate estimate to separate carbonate calcium from anhydrite calcium. Two estimates of anhydrite are made, one from sulfur and one from calcium, according to stoichiometric relationships where the sulfur concentration in anhydrite is 23.55 wt. % and the calcium concentration is 29.44 wt.%.

Anhl = S/23.55

(7)

Anh2 = Ca/29.44.

(8)

The final anhydrite estimate is the minimum of these two to account for the possibility of nonanhydrite sources of either sulfur or calcium. The anhydrite computation precedes the carbonate and clay estimate's and the anhydrite calcium is subtracted from the total calcium prior to the other lithological computations. When solving for anhydrite, the Q - F - M fraction is determined by subtracting the clay, carbonate, and anhydrite fractions from 100 wt%. Fig. 15 presents a comparison of anhydrite measured by FT-IR and anhydrite using calcium and sulfur from a single well in West Texas. 40 35 30 E ~=25 (3.

(-920 +

e15 -E

"O

~r 1 0 < 5 I

I

I

A

10 20 30 Estimated Anhydrite wt%

40

Fig. 15. Comparison of estimated and measured quantity of anhydrite on a single dataset.

Application to log data The ultimate goal of this study is to identify an objective, robust, and efficient means of estimating lithology from spectroscopy logs. The two simultaneous developments that have made this possible are the determination of elemental

QUANTITATIVE LITHOLOGY concentrations from induced gamma ray spectroscopy logs and the derivation of the lithology algorithms presented above. To apply these relationships using the data from Figs 1 and 2 requires that the clay algorithms be modified to account for the known aluminium interference in the iron measurement. Equations (3), (4) and (5) for computing clay or clay plus mica become: ClayL = 1.91(100 -- SiO2 - CaCO3 - 1.99FeA1) (9) Clay + MicaL = 2.43(100

-- SiO2 -

(10)

CaCO3-1.99FeA1)

Clay2L = -- 18.5 + 3.34(100-SiO2-- CaCO3 - 1.99FeA1)

(11)

where the L subscript designates the application to log data. FeA1 designates the quantity that would be detected as iron by a spectroscopy device and is equal to Fe + 0.14A1. The clay, carbonate and Q - F - M fractions calculated using the Fig. 1 open hole spectroscopy data from Well 8 are presented in Fig. 16. Also shown are the core clay, carbonate and Q F - M fractions determined from the F T A R mineralogy. The agreement between core and log data is quite good, in spite of the fact that

93

Well 8 is probably the worst example of the A1clay relationship. The interpretation of the cased hole spectroscopy logs from Well 3 (Fig. 2) is presented in Fig. 17. The agreement between core and log data is quite spectacular considering that these measurements are made with a ll~in, diameter tool through casing and cement. Conclusions

The quantitative lithology presented here has been optimized on core data from numerous wells from around the world. The lithological fractions of clay, carbonate, anhydrite, and quartz-feldspar-mica are ideally suited for the elemental concentration logs of silicon, calcium, iron, and sulfur, which can be acquired by single, induced gamma ray spectroscopy logs. These elemental concentration logs could be available in both open and cased hole. The strength of this elemental approach to estimating lithology lies in the use of major element chemistry as opposed to trace element chemistry which can be so easily impacted by sediment diagenesis, depositional environment, or the spurious introduction of small amounts of heavy minerals. The elements used are major element contributors to the rockforming minerals. Their concentrations in a given mineral are relatively stable, and the

20("

40(

=...... w

9

E

60(

80( l_ t-t

A

100(

=

120(

F"-"

1400

160C 0

50

Clay, wt%

1 O0

0

50

Carbonate, wt%

1 O0

0

50

Quartz-Feld-Mica, wt%

1 O0

Fig. 16. Quantitative lithology logs for Well 8 using the openhole elemental concentration logs shown in Fig. 1. FT-IR core measurements are provided for comparison.

94

M.M. HERRON & S. L. HERRON x 10 4 1.01

! w

1.03

L

[1.05

B i

L 1.07

0

50 Clay, wt%

1 O0

~:" 0

i 50 Carbonate, wt%

O0

0

50 1 O0 Quartz-Feld-Mica, wt%

Fig. 17. Quantitative lithology logs for Well 3 using the cased hole elemental concentration logs shown in Fig. 1. FT-IR core measurements are provided for comparison. minerals in which they occur are generally abundant. The S i - C a - F e aluminium emulator gives a demonstrably superior clay interpretation compared to that available from gamma ray. Its strength lies in the near constant slope, small degree of scatter, and near zero intercept. It is also independent of fluid volume, type and density, rendering it free from gas or light hydrocarbon effects, unlike the neutron-density separation. The calcium log provides an unparalleled carbonate estimation. It provides carbonate quantification in complex lithologies. In heavy barite muds, it easily and accurately locates carbonate cementation at levels of 10 to 20 wt% which were previously undetected by conventional log interpretation. The sulfur log provides a very accurate estimate of anhydrite which is of greatest value in carbonate/evaporate lithologies. While the relationships presented here have demonstrated a large degree of universality, each algorithm can be further optimized on a field or regional basis to give improved lithological estimates.

References BHVVAN, K. & PASSEY, Q. R. 1994. Clay estimation from GR and neutron~tensity porosity logs,

-

paper DDD. In: 35th Annual Logging Symposium Transactions: Society of Professional Well Log Analysts, pp. D1 15. ELLIs, D. V. 1987. Well Logging for Earth Scientists. Elsevier, New York. GRAU, J. A. & SCHWEITZER, J. S. 1989. Elemental concentrations from thermal neutron capture gamma-ray spectra in geological formations. Nuclear Geophysics, 3, 1 9. --, ELLIS, D. V. & HERTZOa, R. C. 1989. A geological model for gamma-ray spectroscopy logging measurements. Nuclear Geophysics, 3, 351-359. HERRON, S. L. 1995. Method and apparatus for determining elemental concentrations for "/ ray spectroscopy tools, U.S. Patent 5,471,057. & HERRON,M. M. 1996. Quantitative lithology: An application for open and eased hole spectroscopy. In. 37th Annual Logging Symposium Transactions: Society of Professional Well Log Analysts, pp. E1 14. HERTZOG,R. C., COLSON,L., SEEMAN,B., O'BRIEN,M., SCOTT, H., McKEoN, D., WRA~GHT,P., GRAU, L, ELLlS, D., SCHWEITZER, J. & HERRON, M. 1987. Geochemical logging with spectrometry tools, SPE-16792. In. 62nd Annual Technical Conference and Exhibition Proceedings: Society of Petroleum Engineers. HURST,A. & MILODOWSK1,T. 1994. Characterization of clays in sandstones: Thorium content and spectral log data, paper S. In: Sixteenth European Formation Evaluation Symposium: Society of Professional Well Log Analysts. -

QUANTITATIVE LITHOLOGY KATAHARA, K. W. 1995. Gamma ray log response in shaley sands. The Log Analyst, 36, 50--55. MATTESON, A. & HERRON, M. M. 1993. Quantitative mineral analysis by Fourier transform infrared spectroscopy, Society of Core Analysts Technical Conference, August 9 11, 1993, SCA 9308. RoscoE, B., GRAU, L, CAO MINH, C. (~; FREEMAN, D. 1995 Non-conventional applications of through-

95

tubing carbon-oxygen logging tools, paper QQ. In: in 34th Annual Logging Symposium Transactions: Society of Professional Well Log Analysts. SCHWEITZER, J. S., ELLIS, D. V., GRAU, J. A. & HERTZOG, R. C. 1988. Elemental concentrations from gamma-ray spectroscopy logs. Nuclear Geophysics, 2, 175 181.

The comparison of core and geophysical log measurements obtained in the Nirex investigation of the Sellafield region A. K I N G D O N , S. F. ROGERS, C. J. E V A N S & N. R. B R E R E T O N

British Geological Survey, Keyworth, Nottingham, NG12 5GG, UK

Abstract: The Sellafield region, west Cumbria, is the focus of one of the most thorough geological investigations in the United Kingdom. The Sellafield Site is defined as an area immediately around the potential repository, extending 6.5 km north-south by 8 km eastwest. Twenty six deep boreholes were drilled within the area up to the end of 1995, with a total depth of approximately 28 km. Most of these boreholes have been continuously cored, a total of over 17 kilometres of core, with average core recovery well in excess of 90%. All boreholes were logged with a comprehensive suite of geophysical logs, including many state of the art tools. Laboratory physical property analysis of hundreds of sample cores has been carried out. Pilot studies were carried out to compare and contrast datasets and to investigate the relationships between the different data scales. Various techniques, including fractal analysis and Artificial Neural Networks, were tried in order to explore the relationships of these data at a variety of measurement scales. The pilot study was conducted in two stages: (1) evaluation of the primary controlling factors of the physical properties; (2) testing the validity of 'Up-scaling'. The rocks of the Borrowdale Volcanic Group provided the most challenging problems due to the physical properties being dominated by fracturing and associated alteration zones. Relationships between data types at different scales were established suggesting that the extrapolation of properties derived from core and wireline logs across three-dimensional seismic grids would allow an understanding of the properties throughout a threedimensional volume. Nirex is responsible for the development of a deep geological repository for solid, intermediate level and some low-level radioactive wastes. Following preliminary geological investigations of two sites, an area near Sellafield, west Cumbria, was chosen in 1991 for further study. The Nirex science programme aimed to assess the suitability of the Sellafield site as the host for the repository. Such an assessment required, among other things, an understanding of the geology and hydrogeological characteristics of the area. The Sellafield region in west Cumbria, England was the focus of one of the most detailed site investigations projects ever undertaken. This investigation aimed to characterize the geology and hydrogeology of the site to determine whether the site at Sellafield showed sufficient promise of meeting regulatory targets to permit Nirex to submit a planning application for a deep repository. An underground Rock Characterization Facility (RCF) had been proposed in order to allow more detailed characterization of the geology and hydrogeology of the area using direct observations from underground

excavations and to allow in situ experiments on rock and groundwater behaviour. These measurements were required to provide information on ground conditions that could only be obtained from an underground facility and to test models of the geology, hydrogeology and geotechnical characteristics and behaviour of the rocks. In the course of the Sellafield site investigations, data at a range of scales from microscopic to regional have been collected. The large volume of data available from the Nirex investigations presents problems with respect to the estimation of properties at the very large scales required by performance models. In most practical applications, the scale of the sample measurements is not directly comparable with the scale required for the model estimates needed for the calculations. It is important to evaluate the scale of the sample data and the scale required for the final estimates and to apply some correction to the sample scale, if they are different. This corrective process is generally termed 'up-scaling'. In the context of Sellafield, physical property parameters important to the

KINGDON, A., ROGERS, S. F., EVANS, C. J. & BRERETON,N. R. 1998. The comparison of core and geophysical log measurements obtained in the Nirex investigation of the Sellafield region. In: HARVEY,P. K. & LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 97-113

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Fig. 1. Location of the Sellafield boreholes and the potential repository zone.

construction of underground vaults required, on the scale of tens of metres may only be measured on core samples at the scale of centimetres or from geophysical logging of the boreholes at a scale of a few metres. The difficulty of extrapolating properties using data from varying scales makes it difficult to use data derived at one scale, for example borehole core, to another, such as a threedimensional seismic survey. In the context of the Sellafield investigations, parameters that are important to tunnelling, such as indices of rock strength need to be derived at one scale and then extrapolated to another scale. Techniques to allow this to be undertaken must have therefore to be both derived and tested. This paper examines the possible techniques for comparing data derived at three separate scales: borehole core (centimetre scale), geophysical borehole logs (metre scale) and threedimensional seismic survey data (10 metre scale). In particular, mathematical techniques were studied that examine relationships between data scales; thus demonstrating the validity of the methodology of 'up-scaling'. This study largely concentrated on the Potential Repository Zone (PRZ) an approximately four square kilometre area near the village of

Gosforth. The key task of this study was to define an index of rock properties derived from geophysical log measurements down each of the boreholes in the PRZ. This index was then used to extrapolate those properties across a volume, as sampled by the three-dimensional seismic survey, aiming to allow prediction of rock properties at any location within that volume.

Location and geological setting The Sellafield site is in west Cumbria, England and situated between the coast of the East Irish Sea and the Lake District National Park. A map of the area is shown as Fig. 1. Up to the end of 1995 twenty-six boreholes were drilled within the area as part of the site investigation. The geology from each borehole has been fully described ( Nirex 1993; 1995a,b). The regional basement in the Sellafield area is the Borrowdale Volcanic Group (BVG) which consists of a complex group of Ordovician tufts, lapilli tufts and acidic lavas with local intermediate and basic intrusions, and volcaniclastic sediments. (Millward et al. 1994). The BVG was deposited as a largely sub-aerial volcanic system formed by an island arc on the southern margin of the Iapetus Ocean. The BVG is unconform-

THE NIREX INVESTIGATION OF THE SELLAFIELD REGION ably overlain by a south-westerly thickening Carboniferous Limestone and Permo-Triassic succession. The Permo-Triassic forms the subcrop across most of the Sellafield area. The BVG and (where present) the Carboniferous Limestone are unconformably overlain by the Brockram, a Permian fluvial breccia conglomerate with up to cobble sized clasts. The upper part of the Brockram near the coast passes laterally into the St Bees Shale and Evaporite (Nirex 1993). The St Bees Evaporite comprises dolomite and anhydrite, and the St Bees Shale is a laminated sandstone, siltstone and claystone formation. The St Bees Shale is conformably overlain by the dominantly fluvial St Bees Sandstone (Barnes et al. 1994) of Triassic age. This is a sandstone and claystone, with the claystone increasing markedly down succession, particularly in the North Head Member at the base. The St Bees Sandstone is overlain by the Triassic aeolian Calder Sandstone which forms the subcrop in the PRZ area. The easternmost of the Sellafield boreholes (9A and 9B) were drilled into outcropping BVG with the Permo-Triassic succession outcropping to the southwest of these boreholes. This succession thickens towards the southwest reaching a thickness of 1700m at the Irish Sea coast. In the PRZ area there is 400 to 500 m of sedimentary cover overlying the basement. The Permo-Triassic succession occurs on the eastern margin of the East Irish Sea Basin, an extensional basin associated with prolonged east-west extension resulting in the dominantly north-south faulting seen today (Jackson et al., 1995).

Data sources High quality geological and geophysical data have been acquired across the Sellafield region during the site investigation. All twenty-six boreholes have been geophysically logged using comprehensive suites of state of the art tools, including borehole imaging. In addition, the boreholes have been extensively cored, allowing continuous detailed geological and discontinuity description to be undertaken. Detailed gravity and magnetic survey data has been acquired across the Sellafield region, as well as twodimensional seismic data. The geology of the PRZ area has been the subject of a highly detailed investigation. Up to the end of 1995 eleven boreholes (Boreholes 2, 4 & 5; RCF1, 2 & 3, RCM1, 2 & 3; PRZ2 & 3) were drilled within an area measuring only 1200 m by 800 m across the ground surface. All penetrated to the BVG, the deepest borehole

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penetrated to 1600m below ground level. All boreholes have been cored from within the St Bees Sandstone succession to terminal depth within the BVG, with total core recovery in excess of 95% (close to 100% in some of the later boreholes). In addition, a high quality trial three-dimensional seismic survey has been acquired across part of the PRZ area. Data acquired within the PRZ area therefore allows particular scope for both deriving detailed rock properties and up-scaling between different datasets.

Deriving characteristic rock properties The first stage of this project involved the derivation of the average rock properties in each borehole, for each of the major formations in the Sellafield area. These average properties were then used to determine whether a particular formation was essentially constant across the area or whether there were significant regional and/or local variations in the rock properties. Where significant variations in rock properties were found the possible causes for the variation were examined. This exercise was first carried out on a regional scale and then concentrated in more detail upon the PRZ area. Rock properties were studied by comparison of geophysical borehole logs from across the area. Geophysical logs were chosen because of the consistent way that the data was acquired, both in terms of techniques and sampling rates. This allows for easy comparison between boreholes some distance apart. The main characteristics of the rock properties studied were identified by statistical and graphical techniques of data comparison.

Stud), o f velocity Although many rock properties have been measured at various scales, compressional velocity is one of the few to have been measured at all scales, from core to seismic scale. It was therefore chosen as the most representative property for analysis as an example of the average rock property behaviour. The compressional velocity of a rock formation is controlled by the matrix density, the porosity and the fluid composition. Compressional velocity data for each of the three data scales were derived by different techniques. Core scale data for each of the main rock types were provided by laboratory testing on core samples. Wireline log scale data were derived from sonic velocity logging. Larger scale

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Fig. 2. Percentage frequency histogram of bulk compressional velocity for the main stratigraphic units of the PRZ.

data were derived directly from the two way transit velocities from seismic survey information. Figure 2 shows a frequency histogram of bulk compressional velocity. This shows the velocity distributions for the three rock types present in this area (the St Bees Sandstone, Brockram and BVG) in the PRZ. The statistics are derived from the total geophysical logging measurements in each borehole from within the area. The mean velocity of the St Bees Sandstone is shown to be between 3.5 to 4.5 kms -l, the Brockram between 4.5 to 5.5 kms -1 and the BVG between 6.0 to 7.0 km s 1. Variations in velocity within the range for the individual rock type are caused by differences in the properties of the materials. This study aimed to identify these differences and to attempt to understand their origin. More detailed studies of the nature of the velocity distributions have been made for two rock types: the St Bees Sandstone and the BVG. This was done initially on a regional scale and subsequently more locally in the PRZ area. The Brockram is of a fairly consistent thickness across the Sellafield Region (approximately 100m) and shows remarkably homogeneous properties. As a consequence, no further attempt has been made to characterize variation in rock properties for this lithology.

Regional studies of velocity The regional pattern of velocity was studied using graphs of midpoint depth against mean formation velocity for each borehole. The midpoint depth of a formation is defined as the point equidistant between the top and base of the sampled section of a formation, regardless of whether the borehole had sampled the entire thickness of the formation. This allows comparison of the compressional velocities between boreholes without any overprinting of the effects of velocity changes within the formation. The mean velocities have been derived from geophysical logs of the formation and are expressed on the graph as kilometres per second. Figure 3 is a graph of midpoint depth against velocity for the St Bees Sandstone in each of the boreholes in the Sellafield region where the formation is present. Figure 4 shows the same data types for the BVG. Boreholes are shown using different symbols depending on whether they fall inside or outside the boundaries of the PRZ area. Also plotted on the graph are typical core sample data that have been pressurized under laboratory conditions to simulated depths.

Results of studies of velocity against midpoint depths. Figure 3 shows that mean compressional

THE NIREX INVESTIGATION OF THE SELLAFIELD REGION

Fig. 3. A graph of midpoint depth against compressional velocity for the St Bees Sandstone.

Fig. 4. A graph of midpoint depth against velocity for the Borrowdale Volcanics Group.

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velocity of the St Bees Sandstone increases with midpoint depth in a smooth curve. This exponential increase in velocity with depth is well documented as being caused by decreasing effective porosity due to increased overburden pressure (Birch 1960). The results from the core samples also demonstrate that increasing depth results in an increase in compressional velocity. The velocity results from the core samples is somewhat lower than the velocities from equivalent bulk depths derived from geophysical logs in the boreholes. This is a consequence of the samples being tested whilst dry (i.e. the pore space was air filled rather than saturated with water). Figure 4 shows a plot of midpoint depth against compressional velocity for those boreholes in the Sellafield region where the BVG is present. This plot shows a relatively complex pattern in comparison with the St Bees Sandstone. Most boreholes show a mean velocity over the BVG interval of between 5.0 to 5.5 km s l.The boreholes in the PRZ area (with the exception of borehole PRZ3) showing a distinct clustering of mean velocities. Three boreholes 9B, 8B and PRZ3 show significantly lower mean velocities. The first two of these boreholes penetrate a short distance into the BVG. Detailed logging of the Borehole 8B core (Nirex 1995a) suggested that the top section of the BVG is highly altered, which was the only part of the BVG sampled in this borehole. In the case of Borehole 9B, which was drilled where the BVG outcrops at surface, the rocks will have been affected by recent weathering. As these effects will have had a significant influence on rock properties of these two boreholes, the data are not comparable with the other boreholes and they have not therefore been included in the study of the average rock properties of the deep BVG. In the case of borehole PRZ3, where the BVG is covered by a thick Permo-Triassic succession, the difference could not be readily explained in this way and the BVG velocities from this borehole are therefore seen to be significantly anomalous. An independent quality assurance check of the geophysical logging of Borehole PRZ3 did not indicate any systematic error in the acquisition and processing stages. Borehole PRZ3 was targeted to intersect a fault, Fault F1, in the BVG and it is likely that the mean velocity results from this borehole reflect a large proportion of 'faulted rock'. The velocities of the available core samples in the BVG are slightly higher than the wireline derived mean formation velocities, despite the core samples again having been tested whilst dry. This is inferred to be due to the porosity of

the material being sufficiently small that the compaction effect is not as significant. Of greater significance to the properties of the core samples is the fact that core tests were by definition carried out on samples of intact rock. The properties of these samples therefore varies from the bulk rock sampled by geophysical logs, which includes the effects of non-intact and fractured rock. This suggests that the variations of the bulk rock properties from those of intact rock may be a consequence of the discontinuities within the rock mass.

Local studies gf velocity More detailed analysis of the bulk rock velocity properties for the boreholes in the PRZ region was carried out using box and whisker plots. Box and whisker plots (Figs 5, 6 and 7 and 11) are a graphical technique which permits an overview of a complete data distribution, excluding only anomalous data at the extremes of the distribution. This permits the statistical comparison of almost the entire data distribution between all the boreholes. The variation in the range of data as well as average properties can therefore be assessed. Figure 5 shows the symbols used to describe different parts of the data distribution on box and whisker plots. Figure 6 is a box and whisker plot of the velocity distributions of the St Bees Sandstone for the boreholes in the PRZ. The column on the right-hand side of this diagram shows the combined properties for all the boreholes. The quartile range of the velocity for all the PRZ boreholes is between 3.6 and 4.4 kms 1. The bulk rock properties from all boreholes are essentially consistent between all the PRZ boreholes. This indicates that there is little regional variation in the bulk rock properties of the St Bees Sandstone in this area. Two additional datasets are also displayed on this plot, the core properties and the faulted rock properties. Core properties were derived from laboratory tests on intact core samples. Laboratory testing of the properties of the fault rock was difficult as fault rock is by definition nonintact. The fault properties shown here were therefore derived from geophysical log measurements. The standard geophysical log measuring increment of 6 inches (15.24cm) means that statistically valid samples are hard to obtain from faults with limited borehole intersections. Therefore properties were only derived for faults with borehole intersections greater than 50 centimetres. The core sample seismic velocities are seen to be much lower (interquartile range for all

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datasets was hampered by the small number of sample points and the sampling bias, it is clear that the properties of fault rock are significantly different to the bulk rock. This can be seen in the 'total column' which includes the summed data

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Fig. 8. Cross-plot of density against neutron porosity fo the St Bees Sandstone Group showing depth as the z-axis.

THE NIREX INVESTIGATION OF THE SELLAFIELD REGION for all boreholes. As can be seen in Figure 7 most boreholes in the PRZ area shows a consistent set of bulk rock velocity (interquartile ranges between 5.0 to 6.1 kms-1). Only borehole PRZ3 displays significantly different properties with lower values (interquartile range 4.5 to 5.0 kms-l). Comparison of the three measurements for each borehole provided important evidence to the controlling mechanism for bulk rock properties. Whilst core derived intact rock properties showed somewhat higher velocities than the bulk rock properties in almost all cases, the fault derived velocity values were significantly lower than the equivalent bulk rock properties and showed greater variability. The difference between bulk rock and intact rock is, by definition, the discontinuities of which fault rock was the only measurable example. Hence the discontinuities must be the dominant controlling factor on the bulk rock properties of the BVG. In the case of borehole PRZ3 the velocity measurements showed a very localized anomaly, consistent with the targeting of the borehole into a faulted zone.

Causes of variataions of rock properties in the St Bees Sandstone The compressional velocity distribution of the boreholes described above shows that the

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velocity profile of the St Bees Sandstone largely reflects the depth of burial and there is therefore an increase in average velocity to the south-west where the midpoint depth of the formation is greater. Figure 8 shows a typical cross plot of percentage porosity against density of the St Bees Sandstone from Borehole 2. The depth of each point is displayed as the z-axis (the colouration of the points in Fig. 8). The diagram shows that most of the data plots along a line, with density increasing as porosity decreases and depth increases. This distribution is caused by compaction (due to increasing overburden pressure) leading to decreasing porosity with depth. Some variations from this simple distribution are seen. In order to understand the anomalous points, the effects of variations in lithology had to be quantified. Figure 9 shows the densityporosity cross plot for the same data but with the z-axis now showing the gamma-ray count from each point. This clearly shows the effects of lithological change as higher gamma counts occur in those parts of the distribution which do not follow the simple trend. This is because these zones are not clean sandstone but contain a significant proportion of claystone. These two diagrams therefore indicate that the dominant control on the bulk rock properties of the St Bees Sandstone was depth of burial and lithological variation.

Fig. 9. Cross plot of density against neutron porosity for the St Bees Sandstone Group showing gamma ray as the z-axis.

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Fig. 10. Cross plot of shallow resistivity against neutron porosity for the Borrowdale Volcanic Group.

Fig. 11. Box and whisker plot of gamma ray for the Borrowdale Volcanic Group.

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Causes of variations of r o c k properties in the Borrowdale Volcanic Group Figure 8 showed that whilst the BVG showed fairly homogeneous properties between boreholes across most of the P R Z area, there is significant variation of properties within each borehole. The nature of these variations was therefore investigated further using an example borehole. Figure 10 shows a neutron porosity against shallow resistivity cross plot with gamma ray counts as the z-axis. Two main clusters are seen on this graph. The bulk of data points are shown to be highly resistive, low porosity with a low gamma ray count. These values represent the properties of the intact rock. In addition a smaller cluster of points with low resistivity, higher porosity and high gamma ray counts are also seen. The higher gamma ray counts are probably caused by the alteration minerals found around discontinuities within the rock mass. This data acted as a further indication that the dominant control over the bulk rock properties of the BVG are the nature of the discontinuities within the rock mass rather than the intact properties of the rock itself. In an attempt to quantify the effects of the properties of the faults on the bulk rock properties a box and whisker plot of the gamma ray counts for the BVG of the P R Z boreholes was produced (Fig. 11). In most of the boreholes with a statistically significant sample of fault rock, the gamma ray response is approximately 5 API higher in the fault rock than in the bulk rock. This can be seen most clearly in the total (all boreholes) column on the right-hand side of the diagram. This is not an ideal presentational medium because a fault in an already low gamma ray formation may have a lower count than high gamma background elsewhere in the borehole. Variations in the condition of the boreholes will also significantly affect the results. The data for Borehole RCM3 is dominated by a single large fault close to the top of the BVG where low gamma is recorded because of poor hole conditions (the caliper increases from 6 to 16 inches through this fault). Despite these problems the diagram does clearly show that gamma ray counts are higher in fault zones than in bulk rock.

Data scales and up-scaling Relating physical properties derived from one scale to another represents a significant problem. Prediction of the rock properties through a given

Fig. 12. A diagrammatic fractal distribution: the Sierpinski Gasket.

volume, such as those sampled by the trial 3-D seismic survey are important for successful engineering design of tunnels, shafts etc. The P R Z area has eleven deep boreholes drilled by Nirex, and several drilled previously by British Steel and its precursors, and yet less than one five millionths of the total volume of the P R Z has been directly sampled by coring. In order to scientifically justify the up-scaling of known properties (derived from either direct measurements on core or indirect measurements from geophysical logging tools) it is important to demonstrate that at least over a small but significant part of the scale, properties are comparable. If this can be done then 'up-scaling' of data can be seen as a legitimate concept, although it should be treated with caution.

Fractals A true fractal relationship is a relationship between two variables that does not change with scale. Whilst it is unlikely that any relationship is truly fractal in a natural system, if a relationship could be demonstrated over a number of orders of magnitude then this could be used to justify up-scaling of data from one scale to another. Figure 12 shows a diagrammatic fractal relationship, the Sierpinski Gasket. Each size of triangles is related to the next largest and next smallest size of triangles by the same scale and geometric relationships, up to the limits of page size in one extreme and print resolution in the other. An attempt was made to study discontinuities in the Sellafield area at two separate scales: distances between individual discontinuities measured directly from the core and distances between seismically resolved faults. This was

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Fig. 13. Log-log plot showing fractal distribution of borehole discontinuities in borehole 8B.

done firstly to assess whether fracture distributions were fractal at each scale and then to see whether any link between data at the two scales could be established.

Discontinuity separation Various techniques have been derived to study the fractal dimension for a distribution of naturally occurring phenomena. This study was carried out using the Spacing Population Technique (after Harris et al. 1991) which is both straight forward and applicable to the type of data to be examined. The basic dataset for this study was the borehole discontinuity log, produced for Nirex by Gibb Deep Geology Group (GDGG) from direct measurement of the core. This lists, for each borehole, all the occurrences of faults, veins, joints and other discontinuities, ordered by depth. All discontinuities with a non-structural origin were removed, such as bedding features, stylolites in the Carboniferous Limestone and those fractures in the core that were induced by the drilling process.

Methodology The Spacing Population Technique is based on cumulative frequency distributions derived incrementally from large (infrequent) to small

(frequent) events. In this case, classes of 0.1 m to 100m were used as applicable to borehole discontinuity spacing, covering three full log cycles. In order to analyse the data an approximate geometric progression was used to divide the data up into frequency classes suitable for log-log output. The cumulative frequency data wwere plotted as a log-log plot. To be considered fractal the distribution had to plot as a straight line (showing that the relationship is scale invariant and conforms to the following function):

y=ax - D where: y = probability (cumulative frequency); a = a prefactor; x = the discontinuity spacing; D = t h e line gradient (i.e. the fractal dimension). For a distribution to be considered fractal the data should be linear across at least one order of magnitude.

Results of fractal analysis Figure 13 shows a cumulative frequency log-log plot for Borehole 8B, which gives the results of the fractal analysis of borehole discontinuities in this borehole. Some of the limitations of the fractal technique are demonstrated by this dataset. Whilst natural fractals should be proved

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Fig. 14. Log-log plot showing fractal modelling of seismic scale faults for the base Carboniferous.

to exist in any relationship over several orders of magnitude, any single measurement technique may only characterize a subset of this total range. The limits for identification of fractal patterns are often therefore controlled by limitations in the sampling method. In this study for instance the core fracture dataset was reliant on the human eye to identify individual fractures. Very closely spaced fractures lead inevitably to highly broken core and poor core recovery, so that such zones are preferentially undersampled. Rock, heavily fractured by localized, closely spaced events is essentially indistinguishable from large fractures and will behave in a similar way. Major fault systems have not been sufficiently sampled by boreholes to permit fractal analysis at this scale, whereas the threedimensional seismic survey only identifies faults either by 'significant' offset of marker lithological contacts or directly where the thickness of fault-rock is sufficient to cause a velocity contrast. Also the Sellafield Site boreholes cannot be labelled a random unbiased dataset, as some of the boreholes were specifically targeted at some of the major faults in the region. The borehole 8B fracture set shows a clear fractal relationship over two orders of magnitude, i.e. at fracture spacings from 20cm to 10m, with a regression coefficient of R 2= 0.9996, very close to a perfect straight line.

Fractal events at the seismic scale Large events, such as major faults, although

sampled by boreholes, occur only infrequently and the dataset is statistically insignificant in any one borehole. Therefore another measurement technique must be used to sample the larger faults. An obvious alternative method is to examine faults identified from a two-dimensional seismic grid. This dataset was used in this study for a comparison with the borehole derived results. It was important to make clear at this stage that these were not identical datasets simply measured at different scales. Seismic reflection profiles (and in particular widely spaced two-dimensional seismic data) tend to resolve only large scale fault zones rather than distinguishing individual minor fault strands such as those which would be delineated from borehole core.

Methodology In order to get an acceptable level of coverage of fault features with a common resolution, offshore seismic reflection data from near the Sellafield site were used for this study. Unlike boreholes, which essentially sample a onedimensional environment, the interpreted seismic fault maps used in this part of the study were two-dimensional in character. The dataset in this case were fault maps stored in a database of faults derived from V U L C A N software modelling of the regional structure. A different sampling technique was used in order to develop cumulative frequency data. In this case a two-dimensional 'box counting' method was applied. This was done by overlaying the maps to be studied with grids of

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Fig. 15. Log-log plot showing fractal modelling of seismic scale faults for the base permo-trials.

square boxes. These boxes each had sides of length d and the number of boxes containing fault features was counted (given as Nd). The exercise was repeated several times with boxes of progressively shorter side length d (i.e. the grids become finer). The number of filled boxes (Na) was plotted on a log-log plot against box size dimension (d). If the relationship between the two variables is fractal it produces a straight line of gradient - D , which should be in the range 1.0 < D < 2.0 (Hirata 1989)

Results of fractal modelling of seismic scale

faults Two different seismic base maps of the East Irish Sea basin were studied (Nirex 1995b); The base Carboniferous (Fig. 14) and Base Permo-Triassic (Figure 15). Both showed very clear fractal patterns over the scale range from 200m to 1 km, with regression coefficients of R 2= 0.999 in both cases. Fractal patterns have been demonstrated over two different scale ranges for discontinuity spacing events. The regression coefficient for both sets of events was very close to one (i.e. a completely fractal pattern). However the scaling exponents, sometimes known as the fractal dimension, differ suggesting that fracture spacing is a scale dependent parameter. These relationships provide evidence that up-scaling of discontinuity events from features measured in core and at the seismic scale are valid within

Fig. 16. An idealized artifical neural network.

their respective scale ranges. It is also possible to debate that if up-scaling is valid over both these ranges there may be the possibility of establishing a relationship between the different fractal equations and thus defining an up-scaling function all the way from micro fracture scale to major faulting.

Neural network modelling Artificial Neural Networks (ANNs) are a computer modelling technique that work in a manner analogous to the processes of a mammalian brain. They are based on simple linear processing elements which interact to form

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Fig. 17. Results of neural network modelling for RCFl: zonation of fracturing from actual and predicted fracture frequency.

Fig. 18. Results of neural networks modelling for RCF2: zonation of fracturing from actual and predicted fracture frequency.

complex non-linear behaviour. A N N s can 'learn' to recognize patterns in data and develop their own generalizations. A diagrammatic model of an idealized artificial neural network is shown in Fig. 16. Fracture frequency measured from borehole core was not easy to predict with any degree of accuracy from conventional geophysical log measurements. Whilst borehole imaging tools go some way to addressing this issue, it was not always possible to distinguish between features such as bedding features and discontinuities.

Neural networks may allow another approach in identifying fracture frequency.

Multi-layer preceptron This study used a type of A N N called a multilayer preceptron (MLP) to model the relationship between core derived fracture frequency and geophysical log measurements. The MLP consists of a series of simple processing elements (nodes) connected to one another. In operation the node receives several

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inputs which it sums. The strength of the node's response is proportional to the sum of the inputs. Nodes are placed in layers such that each node from one layer is connected to every node in the next layer. These connections are weighted and weights are changed according to the relative importance accorded to each layer. Input data are fed through the network and compared with the output data. Discrepancies between the input and output datasets result in changes in the weighting in connections. Over a number of iterations the network 'learns' which inputs have the greatest effect on output. This type of ANN, where data are fed through the network and error fed back, is known as a feed forward back-propagating network.

Use of artificial neural networks in this study Artificial neural networks were used in this study to attempt to model fracture frequency from conventional geophysical log inputs. Fracture frequency was derived from the borehole discontinuity logging file, binned at intervals of one metre. The two datasets were not immediately analogous because fracture frequency had been calculated per metre whereas geophysical logs conventionally sample at 0.1524m (6 inches). Geophysical logs were filtered using a twelve point moving average filter using BGS WELLOG software. Data were then interpolated to a one metre value and extracted in EXCEL 5.0 for manipulation. Six geophysical logs were used as input for this study: density, neutron porosity, gamma ray, shallow resistivity, compressional velocity and shear velocity. The fracture frequency data were also subject to some biasing and were therefore subjected to a five point moving average filter. These were also exported from BGS WELLOG software to EXCEL 5.0. Neural network modelling for this study used Neural Connections V1.0 software from SPSS. Various network topologies and statistical test were applied to validate the results. The software selected the network topology, usually the X-3-1 layout (X nodes in the input layer, three hidden layer nodes and a single output node).

Network training Training was highly important to the performance of a neural network. Although it was possible for ANNs to generalize and infer noise obscured properties, the network response was better where it has been trained by high quality data. In this exercise data from boreholes in the PRZ area were used to model the fracture

Fig. 19. Comparison of RMR and wireline logs for borehole RCF2.

frequency values for BVG sections in boreholes RCF1 and RCF2. The training dataset consisted of the following data segments 840-1015 mbRT (metres below the rotary table datum) from RCF1, 525.5-750 mbRT from RCF2 and 732.5-932.5 mbRT from RCF3. The data were run through a network in its natural order and then randomized to compare the performance of the network.

Results of neural network analysis Figures 17 and 18 show the results of the neural network analysis for boreholes RCF1 and RCF2. This dataset shows clearly both the uses and the limitations of using ANNs for modelling. Whilst in some parts of both boreholes, the actual fracture frequency had been modelled with some accuracy, in others the modelling had not adequately resolved the distribution. The actual fracture frequency was shown at the top of both diagrams with zones of similar levels of general fracturing marked by a black line. The bottom diagram shows the A N N predicted results, again with a black line marking the zones of similarity. Comparison of both boreholes shows that the models were good at distinguishing the background level of fracturing in the boreholes. The biggest problems in the models were at the data extremities. Although this technique was not perfect it does again give clear indications that the fracture frequency data

THE NIREX INVESTIGATION OF THE SELLAFIELD REGION derived from core can be up-scaled to be modelled by geophysical logs.

Comparison of RMR and conventional wireline logs The rock mass rating (RMR) is an industry standard rock quality and strength index derived from direct measurement of the physical attributes of the core and is completely independent of wireline log measurements. This measurement allows an accurate assessment of rock strength, but is labour intensive and therefore expensive to collect. R M R is calculated for whole and partial core runs and is reported for Boreholes RCF1, RCF2 and RCF3 in 3 m intervals. Figure 19 shows the results of a comparison of R M R with two conventional wireline log measurements from the same borehole over a given interval. The degree of correlation between these two sets of measurements is high despite the wholly different derivation and supports upscaling of the wireline log data from a measurement scale of 15cm to at least 3 m by simple arithmetic averaging.

Conclusion Whilst neither the fractals nor the artificial neural network derived models showed exact matches with the core derived data from which they were extrapolated, both showed that there was considerable scope for the belief that using the correct criteria, it is possible to up-scale data to match both wireline and seismic scale data. The Rock Characterization Facility (RCF) proposed at Sellafield requires detailed rock properties to be derived from boreholes and extrapolated across a wider area to allow for prediction of the likely tunnelling parameters. Where three-dimensional seismic survey data are available across an area, it should be possible to derive rock properties at a borehole scale and extrapolate them across a three-dimensional volume to give an accurate prediction of the nature of the RCF site. This was dependent upon a detailed knowledge of the rock properties and accurate correlation of core and seismic properties. The concept of up-scaling parameters derived at one scale to another may be feasible but needs

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considerable more research to prove valid. If suitable algorithms can be derived, then extrapolation of geophysical parameters derived from geophysical logs or cores, across a three-dimensional seismic grid, should allow detailed prediction of the properties for that volume of the rock mass.

