Well testing

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk

BASIC WELL TEST DESIGN AND ANALYSIS (5 Days) FOR

BP EXPLORATION OPERATING COMPANY

COURSE NOTES

May 2001

BY

DOMINIQUE BOURDET AND PIERS JOHNSON

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk CONTENTS Page 1.

INTRODUCTION .......................................................................................................................................................... 7

2.

FUNDAMENTALS OF WELL TESTING................................................................................................................. 9

2.1 2.2 2.3 3. 3.1 3.2 3.3 4. 4.1 5. 5.1 5.2 5.3

DESCRIPTION OF A WELL TEST..................................................................................................................................... 9 TERMINOLOGY AND DEFINITIONS ................................................................................................................................ 9 INPUT DATA REQUIRED FOR AND INFORMATION GAINED FROM WELL TESTING ........................................................ 11 AN OVERVIEW OF PRESSURE TRANSIENT ANALYSIS.............................................................................. 15 BASIC EQUATIONS....................................................................................................................................................... 15 WELL TEST INTERPRETATION METHODOLOGY ......................................................................................................... 16 TYPES OF WELL TESTS .............................................................................................................................................. 17 TYPICAL TEST PROCEDURE................................................................................................................................ 21 OPERATIONAL TIPS ..................................................................................................................................................... 21 FLOW STATES............................................................................................................................................................ 23 STEADY STATE............................................................................................................................................................ 23 PSEUDO-STEADY STATE ............................................................................................................................................. 23 TRANSIENT STATE ...................................................................................................................................................... 23

6.

DARCY’S LAW............................................................................................................................................................ 24

7.

THE DIFFUSIVITY EQUATION AND ITS SOLUTIONS .................................................................................. 26

7.1 7.2 7.3 7.4 7.5 7.6 8. 8.1 8.2 8.3 9.

HYPOTHESES ............................................................................................................................................................... 26 DARCY'S LAW.............................................................................................................................................................. 26 PRINCIPLE OF CONSERVATION OF MASS (CONTINUITY EQUATION)............................................................................ 26 EQUATION OF STATE OF A CONSTANT COMPRESSIBILITY FLUID ................................................................................ 26 DIFFUSIVITY EQUATION .............................................................................................................................................. 27 DIFFUSIVITY EQUATION IN DIMENSIONLESS TERMS ................................................................................................... 27 RESERVOIR AND FLUID ASSUMPTIONS FOR SOLVING THE DIFFUSIVITY EQUATION .............. 29 THE LINE SOURCE SOLUTION ...................................................................................................................................... 29 SEMI-LOG APPROXIMATION : RADIAL FLOW REGIME ................................................................................................. 29 RADIUS OF INVESTIGATION......................................................................................................................................... 30 WELLBORE STORAGE............................................................................................................................................ 31

9.1 9.2 9.3

DEFINITION ................................................................................................................................................................. 31 CARTESIAN PLOT ANALYSIS........................................................................................................................................ 32 ESTIMATING WELLBORE STORAGE FROM COMPLETION ............................................................................................. 33

10.

SKIN ............................................................................................................................................................................... 35

10.1 10.2 10.3 11. 11.1 11.2 12.

DEFINITION.................................................................................................................................................................. 35 RADIAL FLOW REGIME ................................................................................................................................................ 36 SEMI-LOG EQUATION................................................................................................................................................... 37 SUPERPOSITION THEORY..................................................................................................................................... 39 MULTI RATE THEORY : TIME SUPERPOSITION ............................................................................................................. 39 IMAGE WELL THEORY TO MODEL BOUNDARIES : SPACE SUPERPOSITION ................................................................... 42 LOG LOG ANALYSIS................................................................................................................................................ 44

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk 12.1 12.2 12.3 13. 13.1 13.2 14. 14.1 14.2 14.3 14.4 15. 15.1 15.2 15.3 15.4 15.5 16. 16.1 16.2 16.3 16.4 16.5 16.6 16.7 17. 17.1 17.2 18. 18.1 18.2 18.3 18.4 19. 19.1 19.2 19.3 19.4 19.5 19.6 20. 20.1 20.2 21.

