Polymer Flood Process Manual Revision 0I
By Computer Modelling Group Ltd.
This publication and the application application described in it are furnished under license exclusively to the licensee, for internal use only, and are subject to a confidentiality agreement. They may be used only in accordance with the terms and conditions of that agreement. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic, mechanical, or otherwise, including photocopying, recording, or by any information i nformation storage/retrieval system, to any party other than the licensee, without the written permission of Computer Modelling Group. The information in this publication is believed to be accurate in all respects. However, Computer Modelling Group makes no warranty as to accuracy or suitability, and does not assume responsibility for any consequences resulting from the use thereof. The information contained herein is subject to change without notice.
Copyright
2012 Computer Modelling Group Ltd.
All rights reserved.
Builder, CMG, and Computer Modelling Group are Group are registered trademarks of Computer Modelling Group Ltd. All other trademarks are the property of their respective owners.
Computer Modelling Group Ltd.
Office #150, 3553 - 31 Street N.W. Calgary, Alberta Canada T2L 2K7
Tel: (403) 531-1300
Fax: (403) 289-8502
E-mail:
[email protected]
Contents Introduction
3
Purpose ................................................................................................................................. 3 Organization ......................................................................................................................... 3 Polymer Flood Process ......................................................................................................... 3
Polymer Flood
5
Introduction Introduc tion .................................... .................. .................................... ................................... ................................... .................................... ................................. ............... 5 Theoretical Phenomena ........................................................................................................ 5 Polymer Adsorption................ Adsorpti on................................. ................................... .................................... ................................... ................................... ....................6 Permeability Reduction ................................................................................................... 7 Inaccessible Pore Volume (IPV) ................................................................................... 10 Relative Permeability/Wettability Alteration Effects .................................................... 11 Polymer Degradation ................................. ................ ................................... .................................... ................................... ................................ ............... 14 Composition-Dependent Viscosity Effects ................................................................... 17 Shear-Dependent Viscosity Effects ............................................................................... 22 Power-Law Expression for Shear-Thinning or Pseudoplastic Fluids ....................... 26 Power-Law Expression for Shear-Thickening or Dilatant Fluids ............................ 27 Tabular Input Option for Velocity/Shear-Rate-Dependent Viscosity ...................... 30 Velocity Dependent Skin Factor .............................................................................. 31 Convert Shear Rates to Velocities ............................................................................ 32 Salinity-Dependent Salinity-Depen dent Viscosity Effects Ef fects ................................... ................. ................................... ................................... ........................ ...... 33 Lab and Field Information .................................................................................................. 34 Using the Process Wizard to Model a Polymer Flood ........................................................ 35 Viewing and Adjusting the Process Wizard Results .......................................................... 39 Components Generation .................................. ................ .................................... ................................... ................................... ........................... ......... 39 Polymer Consumption Consumptio n Reaction .................................. ................ ................................... ................................... ................................. ............... 39 Polymer Adsorption................. Adsorptio n................................... ................................... ................................... .................................... ................................. ............... 40 Polymer Adsorption Table ....................................................................................... 40 Langmuir Isotherm Option ....................................................................................... 40 Polymer Viscosity ......................................................................................................... 41 Other Considerations and Troubleshooting Information .................................................... 42 High Molecular Weight (or Low Mole Fractions) ........................................................ 42 Disproportionate Permeability Reduction Effect .......................................................... 43 Interpreting Polymer Flood Model Outputs........................................................................ 44
Appendix A – Equations
45
Introduction Introduc tion .................................... .................. .................................... ................................... ................................... .................................... ............................... ............. 45 General Formulas............................ Formulas.......... .................................... ................................... ................................... .................................... ............................... ............. 45 Revision 0I
Process Manual - Polymer Flood
1
Parts-per-million (ppm) ........................................................................................... 45 Weight Percentage ................................................................................................... 45 Mass Fraction (wt) ................................................................................................... 45 Mole Fraction (dim) ................................................................................................. 45 Polymer Flood Calculations ............................................................................................... 46 Polymer Mass Fraction ............................................................................................ 46 Polymer Mole Fraction ............................................................................................ 46 Volumetric Reaction Rate ........................................................................................ 46 Stoichiometric Coefficients ..................................................................................... 48 Polymer Adsorption Table ....................................................................................... 49 Langmuir Isotherm Option ...................................................................................... 50 Permeability Reduction............................................................................................ 52 Polymer Viscosity .................................................................................................... 53
Appendix B – Conversion of Eclipse Polymer Option to IMEX
64
Example of Eclipse Data .................................................................................................... 64 PLYVISC and PLYSHEAR Conversion to IMEX ............................................................ 65 PLYROCK Conversion to IMEX ...................................................................................... 66 PLYADS Conversion to IMEX.......................................................................................... 66
Appendix C – Conversion of IMEX Polymer Option to STARS
68
Step 1: Builder Convert Simulator Type ............................................................................ 68 Step 2: Process Wizard ....................................................................................................... 68 Input Polymer Data ....................................................................................................... 68 Input Adsorption Data ................................................................................................... 68 Input Polymer Viscosity................................................................................................ 69 Step 3: Shear Dependent Viscosity .................................................................................... 69
Appendix D – Example IMEX and STARS Simulations of Polymer
72
Comparisons of IMEX and STARS ................................................................................... 72 STARS Options For Real Polymer Phenomena ................................................................. 73
2
Process Manual - Polymer Flood
Revision 0I
Introduction
Purpose The purpose of this manual is to provide users with the i nformation they need to model polymer flood processes using the CMG STARS simulator.