References BARNES, R. P., AMBROSE, K., HOLLIDAY, D. W. & JONES, N. S. 1994. Lithostratigraphic subdivision of the Triassic Sherwood Sandstone Group in West Cumbria. Proceedings of the Yorkshire Geological Society, 50, 51-61. BIRCH, F. 1960. The velocity of compressional waves in rocks to l0 kilobars, Part 1. Journal of Geophysical Research, 65, 1083-1102. CHADWICK,R. A., KIRBY, G. A. & BAILY,H. E. 1994. The post-Triassic structural evolution of northwest England and adjoining parts of the East Irish Sea. Proceedings of the Yorkshire Geological Society, 50, 91-103. CHAeLOW, R. 1996. The geology and hydrogeology of Sellafield : an overview. Proceedings of the NIREX seminar, 11 May 1994. Quarterly Journal of Engineering Geology, 29, Supplement 1. HARRIS, C., FRANSSEN, R. & LOOSVELD, R. 1991. Fractal analysis of fractures in rocks: the Cantors dust method-comment, Tectonophysics, 198, 189197. HIRATA,T. 1989. Fractal Dimension of fault systems in Japan: fractal structure in rock fracture geometry at various scales. Journal of Geophysical Research. 94, 7507-7514 JACKSON,D. I., JACKSON,A. A., EVANS,D., WINGEIELD, R. T. R., BARNES,R. P. & ARTHUR, M. J. 1995. United Kingdom offshore regional report. the geology of the Irish Sea. British Geological Survey. MILLWARD, O., BEDDOE-StEPHENS, B., WILLIAMSON, I. T., YOUNG, S. R. & PETTERSON, M. G. 1994. Lithostratigraphy of a concealed caldera-related ignimbrite sequence within the Borrowdale Volcanic Group of west Cumbria, Proceedings of the Yorkshire Geological Society, 50, 25-36. NIREX, 1993. The Geology and hydrogeology of the Sellafield area, Volume 1: The Geology. Nirex report 524. NIREX, 1995a. The Geology of the Sellafield Boreholes Nos. 8A and 8B. Nirex report 638. NIREX, 1995b. Sellafield geological and hydrogeological investigations. Factual report-compilation of maps and drawings, Volume 1 of 2. Nirex report SA/95/ 02.

Forward modelling of the physical properties of oceanic sediments: constraints from core and logs, with palaeoclimatic implications C. LAUER-LEREDDE, 1'2, P. A. PEZARD, 1'3, F. TOURON 4 & I. D E K E Y S E R 2 t Laboratoire de Mesures en Forage (ODP), IMT, 13451 Marseille cedex 20, France 2 Centre d'Oc~anologie de Marseille, CNRS (URA 41), Universitd d'Aix-Marseille H, 13288 Marseille cedex 09, France 3 Laboratoire de POtrologie Magmatique, CNRS (UPRES A 6018), CEREGE, 13545 Aixen-Provence cedex 04, France 4 Gafa Entreprises, 16 Boulevard Notre-Dame, 13006 Marseille, France

Abstract: A new methodological approach based on the analysis of core data, logs and highresolution electrical images of borehole surfaces (FMS) is developed in order to improve the study of oceanic sediments from physical properties. This approach is tested on data obtained in the context of the Ocean Drilling Program (Japan Sea, Leg 128, Hole 798B). The downhole measurements and FMS images exhibit a cyclic pattern reflecting variations in oceanic surface productivity combined with continental aeolian supply due to palaeoclimatic changes. On the basis of m-scale physical measurements, cm-scale FMS images and measurements on core, the objective is to deconvolve the variations in sedimentary supply of oceanic and continental components through time and to compute the intrinsic formation factor versus depth. The latter topic is approached in two ways: first by conventional log analysis, then with a new iterative forward modelling method. In the second case, the low frequency electrical resistivity log (SFL) is modelled using a numerical modelling code (Resmod2D e:) in order to obtain an accurate formation electrical resistivity model (Rt), where individual beds are derived from FMS images. An analytical routine is also used to model the natural gamma-ray measurement (CGR). While the conventional log analysis allows deconvolution of the sedimentary supplies, the forward modelling leads to a greater resolution and accuracy in more precise sediment characterization, such as that obtained from the derivation of the formation factor.

Unlike the core material, downhole logs provide continuous high resolution records. The logs reflect the physical and chemical variability of the drilled sequence. Several logging tools based on widely varying physical principles (electric, acoustic, nuclear . . . . ) are used. The logs offer different perspectives about changes in sediment composition. Hence, extracting sediment characteristics or palaeoclimatic information from downhole logs appears as a promising field of application. The principal limitation on integrating logging data for sedimentary and palaeoclimatic studies is the absence of a generally applicable method to transform logging data into reliable sediment physical properties or palaeoclimatic data. The major objective of this study is to develop a new methodological a p p r o a c h using, in combination, logging, coring data and highresolution electrical images (FMS) to derive the detailed structure of near sea-floor sediments. The method is tested on data obtained in the

context of the Ocean Drilling Program (ODP) at Oki Ridge in the Japan Sea (Leg 128 Hole 798B). Core data are first used to construct a mineralogical model of the sedimentary formation at Site 798. Classical log analysis is then applied to deconvolve the different sedimentary inputs and to compute a continuous formation factor (FF), which offers a tool to describe the sediment pore structure. However, this approach is limited by the vertical resolution of each sensor, that is half a metre on average for traditional downhole measurements (e.g. logs). An original approach combining analytical and numerical modelling is proposed here to perform a small scale analysis of downhole logs through the computation of the formation factor.

Geological setting at Site 798 Site 798 (37~ 134~ is located in the southeastern Japan Sea, about 160km north of the western coast of Honshu. The site is

115 LAUER-LEREDDE,C., PEZARD,P. A., TOURON,F. & DEKEYSER,1. 1998. Forward modelling of the physical properties of oceanic sediments: constraints from core and logs, with palaeoclimatic implications. In: HARVEY,P. K. & LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 115-127

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Fig. 1. Location map of the area surrounding Hole 798B.

positioned over a small sediment-filled graben on top of Oki Ridge, in 911.1 m water depth (Fig. 1). A 517m thick sediment sequence of late/early Pliocene to Holocene age was drilled; diatomaceous ooze, diatomaceous clay, silty clay, clay, and siliceous claystone are the predominant sediments. The primary drilling objective at this site was to obtain a complete Neogene sequence of pelagic-hemipelagic sediments deposited above the local carbonate compensation depth (CCD), currently near 1500 m, in order to obtain a detailed description of the sedimentary input at the site. The strategically positioned location and the high avera/~e sediment accumulation rate (about 12 cm ka -~) at Site 798 are ideal to study the local sedimentology in relation to global palaeoclimatology. This site is of great interest for two prevailing sedimentary supplies are defined from smear slides observations (Ingle et al. 1990) and FMS images (Fig. 2). The upper 300 m of FMS images (late Pliocene/Pleistocene) are characterized by rythmic changes between dark, laminated, diatom- and organic carbon-rich conductive intervals, and light-coloured, nonbioturbated to bioturbated, clay-rich, resistive intervals (F611mi et al. 1992). To investigate the sedimentary origin of these cycles, Dunbar et al. (1992) analysed a total of 913 samples for biogenic opal content (Fig. 3): major features of the opal record are a general trend of increasing opal fraction with depth, and cyclic variations between high and low values at a period of approximately 40 ka. The opal content varies between 3 and 43 Wt% in the upper 320m. DeMenocal et al. (1992) also analysed contiguous samples over three intervals located between 100 and 320 mbsf (metres below sea

Fig. 2. Formation MicroScanner (FMS) micro-resistivity images from the ODP Hole 798B (from 200 to 300 mbsf). The images are azimuthal traces of the four pads pressed along the borehole wall. Black represents low resistivity, and white, high resistivity.

FORWARD MODELLING OF OCEANIC SEDIMENT PHYSICAL PROPERTIES Core

SVL (Ohm m)

Opal

recovery _

o~

~o

(wt%) 20 30

117

0.45

40

so

loo

0.55

0.65

100

OPAL (%) II0

10

.

lo

,,0

110

120

120

130

130

100 I

s

140

m

140

8 150 200 i

150

Fig. 4. Correlation between the SFL log and opal percent measured on core in ODP Hole 798B (after DeMenocal et al. 1992).

I

No data 2so

300

Fig. 3. Weight percent biogenic opal versus depth in ODP Hole 798B (after Dunbar et al. 1992).

floor). These samples were analysed for major sediment composition: biogenic opal content varies between 5 and 40%, and terrigenous silts and clays, between 40 and 80%. Core-log correlations were established using ash layers identified in core photographs and Formation MicroScanner T M (FMS) images. High opal values result in low gamma ray, bulk density, grain densities, and resistivity log values. There is a close correspondance between the SFL and the opal data (Fig. 4). Low opal content is balanced by increases in terrigenous sediment, and this is recorded by high gamma ray log values (DeMenocal et al. 1992). Core-log comparisons therefore demonstrate that log cycles reflect variations in terrigenous sediment supply and diatomaceous opal. Diatom tests are

the dominant opaline component throughout the upper 300m; radiolarians and silicoflagellates contribute in a minor way to the opal flux (Ingle et al. 1990). The periodicity of the sedimentary cycles was estimated with standard-power spectral analysis method (Imbrie et al. 1984): the power spectra of the gamma-ray (SGR) time series showed a peak at about 40 ka, probably a climatic expression of the 41ka 'Milankovitch-type' cyclicity (DeMenocal et al. 1992). This suggested that the earth obliquity was the driving factor of climate and sedimentary supply in this region over the last 3 Ma. The diatomaceous sediments of the dark facies, and the terrigenous-rich signature of the light-coloured lithofacies suggested that these cycles also reflect variations in oceanic surface productivity combined with continental aeolian dust from central Asia, as a consequence of palaeoclimatic changes. The terrigenous mineralogy assemblage is similar to that of Chinese loess, a probable up-wind source of the aeolian dust. The Chinese loess deposits may indicate a linkage between glacial climate and Asian aridity (Kukla et al. 1988), so the periodic increases in terrigenous concentration may reflect the downwind propagation of this signal.

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Table 1. Chosen physical properties fop" mah7 components Phase Continental

Component

Densit~r gcm -

PEF ba e 1

CEC meq gq

Illit e Chlorite Kaolinite Smectite Quartz

2.50 2.60 2.42 2.12 2.65

3.5 6.3 1.83 2.04 1.8

0.1-0.4 0.05-0.4 0.03-0.15 0.8-1.5 0

Table 2. Clay composition re[erred to 100 Wt% clav.fi'action Zones* (mbsf) Za (200 220) Zb (220~ 225) Zc (225- 260) Zd (260 280) Ze (280-300)

Illite (%)

Chlorite (%)

Kaolinite (%)

Smectite (%)

85 80 90 85 80

10 10 10 10 5

0 10 0 5 10

5 0 0 0 5

*The studied interval was split into five zones, each with a constant clay mineralogy, on the basis of Dersch & Stein data (1992}.

Core and log data This work is focused on a 100-m-long interval (from 200 to 300 mbsf) because of the wellexpressed cyclicity over this segment (Fig. 2). Mineralogical model

In the following study, the sediment physical properties and the main mineralogical components are used to compute the relative proportions for oceanic and continental supplies, and to determine the formation factor (FF). A first order mineralogical model of Hole 798B is deduced from smear slide observations of dominant lithologies, and from previous sediment composition studies. The oceanic input, essentially diatoms, is associated with opal, on the basis of Ingle et al. (1990), DeMerlocal et al. (1992), and Dunbar et al. (1992) works. The continental one is deduced from Dersch & Stein (1992) core analyses at Site 798. In order to get information about the composition of the terrigenous sediment fraction, Dersch & Stein (1992) determined the average amounts of quartz and clay minerals. The entire sequence is characterized by quartz amount ranging between 5 and 20%. In the upper 413m, the clay fraction is dominated by illite with values between 60 and 88% and chlorite, between 0 and 27%. Calcareous components are either absent or poorly preserved,

and carbonate contents average less than 4% between 200 and 455 mbsf. In this section, volcanic ash layers are thin and scarce. The continental input is therefore assumed to be composed at this site of four clay minerals (illite, chlorite, kaolinite, and smectite) and quartz. Six components are consequently taken into account in this study, and characterized by three physical properties: density (g cm 3), photoelectric-effect (ba e q ) and cation exchange capacity (meq g l). The reference values for each of these components (Table 1) are chosen from the literature (e.g. Grim 1968; Fertl & Frost 1980; Juhasz 1981; Caill6re et al. 1982; Drever 1982; Schlumberger 1994). Our objective is to obtain information on oceanic and continental supplies, rather than on the relative fractions of the main mineral components.The proportions of each element for the continental phase are, however, needed in order to estimate the physical properties of this phase. A short interval from 200 to 300 mbsf (1.7 to 2.5 Ma) was chosen as a first step of this analysis. This interval was divided in five zones characterized by average clay fractions (Table 2), on the basis of previous analyses (Dersch & Stein 1992). This division in zones allowed to simplify the mineralogical model still further, and to reduce the number of unknowns: for example, the continental phase is constituted with only three elements (illite, chlorite, quartz) for zone C (Table 2). The sediment averages

FORWARD MODELLING OF OCEANIC SEDIMENT PHYSICAL PROPERTIES Natural G a m m a Ray CGR (API) 200

20

40

Electrical Resistivity

B u l k density

(fl m)

(g ce-l)

60

0.4

0.5

0.6

0.7

1.4

1.6

Photoelectric effect (ba/e') 1.9 2.2

2,6

119

N e u t r o n Porosity

(%)

I

6O

I

70

I 'T'" I

8O

I~l

II

220

240

g

260

280

41 Fig. 5. Downhole measurements from 200 to 300 mbsf in ODP Hole 798B.

10% quartz for the whole interval, 50% clay between 200 and 260 mbsf and 60% clay between 260 and 300 mbsf (Ingle et al. 1990, Dersch & Stein 1992). The percentages of the continental phase are then deduced for each zone.

Downhole measurements

At the completion of coring operations at Hole 798B, four logging runs were completed from 70 to 518 mbsf. During the first phase, the phaser dual induction tool (DIT), the long-spacing digital sonic tool (SDT), and the natural gamma-ray spectrometry tool (NGT) were run (seismic stratigraphic tool string). The second phase consisted of the lithoporosity combination tool string including the lithodensity (LDT), compensated neutron (CNT-G) porosity, and natural gamma-ray spectrometry (NGT) tools. After the Formation MicroScanner T M (FMS) had been lowered downhole, the geochemical tool string, including an induced gamma-ray spectroscopy tool (GST), an aluminium clay

tool (ACT) and the NGT, was run (Ingle et al. 1990). The depths of investigation are sensordependant, and data are typically recorded at intervals of 15cm. The quality of the logs obtained is generally excellent: most of the logs reflect variations in biogenic opal production (diatomaceous) resulting from glacial-interglacial changes in surface productivity (Matoba 1984; Zheng 1984; Morley et al. 1986). Downhole geophysical logs (m-scale). The following analysis focuses on the resistivity (SFL) and natural gamma ray (CGR) logs from 200 to 300 mbsf in Hole 798B. These logs were selected because the resistivity is influenced both by the clay fraction and diatoms (oceanic productivity input), whereas the natural gamma ray is mainly sensitive to the clay fraction (aeolian continental input in this case). The CGR is often used to indicate downhole variations in clay minerals content, because it reflects gamma-ray radioactivity from the decay of potassium and thorium which are common elements in clay mineral structures (Hassan et al. 1976). The

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CGR may then serve as a proxy of variations in terrigenous aeolian component.

Deconvolution o f cont&ental and oceanic inputs

Throughout the studied depth interval, the highest CGR value corresponds to the highest bulk density values (Pb), the highest resistivity values (R0), and the lowest porosity values (~b) (Fig. 5), reflecting a high terrigenous content relative to the biogenic supply. Terrigenous clays have high K and Th contents and relatively higher density and lower porosity than sediment with higher opal content: the clay particles filling the pores induce a lower porosity, hence a higher resistivity. Porosity is, to a first order, proportional to the inverse square-root of resistivity (Archie 1942). The sediments rich in diatomaceous opal commonly have high porosities because of the intrinsically high porosity of diatoms themselves. These cycles are also apparent in the recovered sediment record: the high gamma-ray, high density, high resistivity, and low porosity levels correspond to the massive clay-rich intervals, whereas the low density, low gamma-ray, low resistivity, and high porosity units correspond to the darker, diatom-rich intervals.

The aim is to analyse the downhole measurements in order to deconvolve both oceanic and continental inputs. The model of the formation consists of only two known inputs in unknown proportions. Bulk and matrix densities (Pb, Pma, g CC-1) and photoelectric effect (Pef, ba e-1) were chosen to define proportions of the two components. Whereas Pb responds primarily to porosity, the Per responds primarily to rock matrix (lithology). The combination of Pb and the Pef, the photoelectric absorption cross-section (Schlumberger 1994), is:

High-resolution (cm-scale) electrical images. The Formation MicroScanner TM (FMS) creates a picture of the borehole wall by mapping its electrical conductance using an array of 16 small and pad-mounted electrodes on each of four pads (Ekstrom et al. 1986; Luthi & Banavar 1988; Pezard et al. 1990). FMS data are recorded each 2.5 mm as the tool moves up the borehole. The vertical resolution of individual features is about a centimetre. The tool can, however, detect thinner features, provided they have sufficient resistivity contrast to the surrounding matrix. The images registered with the FMS show qualitative conductivity changes, particularly due to the different physical properties of the beds (for example porosity, resistivity of pore fluid or the presence of clays). The electrical images obtained at Hole 798B (Fig. 2) resolve the cyclicity of sedimentary processes at the site extremely well. Light (dark, respectively) colour is related to the continental (oceanic) input.

Log analysis The downhole logs and core measurements, associated with the proposed mineralogical model, are used here to determine variations in sedimentary inputs, and to compute the formation factor.

U = Pef x Pb

(1)

and obeys a linear mixing law such as: U=~

Uf-~-(1--(~) Uma

(2)

where U, Uf, and Uma are for example the photoelectric absorption cross-sections of the media, pore fluid and matrix, respectively. As our matrix consists of a mixture of two inputs (oceanic and continental) with relative weight fraction (#o and #c) and photoelectric absorption coefficients Uo and Uc: Uma =/to Uo + #c U~= Pef • Pma

(3)

The relation necessary to solve for these two unknowns is the closure relation of partial fractions: l=#o+#c

(4)

The solution can most easily be seen in terms of the matrix representation of the set of simultaneous equations: A=R Y

(5)

where A is the vector of measurements, R is the matrix of known coefficients, and Y is the vector of unknown volumes. The porosity and density logs are first used to compute the matrix grain density Pma. The wet bulk density Pb is related to the porosity through a simple mixing law: Pb = Pwqb + Pma (1 -- qb)

(6)

where Pw is the density of seawater. On the basis of our preliminary mineralogical model which consists of six major components (opal, illite, chlorite, kaolinite, smectite, quartz),

FORWARD MODELLING OF OCEANIC SEDIMENT PHYSICAL PROPERTIES Uo and Uc are computed for the five zones previously determined (Table 2) as follows: Uo = Pef(opal) • Pma(opa,)

u~ = L #i • Pefi • Pmai

(7)

(8)

i=1,5

with ~i as weight percentage of the component i in the continental phase. The system resolution leads to the weight fraction of both oceanic and continental phases.

Computation o f the f o r m a t i o n f ac t or The electrical resistivity of saturated sediments is usually quoted in terms of a formation factor (FF) to remove the effect of the pore-fluid resistivity, because the grains themselves are considered as insulators (Archie 1942): FF = Ro Rw-1 = Cw Co 1

(9)

where Ro (respectively Co) is the resistivity in 12 m (conductivity in S m -1) of the porous medium, and Rw (respectively Cw), the resistivity (conductivity) of the pore-fluid. The formation factor of the porous medium depends on the intrinsic geometry of the pore channels, and therefore describes the manner in which the grains are arranged in a sedimentary formation (Winsauer et al. 1952). Archie's equation is generally considered to apply satisfactorily to clean sands. The presence of clay minerals, however, has a detrimental effect on Co computations: the capacity of a clay to exchange cations at the pore-mineral interface induces the presence of a surface conductivity term (Waxman & Smits 1968). A resistivity model taking into account the effects of dispersed clays was proposed by Waxman & Smits (1968) and Waxman & Thomas (1974): Co = (Cw+ BQv ) FF -1

(10)

Qv=pma CEC (1-~)qb -1

(11)

where B represents the equivalent conductance of clay-exchange cations (S m 2 meq-1), as a function of salinity and temperature, Qv describes the cation exchange capacity or CEC (meq g-a) per unit pore volume (meq cm 3), and Pma (g cm-3) is the matrix grain density of the sediment. In the following, the successive stages of the computation of the formation factor are detailed.

121

Cation exchange capacity. Values of CEC can be measured directly on rock samples, but not directly in situ. Several attempts have consequently been made to derive CEC from existing logs. Previously developed CEC or Qv estimates from well-logs based on the spontaneous potential curve (Smits 1968; Johnson 1978), dielectric constant (Kern et al. 1976), reservoir porosity (Lavers et al. 1974; Kern et al. 1976; Neuman 1980) and gamma ray (Koerperich 1975; Clavier et al. 1977; Johnson 1978) have been discussed. For this study, the correlation between the natural radioactivity from K and Th elements (CGR) and the CEC was selected. Most shale are radioactive due to the presence of K 4~ in the potassium-bearing clay mineral illite. A correlation between gamma ray counts and CEC may then be expected. Johnson (1978) showed such a correlation for formation containing largely illite and kaolinite where the relatively high gammaray count of the illite corresponded to high potassium content thus making it an excellent shaliness indicator. Scala (see Clavier et al. 1977) found a strong correlation between gamma ray count rate divided by the porosity and Qv. In other words, gamma ray log can be used in some cases and after calibration on core as a substitute of the CEC measurement. On the basis of Scala data, we estimated the proportionality constant between the two quantities as follows: CEC = (0.005) CGR

(12)

The computed values of CEC are then converted into Qv using (11). To check the validity of (12), an analytical maximum and minimum CEC are estimated with CEC values from Table 1 in each zone (Table 2). Using the relative proportions of each clay mineral, an estimate of the CEC of the clay assemblage can be computed, using a linear summation.

Formation factor. Waxman & Thomas (1974) found that B can be related to an exponential function of the conductivity, and Juhasz (1981) proposed the following expression: B = -(1.28) + (0.225)T-(0.0004059)T 2 (13) 1 + Rw kz3(0.045T--0.27) where T is the temperature in ~ and Rw the fluid resistivity in f~m. The mean value of B obtained for Hole 798B from (13) is 3.8 S m2meq -1. Continuous FF values versus depth may then be evaluated from (10).

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C. LAUER-LEREDDE ET AL.

Fig. 6. Log analysis results. (a) Grain density; from core (solid squares) and computed (solid line) (b) Opal fraction from core (after Dunbar et al. 1992) and computed. (c) Computed continental sedimentary fraction. (d) Computed CEC (derived from CGR) and Qv values. (e) Computed formation factor from definition (dash) and of Waxman & Smits (1968) (solid).

Results Grain density. The computed matrix density (Fig. 6a) exhibits a high degree of variability. The matrix density reflects the varying clay and diatom contents. Diatoms tend to have low densities, sometimes lower than 2.0g cm -3, whereas clay minerals have densities ranging as high as 2.80g cm -3 (Johnson & Olhoeft 1984). The estimated values and the core measurements are in general agreement over the interval, although fine-scale correlations between the two quantities are difficult. This difficulty results mainly from the discrepancy between the core and log measurements themselves. One of the problem with gaseous sediment is that the core recovery is often fragmented and the section is expanded and disturbed, leading to differences between the core and log depth-scales (e.g.

Hagelberg et al. 1992). Hence, measurements on core cannot been compared readily with downhole logs. Oceanic and continental fractions. The agreement between the reconstructed opal fraction curve and core measurements from Dunbar et al. (1992) is very good throughout the section (Fig. 6b), although more measurements in the upper part would be desirable for a better comparison. The major variations are well in phase: for example, Dunbar et al. measured an abrupt decrease of opal content at about 269 and 287 mbsf, and our estimated values present the same feature. Moreover, fine variations appear in the reconstructed opal fraction curve. The amount of computed opal is however overestimated, especially in the upper part (about 20%). This last point might originate in the

FORWARD MODELLING OF OCEANIC SEDIMENT PHYSICAL PROPERTIES mineralogical model: the oceanic input is assumed to be entirely opal, whereas other components are also present. For example, we considered as insignificant the biogenic carbonate component, although oceanic intervals are enriched in foraminiferas, essentially in the upper 250 mbsf. Also, the values of the physical properties chosen for this first-step model are only reference values. The true values for the components at Hole 798B are not known exactly. An additional cause of the difference between core and computed opal might be the methods chosen by Dunbar et al. (1992) to measure the opal content. They used a timeseries dissolution technique and a one-step dissolution method. In general, the results from both techniques are comparable, but the onestep method tends to yield opal contents consistently lower by 5 to 10% in enriched samples. As measurements on core for the continental fraction was not available, a precise comparison to validate our model was not possible. The computed values ranging between 40 and 90% (Fig. 6c) are in agreement with the measurements of Ingle et al. (1990). Moreover, the reconstructed continental fraction curve is characterized by a significant increase in clay content between 278 and 286 mbsf, as suggested by the increase in gamma-ray, bulk density and resistivity (Fig. 5). Cation exchange capacity. The computed CEC and Qv logs (Fig. 6d) follow the variations of clay abundance and are restricted to analytical boundaries. The proposed proportionality constant fits well. Guo (1990) measured the CEC of several loess samples from China. The CEC ranged between 0.07 and 0.28 meq g 1, which is within the range of the present results. Formation .factor. The formation factor derived

from the Archie formula is lower than that derived from Waxman & Smits formula (Fig. 6e), particularly in high resistivity zones. The data set can be represented by a regression similar to that proposed by Winsauer et al. (1952), and such as F F = a ~ .... , with a =1.45 and m = 2.38 (Fig. 7). This result is in the range typical of marine sediment. In a similar approach, Henry (1997) analysed clay-rich sedimentary samples for CEC from the Barbados wedge (ODP Site 948), similar to those from Oki Ridge: the electrical resistivity varies from 0.5 to 0.8 f~ m, the porosity is larger than 50%, and the grain densities measured on samples are close to 2.80 g cm 3. The CEC measured on core by Henry (1997) ranges between 0.2 and 0.5 meq g-i

123

Fig. 7. Formation factor versus porosity plotted on double logarithmic scale. Jackson et al. (1978) and Taylor Smith (1971) results are displayed (A, B, C, D, E; F). The present data (G) define a trend described by: FF = 1.45qb-2'38.

and the relationship F F = 1.24qb 2.31 is close to that from Oki Ridge. Taylor Smith (1971) analysed samples from Mediterranean Sea clays and found a m value close to 2.20 (Fig. 7). The results of Jackson et aI. (1978) show that the exponent m depends entirely on particle shape for unconsolidated sands (Fig. 7). Similar measurements on assemblages of shell fragments, kaolinite particles, and marine illite clays produce similar values of m (close to 2.0), suggesting that the platey nature of the particles within clays controls the relationship between FF and qb. The high value of m derived for Oki Ridge sediments is then in agreement with similar results in formations with large amounts of clays (Jackson et al. 1978), especially illite. The results obtained for Oki Ridge sediments are also typical with regard to the large spread of F F values. This spread reflects the change in shape of particles in relation to the supplies cyclicity. High values of FF correspond to the continental input, i.e. clays, whereas low values of FF correspond to the oceanic input. As a conclusion, the simple mineralogical model used here appears as well adapted to the description of sedimentary formations with high porosities (greater than 60 %) and clay content. These first results also demonstrate that the computation of the oceanic and continental

124

C. LAUER-LEREDDE ET AL. C G R (API) --- computed - - measured

200

30 tl%[

I

50 I

C G R model (API) 30 I

I

~

I

50 i

S F L (f2 m) ... computed - - measured I

II

I 4

0.5 1

]

0.7 I

Rt model (fi m) 0~5 I

[

I

0.7 I

FFs ... from raw logs -- from modelled logs t

II

2.5 ;ll=1

3.5 [

4,5

205

"-~21q

l

(a)

(b)

(c)

(d)

(e)

Fig. 8. Forward modelling results. (a) Computed and measured gamma ray values (CGR). (b) Formation natural gamma ray, from K and Th, model expressed in terms of CGR. (c) Computed and measured electrical resistivity values (SFL). (d) Formation electrical resistivity model (Rt). (e) Formation factor as determined from downhole measurements and the numerical model

fractions using the photoelectric absorption cross section (U) is in agreement with core measurements and, so, might be used to predict the core data. Nevertheless, the vertical resolution of the downhole logs and the computed formation factor is rather poor in some zones, especially in the upper part of the section. A new forward modelling method is therefore proposed in the following to improve the vertical resolution and derive more accurate Rt, CGR and FF profiles. Forward

model

The aim is to obtain an accurate formation resistivity model (Rt) from the numerical modelling of the electrical resistivity log (SFL), constrained by the high-resolution electrical images of borehole surfaces (FMS). A statistical

method is also used to model the natural gamma ray data (CGR). This study is restricted to a 20 m-long interval (200-220 mbsf/1.6 to 1.9 Ma).

Numerical modelling Modelling code. Resmod2D ~ is a newly developed two-dimensional finite element numerical code. It allows modelling of the response of electrical resistivity downhole probes, such as the Spherically Focused tool (SFL). In brief, a formation resistivity model composed of horizontal sedimentary beds (layers) with fixed thicknesses and resistivities, is entered in the code in order to compute the response of the probe in front of this formation. The resistivities of the model are referred to as 'true', whereas the computed resistivities (so the simulated response of the tool) are referred to as 'apparent' because

FORWARD MODELLING OF OCEANIC SEDIMENT PHYSICAL PROPERTIES in an inhomogeneous formation, it depends on the resistivity of the bed next to the probe and also that of the adjacent formations. The measure of the resistivity by the SFL is therefore lower than the true resistivity. Res&tivity modelling. Using Resmod2D :t:, a formation resistivity model (Rt) is created on the basis of cm-scale electrical images (FMS) for bed thickness and m-scale electrical log (SFL) for individual bed resistivity. The layer boundaries are determined from FMS images by distinct colour contrasts; the gradual transitions are disregarded here. This initial model is then processed with Resmod2D ~ to simulate the SFL tool and compute a theoretical resistivity log (SFLc). By comparison between SFLc and SFLm, the formation model is modified step by step (resistivity values and frame). Thickness changes as well as layer additions in the iterations are constrained by FMS images. This process is iterated until the best fit between SFLc and SFLm is obtained. Each processing lasts about four hours for an evaluation every 5 cm and over a 20 m-long interval (from 200 to 220 mbsf). Natural gamma ray modelling. A statistical method is used to model the natural gammaray tool in an analytical manner. The aim is to determine the natural gamma activity of each layer defined in the resistivity model. This simple method is based on an exponential attenuation of the gamma ray flux versus depth (Ellis 1987). Using the lithological frame established for the resistivity model, and the natural gamma ray measurements (CGRm), an initial model is established to estimate the C G R (CGRc). By comparison between CGRc and CGRm, the model is modified step by step and the chosen model corresponds to the best fit between CGRc and CGRm. Results Formation electrical resistivity and gamma ray models. The chosen models, obtained after about 80 iterations, correspond here to a near-perfect fit between the measured and computed values (Figs 8a, 8c). The initial Rt model took into account the major layers seen on the FMS images, not the discrete ones. The SFLc then presented the major variations of the SFLm but not the small ones. In order to reproduce these small events and to take the gradual transitions into account, the basic frame was refined by adding small layers. Whereas the initial models were composed of 47 layers, the chosen ones are

125

made of 76 layers, the smallest one measuring 8 cm and the greatest, 90cm. In order to validate the models, several precision and robustness tests were run. For example, the error E between the downhole logs and the computed theoretical logs was computed using Whitman (1989) method: E(%) + 100 (10 El~

E l o g = ~l Z i=l,U

1)

(log(mi) -- log(ci)) 2

(14)

(15)

N

where N is the number of records for the chosen downhole log, and mi (respectively ci) is the value of the record i for the downhole log (for the computed log). This estimated error is on the order of 1 % for the SFL, and 3 % for the CGR. Due to the integration of high-resolution FMS results, the models (Figs 8b, 8d) have a much better resolution than the raw logs (Figs 8a, 8c). Whereas the logs show essentially three continental events between 200 and 220 mbsf, the models show the same main three events, but also several small ones. For example, while the SFL seems rather linear over the first five metres, the Rt model brings out an alternance of minor troughs and peaks suggesting little changes in lithology, such as clay content decreases corresponding to the troughs. Whereas other lowresistivity units seem to be massive on the SFL, they are composed of several fine layers in the model. The high-resistivity units, related to colder periods, are characterized in the raw log by two or three regular peaks, whereas the model displays a much more irregular profile. The major peaks are more pronounced and the contrast is greater: the peak at about 211.15 mbsf has a value of 0.58 f~ m for the raw log, and 0.80 f2 m for the model. Moreover, the transition from the low-resistivity interval upward into the high-resistivity one is rather gradual for the raw log, whereas the model seems to show that a sharp boundary is present at the base of the high-resistivity unit, suggesting an abrupt initiation of each glacial period. All these features revealed by the models are confirmed by core observations (Ingle et al. 1990): the vertical lithologic variations within the dark/light cycles are remarkably constant. The dark-coloured intervals are either thinly to thickly laminated and finely bedded. These intervals generally possess a well-defined and sharp base that grades upward into light-coloured/high-resistivity sublayer (Ingle et al. 1990); the lower portion of the light-coloured intervals is commonly gradational

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C. LAUER-LEREDDE ET AL.

and mostly obliterated by bioturbation. The determination of the boundaries in the model seems therefore to be relatively accurate. Formation factor, The formation factor is computed for the modelled logs (Rt and CGR) on the basis of the method presented in the log analysis section. The results for the F F model are similar to those for the Rt model. The F F model has a better resolution than the F F computed from logs, as the former displays small events not detected by the latter (Fig. 8e). The major peaks are also more pronounced: the peak at about 211.15 mbsf has a value of 3.48 for the raw log, and 4.62 for the model. Changes between glacial and interglacial periods also present the same characteristics as the Rt model (sharp transition from dark laminated interval upward into lightcoloured interval, and gradual transition from light interval upward into dark one).

Conclusions The first results of the method using the raw logs show that the proposed mineralogical model is well representative of the sediment from ODP Hole 798B. The photoelectric absorption crosssection (U) allows differentiation and computation of the oceanic and continental fractions. The vertical resolution of the raw logs and of the computed formation factor curve being however poor in some zones, a new forward modelling method is proposed in this paper to improve this study. The m-scale electrical log (SFL) and the natural gamma ray log (CGR) are modelled using cm-scale electrical images (FMS) to define and map high-resolution layers, The first results show that the Rt, C G R and F F models are more precise than the Rm, C G R and FF obtained from log analysis, insofar as the models bring out small layers not detected by the raw logs. The modelling approach allows the study of changes from oceanic to continental supply hence from interglacial to glacial periods: the continental input tends to increase abruptly from warm periods to colder ones suggesting abrupt initiation of glacial cycle, whereas it seems to decrease gradually from cold to warmer periods. This study provides a continuous description of changes in intensity of the different sedimentary sources within the analysed interval. While FMS images reveal the presence not only of large-scale layers but also of thin (short) events, the numerical modelling enhances the nonlinearity of m-scale logging devices, stressing

for example the importance of cm-scale resistive beds on the response of m-scale logs. This case study, which now requires additional measurements on core to further improve the precision of the method, could become a parallel method to obtain meaningful physical properties and palaeoclimatic data from future sites. This work was carried out by the main author with financial support from the French 'Minist~re de la Recherche et de l'Enseignement Sup6rieur'. The authors wish to acknowledge the contribution of GaYa Entreprises (Marseille) for the use of the forward modelling code Resmod2D". They also wish to thank S. Brower (LDEO) for providing the logging data, C. Robert (COM, Marseille) and the two anonymous reviewers for their helpful comments.

References ARCHIE, G. E. 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Petroleum Transaetions of the AIME, 146, 54-62. CAILLERE, S., HENIN, S., RAUTUREAU, M. 1982. Min{ralogie des argiles. 2. Classification et nomenclature. Masson, Paris. CLAVIER, C., COATES, G. • DUMANOIR, J. 1977. The theoretical and experimental bases for the dualwater model for the interpretation of shaly sands. Society of Petroleum Engineers 52nd Annual Fall Technical Conference of AIME, Denver. DEMENOCAL, P. B., BRISTOWJ. F. & STERN,R. 1992. Paleoclimatic applications of downhole logs: Pliocene Pleistocene results from Hole 798B, Sea of Japan. Proceedings of the Ocean Drilling Program, Scientific Results, 127/128, 393407. DERSCH, M. & STEIN, R. 1992. Pliocene-Pleistocene fluctuations in composition and accumulation rates of Polo-marine sediments at Site 798 (Oki Ridge, Sea of Japan) and climatic change: preliminary results. Proceedings of the Ocean Drilling Program, Scientific Results, 127/128 (1), 409-422. DREVER,J. I. 1982. The geochemistry of natural waters, Prentice-Hall, New Jersey. DUNBAR, R. B., DEMENOCAL, P. B. & BURCKLE, L. 1992. Late Pliocene-Quaternary biosiliceous sedimentation at Site 798, Japan Sea. Proceedings of the Ocean Drilling Program, Scientific Results, 127/128 (1), 439~455. EKSTROM, M. P., DAHAN, C. A., CHEN, M.-Y., LLOYD, P. M. & Rossl, D. J. 1986. Formation imagining with microelectrical scanning arrays. Transactions of the Society of Professional Well Log Analysts, 27th Annual Logging Symposium, Paper 88. ELLIS, D. V. 1987. Well logging/or earth scientists. Elsevier, New-York. FERTL, W. H. & Frost, E. 1980. Evaluation of shaly clastic reservoir rocks. Journal of Petroleum Teehnology, 31, 1641 1646. FOLLMI, K. B., CRAMP, A., F(SLEMI, K. E., ALEXANDROVlCH, J. M., BRUNNER, C., et al. 1992. Darklight rhythms in the sediments of the Japan Sea:

FORWARD MODELLING OF OCEANIC SEDIMENT PHYSICAL PROPERTIES preliminary results from Site 798, with some additional results from Sites 797 and 799.

Proceedings of the Ocean Drilling Program, Scientific Results, 127]128 (1), 559-576. GRIM, R. E. 1968. Clay mineralogy. Second Edition, Mac Graw Hill Book Company, New York. Guo, Z. T. 1990. Succession des paleosols et des loess du

Centre-Ouest de la Chine: approache micromorphologique. PhD Thesis, University of Paris 6. HAGELBERG, T., SHACKELTON, N., PISlAS, N & The Shipboard Scientific Party 1992. Development of composite depth sections for Sites 844 through 854. Proceedings of the Ocean Drilling Program, Initial Reports, 138, 79-85. HASSAN, M., HOSSIN, A. & COMBAZ, A. 1976. Fundamentals of the differential gamma-ray log. Transa c t i o n S P W L A , 17th A n n u a l L o g g i n g Symposium, Paper H, 1-18. HENRY, P. 1997. Relationship between porosity, electrical conductivity and cation exchange capacity in Barbados Wedge sediments. Proceedings of

the Ocean Drilling Program, Scientific Results, 156.