LOG-LOG SCALE .......................................................................................................................................................... 44 PRESSURE CURVES ANALYSIS : EXAMPLE OF "WELL WITH WELLBORE STORAGE AND SKIN, HOMOGENEOUS RESERVOIR" ................................................................................................................................................................ 45 BUILD-UP ANALYSIS : BUILD-UP TYPE CURVE ............................................................................................................ 48 SEMI LOG ANALYSIS............................................................................................................................................... 50 M.D.H. ANALYSIS : ∆P VS LOG∆T .............................................................................................................................. 50 HORNER ANALYSIS...................................................................................................................................................... 50 DERIVATIVE ANALYSIS......................................................................................................................................... 52 DEFINITION.................................................................................................................................................................. 52 DERIVATIVE TYPE-CURVE : EXAMPLE OF "WELL WITH WELLBORE STORAGE AND SKIN, HOMOGENEOUS RESERVOIR" ................................................................................................................................................................ 52 DATA DIFFERENTIATION ............................................................................................................................................. 55 THE ANALYSIS SCALES ................................................................................................................................................ 56 PRINCIPAL FLOW REGIMES ................................................................................................................................ 58 RADIAL FLOW ............................................................................................................................................................. 58 LINEAR FLOW.............................................................................................................................................................. 59 BI-LINEAR FLOW ........................................................................................................................................................ 63 SPHERICAL FLOW ........................................................................................................................................................ 66 PSEUDO STEADY STATE............................................................................................................................................... 67 BOUNDARY THEORY .............................................................................................................................................. 68 ONE SEALING FAULT ................................................................................................................................................... 68 TWO PARALLEL SEALING FAULTS ............................................................................................................................... 70 TWO INTERSECTING SEALING FAULTS ........................................................................................................................ 77 CLOSED SYSTEM.......................................................................................................................................................... 81 CONSTANT PRESSURE BOUNDARIES............................................................................................................................ 88 SEMI PERMEABLE BOUNDARY..................................................................................................................................... 92 PREDICTING DERIVATIVE SHAPES ............................................................................................................................... 94 RESERVOIR PRESSURE .......................................................................................................................................... 96 DEFINITIONS ................................................................................................................................................................ 96 APPLICATIONS OF RESERVOIR PRESSURE .................................................................................................................... 97 MOBILITY CHANGE THEORY ........................................................................................................................... 101 DEFINITIONS .............................................................................................................................................................. 101 RADIAL COMPOSITE BEHAVIOR................................................................................................................................. 102 LINEAR COMPOSITE BEHAVIOR ................................................................................................................................. 107 MULTICOMPOSITE SYSTEMS ..................................................................................................................................... 109 PARTIAL PENETRATION THEORY .................................................................................................................. 110 DEFINITION................................................................................................................................................................ 110 CHARACTERISTIC FLOW REGIMES ............................................................................................................................. 110 LOG-LOG ANALYSIS .................................................................................................................................................. 111 SEMI-LOG ANALYSIS ................................................................................................................................................. 112 GEOMETRICAL SKIN SPP ........................................................................................................................................... 112 SPHERICAL FLOW ANALYSIS ..................................................................................................................................... 113 HYDRAULIC FRACTURE THEORY................................................................................................................... 115 INFINITE CONDUCTIVITY OR UNIFORM FLUX VERTICAL FRACTURE ......................................................................... 115 FINITE CONDUCTIVITY VERTICAL FRACTURE ........................................................................................................... 117 HORIZONTAL WELL THEORY .......................................................................................................................... 119

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 22. 22.1 22.2 22.3 23. 23.1 23.2 23.3 23.4 23.5 24. 24.1 24.2 24.3 24.4 25. 25.1 25.2 25.3 25.4 25.5 25.6 26. 26.1 26.2 26.3 26.4 26.5 26.6 26.7 27. 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8

DEFINITION................................................................................................................................................................ 119 CHARACTERISTIC FLOW REGIMES ............................................................................................................................. 120 LOG-LOG ANALYSIS .................................................................................................................................................. 120 VERTICAL RADIAL FLOW SEMI-LOG ANALYSIS ......................................................................................................... 122 LINEAR FLOW ANALYSIS ........................................................................................................................................... 123 HORIZONTAL PSEUDO-RADIAL FLOW SEMI-LOG ANALYSIS ...................................................................................... 124 DISCUSSION OF THE HORIZONTAL WELL MODEL ...................................................................................................... 126 OTHER HORIZONTAL WELL MODELS ......................................................................................................................... 132 SKIN FACTORS ........................................................................................................................................................ 136 THE DIFFERENT SKIN FACTORS ................................................................................................................................. 136 GEOMETRICAL SKIN .................................................................................................................................................. 136 ANISOTROPY PSEUDO-SKIN....................................................................................................................................... 137 PERFORMING A TEST DESIGN.......................................................................................................................... 138 INTRODUCTION.......................................................................................................................................................... 138 HARDWARE ............................................................................................................................................................... 139 GAUGES ..................................................................................................................................................................... 139 PRESSURE RESPONSE ................................................................................................................................................ 140 AN EXAMPLE TEST DESIGN....................................................................................................................................... 142 GAS WELL TESTING .............................................................................................................................................. 145 GAS PROPERTIES ....................................................................................................................................................... 145 TRANSIENT ANALYSIS OF GAS WELL TESTS .............................................................................................................. 146 DELIVERABILITY TESTS............................................................................................................................................. 150 ODEH-JONES ANALYSIS ............................................................................................................................................ 155 FISSURED RESERVOIRS....................................................................................................................................... 159 PRESSURE PROFILE .................................................................................................................................................... 159 DEFINITIONS .............................................................................................................................................................. 161 DOUBLE POROSITY BEHAVIOR, RESTRICTED INTERPOROSITY FLOW (PSEUDO-STEADY STATE INTERPOROSITY FLOW). ....................................................................................................................................................................... 164 DOUBLE POROSITY BEHAVIOR, UNRESTRICTED INTERPOROSITY FLOW (TRANSIENT INTERPOROSITY FLOW)......... 178 MATRIX SKIN............................................................................................................................................................. 184 EXAMPLES OF COMPLEX HETEROGENEOUS RESPONSES ........................................................................................... 186 FACTORS COMPLICATING WELL TEST ANALYSIS.................................................................................. 188 RATE HISTORY DEFINITION ....................................................................................................................................... 189 ERROR OF START OF THE PERIOD .............................................................................................................................. 190 TIME ERROR CORRECTION........................................................................................................................................ 193 CHANGING WELLBORE STORAGE............................................................................................................................. 194 TWO PHASES LIQUID LEVEL ...................................................................................................................................... 195 PRESSURE GAUGE DRIFT ........................................................................................................................................... 197 PRESSURE GAUGE NOISE ........................................................................................................................................... 199 WELL TESTING HARDWARE ............................................................................................................................. 200 SURFACE TEST EQUIPMENT ...................................................................................................................................... 200 SUBSEA EQUIPMENT ................................................................................................................................................. 210 PRESSURE MEASUREMENT ....................................................................................................................................... 211 DOWNHOLE EQUIPMENT ........................................................................................................................................... 212 QUALITY CONTROL CHECKS .................................................................................................................................... 215 SAMPLING ................................................................................................................................................................. 216 SAFETY ...................................................................................................................................................................... 218 ENVIRONMENTAL ISSUES .......................................................................................................................................... 220