IMBRIE, J. J., HAYS, J. D., MARTINSON, D. G., MCINTYRE, A., MIX, A. C., MORLEY, J., PISIAS, N. J., PRELL, W. L. • SHACKLETON,N. J. 1984. The orbital theory of Pleistocene climate: support from a revised chronology of the marine oxygenisotopic record. In: BERGER,A., IMBRIE,J., HAYES, J., KUKLA,G. & SALTZMAN,B. (eds), Milankovitch and Climate, Part L Dorrecht, Holland, 269-305. INGLE, J. C., JR., SUYEHIRO,K., VONBREYMANN,M. T., et al. 1990. Proceedings of the Ocean Drilling Program, Initial Reports, 128. JACKSON,P. D., TAYLORSMITH,D. & STANFORD,P. N. 1978. Resistivity-porosity-particle shape relationships for marine sands. Geophysics, 43, 12501268. JOHNSON W. 1978. Effect of shaliness on log response. Canadian Well Logging Society Journal, 10, 2957. JOHNSON, G. R. & OLHOEFT, G. R. 1984. Density of rocks and minerals. In:: CARMICHAEL,R. S. (eds)

CRC Handbook of Physical Properties of Rocks. Boca Raton, FL (CRC Press, Inc.), 3, 1-38. JUHASZ, I. 1981. Normalised Qv - - the key to shaly sand evaluation using the Waxman-Smits equation in the absence of core data. Transaction SPWLA 22nd Annual Logging Symposium, Paper Z. KERN, J. W., HOYER, W. A. & SPANN, M. M. 1976. Low porosity gas sand analysis using cation exchange and dielectric constant data. Transaction of the Society of Professional Well Log Analysts, 17th Annual Logging Symposium, Paper PP, 17 p. KOERPERICH,E. A. 1975. Utilization of Waxman-Smits equations for determining oil saturation in a low-

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salinity, shaly sand reservoir. Journal of Petroleum Technology, 27, 1204-1208. KUKLA, G., HEELER, L., MING, X., CHUN, X. T., SHENG, L. T. & SHENG, A. Z. 1988. Pleistocene climates in China dated by magnetic susceptibility. Geology, 16, 811-814. LAVERS,B. A., SMITS,L. J. M. & VANBAAREN,C. 1974. Some fundamental problems of formation evaluation in the North Sea. The Log Analyst, 12, 1-10. LiiTH1, S. M. & BANAVAR,J. R. 1988. Application of borehole images to three-dimensional geometric modelling of eolian sandstone reservoirs, Permian Rotliegende, North Sea, American Association of Petroleum Geologists Bulletin, 72, 1074-1089. MATOBA, Y. 1984 Paleoenvironment of the Sea of Japan. In: OERTLI, H. J. (ed.) Benthos '83 2nd

International Symposium on Benthic Foraminifera, 409-414. MORLEY, J., HEUSSER, L. & SARRO, T. 1986. Latest Pleistocene and Holocene paleoenvironmnet of Japan and its marginal sea. Palaeogeopraphy, Palaeoclimatology, Palaeoecology, 53, 349-358. NEUMAN, C. H. 1980. Log and core measurements of oil in place. Journal of Petroleum Technology, 32, 1309-1315. PEZARD, P. A., LOVELL, M & The Ocean Drilling Program Leg 126 Shipboard Scientific Party 1990. Downhole images: electrical scanning reveals the natur of subsurface oceanic crust. EOS, 71, 709 SCHLUMBERGER 1994. Log interpretation charts. Schlumberger Wireline & Testing, Houston. SMITS, L. J. M. 1968. SP log interpretation in shaly sands. Society of Petroleum Engineers Journal, 8, 123-136, Transaction of AIME, 243. TAYLOR SMITH,D. 1971. Acoustic and electric techniques for sea-floor sediment identification. Proceeding Symposium on engineering properties of sea-floor soils and their geophysical identification, Seattle, Washington. WAXMAN, M. H. & SMITS, L. J. M. 1968. Electrical conductivities in oil-bearing shaly sands. Society of Petroleum Engineers Journal, 8, 107-122. - & Thomas, E. C. 1974. Electrical conductivities in shaly sands--I. The relation between hydrocarbon saturation and resistivity index; II. The temperature coefficient of electrical conductivity. Journal of Petroleum Technology, 6, 213-225. WINSAUER,W. O., SHEARtN,H. M., MASSON, P. H. & WILLIAMS, M. 1952. Resistivity of brine-saturated sands in relation to pore geometry. Bulletin of the American Association of Petroleum Geologists, 36, 253-277. WHITMAN, W. 1989. Inversion of normal and lateral well logs. The Log Analyst, 30, 1-11. ZHENt, H. H. 1984. Paleoclimatic events recorded in clay minerals in loess of China. In."PECSI, M. (ed.)

Lithology and Stratigraphy of Loess and Paleosols. Geographic Research Institute.

Lithological classification within ODP holes using neural networks trained from integrated core-log data G. W A D G E 1, D. B E N A O U D A 1, G. FERRIER l, R. B. WHITMARSH 2, R. G. ROTHWELL

2 & C. M A C L E O D

3

1Environmental Systems Science Centre, University of Reading, PO Box 238, Reading RG6 6AL, UK 2 Southampton Oceanography Centre, University of Southampton, Empress Dock, European Way, Southampton S014 3ZH, UK 3Department of Earth Sciences, University of Wales College of Cardiff, PO Box 914, Cardiff CF1 3 YE, UK Abstract: Neural networks offer an attractive way of using downhole logging data to infer the lithologies of those sections of ODP holes from which there is no core recovery. This is best done within a computer program that enables the user to explore the dimensionality of the log data, design the structure for the neural network appropriate to the particular problem and select and prepare the log- and core-derived data for training, testing and using the neural network as a lithological classifier. Data quality control and the ability to modify lithological classification schemes to particular circumstances are particularly important. We illustrate these issues with reference to a 250 m section of ODP Hole792E drilled through a sequence of island arc turbidites of early Oligocene age. Applying a threshold of > 90% recovery per 9.7 m core section, we have available about 50% of the cored interval that is sufficiently well depth-matched for use as training data for the neural network classifier. The most useful logs available are from resistivity, natural gamma, sonic and geochemistry tools, a total of 15. In general, the more logs available to the neural network the better its performance, but the optimum number of nodes on a single 'hidden' layer in the network has to be determined by experimentation. A classification scheme, with 3 classes (claystone, sandstone and conglomerate) derived from shipboard observation of core, gives a success rate of about 76% when tested with independent data. This improves to about 90% when the conglomerate class is split into two, based on the relative abundance of claystone versus volcanic clasts.

Within the Ocean Drilling Program (ODP), one c o m m o n application of d o w n h o l e logs is to c o m p l e m e n t and calibrate measurements m a d e on cores and to fill in the gaps left by incomplete core recovery. Below the range of the Advanced Piston Corer (typically about 200 m sub-bottom) core recovery is rarely m o r e than about 50% for sediments and 40% for basement rocks ( O D P 1990). D o w n h o l e logs make measurements at ambient temperatures and pressures and sense a volume a r o u n d the borehole greater than the core itself. Such measurements provide a continuous stream of in situ data on the wall rocks and borehole fluids. The above figures for typical core recovery are aggregate values. Our knowledge of the exact depths of recovered core samples is, in general, worse than these figure imply. In the ODP, coring advances in steps of about 9 . 7 m (the length of individual core barrels). Unless core recovery for this 9.7 m interval is complete we do

not k n o w the exact sub-bottom depth of the core samples that are recovered, though we may assume their relative original positions are preserved. Thus, at the limit, a continuous 1.5 m section recovered from a 9.7 m core may have originally come from the top or the b o t t o m 1 . 5 m interval. A g r i n i e r & A g r i n i e r (1994) showed that the best estimate of the position within finite limits of any arbitrary length of core sample is given by Euler's Beta distribution. This can be given as a probability density function of position in terms of the lengths of core, section and the n u m b e r and positional order of core sample. Therefore, d o w n h o l e logs play an even more important part in filling the gaps in our knowledge of rock sequences for which there is incomplete core recovery. If we can identify the characteristic ranges of combined log values that correspond to different lithologies penetrated by the hole then we have a means of assigning lithological class labels to the

WADGE,G., BENAOUDA,D., FERRIER,G., WHITMARSH,R. B., ROTHWELL,R. G. & MACLEOD,C. 1998. Lithological classification within ODP holes using neural networks trained from integrated core-log data. In: HARVEY,P. K. t~ LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 129-140

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total interval from the downhole logs. We show how this can be done for ODP data when we can assign the lithological classes from those sections where we do have 'complete' core recovery and extend the classification to the full hole. Our approach has been to develop software that supports a general user in completing this task. There are a number of methods by which such a classification scheme can be driven (e.g. discriminant functions, principal components analysis and cluster analysis; Doveton 1994). We have chosen to use classifiers based on artificial neural networks, principally because of their ability to cope with complex non-linear problems. Also, neural network classifiers have been shown to be of value for lithological classification of downhole logs in hydrocarbon exploration wells, in many cases with superior results to other techniques such as discriminant analysis (Baldwin et al. 1990; Rogers et al. 1992; Wong et al. 1995). Goncalves (1995) reports similar findings for ODP data. This paper has three main sections. Firstly we present the main factors involved in the classification task. These are how the problem is defined, the constraints imposed by the data available and how to validate the results and assess performance. Next we describe how we have implemented the neural network method on our computer system. Finally, we present classification results from ODP Hole 792E. The succession represented in this hole is a complex sequence of island arc lithologies that is a good test of the general usefulness of the technique.

ODP lithological classification The lithologies encountered in ODP holes are usually deep-sea sediments and oceanic crustal rocks and are generally distinct from those encountered during drilling in sedimentary basins underlain by continental crust. Deep sea sediments are often relatively unconsolidated and rich in carbonates and/or silica or composed of terrigenous or volcanic detritus; they may be underlain by a basaltic basement. Porosity is typically high, with ubiquitous saturation by sea-water. The classification framework of Mazzullo et al. (1987) is widely employed for sediments by ODP. The highest-level division is into granular and chemical sediments. Granular sediments are subdivided into pelagic, neritic, siliciclastic, volcaniclastic and mixed sediments and chemical sediments into carbonaceous, evaporites, silicates/carbonates and metalliferous sediments. Below this level classes are based on principal names (e.g. ooze, chalk) together with major or minor modifiers (e.g. nannofossil,

foraminiferal). This nomenclature is applied by the shipboard petrologists when the cores are split and each 1.5m section of recovery is described individually on the Visual Core Description sheets in freehand. This description may show some variation from one petrologist to another. From this initial detailed visual description a more generalised sequence of graphical codes (from a total of about 50) are assigned to each interval of core to denote a lithological class label (e.g. T6=sandstone; C34= foraminiferal chalk) so that a composite graphical log (Barrel Sheet) of all the core recovery can be drawn for publication in the Initial Report series of ODP publications. Beyond this the shipboard scientists can, and sometimes do, erect other, non-standard but complementary, classification schemes, perhaps based on local variation of the sediment. Within the ODP there is no official archived digital version of the lithological classification of core. Hence working on core classification off the ship requires digital recoding of the shipboard scheme(s). The neural network approach is a supervised classification scheme. It requires that a sufficient number of training examples of the logs from each separate lithological class be made available for the algorithm to learn the character of that class. Two general rules apply here. First, if there are too few samples within a class then those samples will not fully represent the distribution of values that the classifier might meet through the whole borehole. Second, the number of samples presented to the classifier from each class should be approximately the same. If the number of samples from one lithology presented to a neural network classifier is much greater than for the other classes then the network will tend to bias its classification in favour of this class. This problem becomes serious whenever the logs do not provide a clear separation of the lithological classes. The quality of log samples used to train the classifier is also important. In addition to checking for spurious outliers we use three logs for quality control. Samples exceeding any of the threshold values for the caliper, density correction and geochemical factor logs are not used for supervising or testing the classifier. Classification choice

The choice of what classification to attempt is of vital importance. The ideal is to have a set of lithological classes that best represents the geological information required from the hole and which produces distinctive responses in the

ODP LITHOLOGY USING NEURAL NETWORKS suite of available downhole logs. The usual starting point will be the principal-names level of shipboard classification of the core. Classes with very few member samples may need to be amalgamated with other classes. The lithological information required from the hole may not be the most obvious. For example, a hole may penetrate a succession of oozes above siliciclastic rocks lying on a basaltic basement. Classifying such a tripartite division should be trivially easy and the real problem of interest may be in the second-order variability, say, distinguishing volcanic from non-volcanic rocks in the siliciclastic sequence. In this case the classification task can be constrained by choice of depth interval. Alternatively, the need to change the class labelling given to the core samples to best fit the problem may only become apparent after an initial attempt at classification. Merging and splitting of classes may be required. There is a clear general need for more than one classification scheme to be tested and for the editing facilities to support that need. There is no guarantee that the recovered core, and hence any classification scheme based on it, is fully representative of the lithologies in the missing intervals. Examples of preferential recovery of, say, clays relative to sands are well-known. At the extreme a relatively common lithology may not be recovered at all. It is more likely that a lithology only ever exhibits low recovery and hence cannot be matched to specific depth intervals and used with confidence to train the classifier. This problem of a missing class(es) can be partly addressed using exploratory data analysis of the logs themselves. If it is clear that some populated area of log-space is not represented by the current classes then a search can be made to identify the missing class.

131

sub-populations are used to train and test the performance of the classifier (e.g. discriminant analysis) and the classification rates of the two classifiers can now be compared.

Implementation of a neural network method

System design The quite complex processing chain implicit in the above discussion is best handled by a computer system designed for the job. We have designed such a system, the essential elements of which are shown in Fig. 1. The computing platform is a Sun Sparcstation and the graphical user interface is designed using PV-WAVE visualization software. There is a separate development environment for designing the neural networks that the user does not see, but which can create portable networks (as C code) that can be retrained. The user must define the problem by choosing appropriate depth intervals, lithological classes, logs and a neural network. The results of running the network are displayed graphically and in terms of relative performance of the classification rate. There are three main functional components to the system. These are shown in Fig. 2 and are described in detail in the following sections.

Performance measures Having trained a neural network classifier, some way of assessing its performance is required. The standard way to do this is to take a separate subpopulation of core-classified samples from the same general population and classify it independently with the network. The goodness of fit of the two classifications (classification rate) gives a measure of how well the network classifier performs relative to the visual description classification. If this performance is thought satisfactory then the network can be run on the full problem interval. What is 'satisfactory' in this context is best left to the geologist. One, albeit relative, benchmark by which to judge satisfactory performance is to compare with another classification technique. Again, the same

Fig. 1. Schematic structure of our computer system to derive lithological logs from ODP core-log data.

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Fig. 2. Functional schematic of the way data is explored, selected and classified in our method.

Log data exploration The purpose of log data exploration is to enable the user to become familiar with the data before making explicit choices. The ability to plot logs against depth and cross plots of one log against another is standard. In our system there is also the ability to display simultaneously, selected sample populations both in terms of their depth and their position in log space. This is done by manipulating a graphical cursor. It is a valuable facility for deciding whether some 'extreme' values in a cross plot, say, correlate with a specific bed or are scattered throughout a sequence. Principal components analysis and unsupervised cluster analysis are also available for any selection of samples and logs. These exploratory analytical functions help decide the following: (1) what is the effective dimensionality of the log data (i.e. how many distinct classes will the data support)?; (2) at what depth intervals do the most representative samples lie?; (3) are any samples obviously not represented by core intervals with good depth matching?

Data selection Explicit selections of depth interval, logs and classes must be made. As we show later, the

neural networks tend to perform better with as many 'useful' logs as possible and hence the default is to use all logs. However, some logs may only be available for restricted depth ranges. Hence the choice would be between fewer logs or more logs for a reduced interval. Class selection is a more complex issue. There are two main requirements: to be able to edit a classification, to create a new classification scheme and to give each such scheme source information; who created it, when and how. Editing can involve merging and splitting classes and assigning new labels. Thus a library of classifications can be created. Class labels are assigned at each log sampling interval, nominally every 15 cm. The shipboard petrologists also log sedimentary and structural discontinuities some of which form class boundaries. In one ideal situation, each thick (> > 15 cm) sedimentary bed would be of uniform lithological character with sharp boundaries and have contrasting neighbours giving the logs the character of step functions across the boundaries. This ideal is the basis of log segmentation algorithms (e.g. Vermeer & Alkemade 1992) which seek to segment the borehole into uniform intervals to which single (lithological) labels can be attached. This can be helpful in constraining classes in intervals of incomplete core recovery. The data selection process creates a Log-Class File (Table 1), whose values are used directly by the neural network classifier.

Neural network classification Samples from the Log-Class File are separated into class populations and counted. The total of the smallest population is then used to select samples for training and testing. Classes with larger p o p u l a t i o n s are subsampled evenly throughout their range to give a total equal to that of the smallest class. Each same-size class population is then split into two sub-populations by alternate sampling to give training and testing sample populations for each class. The log values of these populations are then examined graphically to check that; the distributions of the training and testing samples are similar, and that the distributions of the core-classified samples are representative of the whole interval under investigation. If these conditions are not met then other data selections must be made. The neural network used is the feed-forward back-propagation type which is standard for classification problems. The selection of logs and classes constrains the structure of the network. The input layer consists of one node for each log and the output layer consists of one node for

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Table 1. Representative part of a L O G - C L A S S file with 4 classes. Only 3 o f the logs are shown. There is no sample classified as Conglomerate 2 in this selection shown

SGR

CGR

A1203

26.6793 26.8207 26.6378 12.6669 12.1269 11.7988 12.1286 11.8547 11.7594

24.7285 25.1096 25.287 9.3789 8.8892 8.7609 8.1325 7.9513 7.9992

21.4907 20.9049 20.0691 23.0037 21.9625 21.4303 19.5016 18.8318 17.9526

-

each class. There is at least one other, 'hidden', layer of nodes between the input and output layers with weighted connections between nodes of different layers. The number of hidden nodes is not externally constrained and can be changed to suit a particular problem. The other network parameters are rnainly related to the weightings applied to the connections. These can be tuned to improve performance, but detailed optimization of neural networks is a complex issue. Our strategy is to make available a limited number of default networks initially and optimize individually applied networks later. Once the network has been selected it begins training with the prepared training data by selecting samples, at random, and presenting their log values to the input layer of the network. The effect of these values propagates through to the output layer where the 'error' between the network node values and the 'correct' values is then propagated back through the network, thereby changing network weightings. In this way the network, after hundreds to thousands of learning cycles, improves its ability to recognize classes until no further improvement is achieved and the network is said to be trained. The trained network can now be tested by presenting each of the test samples to the network once, and recording how close the network result is to the correct classes. The network gives proportional values for each class within the range 0-1, whereas the core-derived class labels are binary (0 or 1). The network results are thus essentially probabilistic. We express the test result as a thresholded classification rate. For example, at a user-defined threshold of 70% probability, a test result of 0.76 sandstone, 0.20 siltstone and 0.04 claystone for a sample with class values of 1,0,0 would count as a correct classification, though not at a threshold of 80%. 92 such correct results out of 100 test samples, for example, would give a classification rate of 92%. If the

Clay

Sst

Cong 1

Cong2

1 1 1 0 0 0 0 0 0

0 0 0 1 1 1 0 0 0

0 0 0 0 0 0 1 1 1

0 0 0 0 0 0 0 0 0

outcome of the training and testing cycle is considered satisfactory then the network can be applied to the full interval under consideration.

Application to Hole 792E Hole 792E of the ODP was drilled in the IzuBonin foreare sedimentary basin in 1989 (Taylor et al. 1990). The primary objective of drilling at Site 792 was to understand the stratigraphy of the forearc and the temporal variations in sedimentation and volcanism that controlled it. About 800m of sediment were drilled above volcanic (andesite) basement, including rocks of Pleistocene, !ate Pliocene, Miocene and early Oligocene age. The lower part of this section is a more volcaniclastic-rich sequence. The interval between 482-732 m below sea floor (mbsf) is the focus of this study and comprises a large part of Unit IV, a sedimentary succession of early Oligocene age (Fig. 3). Overall, Unit IV is composed of vitric sandstone (58%), sandy pebble-granule conglomerate ( 10%), silty claystone (9%), nannofossil-rich silty claystone (5%), claystone (4%), siltstone (4%), nannofossil c l a y s t o n e ( l % ) , clayey siltstone (1%), sandy mudstone (1%) and sandy siltstone (1%). This unit is interpreted by Taylor et al. (1990) as a rapidly deposited turbidite blanket in an oversupplied basin or distal fan. The pumice clasts of some of the coarse sandstones and conglomerates indicates contemporary volcanism but most of the andesite and dacite clasts are probably the result of erosion from the arc volcanoes. Core recovery

Hole 792E had a recovery of 48.2% of total possible core length. Recovery for the 482-732 mbsf interval was 79.1%. However, as discussed

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Fig. 3. Summary graphical log of the stratigraphy of the 482-732 mbsf interval of ODP Hole 792E (after Taylor et al. 1990). The symbols represent: Inverted 'T'= nannofossil ooze, dashes=claystone-siltstone, check = sandstone, dot-ellipse=conglomerate. Grain sizes are represented by c=claystone, s=siltstone, fs = fine sandstone, cs = coarse sandstone and g = gravel/conglomerate.

earlier, many individual cores contained only a fraction of the full core length and hence cannot be matched to the logs with confidence. We have used only individual cores that have greater than 90% recovery to form the basis of our classification. These 13 out of 26 cores (Fig. 3) therefore represent a useable recovery of 50%. Each of these cored intervals have had their depth assignments normalized to 100% recovery after closing any gaps between core sections. Notice that we have no matched core for the interval 617-655 mbsf. Five lithological classes based on shipboard visual description were used in the 482-732 mbsf interval: claystone, silty/sandy claystone, muddy siltstone/sandstone, siltstone/sandstone and gravel/conglomerate. One of these five classes was initially assigned to each (0.15m) log interval. A number of thin (< 0.15 m) , mainly claystone, beds were ignored in this process. However, the claystone and muddy siltstone/ sandstone classes had so few samples (8 and 37, respectively) that they were both merged with the silt/sandy claystone class. For simplicity the remaining three classes were called claystone, sandstone and conglomerate.

measurements

The sediments in Hole 792E are well-indurated. The borehole was close to cylindrical for much of its depth with a diameter < 3 0 c m , and conditions made for good-quality logs. There is reasonable correlation between the log values and shipboard core measurements except for SiO2 content. The tools (sensors) used that are relevant to this study were Resistivity (DEL), Sonic (LSS), Natural Gamma (NGT), Geochemistry (GST and ACT) and Lithodensity (HLDT) and they acquired data in 4 logging runs, that were then depth-matched. Seventeen log parameters were considered for use in the classification: spectral gamma, computed gamma, radioactive potassium, thorium and uranium, deep, medium and shallow resistivity, density, photoelectric effect, sonic velocity and the oxide contents of calcium, silicon, iron, titanium, potassium and aluminium. Unfortunately, no density correction and photoelectric effect measurements are available below about 550 mbsf. We removed low-quality log data that exceeded any of the following thresholds for the three quality-control logs: Caliper (29.5cm Density Correction (0.1 gm cc l) and Geochemical Factor (800). These thresholds were determined empirically by e x a m i n i n g the log distributions. This reduced the number of samples available by about 3%. Within the 482-732 mbsf interval Taylor et al. (1990) and Pratson et al. (1992) observed the following relationships between log and core: (1) Natural gamma spectrometry shows that potassium is the dominant radioactive source mineral and is inversely related to values of resistivity, velocity and density, and in some cases, grain size (482-500 and 555-585 mbsf). Uranium and potassium contents are generally negatively correlated. Beds with high mud contents have high values of potassium content and natural gamma. (2) Above about 515 mbsf the sequence has a bimodal character with high resistivity/ velocity/density - low natural gamma beds alternating with beds of opposite character. Below this depth the logs lose their high frequency nature and generally have raised resistivity/velocity/density values. (3) There is correlation between upward-fining sandstone/conglomerate beds and a sawtooth response of resistivity in the 540-590 mbsf interval. Of particular importance is the reduction in resistivity at 587 mbsf, where the base of a large conglomerate bed

ODP LITHOLOGY USING NEURAL NETWORKS Table 2.

Networkperformance results

Network Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

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Network Structure 1-717-3 15-15-3 15-15-3 15-15-4 4-8-4 5-15-4 6-15-4 11-10-4 15-02-4 15-04-4 15-06-4 15-08-4 15-10-4 15-12-4 15-14-4 15-16-4 15-18-4 15-20-4 15-25-3 15-30-3 15-25-10-3 15-25-20-3

Depth Interval (mbsf)

Classification Total

Clay

Sst

Cong (1)

482-550 482-550 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 482-732 483-732 482-732 482-732

88.4 85.5 75.8 90.0 78.1 80.0 81.9 86.3 71.9 82.5 83.1 86.1 86.9 86.9 88.1 86.9 89.4 88.1 78.0 76.6 80.2 78.8

87.0 87.0 83.5 92.0 85.0 82.5 87.5 85.0 87.5 90.0 85.0 87.5 90.0 90.0 85.0 92.5 92.5 90.0 86.8 79.1 84.6 82.4

78.3 73.9 59.3 80.0 47.5 52.5 67.5 65.0 92.5 47.5 60.0 85.5 62.5 72.5 72.5 70.0 72.0 77.5 57.1 69.2 72.5 65.9

100 95.7 84.6 87.5 82.5 85.0 72.5 95.0 12.5 92.5 87.5 75.0 95.0 85.0 95.0 85.0 95.0 85.0 90.1 81.3 83.5 87.9

also marks the d o w n h o l e increase in smectite concentration and magnetic susceptibility.

Performance of different neural networks There is no one single neural network that will work for all classification problems. The basic type used here, whose structural variants we now discuss, is a back-propagation network with a single hidden layer and a sigmoidal activation function at each node. As part of the preprocessing for neural network training the data from each log that are input to the network are normalized to the range 0-1. Logs with large potential ranges, such as the resistivity tools, may be best converted to a logarithmic scale first. However, the resistivity values of Hole 792E did not show a very great range and this was not done. As was discussed earlier, the number of nodes in the input and output layers is at least partly determined by the nature of the data and the problem to be solved; the number of nodes in the hidden layer is chosen to optimize performance once the input and output layers are fixed. In the performance results reported in Table 2 we use a convention in which a 15-10-4 network means 15 input nodes (downhole logs), 10 hidden nodes and 4 output nodes (lithological classes).

Rate(%) Cong(2)

100 97.5 100 100 100 95.5 100 100 100 100 100 100 100 97.5 100

There are 17 logs available for the interval 482-550 mbsf, but only 15 (no density and photoelectric logs) were considered for the full interval between 482-732 mbsf. Using the basic rock type classification, the 482-550 mbsf interval has 98 claystone, 164 sandstone and 46 conglomerate samples available for training and testing. Network 1 (Table 2) then, is a 17-17-3 network used for 482-550 mbsf that gives a total classification rate of 88.4%. Using only 15 logs for the same interval in network 2 gives a reduced rate of 85.5%. Hence density and photoelectric effect logs do have some extra capability to discriminate between these rock classes in addition to that present in the other 15 logs. However, when we use the same type of network for the 482-732 mbsf interval, but trained using the samples from a 183 claystone, 407 sandstone and 185 conglomerate pool of samples (network 3), the classification rate falls to 75.8%. This means that the claystones a n d s t o n e - c o n g l o m e r a t e classification that worked well from 482-550 mbsf is much less appropriate below 550 mbsf. There is a distinct fall in the capability of the network to recognize the conglomerate and sandstone class samples. Exploring the log data over this wider interval suggests that core samples classed as conglomerate may be usefully split into more than one type. For example, principal components analy-

136

G. WADGE E T AL. 100

60 x

9

90

~

50

80

o

40 x

x

=

O

70

i

30

60

2

9

Classification Rate

x

Computing Time

20

!

n

!

i

I

l

4

6

8

10

12

14

16

Number of Logs Fig. 4. Plot of classification rate performance and elapsed computing time versus increasing numbers of geophysical logs as input to the neural networks (networks 4-8). B

90 ra

88

9

m

ra

86 84 82 o

80 78

76 .--4

74 72 70

9

0

i

2

9

i

4

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8

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i

10

,

i

12

9

i

9

14

1

16

9

i

18

9

i

20

Number of Hidden Nodes

Fig. 5. Plot of classification rate performance versus the number of nodes in the hidden layer (networks 9-18). sis of shallow resistivity, sonic velocity, spectral gamma, computed gamma and potassium oxide logs shows that some of the conglomerate class samples give much lower values of principal component 3 and higher values of principal component 4 than the other conglomerate samples. Thus we have created a second classification scheme with four classes: claystone, sandstone, conglomerate 1 and conglom-

erate 2. Conglomerate 1 includes those samples classed as conglomerate in networks 1 and 2; conglomerate 2 (the samples described above) corresponds to core which is conglomeratic but has higher proportions of large ( > 5 cm) claystone clasts than conglomerate 1. In the logs, conglomerate 1 has distinctly lower spectral gamma and potassium values than those of conglomerate 2. Sonic values are also lower in

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137

Fig. 6. Component lithological classification using neural network 4. The four columns display the component contribution of the rocks types (claystone, sandstone, conglomerate 1 and conglomerate 2) for each sampling interval of the logged hole. The depth in mbsf is shown on the left and the core number on the right of each column. The same colours are also used to display the classification in the visual core descriptions in the narrow column to the left of the core numbers. conglomerate 1 but the separation is less distinct. With four classes, network 4, otherwise equivalent to network 3, gives a much improved classification rate for the whole 482-732 mbsf interval of 90.0%. We saw an example of improvement in performance with increased numbers of logs (from network 1 to 2) for the 482-550 mbsf interval. For the full interval with 4 classes it is also generally true that the more logs input to the network the better the performance (networks 4, 5 to 8 inclusive; Fig. 4). There is a penalty to pay in terms of increased computing time (Fig. 4) but this is not too great a burden. Hence it makes sense to use as many useful logs as are available at the outset. Network 4 has a 15-15-4 structure. The

justification for the 15 nodes in the hidden layer is provided by a systematic test of performance in a series of networks with variable numbers of hidden nodes (networks 4, 9 to 18 inclusive; Fig. 5). The optimum configuration of the hidden layer of 15 nodes is given by the maximum performance value. In this case the number of hidden nodes equals the number of input nodes. This would be a useful rule-of-thumb for initial network configuration but it does not guarantee the optimum solution. For instance, as can be seen from networks 3 and 19 to 22 inclusive, greater numbers of hidden nodes (and even a second hidden layer) can give improved performance, but at the cost of increased computing time.

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G. WADGE ETAL.

Computed lithological log results Figure 6 shows the output of network 4 when applied to the whole 250 m interval of downhole logs from 482-732 mbsf. The aggregate thicknesses of the lithologies according to this classification are: c l a y s t o n e = 4 4 m , sandstone = 130 m, conglomerate 1 = 42 m, conglomerate 2 = 34 m. Some sample intervals are classed as 100% of a particular lithology but many are classed as mixtures, with one dominant lithology and one or more minor components. This is particularly noticeable for mixtures of sandstone and conglomerate 1, but much less so for mixtures involving the other two lithologies. In Fig. 7 the results from this network have been recast such that the major ( > 5 0 % ) lithology in the output is attributed to that depth interval. This gives a columnar plot that mimics a traditional Lithological log and allows direct comparison with the visual core classification. The change in character of the rocks at about 515 mbsf noted above is apparent but is overshadowed by the decrease in claystone which occurs about 20 m higher. Lower down the hole the occurrence of conglomerate 2 is restricted to 3 zones where there is an apparent association of claystone-conglomerate 2. The base of the shallowest of these zones corresponds to the major break noted at 587 mbsf, though there is no obvious change in general lithological character below this. The log gives the impression of three major cycles of mixed conglomerate and sandstone sitting above conglomerate 2 and claystone (515-587, 587-660, 660-732 mbsf). The second thickest interval classed as conglornerate 2 is from around 640 mbsf, where there is no core recovery. In fact there is no sense of this second cycle in the recovered core. The lowest of the three cycles is richer in sandstone at the expense of conglornerate 1. As discussed earlier, the rocks recovered from only 50% of the full 482-732 mbsf interval were used to train and test the neural network. Figure 7 displays these core (core numbers 37-39, 40, 42-43, 46, 48-50, 56-57, 60, 61) together with the additional recovered core, that comprised 29% of the total interval, that was not used in training and testing the network because of poor depth control (core numbers 39, 41, 44-45, 47, 51-55, 58-59, 61). For many of the intervals used in the training and testing there is a high degree of detailed correspondence between the core and the network classifications (e.g. core numbers 37-38, 50, 62) as we would expect. For a few, the correspondence is weaker (e.g. core 43). For the core intervals with < 90% recovery any corre-

spondence is more difficult to assess. For some cores such as 39 and 55, correspondence could be achieved by appropriate expansion of the core lithology down section to match the network lithological log results. For other intervals no such a c c o m m o d a t i o n can be achieved (e.g. core numbers 45, 52 and 59). The two main possible explanations of this are that the network is 'overtrained' and has lost its ability to generalize when exposed to new data, and that the classification scheme is not optimal. The way ahead in our system would be to explore the second possibility by choosing another classification scheme. Because the sandstone group of samples is the largest and shows the poorest general classification performance figures (Table 2) this is the most likely group for possible splitting into two or more classes. Some of the geochemical logs such as TiO2 and CaO show clear evidence of alternating high and low valued sandstone horizons (e.g. 670--682 mbsf) that could form one of the criteria of such a new classification scheme, though this is not pursued here.

Discussion We have chosen to ignore a number of major issues of core-log-driven classification including graded bedding, the differences in spatial resolving power of the logs and the use of segmentation, in order to emphasize the value of quality control of the data and careful consideration of the optimal structure of the neural network. In particular, we wish to stress the need to have a flexible mechanism for changing the classification scheme of rock types based on the information content in the logs and the shipboard-derived classification scheme. Such an approach is inherently hole-specific. It lies at an intermediate position between a totally empirical approach, driven solely by the log data, and one that might use a universal library of log responses derived from fundamental core components (e.g. sand, carbonate, sea-water etc.). If the data can support it, the refinement of the classification scheme in a hole will be essentially hierarchical. However, there is no guarantee that the way that the log data can be optimally divided will correspond to the classification scheme that the geologist wants or expects. This sort of approach should be of value to ODP scientists both on and off the ship. Results of our work using data from other ODP holes will be presented elsewhere. We also envisage that this technique might be of value for providing rapid lithological analysis of

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Fig. 7. Majority component lithological log output of the neural network 4. The main column is the network classification, the narrow column to the right is that classified from recovered core.

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piston cores from which horizontal-track logs have been collected o n - b o a r d ship.

This work is funded by a grant (GST/02/993) to RBW and GW under the NERC Special Topic--UK ODP Science Programme. ESSC work is supported by NERC grant F60/G6/12/02. We are very grateful to our collaborators Drs P. Harvey and H. Grubb, for their help and the Borehole Research Group at LDEO and ODP/TAMU for supplying data.

References AGRINIER, P. & AGRINIER, B. 1994. A propos de la connaissance de la profondeur a laquelle vos echantillons sont collectes dans les forages.

Comptes Rendus de la Academie Sciences de Paris, 318, serie II, 1615-1622. BALDWIN, J. L., BATEMAN,A. R. M. & WHEATLEY,C. L. 1990. Application of neural networks to the problem of mineral identification from well-logs. The Log Analyst, 3, 279-293. DOVETON, J. H. 1994. Geologic log analysis using computer methods. Computer Applications in Geology, 2. American Association of Petroleum Geologists, Tulsa.

GONCALVES, C. A. 1995. Characterisation of formation heterogeneity. PhD Thesis, University of Leicester. MAZULLO, L, MEYER, A. & KIDD, R. B. 1987. A new sediment classification scheme for the Ocean Drilling Program. ODP Technical Note, 8. ODP 1990. Wireline Logging Manual, Ocean Drilling Program. Borehole Research Group, LamontDoherty Geological Observatory. PRATSON, E. L., REYNOLDS, R., LOVELL, M. K., PEZARD, P. A. & BROGLIA,C. 1992. Geochemical well logs in the lzu-Bonin arc-trench system, Sites 791, 792, and 793. Proceedings of the Ocean Drilling Program, Scientific Results, 126, 653-676. ROGERS, S. J., FANG, J. H., KARR, C. L. & STANLEY,D. K. 1992. Determination of lithology from well logs using a neural network. American Association of Petroleum Geologists Bulletin, 76, 731-739. TAYLOR, B., FUROKA, A. & OTHERS 1990. Proceedings of the Ocean Drilling Program, Initial Results, 126. VERMEER, P. L. & ALKEMANDE, J. A. H. 1992. Multiscale segmentation of well logs. Mathematical Geology, 24, 27-43. WONG, P. M., JIAN, F. X. & TAGGART, I. J. 1995. A critical comparison of neural networks and discriminant analysis in lithofacies, porosity and its permeability predictions. Journal of Petroleum Geology, 18, 191-206.

Core-derived acoustic, porosity & permeability correlations for computation pseudo-logs A. C. B A S T O S , L. D. D I L L O N , G. F. V A S Q U E Z & J. A. S O A R E S Petrobras Research Center-SEGEST,

C i d a d e Universitaria - Q . 7 - P r e d i o 20, Ilha do

F u n d a o - R i o de Janeiro, 2 1 9 4 9 - 9 0 0 , B r a z i l

Abstract: In order to improve hydrocarbon production, it is often necessary to obtain more

accurate rock, fluid and petrophysical information. For example, to obtain a reservoir porosity map using seismic data as reference, it is necessary to generate reliable correlations between seismic attributes and petrophysical properties like porosity and permeability. Again, to optimize drilling and/or hydraulic fracturing programs, it is also necessary to estimate better formation static mechanical behaviour from geophysical data. The main goal of this work is to establish for an offshore Brazilian field, relationships between compressional and shear wave velocities and petrophysical properties such as porosity and permeability.The large number of limestone samples (120) gave us a precise empirical relationship between Vs and Vp for limestone. In order to obtain a calibration reference, we also made, with the same samples, simultaneous measurements of dynamic and static elastic constants. Using all these laboratory relationships, it was possible to generate unmeasured pseudo-logs of in situ parameters, which include: shear wave velocity, static and dynamic elastic constants and permeability. The good experimental relationships obtained between k-~b and Vp-~b in this work together with available logs give us an additional method to estimate permeability which is impossible to obtain from in situ measurements.

Indirect generation of unmeasured in situ logs like shear wave velocity (Vs), permeability (k) and elastic constants (Young (E), shear (G) and bulk (K) modulus) have been the subject of various works in geophysics (Wendt et al. 1986; Castagna et al. 1993; Bastos et al. 1995; Tang et al. 1996). In this paper we present, for three Brazilian offshore wells, a generation procedure for Vs, k and elastic constants logs calculated from laboratory data: Vp, Vs, porosity (~), (k) and static and dynamic elastic constants on cores. The importance of the generation of unmeasured in situ logs includes the possibility of obtaining more accurate information about lithology and fluid content in reservoir rocks and, in this way, contributing to generating more reliable AVO and seismic models, and also optimizing drilling and hydraulic fracturing programes. For reservoir development, these kind of data are also helpful for generating correlations between seismic attributes and petrophysical properties and for monitoring subsurface fluid flow. So, our main goal in this work was to: (1) obtain empirical correlations between Vs and Vp from laboratory data in order to generate unmeasured Vs logs from measured Vp logs; (2) generate logs of static and dynamic elastic constants using the simultaneous labora-

tory measurement of static and dynamic elastic constants as a calibration reference; (3) obtain empirical correlations, for each well, between Vp, k and q~, thereby yielding a calculated permeability log.

Methodology Ultrasonic P and S wave velocities were measured in about 120 samples of limestone from an offshore Brazilian field. These samples were retrieved from three vertical wells at depths of about 2350m to 2550m and vertically cut as right cylindrical plugs with diameter 2.5 cm and 3.75 cm and length 3.75 to 5cm. The measurement frequency was 500 kHz for both Vp and Vs and over a range of confining pressure of 1000 psi to 5000 psi at room temperature. The porosity and permeability range were 5% to 35% and 0.1 mD to 1800mD, respectively. The same measurements were made under dry and formation water saturated conditions. However, the results showed only small variations due to saturation, as noted by Bastos et al. (1995). Simultaneous measurements of static and dynamic elastic constants were made on some samples of diameter 5cm and length 12.5cm. These samples were placed in a triaxial cell and subjected to an in situ confining stress of about 5000 psi, and to a deviatoric stress which was increased up to the sample failure. The deforma-

BASTOS, A. C. DILLON, L. D. VASQUEZ,G. F. & SOARES,J. A. 1998. Core-derived acoustic, porosity & permeability correlations for computation pseudo-logs In." HARVEY,P. K. • LOVELL, M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 141-146

141

142

A . C . BASTOS E T A L . 4000

tion related to the increasing deviatoric stress allowed us to determine the static constants. The dynamic constants are obtained simultaneously, by monitoring changes in transit time.

I

Vm - 0 , 5 5 V p + 4 1 , 6 0 c c " 0,96

Procedure and results

Calculated logs o f Vs and Elastic constants

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Vp (m/s)

Fig. 1. Vs vs Vp for limestone plugs.

The three wells that are the subject of this work do not have in situ Vs logs. Therefore, a laboratory relationship was obtained between Vs and Vp in order to generate a pseudo Vs log. Figure 1 shows the linear fit to the Vs-Vp cross plot (equation 1). As shown in this figure, an excellent correlation was obtained with a correlation coefficient of 0.96. For the case of these samples, this linear fit was better than the WELL - B

WELL - A Velocity (m/s) 1000 2000 3000 4000 5000 6000 2380

WELL - c

Velocity (m/s)

Velocity (m/s)

1000 2000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

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E

.....

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Q 2460 247O 2480 249O 2500 2510 2520

-

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~

Vs log

9 Vp lab

9 V s lab

Fig. 2. Vp and Vs from laboratory data (symbols) and calculated Vp and Vs logs (curves). The three wells show good agreement between laboratory and log data.

CORE-DERIVED COMPUTATION OF PSEUDO-LOGS '

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2). There is good agreement between pseudologs and laboratory data. With the Vp, Vs and density (p) logs and the following elastic theory equations:

(1)

Using this relationship and the in situ Vp logs it was possible to calculate Vs pseudo-logs (Fig.

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144

A.C. BASTOS E T AL. WELL - A

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where: K is the bulk modulus, # is the shear modulus and Pb is the Bulk density, pseudo-logs of dynamic elastic constants have been calculated, In fact, to optimize drilling and/or hydraulic fracturing programs, it is often necessary to

obtain logs of the static and not the dynamic elastic constants. For this purpose, we use simultaneous laboratory measurements of static and dynamic constants in order to transform the dynamic to the reference static. Figure 3 shows a cross plot between static and dynamic constants for sedimentary rocks and illustrates strong empirical relationships which are expressed mathematically as follows:

CORE-DERIVED COMPUTATION OF PSEUDO-LOGS WELL- B

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Estat = 0.675 Edyn -- 3.84; correlation coefficient --- 0.95

(4)

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(5)

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(6)

where the subscripts 'stat' and 'dyn' denote static and dynamic moduli, respectively. Figure 4 shows the calculated log of static and dynamic constants obtained from equations (4) to (6) for well C. As expected, the logs of the dynamic elastic constants show higher values than their static equivalents.

Calculated logs of permeability The next step was to calculate permeability logs for the three wells using algorithms based on

laboratory permeability, porosity and velocity data. Figure 5 shows core data, the cross plots of velocity against porosity, and permeability against porosity. From these plots it has been possible to deduce a relationship between Vp, ~b and k. As can be seen in Fig. 5, an exponential fit was the best one obtained for both the Vp-q$ and the k-~b relationships for the three wells. Thus, with the equations obtained (equations (7), (8), (10), (11), (13) and (14)) we can isolate qb from Vp-q) and k-q5 relations and then obtain k-Vp relationships (equations (9), (12) and (15)) which can be used to calculate the k-log shown in Fig. 6. In order to check these relationships we include some points in well A (cross points in Fig. 6) which were not used to obtain equations (7) to (15). Again, it can be seen that there is a good correspondence between these points and the obtained log: Well A Vp = 5868e~~

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(7)

146

A.C. BASTOS E T AL. k = 0.05e~ k :

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(9)

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(8)

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(13)

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(15)

Figure 6 shows a good correspondence for wells A and C, but not for well B. In this well the good correlation coefficient for the k-qb relationship, 0.77, was lower.

Conclusions (1) The large number of limestone samples gave us a precise empirical relationship between Vs and Vp for limestone, and this differs from the earlier work of Castagna et al. (1993), even for Vs close to 1500 ms -1. (2) Good relationships between static and dynamic elastic constants were obtained for sedimentary rocks, and these have allowed us to generate logs for these constants. As expected, dynamic constants are greater than static ones. (3) The capacity to obtain a relationship between static behaviour of rocks from dynamic properties combines the advantages of both methods in one. Thus, the resultant properties

of this relationship give us the static mechanical behaviour, characteristic of production engineering, but, with the continuous character of geophysical logs. (4) Cross plots between Vp-qb and k-~b indicated good exponential fits for the three wells that formed the subject of this work; (5) The good experimental relationships obtained between k-qb and Vp-qb (see correlation coefficients in equations (7) to (15)), together with available logs give us an additional method to estimate permeability. (6) There is good agreement between laboratory permeability measurements and synthetic permeability logs from velocity data, even for points that were not used in the generation of these pseudo-logs.

References BASTOS, A. C., DILLON, L. D., SOARES, J. A. & VASQUEZ, G. F.. 1995. Estimativa dos perils de

constantes elfisticas em carbonatos pouco permefiveis a partir de dados laboratoriais. 4th International Congress of the Brazilian Geophysical Society and the 1st Latin American Geophysical Conference. Volume II. CASTAGNA, J. P., BATZLE, M. L. 8r KAN, T. K. 1993.

Rock Physics: The link between rock properties and AVO response. In: CASTAGNA, J. P. t~ BACKUS,M. M. (Eds) Offset-dependent reflectivity: SEG, 124-157. TANG, X. • CHENG, C. H. 1996. Fast inversion of

formation permeability from Stoneley wave logs using a simplified Biot-Rosenbaum model. Geophysics, 61, 639-645. WENDT, W. A., SAKURAI, S. t~ NELSON, P. H. 1986.

Permeability prediction from well logs multiple regression. In: LAKE, L. W. & CARROLL, H. B. Jr

(eds) Reservoir characterization. Academic Press, San Diego, California, 181-221.

Effects of water salinity, saturation and clay content on the complex resistivity of sandstone samples P. S. D E N I C O L 1 & X. D. J I N G

Centre for Petroleum Studies, Imperial College of Science, Technology and Medicine, London S W 7 2BP, UK 1Present address." Petrobras S.A., Exploration Department, 27913-350, Macae, R J, Brazil

Abstract: Complex resistivity measurements were made on sandstone samples in the frequency range from l0 Hz to 2 MHz. The main objective was to investigate the frequency response of complex resistivity and phase angle as a function of salinity, water saturation and clay content. The results showed the classical frequency dependence behaviour where the complex resistivity decreases with increasing frequency. The complex impedance behaviour in the intermediate frequency range (10-100 kHz) was used to relate the effect of frequency dispersion with interface polarization and, hence, pore geometry, specific surface area and permeability. Both water saturation and salinity were found to influence the gradient and the relaxation frequency of the complex resistivity versus frequency relationship. A variation in water saturation from full to partial saturation resulted in a dramatic increase in the gradient and a clear shift of the relaxation frequency. Both the saturation and salinity dependence can be attributed to the polarization of both the rock-fluid and fluid-fluid interfaces within the pore space, which depend on the geometry and physical characteristics of the interfacial layers. The results presented in this paper can have important applications in identifying low resistivity and low contrast pay zones. The complex electrical behaviour of a rock results from its conductive and dielectric response in the presence of an electric field; the former is related to the transport of free charge carriers and the latter is due to geometrical, interfacial and electrochemical mechanisms (Sen 1980, 1981). A complex impedance vector (Z*) consists of a real part ( in-phase or resistance, R) and an imaginary part (out-of-phase or reactance, X). Using the rectangular-coordinate form, the complex impedance can be expressed as follows, Z*= R + jX

(1)

where j = v / - 1 is the complex operator. The phase angle (0) by which current and voltage are shifted is given as: 0 = tan I(X/R)

(2)

The complex resistivity p* can be calculated from Z*, p* = Z* A/L = p ' + j p "

(3)

where A is the cross-sectional area of the sample and L is its length, and p' and p" are real and imaginary parts of the complex resistivity, respectively. In some cases, using the reciprocal

of impedance is mathematically expedient. For example, when the real and imaginary components are paralleled, it is better to use admittance (Y*), Y* = 6+ jB

(4)

where G is the conductance and B is the susceptance. The complex conductivity or* can be calculated from Y*, or* = Y* L/A = or'+jcr"

(5)

where a' and or" are the real and imaginary conductivities, respectively.

Background Complex electrical impedance measurement is a non-invasive technique where an electrical current flows through the sample at different frequencies. Experimental measurements of the electrical properties of rocks, when submitted to an alternating electrical field at different frequencies, have shown that both the resistive and reactive components of the complex impedance vary over the frequency spectrum. These two features (complex quantity and dispersion or

DENICOL,P. S. & JING, X. D. 1998. Effects of water salinity, saturation and clay content on the complex resistivity of sandstone samples In: HARVEY,P. K. • LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 147-157

147

148

P.S. DENICOL & X. D. JING

Table 1. List of petrophysieal parameters and chargeability at full and partial water saturation. Sample

Density grams cm-3

Porosity %

Kair mD

Saturation Sw(%)

Chargeability Partial Sat.

Chargeability Full Sat.

Z1 Z3 Z4 Z5 Z7 Z8 Z9

2.66 2.66 2.64 2.65 2.71 2.69 2.64

22.4 14.1 12.2 20.1 25.8 21.5 29.1

1760 38.7 3.51 163 23.1 101 819

33 39 61 47 77 82 44

0.74 0.81 0.68 0.55 0.54 0.52 0.53

0.53 0.53 0.54 0.52 0.53 0.54 0.50

Table 2. List of synthetic shaley samples Sample

Clay Type

Clay Length Content cm

Area cm2

Grain Porosity Density % grams cm-3

Kair mD

SZ1 SZ2 SZ3 SZ4

clean montmorillonite montmorillonite montmorillonite

0 5 10 15

10.75 10.75 10.75 10.46

2.65 2.66 2.66 2.66

337 235 146 105

6.41 6.49 6.53 6.37

frequency dependence) can be used to estimate rock petrophysical properties, such as specific surface area and permeability. The origin of the frequency dependence can be related to geometrical effects of the clay particles (Sen 1980) or electrochemical phenomena at the fluid-grain (Rink & Schopper 1974) and/or fluid-fluid interface (Knight & Endres 1991). The interface region between matrix and the fluid-filled pore space is complicated due to the existence of the ionic double layer. The concept of the electrical double layer forms the theoretical basis for understanding the electrical properties of rocks, especially shaley sandstones. Electrochemical theory suggests that the surface of clay minerals carries excess negative charges as a result of the substitution of certain positive ions by others of lower valence. When the clays are brought in contact with an electrolyte, these negative charges on the clay surface attract positive ions and repulse negative ions present in the solution. As a result, an electrical ionic double layer (or diffuse layer) is generated on the exterior surface of particles. Typical distribution for ionic concentration and electric potential can be predicted by the Guoy (1910) theory. The Gouy theory also predicts that the double-layer thickness (Xd) is reduced as the concentration of the bulk solution increases. The region outside the electric double layer (distance > Xd) is called the free-water region. Ionic double layers exist between rock and fluid interfaces. The perturbation of the double

29.1 28.1 27.4 27.9

layer by an oscillating electrical field is usually accepted (Lima & Sharma 1992) as the main mechanism for the frequency dependence of rocks. Therefore, this interface polarization may provide a link between complex resistivity data and pore-scale attributes, such as pore geometry and specific surface area, which in turn can be related to rock permeability through a KozenyCarman type of relationship ( Borner 1995; Denicol & Jing 1996). Since the frequency dependence is reflecting interface phenomena, salinity of the pore water also influences the dispersion due to the variation in the double layer thickness and ion mobility. Furthermore, fluid saturation also plays a role due to addition of the water/oil interfacial area, an increase in the tortuosity of the brine-phase distribution and the presence of a non-ionic fluid. The main objective of this paper is to investigate, experimentally, the effects of brine salinity, fluid saturation and clay minerals on the complex impedance of different rock samples with varying porosity and permeability. The samples include outcrop cores, oil-field reservoir rocks and synthetic shaley rocks (Tables 1 and 2). A brief geological description of all sandstone samples is given in the Appendix.

Experimental apparatus and procedures Complex impedance measurements were performed using a multi-sample rock testing system. The apparatus can accommodate five

Fig. 1. Schematic representation of the experimental apparatus. samples simultaneously under varying hydrostatic confining pressure, temperature and independently controllable pore pressure. Since all the samples are under the same conditions of pressure and temperature, it eliminates experimental comparison errors due to fluctuations during the period of testing (Jing et al. 1992). The experimental system is shown schematically in Fig.1. Complex impedance measurements were made using the frequency response analyser (QuadTech Model 7600 RCL) in the frequency range of 10 Hz to 2 MHz. The instrument is capable of compensating for the residuals of test fixture and cables based on the open/short circuit compensation technique in the whole frequency range. The instrument is equipped with four coaxial BNC terminals on its front panel which locate its calibration plane. The calibration plane is the position where the instrument measures within its specified accuracy (0.05%). In our experiment, test fixture and cables were used to interconnect the sample to the instrument in a four-terminal configuration (4T). The parasitics related to test fixture, cables and connections are frequency dependent and they were minimized using the 4T configuration and by applying the open/short compensation technique in the whole frequency range similar to the technique used by Taherian et al. (1990). The effect of salinity was investigated for two brine concentrations: 20 g and 50 g of sodium chloride (NaCI) per litre of solution (i.e. 2% and 5% NaC1). The solution is made up of NaC1 dissolved in de-aerated and de-ionized distilled water. Initially, the rock samples were fully saturated with 2% brine solution and loaded in the test cell. The samples were considered fully saturated when the resistance of the samples

measured continuously at 2KHz frequency, showed no significant variation (i.e. < 1% change over a period of 12 h) with brine displacement. The RCL meter was then connected and a frequency sweep performed on each sample. After the frequency measurement, 5% brine solution was injected through the samples to displace the original brine. The resistance was observed continuously. A sharp decrease was observed during the first few pore volumes of displacement, when the more conductive brine became continuous. Then, the decrease was less accentuated and reached equilibrium after about 20 pore volumes of injection. A frequency sweep was then repeated at 5% brine salinity. In order to study the frequency dependence of partially saturated rocks, the desaturation technique using semi-permeable capillary diap h r a g m s has been used f o l l o w i n g the laboratory procedures described by Elashahab et al. (1995). The main advantages of the method are the reduction of capillary end effects and uniform saturation distribution along the core length. These improvements are achieved by using highly hydrophilic ceramic membranes positioned between the sample and the end plate. The resistivity distribution along the core is monitored by six potential electrodes equally spaced along the rock sample so that resistivity measurement can be taken at pairs of electrodes (four-electrode configuration) and also between the top and base current electrodes which give the total resistivity (Fig. 2). The resistivity measurements for saturation monitoring based on the Archie type of equations are taken at a frequency of 2 kHz. The volume of brine produced during the desaturation process was

150

P. S. DENICOL & X. D. JING

Fig. 2. Core sleeve with multiple electrodes.

Fig. 3. General frequency dependence behaviour for sample Zl. carefully measured to allow the calculation of average sample saturation by material balance. The effect of clay minerals on the complex resistivity was investigated using synthetic shaley samples following the method established by Jing et al. (1992). According to this technique, mixtures of sands with different ranges of grain sizes and different clay types and contents can be prepared and consolidated through cycles of loading/unloading and heating/cooling in a high pressure and high temperature cell. The main advantage of the technique is full control of the sample preparation so that the desired variation of clay type, content and distribution can be systematically obtained under laboratory conditions. Five synthetic samples of different clay contents were prepared , namely SZ1 (clay free), SZ2 (5% montmorillonite), SZ3 (10% mon-

tmorillonite) and SZ4 (15% montmorillonite). The sand and clay mixtures were mixed uniformly to achieve homogeneous samples. Table 2 lists the petrophysical characteristics of the synthetic samples. After loading the samples in the high pressure cell, they were saturated with 5% by weight of NaCI brine and the consolidation process was started. Repeated loading and unloading cycles were performed with confining pressures varying from 500 psi to 4000 psi until sample consolidation.

Results and discussion

Frequency effect Figures 3 and 4 show the real component and phase angle versus frequency for two reservoir core samples. This plot of resistivity and phase

THE COMPLEX RESISTIVITY OF SANDSTONE SAMPLES

151

Fig. 4. General frequency dependence behaviour for sample Z3.

Fig. 5. Argand diagram with the critical frequency (fc) separating electrode polarization and bulk sample response for sample Z1.

Fig. 6. Argand diagram with the critical frequency (fc) separating electrode polarization and bulk sample response for sample Z1. angle against frequency can be divided into polarization and sample response regions. The electrode polarization region (e.g. < 10 KHz) is strongly influenced by polarization at the rockelectrode interface and can be identified from the

bulk rock response by plotting the real and imaginary components of the impedance on the complex plane as shown in Figs 5 and 6 (i.e, Argand diagram, Debye 1929). The sample response region (i.e. the Cole-Cole region, Cole & Cole 1941) can be divided into two straightline regions of distinctive frequency dependence: the intermediate frequency range (10-100 kHz) characterized by a small and gradual change in impedance and phase angle followed by the high frequency range (100-2 MHz) characterized by a sharp change in impedance and phase angle. The transition between the intermediate and highfrequency region is characterized by the relaxation frequency of the interface polarization process. Figures 5 and 6 plot the Argand diagrams for samples Z1 and Z3 showing the separation of sample response from electrode effects. The experimental data can be fitted by the classic Cole & Cole (1941) model of a depressed semicircle on the Argand plot. According to Lockner & Byerlee (1985), existing theoretical models are most useful in the analysis of data near the peak loss frequency but they may not be capable of fitting experimental data over the entire frequency range.

Salinity dependence The general frequency behaviour of the complex impedance is shown in Fig. 7 for the reservoir sample Z7 at two different brine concentrations. The effect of increasing the pore electrolyte salinity on the frequency behaviour of the sample can be summarized as follows:

152

P.S. DENICOL & X. D. JING

Fig. 7. General frequency behaviour for sample Z7 at two brine concentrations.

Fig. 8. Normalized impedance at two brine concentrations showing salinity dependence for sample Z7.

(1) The complex impedance decreases as the brine salinity increases in the whole frequency range; (2) The complex impedance decreases with frequency for both brine concentrations; (3) The rate of decrease is more pronounced for the lower brine concentration, that is, the lower the salinity of the brine the higher the frequency dependence. This behaviour is best illustrated when the normalized impedance is plotted against frequency in the range from 10 to 100 kHz (Fig.8); (4) As the salinity of the brine increases, the relaxation frequency increases. The frequency dependence as a function of salinity variations is related to the electrical double layer, the thickness of which varies with the brine concentration. High solution concentrations are associated with the compression of the double layer whilst low concentrations

favour the expansion of the double layer. The frequency dependence, as expressed by the slope taken from the semi-log plot of the normalized impedance in the frequency range from 10 to 100 kHz, is found to increase from 5% to 2 % NaC1. Similar results were reported by Kulenkampff et al (1993) and Kulenkampff & Schopper (1988). This salinity dependence is also related to the relative mobility of the ions in the pore space from the free water to the double layer near the solid surface. In the free water region, the charge carriers are free to move and therefore follow the alternating electrical field. On the other hand, in the double layer region, the movement of ions is partially restricted by the electrostatic potential. The result is a delayed oscillation of the diffuse layer when compared to the free ions of the bulk solution that react promptly to the alternating electrical field. Consequently, a phase lag is established between the input voltage and the corresponding current flowing through the pore

THE COMPLEX RESISTIVITY OF SANDSTONE SAMPLES

Fig. 9. Frequency dependence of resistivity and phase angle at partial saturation for sample Zl.

Fig. 10. Frequency dependence of resistivity and phase angle at full brine saturation for sample ZI.

Fig. 11. Saturation dependence of the resistivity for sample Z1 as characterized by the chargeability (m)

153

154

P.S. DENICOL & X. D. JING

space. If the concentration of NaCl decreases, the double layer thickness increases and the phase lag is more accentuated. Additionally, an increase of the diffuse layer thickness favours the blockage of ions, especially at narrowing pores, with consequent accumulation of charges and local concentration gradients.

080 E_075 ~"070 ~ 065 ="0.60

Z3 Zl

The saturation dependence was studied by comparing the frequency spectrum of the real part of the resistivity at full and partial water saturation. The partial saturation was arrived at by displacing brine with Isopar H which has a dielectric constant of 2.02 at 25 ~ So far, only water-wet samples have been tested. The frequency dependence of the in-phase resistivity and phase angle are shown in Figs 9 and 10 for sample Z1 at 33% and full brine saturation, respectively. The saturation dependence becomes clearer when both resistivity curves are displayed in a log-log plot (Fig. 11). The fully saturated curve is almost flat for the whole frequency range. On the other hand, the partially saturated curve is flat in the low frequency range and shows clear frequency dependency above the relaxation frequency. The frequency effect can be better analysed by the empirical parameter chargeability (m) defined as follows (Siegel 1959): (6)

where R1 and R2 stand for the low and high resistivity asymptotes, respectively. Table 1 summarizes the results obtained for the chargeability of the samples. For a given sample, there is a consistent increase in m when brine is displaced by oil. The correlation between m and the water saturation is shown in Fig. 12 for all the samples. Although a general trend of higher m for lower saturation can be observed, the correlation is weak. Samples Z3 and Z9 showed a more remarkable deviation from the trend, possibly due to the high iron oxide content in the former and dispersed glauconite in the latter. Knight & Nur (1987) also observed that a sample with high iron oxide content (Indiana Dark sandstone) had an anomalous dielectric exponent apparently due to the effect of the magnetic susceptibility on the dielectric response. The interpretation of the saturation dependence upon frequency is difficult due to the intricate geometry of the pore space and its effect on distribution of fluids within the rock. Mineralogical complexity, mainly related to clays and

9

Z4

0.55

0.50 0.3

Saturation dependence

m = R1/(R1 +R2)

0.85

0.4

0.5 0.6 Sw (fraction)

0.7

0,8

0,9

Fig. 12. Correlation between chargeability (m) and water saturation.

metallics, also plays an important role in increasing the complexity of the frequency dispersion. However, the general behaviour of the saturation dependence is characterized by an increase of the frequency effect in response to the oil saturation, as distinguished by the phase angle and chargeability results. It is important to note that in two-phase systems, the frequency dispersion due to the polarization at the solid-liquid interface (poregrain) may be added to by polarization at the liquid-liquid interface (oil-water). As the water saturation decreases, there is an increase in the water-oil interfacial area and an increase in the complexity of the brine phase topology. For any rock-fluid systems, wettability plays a significant role in controlling fluid distribution at the pore scale. Therefore, it might be possible to derive wettability information based on the frequency dispersion measurements of reservoir rock-fluid systems. However, further research is needed in this area.

Clay effects Synthetic shaley samples with controlled clay type, content and distribution were used to investigate the effects of clay minerals on complex impedance measurements. Figure 13 shows the results for the synthetic sample SZ4. The low-frequency region from 10 Hz to ~10 kHz indicates strong dispersion in both impedance and phase angle which is attributed to electrode polarization. In the intermediate frequency range (1 to ~100 kHz) the impedance decreases monotonically while the phase angle reaches a minimum and then starts increasing. The high frequency region is characterized by the relaxation frequency at N800 kHz where the phase angle reaches a maximum and the impedance decreases more drastically. All the synthetic samples present the relaxation frequency at around the same position. However, the value of the phase angle at the relaxation

THE COMPLEX RESISTIVITY OF SANDSTONE SAMPLES

155

Fig. 13. General frequency dependence behaviour of impedance and phase angle for sample SZ4.

Fig. 14. Normalized impedance versus frequency relationships of four synthetic samples containing various amounts of montmorillonite.

Fig. 15. Correlation between clay content and frequency dependence for the synthetic samples.

156

P.S. DENICOL & X. D. JING

frequency increases with the amount of clay, varying from 1 degree for the clay-free sample to 5 degrees for the 15% montmorillonite sample. This observation suggests that a polarizationlike process is being caused by the clay presence although the classical induced polarization effect would be expected at lower frequencies. A possible explanation for this frequency effect may be related to the electro-osmotic coupling due to the accumulation of charges at narrowing pores (Marshal & Madden 1959; Dankhazi 1993). Although its effect is found to be very weak, this type of polarization is expected to increase with a reduction of the sample permeability. Indeed, the synthetic samples show a decrease in permeability with increasing amount of clay (Table 2) that leads to the narrowing and reduction of effective pores and hence the electro-osmotic coupling. The slope of the impedance curve in the range from 10 to 100 kHz is also found to correlate with the clay content of the samples. Figure 14 shows the normalized impedance versus frequency for the samples containing montmorillonite. The graph indicates a consistent increase in the frequency slope from sample Z1 (clayfree) to sample Z4 (15% montmorillonite). A plot of the rate of impedance decrease with frequency versus clay content is shown in Fig. 15, where the clay effect appears to decrease at higher clay contents.

Conclusions The frequency effect in the intermediate frequency range (10-100 kHz) increases when the solution concentration is decreased from 5% to 2% NaC1. This salinity dependence may be explained by variations of the double layer thickness and ion mobility. At high salinity, the double layer is compressed to the pore surface and gradually expands with decreasing brine concentration. As a consequence, the mobility of the ions in the diffuse layer is reduced at high salinity preventing them from following the alternating field as opposed to the free ions in the centre of the pore. Additionally, the expansion of the double layer supports the blockage of ions particularly at the smaller pores with subsequent electro-osmotic polarization due to the accumulation of charges. The frequency effect is found to increase for the whole frequency range when brine is displaced by oil (Isopar H). A variation in water saturation from full to partial saturation resulted in a dramatic increase in the frequency dispersion and a clear shift of the relaxation frequency. This observation may have potential

applications for the evaluation of low resistivity and low contrast pay formations. The frequency dispersion consistently increases with the amount of clay in the sample. This effect is better illustrated when the normalized impedance is plotted in the frequency range from 10 to 100 kHz . The impedance slope is relatively flat for the clay-free sample (SZ1) and increases with the content of montmorillonite for the shaley samples. A plot of the clay content versus the frequency dependency clearly shows a relationship. We would like to thank Petrobras S.A. for sponsoring P.S. Denicol and for providing reservoir rock samples. We also wish to thank M. S. King for many valuable discussions.

References BORNER, F. D. 1995. Estimation of hydraulic conductivity from complex electrical measurement. International Symposium of the Society of Core Analysts, paper 9523. COLE, K. S. & COLE, R. H. 1941. Dispersion and absorption in dielectrics. Journal of Chemistry and Physics, 9, 341. DANKHAZI, G. 1993. A new principle approach to induced polarization in porous rock. The Log Analyst, 34, 54-66. DEBVE, P. 1929. Polar molecules. Chemical Catalogue Co. DENICOL, P. S. & JING, X. D. 1996. Estimating permeability of reservoir rocks from complex resistivity data. Society of Professional Well Log Analysts, 37th Annual Logging Symposium, paper X. ELASHAHAB,B. M., JING, X. D. & ARCHER,J. S. 1995. Resistivity index and capillary pressure hysteresis for rock samples of different wettability characteristics. SPE paper No. 29888, the 9th Middle East Oil Show and Conference, March, Bahrain. Gouv, G. as discussed in HUNTER, R. J. 1988. Zeta Potential in Colloid Science, Academic Press. JING, X. D., ARCHER, J. S. 8r DALTABAN,T. S. 1992. Laboratory study of the electrical and hydraulic properties of rocks under simulated reservoir conditions. Marine and Petroleum Geology, 9, 115-127. KNIGHT, R. & NUR, A. 1987. Geometrical effects in the dielectrical response of partially saturated sandstones. The Log Analyst, 28, 513-519. KNIGHT, R. & ENDRES,A. 1991. Surface conduction at the hydrocarbon/water interface. Society of Professional Well Log Analysts, 32nd Annual Logging Symposium, paper I. KULENKAMPFF,J. M. & SCHOPPER,J. R. 1988. Low frequency conductivity--a means for separating volume and interlayer conductivity. Society of Professional Well Log Analysts, 12th European Formation Evaluation Symposium, paper P.

THE COMPLEX RESISTIVITY OF SANDSTONE SAMPLES --,

BORNER, F. D. & SCHOPPER,J. R. 1993. Broad band complex conductivity lab measurement enhancing the evaluation of reservoir properties. Society of Professional Well Log Analysts, 15th European Formation Evaluation Symposium, paper A.

LIMA, 0. A. L. t~ SHARMA, M. M. 1992. A grain

conductivity approach to shaly sandstone. Geo-

physics, 55, 1-10. LOCKNER, D. A. & BYERLEE, J. D. 1985. Complex

logically mature.

mature,

texturally

157 submature

to

Sample Z3 (Block 18-2)." Lower Permian "Penrith Red Sandstone", predominantly quartz grains cemented by quartz over-growths with iron oxide petina, subrounded-rounded, mineralogically and texturally sub-mature.

resistivity measurements of confined rock. Journal

of Geophysical Research, 90, 7837-7847. MARSHALL, D. J. t~ MADDEN, T. R. 1959. Induced

polarization, a study of its causes. Geophysics, 24, 790-816. RINK, U. • SCHOPPER,J. R. 1974. Interface conductivity and its implications to electrical logging.

Society of Professional Well Log Analysts, 15th Annual Logging Symposium, paper J. SEN, P. N. 1980. The dielectric constant and conductivity response of sedimentary rocks. Society of Petroleum Engineers, paper 9379. SEN, P. N. 1981. Relation of certain geometrical features to the dielectric anomaly of rocks. Geophysics, 46, 1714. SEIGEL,H. 0. 1959. A theory for induced polarization effects (for step excitation function). In: WArr, J. R. (ed.) Over Voltage Research and Geophysical Applications. Pergamon Press Inc., 4-21. TAHERIAN, M. R., KENYON, W. E. & SAFINYA, K. A. 1990. Measuremen of dielectric response of watersaturated rocks. Geophysics, 55, 1530-1541.

Appendix: geological description of sandstone rocks (a) Outcrop rocks Sample Z1 (Block 15-8): Lower Carboniferous sandstone, average grain size 0.2 ram, 95% q u a r t z , alkali feldspar, clay, biotite, alcite cement (5%) with some chert, angular to sub-angular, poor sphericity, minera-

Sample Z4 (Block 16-2): Upper Carboniferous sandstone, grain size : 0.10.3 mm, 85% quartz, 0% alkali feldspar, 5% mica, very irregular, poor sphericity, texturally immature and mineralogically submature.

Sample Z5 (Block 19-4): Lower Triassic 'Bunter' sandstone, fine to medium grain sizes (< 0.5 mm), 95% quartz, % alkali feldspar and calcite, sub-rounded, poor sphericity, texturally and mineralogically mature.

(b) Reservoir rocks Sample Z7: Glauconitic sandstone, semi-friable, grains are sub-rounded with regular to good selection. Mineralogy also includes quartz, feldspar and mica.

Sample Z8." Sandstone with pseudo-argilaceous matrix (27 %), quartz (31%), K-feldspar (18%), glauconite (6%), plagioclase (5%), others (2%). Cements include dolomite and pyrite.

Sample Z9." Sandstone with pseudo-argilaceous matrix, quartz, K-feldspar, glauconite, and plagioclase.

Acoustic wave anisotropy in sandstones with systems of aligned cracks A. S H A K E E L 1 & M . S. K I N G 2

1Production Department, Oil and Gas Development Corporation, F-8 Markaz Islamabad, Pakistan 2 Department of Earth Resources Engineering, Royal School of Mines, Imperial College, London SW7 2BP, UK

Abstract: Seismic anisotropy has been studied on a number of dry cubic sandstone

specimens, of 51 mm side, in which a system of aligned cracks has been first introduced progressively by the application of a polyaxial state of stress, and then closed by hydrostatic stress. One P- and two S-wave velocities polarized at right angles, along with the deformation, have been measured at each stress level in each of the three principal stress directions. Thomsen's (1986) anisotropy parameters (e, 7, 6) have been calculated at each stress level during the cracking and crack closing cycles using Nishizawa's (1982) theory. Test results indicate that anisotropy in the P-wave velocity is greater and more sensitive to the presence of aligned cracks than that observed for S waves. Modelling studies show that the P-wave anisotropy parameter e is always greater than that of anisotropy parameter 8, for low crack densities and for small aspect ratios. The reverse is true for high crack densities and low aspect ratios. The results of numerical studies indicate that S-wave anisotropy is independent of the nature of the saturating fluid and that it is possible to observe elliptical anisotropy in a medium containing aligned dry ellipsoidal inclusions. It is well known that the presence of microcracks and fractures reduces the acoustic velocities of P- and S-waves in rocks. When the principal stresses are altered on a rock that initially has a random distribution of cracks, the crack distribution no longer remains randomly oriented. The effect of an applied non-hydrostatic stress is to close cracks in some directions and leave cracks open in others (Sayers 1988). Those cracks with their normals lying close to parallel to the new major principal stress will tend to be closed more than those with their normals subparallel to the new minor principal stress (Sayers 1988). The elastic and transport properties of the rock then become anisotropic in their behaviour, with the degree of anisotropy depending on the magnitude of the principal stress differences, the type of fluid filling the cracks (Xu & King 1989, 1992; King et al. 1995a,b). Seismic anisotropy was studied more than 40 years ago by Postma (1955) and Uhrig & Melle (1955), but for a long time its effect was ignored or considered insignificant, due to the fact that most of the seismic surveys carried out were for P-wave reflection and conducted at small angles to the vertical. However, for seismic surveys conducted with large angles of the incidence waves (such as VSP surveys), the effect of a n i s o t r o p y c a n n o t be i g n o r e d ( C r a m p i n 1985a,b). Seismic anisotropy due to aligned

cracks has been extensively studied by, amongst others, Crampin (1984, 1985a,b) and Crampin & Atkinson (1985), who are of the opinion that Swave velocities are more sensitive to the presence of aligned cracks and that they provide a better quality of information on anisotropy effects than does the P wave. Crack orientation, when cracks are aligned vertically, can easily be determined by the splitting of vertically propagating polarized shear waves. This splitting occurs as a result of azimuthal anisotropy induced by the microcracks and fractures. A knowledge of seismic anisotropy can provide useful information about the mineralogy, the orientation of cracks and pores, the degree of cracking and crack geometry, orientation of the in situ stress field, and the possible proportion of gas and liquid within the inclusions in hydrocarbon reservoirs (Crampin 1985a). Thomsen (1986) has derived a set of three dimensionless anisotropy parameters (e, 7 and 8) to describe weak to moderate transverse isotropy of a medium. These parameters are defined in terms of the five components of the stiffness tensor (Cll , C33 , C13 , C44, C66) relating stress and strain for the transversely isotropic medium as follows:

Cll -C33 V 2 1 - V22 -- - -2C33 V 22

SHAKEEL,A. & KING, M. S. 1998. Acoustic wave anisotropy in sandstones with systems of aligned cracks In. HARVEY,P. K. & LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 173-183

(1)

173

174

A. SHAKEEL & M. S. KING C66 - C44

V 21 - V 22

2C44

V 22

(2)

(~ ~__ (C13 + C44) 2 - (C33 - C 4 4 ) 2 2C33 (C33 - C44)

(3)

The parameters are all zero for an isotropic medium and their deviation from zero represents the degree of anisotropy. The value of ~, which is always positive, represents the relative difference between the P-wave velocities propagating perpendicular (Vp1) and parallel (Vp2) to the axis of symmetry. The general term 'anisotropy' of a rock usually refers to the quantity e, calculated using the following equation for small values o f e, Vp 1 B Vp 2 E -- - -

re2

(4)

The parameter 3' describes the S-wave anisotropy of a transversely isotropic medium. It is the relative difference between the faster S-wave velocity (Vsl) and the slower S-wave (Vs2) velocity travelling in a transversely isotropic medium. Thus, for small values of 7, it can be used to define 'S-wave anisotropy' of a medium (Thomsen 1986) as VS1 m Vs 2

7 -- -

Vs2

(5)

where Vsl and Vs2 are S-wave velocities propagating parallel to the plane of cracks with their polarization parallel and perpendicular to the plane of cracks, respectively. The parameter dominates the anisotropic response when the acoustic wave propagates in a plane which is parallel or approximately parallel to the axis of symmetry. It is independent of the seismic velocities of the medium perpendicular to the axis of symmetry and can take either positive or negative values. As shown by Thomsen (1986), the parameters ~, 3" and g are less than 0.2 in magnitude for weak-to-moderate anisotropy. Furthermore, Thomsen (1986) states that elliptical anisotropy will be observed if 6 = ~. Since the parameters ~, 3' and ~ are easily interpretable and can be calculated from the five elastic constants obtained from Nishizawa's (1982) theory, they are used here to model and study the variation in anisotropy as a function of aspect ratio, crack density and stress.

Experimental system A polyaxial stress loading system, developed at

Imperial College of Science and Technology London, has been used for testing 51mm-side cubic rock specimens. The system, described in a preliminary technical note by King et al. (1995a) and in detail by Shakeel (1995), consists of a loading frame in the form of an aluminium alloy ring within which two pairs of hydraulic rams and ultrasonic transducer holders are mounted to provide orthogonal stresses on the cubic rock specimen in the horizontal plane. Each of the three principal stresses may be varied independently in the range 0 to 115 MPa in the horizontal principal directions and to over 750 MPa in the vertical major principal direction. The horizontal principal stresses may be servocontrolled using facilities associated with a Schenk compression testing machine. The vertical major principal stress is provided through ultrasonic transducer holders mounted in a Schenk 160-tonne closed-loop servo-controlled compression testing machine. Stress is transmitted to each of the six faces of the cubic rock specimen through 5 ram-thick magnesium faceplates matching approximately the elastic properties of the rocks being tested. Deformation of the rock specimen is measured by pairs of extensometers (LVDTs) mounted in each of the three principal directions. An isometric view of the polyaxial loading frame is shown in Fig. 1. Each of the three pairs of transducer holders contains stacks of piezoelectric transducers capable of producing or detecting pulses of compressional (P) or either of two shear (S) waves polarized at right angles propagating in one of the principal stress directions. The transducer holders have a bandwidth in the range approximately 450 to 800 kHz for P-wave and 350 to 750 kHz for S-wave pulses. Loading in the 1-direction is characterized by the major principal compressive stress (cq) direction and that of 2- and 3- as the intermediate (or2) and minor (a3) principal stress directions, respectively. The wave type nomenclature employs two suffixes 'i' and 'j' (as with Vij) where T refers to the propagation direction of the wave and 'j' to the polarization (particle motion) direction. Thus V33 is the P-wave velocity propagating in the minor principal stress direction and V13 is the S-wave velocity propagating in the major principal stress direction with polarization in the 1-3 plane. A total of nine components of velocity are measured: three compressional VPll , VP22 and VP33 and six shear VS12, VS13, VS21, VS23, VS31 and VS32 Both the P- and S-wave velocities are measured with an accuracy of +1% and a precision of +0.5%.

ANISOTROPY IN CRACKED ROCKS

175

LOAD IN 1-DIRECTION APPLIED IN I~I~pRSCHENK

160-TONNE S E R V O - C O N T R O k L E D

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TRANSDUCER HOLDERS HYDRAULIC PRESSURE, 2-DIRECTION HYDRAULIC RAM, 2-DIRECTION HYDRAULIC PRESSURE, 3-DIRECTION HYDRAULIC RAM, 3-DIRECTION "fRANSDL~ER HOLDERS CUBIC ROCK SPECIMEN REACTION RING

Fig. 1. Isometric view of the polyaxial loading system.

Results and discussion First a numerical example is provided to enable a better understanding of the effects of the different parameters, such as crack aspect ratio, crack density and type of saturating fluid on the anisotropy parameters and on the acoustic velocities of such a cracked solid permeated with aligned ellipsoidal inclusions. Finally, the theory is used to study the anisotropy as a function of stress for a solid progressively permeated with a system of aligned cracks.