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk 28. 28.1 28.2 28.3 28.4 29. 29.1 29.2 29.3 29.4

INTERPRETATION PROCEDURE, REPORTS AND PRESENTATION OF RESULTS.......................... 222 METHODOLOGY ........................................................................................................................................................ 223 THE DIAGNOSIS : TYPICAL PRESSURE AND DERIVATIVE SHAPES .............................................................................. 225 SUMMARY OF USUAL LOG-LOG RESPONSES .............................................................................................................. 227 CONSISTENCY CHECK WITH THE TEST HISTORY SIMULATION .................................................................................. 231 APPENDICES............................................................................................................................................................. 237 NOMENCLATURE ....................................................................................................................................................... 237 LIQUID TO GAS CONVERSION CHART ........................................................................................................................ 241 FLARING FLOW CHART ............................................................................................................................................. 242 TESTING FLOW CHART .............................................................................................................................................. 243

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk OVERVIEW

This intensive course teaches participants how to design and analyse pressure transient tests, for both oil and gas, commonly used by the petroleum industry. Participants are taught how to properly design tests to achieve specific objectives and how to use both classical and interactive computer analysis methods (PIE) to analyse data. The course covers both pressure transient theory and the practical aspects of well testing, including the equipment employed, using both lecture and problem sessions.

OBJECTIVES

Participants will: • • • • •

Be able to design and analyse well tests with classical and software tools Gain experience with real test data sets Learn about the equipment used for well testing Become aware of the implications of accurate planning Appreciate how the theory can affect the practical aspects of testing and interpretation.

Acknowledgements are due to Mike Wilson of Well Test Solutions Ltd., for his support in the preparation of these notes and his permission to include examples generated in PIE, the well test interpretation software package.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk

1. INTRODUCTION The pressure behaviour of a well can be easily measured and is extremely useful in analysing and predicting reservoir performance or diagnosing the condition of a well. Various instruments to measure flowing and static pressures in oil and gas wells have been in use since the 1920's. The recording devices that have been used include mechanical, (the Borden tube which records via a stylus mark on a blackened metal sheet), sonic (echometers which measure liquid levels) and electronic instrumentation (which measure pressure and temperature). Continuous recording instruments, such as the Amerada gauge, have been available since the early 1930's. Today the preferred instrument is the electronic (memory) gauge. One of the earliest applications of bottom-hole pressure measurements in wells was the determination of static or average reservoir pressures from the bottom-hole pressure measured after a well had been shut-in for between 24 and 72 hours. Although this static measurement indicated the average formation pressure in the permeable and productive reservoir it soon became apparent to engineers that static pressure measurements depended considerably on the time for which the well had been shut-in. Thus, the lower the permeability, the longer the time required for pressure stabilisation in the well. This lead to the realisation that when a well was shut-in, the rate of the pressure build-up would be a reflection of the reservoir permeability around the well. Since a well test and subsequent pressure transient analysis is the most powerful tool available to the reservoir engineer for determining reservoir characteristics and planning production schedules, the subject of well test analysis has attracted considerable attention. Petroleum Engineering literature alone includes more than 500 published technical papers on this subject whilst the field of ground water hydrology also contains a similar number of publications on pump test analysis. A well test is the only method available to the reservoir engineer for examining the dynamic response in the reservoir and considerable information can be gained from a well test. Therefore, well testing is a subject which should be considered seriously. After static pressure measurements, the most common methods of transient (time dependant) pressure analysis required that data points be selected such that they fell on a well-defined straight line on either semi-logarithmic or cartesian graph paper. The well test analyst must then insure that the proper straight line has been chosen if more than one line can be drawn through the plotted data. This aspect of interpretation of well test data requires the input of a reservoir engineer. Equally important is the design of a well test to ensure that the duration and format of the test is such that it produces good quality data for analysis.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk With the advent of powerful desktop computers and software, analysis of transient well test pressure data took another step forward with the introduction of type curve analysis. The computer can perform large numbers of calculations necessary to generate a type curve which is specific to the reservoir itself and also takes into account many different flow periods which not all straight line analysis did. This eliminates generalisations but still requires interpretation of the data set which the reservoir engineer must perform. This is considered to be the best and most efficient method of well test analysis currently available. The results obtained from transient pressure analysis are used to set up numerical simulation models for predicting future production and to assist in making estimates of the Hydrocarbons Originally in place. Both explicitly compelling reasons to carry out well tests. It should also be noted that all units within these course notes where not clearly stated are “oilfield” units which means psi, feet, Barrels etc rather than S.I. Units.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk

2. FUNDAMENTALS OF WELL TESTING 2.1 Description of a Well Test A Well Test is the examination of the transient behaviour of a porous reservoir as the result of a temporary change in production conditions performed while measuring all the relevant parameters. It is usually performed over a relatively short period of time in comparison to the producing life of a field. 2.2 Terminology and Definitions Drawdown/Injection period The drawdown can be both the part of the test when the well is flowing (fluid extracted from the reservoir) and a value represented by the difference in pressure between the initial static reservoir pressure and the flowing bottom hole pressure. The injection period is the opposite of a drawdown in that fluid is injected into the reservoir creating an increase of pressure in the near well bore area and the reservoir. Build up/Fall off The build up can be both the part of the test when the well is shut in (not flowing) and a value represented by the difference in the pressure measured at any time during the build up and the final flowing pressure. A fall off is the time after the ending of an injection period where the pressure falls. In both cases the flow rate is known to be zero. Perforating This is the activity of making holes in the casing and/or reservoir so that there is communication between the reservoir and the well bore. This is usually achieved by detonating explosives when the perforating guns are known to be at the correct perforating depth. If the pressure in the wellbore prior to perforating is less than the reservoir pressure, this is known as underbalanced perforating. This can have the effect of improving well productivity by allowing the perforations to flow immediately after perforating reducing the skin (see below for definition). When the pressure in the well is greater than in the reservoir, this is overbalanced perforating. Underbalanced perforating is preferred whenever practical and safe and is widely used today. It can also be useful to replace the drilling mud with specialised completions fluids (brine, diesel, base oil for example) to improve well productivity on perforating. Well Bore Storage

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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Wellbore storage is an early transient phenomenon whose effect decays in time and occurs every time a rate change takes place. Usually the well rate is controlled at the surface by means of a valve or choke. When the valve or choke is opened, wellbore fluids are initially produced at the wellhead while production at the perforations remains zero. During this early time period the wellbore is said to be unloading or decompressing. Eventually, the perforations will also start to produce and in time equal the production at the wellhead. During constant production, wellbore storage effects are negligible. At the point of shut-in, wellbore storage is referred to as afterflow. Whilst the rate at the wellhead is zero, production at the perforations continues, gradually decaying to zero. Well bore storage is expressed in units of volume per unit of pressure, barrels per psi, with the nomenclature of C. Skin This is a dimensionless value attributed to the near well bore damage or stimulation. Reservoir permeability in the near wellbore area is frequently altered as a result of drilling, production, or stimulation of the well. For example, the invasion of drilling fluids, or migration of fines during production tends to lower the permeability in the near wellbore region. The well is subsequently referred to as damaged under these circumstances and this is represented by a positive skin value. Conversely, stimulation treatments such as acidizing or fracturing may create an increase in the near wellbore permeability relative to the overall reservoir permeability. This is summarised below; Skin > 0 Damaged Skin = 0 Neutral Skin < 0 Stimulated (not usually less than -5) The value is dimensionless and is represented by the letter S. Permeability Permeability is a measure of the ability of a porous rock to transport a fluid through it and is measured, usually, in Darcys, D, or millidarcies, mD. Its units are L2. Porosity Porosity is the amount of void (space) in a porous rock measured as a percentage of the whole rock. Mobility

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk Mobility is the combination of the ability of a rock to transport a certain fluid through it given a fluid’s viscosity and is permeability divided by viscosity, k/µ. Partial Penetration This describes a well completion where only part of the total permeable formation is perforated or communicating with the well. Hydraulic Fractures These are, usually, purposefully induced cracks in the formation rock which allows a much greater wellbore contact with the formation and should not be confused with Natural fractures explained below. Natural Fractures (or Double Porosity) This is where naturally occurring fractures in the formation rock exist meaning there are two different porosities, one for the fractures and one for the rock between the fractures. In order for this effect to be observed in transient test analysis, the difference in the two porosities must be significant, generally an order of magnitude. Radius of Investigation. When a change of flow rate occurs in a well, ie, initial flow, a change in the reservoir pressure from its initial undisturbed state is created. Over time this pressure disturbance propagates further away from the wellbore. The radius of investigation is defined as the distance that a significant pressure disturbance has propagated away from the well. The mathematical description is given in section 8.3. 2.3 Input data required for and Information gained from well testing The fundamental role of the reservoir engineer is to produce oil and gas reservoirs having determined the characteristics of the in-place fluids and the reservoir. In general, the characteristics are listed below and it should be noted that whilst the first four parameters are used to estimate the amount of hydrocarbons in place the reservoir permeability establishes the ability of the fluids in place to flow through the reservoir: a)

Net pay.

b)

Porosity.

c)

Reservoir description;

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk

-

Lateral extent, Shape, Heterogeneities, Boundaries.

d)

Average reservoir pressure (static pressure) and temperature.

e)

Formation permeability given net pay.

In practice net pay, porosity and the reservoir description are derived from the geological interpretation of core data, log data and geophysical surveys. Pressure transient tests are generally conducted to determine the average reservoir pressure, the effectiveness of the well completion (determining a value of skin - see below), the well productivity/deliverability, distances to boundaries and permeability of the reservoir volume drained by the well. It should also be noted that pressure transient tests can be designed to estimate the size and shape of the drainage volume. Other reasons for testing may be to determine the nature of the produced fluids, production problems, to clean up the well for production, the maximum possible flow rate, and connectivity in the reservoir. For any well production (or injection) usually takes place via the drilled wellbore hence the conditions prevailing around the wellbore are of particular interest particularly if the sand face may be damaged during drilling or as a result of production operations. Quantitative information gained from a welltest, therefore, enables the reservoir engineer to determine whether or not low productivity in a well is due to damage, low formation permeability, or a low driving force for moving fluid to the well. Similarly if a well has been stimulated to remove formation damage the success of the operation can be evaluated hence the reservoir engineer can make practical decisions regarding future well stimulation treatments and/or operating practices. Thus it can be said that a pressure transient test is a fluid flow experiment used to determine one or more of the reservoir characteristics and properties mentioned above. Input Data Required To perform a test analysis a considerable amount of information is required. The following list summarises this to perform an interpretation of a single pressure test. a) through g) are mandatory while h) and i) are optional. a)

The well production rates as a function of time.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk b)

The bottom-hole pressure as a function of time.

c)

The wellbore configuration; -

d)

A documented test history including; -

e)

a complete sequence of events. any operational problems.