Numerical results and discussion In this numerical example, P- and S-wave velocities and Thomsen's (1986) anisotropy parameters are calculated as a function of aspect ratio for a solid permeated with aligned ellipsoidal inclusions. Nishizawa's (1982) theory is used to calculate the elastic constants. The aspect ratio of the inclusions is varied from a =0.0001 (almost flat cracks) to a = 1 (spheres). Four crack densities are studied, ~=0.01, 0.05, 0.10 and 0.20. Both types of inclusions are investigated: dry inclusions with a fluid bulk modulus

of 1.5• -4 GPa, and liquid-filled inclusions with a fluid bulk modulus of 1.5 GPa. The isotropic background material is the same as that used by Nishizawa (1982): matrix density 2.7 g cm -3 and Lame's constants A = # = 39 GPa. Figures 2 and 3 show results of the Thomsen's anisotropy parameters as a function of aspect ratio for dry and liquid-filled inclusions, respectively, for four different crack densities ~= 0.01, 0.05, 0.10 and 0.20. It is clear from these figures that the values of anisotropy parameters increase as the crack density is increased from ~ = 0.01 to 0.20. They all become zero for an aspect ratio a = 1, corresponding to the isotropic situation. Note that for dry inclusions (Fig. 2) all the anisotropy parameters have a non-zero constant value for a large range of small aspect ratios and that they only tend to zero for large aspect ratios approaching a = 1. Hence, for a large group of small aspect ratios the resultant anisotropy is hardly affected by a change in aspect ratio for the case when solid is permeated by dry inclusions. The non-zero constant values of the parameters ~ and 7, for a large group of small aspect ratios for dry inclusions, indicate that

176

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there is also a constant difference between the two P- and two S-wave velocities propagating both parallel and perpendicular to the plane of cracks for the same range of aspect ratios. This conclusion corresponds to Fig. 4 which shows a very small variation in P- and S-wave velocities propagating both parallel and perpendicular to the plane of cracks as the aspect ratio is changed

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densities ~>_0.1, 6 > ~ > 7 (Figs 2 c-d). However, for a solid permeated with liquidfilled inclusions, a large variation in anisotropy parameters ~ and 6 is observed as the aspect ratio is changed (Fig. 3). The changes in e are related to P-wave velocities, especially VP2 which is strongly influenced by the liquid-filled inclusions as the aspect ratio is changed. This

result corresponds to Fig. 5a which shows a significant variation in V P 2 a s the aspect ratio is changed for liquid-filled inclusions of crack density ~=0.01. It can be seen from Fig. 3 that the value of ~ tends to zero for very small aspect ratios for all the crack densities, indicating that the difference between the P-wave velocities in both the directions parallel and perpendicular to

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Fig. 4. Changes in acoustic wave velocities as a function of aspect ratio for dry inclusions (a) P-wave velocities and (b) S-wave velocities. The crack density is ( = 0.01.

the plane of cracks also tends to zero. This effect is clearly shown in Fig. 5a. The changes in ~5are related to those P- and S-wave velocities which are either propagation or polarization perpendicular to the plane of cracks (3-direction). A comparison of Figs 2 and 3 with each respective crack density, indicates that there is hardly any difference in the value of anisotropic parameter 7 for a large range of aspect ratios when either dry or liquid-filled inclusions are used. This behaviour corresponds to the fact that S-wave velocities are not affected much as the condition of inclusions is changed from dry to liquid-saturated. Since the parameter 7 is constant for a large range of aspect ratios for

both dry and liquid-filled inclusions, the acoustic velocities VS1 and VS2 are not strongly affected by aspect ratios (Figs 4b and 5b for a crack density ( = 0.01). For all the cases studied for dry and liquidfilled inclusions, the values of e, 7 and 6 are always positive, indicating that the P- and Swave velocities (VP 1 and VS1) propagating perpendicular to the axis of symmetry are always greater than those propagating along (VP2 and VS2) the symmetry axis (Figs 4 and 5). Finally, Figs 2 and 3 show that the parameters e and 6 are equal for aspect ratios lying between a = 0.4 and 1 for both dry and liquid-filled inclusions. This suggests that the resultant anisotropy is

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Tests have been performed on five dry sandstone specimens, in which a system of aligned cracks has been first introduced by increasing the major (el) and intermediate (~2) principal stresses in unison to near failure, while keeping the minor (or3) principal stress constant at some low level. The aligned cracks are then closed by the application of a hydrostatic compressive stress. The nine components of velocity are measured throughout three separate stress cycles. The first

involves measurements on the flesh, uncracked rock specimen during the application of an increasing hydrostatic stress. The second cycle involves measurements while a system of aligned cracks, with their normals parallel to the minor stress direction, is formed in the rock specimen (cracking cycle). The third cycle involves measurements during the application of a further increasing hydrostatic state of stress to close the cracks formed during the cracking cycle (crack closing cycle). Discussed here as being characteristic of the studies made on five sandstones tested in this research programme will be that of Penrith sandstone. This is a fine-to-medium grained sandstone of lower Permian age having a low

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clay content (3%), an effective porosity of 13%, a permeability of ~150 mD, a grain density 2.6 gcm -3 and a bulk density of 2.26 gcm -3 in its dry state. Figure 6 shows changes in the three P- and six S-wave velocities plotted as a function of hydrostatic stress on the fresh uncracked rock specimen. Although loading in the 1-, 2-, and 3directions is identical there is a small difference between the changes in P- and S-wave velocities which is due to the differences in the initial elastic properties between these three directions. It will be observed that the sandstone exhibits behaviour that is close to being isotropic, with both sets of P- and S-wave velocities increasing in magnitude with increasing stress and lying within + 1% error bar, except at the lowest stress level. Figure 7 shows changes in the three P- and six S-wave velocities during the cracking cycle. The minor principal stress (o'3) was kept constant at 3 MPa while o']--o'2 were increased in unison in steps from 3 to 100 MPa. Then, while maintaining the intermediate principal stress at 100 Mpa (limited by the experimental system), the major

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of stress

during the cracking cycle for Penrith sandstone sample, (a) P-wave velocities and (b) S-wave velocities.

principal stress was increased in steps to 132 MPa until the specimen was near failure. The acoustic velocities propagating in the 3direction show an initial increase with stress due to the closure of pre-existing cracks with their normals in the 1- and 2-directions, followed by a decrease as dilatant cracks with normals parallel to the 3-direction begin to form and open up. It is concluded from Fig. 7, with VPll~VP22 and VS12~,~VS21 all increasing monotonically, that the majority of the cracks formed are aligned in the 1-2 plane, perpendicular to the 3-direction. Shear wave birefringence occurs in all directions of propagation except along the symmetry axis (3-direction) for obvious reasons of symmetry. This effect was also observed in the experiments of Nur & Simmons (1969). The cracking cycle velocity data plotted in Fig. 7 indicate that the magnesium plates match the sandstone well in elastic properties up to stresses of o1 = cr2 = 100 MPa, when the majority of the aligned cracks are formed. As o'] is further increased (with o'2 constant), the platens cause confinement and the S-wave velocities propagating in the 1- or 2-direction and polarized in the 3-direction (V13 or V23) become higher than the

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Fig. 9. Thomsen's (1986) anisotropy parameters for Penrith sandstone sample during the cracking cycle as a function of (a) stress and (b) crack density of the aligned cracks.

velocities that are propagating in the 3-direction (V31 or V32). This behaviour suggests that the aligned crack density towards the extremities of the specimen in the 3-direction is higher than in the centre for values of stress greater than 100 MPa. Figure 8 shows changes in three P- and six Swave velocities plotted as a function of hydrostatic stress during the subsequent crack closing cycle. As the stress is increased, both sets of Pand S-wave velocities appear to be approaching asymptotic values that are only slightly lower in magnitude than those shown in Fig. 6 for the preliminary uncracked cycle. Upon removal from the loading frame after completion of the tests, the specimens all showed signs of throughgoing fractures aligned close to normal to the 3direction. The nine components of velocity determined as a function of stress during the cracking and subsequent crack closing cycle have been used to evaluate the Thomsen's (1986) anisotropy parameters and crack density for the cracks aligned perpendicular to the symmetry axis (3-direction). The procedure, employing Nishizawa's (1982) theory, first to model the velocity data, is

described in detail by Shakeel (1995), who found excellent fits (within 4-1% at all stress levels) in comparing the theoretically modelled and the laboratory measured velocities during both the cracking and crack closing cycles. As the Penrith Sandstone was tested in its dry state, a value of 1.5x 104 GPa was chosen for the fluid bulk modulus. A range of aspect ratios (0.0005 to 0.002) was employed during each of the stress cycles to obtain the best match between the modelled and experimental velocities. It was found that a value of aspect ratio c~--8.0xl0 ~ provides the best match between the modelled and the experimental velocities during the cracking cycle and for the crack closing cycle for most of the stress levels. Figure 9a shows changes in the anisotropy parameters e, 7 and 6 as a function of (71 and 0"2 during the cracking cycle, during which o.3 was kept constant at 3MPa. All the anisotropy parameters increase as the stress is increased due to an increase in crack density (Fig. 9b). The rate of increase in the value of these parameters is lower as the stresses o-~ =o-2 are increased initially from 2 to 100 MPa, but it becomes much

182

A. SHAKEEL & M. S. KING .

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. . . .

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Fig. 10. Thomsen's (1986) anistropy parameters for Penrith sandstones sample during the crack closing cycle as a function of (a) stress and (b) crack density of the aligned cracks.

Fig. 11. Thomsen's (1986) anistropy parameters for Crosland Hill sandstone sample during the cracking cycle as a function of (a) stress and (b) crack density of the aligned cracks.

higher at higher stresses. The higher rate of increase of anisotropy parameters for stresses o'1 >a2 = 100MPa is due to the nucleation and coalescence of the majority of the aligned cracks, which is also clear from the sharp decrease in V33 and S-wave velocities propagating or polarized perpendicular to the plane of cracks (Fig. 7). Figure 10a shows changes in the anisotropy parameters e, 7 and 6 as a function of hydrostatic stress during the crack closing cycle. All the anisotropy parameters decrease as the stress is increased due to a decrease in crack density (Fig. 10b). Cracks close very quickly during the initial loading, resulting in a consequent rapid decrease in the value of the anisotropy parameters. When the stress is increased further, a major fraction of the crack surface area comes into close contact which slows down the closure of cracks and the anisotropy parameters decrease much more slowly than before. Results in Fig. 10 show that the anisotropy becomes weakto-moderate and elliptical (e = 6) for hydrostatic stresses >10 MPa.

The anisotropy parameters follow the same pattern during the cracking and crack closing cycles, i.e. at each stress level ~ > 7 indicates that the anisotropy in P-wave velocities is greater and more sensitive to the crack density than the anisotropy in S-wave velocities. Furthermore, for higher crack densities (~> 0.08), ~ is greater than ~, which is in accordance with the prediction of Nishizawa's theory as shown in Fig. 2. A study of Figs 9 and 10 also indicates that elliptical anisotropy is only possible in the weak anisotropic region (anisotropy p a r a m e t e r s < 0.2) which occurs only at low crack densities (~ < 0.06). These results are true for all the other sandstones tested in this research program. As an example, Figs 11 and 12 show similar anisotropy results for the Crosland Hill (low clay content [< 1%], effective porosity 6% and permeability < l mD) sandstone specimen during the cracking and crack closing cycles.

Conclusions (1) The results of the experimental study for

ANISOTROPY IN CRACKED ROCKS .

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We wish to acknowledge with thanks, the support provided by Shell Expro, British Gas, BP Exploration and AGIP for this research project. The senior author is especially indebted to N. Hyder of the Joint Venture Department, OGDC, for arrangements, and the Oil and Gas Development Corporation of Pakistan for providing the finance necessary to present this paper. Special thanks are also due to Dr N. A. Chaudhry for providing data of one of his specimens to conduct some of the modelling work.

ioo

c 3 (MPa)

o z =

(a) References

. . . . . . .

i

. . . .

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/

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o.3

S. 1984. Anisotropy in exploration seismics. First Break, 2, 19-21. - 1985a. Evaluation of anisotropy by shear wave splitting. Geophysics, 50, 142-152. 1985b. Evidence for aligned cracks in the Earth's crust. First Break, 3, 12-15. - • ATKINSON, B . K . 1985. Microcracks in the Earth's crust. First Break, 3, 16-20. KING, M. S., C H A U D H R Y , N. A. & SHAKEEL, A. 1995a. Experimental ultrasonic velocities and permeability for sandstones with aligned cracks. International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts, 23, 291-302. - - , SHAKEEL, A . & C H A U D H R Y , N . A. 1995b. Acoustic wave propagation and permeability in sandstones with systems of aligned cracks. Presented at the Geophysical Society of London, Borehole Research Group, Conference on Developments in Petrophysics, Sept, 1995. NISHIZAWA,O. 1982. Seismic velocity anisotropy in a medium containing oriented cracks--transversely isotropic case. Journal of the Physics of the Earth, 30, 331-347. NUR, A & SIMMONS,G. 1969. Stress-induced velocity anisotropy in rocks: An experimental study. Journal of Geophysical Research, 74, 6667-6674. POSTMA,G. W. 1955. Wave propagation in a stratified medium. Geophysics, 20, 780-806. SAYERS, C. M. 1988. Stress induced ultrasonic wave velocity anistropy in fractured rock. Ultrasonics, 26, 311-317. SHAKEEL, A. 1995. The effect of oriented fractures on elastic wave velocities, attenuation and fluid permeabilities of sandstones. PhD Thesis, Imperial College of Science, Technology and Medicine, University of London. THOMSEN, L. 1986. Weak elastic anisotropy. Geophysics, 51, 1954-1966. Xu, S & KING, M. S. 1989. Shear-wave birefringence and directional permeability in fractured rock. Scientific Drilling, 1, 27-33. & - 1992. Modelling the elastic and hydraulic properties of fractured rocks. Marine and Petroleum Geology, 9, 155-166 U H R I G , L. F & VAN MELLE, F. A. 1955. Velocity anisotropy in stratified media. Geophysics, 20, 774--779 CRAMPIN,

0.4

Fig. 12. Thomsen's (1986) anistropy parameters for Crosland Hill sandstone sample during the crack closing cycle as a function of (a) stress and (b) crack density of the aligned cracks.

dry sandstones suggest that the anisotropy parameter 6 is the most sensitive to the crack density. Moreover, for the dry rocks, the anisotropy in P-wave velocities is greater and more sensitive to the crack density than the anisotropy in S-wave velocities. (2) The results of the numerical study suggest that the anisotropy in P-wave velocities is greater when the saturating fluid is very compressible (gas) and when the cracks are flat (small aspect ratios), while the anisotropy in S-wave velocities is almost unaffected by the nature of the saturating fluid. (3) For dry inclusions over a large range of aspect ratios less than 0.1 the resultant anisotropy is hardly affected by a change in the aspect ratio. (4) The results of the numerical and experimental studies suggest that elliptical anisotropy will be observed in a m e d i u m containing aligned ellipsoidal inclusions of aspect ratios greater than 0.4.

Complementary functions reveal data hidden in your logs J. R. S A M W O R T H Wireline Technologies Limited, East Leake, Loughborough, Leicestershire L E 1 2 6JX, U K

Abstract: Many logging tools make multiple measurements of the same type that have more than one depth of penetration. Common examples are Compensated Density, Compensated Neutron and Array Induction logs. The purpose of the compensation is to reduce or remove the effects of a disturbance that distort the true measurement. Examples of this disturbance are the borehole size, mudcake and salinity. A general technique can be derived based on a theory of Linear Perturbation which requires no prior knowledge of the nature of the perturbation, the only requirement being that it is approximately locally linear. Various interpretations can be made of the general equation depending on the particular circumstances. The technique also produces a Complementary Parameter associated with the degree of correction. This parameter is usually discarded or paid scant regard, but can often be of some significant value and exposes surprising information. A number of examples can be used to illustrate these techniques, showing that they have wide applicability in situations ranging from difficult logging conditions (e.g. density through casing) to the apparently routine, where unusual and unexpected borehole fluids are revealed from neutron logs.

A very common method in wireline logging is to employ a system of transducers making similar measurements, spaced out along the logging tool. The main reason for this is to provide measurements with multiple depths of penetration in order to compensate for the effects of some disturbance to the measurement. This disturbance can have a multitude of origins, such as the borehole itself, its size, fluid nature, caliper fluctuations, etc., or near-borehole effects such as invasion. The compensation relies on the disturbance being common to the array of transducers, and requires a model to describe the disturbance (e.g. a step invasion profile). The multiple spacings employed have differing vertical resolutions, and much effort in recent years has been spent optimizing this resolution by ensuring that boundary information is not lost. The V E C T A R (Vertical Enhancement by Combination and Transformation of Associated Responses) computational technique is one such method (Elkington et al. 1990). In this paper, we will consider the converse of this combination method and develop equations which are not dependent on a pre-imposed model but are very general. In the process of doing this, we will see that another parameter is revealed that is orthogonal to the true value that is being examined.

Orthogonalization A definition of an orthogonal pair of parameters

is that although they are associated, varying one of them does not vary the other. For example, invasion depth and Rt (resistivity) are orthogonal, because varying Rt does not affect the invasion depth, and vice versa. However, if we measure resistivity using a dual induction tool, the deep and medium measurements are not orthogonal since variation in R t affects both deep and medium logs. The tornado chart shown in Fig. 1 is an attempt to transform the measurements into an orthogonal set, the tornado being a skewed orthogonal co-ordinate system. All dual or multiple measurements are intended to achieve similar objectives. It will, however, be noticed that the transformed orthogonal pair has two parameters--we get depth of invasion as well as Rt. This value of depth of invasion is an example of the orthogonal Complementary Parameter.

Linear perturbation and sharpness Let us consider an observation O, looking at a true value V, subject to a perturbation P. Let us suppose we perform all the chart book corrections we can (borehole size, etc.) but we are still left with a perturbation we cannot measure directly. Let us further assume that the perturbation is reasonably small and that it disturbs the observation from its true value in a linear way. We can then write:-

0 = V+ KP

where K = t h e proportionality constant i.e. the

SAMWORTH,J. R. 1998. Complementary functions reveal data hidden in your logs. In." HARVEY,P. K. & LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 159-171

(1)

159

160

J.R. SAMWORTH

Fig. 1. A Tornado Chart--an example of a skewed orthogonal co-ordinate system.

perturbation rate. If we make two observations with different transducers but subject to the same perturbation we get:0 1 = V-t-

K1P

02 = V+ K2P.

(2)

(3)

We can eliminate the perturbation P from the two equations and solve for the true value V. With some re-arrangement, we then get: V -- O 1 ~-

(O1 - 0 2 )

(4)

K1 This is arranged in the following form:(True value) = (Observed value) + (Correction). It is important to note that the correction depends on the two observations and the ratio of the perturbation rates K2/K1 and not the individual rates themselves. This is very signifi-

cant, as the ratio of perturbation rates is easier to calculate, and additionally the rates can change their absolute values without invalidating equation (4) as long as the rate ratio is unchanged. We can also solve equations (2) and (3) for the perturbation P by eliminating V:/9__ 0 2 -- O1 K2 -- K1

(5)

This parameter is the Complementary Parameter and is orthogonal to the true value. It can often be numerically scaled into some useful unit but is frequently ignored. If the perturbation is due to a variety of different effects they become lumped into a correction that cannot be assigned an explicit physically meaningful value, so P becomes Unsharp. This is the price of getting a good assessment of the true value, V, which is Sharp. It is, however, often the case that many of the lumped parameters are constant over the length of the borehole. If these values can be ascertained independently, and any one of the

HIDDEN DATA IN LOGS

161

Fig. 2. Mudcake thickness from Density logs.

perturbations varies significantly over the borehole, this variable parameter can be derived explicitly and a curve plotted. That is, it becomes

is usually one of optimization. We can encapsulate this principle thus:-

Sharp.

a computational process on a measurement can only be justified if the result after the process is better than the original.

Principle of betterness Before considering examples of the application of Linear Perturbation it is prudent to consider our objectives. The main objective is to improve the quality of a measurement, not necessarily to make it absolutely correct, because this depends on the quality of our assumed model. We can often become unnecessarily obsessed with correctness, whereas the log interpretation process

Alternatively:if a measurement can be improved by applyNg a computational process it is usually worth doing. The result does not have to be correct, only better.

An example of this principle at work is the Compensated Density Log. In the presence of a

162

J.R. SAMWORTH

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Fig. 3. Compensated Density through casing.

mudcake, the corrected log is usually more accurate than either of the two component originals. If, however mudcake is not present, the compensated log is subject to composite errors from both measurements and can actually be worse than either of them. This situation can often occur in practice, especially in slim wells. We can see that we must, therefore, apply the technique circumspectly.

Application of linear perturbation We will now consider several applications of the theory.

Density logs We can apply equation (4) directly to the long and short-spacing density logs.

We then get:-

pt=pn+

where pt PL Ps Ks & KL

11 ] ~

= = = =

(PL--PS)

(6)

True Density Long Spacing Density Short Spacing Density Perturbation rates.

This equation is identical to that derived by applying the geometric factor theory to density logs (Samworth 1992). If we wish to explore the complementary parameter we need to set up the original equations. Density logs can be expressed in terms of a Geometric Factor J:

HIDDEN DATA IN LOGS

163

Fig. 4. Use of a derived Apparent Caliper to improve Slim Array Induction logs.

PA= Jpm~+ (1 - J ) Pt Pmc = mudcake density. Rearranging; PA = Pt + J(Pmc -- Pt).

(7)

(8)

If we approximate J to a straight line function of standoff, d, i.e. we get:-

J = Kd,

PA = Pt + Kd (Pine-- Pt).

(9) (10)

This is the linear perturbation equation from which (6) can be derived. We can now use equation (5) to derive the standoff, d i.e.

Ps--PL d=(Pmc-P,)(Ks-KL)"

(11)

A log of this mudcake thickness is shown in Fig. 2. It is, of course, similar in character to the density correction but is scaled in inches.

Density log through drill pipe Occasionally, circumstances arise when the borehole stability is so poor that it is not possible to leave the hole open for conventional logging. It is then possible to run a variant of the density tool inside the drill pipe to log the density of the formation outside the pipe. In this case, there is no mudcake and we have no knowledge of the borehole caliper. A special form of density tool is employed which has no preferential circumferential collimation, i.e. it looks all round the hole. The long and short detectors are calibrated for the through-pipe conditions, and linear perturbation

164

J.R. SAMWORTH

Fig. 5. Invasion indications from a Slim Dual Induction Log.

applied. The degree of correction and complementary functions are not now associated with mudcake. Figure 3 shows a compensated density log obtained in this manner. If the original sharp value required is the bulk density, we do not have to assign an explicit meaning to the density correction; it can remain largely unsharp. Although unsharp, it is still probably safe to

assume that areas of high corrections are areas of hole enlargement. If we pursue this assumption, we can compute a caliper log using equation (11). This caliper log is shown in Fig. 3.

Caliper from array induction logs Induction logs can be combined in a similar way. Since inductions measure conductivity, we can

HIDDEN DATA IN LOGS

165

~.;~nc~easing ,~ ~

,,"

~176176

..-""

~176176176

Short count rate

Long count rate

Fig. 6. Cross plot to indicate effect of perturbations on Neutron log count rates. set up the linear perturbation system as in equations (2) and (3). This has been previously explored for slimline array tools (Samworth et al. 1994). Figure 4 shows an example of this application. A difficult horizontal well was logged with a slim array induction tool, without an opportunity to run any other log. The borehole fluid was saline (.07 52 f2m) and since no caliper was available to correct the logs, they were apparently quite poor. (The right hand set of curves in Fig. 4). Since we know the mud resistivity, by assuming that the two shallowest measurements see no further than the invaded zone we can use linear perturbation to calculate an apparent caliper. This caliper, shown in the left-hand track, was then used to correct the deeper reading measurements. A much more systematic log then results (in the centre track of Fig. 4). This is a form of optimization of the induction logs, and it leads to a better product without necessarily being absolutely correct.

Invasion indication from induction logs Figure 5 shows what can be achieved with a simpler slim dual induction tool. Only two conductivities are measured here, but unlike the previous example, the caliper is known as well as the mud resistivity, and the appropriate corrections can be applied. When linear perturbation is applied here, as well as deriving Rt, we get a lumped complementary function associated with both Rxo and invasion diameter. This is shown as the shaded curve in Fig. 5 and gives some indication of the character of the invasion. It can be seen, for

example, that there are three permeable zones, the invasion of the lower two being uniform since the invasion indicator is of a trapezium shape. However, the upper zone shows a graded form on its top edge, probably indicating a gradation in permeability.

Borehole fluid salinity from neutron logs We can adapt linear perturbation to the dual neutron tool. Dual neutron tools are usually designed so that the ratio of the count rates from near and far detectors is related to the formation porosity. The design is normally such that the sensitivity of this ratio to such things as borehole fluid salinity is minimized. However, a complementary function can be calculated specifically to be sensitive to this salinity. This can be seen in Fig. 6 where we have cross plotted the short spaced count rate against the long spaced. On this plot, all points on a straight line through the origin have the same ratio, and this represents the same porosity. A line can also be drawn for constant salinity but with porosity varying. This mesh is a skewed orthogonal system, as described earlier. In setting up the linear perturbation equations in this case, we shall use the two count rates V1 and V2, which are the unperturbed values. So we now get: O1 = V1 +K1P

(12)

0 2 = V 2 + K2P.

(13)

We can establish a relationship between 01 and 02 by eliminating P. We get:

166

J.R. SAMWORTH

Fig. 7. Borehole salinity from Neutron logs (1).

H I D D E N DATA IN LOGS

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-g 2~."

%-N

168

J.R. SAMWORTH

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7400 7~00 7600 7700

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K1

Kx V2).

0 1 "-" ~22 O 2 "~- ( Vx - - ~ 2

(14)

This is a straight line equation of the form O1 = m 0 2 + (constant).

(15)

For the particular case of ratio processing: K1 01 V1 m = / ( 2 - 02 -- V2"

(16)

Since we actually observe Ol and O2, m can be calculated and we can migrate along the line until we reach V] and V2. This method has

previously been explored in some detail (Samworth, 1991). If, however, we can identify the positions of O] and 02 on the ratio line, we can identify which line of constant salinity we are on, and we can then estimate the borehole salinity. Some examples now follow to show the usefulness of this complementary parameter. Figures 7, 8 and 9 show sets of logs, on a compressed vertical scale in a dolomite reservoir. The field was being produced by an injected waterflood, and the wells were close to each other. The reservoir section is the whole of the lower halves of the wells where the gamma ray log activity increases.

170

J. R. SAMWORTH )

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Fig. 11. Borehole salinity in a horizontal well (2). Figure 7 shows a well where the well fluids were static. The salinity indicator shows low salinity, i.e. oil, above a high salinity sump in the reservoir section. Figure 8 shows a log taken with the well flowing, i.e. the injector had not been turned off. Here the salinity profile is inverted, but the inversion starts several hundred feet into the reservoir. Figure 9 is similar to Fig. 7, but with a blip at a similar place to where there is a change in Fig. 8. The conclusion from these logs must be that the waterflood is breaking through at the top of the reservoir and not efficiently sweeping the lower levels.

Figure 10 shows a horizontal well where there are several intervals with an anomalous Array Induction response (e.g. at 5810-5910). The neutron based salinity indicator shows high levels at these points indicating water plugs in an otherwise oil-filled well. The nuclear logs are shown in Fig. 11 for reference. Comparison of the logs with a plot of the hole trajectory shows depressions at these points, the salinity indicator showing that these are full of water.

Conclusion There is much information to be had from well logs by interpreting them in a slightly unconven-

HIDDEN DATA IN LOGS tional way, so it is imprudent to discard any data, especially raw data. The linear perturbation technique is completely general, and does not rely on any particular physical model. It is applicable to a wide variety of logs where multiple measurements of a similar type are made. The method also produces a complementary parameter which can be very useful in revealing effects not apparent on the normal logs.

This paper illustrates some of the work carried out by the Research and Development Department of Wireline Technologies Ltd, and grateful thanks are given to that company for permission to publish.

171

References ELKINGTON,P. A. S., SAMWORTH,J. R. & ENSTONE,M. C. 1990. Vertical enhancement by combination and transformation of associated responses. Transactions of the 31st Annual Logging Symposium, SPWLA, Paper HH. SAMWORTH, J. R. 1991. Algorithms for compensated neutron logging--57 varieties. Transactions of the 14th European Logging Symposium, SPWLA, Paper A. - 1992. The dual-spaced density log, characteristics, calibration and compensation. Log Analyst 33, 4249. , SPENCER, M. C., PATEL,H. K. & ATACK,N. A. 1994. The array induction tool advances slim hole logging technology. Transactions of the 16th European Logging Symposium, Paper Y.

In situ stress prediction using differential strain analysis and ultrasonic

shear-wave splitting B. W I D A R S O N O , 1 J. R. M A R S D E N 2 & M. S. K I N G 2 1Lemigas, Jakarta, Indonesia 2 Department o f Earth Resources, Engineering Royal School o f Mines, Imperial College, London S W 7 BP, U K Abstract: Knowledge of the /n situ states of stress in rock masses is of considerable importance to a number of subsurface engineering activities, including those involved in exploiting petroleum and geothermal energy reserves. In this paper, a comparison is made of two laboratory techniques, based upon stress-relief microcracks, for determining the in situ state of stress: differential strain analysis (DSA) and ultrasonic shear-wave splitting (USWS). Measurements on ten sandstone samples recovered from deep boreholes, made using the well-established technique of DSA, have been compared to those made by the comparatively new technique of USWS and to sleeve fracturing measurements of in situ stress made in the corresponding boreholes. The results obtained indicate that the USWS technique, with its ability to test a large number of samples quickly, provides a useful adjunct to DSA and sleeve fracturing in determining trends in in situ stresses. Used in combination, the two laboratory techniques have also proved useful for examining rock micro-structural features.

A number of operations involved in the exploitation of petroleum and geothermal energy resources require a knowledge of the in situ state of stress. Such data are required for determining borehole stability in the drilling phase, for avoiding solids production problems and for hydraulic fracturing stimulation in the production phase, and for reservoir characterization in reservoir engineering. A common method for obtaining in situ stress data from great depth is indeed by hydraulic fracturing or, alternatively, sleeve fracturing (Desroches et al. 1995). These techniques, however, possess certain disadvantages with regard first to cost and second to technical considerations in fractured formations, deviated well bores and high pressures and high temperature formations. Results obtained from these methods are often influenced and biased by stresses close to the well bore and hence do not reflect the governing in situ stress field. To overcome some of these problems, the technique of differential strain analysis (DSA) has been developed. Since it was first suggested by Strickland & Ren (1980) as a tool for in situ stress determination, DSA has been used frequently; successful applications have been reported by various investigators (Dey & Brown 1986; Dyke 1988; Oikawa et al. 1993). Nevertheless, considerations of the length of time required for a DSA test have led to efforts to find alternative methods. Early studies (Yale & Sprunt 1989) utilized the phenomenon of ultrasonic S-wave splitting on rock specimens

taken from great depth which contain stress relief microcracks. The main objective of this study is to contribute to the development of the technique and to compare the results obtained with those from other proven methods. For the purpose of this study, specimens were prepared from core samples taken from various petroleum wells in the Irish and North Seas. The samples comprised ten sandstone specimens from depths lying between 1361 and 1422 m and between 3232 and 3304 m, eight of which (SSA) were oriented and so could be used for determining the actual orientation of the in situ stresses. The other two samples (SSB) were not oriented; they are, however, considered valuable for further comparison studies. Descriptions of the rock samples are provided in Table 1.

Differential stain analysis (DSA) Technique DSA is a method based on the existence of oriented microcracks generated within core samples as a result of stress relief processes which occur during the core process and recovery of the cores from depth. Evidence of the existence of this type of microcracks has been reported by various investigators using different approaches (Kowallis & Wang 1983, amongst others), such as comparing images from scanning electron microscopy (SEM), studying P- and S-wave velocities adjacent to

WIOARSONO,B., MARSDEN,J. R. & KIN6, M. S. 1998. In situ stress prediction using differential strain analysis and ultrasonic shear-wave splitting In. HARVEY,P. K. & LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 185-195

185

B. WIDARSONO ET AL.

186

Table 1. Description of sandstone samples Sample

Depth (m)

Grain size (mm)

Comments

SSA-1 SSA-2 SSA-3 SSA-4 SSA-5 SSA-6 SSA-7 SSA-8 SSB-1 SSB-2

1361 1363 1364 1366 1374 1399 1409 1422 3232 3304

0.5 0.1-1.0 0.5-1.0 0.54).75 0.5 0.14).5 0.14).5 0.5 0.14).5 0.14).5

Well cemented, very weak bedding Well-cemented, poorly-sorted, weak bedding Fairly well-cemented, strong bedding Well-cemented, no sign of bedding Well-cemented, weak bedding (possible micaceous laminae) Dark red, very weak bedding Well-cemented, weak bedding/laminae Well-cemented, strong bedding Well-cemented, no bedding/laminae Well-cemented, no bedding/laminae

the borehole and in the laboratory, and employing differential strain analysis itself. For example, Teufel (1983) observed anisotropy of P-wave velocity measurements and correlated this with results from the anelastic strain recovery technique (ASR). Basic assumptions of the technique are presented in length by Strickland & Ren (1980) who, in brief, assume that aligned microcrack densities in different axes are proportional to the relieved stress magnitudes in these axes. Consequently, when the sample is compressed hydrostatically, the resulting strains will show preferential orientation in magnitudes which are proportional to the microcrack densities. A further assumption is that all microcracks existing within a tested sample are of stressrelief type, or at least that all pre-existing microcracks do not affect sample deformation significantly.

Experimental procedure Three basic steps are followed in specimen preparation: machining the specimen, attaching the strain gauges and encapsulating the specimen. Each step in specimen preparation must be performed carefully in order to prevent generation of new microcracks in the rock sample. Flat surfaces are machined on each specimen in at least three orthogonal directions, by first sawing them with a diamond saw and then by hand lapping or surface grinding. After ovendrying at 35 ~ strain gauge rosettes are attached to the specimen following the arrangement shown in Fig. 1. The rock sample is finally encapsulated with epoxy resin in an elastomer membrane. The strain gauged and encapsulated specimen is placed in an oil-filled pressure vessel and left for approximately 24 h in order to ensure temperature stabilization. This procedure avoids any temperaturerelated fluctuations while strain

Fig. 1. Axes system and strain gauge orientations.

gauge readings are made during the test. Hydrostatic pressure on the specimen is first increased in steps of 200 psi to 21 MPa (3000 psi), then in steps of 500 psi to 55 MPa (8000 psi). During this loading procedure, a transition from microcrack closure to intrinsic elastic deformation is generally found to occur. From 55 MPa (8000 psi) to the maximum pressure (usually around 83 MPa-12000 psi) 1000 psi increments are usually chosen since microcrackfree linear stress-strain behaviour generally occurs in this range of pressures. A strain gauged and sleeved fused silica specimen of known physical properties is also tested adjacent to the rock test specimen to provide any corrections necessary for environment-related non-linearities in the specimen and strain gauge responses.

Procedure of analysis Additional input data is required for analysing DSA measurements, including: vertical in situ or

IN SITU STRESS PREDICTION Pressure

(MPa)

100

/

80

60

~G a u g, e _ _ _, _

40

,

6

2O 0 0

1

2

Strain(millist rains)

3

Fig. 2. Typical compression curves from DSA test. overburden stress, /n situ pore pressure, and Poisson's ratio for the tested rock. The orientation of the reference line with regard to the axes of the cubic specimen is also required if the true orientation of the in situ stress field is to be determined. The strains recorded by the data logger are fitted by a series of curve-fitting programs to produce the pressure-strain curves by way of a quadratic fit using five adjacent data points (Dyke 1988). A microcrack closure strain tensor is obtained from these quadratic compression curves (Fig. 2) for each of the specimens tested. To create a complete microcrack strain tensor, six components only are required from the twelve strain gauge measurements. This permits a statistical analysis to be made of the redundant data. From the microcrack strain tensor, the principal microcrack strains and their orientations relative to the reference line are calculated using the method proposed by Strickland & Ren (1980). The ratios of principal strains are taken as the ratios of the principal effective stresses and, by a series of tensorial transpositions to vertical and horizontal planes, the principal strains can be converted to principal in situ stresses using values of overburden stress, pore pressure and Poisson's ratio. Furthermore, the true orientations of the stresses can be determined if the true orientation of the reference line is known.

Ultrasonic shear wave splitting (USWS) Technique The use of acoustic S-wave splitting (birefringence) as a source of information regarding the

187

medium through which it propagates remains relatively novel despite its origins in studies of earthquake seismology. Despite the abundance of observations, it is still not clear exactly what causes S-wave splitting in the Earth's crust (Crampin & Lovell 1991), although it is generally taken to be caused by aligned discontinuities. Crampin (1978) recognized that most rocks in the crust are likely to contain discontinuities, and that S-wave splitting is probably the most diagnostic feature of wave propagation in such anisotropic rocks. Attempts have been made to relate S-wave splitting to the orientation of in situ stress-relief induced microcracks in cores taken from great depths. Yale & Sprunt (1989) utilized ultrasonic S-wave splitting on oriented core samples, and concluded that this approach can be used to predict the orientation of the major horizontal in situ stress. Shear-wave splitting results from the division of a polarized S-wave into two separate polarized S-waves travelling at different speeds when a source of anisotropy is encountered in its path. When a plane polarized S-wave is propagated through a medium containing a set of aligned microcracks it will be split into two orthogonally polarized S-waves, with one polarized parallel to the plane of the microcracks and the other, travelling at a lower velocity, polarized perpendicular to the plane of the microcracks. Garbin & Knopoff (1975) proposed a theory to explain the velocity variations caused by a single set of parallel cracks which is based on scattering of elastic waves by penny-shaped cracks. The theory explains the variation of S-wave velocity with changes in ray path angle and wave polarization relative to the crack plane. The degree of splitting is related to the time lag between the arrival of the two waves at the receiver. The degree of S-wave splitting and hence velocity anisotropy increases with an increase in crack density.

Experimental procedure and analyses As part of this study, S-wave splitting tests were conducted on the same specimens as used in the earlier DSA tests, except in the case of one which exhibited such a poor degree of cementing that satisfactory acoustic coupling between specimen and transducers could not be achieved. The elastomer sleeves were removed from the DSA samples tested earlier and the latter were re-cut with flat surfaces perpendicular to the vertical (Z-axis) and horizontal (X- and Y-axes). They were then oven dried at 35~ so that the specimens could be tested dry. The principal

188

B. WIDARSONO ET AL.

Table 2. In situ stress data from DSA tests 0.1

0.2

0.3

Sample

o1/0. V 1

Azimuth (0)2

Dip (0)2

0"2/0"1

Azimuth (0)2

SSA-1 SSA-2 SSA-3 SSA-4 SSA-5 SSA-6 SSA-7 SSA-8 SSB-1 SSB-2

1.005 1.017 1.010 1.130 1.000 1.059 1.001 1.004 1.004 1.008

204N 106N 116N 74N 38N 331N 229N 164N 240 179

80 73 76 59 87 66 86 81 83 74

0.892 0.824 0.877 0.939 0.832 0.760 0.902 0.866 0.888 0.928

71N 3 08N 213N 351N 293N 52N 326N 20N 132 88

Dip 0"3/0"1 (O) 7 17 2 4 3 2 0 7 2 1

0.849 0.807 0.832 0.805 0.817 0.676 0.824 0.835 0.763 0.879

0"3/0"2

Azimuth (0)2

Dip (o)

0.955 0.982 0.948 0.858 0.982 0.983 0.914 0.966 0.858 0.948

340N 219N 304N 262N 203N 140N 57N 290N 42 358

7 1 14 26 3 23 4 6 7 16

1 0.v = vertical or overburden stress. 2 Azimuths measured clockwise with respect to North (Z-axis) or, for unoriented cores (SSB), clockwise from reference line (X-axis).

axes (Fig. I) and reference lines used were the same as those used in the DSA tests, in order to maintain compatibility between the DSA and Swave splitting results. USWS measurements are performed by rotating the rock specimen containing stress relief microcracks while pulses of planar S-wave are transmitted parallel to the specimen axis under nearatmospheric pressure conditions. In the presence of aligned microcracks, S-wave first arrivals observed by the receiving transducer (polarized parallel to the polarization of the transmitter) show changes in magnitude as the specimen is rotated. When the direction of polarization of the transducers is parallel to the aligned microcracks, the S-wave first arrival time is a minimum. Conversely, when the transducer polarization is perpendicular to the aligned microcracks, the first arrival time is a maximum. This direction is that of the greatest stress relaxation and hence is the major in situ stress direction. Each specimen was first assembled between pairs of broadband transducers having S-wave frequencies in the range 300 to 800 kHz (as described by King et al. 1995) with a proprietary visco elastic S-wave couplant and a stress of 2.5 MPa applied to the transducers to provide good acoustic coupling. This level of axial stress has been shown experimentally to have a negligible effect on cracks oriented sub-parallel to this direction of propagation of S-waves. At the start of a test, each specimen is arranged so that the transducer polarization is in the Y-axis direction and the propagation of acoustic energy is either in the Z-axis direction (vertical) or X-axis direction (horizontal). During a test, the specimen is rotated through an angle between 0 ~ and

180 ~, measured relative to the reference line, in increments of 15~ At each 15~ step, the transit time of first arrivals and waveforms in digital form are recorded. After each test, the S-wave transit time is converted to velocity.