Well data -

f)

completion report. string diagram. gauge depths.

drilled v true depths if well not vertical. direction and length of horizontal or inclined sections relative to reservoir boundaries or discontinuities. Well bore radius (drill bit size not casing size)

Rock and fluid properties Net pay (formation thickness, h) Porosity Water Saturation Oil viscosity Water compressibility* Oil compressibility* Rock compressibility*

g)

Geological interpretation characteristics.

of

the

reservoir

extent

and

likely

General information obtained from Geologists and Geophysicists h)

Production logs (optional but recommended with large h) To determine Producing intervals.

i)

Gradient surveys (optional but recommended) to confirm; -

Static fluids levels and fluid contacts/interfaces Static fluid densities.

formation

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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* Individual compressibilities can be combined and represented by ‘Total Compressibility’ of the reservoir. Whenever possible, the above data should be obtained prior to performing the test and used to run a test design to examine the theoretical response for the planned test. Failing to plan the test is planning to fail. For exploration well testing where test parameters may not be readily available, Robert C Earlougher’s SPE Monograph Advances in Well Test Analysis has an appendix in which many of the above parameters can be derived from correlations. Why perform well tests? A large amount of information can be gained from performing well tests. A non exhaustive list of this information follows; Well Tests (Transient Pressure Tests) are performed to Determine: Nature of produced fluids. Rates of produced fluids. Reservoir and well characteristics. Location of reservoir limits (or not). Well deliverability (drawdown/rates). Sand production (if any). Maximum rate. Hydrocarbons in place. Well connectivity (interference tests). Reservoir layers. Production characteristics and any production problems. The long term productivity from a short term test operation. When well tests can derive such a large amount of information it should be evident that Well Testing is a valuable tool to the reservoir engineer. Therefore:

PERFORM WELL TESTS WHENEVER POSSIBLE

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk

3. AN OVERVIEW OF PRESSURE TRANSIENT ANALYSIS 3.1 Basic equations Transient pressure analysis models are solutions to the diffusivity equation obtained by a combination of Darcy’s law and various hypotheses for the fluid in the reservoir. When it is assumed that the fluid density remains constant and that the flow is through a horizontal linear porous medium then Darcy’s law can be expressed as follows;

q=−

kA ∆ p l µ

(Eq. 3-1)

where, q k A µ l ∆P

is the flow rate is the permeability of the porous medium, is the area available to flow, is the viscosity of the fluid flowing through the porous medium, is the length of porous medium through which the flow is transported. is the pressure drop over the length l

For radial flow, which is flow in a hydrocarbon reservoir into a well bore, Equation 3.1 becomes; q = 2π

kh dp µ dr

(Eq. 3-2)

which, after separating the variables, integrating with respect to r from well bore, rw to the effective radius of investigation, re, introducing an equation for skin by van Everdingen and expressing the equation in field units the equation becomes; pe − p wf = 1412 .

 qBµ  re  ln + S  kh  rw 

(Eq. 3-3)

In summary, for radial flow into a well bore, the pressure difference (drawdown) is directly proportional to the following parameters; Flow rate

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk Viscosity Formation volume factor Permeability formation thickness well bore radius (limited effect because of the ln term) skin The application of Darcy’s Law and the different solutions to the diffusivity equation will be explained in more detail later in this text. References: L.P Dake, Fundamentals of Reservoir Engineering, Chapter 4, sections 4.1 to 4.7

3.2 Well Test Interpretation Methodology Well test interpretation can be simplified if it is considered as a special pattern recognition problem. This concept is illustrated by the following schematic;

INPUT(I)

SYSTEM (S)

OUTPUT (O)

Thus, the problem is to define the system when knowing the output for a given input. In a well test, a known constant signal, I (a constant production rate) is applied to a system, S (the well and reservoir) and the response of that system, O, (the change in bottom hole pressure) is measured. The aim of well test interpretation is, therefore, to identify and characterise the system knowing only the input and output signals. This is called the INVERSE PROBLEM where; O / I ----> S The solution to this problem involves the selection of a well defined theoretical model where output for the same input signal is as close as possible to that of the actual reservoir. Hence, the construction of the model response involves the DIRECT PROBLEM where; I * S ----> O

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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Interpretation therefore relies on theoretical models which are assumed to have characteristics which are representative of those of the actual well and reservoir. The solution to the inverse problem is not unique but the number of possibilities decreases as the number of output responses increases and measurements become more accurate. The aim of well testing is to evaluate the well and reservoir system under dynamic conditions. The interpretation of measured data combined with reservoir engineering expertise results in the production of a reservoir model. The reservoir model subsequently enables the prediction of field production in terms of production rate and fluid recovery. Together with economic considerations, the reservoir model can be used to formulate a development strategy. Having determined the development strategy, the production facilities and completion can then be optimised accordingly.

3.3 Types of Well Tests Throughout this course a number of different tests will be considered and discussed. The following sections illustrate the wide variety of tests available to the reservoir engineer. Classification by Completion Production Test The well is completed as a production well in cased hole hence the well completion is permanent, even though it may be pulled out of the well on completion of the test. Production tests are generally carried out on initially completing development wells to define reservoir parameters and then routinely run as part of the reservoir management strategy. DST (Drill Stem Test) In a DST, the well is completed temporarily with down-hole control provided by conventional DST tools. This type of completion can be used in cased or in open hole, and is usually associated with exploration and appraisal wells where the aim of the test is to determine as many reservoir parameters as practically possible or to confirm the observations of previous tests on other exploration wells. Drill Stem tests are so called because originally the drill string (drill pipe) was used as the production string. This is now considered unsafe in all parts of the world and production tubing is employed. High Pressure High Temperature Tests