Experimental results D i f f e r e n t i a l s t r a & analysis

Results of the in situ stress predictions for all specimens tested are shown in Table 2, in which stress magnitudes are presented as ratios in order to provide a comparison of results. Figure 3 shows plots of the results for SSA sandstones in the form of an equal-angle stereonet (lowerhemisphere projection). Trends of the stresses determined from the oriented cores of the SSA specimens are given in degrees measured clockwise from North, whereas those obtained from the two unoriented SSB sandstones are simply measured clockwise from an arbitrary reference line. Consequently, the results for SSB samples are not plotted on stereonet projection, since no common reference line exists among the specimens tested, and such plots could imply misleading relations. The results shown in Table 2 and Fig. 3 show that the major principal stress (o.~) lies near vertical, to within 0 ~ to 23 ~ This result can be regarded as sufficiently precise for a technique based on stress relief microcracks, since it is common that the orientations of the microcracks are modified by grain scale inhomogeneities. The similarity in magnitudes between major (o1) and vertical (i.e. overburden) stresses (o'v), represented by the ratio o'1/o'v being near to unity, also indicates that o'1 lies in the vertical

IN SITU STRESS PREDICTION

North f 1

2

6 b

7%o8~3 2 1

3 0(~. 2 1,2,3 ... sample number

A~ 3

Fig. 3. Lower hemispherical projection showing in sltu stress orientations from DSA tests on sandstone SSA.

direction. It can also be concluded from the results for SSA sandstone that the depths from which the core samples were recovered are not far above the depth at which o.H becomes equal to o-1, as indicated by the closeness of the ratios o.2/o.1 and o.3/0-~ to unity. This interpretation is in accordance with global data for the vertical horizontal stress ratio versus depth compiled by Brown & Hoek (1978). In the case of the intermediate and the minor stresses, 0-2 and 0-3, it is evident that these lie in a horizontal plane, or at least sub-parallel to horizontal. However, it is obvious from the scatter observed that the orientations of the two horizontal stresses are interchangeable. This is understandable, since the two stresses are very close in magnitude, and each has caused a similar degree of oriented microcracking in the samples. If these ratios (0"3/0" 2 column in Table 2) are averaged, a minor-intermediate stress ratio of 0.95 (with the exclusion of SSA-4, which is significantly different from the others) is obtained. Thus the difference of stress relief microcrack density in the two principal directions is minimum and, taking into account experimental and analytical error (e.g. determining ranges for slopes of the pressure-strain curves), the implied stresses could be interchanged in direction and magnitude. At this point, it is worth noting that, with a mere 5% error bar to represent the errors, both trends and magnitudes of the two horizontal stresses are interchangeable. In fact statistical analysis of each over-determined DSA dataset (which was necessary to obtain the best fit tensor of crack closure strains) yielded a maximum error of

189

between approximately 2% and 7% with regard to the principal stress ratios from any single DSA tests, and an error 'cone' of approximately 5~ to 12~ for the principal stress orientations from any single test. From the hemispherical plot of all the oriented DSA data (Fig. 3) it can be seen that the combined results yield a scatter of approximately 30 ~ in the azimuths of the horizontal (i.e. intermediate and minor principal) stresses. However, this does not imply the statistical analyses of the DSA results could just have easily yielded horizontal stress orientations in any azimuths from 0~ ~ since this would have necessitated the microcrack densities and stress magnitudes being isotropic in the horizontal plane. Whilst this is possible, it is only so for those relatively few cases where the magnitudes of the minor and intermediate stresses are exactly the same. For all other combinations within the limits or error, the general directions of the principal stress orientations are as seen in Fig. 3 and only the magnitudes vary. Thus, although the intermediate and minor stresses are very close in magnitude, the DSA method has still been able to identify the general orientations of the stresses. From the hemispherical projection, it is clear that one of the two horizontal stresses lies within the range 290 ~ to 350 ~ from North, with the scatter in azimuth due probably to variation in the orientation of the stress-relief microcracks caused by grain-scale heterogeneities. On the other hand, the other horizontal stress lies within the range 20 ~ to 71 ~ from North such that, with the two horizontal stresses being similar in magnitude, the intermediate principal stress (o.H) can lie in either of the ranges 290 ~ to 350~ or 20 ~ to 71~ Arguably, therefore, o.H can lie in either of the ranges 310+10 ~ N (or 130+10~ or 220+10~ (or 40+10~ These results are in reasonably good agreement with results of an earlier study reported by Desroches et al. (1995), who conducted analyses of the in situ state of stress in this area using DSA on samples from the very same core sections as tested in this study, as well as using hydraulic fracturing and sleeve fracturing in downhole tests in the same well and at the same depths. The earlier combination of the results from these three techniques indicated o.h to lie in the range N65~ ~ Note also that this earlier study showed that stress data from DSA analyses on these core sections were not influenced by slight anisotropy in the samples nor by variations in the elastic properties or rock strengths over the cored intervals. The in situ stress prediction from the two SSB

190

B. WIDARSONO ET AL.

136oN

166oN

196~

226oN

256oN

286oN

316oN t

60

63

66

69

72

75

Transit time (pSec)

60

63

66

69

72

Transit time (pSec)

Fig. 4. S-wave waveforms for sample SSA-1 at various rotation angles. (Propagation in vertical Z-axis, and polarized in Y-axis direction at X-axis reference line. Arrows indicate detected first peak).

Fig. 5. S-wave waveforms for sample SSA-I at various rotation angles. (Propagation in horizontal X-axis, and polarized in Y-axis direction at X-axis reference line. Arrows indicate detected first peak).

sandstone specimens is similar to the results for SSA, even though the true orientations cannot be determined due to the unoriented nature of the core. Since the core is from vertical boreholes, it can be inferred from Table 2 that the major principal stress lies near-vertical; consequently the other two principal stresses lie nearhorizontal.

in other directions. Although this behaviour is exhibited by all specimens tested in this study, there is one case (SSA-8) where signal attenuation was so severe that it proved impossible to pick the first arrival time. The degree of attenuation, nevertheless, varies from one specimen to another in a manner related to the state of cementation of the specimens (Table 1). For the purpose of predicting in situ stress orientations, transit time values were identified and selected from the waveforms. Since the Swave signals observed during the experiment vary in quality due to different degrees of attenuation, it was found that the S-wave velocity calculated from the first peak (or trough) is more reliable for interpretation than the group velocity calculated from the first arrival. Figure 6 shows examples of the variation in first peak velocity with rotation angle as seen for sample SSA-1. The velocity plots are shown with an error bar of +0.5 %, estimated as representing the confidence in picking transit time values (+0.125 #s) from waveforms due to variations in signal quality and oscilloscope resolution. In general, the velocities plotted against rotational

S h e a r w a v e splitting

During each test, a set of waveforms was recorded for each 15~ rotation relative to the reference line (X-axis for the vertical, and Z-axis for the horizontal wave propagations). Figures 4 and 5 illustrate examples of waveforms recorded during measurements on SSA-1 in the vertical (Z-axis) and horizontal (X-axis) directions. As expected, the plots show that the transittime (At) varies with rotation angle. This variation in At can be considered as an indication of the existence of an oriented set of cracks, or at least (provided that a homogeneous background pore system exists) is more influential in reducing S-wave velocity than any other sets of microcracks with lower density oriented

IN SITU STRESS PREDICTION

S-wave [first peak] velocity (m/s) 2000 a) Z-direction propagation Y-axis polarization

191

minimum velocity direction. For horizontal propagation (X-axis), the vertical (or sub-parallel) in situ stress (o-v) coincides with the direction of maximum velocity, as in the case of 0-H for vertical propagation. Both 0-H and 0"h are orthogonal to O-v.

19oo

Table 3. in situ stress orientations from USWS tests

1-_+0.5%

18oo

1~o

'

18o

2~o

'

'

24o

Sample 270

300

crI inclination O"H azimuth (~ vertical) (o)l

~h azimuth (o)l

o from North

S-wave [first peak]

velocity (m/s) 2100 b) X-direction propagation Y-axis polarization

2000

9

1•

19oo

t

9

~b

I

6;

i

9'o 90

I

120 o from vertical

150

180

Fig. 6. Variation of S-wave first peak velocity with rotation angle for sample SSA-1. (a) Vertical Z-axis propagation, polarized in Y-axis direction; (b) horizontal X-axis propagation, polarised in Y-axis direction.

angle result in a sinusoidal pattern, indicating the presence of azimuthal velocity anisotropy over 90 ~ As shown in Fig. 6, similar behaviour is also observed in both the vertical and horizontal directions, indicating the presence of aligned stress relief microcracks of different densities as the source of anisotropy. Generally, for SSA sandstone specimens, S-wave velocity splitting of 1 to 3.5% and 3 to 13.5% (relative to the highest velocity) for vertical and horizontal propagation, respectively, are observed. For SSB samples, SSB-1 shows 2.2% splitting, whereas SSB-2 shows 1.1% and 1.6% velocity splitting, respectively in the vertical and horizontal propagation direction. Accepting the hypothesis of a relation between S-wave splitting and in situ stress relaxation and orientation of stress relief microcracks, velocity plots such as in Fig. 6 indicate the orientations of the in situ stresses. From the velocity profiles, for S-waves propagating in the Z-axis direction, the major horizontal stress (O-H) lies in the direction at which maximum velocity occurs, whereas the minor horizontal stress (o-h) lies at right angles to it, as indicated by the

SSA-1 SSA-2 SSA-3 SSA-4 SSA-5 SSA-6 SSA-7 SSA-8 SSB-1 SSB-2

0 75 2 0 0 0 0 0

7 6 ( 2 5 6 ) N 166(346)N 5 3 ( 2 3 3 ) N 143(323)N 83(263)N 197(17)N 120(300)N 343(163)N 106(286)N 105(=285) 75( = 255)

173(353)N 107(287)N 210(30)N 253(73)N 196(16)N 15(--195) 345(= 165)

1Azimuths measured clockwise with respect to North (Z-axis) or, for unoriented cores (SSB), clockwise from reference line (X-axis). 2 = Poor acoustic coupling due to poor cementation of the rock. Table 3 summarizes the results of the S-wave splitting measurements. Note that USWS measurements on SSA-3 and SSA-8 (Z-axis propagation) were not carried out, due to poor transducer-sample acoustic coupling. The results show that one of the principal in situ stresses lies in the vertical direction, even though accuracy is limited by the 15 rotational sampling. The vertical stress lies within 7.5 of the peak of the velocity profiles shown in the plots (except for sample SSA-2). The same resolution limit applies to 0-H. Furthermore, from comparisons between the horizontal and vertical velocity plots, it is apparent that 0-v is the major principal stress, o1, as indicated by relatively larger velocity anisotropy for horizontal than for vertical propagation. To illustrate this, 1 to 3.5% velocity variation exists over 0~ ~ relative to the highest velocity for vertical propagation, in comparison to 3 to 13.5% for horizontal propagation in the SSA sandstone. Consequently, 0-2 and 0-3 lie in the horizontal plane. As seen from DSA, the trends of the horizontal in situ stresses are more easily identified if illustrated on stereonet projections. Figure 7 illustrates the orientations of the major horizontal in situ stress axes for the SSA sandstones plotted. As with the DSA stereonet projections, the orientations are relative to

192

B. WIDARSONO ET AL. Reference line ~ / 7 7

f

1

/ e C~,H 1,2,3 ... sample number

Fig. 7. Lower hemispherical projection showing rh orientations from DSA tests on sandstone SSA.

North. The projection in Fig. 7 and the corresponding DSA results (Fig. 3), show that the major horizontal stress can lie either in the N W - S E or N E - S W directions. At this stage, therefore, no definitive conclusion can be drawn regarding the orientation of 0.iJ.

Comparison of the two techniques Orientation o f in situ stresses

In comparing the results from the DSA and the S-wave splitting, only the orientations of the stresses can be considered. No comparison can be made of stress magnitudes, since S-wave splitting tests do not provide stress magnitudes, even though a limited qualitative assessment can be made using velocity anisotropies. A summary of results of the two techniques are listed in Table 4. In the table, only the results for aH and ah from acoustic measurements and 0.2 and 0.3 from DSA are compared, since almost all analyses of S-wave splitting tests have shown that the principal stress 0.1 is essentially vertical (i.e. they show a minimum velocity at 90 to the vertical). In general, the results for SSA sandstone have shown that there is a reasonable agreement between the two techniques, although some inconsistencies appear when individual results are studied. It is clear that only SSA-I and SSA7 exhibit total agreement between trends for ei-i (USWS) and o2 (DSA), which is by definition correct for this case (i.e. intermediate principal stress is the major horizontal stress). The rest of the samples have, in contrast, tended to show

agreement between trends for 0.I-1 (USWS) and 0.3 (DSA), which is incorrect by definition, since 0.3 is the minor principal stress, and for this case it should coincide with the minor horizontal stress (0.h). This behaviour can be explained by the ratio 0.3/0.2 approaching unity (approximately 0.95), such that differences in microcracking in the two principal directions are minimal. Nevertheless, as indicated by the stereonet projection in Fig. 7, there is also no clear consistency in 0.n orientations, suggesting no clear consistency in the orientation of the vertical microcracks. This appears to be due to the effect of grain scale heterogeneities, over which the far-field horizontal in situ stresses are not large enough to maintain sufficiently large and uniform tensile forces across the rocks at the granular scale. Grain scale heterogeneities certainly appear to have their effects in 0.1 prediction. The DSA results for SSA sandstone in Table 4 show that the orientation of 0.1 varies within a range 00-23 ~ from the vertical, whereas the USWS results show almost all the 0.1 to be vertical (Table 3). Undoubtedly, rotational sampling of 15~ reduces the accuracy of stress orientation, and it is likely that grain scale heterogeneities (reflected in local preferential orientation of the microcracks) contribute significantly to any disagreements between the two techniques. Such heterogeneities certainly have greater effects on DSA measurements, since the portions of the specimen measured in DSA are limited to the surface areas underneath the strain gauges. This is much less representative than the rock mass tested by the USWS technique. The results from S-wave splitting are probably more reliable in this particular case. The results for SSB sandstone in Table 4 show a reasonable agreement between the two techniques, even though the results for SSB-2 exhibits about 30 ~ difference between o-2 and 0.H, and between 0.3 and 0.h- Although there is no evidence, this disagreement is probably caused by other sources of acoustic velocity anisotropy such as preferential alignment of sandstone grains. The differences in the fundamental concepts of the two techniques provide, nevertheless, advantages and disadvantages for both techniques. In S-wave splitting, any acoustic propagation is influenced by the 'averaged' properties of the whole specimen volume, and therefore representative of the whole specimen. In contrast, any microcrack strain measured in a DSA test represents only the areas covered by the strain gauges, which are generally small compared to the overall specimen dimensions.

IN SITU STRESS PREDICTION

193

Table 4. Comparison of/n situ stress orientations from DSA and USWS DSA

0-1

S-Wave Splitting

O'H

Oh

Sample

Azimuth

Dip

Azimuth

Dip

Azimuth

Dip

Azimuth

Azimuth

SSA-1 SSA-2 SSA-3 SSA-4 SSA-5 SSA-6 SSA-7 SSA-8 SSB-1 SSB-2

204 106 116 74 38 331 229 164 240 179

80 73 76 59 87 66 86 81 83 74

71 308 213 351 293 52 326 20 132 88

7 17 2 4 2 2 0 7 2 1

340 219 304 262 203 140 57 290 42 358

7 1 14 26 3 23 3 6 7 16

76(= 256) 53(-- 233) 2 83(= 263) 197(= 17) 120 = 300) 343 (= 163) 106(=286) 105(= 285) 75(=255)

166(= 346) 143(= 323) 2 173(= 353) 107(= 287) 210( = 30) 253(= 73) 196(= 16) 15(= 195) 345( = 165)

(o)l

~ (o)

(o)1

~ (o)

(o)1

(o)

(o)1

(o)1

1Azimuths measured clockwise with respect to North (Z-axis) or, for unoriented cores (SSB), clockwise from reference line (X-axis). 2 = Poor acoustic coupling due to poor cementation of the rock.

However, in the presence of large discontinuities, the reverse is true. Large discontinuities in specimens influence acoustic wave propagation, whereas any non stress relief behaviour in the DSA tests can usually be avoided by strain gauge emplacement. Consequently, DSA can produce more reliable results in this case. The DSA results in Table 2 show that the principal stresses do not lie in exactly horizontal or vertical directions. In other words, the induced cracks in most cases are not exactly parallel or perpendicular to the vertical axis in situ. However, the reasonably good agreement between the two techniques has shown that acoustic velocity anisotropy can still be observed even though the microcracks dip from these directions, which is more often than not likely to be the case. This fact is very important in any effort to establish USWS as an alternative technique for in situ stress determination, bearing in mind that it is most likely that grain scale heterogeneities can cause local deviations in microcrack orientations.

Configuration system

o f stress relief microcrack

In DSA the principal strains are determined from analysis of the microcrack closure strain tensor obtained from a test. The principal strains obtained provide the orientations of the stress relief microcracks, since it is assumed that the greatest strain occurs in the direction normal to the plane of the microcracks. In other words, it is assumed that it is represented by three

dominant and mutual perpendicular microcracks sets. Although this assumption is logical, as demonstrated by Charles et al. (1986), DSA does not provide a direct illustration of the microcrack system. Direct observation such as scanning electron microscope (SEM) of oriented samples used in conjunction with DSA can, however, provide an insight into microcrack orientations and distributions. The results of S-wave splitting measurements can provide, to some extent, additional information on microcrack configurations. Velocity plots, such as shown in Fig. 6, have demonstrated that velocity anisotropy can occur between measurements in the vertical and horizontal directions. There are several factors that can lead to such acoustic anisotropy, and to S-wave splitting in particular, but it is generally accepted that aligned cracks are the major cause of S-wave splitting (Crampin & Lovell 1991). At the small scale, such as in USWS tests, there is always a possibility that other sources of anisotropy, such as lamination and crystal alignment, can contribute to the overall anisotropy. As shown in Table 1, SSA sandstone samples exhibit signs of bedding (between 4 ~ and 22 ~ from the horizontal), even though not all samples were found to exhibit dominant bedding. However, in this study, there is evidence that the presence of bedding planes has not contributed to the velocity anisotropy for the Xaxis (horizontal) propagation direction. For example, the results for SSA-5 (Table 3) show that, despite the 18.5 ~ dip in bedding (Table 1), the USWS measurements indicate the presence of a set of horizontal microcracks as indicated

194

B. WIDARSONO E T AL.

by 0 ~ in the O 1 column. Another example is seen with SSA-2, for which the bedding dipped at 22 ~ from the horizontal and where measurements in the horizontal direction indicated the minimum velocity to be reached at a rotation angle of 165~ (i.e. 15~ from the vertical, implying Crl acts at 75 ~ from the vertical. Clearly this is incorrect if one is to take the results of the DSA to be reliable (Table 3); the real cause of the anisotropy is unclear, although it may be caused by strong crystal alignment. The evidence of results for SSA-2 and SSA-5 have shown that bedding planes do not, in these cases, strongly influence velocity anisotropy for the horizontal direction, and hence do not confuse the subsequent interpretation of USWS measurements. The results obtained from the S-wave splitting tests do, however, tend to support the existence of aligned horizontal microcracks. In the vertical direction, results of the acoustic test have shown that it is most likely that vertical aligned microcracks cause S-wave velocity splitting, since no other apparent causes are observed. The question arises whether the suggested presence of two sets of mutually perpendicular vertically aligned microcracks, as implied by DSA, can be justified. For this, the results of Swave splitting cannot be used, since they do not show the existence of the second (i.e. the less dense) vertical set of microcracks (if it does exist, its existence is probably 'overlooked' by the transmitted acoustic energy and treated as merely a background for the first and more dense vertical microcrack set). Charles et al. (1986) outline theories of brittle fracture mechanics which explain crack opening under tensile forces (as might occur in the case of stress relaxation). If the existence of two sets of microcracks (one vertical and the other horizontal) whose generation is related to principal in situ stress relaxation can be proven experimentally, it is likely that a third set of microcracks (i.e. the second and less dense set of vertical microcracks) also exists, since the processes leading to it are essentially the same as those causing microcracks in the other two principal directions. Comparing results for the two techniques has demonstrated directly that three sets of mutually perpendicular microcracks exist in a rock material experiencing a process of relaxation from three in situ principal stresses, provided the relaxation forces are sufficient to generate them.

Conclusions A series of investigations of in situ state of stress using DSA and USWS has been conducted

successfully. In general, individual results of the two techniques are found to be in agreement, taking into consideration the facts regarding the local in situ state of stress field. The DSA and USWS results are also found to be in reasonable agreement with results from hydraulic fracturing and sleeve fracturing. Grain scale heterogeneities strongly influence the deviation of stress relief microcracks, as reflected by the scatter in horizontal in situ stress orientations shown by both techniques. Results for SSA sandstone samples have shown that, in areas with small differences in principal stresses, a greater number of samples will be required to overcome the influence of grain scale heterogeneities. Comparisons between individual results obtained from the two techniques have shown that S-wave splitting is a reliable one for determining orientations of in situ stresses by virtue of the existence of stress relief microcracks. The study has also shown that S-wave splitting analysis can be used independently with reliable results. This confidence, together with simplicity in sample preparation and speed in conducting tests, can be considered as the major advantage of this technique compared to other techniques based on stress relief microcracks such as DSA, differential wave velocity analysis, anelastic strain recovery or differential thermal analysis. Despite the indicated advantages, the study has also revealed some disadvantages in the acoustic technique. Its major limitation is its inability to provide estimates of in situ stress magnitude. Another less important disadvantage is the necessity to perform the test only in vertical and horizontal directions without compromising the simplicity in sample preparation and analysis of results. This requires that the principal in situ stresses always lie in vertical and horizontal planes, which is not necessarily true in all cases. Theoretically, however, this disadvantage can be reduced by reducing the sampling rotational interval, hence enabling more careful examination of the alignments of sets of microcracks. The fact that stress relief microcracks are not the only source of S-wave splitting is another disadvantage. However, wellprepared samples can minimize this significantly. When the two techniques are employed together, DSA provides information on in situ stress orientations and magnitudes, whereas Swave splitting provides confirmation of the orientations bearing in mind that the USWS 'sees' a larger volume of the sample than DSA. Combined utilization of the two techniques has also shown the potential for examining rock microfeatures, such as microcrack systems present in the rocks.

IN SITU STRESS PREDICTION We would like to thank British Gas and Chevron for their support in supplying core samples, and the British Geological Survey and PPPTMGB 'Lemigas' Indonesia for partially funding the research. We also wish to thank J. W. Dennis for his support during the project.

References BROWN, E. T. & HOCK, E. 1978. Trends in relationships between measured in-situ stress and depth. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 15, 211215. CHARLES, Ph., HAMAMDJIAN,C. • DESPAX, D. 1986. Is the microcracking of a rock a memory of its initial state of stress? Proceedings International Symposium on Rock Stress and Rock Stress Measurements, Stockholm, 341-349. CRAMPIN, S. 1978. Seismic wave propagation through a cracked solid: polarisation as a possible dilatancy diagnostic. Geophysical Journal of the Royal Astronomical Society, 53, 467-496. - & LOVELL,J. H. 1991. A decade of shear-wave splitting in the earth's crust: what does it mean? what use can we make of it? and what should we do next? Geophysical Journal International, 107, 387-407. DESROCHES,J., MARSDEN,J. R. & COLLEY, N. M. 1995. Wireline open-hole stress tests in a tight gas sandstone. Proceedings International Gas Conference, Cannes. DEY, T. N. & BROWN, D. W. 1986. Stress measurements in a deep granite rock mass using hydraulic fracturing and differential strain curve analysis. Proceedings International Symposium on Rock Stress and Rock Stress Measurements, Stockholm, 351-357.

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DYKE, C. G. 1988. In-situ stress indicators for rock at great depth. PhD Thesis, Imperial College of Science and Technology, University of London. GARBIN, H. D. & KNOPOFF, L. 1975. The shear modulus of a material permeated by a random distribution of free circular cracks. Quarterly Applied Mathematics, 33, 296-300. KING, M. S., CHAUDHRY, N. A. & SHAKEEL, A. 1995. Experimental ultrasonic velocities and permeability for sandstones with aligned cracks. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 32, 155163. KOWALLIS, B. J. & WANG, H. F. 1983. Microcrack study of granite cores from Illinois deep borehole UPH3. Journal of Geophysical Research, 88, 73737380. OIKAWA, Y., MATSUNAGA, I. & YAMAGUCHI, T. 1993. Differential strain curve analysis to estimate the stress state of the Hijiori hot dry rock field. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 30, 1023-1026. STRICKLAND, F. G. & REN, N. K. 1980. Use of differential strain curve analysis in predicting insitu stress state for deep wells. Proceedings 21st US Symposium on Rock Mechanics, Rolla, Missouri, 523-533. TEUFEL, L. W. 1983. Determination of the principal horizontal in-situ stress directions from anelastic strain recovery measurements of oriented core from deep wells: application to the Cotton Valley formation of East Texas. In." NEMAT-NASSER, S. (ed.) Geomechanics, American Society of Mechanical Engineers, New York, 55-63. YALE, D. P. & SPRUNT, E. S. 1989. Prediction of fracture direction using shear acoustic anisotropy. The Log Analyst, 30, 65-70.

Dolomite cement distribution in a sandstone from core and wireline data: the Triassic fluvial Chaunoy Formation, Paris Basin R. H. W O R D E N

School of Geosciences, The Queen's University, Belfast, BT7 INN, UK

Abstract:The distribution of mineral cements in oil fields is critical to the spatial variation of porosity and permeability. The distribution of dolomite cement within fluvial Triassic Chaunoy sandstones in the Paris Basin was studied using core description, petrography, core analysis (porosity and permeability), wireline data interpreted to give mineralogy, porosity and permeability data and geochemical data. Petrographic analysis revealed that dolomite and quartz cements are the main diagenetic minerals. Using sonic transit time, density and neutron porosity log, the overall proportions of quartz, dolomite and shale as well as porosity for each depth interval could be resolved. Petrographic and core analysis data showed that permeability could be calculated from wireline-derived porosity and mineralogy data. There is excellent correlation between core analysis porosity and permeability and their wireline-derived equivalents. There is also excellent correlation between wireline-derived mineralogy data and quantitative petrographic mineralogy data. The wireline-derived mineralogy data show that dolomite is preferentially concentrated at the tops of most sand bodies. Porosity and permeability are consequently lowest at the tops of individual sand bodies due to the localized dolomite cement. There are a number of potential causes for this distribution pattern although geochemical and petrographic data showed that a combination of early pedogenetic dolomite cementation and later recrystallization, possibly due to an influx of organically-derived CO2, are most likely.

Knowledge of the way in which porosity and permeability are distributed throughout an oil field is an important building block in a reservoir model. The key factors which control porosity and permeability in sandstones are depositional characteristics such as grain size and sorting and diagenetic features such as cements and secondary porosity. Most reservoir simulation models incorporate sub-units of common primary sedimentary origin. The distribution of reservoir quality is thus usually defined in terms of the morphology of the sedimentary architecture. However, reservoir rocks seldom retain their depositional porosity. Instead, porosity is usually degraded by a variety of diagenetic processes. The effects of these processes are not necessarily confined to the boundaries of depositional sedimentary units. Common diagenetic processes may commonly either transcend sedimentary architecture or may lead to the subdivision of self-contained sedimentary units in terms of porosity and permeability. There is no framework for predicting diagenetic cement distribution in sandstones on the reservoir scale. It is not yet generally possible to predict or model reservoir porosity and permeability variations over the distribution of the primary sedimentary units due to the impact of diagenesis. This is clearly unsatisfactory and may lead to systematically incorrect reservoir models.

One of the key problems involved in describing the distribution of diagenetic cement is the cost (in terms of time and money) of acquiring the data. Petrographic data are usually collected at a far lower density than core analysis data (if at all), are harder to quality-control and are highly operator-dependent. In this paper, the method of assessing carbonate cement distribution in sandstones using petrophysical logs (hereafter known as wireline logs) will be described. This method was used to describe the distribution of dolomite cement in Triassic fluvial clastic sediments of the Chaunoy Formation in the Paris Basin, France. The controls on dolomite cement distribution will be discussed, the effects of dolomite cement (and by inference, quartz cement) on reservoir flow properties, defined, and possible mechanisms that controlled the carbonate cement distribution pattern investigated.

Geological setting The Paris Basin is an intracratonic basin with an aerial extent of approximately 6000km 2 and about 3000m of present day sediment infill deposited on Hercynian basement (Fig. 1; Pommerol 1974, 1978). There are two main permeable, petroleum-bearing reservoir units in the central part of the Mesozoic of the Paris

WORDEN,R. H. 1998. Dolomite cement distribution in a sandstone from core and wireline data: the Triassic fluvial Chaunoy Formation, Paris Basin. In. HARVEY,P. K. & LOVELL,M. A. (eds)

Core-Log Integration, Geological Society, London, Special Publications, 136, 197-2t 1

197

198

R.H. WORDEN

Fig. 1. Geological map of the Paris Basin with the approximate extent of the Triassic sandstones. The well under investigation (L) is marked. Basin; the Late Triassic (Keuper) fluvial sandstones and the Middle Jurassic marine carbonates (Pages 1987). The Paris Basin experienced a simple subsidence history that included periods of relatively rapid burial. Rifting started in the Permo-Triassic followed by thermal subsidence in the Jurassic and Cretaceous (Pommerol 1978; M6gnien 1980a,b; Brunet & Le Pichon 1982; Loup & Wildi 1994). Maximum burial in the central part of the basin occurred during the Oligocene-Miocene and was followed by minor uplift during and following Alpine and Pyrenean tectonism (M6gnien 1980a,b; Brunet & Le Pichon 1982; Pages 1987). Triassic sediments in the central part of the basin reached maximum burial depths of about 3000-4000 m. The Chaunoy Formation in the well examined is presently buried to between 2200m and 2500m. Sandwiched between the Triassic sandstones and the Mid Jurassic carbonates are organic-rich Liassic shales. They are mature to the point of oil generation and expulsion at the base of the Lias, in the centre of the basin (Herron & Le Tendre 1990). This source rock reached maturity at the time of maximum burial and charged both Triassic and Mid Jurassic reservoirs with oil (Poulet & Espitalie 1987). The Triassic sandstones are composed of several reservoir units. The Late Carnian to Norian Chaunoy Formation has limited aerial extent, lies in the deepest part of the basin, slightly to the West of the basin centre and has no outcrop (Fig. 1; Bourquin & Guillocheau 1993; Bourquin et al. 1993; Fontes & Matray 1993. Matray et al. 1993). The Chaunoy was deposited as a minor transgressive-regressive cycle within an overall transgressive phase that ended with Rhaetic marine sediments (Bourquin & Guillocheau 1993). The Chaunoy Formation

is composed of alluvial fan conglomerates, coarse-grained channel-fill fluvial sandstones and flood-basin siltstones. It was deposited in an arid environment as an alluvial and fluvial fringe to the western rifted margin of the basin (Bourquin & Guillocheau 1993; Bourquin et al. 1993). Locally important pedogenic and phreatic dolomite cements are found within the Chaunoy Formation (Sp6tl & Wright 1992). Burial diagenesis resulted in precipitation of abundant quartz and dolomite, and less common calcite and saddle dolomite cement (Demars & Pagel 1994; Worden & Matray 1995). Previous diagenetic studies of the Chaunoy Formation showed that quartz cement grew at temperatures a little lower than those attained at maximum burial, whilst sparry, rhombic ferroan dolomite cement grew at maximum burial (Demars & Pagel 1994). The pedogenic dolocrete has a limited range of 613C values ( - 7 to 0%o; Sp6tl & Wright 1992).

Methods Core description and petrography Slabbed core from the well was examined for general lithology, facies variations, sedimentary structures and grain size. Grain size of the core was measured at regular intervals by comparing core to standard grain size charts under a binocular microscope. Petrographic analysis was performed on 22 thin sections stained for carbonates and feldspars and impregnated with blue-dyed epoxy resin. Grain size and sorting class were assessed quantitatively in thin section by measuring sizes of one hundred grains per section. Detrital grains, cements and porosity were quantified by point counting using three hundred grain counts per section.

Petrophysical (wireline and core analysis) data Porosity and permeability core analysis data for the sampled well were made available to the authors by Elf (99 data points from the interval under investigation). Core porosity data have an uncertainty of somewhat less than 0.5% that arises due to the variable amount of stress relaxation following withdrawal of the core from the subsurface. Analytical errors are insignificant. Sonic transit time, neutron porosity, density and other wireline data, recorded at 5 cm intervals by petrophysical logging methods, were also made available by Elf. These data have been used to derive porosity and mineral

DOLOMITE AND CEMENT DISTRIBUTION IN A SANDSTONE

199

Table 1. Definition of terms and units used in equations 1 to 7 Term Definition At Atminx

At e P Pminx

p4

~bn (~nminx

4~n, minX pi ps qtz%

sonic transit time recorded by log (#see fl-1) sonic transit time of mineral X (#sec fl-l) sonic transit time of fluid in pore space (#sec fl 1) density recorded by log (g cm-3) density of mineral X (gcm -3) density of fluid in pore space (g cm-3) neutron porosity recorded by log (porosity units) neutron porosity of mineral X (porosity units) neutron porosity of fluid in pore space (porosity units) proportion of mineral X (as fraction of total rock volume) porosity (as fraction of total rock volume) permeability intercept of a regression line on a porosity--permability cross plot slope of a regression line on a porosity-permability cross plot percentage of quartz in a depth interval derived from wireline logs

proportions using methods outlined by Hearst & Nelson (1985) and Doveton (1994). The gamma log is commonly used to define the 'shaliness' (where shale in this context routinely describes the overall clay mineral content of the rock and is not a reference to the grain size or texture of the sedimentary rock) of sandstones although this approach is invalid for simple crystal chemical reasons. Composite gamma logs record the total potassium, thorium and uranium contents of the rock by detecting the -,/-rays associated with decay of the radioactive isotopes of these elements and their daughter products. Spectral gamma logs differentiate the v-radiation from the three elements. However, using any of the gamma logs for a shale or total clay mineral estimate is invalid. Potassium is commonly held in the minerals: Kfeldspar, illite and the mica group of minerals. Most clay minerals apart from illite do not contain potassium. Thus the potassium gamma signal records the relative abundance of Kfeldspar, illite and mica indiscriminately and does not record the shale or clay mineral content. The thorium gamma signal, often mistakenly thought to reflect specific clay minerals, records the abundance of thoriumbearing trace minerals and cannot be used to estimate volumes of clay minerals (Hurst & Milodowski 1996). Consequently, a multiple logtransformation approach was used to derive the shale content (as well as the dolomite and quartz contents) and gamma ray logs have not been used to derive the shale content. The signals from the sonic transit time (At), neutron porosity (On) and density logs (p) can be integrated and resolved for three mineral types and total porosity using three algorithms relating each separate log signal at any given

depth to solid grain volume (occupied by the three minerals) and the assumption that the sum of the three minerals fractions plus porosity equals unity. This also assumes linear relationships between mineral proportions and their contribution to the petrophysical signal. Thus, with four equations and four unknowns (proportions of three minerals plus porosity), the following algorithms can be solved simultaneously at each depth interval: At = mini. Atminl q- min2.Atmin2 + min3.Atmin3 + &to

(1)

p = minl .Pminl + min2.Pmin2 + min3.Pmin3 + CrO(2)

On = min 1. Onmi n 1 ~- min2. Onmin2 -4min3.Onmin3 + Ono

(3)

1 + min 1 + min2 + min3 + O.

(4)

The terms used in the equations above are defined in Table 1. Petrophysical responses of each mineral were taken from Rider (1986). Geochemical data

Fluid inclusion thermometry was performed using a Linkam THM600 heating-cooling stage with 0.1~ precision. Phase transition temperatures were determined by temperature cycling; heating experiments were conducted before freezing to prevent inclusion deformation by ice growth that would effect homogenization temperatures. Fluid inclusion homogenization temperatures were collected from quartz and

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Results Core description and p e t r o g r a p h y

Grain size data are displayed in Fig. 2. Most of the core is either fine-grained (silt/mud, grain size < 62 #m) or coarse-grained (coarse sand to conglomerate, i.e. grain size > 1000 #m). Fine-grained core is mottled in appearance, very well lithified and shows abundant evidence of pedogenesis with rootlet structures, rhizoeretions and nodules (see, for example, Sp6tl & Wright 1992). Petrographic analysis showed that fine grained units are highly dolomitic with a substantial clay mineral component. The dolomite is finely crystalline non-ferroan dolomite. The coarse grained sandbodies are composed of massive, largely structureless sediments. Petrographic analysis showed that the sandstones are sub-lithic to sub-arkosic (according to Folk 1974) with a significant volume of polycrystalline quartz grains ( 1 0 ~ 0 % of quartzose grains). The feldspar population is approximately equally split between plagioclase and Kfeldspar. An average sandstone composition is given in Table 2. Table 2. Average petrographic data from the Chaunoy Formation sand bodies. Twenty two samples were examined petrographically. The figures illustrate the importance of dolomite in the Chaunoy Formation Grain/cement type Fig. 2. Core description and petrographic data. Grain size is shown as a continuous log. The petrographic data are represented by bars at the appropriate depths with mineralogy represented (see key). Core analysis data are also displayed on this diagram. There are 99 porosity and permeability data points.

ferroan (rhombic) dolomite cements. Fluid inclusions could not be examined in the microcrystalline dolomite because of the limited resolution of the microscope. Six core samples from this well were examined by this technique giving more than one hundred data points. For carbon isotope analysis, N d - Y A G laser sampling was used following Smalley et al. (1992). This has a spatial resolution of about 50#m (ablation pit diameter) with analytical precision of +0.1%o for ~513C. Samples for laser ablation were plasma-ashed to remove any organic material (oil) in the pore system. The laser could be used to sample individual dolomite crystals within pores, without fear of contamination from any other crystals. Eight core samples were examined by this technique giving more than fifty data points.

Polycrystalline quartz Monocrystalline quartz (Total detrital quartz K-feldspar Plagioclase Quartzose lithic fragments Detrital mica Detrital clay Kaolinite Illite Chlorite Authigenic K-feldspar Authigenic Quartz Calcite cement Dolomite cement

Mean % 21.1 13.0 34.1 8.9 4.6 13.2 0.8 3.2 2.5 0.4 0.5 1.1 11.6 1.4 16.4

Standard deviation % 8.6 8.2 6.6) 4.1 3.5 8.8 1.1 5.4 4.2 1.1 0.9 1.4 8.5 5.9 22.0

Sandbodies contain two distinct dolomite morphologies. Sandbodies contain rhombic, pore-filling, ferroan dolomite crystals that are generally greater than 200#m in size (Fig. 3b). The rhombic ferroan dolomite is texturally and mineralogically chemically distinct from the dolocrete. The dolomite in the top portions of most sand bodies grades into the overlying silty

DOLOMITE AND CEMENT DISTRIBUTION IN A SANDSTONE

201

Fig. 3. Photomicrographs of (a) microcrystalline non-ferroan dolomite at the very top of a sand body with partial replacement of detrital silicate grains and (b) grain-rimming quartz cement (Q) and pore-filling rhombic ferroan dolomite (DOL) enclosing the quartz cement. Remnant porosity (~) is minor and occupies pore centres. Scale bars are 200 #m.

dolocrete layers and tends to be extremely finely crystalline. The proportion of microcrystalline dolomite increases upwards to the top of sand bodies. A 'floating grain texture' is present at the tops of sand bodies due to mass silicate graindissolution and replacement by microcrystalline dolomite (Fig. 3a). The sandstone also contains localized quartz cement (e.g. minor quartz cement labelled in Fig. 3b). Textural considerations show that the microcrystalline dolomite pre-dated the ferroan rhombic dolomite. To facilitate the subsequent comparison between petrographic data and wireline-derived

mineralogical data, the petrographic data have been coverted into proportions of quartz, dolomite and shale. In this manipulation, quartz is the sum of detrital quartz grains, quartz cement, quartzose lithic fragments and feldspar; dolomite is the sum of all type of dolomite and other carbonate minerals; shale is the sum of clay, micas, and micaceous lithic fragments. There is a broad correlation between grain size and p e t r o g r a p h i c a l l y - d e f i n e d m i n e r a l o g y : coarse- grained intervals are mostly quartz-rich, the finer intervals are relatively shale and dolomite rich (Fig. 2). However, the correlation

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Fig. 4. Porosity-permeability data from sandstones. Data have been subdivided by petrographicallydefined mineral proportions. High quartz content samples are those with greater than 80% quartz; medium quartz content samples have between 60% and 80% quartz; low quartz content samples have less than 60% quartz. Regression lines have been plotted through the core data for the high, medium and low quartz content samples. Note that the slope and the intercept of these regression lines changes systematically as the quartz content changes.

between grain size, mineralogy and reservoir properties is not perfect. Sand bodies can also have high dolomite contents (e.g. 2457-2458 m 2472-0m, 2482.5-2483.5 m etc., on Fig. 2). This pattern shows that dolomite content and grain size together, probably control the reservoir properties of the sandstone. The petrographic data seem to show that dolomite is concentrated in the top portions of the sandstone units (e.g. 2457m and 2472m) although insufficient samples were examined petrographically to prove that this pattern was common and predictable.