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk These tests are classified separately since the pressures and temperatures encountered give rise to special considerations. However, permanent production equipment is usually used and in all other ways the test will be similar to a production test. Classification by Test Procedure Pressure build-up Pressure build-up tests are performed with the well is shut in and not flowing. In all cases a build up is recommended. The well must be flowing, ideally at a constant rate, before the well is shut-in and the rise in bottom-hole pressure recorded. Almost without exception, a build up will produce better quality pressure data than a drawdown. Besides the issue of data quality which in itself is important, the other compelling reason a build up is used is that it is the only time in a well test when the flow rate is categorically known without any margin of error. It is always zero. Pressure drawdown In a pressure drawdown test the well is shut-in prior to commencing the test so that pressure can equalise throughout the formation. Having run pressure measuring equipment into the wellbore the flowing pressure is recorded as the well is produced at a nominal constant rate. Data quality can be erratic but with good data and a constant rate, drawdowns can be used to derive drainage areas as well as to derive reservoir properties by normal type curve analysis. Injection Injection tests are usually only performed to determine maximum sustainable injection rates for reservoir injection projects or stimulation operations. In practice injection tests are normally followed by fall-off tests. Note that drawdown and injectivity tests are not popular as it is frequently not possible to hold the rate at a constant level throughout the test period. These tests can be analysed, as a stand alone test or as part of a subsequent production test/DST, in a similar way to any other test, by making the production rate negative. Pressure fall-off Pressure fall-off tests, which are similar to build-up tests in that the production rate is zero, follow injection tests. Ideally the injection rate is stabilised and held constant for a predetermined duration prior to ceasing injection. The decline in the bottom-hole pressure is then recorded as the reservoir pressure stabilises.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk Step-rate Step rate tests involve flowing the well at different rates. The main advantage of these tests is that the well is not shut-in between rates saving time. Flowing the well at different rates helps establish production characteristics from low to high rates for future reference and to determine rate dependant phenomena. (See gas well testing below) Gas well testing In gas wells special tests are used to determine the rate dependent skin factor and the Absolute Open Flow (AOF) potential of the wells tested. Some of the most common tests encountered are;

i)

Flow after flow (FAF) and multi-rate tests.

ii)

Isochronal tests.

iii)

Modified Isochronal tests.

Whilst the flow after flow test can be conducted without shutting-in the well thus saving time, the isochronal and modified isochronal test sequences require the well to be shut-in between different flow rates. In an isochronal test the well is shut-in after each flow period until the previous shut-in pressure is reached, (ie, all flow and build-up periods may be different). For the modified isochronal test all flow and build-up periods are equal in duration except for the final stabilised flow. Generally, it has been found that isochronal tests (of both types) produce better results and more build ups for analysis and a modified isochronal test takes less time and is therefore popular with financial managers. Interference and Pulse Tests Interference and Pulse tests are used primarily to define reservoir rather than individual well characteristics. They are commonly used to evaluate communication between wells completed in the same formations and are therefore excellent for determining average reservoir perrmeabilities between wells. A typical test would involve the measurement of the pressure response at a shut-in observation well or wells due to a rate change (interference test) or a series of rate changes (pulse test) at another well. In vertical interference tests the test is designed to evaluate communication between different formations in the same well, where the same formation is encountered at different depths or is vertically displaced in a faulted reservoir. Classification by Operational phase

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk Exploration The initial exploration phase of drilling a well into a structure about which nothing is known other than from geological and seismic data (sometimes referred to as a wildcat) carries the most risk of not being tested. If hydrocarbons are identified from mud logs and electric logs and a test is performed, these are usually the simplest and shortest. The primary aim will be to confirm the presence and nature of hydrocarbons, take a some samples of the produced fluids, obtain an indication of the flow rates and to determine a value of permeability and skin. Historically, wildcat wells have had approximately a one in ten chance of finding commercial hydrocarbons. This ratio is lower in known hydrocarbon provinces, such as the North Sea or the Gulf of Mexico, perhaps one in eight. Usually the transient solution to the diffusivity equation is employed for this type of testing where the limits of the reservoir are not encountered by the “pressure transient”. Appraisal Once the presence of hydrocarbons has been confirmed from an exploration well test, the structure is appraised by drilling further wells to examine the extent of the hydrocarbons. Appraisal well tests will usually be designed specifically to clarify any structure/reservoir uncertainty such as the limit of the reservoir or changes in fluid phases across the structure (as may happen in a large gas condensate field). Development At the field development phase, the well may not even be tested or it may be completed, cleaned up and suspended for future production. Only if something unexpected is found from drilling or logging is the well fully tested.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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4. TYPICAL TEST PROCEDURE For any test, drawdown or build-up the following procedures should be incorporated into the test programme; a) Prepare the well. This can mean running casing, changing the completion fluid from mud to brine, which can allow the annular pressure operated downhole tools to operate more reliably, or place a plug or cement in the well. b) Run a bottom-hole pressure gauge and a completion in the well. Ideally the gauges should be located opposite or below the perforations and below any fluid contacts in the wellbore. c) Produce the well (ideally at a constant rate or rates) for some period of time, tp, (hours). d) During the flow period measure the relevant parameters, determine produced fluid properties and take PVT samples. Take some samples early in the test in case of subsequent problems. e) Shut the well in and monitor the bottom-hole pressure response if surface read-out is available. When using downhole shut-in tools monitor the wellhead pressure (which should not be bled down to zero) response to ensure that the well is shut-in and remains shut-in throughout the test. f) Make well safe to allow retrieval of gauges and completion if applicable. g) Retrieve gauges and validate data before terminating operations. Repeat test if data quality is poor or corrupt. h) Proceed with interpretation. 4.1 Operational Tips Pressure test everything on site. Ensure sufficient fixed chokes are available, usually from 16/64” to 1” every 4/64 and always flow for long periods of time after clean up on a fixed choke. Examine adjustable choke tip and zero before each test. Ensure sufficient orifice plates are available for the Daniel meter.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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Calibrate the measuring instruments on the separator; liquid meters with pumps and tank, Barton with Dead Weight Tester and calibrated air supply. Verify the separator’s safety valve certification and all equipment certification if applicable. Ensure remote ignition system of burners works if offshore. Ensure burner booms are hung and rigged correctly to avoid problems during adverse weather conditions. Record high and low tides throughout the test. Record every pressure cycle of the annulus if using annular operated downhole tools. Do not move or hit anything connected to the well during the build up as long as all is well. Check policy on opening the well in the dark and encountering H2S prior to commencing operations. Make friends with the Chef. You may miss regular meals when testing so it is useful to have an ally in the galley!