Fig. 5. Wireline sonic transit time, density and neutron porosity through the cored portion of the Chaunoy Formation.

is considerable scatter in the data; there is a wide range of permeability for a given porosity. This probably signifies that there is more than one control on the evolution of porosity and permeability.

Core analysis data

Wireline log analysis

Core analysis data are displayed as continuous logs in Fig. 2. Porosity 1.1-19.0%. Permeability varies from < 0.1 mD to > 5000 mD. Porosity and permeability are highest where the rocks are most coarse grained. However, again the correlation is not perfect; the tops of the sandbodies tend to have low porosity and permeability values relative to the middle and lower portions of sand bodies (Fig. 2). Consequently, grain size and facies variations cannot be used in isolation to understand or predict variations in reservoir quality. Core analysis data are also plotted on a conventional log-linear diagram (Fig. 4). There

Wireline log analysis has been used to determine porosity and mineralogy (with three components; quartz, dolomite and shale). These data have then been used to compute permeability. These data will be used subsequently to assess dolomite cement distribution within the reservoir. Sonic transit time, neutron porosity and density log data for the cored interval are presented as functions of depth in Fig. 5. The same data are cross-plotted in Fig. 6 with the positions of the three minerals added. Equations 1-4 can be solved for porosity plus three solid grain components. The logs have been converted

DOLOMITE AND CEMENT DISTRIBUTION IN A SANDSTONE

203

Fig. 6. Cross plots of (a) sonic transit time against density and (b) neutron porosity against density. The positions of the three mineral groups (quartz, dolomite and shale--where shale refers to all clay minerals and not a texture or fabric) used to define the mineralogy of the formation are marked on both plots. The position of the pore fluid is off the scale but the general direction is marked.

Fig. 7. Data quality assurance: (a) comparison of wireline-derived porosity and core analysis-derived porosity. There is a good correlation between the two datasets. The intercept on the x-axis shows that the wireline porosity data are over-estimating porosity by about 0.024 (note that this over-estimate is subsequently accounted for in all the following calculations and plots); (b) comparison of petrographically-determined quartz and wireline- derived quartz; (c) comparison of petrographically-defined dolomite and wireline-derived dolomite. Porosity and mineralogy from core and petrographic sources is well matched by the values defined from the transformed wireline logs.

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Fig. 8. Combination diagram of grain size data (derived from core description, Fig. 2) and mineral proportions, porosity and permeability (derived from wireline log analysis). There is excellent agreement between quartz proportion and reservoir quality. The agreement of these with grain size is complex. The tops of some sand bodies have a high dolomite content and correspondingly poorer reservoir quality (e.g. 2470-2471 m). Sand bodies are numbered for reference to Figs 2 and 9. Core analysis porosity and permeability data (dashed and faint) have been added to the diagram for comparison with the wireline-derived data.

into fractional porosity, and the fractional quantities of quartz, dolomite and shale. The rock was thus assumed to consist of three minerals; 'quartz' (all silica minerals and feldspar), 'dolomite' (all carbonate minerals) and 'shale' (all clay minerals). Each individual group of minerals 'quartz', 'dolomite' and 'shale') was assumed to have effectively uniform responses to the three wireline logging tools. Petrographic analysis shows that the quartz/feldspar ratio is generally much greater than about 4 (Table 2), suggesting that the assumption about the quartz component is reasonable. Feldspar and quartz have similar wireline responses (at least for sonic, density and neutron porosity logs) so that the arkosic portion of the sandstone is probably adequately accounted for. The lithic portion of the sandstone is probably represented by 'shale' together with quartz. Dolomite dominates the carbonate mineral population within the rock.

Shale represents the sum of all clay minerals in the rock, although preliminary quantitative Xray diffraction (XRD) data show that these are dominated by kaolinite and illite. Water saturation was calculated using resistivity logs, the Archie equation and neutron porosity values (and the ultimate porosity values computed from the simultaneous solution of the neutron porosity, density and sonic transit time logs were iteratively fed back into the Archie equation until convergence was achieved). The average wireline response properties of the mixed wateroil fluid were calculated depending on the specific saturation (Sw) at the depth interval. Fluid type was found to have little effect upon the subsequent calculations. The wireline-derived porosity data compare favourably to core analysis porosity data with a correlation coefficient of 0.74 (Fig. 7). The wireline porosity values slightly over-estimate

DOLOMITE AND CEMENT DISTRIBUTION IN A SANDSTONE the porosity (if the core porosity data are correct). Consequently, wireline-derived porosity data have been corrected for this slight overestimate by subtracting 0.024 from the fractional wireline porosity values to take the intercept through the origin (Fig. 7). The wireline-derived mineralogical data also compare favourably to the quantitative petrographic data, the two having very good correlation coefficients (average correlation coefficient of 0.84; Fig. 7). Thus, despite the paucity of petrographic data, it is possible to derive continuous and credible mineralogical data from wireline data. Porosity and mineral proportion data were smoothed by averaging over a 0.3 m interval to reflect the realistic resolution of the logging tools (Fig. 8; Hearst & Nelson 1985; Doveton 1994). The results of the wireline data transform into mineral proportions and porosity are given in Figs 8 and 9. There are distinct intervals that are enriched in dolomite and others enriched in quartz. The shale fraction tends to be highest in the dolomite zones. However, the tops of sand bodies have high dolomite contents in the absence of shale (e.g. 2470-2472m) without any corresponding change in grain size. This leads to asymmetry in the mineralogy of individual sandstone beds. The summary diagram, Fig. 9, shows that, on average, sand bodies have the most dolomite in the top quarter. The derivation of permeability from porosity is not a simple task. Permeability is, of course, affected by porosity, but it is also controlled by the shape and size of pore throats that connect pores. The degree of connectivity of the total porosity and the dimensions of pore throats are critical to permeability. It is not possible to derive permeability from a simple porosity value with any degree of accuracy using a simple transform in these rocks. However, recent network modelling work by Bryant et al. (1993) and Cade et al. (1994) has shown that permeability may be predicted from porosity if the fundamental controls on porosity evolution are known. The main generic controls on porosity loss are compaction and cementation. Cementation may be subdivided further between grainrimming cements and pore-filling cements. The different cement morphologies have different effects upon permeability for unit porosity loss due to their different effects upon the pore network. Chaunoy sandstones of the same depositional facies are cemented by both quartz and dolomite (Fig. 3b). Quartz cement forms approximately equal thickness overgrowths whilst dolomite cements tend to fill pores (Fig. 3b; Cade et al.

205

Fig. 9. Summary diagram illustrating the non-uniform distribution of dolomite and porosity in the Chaunoy Formation sand bodies. The numbers refer to the sand bodies on Figs 2 and 8. (a) Dolomite is preferentially concentrated in the top quarter of each sand body. (b) Conversely, porosity is concentrated in the middle two quarters of each sand body. 1994). These two different cement morphologies have profoundly different effects upon the pore network. Core analysis data from the Chaunoy Formation were subdivided on the basis of the quartzdolomite ratios using the wireline-derived mineralogy data. Regression analysis (Fig. 4) shows that the quartz-rich (and thus presumably quartz-cemented) samples have shallower porosity-permeability slopes (ps) and higher permeability intercepts (pi) than quartz-poor (and thus presumably dolomite-cemented) samples in accord with the network modelling discussed above. Algorithms were derived for describing the change in both slope and intercept of the porosity-permeability curves as a function of total quartz content: (intercept) pi = 2.777x 104X 10 (4"55xl~

(5)

(slope) ps = 30.75x 10 (-3"077x ~~ xqtz%)

(6)

in which 'qtz%' is the quartz fraction of the rock as defined by wireline analysis. It was thus possible to predict permeability as a function of the wireline-derived porosity and mineralogy using the following algorithm: permeability (mD) = pi x 10(ps•

(7)

The results of these calculations are displayed in Fig. 8. Inspection of Figs 2 and 8 shows that the wireline-derived permeability curve corresponds well to the core analysis data. Geochemical data

Fluid inclusion data are reported in Fig. 10. Rhombic ferroan dolomite grew at a range of

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R.H. WORDEN

Fig. 10. Fluid inclusion homogenization data from quartz and rhombic ferroan dolomite. Whilst there is overlap between the temperatures of growth of dolomite and quartz, these data support the late (maximum burial) growth of rhombic ferroan dolomite cement following quartz cement growth in the Chaunoy Formation.

temperatures with a mean of 119~ This is a considerably higher temperature than the quartz cement (mean 103~ and confirms the textural evidence (Fig. 3b) that ferroan rhombic dolomite grew after quartz. The temperature for dolomite growth corresponds to maximum burial and the time of oil generation from the Liassic source rocks. Stable isotope data from ferroan rhombic dolomite are given in Fig. 11. These data are compared to carbon isotope data from pedogenic dolomite. The ferroan rhombic dolomite has considerably lighter carbon isotopes than the pedogenic dolomite. The ferroan rhombic dolomite has a range of 813C values consistent with input from recrystallzed pedogenic dolomite and input from a source depleted in 13C.

Fig. 11. Carbon isotope data from rhombic ferroan dolomite with data from the pedogenic dolomite (after Sp6tl & Wright 1992; Sp6tl et al. 1993). The rhombic ferroan dolomite represents mixing between the indigenous pedogenic carbonate and a source of carbonate characterized by carbon relatively depleted in 13C. This must indicate a major organic input into the system (probably in the form of either aqueous bicarbonate, or CO2 dissolved in oil or water).

used to define the spatial distribution of dolomite cements in these sandstones. The derivation of porosity, mineralogy and permeability from wireline data has distinct advantages over core analysis and petrographic data. Most importantly, mineralogical data from logs can be derived for uncored intervals. Petrographic data are usually sparse (due to cost and time) and are 'operator'-dependent. In contrast, wireline data are typically available for most wells in a reservoir and are (in principle) operator-independent. Petrographic data are rarely collected in such abundance that cement distribution can be observed within reservoir units, whereas such data can be derived from wireline mineralogical analysis.

Discussion Quantitative mineralogical data have been generated from sonic transit time, density and neutron porosity wireline logs. Gamma logs cannot be used for mineral identification due to the variable site of radiogenic potassium in a variety of minerals and the non-concordance between uranium and thorium and specific minerals (Doveton 1994; Hurst & Milodowski 1996). The Triassic sandstones and mudstones of the Paris Basin have been resolved into quartz, shale and dolomite. Dolomite has a diagenetic (i.e. non-primary) origin. Wireline logs can be

Amount and distribution of dolomite cement in the Chaunoy sandstone Petrographic analysis hinted at the heterogeneous distribution of dolomite cement in the Chaunoy formation sandstones (Fig. 2). Without a major sampling and petrographic analysis programme, it would be difficult to analyse and describe that heterogeneity. The interpreted wireline data have confirmed that dolomite is not homogeneously distributed throughout the Chaunoy Formation sandstone (Figs 8 and 9).

DOLOMITE AND CEMENT DISTRIBUTION IN A SANDSTONE

207

Fig. 12. Theoretical dolomite distributions from four potential controlling processes. The model represents a sand body sandwiched between pedogenic dolocrete layers. (a) Pedogenic dolomite cement; there would be most dolomite at the top of each sand body. (b) Dolomite cemented, sourced from the dolocrete during burial, transported by diffusion; cement should be equally abundant at the tops and bases of sand bodies with a minimum at the centre. (c) Dolomite distribution controlled by high permeability streaks enabling input from external sources; fluvial sandstones usually fine upwards leading to high permeability bases and thus most dolomite at sand body bases. (d) Dolomite distribution controlled by the relative buoyancy of oil (which may have carried dissolved CO2) or a separate CO2 gas phase caused dolomite cementation and thus leading to most dolomite at the tops of sand bodies.

Dolomite in the Chaunoy has either a pedogenic (i.e. very early diagenetic) or burial diagenetic origin (Fig. 12). Detrital dolomite may be discounted as an option because of the relatively soluble nature of dolomite and the perfect crystal forms observed in core and thin section (Fig. 3). Wireline data cannot be used to discriminate between different dolomite grain morphologies (e.g. microcrystalline or coarse rhombic) or between dolomites of different mineral chemistry (e.g. non-ferroan or ferroan dolomite). The wireline data have shown that the tops of most coarse grained sandbodies have the greatest quantity of dolomite (Figs 8 and 9). The dolomite content varies between, as well as within sandbodies. Sand bodies 3, 4, 5, 7, 8 and 9 all have significantly more dolomite in the top quarter of the sand body than in other quarters. However, sand body 1 has much more dolomite than sand body 5. Dolomite can occupy more than 50% of the solid portion of a sand body (e.g. sand body 1). The partially replacive nature of the dolomite within sand bodies has already been established from petrographic data (Fig. 3a) so that the high dolomite contents probably

reflect partial replacement of detrital silicate mineral grains as well as precipitation of dolomite into pre-existing pore spaces.

Effect of dolomite cement upon the reservoir properties of the Chaunoy Formation sandstone The present day porosity of the quartz-rich samples is significantly less than the porosity that would result from compaction alone (with no cementation) of quartzose sandstones at these depth of burial. Quartzose sandstones should have approximately 25-30% porosity after compaction during maximum burial to about 3000m (see, for example, North 1985). The actual porosities, even in the quartz-rich intervals, are only as high as about 19% indicating that some of the quartz in the rock must be quartz cement. The main control on porosity and thus permeability in the quartz-rich portions of the rock must be the extent of quartz cementation. Quartz-rich portions of sandbodies have

208

R.H. WORDEN Thus, not only does the dolomite cement preferentially obscure porosity at the tops of the sandstone units, but it also leads to disproportionately lower permeabilities than quartz-cemented sandstones of similar porosity.

Origin of dolomite cement in the Chatmoy Formation sandstone

Fig. 13. Sketch of the morphologies of quartz cement and dolomite cement in a porous sandstone matrix. Quartz cement typically forms overgrowths and tend to leave pores relatively unobstructed and thus has a minimal impact upon permeability (see also Fig. 4). Dolomite tends to form rhombic euhedral crystals that sit in pores, blocking porosity to flowing fluids and thus reducing permeability to a greater degree than an equivalent volume of quartz cement. better permeabilities for a given porosity than their quartz-poor equivalents (Figs 2 and 4). For example, in dolomite-rich, quartz-poor samples with 10% porosity, permeability is typically about 1-2mD. In dolomite-poor, quartz-rich samples with 10% porosity, permeability is typically, about 10-100mD. This is reflected by the slightly steeper permeability-porosity gradient and higher permeability intercept of the regression line through the dolomite-rich, quartz-poor samples than the regression line through the dolomite-poor, quartz-rich samples on Fig. 4. This pattern confirms that the main mechanism of porosity-loss in the quartz-rich samples (quartz cementation) is less detrimental to permeability than porosity-loss in the quartzpoor samples (dolomite cementation) as suggested by Cade et al. (1994). Dolomite cement in the Chaunoy Formation sand bodies tends to fill pores and block pore throats thus degrading permeability at a greater rate than quartz cement that forms equal-thickness rims to grains (Fig. 13).

The dolomite-rich fine-grained (mud and silt) beds in the Chaunoy Formation resulted from dolocrete pedogenesis (Sp6tl & Wright 1992) in inter-channel facies. The similarity between the (very fine) crystal size and texture of the dolomite in the fine beds and the dolomite at the very tops of the sand bodies (Fig. 3a) suggests that some of the dolomite in the sand bodies may be related to the formation of the dolocrete during pedogenesis The replacive nature of the finely crystalline dolomite in the sand bodies, as indicated by the corrosion of detrital quartz and feldspar grains (Fig. 3a), supports the development of this dolomite by pore waters that simultaneously dissolved silicate minerals and precipitated carbonate minerals during pedogenesis. However, much of the dolomite within the sand bodies does not have the same morphology and chemistry as the dolocrete material: much occurs as coarsely crystalline, ferroan dolomite rhombs (Fig. 3). From the textural and mineral chemical evidence, this must have a different genesis than the dolocrete. Textural evidence shows that rhombic ferroan dolomite post-dates quartz cement overgrowths (Fig. 3b). Aqueous fluid inclusion temperatures in Fig. 10, and also reported by Sp6tl et al (1993) and Demars & Pagel (1994), from rhombic ferroan dolomite are somewhat higher than present day temperatures, suggesting that dolomite grew at close to maximum burial and temperature conditions in the Oligocene/Miocene (Loup & Wildi 1994). Maximum burial of the sedimentary pile during the Oligocene/Miocene was also the time of petroleum generation and migration from the Liassic source rocks into the Chaunoy Formation. Rhombic ferroan dolomite cement therefore grew in the Chaunoy Formation at approximately the same time as oil was being generated from the overlying Liassic source rocks (Poulet & Espitalie 1987). Carbon stable isotope data for the burial diagenetic dolomite cements (Fig. 11; Worden & Matray 1995) indicate that carbon depleted in 13C has been added to the dolomite relative to the pedogenic dolocrete (Sp6tl & Wright 1992). Carbon depleted in 13C is thought typically to

DOLOMITE AND CEMENT DISTRIBUTION IN A SANDSTONE have an organic origin (e.g. Longstaffe 1989). The most obvious source of organically-derived bicarbonate or CO2 in the Paris Basin is the Liassic shale source rock. pH-buffered rocks undergo carbonate mineral precipitation when the partial pressure of CO2 is increased (Lundegaard & Land 1989) suggesting that at least some of the rhombic ferroan dolomite cement may be the direct result of bicarbonate or CO2 influx increasing the partial pressure of CO2. Liassic source rocks may have expelled CO2 during or before oil generation. The Triassic sandstones in the Paris Basin are presently in equilibrium with CO2 in the reservoir; that is partitioned between the two liquid phases: oil and water (Matray et al. 1993). The equilibrium partitioning of CO2 between formation water and oil suggests that CO2 may have been brought into the reservoir by the oil in solution. Subsequent partitioning of CO2 into the formation water may then have caused dolomite supersaturation and precipitation. Alternatively, CO2 may have migrated into the Chaunoy sand bodies as a separate gas phase resulting from thermal decarboxylation of organic matter prior to the onset of oil generation. Whatever the mechanism, isotopic data dictate that an increase in the partial pressure of CO2 (from an organic source) was most likely responsible for the precipitation of dolomite cement in the sandbodies during diagenesis at close to maximum burial.

Origin o f the dolomite cement distribution pattern Dolomite cement is generally concentrated at the tops of sand bodies in the Chaunoy Formation (Figs 7 and 9). There are several potential generic controls on dolomite distribution patterns (Fig. 12): (1) The cement at the tops of sand bodies may be a direct result of pedogenesis that occurred at the same time as the development of the pedogenic dolocrete in the fine grained units. This would occur preferentially at the tops of sand bodies adjacent to zones of active dolocrete pedogenesis. This process is probably at least partly responsible for the dolomite cement distribution in the sand bodies. (2) In principle, dolomite distribution in sand bodies may be due to diffusion from the pedogenic dolocretes that encase the sand bodies. In this case the dolomite would be redistributed by diffusion from the dolo-

209

crete into the sand bodies. This would influence the top and base of sand bodies eqpally and result in a minimum dolomite cement content at the centre of the sand bodies. Note that this is not observed (Figs 8 and 9) and that rhombic ferroan dolomite has a carbon isotope signature that is different from the pedogenic dolomite (Sp6tl & Wright 1992; Worden & Matray 1995). (3) Cement distribution could be influenced by reservoir quality at the time of cementation. High permeability streaks or gradational permeability may have focussed flow and input of CO2 into specific portions of the rock. Fluvial sandstones usually fine upwards resulting in diminishing permeability towards sand body tops. This would lead to the most extensive dolomite cementation occurring at the bases of sand bodies. However, note that the Chaunoy sandstones do not fine upwards (Fig. 2) and do not have dolomite preferentially at sand body bases. (4) Isotope data (Fig. 11) suggest that some of the carbon in the dolomite has an organic source and might have come from the oil source rock. Oil and CO2 may have migrated into the rock at about the same time (i.e. as CO2 dissolved in oil, Matray et al. 1993). Alternatively, CO2 may have migrated into the rock separately as a free gas phase. Due to buoyancy, the tops of each sand body should be the first part of the sandstone to encounter either oil (laden with CO2) or free CO2 gas. In summary, the tops of each sandbody may have received CO2 preferentially and thus caused localized dolomite precipitation. However, it is generally considered that oil emplacement hinders diagenetic processes so that the opportunity for this process to operate may be limited to a window of opportunity between the onset of oil emplacement and some elevated level of oil saturation (e.g. Worden et al. 1998). The absence of dolomite cement at sand body bases and abundance at sand body tops, the reported organic carbon isotope signal in the rhombic ferroan dolomite and the mixture of pedogenic dolomite textures and burial diagenetic textures in the sand bodies suggest that options 1 and 4 together are probably responsible for the distribution of dolomite in the Chaunoy sandbodies. The key implication from this analysis of dolomite cement distribution is that the dolo-

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R.H. WORDEN

mite is heterogeneously distributed in the reservoir. A reservoir model (e.g. for simulation purposes) should take account of the fact that, despite approximately uniform grain size, porosity and permeability are not uniformly distributed due to preferential cementation at the tops of individual sandbodies. The combination of petrography, geochemistry and petrophysics was necessary to produce a model of cement distribution in this case. There are no 'off the shelf' models that can presently be fitted to the distribution of cements in reservoir sandstones in general. In time, generic models may be available as more case studies of cement distribution are performed, but until that time, each reservoir should be analysed using a similar combination of tools as that used in this study if reservoir quality heterogeneity is an issue.

Conclusions (1) Wireline petrophysical data have been successfully manipulated to give mineralogy in terms of the amounts of quartz, shale and dolomite, as well as porosity. (2) Core analysis data show that dolomite cement has a more detrimental effect upon permeability than quartz cement. Permeability has thus been calculated from the wireline porosity data using algorithms that account for the variation in mineralogy as well as porosity. (3) Petrography and, more importanly, wireline log data, have shown that dolomite c e m e n t is not u n i f o r m l y d i s t r i b u t e d t h r o u g h o u t the sandstones within the C h a u n o y Formation. Rather, dolomite cement is localized within the top portions of individual sandstone units. (4) Reservoir quality in the Chaunoy Formation is not just a function of depositional facies but is also a function of localized cement distribution. Building a reservoir model using primary sand body architecture alone is insufficient to correctly describe reservoir quality. (5) Sand bodies contain microcrystalline nonferroan and replacive dolomite as well as rhombic ferroan and pore-filling dolomite. Textural and mineral chemical data show that the microcrystalline dolomite probably grew during pedogenesis of the overlying fine-grained facies. Fluid inclusion and isotope data, together with textural evidence, show that the rhombic ferroan dolomite probably grew at close to maximum burial in the mid Tertiary in the presence of organically derived CO2.

(6) Dolomite cement may be localized at the tops of the sand bodies because of the proximity of overlying fine-grained units when they were undergoing pedogenesis and because the tops were the first part of each sand body to receive a charge of CO2. The CO2 influx may have occurred as a separate buoyant gas phase or as a gas dissolved in oil. (7) Reservoir simulation of sandstones should account for the fact that cement patterns do not necessarily follow primary sedimentary architecture. Cements may typically be heterogeneously distributed in individual sand bodies and this may have important consequences for how petroleum is produced to optimize flow rate and recovery. I would like to thank Elf-Aquitaine (F. Walgenwitz and G. Sambet especially) for kindly providing the core analysis and wireline data. Part of the study was the result of a collaborative research programme including BP, BRGM, Elf-Aquitaine, the University of Paris V1 and the European Community under contract JOUF-0016c. D. C. Herrick and an anonymous reviewer are thanked for identifying key areas of the manuscript for improvement.

References BOURQUIN,S. 8z GUILLOCHEAU,F. 1993. Gbometrie des sbquences de d6p6t du Keuper (Ladinien Rh&ian) du Bassin de Paris: implications gbodynamiques. Comptes Rendus Acad~mie des Sciences, Paris. 317, S6rie 2, 1341-1348. , BOEHM, C., CLERMONTE, L, DURAND, M. & SERRA, O. 1993. Analyse facio-sbquentielle du Trias du centre-ouest du bassin de Paris fi partir des donnbes diagraphiques. Bulletin de la Societe G~ologique Francais, 164, 177-188. BRUNET, M.-F. & LE PICHON,X. 1982. Subsidence of the Paris Basin. Journal of Geophysical Research, 87, 8547-8560. BRYANT, S., CADE, C. • MELLOR, D. 1993. Permeability prediction from geological models. American Association of Petroleum Geologists Bulletin, 77, 1338-1350. CADE, C., EVANS,I. J. 8s BRYANT,S. 1994. Analysis of permeability controls: a new approach. Clay Minerals, 29, 491-501. DEMARS, C. & PAGEL, M. 1994. Palbotemp6ratures et pal6osalinites dans les gr~s du Keuper du Bassin de Paris: inclusions fluides dans les min6raux authig~nes. Comptes Rendus Acad~mie des Sciences, Paris. 319, serie 2, 427-434. DOVETON, J. H. 1994. Geologic log analysis using computer methods. AAPG computer applications in geology, 2. American Association of Petroleum Geologists, Tulsa, USA. FOLK, R. L. 1974. Petrology of sedimentary rocks. Hemphill, Austin.

DOLOMITE AND CEMENT DISTRIBUTION IN A SANDSTONE FONTES, J. C. & MATRAY, J.-M. 1993. Geochemistry and origin of formation brines from the Paris Basin. Part 2, Saline solutions -A associated with oil fields. Chemical Geology, 109, 177-200. HEARST J. R. & NELSON, P. H. 1985. Well logging for physical properties. McGraw-Hill, New York HERRON, S. L. & LE TENDRE, L. 1990. Wireline sourcerock evaluation in the Paris Basin. In: Huc, A. Y. (ed.) Deposition of organic facies. American Association of Petroleum Geology Studies in geology, 30, 57-71 HURST, A. & MILODOWSKI,A. 1996. Thorium distribution in some North sea sandstones: implications for p e t r o p h y s i c a l e v a l u a t i o n . Petroleum Geoscience, 2, 59-68. LON~STAVFE, F. J. 1989. Stable isotopes as tracers in clastic diagenesis: In: HUTCHEON J. (ed.) Miner-

alogical Association of Canada short course in diagenesis. 201-277. LouP, B. & WILDI, J. W. 1994. Subsidence analysis in the Paris Basin: a key to Northwest European intracontinental basins? Basin Research, 6, 159177. LUNDEGARD, P. D. & LAND, L. S. 1989. Carbonate equilibria and pH buffering--response to changes in PCO2. Chemical Geology, 74, 277-287. MATRAY, J.-M., FOUILLAC,C. & WORDEN, R. H. 1993. Thermodynamic control on the chemical composition of fluids from the Keuper aquifer of the Paris Basin In: PARNELL, J. RUEFEL, A. H. & MOLES N. R. (eds) Extended abstracts from Geofluids '93, 12-16. MEGNIEN, C. 1980a. Tectogen+se du Bassin de Paris: etapes de L'evolution du bassin. Bulletin de la Societe Gdologique Francais 22, 66%680. - - , 1980b. Synthdse gdologique du bassin de Paris. Stratigraphie et paleogeographie. M e m o i r e BRGM 101, 466.

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NORTH, F. K. 1985. Petroleum Geology. Allen and Unwin, Boston PACES L. 1987. Exploration of the Paris Basin. In: BROOKS, J. & GLENNIE, K. (eds) Petroleum Geology of North West Europe. Graham and Trotman, UK, 87-93. POMMEROL, C. 1974. Le bassin de Paris. In: DEBELMAS, J. (ed.) Geologie de la France. Doin, Paris, 230258 , 1978. lEvolution pal6og6ographique et structurale du Bassin de Paris, du Pr6cambrian /t l'actual, en relation avec les r6gions avoisinantes. Geologie en Mijnbouw, 57, 533-543. POULET, M. & ESPITALIE, J. 1987. Hydrocarbon migration in the the Paris Basin In: DOLI6EZ, B. (ed.) Migration of hydrocarbons in sedimentary basins. Editions Technip, Paris, 131-171. RmER, M. H. 1986. The geological interpretation of well logs. Blackie. Glasgow. SMALLEY, P. C., MAILE, C. N., COLEMAN, M. L. & ROUSE, J. L. 1992. LASSIE (laser ablation sampler for stable isotope extraction) applied to carbonate minerals. Chemical Geology (Isotope Geoscience Section), 101, 43-52. SPOTL, C. & WRIGHT, V. P. 1992. Groundwater dolocretes from the Late Triassic of the Paris Basin, France: a case study of arid, contintental diagenetic facies. Sedimentology, 39, 1119-1136. - - , MATTER, A. & BREVART,O. 1993. Diagenesis and pore water evolution in the Keuper reservoir, Paris Basin (France). Journal of Sedimentary Petrology, 63, 909-928. WORDEN, R. H. & MATRAY, J.-M. 1995. Cross formational flow in the Paris basin. Basin Research, 7, 53-66. --, SMALLEY,P. C. & OXTOBY,N. H. (1988) Can oil emplacement prevent quartz cementation in sandstones? Petroleum Geoscience, 4.

Conjunctive interpretation of core and log data through association of the effective and total porosity models P. F. W O R T H I N G T O N

Gaffney, Cline & Associates, Bentley Hall, Blacknest, Alton, Hampshire GU34 4PU, UK Abstract: Traditionally, the deterministic open-hole petrophysical evaluation of non-Archie primary reservoirs has been undertaken exclusively within one or other of two intergranular systems, those of effective and total porosity. Yet, these interpretative models can be considered conjunctively with the object of inter-model validation of petrophysical interpretation. These considerations reveal ways of demonstrating the numerical compatibility of the two approaches. The compatibility is expressed in terms of equalities that contain core-calibrated, log-derived parameters and that are founded on the underlying petrophysics. The equalities must be satisfied if the petrophysical procedures are to be applied consistently and correctly. These inter-model algorithms constitute a basis for a proposed quality assurance scheme in well-log interpretation that goes beyond tying log data back to core. They suggest quality control points at which core-calibrated log data can be examined to assess the meaningfulness and performance of interpretation procedures at different stages of the petrophysical evaluation process. These assessments form a basis for the development of measures of confidence in the practice of open-hole well-log interpretation for porosity and hydrocarbon saturation, regardless of whether the interpretation is ultimately set in the context of the effective or the total porosity model. More generally, the subject matter forms part of a broader thrust to introduce a systematic quality assurance culture into open-hole petrophysical interpretation.

Open-hole petrophysical evaluation of nonArchie rocks, those that do not satisfy the conditions for the application of the laws of Archie (1942), has traditionally drawn upon either effective or total porosity concepts as a basis for the determination of reservoir porosity and fluid saturations. The difference between the two concepts lies in the interpretative treatment of the electrochemically-bound interstitial water. This should not be confused with capillary bound water, whose volume can be an order 9f magnitude greater (Pallatt & Thornley 1990), nor with those dual-porosity waters that are distinguished by pore type. Petrophysicists have usually operated the effective and total porosity models discretely, selecting one or the other at an early stage of the formation evaluation process. This exclusive choice has been driven by company culture, software considerations, statutory requirements, or technical or personal preference. The practice of selecting a discrete interpretative model constrains the manner in which core data can be used to support and validate log interpretation. Thus, for example, effective porosity cannot easily be determined in the laboratory, and yet these data are strictly required by the effective porosity model in order to control the porosity interpretation of neutron~lensity log cross plots. In contrast, the electrochemical shale parameters needed to

evaluate water saturation as per the total porosity model can be determined in the laboratory but they cannot be measured directly downhole. The constraints imposed by an exclusive porosity model therefore limit the benefit that can be derived from the ensuing integrated analysis of laboratory and downhole data. The key to improved core and log interpretation is to operate the effective and total porosity models in parallel, using the cross-linkages between them to transpose the advantages of one in support of the other, especially where core data can be used to provide quality control on the log interpretation. The purpose of this paper is to develop the opportunities for improved quality assurance in formation evaluation, in accordance with earlier projections (Worthington 1991), by considering how the effective and total porosity models can be operated conjunctively to allow inter-model validation of petrophysical interpretation. The primary aim is to demonstrate the numerical equivalence of the two models through equalities that contain core-calibrated, log-derived parameters and that honour the principles of the underlying physics. Thus, the objective is an interpretative scheme that brings together traditionally separate areas of petrophysical systemics within a quality-controlled integrated framework.

WORTHINGTON,P. F. 1998. Conjunctive interpretation of core and log data through association of the effective and total porosity models. In: HARVEY,P. K. 8s LOVELL,M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 213-223

213

214

P.F. WORTHINGTON

Fig. 1. Effective and total porosity models for a water-wet reservoir.

Philosophy of formation evaluation Traditional formation evaluation practice is set within either the effective or the total porosity system, although one or two procedures that are seen as transgressing this otherwise exclusive divide have emerged over the past 15 years (e.g. Juhasz 1981). The basic difference between the effective and total porosity approaches can be summarized with the aid of Fig. 1, which describes the key parameters for a water-wet reservoir. A nomenclature is provided at the end of the text. The effective porosity system regards those waters that are electrochemically bound to (clay) mineral surfaces as an integral part of the minerals themselves. Therefore, the bound-water porosity qbbw is incorporated within a wetted clay-mineral fraction, which is loosely termed a wetted shale volume fraction Vsh, and which is allowed to have different physical properties from those of the clean rock matrix. Only the electrochemically-free fluids comprise the porosity, which is termed 'effective'. Some authors have used the term 'effective clay mineral volume' to be synonymous with Vsh (Hurst & Nadeau 1994), but note with caution that others have used the seemingly related term 'effective clay' specifically to distinguish a clay mineral that is electrochemically active from one that is not (Johnson & Linke 1977). In contrast, the total porosity system separates the electrochemically bound waters from the clay-mineral fraction and groups these with the free fluids that occupy the remainder of the pore space. Therefore, d0bw is distinct from the clay-mineral fraction, which is sometimes loosely termed a dry clay fraction Vd. The dry clay is required to have the same physical properties as those of the clean rock matrix, but it is allowed different electrochemical char-

acteristics, quantified through the cation exchange capacity per unit pore volume Qv. All constituent fluids comprise the porosity, which is termed 'total'. Despite this seemingly all-embracing name, the term 'total porosity' does not include fracture porosity, and the sum of these is better described as 'absolute porosity'. The role of the effective and total porosity systems within the overall scheme of formation evaluation is governed in some quarters by the polarization of the subject area into statistical and deterministic methods of interpretation. These approaches, too, need not be operated exclusively, but their integrated use extends beyond the scope of this paper and is the subject of another that is in preparation. Statistical methods of petrophysical interpretation are based on the global approach to the solution of log response equations (Mayer & Sibbitt 1980). If these equations contain characterizing shale properties and solve for a wetted shale fraction, the computed porosity will be an effective porosity. If the response equations do not contain characterizing shale properties and do not solve for a wetted shale fraction, the implicit requirement for a total porosity approach must be one of identical log responses to clean rock matrix and dry clay minerals for all the log responses represented within the input matrix over the evaluation interval. The highly tenuous nature of this general assumption inhibits the meaningful operation of the global approach in the total porosity system. On the other hand, deterministic methods can be operated in both the effective and the total porosity systems, because logs can be used more selectively on the basis of their being fit-forpurpose. Therefore, the following discussion is set within the context of deterministic petrophysics. The scheme of deterministic open-hole petro-

EFFECTIVE AND TOTAL POROSITY

Effective porosity model

RESERVOIR

t

FORMATIONWATERSALINITY

CLAY-MINERALCONTENT 1

I

ARCHIE

POROSITY

Sw

"7

+ +

NON-ARCHIE

TOTAL I EFFECTIVEpoROSI ] TY I POROSITY

EFFECTIVE Sw

215

+

I

I TOTAL Sw

Fig. 2. Scheme of deterministic open-hole petrophysics. physics is illustrated in Fig. 2. Reservoirs with a high formation-water salinity and a low claymineral content are usually termed Archie reservoirs, wherein the effective and total porosities are essentially the same, because there are negligible bound-water effects. Otherwise, they are termed non-Archie reservoirs, because there can be a significant bound-water saturation. Non-Archie reservoirs can be evaluated in terms of either effective or total porosity but, whichever parameter is adopted, the subsequently derived water saturations must also be set within that same porosity system, for consistency. Exceptions to this simplified distinction include fine silty reservoirs and those where the rock matrix exhibits microporosity. In both cases, non-Archie behaviour can be caused by a low surface charge density integrated over a huge pore surface area rather than the conventional case of a higher surface charge density (due to strong cation-exchange characteristics) integrated over a more limited pore surface area. It is difficult to accommodate such cases of high pore surface area within either the effective or the total porosity system. In the following discussion the context is one of dispersed shales within a water-wet reservoir that has no fracture porosity and whose matrix comprises sandstone, limestone or dolomite, or some mixture thereof.

Because the chemically-bound water is included within a wetted shale fraction, logs are corrected for shale effects so that the bound water might be removed from consideration. The wetted shale is therefore replaced by electrochemicallyinert rock of identical geometry and with the same physical properties as the clean rock matrix. This is done by using the generic correction algorithm:

Xcorr=X - Vsh (Xsh -Xma )

(1)

where X is the log response, Xsh is the log response to shale, Xma is the log response to clean rock matrix, and Xcorr is the log response corrected for the effect of shale. Equation (1) should use Vsh values that are derived from a compatible shale indicator. For example, V~h from the gamma log might not be appropriate to correcting the density-log response whereas V~h derived from a neutron-density shale indicator would be more suitable. In general, the resulting values of Xcorr become less accurate with

increasing Vsh. After applying equation (1) to the sonic, density and neutron logs, effective porosity can then be evaluated as for clean sands:

doe=( x .... --Xma)/(X f --Xma ).

(2)

The results are implemented over net sand intervals, which can be selected subsequently. Effective water saturation Swe is the fractional water content of the free fluid. It is evaluated using a shaly-sand conductivity algorithm, such as the modified Simandoux equation (Bardon & Pied 1969): Ct = (Cw/Fe*)

awen* + Vshfshawe n*-I

(3)

where Ct is the conductivity of the reservoir rock, Cw is the conductivity of the formation water, Csh is the conductivity of the wetted shale, n* is the intrinsic Archie saturation exponent, and the intrinsic formation factor Fe* is compatible with the effective porosity system in that it is calculated from doe as follows:

Fe* = a*/doem*

(4)

where a* and m* are the intrinsic Archie porosity coefficient and exponent, respectively. A scheme for deterministic petrophysical interpretation (with a* = 1) within the effective porosity system is presented as Fig. 3. The immediate deliverables are dOeand She, where She

216

P.F. WORTHINGTON

Shale-corrected Log Response DENSITY NEUTRON SONIC

_I -

Porosity Oe

L F

] ARCHIE'S [ ~ A=W FIRST 1F / Oee.m

Core control in clean zones HELIUM POROSITY Core control INTRINSIC POROSITY

EXPONENT m*

Formation water sample WATER CONDUCTIVITY Cw

UNIFIED SHALE / VOLUME FRACTION Vsh Jl Log Response LATEROLOG

INDUCTION Ct C sh

/

I

I_ ~_1 MODIFIED SIMANDOUX EQUATION Ct=Cw

I

I

F-~

Swen +Vs h Csh Swn-1

Core control INTRINSIC SATURATION EXPONENT

Oe Swe

n*

Fig. 3. Petrophysical interpretation within the effective porosity system.

is the effective hydrocarbon saturation such that She = 1-Swe.

as that of Waxman & Smits (1968): C t = ( C w / F t * ) S w n• -q- (BQv/Ft*)Swtn*-I

Total porosity model The electrochemically-bound water is intuitively separated from a dry clay-mineral fraction and is included within the porosity. Logs are not corrected for the effects of dry shale, which is therefore presumed to have the same physical properties as the rock matrix. The assumption of identical physical properties for dry shale and matrix is approximately satisfied only in the case of density. Total porosity is therefore evaluated from the density log as for clean sands: dot = (Pg-- Pb)/(Pg-- Pf )

(5)

where Pb is the log-measured bulk density, pf is the density of interstitial fluids within the volume sensed by the density tool, and pg is the grain density rather than a pure matrix density. The results are implemented over net sand intervals, which must be specified at the outset, because grain density will take account of constituent shale, and this might cause intervaldependent departures from classical matrix values, giving rise to a potential non-conformance with the assumptions of the method. Total water saturation Swt is the fractional water content of the total fluid. It is evaluated using a shaly-sand conductivity algorithm, such

(6)

where Qv is the cation exchange capacity per unit pore volume (equiv. litre-1), B is the equivalent conductance of the (sodium) clayexchange cations (S m -1 equiv. -1 litre), a function of Cw, and Ft* is compatible with the total porosity system in that it is calculated from dot as follows: Ft* = a*/dotm*

(7)

A scheme for deterministic petrophysical interpretation (with a * = l ) within the total porosity system is presented as Fig. 4. The immediate deliverables are dot and Sht, where Sht is the total hydrocarbon saturation such that Sht = 1-Swt.

Association of the models The effective and total porosity systems are associated through a sequence of relational algorithms that allow parameters calculated in one system to be transposed to the other. These associations form the basis for any conjunctive use of the two systems.

Shale volume fraction The wetted and dry shale fractions are related

EFFECTIVE AND TOTAL POROSITY

_I

Log Response DENSITY

Porosity

Core control in clean zones HELIUM POROSITY

L

ARCHIE'S FIRST ~ W L

[

1,o,

217

Core control INTRINSIC POROSITY EXPONENT m*

Formation water sample WATER CONDUCTIVITY Cw

r ~176 , 89 Log Response LATEROLOG INDUCTION Ct

WAXMAN-SMITS EQUATION C t = C w Swtn*+ BQ v Swtn*-I

Ot

Swt

]

B -- f (Cw) Core control INTRINSIC SATURATION EXPONENT n*

Fig. 4. Petrophysical interpretation within the total porosity system. through the expression: Vsh = Vd

+ ~bw

(8)

where ~)bw: Vsh ~)tsh

(9)

and ~tsh is the porosity of the wetted shale calculated from the expression: ~tsh = (Pcl -- Psh)/(Pcl -- Pf)

(10)

It follows from equations (11) and (12) that grain density can be re-expressed in terms of qbe and Vsh as follows: Pg = P m a ( 1 - - ~ e - - V s h ) + PclVsh(1 --(~tsh) 1 -- qbe -- Vsh ~tsh

(13)

Equation (13) reduces to Pg-----Prna when Fsh=0. In the effective porosity system, pg is taken as the matrix density Pma. In the total porosity system, pg is not necessarily equal to Pma.

where Psh is the density of the wetted shale, pd is the density of the dry shale fraction and for practical purposes pcl is equated to pg. Shale porosity is referred to the volume of wetted shale. By combining equations (8) and (9) we have:

Porosity

Vcl = Vsh ( 1 - (~tsh)-

where Vsh is ideally the wetted shale fraction from the neutron-density log combination. An alternative form of this expression is:

(11)

In the effective porosity system, the estimated Vsh is distinct from the rock matrix: in the total porosity system, the unknown Vcl is grouped with the rock matrix.

Grain density If Vma is the fractional volume of the rock matrix, the grain density can be expressed: Pg = (Pma Vma + Pcl Vcl )/( Vma "[- Vcl).

(12)

Equation (12) reduces to pg= Pma when Vd = 0.

Effective and total porosity are related through the expression: Ct = Ce q- Vsh Ctsh

~)t = q~e-k-~)t Swb

(14)

(15)

where Swb is the bound-water saturation, pursuant upon the dual-water model of Clavier et al. (1984). Equation (15) follows from the equality: Swb = Vsh Ctsh/~)t

(16)

Yet another form of equation (15), based on the normalized Qv concept of Juhasz (1981), is

218

P.F. WORTHINGTON

written: ~t-- ~be-~ ~t

Qv/Qvsh

(17)

to be. Equations (4) and (7) can be combined as follows: (20)

where Qv is relative to the cation exchange capacity per unit pore volume of a reference shale Qvsh. If the bound water has a unit density, a plausible assumption, equation (17) can also be written in the empirical form of Hill et al. (1979):

Equation (20) does not explicitly include the porosity coefficient a*, although that quantity is intuitively related to the value of m* for free-fit regressions of reservoir data.

~)t = ~e nt- ~)t Qv (0.084 Ce~)'5 nt- 0.22)

Conductivity o f reservoir rock

(18)

where Ce is the concentration (in equiv, litre -1) of the equilibrium water in the free pore space, net of cation adsorption, and can be expressed as a calculable function of Qv, Swt and saturating water concentration Cs, at a reference temperature of 25~ Equation (18) has been seen as a quantitative link between the effective and total porosity models (Ruhovets & Fertl 1982), but it is not a generally applicable equality, although Juhasz (1979) did cite evidence that the volume of bound water is effectively independent of temperature over the range 20-200~ Note the complication, to be discussed later, that the conventional laboratory measurement of porosity through helium expansion is often carried out on a humidity-dried sample, and there is a view that the measured porosity is actually a hybrid porosity, being somewhere between the limits of effective and total porosity.

Formation res&tivity factor Laboratory measurements of formation resistivity factor F fall under the umbrella of special core analysis and, as such, are usually carried out on lithologically cleaner samples, because it is the practice to preserve the better quality reservoir rock. Otherwise multiple-salinity measurements of electrical conductivity can furnish an intrinsic formation factor F* for non-Archie reservoirs. The resulting formation factors are then correlated with their respective porosities with the object of characterizing the first Archie equation through the intrinsic porosity coefficient a* and exponent m* so that:

Ft* = Fe* (~)e/~)t) m~

By equating the reservoir rock conductivities of equations (3) and (6) and setting Sw = 1, we have: (Cw + B Qv)/Ft* = (Cw/Fe*) + VshCsh and therefore Qv = Ft* (Cw + Vsh CshFe*) - Fe. Cw

Equation (22) describes the relationship between Qv and Vsh assuming that the water-zone forms of the Waxman-Smits and Simandoux equations are valid within their respective porosity systems. It is interesting to consider the boundary conditions on equation (22). When Vsh=0, Fe* = F t* and therefore Qv=0. When Vsh = 1 for a perfect shale in which Cw approaches the bound-water conductivity Cbw, 4~e= 0 and therefore Fe* is infinite. Under these conditions, equation (22) reduces to: Qvsh =

Ftsh* Csh -- Cbw B

(23)

where Ftsh* is the intrinsic formation factor of the perfect shale. Significantly, equation (23) might allow the determination of Qv for a perfect shale by drawing upon the relationship: ftsh* ~---a*/~)tsh m*

(24)

Equation (23) can be rewritten:

(19)

This equation is applied in both the effective and the total porosity systems, in the form of equations (4) and (7), respectively, according to the nature of the log-derived porosity. There are no separate relationships for the two systems even though the earlier comments about porosity measurement might suggest that there ought

(22)

BF~.

Cbw ~- BQvsh

F* =a*/q~ m*

(21)

(25)

Ftsh* or, alternatively: Ftsh*= Ftsh (1 + (BQvsh/Cbw))

(26)

where Fts h =

Cbw/Csh.

(27)

EFFECTIVE AND TOTAL POROSITY

In practice, however, g s h = 1 will correspond to an imperfect shale that does not fully comprise clay minerals and therefore the limiting conditions will not be attained. Note that equation (27) reveals the same definition of shale formation factor as that related directly to q~tsh through a pseudo-Archie expression in the dual-porosity model of Raiga-Clemenceau et al. (1984).

Fluid saturations The interpreted hydrocarbon-filled porosity must be the same in both the effective and the total porosity systems, otherwise the computed hydrocarbons in place will be different. Therefore: ~e She = ~t Sht

characterization of pseudo-matrix, the average mixture of matrix and dry shale within the net sand, which must be specified at the outset. Fluid density within the flushed zone must also be quantified over the same intervals. The density log remains uncorrected for shale effects and it is used directly to infer total porosity. The computed porosities are input to the first Archie equation to evaluate corresponding intrinsic formation factors. Agreed algorithms for (a) the equivalent conductance B in terms of Cw and (b) the cation exchange capacity per unit pore volume Qv in terms of total porosity have to be established in support of the water saturation equation (Fig. 4). The above contrasting procedures suggest a sufficient degree of difference to allow scope for independent cross-checks between the two approaches.

(28)

Relative strengths

or

(1

- Swt)

(29)

Swt = 1 - (~e/4)t) (1 - Swe)

(30)

Oe (1 -- Swe ) = (~t

219

so that

Equation (30) allows a direct comparison of the water saturations inferred in the two systems.

Quality assurance for formation evaluation The effective and total porosity models can only be used conjunctively to enhance core-calibrated log interpretation if the two approaches are sufficiently different to furnish independent evaluations. The degree of independence is governed by systemic differences in the application of these two models.

Systemic differences The effective porosity system entails the characterization of matrix, fluid and shale points without the need to specify net sand at the outset. The neutron and density logs are corrected for light hydrocarbon effects before all three porosity logs are corrected for shale effects. At that point the corrected porosity logs are deemed to be sensing effective porosity. The interpreted porosities are used to calculate corresponding values of intrinsic formation factor. A unified shale volume fraction and shale conductivity are other essential inputs to the water saturation equation (Fig. 3). The total porosity system entails the density

The relative strengths of the total and effective porosity systems are embodied within the meaningfulness of tying back to core data. This, in turn, raises the question of how the core data were measured. Tying back to core is not possible for the wetted shale fraction Vsh and the practice is uncommon for the dry clay-mineral volume fraction Vd in a solely petrophysical context. Nevertheless, X-ray diffraction, X-ray fluorescence, chemical and thermogravimetric analysis, scanning electron microscopy and infrared spectroscopy can be used to gain a quantitative insight into the occurrence of clay minerals and thereby to establish some reference basis for Vcl, although the subjective nature of some laboratory interpretations might detract from the perceived usefulness of this approach as a groundtruthing facility. In this respect, therefore, the total porosity system is the stronger and it affords some opportunity for tying claymineral content back to core. The relationship of Pma to pg can be used to validate the underlying assumption of the total porosity model, that the density of dry clay minerals equals that of rock matrix. This assumption is more likely to be satisfied where the clean rock matrix has constant density. It is unlikely to be satisfied where the clean matrix properties are markedly variable. Where the assumption is not satisfied but shale density is known, it is theoretically still possible to proceed with a total porosity approach, but on a levelby-level basis. This procedure would require a quantification of Vcl at each digital sampling level of the well logs, so that grain density might

220

P.F. WORTHINGTON

be evaluated at each level. This requirement would, in turn, necessitate a reversion to the relationship between V~h and Vcl. Because of this potential complexity, which many regard as prohibitive, the effective porosity model is seen as the stronger in terms of the opportunities for utilizing and validating the density of reservoir rock. Note, however, that this contention is dependent upon the measurement of a meaningful effective porosity. The tying back to core of log-derived porosity values is fraught with potential difficulty. It has been argued, but not universally, that the oven drying of core plugs at temperatures of around 105-110~ removes chemically-adsorbed waters without altering, chemically, the solid claymineral fabric. Therefore, it has been claimed that helium porosities measured subsequently on these plugs are likely to be total porosities. On the other hand, the humidity drying of core plugs at temperatures of about 60~ is claimed by some to retain the bound waters, while expelling the free water, so that porosities measured subsequently are effective porosities. This contention is at variance with the data of Hill et al. (1979), which suggest that some bound waters are expelled despite the humidifying process and that the measured helium porosities are intermediate relative to the effective and total porosities (Juhasz 1988). The effect may not be serious in reservoir rocks, for Pallatt & Thornley (1990) note that electrochemicallybound water accounts for less than 2.5% of the pore volume: for a rock with 20 porosity units, the estimated bound-water volume is therefore less than 0.5 porosity units, a figure which is equivalent to the uncertainty associated with core porosity measurement. Nevertheless, the only uncontentious way of groundtruthing log-derived porosity to conventionally-measured core porosity is to confine such comparisons to essentially clean zones. Under these conditions, both the effective and the total porosity models are equivalent. A comparison of Fe* and Ft* offers an intrinsic measure of the effect of pore geometry on electrical conduction, subject to the assumptions of equal porosity coefficients and equal porosity exponents for the two systems. Because the definitive multiple-salinity procedures furnish Ft*, the total porosity model provides the sounder physical basis. Laboratory-measured values of Ft* therefore serve as the definitive reference. In a user setting, values of Qv are obtained from a dubious relationship to porosity and estimates of gsh are made from one or more of several tenuous shale indicators. There is no

reference value of Vsh available from the laboratory: there might be values of Qv, which can be taken as definitive if these are determined meaningfully from multiple-salinity measurements of rock conductivity. Therefore, such a Qv database becomes the definitive core reference. The relationship of the equivalent conductance of (sodium) clay exchange cations B to the conductivity of saturating electrolyte Cw remains a weak link in the total porosity system, because several different relationships have been proposed. This weakness is not removed by the use of multiple-salinity conductivity data, which require a value of B before Qv can be quantified. Tying back log-derived water saturations to core is usually founded on the extraction of interstitial waters from vertical plugs cut from the inner parts of whole core pieces that have been drilled using a low-invasion coring bit with an oil-base mud. The procedure is established but not yet standard practice. The plug-extracted water saturations are notionally values of Swt. They can be used as a reference for the effective porosity system through the equivalence of hydrocarbon-filled porosity. In particular, the comparison serves as a validation of the feeder relationships, especially that of Qv vs ~bt, which is often highly tenuous. Q u a l i t y assurance s c h e m e

A quality assurance scheme for deterministic open-hole formation evaluation is shown in Fig. 5. The purpose of this simplistic scheme is to illustrate how the effective and total porosity models can be operated conjunctively to increase confidence in the resulting petrophysical interpretation. It is not intended to constitute the ultimate framework for quality control but rather to indicate how greater confidence in petrophysical interpretation can be secured through an integrated use of the two models. The first element of Fig. 5 is concerned with tying back Vsh to core-derived Vcl through ~tsh, the determination of which requires a knowledge of pcl. A satisfactory tie-back would reconcile wetted shale and dry clay-mineral fractions in the two porosity systems. Failure to secure agreement over net sand intervals could be attributed to an inappropriate log-derived shale indicator, to an unrepresentative dry clay density, or to subjectiveness in the interpretation of core data. As in all cases of tying log data to core, the scale disparity might render the datasets irreconcilable, especially in markedly heterogeneous reservoir zones. Further, an unsatisfactory outcome at the subsequent (second) key stage might suggest an iteration through the

EFFECTIVE AND TOTAL POROSITY

221

Fig. 5. Foundations of a quality assurance scheme for open-hole petrophysical interpretation.

first. The second element is concerned with tying the computed grain density pg back to core through log-derived values of Vsh, q~e and ~btsh, and a knowledge of pc~ and Pma- A satisfactory tie-back would substantiate the assumptions concerning Pcl and Pma, the latter being verifiable over any shale-free intervals of net sand. Failure to secure agreement could be attributed to unrepresentative densities of matrix or dry clay minerals or to errors in q~e, which is not qualityassured until the third key stage, again suggesting some degree of iteration. The third element of Fig. 5 reconciles logderived effective porosity with log-derived total porosity through a comparison of ~bt indirectly calculated from q~e with that interpreted directly within the total porosity system over net reservoir intervals. The third element also allows both the log-derived porosities to be referred to core porosity over net reservoir intervals. Because of the uncertainty associated with the influence of sample preparation on the measured core porosity of shaly plugs, the tying back to core might best be done in two stages. First, the log-core comparison should be restricted to clean intervals to establish that the interpretation systems are functioning under the most straightforward conditions. Second, in view of the earlier comments concerning a hybrid core porosity, the tying back to core over shalier intervals of net reservoir should allow the measured core porosity to be of intermediate value relative to the log-derived effective and

total porosities. Indeed, if the core porosity lies between the corresponding log-derived values, this might be the best quality assurance that one could reasonably expect to achieve. Failure to reconcile the two datasets would suggest shortcomings in Vsh and/or (/)tsh and would require some iteration through elements (1) and (2). The fourth element reconciles log-derived Fe* with log-derived Ft* through a comparison of Ft* indirectly calculated from -be* with that interpreted directly within the total porosity system over net reservoir intervals. This is no more than a check for internal consistency. However, the fourth element also allows both the log-derived intrinsic formation factors to be referred independently to laboratory values of Ft*, preferably those obtained from multiplesalinity conductivity measurements of plugs from net reservoir intervals. Failure to tie back to core would suggest transmitted errors in ~be and/or ~bt, or perhaps the use of an inappropriate value of the intrinsic porosity exponent m*. The fifth element of Fig. 5 allows Qv estimated from a total porosity log to be tied back to core values, preferably those obtained unambiguously from multiple-salinity conductivity measurements of plugs from net reservoir intervals. This exercise serves as a check on the meaningfulness or otherwise of the algorithm used to predict Qv from a porosity log. Since this algorithm is itself characterized using core data, the core-derived Qv data should be distinct from those used to establish the relationship between Qv and qSt. The fifth element also allows log-

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P.F. WORTHINGTON

derived Vsh values to be reconciled with logderived Qv data through a comparison of Qv values calculated from Vsh with those inferred directly from porosity and already validated through reference to core data. Failure to reconcile the data at this key stage would most likely be attributable to uncertainties in B and Csh. The sixth and final element reconciles logderived effective water saturation with logderived total water saturation through a comparison of Swt indirectly calculated from Swe with that interpreted directly within the total porosity system over net pay intervals. The sixth element also allows both the log-derived water saturations to be referred to core-derived water saturation. Failure to reconcile the data at this stage would imply possible errors in 4)e, ~t, B, Csh, Cw, a* or m*, and it would require iterating perhaps as far back as the third key stage. The quantification of the inter-model comparisons should take the form of acceptable tolerances in the agreement between directly and indirectly inferred values of the relational parameters and in their validation against core data. The development of these tolerances would be an immediate sequel to broad adoption of this proposed conjunctive interpretation scheme.

Conclusions A comparison of open-hole petrophysical interpretation practices for non-Archie reservoirs that are set exclusively within either the effective or the total porosity system has identified a set of relational algorithms through which these interpretative models can be associated. This identified numerical equivalence allows intermodel assessments of the consistency and validity of the interpreted data at key stages of the petrophysical evaluation process, so that some measure of reliability may be established. The assessments involve comparisons of interpretations made by separately using the two porosity models as well as the tying of these interpretations back to core. The key stages form the basis for a quality assurance scheme that draws upon the integration of traditionally separate areas of petrophysical systemics. The development of such a scheme in the form of quantitative measures of inter-model agreement would constitute a logical extension of the demonstrated association of the effective and total porosity models. This initiative forms part of an essential thrust to complement the excellent quality control that currently exists in well-log data acquisition. At present, our ability to acquire petrophysical data

exceeds our ability to interpret, especially in the three-dimensional settings of extended reach and multilateral wells. Ongoing advances in the three-dimensional modelling of tool responses will shortly allow meaningful environmental corrections in a way that opens the door to enhanced 3D interpretation of open-hole well logs. If the community is to draw the greatest benefits from that projected situation, a qualityassured interpretation scheme will be required for open-hole petrophysics. This paper has emphasized the nature of the technical positioning that will be needed to secure those benefits as we approach the millennium.

Nomenclature B equivalent conductance of (sodium) clayexchange cations (S m 1 equiv. 1 litre) Cbw conductivity of bound water ( S m ') Csh conductivity of wetted shale fraction (S m -1) Ct bulk conductivity of reservoir rock (S m -1) Cw conductivity of free water ( S m -1) F* intrinsic formation (resistivity) factor in generic form Fe* intrinsic formation (resistivity) factor in the effective porosity system Ft* intrinsic formation (resistivity) factor in the total porosity system Ftsh formation (resistivity) factor of a perfect shale in the total porosity system Ftsh* intrinsic formation (resistivity) factor of a perfect shale in the total porosity system Qv cation exchange capacity per unit pore volume (equiv. litre-1) Qvsh cation exchange capacity per unit pore volume of shale (equiv. litre -1) She fractional hydrocarbon saturation in the effective porosity system Sht fractional hydrocarbon saturation in the total porosity system Swb fractional bound-water saturation Swe fractional water saturation in the effective porosity system Swt fractional water saturation in the total porosity system Vd volumetric fraction of dry clay minerals Vmavolumetric fraction of clean rock matrix Vsh volumetric fraction of wetted shale X generic log response Xcorr generic log response corrected for shaliness Xma generic log response to clean rock matrix Xsh generic log response to shale a* Archie intrinsic porosity coefficient Ce concentration of equilibrium free water (equiv. litre 1) c~ concentration of saturating water (equiv. litre-1)

EFFECTIVE AND TOTAL POROSITY m* Archie intrinsic porosity exponent n* Archie intrinsic saturation exponent Pb log-derived bulk density ( g c m -3) pc~ density of dry clay-mineral fraction (g cm -3) pf density of interstitial fluids (g cm -3) pg grain density over net sand intervals ~g cm 3) Pma density of clean rock matrix ( g c m -~) psh density of wetted shale fraction (g cm -3) Obw bound-water porosity fraction Oe effective porosity fraction Ot total porosity fraction ~tsh total porosity fraction of shale

References ARCHIE, G. E. 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. AIME 146, 54-62. BARDON, C. 8z PIED, B. 1969. Formation water saturation in shaly sands. Trans. SPWLA lOth Ann. Logging Syrup., Zl-19, Society of Professional Well Log Analysts, Houston, Texas. BUSH, D. C. & JENKINS, R. E. 1970. Proper hydration of clays for rock property determinations. Journal of Petroleum Technology, 22, 800-804. CLAVIER, C., COATES, G & DUMANOIR, J. 1984. Theoretical and experimental bases for the dualwater model for interpretation of shaly sands. Society of Petroleum Engineers Journal, 24, 153167. HILL, H. J., SHIRLEY,O. J. & KLEIN, G. E. 1979. Bound water in shaly sands--its relation to Qv and other formation properties. The Log Analyst 20(3), 3-19. HURST, A. & NADEAU, P. 1994. Estimation of water saturation from clay microporosity data. SPE Paper 28850, Society of Petroleum Engineers, Richardson, Texas.

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JOHNSON, W. L. & LINKE, W. A. 1977. Some practical applications to improve formation evaluation of sandstones in the Mackenzie Delta. Trans. CWLS 6th Formation Evaluation Symposium, R1-32, Canadian Well Logging Society, Calgary, Alberta. JUHASZ, I. 1979. The central role of Qv and formationwater salinity in the evaluation of shaly formations. Trans SPWLA 20th Ann. Logging Syrup., AA1-26, Society of Professional Well Log Analysts, Houston, Texas. - 1981. Normalised Qv--the key to shaly sand evaluation using the Waxman-Smits equation in the absence of core data. Trans. SPWLA 22nd Ann. Logging Syrup., Z1-36, Society of Professional Well Log Analysts, Houston, Texas. MAYER, C. t~ SIBBIT, A. 1980. GLOBAL, a new approach to computer-processed log interpretation. SPE Paper 9341, Society of Petroleum Engineers, Richardson, Texas. PALLATT, N. & THORNLEY,D. 1990. The role of bound water and capillary water in the evaluation of porosity in reservoir rocks. In: WORTHINGTON,P. F. (ed.) Advances in Core Evaluation, Gordon and Breach, Reading, 223-237. RAIGA-CLEMENCEAU, J., FRAISSE, C. • GROSJEAN, Y. 1984. The dual-porosity model, a newly developed interpretation method for shaly sands. Trans. SPWLA 25th Ann. Logging Syrup., F1-16, Society of Professional Well Log Analysts, Houston, Texas. RUHOVETS,N. & FERTL, W. H. 1982. Digital shaly-sand analysis based on Waxman-Smits model and logderived clay typing. The Log Analyst 23(3), 7-23. WAXMAN, M. H. & SMITS, L. J. M. 1968. Electrical conductivities in oil-bearing shaly sands. Society of Petroleum Engineers Journal, 8, 107-122. WORTHINGTON,P. F. 1991. The direction of petrophysics: a five-year perspective. The Log Analyst 32(2), 57-62.

Permeability prediction in anisotropic shaly formations S. X U & R. W H I T E

Exploration Geophysics Group, Research School of Geological & Geophysical Sciences, Birkbeck College & University College London, Malet Place, London WC1E 6BT, UK Abstract: We present a unified model for simulating the permeability and electrical

conductivity of anisotropic shaly formations. The model is based on Willis' formulae and the concept of a host medium, the selection of which is crucial in predicting these transport properties. Different rock components, including shales and mudrocks, are characterized by parameters typifying their pore geometry, namely the aspect ratio, size and orientation distribution of the pores. In this regard the model is an extension of the elastic model of Xu & White for predicting P- and S-wave velocities in siliciclastic rocks. The electrochemical effect of clay minerals on electrical conductivity is simulated by Waxman & Smits' model. A novel feature of the permeability model is that its percolation factor is estimated by a nonlinear transformation of the percolation factor found from conductivity measurements. The model was tested on the laboratory measurements published by Waxman & Smits. Comparison of the results with those from the Waxman & Smits, Dual-Water, and K o z e n ~ Carman models, and with multilinear and non-linear regression techniques, demonstrated that the unified model predicted conductivity and permeability more accurately than any of these models from the same number or fewer parameters. The improved prediction was most noticeable in samples containing a significant clay mineral fraction. Apart from Waxman & Smits' data, we have found no published dataset that is comprehensive enough to test physical predictions of both conductivity and permeability.

Permeability is one of three key rock parameters in reservoir simulation and the provision of detailed estimates of permeability is a prime objective of applied petrophysics. Since permeability cannot be measured directly by logging tools, it is usually estimated indirectly from well logs with calibration from cores. A common practice is to use core measurements to establish an empirical relationship between permeability and properties such as porosity and formation factor and then to apply that relationship to well logs to construct permeability logs. Permeability is a complex property to predict empirically and it is not easy to obtain detailed information on the parameters that control the flow of fluids through rocks. Needless to say, the prediction of permeability is problematic. It is well understood that permeability is controlled by five key factors: porosity, the size, shape, orientation and connectivity (percolation or tortuosity) of pores. Both laboratory measurements (e.g. Beard & Weyl 1973) and theoretical analysis (e.g. Carman 1956) indicate that permeability is more sensitive to pore size than porosity. Pressure, cementation, grain size, clay content, sorting and irreducible water saturation affect permeability indirectly by modifying or controlling the five key parameters mentioned above. Porosity can be determined

reasonably accurately from well logs but there are no direct measurements of pore size, shape and connectivity. Consequently, permeability prediction has to rely on indirect measures of these parameters. The danger of resorting to purely ad hoc empirical relationships is that they can end up eclectically tuned to a particular dataset. The effect of clay content on permeability has long been recognized. Thompson & Callanan (1981) measured porosity and permeability of synthetic clay samples at pressures in the range 0 to 10000 psi. Although the measured porosities were high (in the range of 20% to 50%), the permeabilities are 3 to 4 orders of magnitudes lower than those measured from artificial sand packs by Beard & Weyl (1973). The low permeabilities were explained as a result of the remarkable sealing power of clay particles. Thomson (1978) observed a progressive decrease in permeability with clay content from rock samples with clay content in the range of 5% to 15%. A number of authors observed a linear trend between log(k), the logarithm of permeability, and porosity 4) which was later explained as a result of a systematic reduction in both k and 4 by dispersed clays (Bos 1982). From laboratory measurements on over 100 shaley sand samples, Goode & Sen (1988) found a good

XU, S. • WHITE,R. 1998. Permeability prediction in anisotropic shaly formations. In- HARVEY, P. K. 8z LOVELL, M. A. (eds) Core-Log Integration, Geological Society, London, Special Publications, 136, 225-236

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correlation between log(k) and log(qSm/Qv), where m is the cementation factor and Qv the exchange cation molarity. Sen et al. (1990) measured Qv , the inverse surface-to-volume ratio (Vp/S), proton N M R decay time T1 and permeability k of some 100 sandstone core samples and found good correlations between k and log(q~mVp/S), log(q~m/Qv) and log(~bmT1). This is understandable since Vp/S, Qv and T1 are three different measures of clay content. The authors concluded that clay affects the permeability more in rocks where it adheres in pore throats than in those where it adheres in the pore pockets. Although considerable understanding of how clay affects permeability has been gained from laboratory measurements, little theoretical work has been done to model the effect. The majority of the models that relate permeability to clay content combine empirical and simple logical considerations (e.g. permeability must be dimensionally length squared). Starting with the Kozeny-Carman equation (Carman 1956), de Lima (1995) obtained some relationships between k, 49, Vp/S and Qv similar to those obtained empirically by Sen et al. (1990). We have developed a model for elastic wave velocities (Xu & White 1995a,b,c, 1996a) which can accurately simulate the combined effects of porosity, clay content, fluid content and frequency on elastic wave velocities in clastic silicate rocks. The model is founded on physical concepts and has demonstrated its practical utility in a number of case studies involving reservoir geophysics (formation evaluation, seismic modelling and interpretation). In addition to validation on published laboratory measurements, the model has been successfully tested on numerous wells, including four blind tests (Xu et al. 1997). The key feature of the model is its ability to predict the effect of clay content on wave velocities, including the two distinct porosityvelocity trends observed in the laboratory: one for shaly sands and the other for sandy shales (Marion et al. 1992). Empirical models that treat clay content purely as a lithological factor cannot explain this. Laboratory measurements and well logs indicate that two factors need to be considered; lithology and the influence of clays on pore compliance. Not only are clay particles more compliant than sand grains, their sheetlike nature tends to make the pore space more compliant. This greater compliance can be modelled by introducing an additional pore space characterized by a smaller aspect ratio than that of clean sand grains. Thus the model predicts the higher Vp/Vs values observed for

shales than sands. The elastic anisotropy of shaly formations is modelled through a preferred orientation for clay-related pores. Here we extend the model to predict the conductivity and permeability of shaly formations. Each pore is assigned an idealized ellipsoidal shape and embedded in a porous medium. We use Willis' (1977) formulae to compute its contribution to the overall conductivity and permeability. The interaction between this pore and other pores is modelled via the concept of a host medium. The properties of the host medium are then tuned to model the observed conductivity and permeability. The concept of the host medium was originally proposed by de Kuijper et al. (1995). In Xu & White (1996b) we show that alternatives such as the self-consistent scheme (SC) and the differential effective medium scheme (DEM) cannot model with Archie's law for clean sands whereas modelling with a host medium hunting technique reproduced Archie's Law when the fluid percolation factor was selected as 0.04q~. The next section describes the model which is then tested using published laboratory measurements. The results show that the transport properties of anisotropic shaly formations can be modelled by assigning a characteristic pore size, shape and orientation to their clay fraction. The model provides a permeability predictor that estimates a percolation factor from resistivity measurements, if available, and then applies it to permeability prediction.

The unified model for shaley formations As in the elastic model of Xu & White (1995a,b, 1996a), we assume that the total pore space can be divided into sand-related pores and clayrelated pores. The pore space is partitioned proportionately:

where Vc ~bc = _---~b 1

(2)

4,s = 4 - 4~c.

(3)

and

Vc is fractional clay content. The sand-related pores are characterized by a pore aspect ratio (ratio of short semi-axis to long semi-axis) C~s and pore size (long semi-axis) as and the clayrelated pores are similarly assigned a characteristic pore aspect ratio O~c and pore size ac. We

PERMEABILITY PREDICTION further postulate that the sand-related pores are randomly oriented whereas the clay-related pores tend to align themselves in a plane. This assumption conforms with observations of strong seismic and ultrasonic anisotropies for shales and isotropic wave propagation in clean sandstones. In modelling logs, Vc is generally replaced by shale volume Vsh, which would lump the fractional volume of silts and various mineral fragments with Vc. The model could in principle take account of these different components and different clay minerals if there were practical log analysis procedures distinguishing them.

227

five phases: 1. a non-conducting solid phase; 2. a clay mineral phase with a finite but very small conductivity; 3. a randomly oriented sand-related pore fluid phase with conductivity Cwe; 4. a clay-related pore fluid phase with the same pore fluid conductivity Cwe but with a preferred pore orientation; 5. a non-conducting hydrocarbon phase. The percolation factor Fc for conductivity is defined as in equation B1 in Appendix B:

CH= FcCwe+(1-Fc) Cm

Conductivity In simulating electrical conductivity special consideration must be given to the electrochemical behaviour of clays. Waxman & Smits (1968) demonstrated that shaley sands behave as perm-selective cation exchange membranes and their electrochemical efficiencies increase with increasing clay content. They modelled this by supplementing water conductivity Cw with a conductivity Ce from the clay counter-ions within the ionic double layers:

Ce = BQv

(5)

where /~eNa is the maximum (sodium) cation exchange ion mobility (in cm 2 Volt 1 s), b and 7 are empirically determined constants. Waxman & Smits (1968) found from their laboratory measurements that B = 1 - 0 . 6 e x p ( - Cw/0.013)]0.046

(6)

where Cw is in ohm m q. The effective conductivity of the formation water Cwe is simply the sum of Cw and Ce. Cwe = Cw + Ce

where Cn, Cwe and Cm denote the conductivity tensors of the host medium, formation water and matrix (mixture of the sand grains and clay particles). Fc describes the degree to which the fluid paths accord with a parallel tube model; it decreases with increasing tortuosity of the fluid paths. There is no information as to the value of Fc and we estimate it from the measurements. Fc can be correlated with other measured parameters, such as q~ and Qv, to see what factors control it.

(4)

where Qv is the molar volume concentration of clay exchange cations per unit pore volume (meq cm 3). Qv is a function of the cation exchange capacity (CEC) of clay minerals, clay content, porosity and the density of dry clays. B is the equivalent conductance of clay exchange cations (in ohm cm 2 meq 1) which is a function of the conductance of formation water Cw. At 25 ~ B = [1 - b e x p ( - Cw/~/)]0.0 l AeNa

(8)

(7)

In order to apply the modified Willis' formulae (equations A5-A11) to the conductivity of shaly sands, we subdivide the formation into

Permeability In simulating permeability, there is a problem in defining the intrinsic permeabilities of the inclusions. One approach is to start from the intrinsic permeability of two parallel plates: be k = -12

(9)

where b is the separation between the two plates. For a spheroidal inclusion defined by xZ/a~2+ y2/ a2+ z2/c 2= 1, equating the hydraulic aperture bh parallel to its long axis with the mean square value of the separation 2z gives: bh2 = 1 .fjs (2z)2dS = -~o~2a 2 = 2C2

(10)

where A=Tr a 2 is the area of the domain S defined by x 2 + y 2 = a 2 and a is the aspect ratio of the inclusion (c/a). For the intrinsic permeability of the inclusion parallel to its long axis we use k = 1__a2a2 = ~1c - ,~. 6

(11)

Strictly this should be a tensor property. A similar equation, but with an undetermined

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S. XU & R. WHITE

numerical constant, is obtained from simple dimensional arguments. Since in practice a bestfit characteristic value is assigned to c, the numerical constant of 1/6 has no real significance. Unlike conductivity, the permeability of a porous rock does depend on pore sizes, especially pore throat diameters. The intrinsic permeabilities for sand- and clay-related pores are taken from equation 11 1

2

9

ks = gO~s as-

(12)

kc = ~1 ac 2ac2.

(13)

and in porosity from 5% to 31%, making it an ideal dataset for testing the model. Electrical conductivity Applying the model to conductivity measurements has two aims: (1) to test its capability of predicting electrical conductivity, and (2) to estimate a percolation factor for each sample for use in permeability prediction.

and

We introduce a separate percolation factor Fp for permeability since the relative weighting of permeability is not necessarily the same as that for conductivity. For example, a clay particle in a pore throat still conducts electricity but seriously impedes fuid flow. By employing a modified Voigt-Ruess-Hill average scheme, we define Fe for permeability as follows: kH = 0.2kll + 0.8k~, kll = Fpks + (1 - Fe)kc, k ~ -1 = Fpks < + (1 - Fp)kc q

(14)

where kH, ks and kc are permeabilities of the host medium, sand-related pores, and clay-related pores. The equation signifies that when the sandrelated pores are selected as the host medium, the system is most percolating and when the clay-related pores are selected, the system is least percolating. To apply Willis' formulae to permeability, the composite is assumed to consist of three phases: 1. an impermeable matrix phase of sand grains and clay particles; 2. a sand-related pore phase with a random pore orientation; 3. a clay-related pore phase with a preferred pore orientation.

Application to laboratory measurements The dataset The model was tested on the laboratory measurements published by W a x m a n & Smits (1968). The dataset provides the porosity, brine permeability, Qv and conductivities at four or more brine salinities of 49 sandstone samples (table 2 in Waxman & Smits 1968). The samples range in clay content from clean to very shaly,

The Waxman-Smits (WS) and the D u a l Water (DW) models (Clavier et al. 1984) were also tested on the dataset for comparison. To simulate electrical resistivity, all three models require porosity, clay content and brine conductivity (Cw) as input parameters. As there were no direct measurements of clay content, we estimated it from Qv using a relation given by Juhasz (1979): V~l(drv) = 9

Qvq~t

(15)

Pcl (dry) C E C c l

where Vcl(dry) denotes the dry clay content as a fraction of bulk volume, Pcl(dry) denotes the average density of the mixture of dry clay minerals (in gcm 3), 4t is the total (fractional) porosity and CECd is the averaged cationexchange capacity of the clay minerals present in the formation (meq gq dry clay). When applying the WS and D W models, the formation factor FF in both models was tuned to get the best fit. It is well recognized that FF is controlled by porosity and cementation factor which is, in turn, a function of pore geometry and tortuosity of the electrical current flow paths. Hence FF is expected to vary from sample to sample. When applying our model to the dataset, the percolation factor Fc was tuned by fitting the predictions with the conductivity measurements. Figure 1 compares sample measured electrical conductivities with predictions from the three models. All three work well for clean sandstone (upper figure). Our model worked slightly better than the WS and D W models for shaley sandstone (lower). The normalized mean square errors of fit (termed incoherence by de Kuijper et al. 1995) for all 49 samples is shown in Fig. 2. Our model (lower) fits the data slightly better than the D W (upper) and WS (middle) models. Figures 3 and 4 show the cross plots of the estimated percolation factor Fc as a function of porosity and shale volume. There are two welldefined trends on the Fc-q~ cross plot: one for

PERMEABILITY PREDICTION

229

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Fig. 1. Comparisons between the measured electrical conductivities (solid squares) and those predicted using the WS (dash60~ Large dots indicate recording file boundaries, explaining the absence of data in places (1800 to 1884 mbsf, for example) and locating where the FMS sensor became stuck during logging due to hole restriction, obliging the operator to close the tool and interrupt the recording. show conductivity changes related to bed boundaries and fractures, either open or mineralized. Each electrode is oriented in space with three-axis accelerometers and flux-gate magnetometers, making it possible to derive the strike and dip of geological features. FMS data processing and analysis in Hole 504B is described by Ayadi et al. (1996). Images were analysed with Fracview TM,a Schlumberger interpretative software package that allows the interactive display and analysis of oriented images (Luthi & Souhait~ 1990). About 34 500 planes were identified and mapped over 1672 m of basement, yielding an average of 20 planes mapped per m. This dataset is analysed here in terms of raw fracture density versus depth (Fig. 3). In order to organize this large dataset, the planes were binned in terms of dip angle as subhorizontal (dip _
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