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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5. FLOW STATES For pressure transient analysis the governing flow equation, referred to as the diffusivity equation, expressed in cartesian coordinates is: 2 2 ∂p k y ∂2 p kx ∂ p kz ∂ p + + = φ ct 2 2 2 µ ∂x µ ∂y µ ∂z ∂t

(Eq. 5-1)

Only the following flow states, as solutions to the above equation, are considered in common well test interpretation theory and in this material. 5.1 Steady State The time derivative is assumed to be equal to zero, ie: ∂p = 0 ∂t

(Eq. 5-2)

This means the pressure in the reservoir never changes with time and occurs when a constant pressure boundary exists at some distance from the well. 5.2 Pseudo-steady State The time derivative in Equation 5.1 is a constant, ie: ∂p = constant ∂t

(Eq. 5-3)

This means that the pressure is changing constantly with time and the value of the constant depends on the reservoir. In other words, all boundaries have been encountered and the reservoir is depleting. 5.3 Transient State The time derivative is expressed as a function of time and space, ie:

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk ∂p = f (x, y,z,t) ∂t

(Eq. 5-4)

This state is most frequently encountered in exploration pressure transient testing. However, as the radius of investigation increases with time Pseudo-steady state may be observed if the radius of investigation reaches the outer boundaries.

6. DARCY’S LAW Darcy's law expresses the rate through a sample of porous medium as a function of the pressure drop between the two ends of the sample. q A dp / dl Figure .6-16-2 : Rate through a sample. q A

=V =

k dp µ dl

(Eq. 6-1)

With : q : volumetric rate A : cross sectional area of the sample V : flow velocity k : permeability of the porous medium µ : viscosity of the fluid The flow velocity V is proportional to the mobility k/µ and to the pressure gradient dp/dl.

In case of radial flow, the Darcy's law is expressed : q 2πrh

=V =

k dp µ dr

(Eq. 6-2)

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk

re

q

q rw

Figure 6-3 : Radial flow. For steady state flow condition, the pressure difference between the external and the internal cylinders is : pe − pw =

qµ 2 π kh

ln

re rw

The relationship is used in the definition of the dimensionless pressure.

(Eq. 6-3)

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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7. THE DIFFUSIVITY EQUATION AND ITS SOLUTIONS

7.1 Hypotheses • Constant properties : k, µ, φ and the system compressibility. • Pressure gradients are low. • The formation is not compressible and saturated with fluid. 7.2 Darcy's law →

V=

→

k µ

(Eq. 7-1)

grad p

7.3 Principle of conservation of mass (continuity equation) The difference between the mass flow rate in, and the mass flow rate out the element, defines the amount of mass change in the element during the time dt. →

div ρV = − φ

The density ρ =

m v

∂ρ ∂t

(Eq. 7-2)

is used.

7.4 Equation of state of a constant compressibility fluid The compressibility, defined as the relative change of fluid volume, is expressed with the density ρ : c=−

1 ∂v v ∂p

=

1 ∂ρ ρ ∂p

(Eq. 7-3)

With a constant compressibility, the fluid equation of state is : ρ = ρ0e

ct  p − p0 

(Eq. 7-4)

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk For a liquid flow in a porous medium, the total system compressibility ct is attributed to an equivalent fluid : ct = co So + cw S w + c f

(Eq. 7-5)

7.5 Diffusivity equation Combining the three equations:  k → div  ρ grad  µ

 ∂ρ ∂p = φ ρ ct p = φ ∂t ∂t 

(Eq. 7-6)

In radial coordinates, and with the condition of low pressure gradients defined with the

( )

∂p approximation ∂r

2

≅ 0 it comes,

 ∂ p ∂ r  → φµ ct ∂ p 1  ∂r    div  grad p = = ∇2 p =   r ∂r k ∂t

The ratio

k φµ ct

(Eq. 7-7)

is called hydraulic diffusivity.

7.6 Diffusivity equation in dimensionless terms (U.S. oil field system of units)

The dimensionless pressure is given by;

pD =

kh 141. 2 qB µ

∆p

with the dimensionless time given as;

(Eq. 7-8)

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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tD =

0. 000264 k φµct rw2

∆t

(Eq. 7-9)

and the dimensionless radius rD =

r rw

(Eq. 7-10)

The diffusivity equation in dimensionless terms becomes:

 ∂ pD  ∂  rD  ∂ pD 1  ∂ rD  = ∇ 2 pD = ∂ rD ∂tD rD

(Eq. 7-11)

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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8. RESERVOIR AND FLUID ASSUMPTIONS FOR SOLVING THE DIFFUSIVITY EQUATION 8.1 The line source solution • Initial condition : the reservoir is at initial pressure. pD = 0 at tD < 0

(Eq. 8-1)

• Well condition : the rate is constant, the well is a "line source".  ∂ pD   = −1 Lim  rD ∂ r   D r→0

(Eq. 8-2)

• Outer condition : the reservoir is infinite. Lim pD = 0 r→∞

(Eq. 8-3)

The solution is called Exponential Integral. p D ( t D , rD ) =−

∞

Ei( − x ) =− ∫ x

1  rD2  Ei  −  2  4t D 

e −u du u

8.2 Semi-log approximation : radial flow regime The Exponential Integral can be approximated with a log. For x < 0.01, Ei( x ) =− ln(γ x )

(Eq. 8-4)

(Eq. 8-5)

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk with γ = 1.78 : Euler's constant p D (t D , rD ) =

[ (

)

1 ln t D rD2 + 0.809 2

p(r,t)

ri1

pi

]

(Eq. 8-6)

log(r) ri2

t1 pw1

t2

pw2

Figure 8-1 : Pressure profile versus the log of the distance to the well.

8.3 Radius of investigation The radius of investigation ri is in general defined with one of the two relationships; t D riD2 =

1 4

or t D riD2 =

1 γ2

.

(Eq. 8-7)

This gives respectively, ri = 0. 032 kt φµct

(Eq. 8-8)

ri = 0. 029 kt φµct

(Eq. 8-9)

and

Time is given in hours, porosity as a decimal and radius of investigation is in feet. Note also that the radius of investigation is independent of the rate.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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9. WELLBORE STORAGE 9.1 Definition The production at surface is due to the expansion of the fluid in the wellbore. The reservoir contribution is negligible. " ! !

!

rw

r

pi

pw

Figure 9-1 : Wellbore storage effect. Pressure profile.

During constant production, wellbore storage effects are negligible. At the point of shut-in, wellbore storage is referred to as afterflow. Whilst the rate at the wellhead is zero, production at the perforations continues gradually decaying to zero. Wellbore storage is defined as the difference between the sandface and wellhead rates and is assumed to be proportional to the wellbore storage constant, C, ie:

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

Rate, q

Pressure, p

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q surface q sand face Time, t

Figure 9-2 : Wellbore storage effect. Sand face and surface rates. q sf − q =

24 C dp w B dt

(Eq. 9-1)

where qsf = the flow rate at the sand face q = the flow rate at the surface B = the formation volume factor dpw = the change in downhole pressure after the rate change dt = the time after rate change

9.2 Cartesian plot analysis Wellbore storage effects dominate the pressure transient response at early time independent of the reservoir characteristics. It is possible to estimate a value of well bore storage, C, during this early time period from or a cartesian plot. Assuming that a well has just been put on production then the sand face rate, qsf, will initially be zero until it stabilises at the constant surface rate, q. Substituting these conditions into equation 9.1 gives: ∆p =

qB∆t 24 C

(Eq. 9-2)

Equation 9.2 above indicates that the wellbore pressure response is linear with time at early time, after a rate change when wellbore storage effects are dominant. A cartesian plot of the early time data will exhibit a straight line which passes through the origin.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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Dp

mWBS

0 0

Dt

Figure 9-3 : Well Bore Storage plot (Cartesian) For the above cartesian plot of ∆t versus ∆p and equation 9.2 the slope of the gradient of the early time data, mWBS,which falls on a straight line will be given as follows; mWBS =

qB 24 C

(Eq. 9-3)

from which the well bore storage constant can be derived with knowledge of the other parameters.

9.3 Estimating wellbore storage from completion An estimate of well bore storage can be made from the volume of the completion and the compressibility of the fluid as follows; C = Vw c

(Eq. 9-5)

where; C is the well bore storage constant Vw is the well bore volume and c is the compressibility of the fluid in the well bore. This method is not as accurate as deriving the well bore storage from the plots described above since the compressibility of the fluid in the well bore will change with pressure

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk (which changes with time), particularly with gas. It does, however, allow the engineer to make a first estimate. Typically, values of well bore storage are less than 1 bbl/psi for both oil and gas and for a downhole shut in, which reduces the compressible well bore volume significantly, values can be as low as 10-3 bbl/psi or less. It is desirable to minimise the well bore storage to eliminate the risk of masking, or hiding, reservoir effects and also to reduce the amount of time required to carry out the test. In order to minimise these effects, the gauge measuring the downhole pressure should be placed as near to the reservoir as possible and a downhole shut in employed. The above theory is applicable for wells which are filled completely. When the well bore is only partially filled and the liquid level is changing, the well bore storage constant C, is given by the following equation; C=

Vu ρ g 144 g c

(Eq. 9-4)

where Vu is the well bore volume per unit length in barrels ρ is the fluid density g is the acceleration due to gravity ft/sec2and gc is a units conversion factor 32.17 lbmft/lbfsec2

Reference: SPE Monograph Advances in Well Test Analysis, Robert C Earlougher.Page 10

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

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10. SKIN 10.1 Definition

S=

kh 141. 2 qB µ

∆pSkin

(Eq. 10-1)

Damaged well (S > 0) : poor contact between the well and the reservoir (mud-cake, insufficient perforation density, partial penetration) or invaded zone Stimulated well (S < 0) : surface of contact between the well and the reservoir increased (fracture) or stimulated zone Steady state flow in the circular zone :

k

rs rw

ks

pw, S − pw, S =0 =

141. 2 qB µ kS h

ln

rS rw

−

141. 2 qB µ kh

ln

rS rw

(Eq. 10-2)

The skin is expressed :

S=

 k  r kh pw , S − pw , S = 0 =  − 1 ln S 1412 . qBµ  k S  rw

(

)

(Eq. 10-3)

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk 10.2 Radial flow regime " ! ! ! " "

!

#

#

# #

rw

r

pi

S=0

pw

Figure 10-1 : Radial flow regime. Pressure profile. Zero skin. rw

r

pi S>0

pw(S=0) pw(S>0)

Dp(skin)

Figure 10-2 : Radial flow regime. Pressure profile. Damaged well, positive skin factor.

Fundamentals of Well Test Design and Analysis, D. Bourdet and P. Johnson

 2001

www.opc.co.uk rw

r

rwe

pi pw(S