Organization The following information is provided: •
Theoretical concepts and how these concepts are represented in the model
•
Lab and field data required for the simulation
•
Procedure for inputting data using the Builder Process Wizard
•
Procedure for viewing and adjusting the input data
•
View the results in Results 3D
•
Appendices B, C, and D provide information for converting an Eclipse polymer option to IMEX, and an IMEX polymer option to STARS.
Polymer Flood Process Polymer flooding, illustrated below, is an EOR (enhanced oil recovery) technique in which water-soluble polymers are added to the injection fluids to increase the viscosity of injected water and/or formation water. This provides mobility control of the fluids, which improves the volumetric sweep efficiency and reduces channeling and water breakthrough, thereby increasing the oil recovery factor.
Revision 0I
Process Manual - Polymer Flood
3
Figure 1 shows a conceptual comparison of cumulative oil recovery for water, polymer, alkaline/polymer, and ASP flooding techniques. Cumulative Oil
ASP Flood
Alkaline/Polymer Flood
Polymer Flood
Continued Water Flood
Pore Volume Injected
Figure 1 Comparison of Chemical Flooding Techniques
Figure 2 illustrates the potential improvement from chemical flood EOR processes: OilRate
WaterFlood
ChemicalFlood EORPotentialto Extendand Enhance Production
Time
Figure 2 Improved Oil Recovery from Chemical Flood Processes 1
1
Adapted from Cairn India brochure “Enhanced Oil Recovery”.
4
Process Manual - Polymer Flood
Revision 0I
Polymer Flood
Introduction Polymer flooding is a process where a thickening agent (polymer) is added to the injected fluid (typically water) to produce a more favorable mobility ratio between the injected fluid and the displaced oil. Polymers are macromolecules composed of repetitive units called monomers. Some common polymers are hydrolyzed polyacrylamide (HPAM), co-polymers of acrylamide (AMPS, NVP) and xanthan gum (biopolymer). The polymer flood mechanisms that can be modeled in STARS include: •
Viscosity and mobility variations of the injected fluid
•
Polymer Adsorption
•
Permeability Reduction
•
Inaccessible Pore Volume (IPV)
•
Relative Permeability/Wettability Alteration Effects
•
Polymer Degradation
•
Composition-Dependent Viscosity Effects
•
Shear-Dependent Viscosity Effects
•
Salinity-Dependent Viscosity Effects
Details about modeling these mechanisms are outlined in Theoretical Phenomena. Modeling a polymer flood requires, as a minimum, the viscosity of the water-polymer solution at different polymer concentrations. Other data, such as polymer adsorption, degradation, and rheology, while not required, will yield a more accurate model. Refer to Lab and Field Information on page 34. As well, refer to Other Considerations and Troubleshooting Information on page 42 for information about specific polymer issues that you may need to address or resolve.
Theoretical Phenomena The following sections describe polymer flood process phenomena and, at a high level, how they are modeled in STARS. For further information, refer to the STARS User’s Guide.
Revision 0I
Process Manual - Polymer Flood
5
Polymer Adsorption Adsorption is the adhesion of ions or molecules onto the surface of another phase 2. It is a physical and/or chemical process by which a porous solid (at the microscopic level), for example, is capable of retaining particles of a fluid on its surface after being in contact with it. Polymer adsorption in an EOR process is related to the amount of polymer retained in the smallest porous spaces or on the rock surface where the solution has passed. The adsorption levels depend on fluid type and concentration, molecular weight, flow rate, temperature, brine salinity, brine hardness and rock type (e.g. rock mineralogy and permeability) 3. Low polymer retention in the reservoir is essential for the success of a polymer EOR operation. A substantial loss of polymer may be detrimental because the polymer concentration reduction could impact its viscosity and cause a loss of mobility control or low displacement efficiency. For this reason, adsorption is usually estimated from laboratory core flood experiments conducted under conditions as close as possible to those prevailing in the field. STARS allows a description of these phenomena, through the input of a set of constant temperature adsorption isotherms (adsorption level as a function of fluid composition). These isotherms can be entered either in tabular form or using the Langmuir isotherm correlation:
Ad =
A × c i
(1 + B × ci )
(1)
where ci is the fluid component composition, and A and B are generally temperature dependent. Note that the maximum adsorption level associated with the formula is A/B. Coefficient B controls the curvature of the isotherm, and the ratio A/B, as mentioned, determines the plateau value for adsorption. This is illustrated in Figure 3: 1.0
1.0
0.9
0.9
0.8
0.8
b constant
n 0.7 o i t a r t n 0.6 e c n 0.5 o C d e 0.4 b r o s 0.3 d A
n o i t a r t n e c n o C d e b r o s d A
b increasing
0.2
0.7 0.6 0.5 0.4
a increasing
0.3 0.2
a/b constant 0.1
0.1
0.0 0
0.0 2
4
6
Concentration
8
10
0
2
4
6
8
10
Concentration
Figure 3 Typical Langmuir Isotherm Shape s3
Refer to Polymer Adsorption Table and Langmuir Isotherm Option in Appendix A – Equations of this manual for more information about the equations used by STARS to model a polymer flood. 2
Ali, L. and Barrufet, M.A., “Profile Modification due to Polymer Adsorption in Reservoir Rocks”. Energy & Fuels Vol. 8, No. 6, (1994), pp.1217-1222. 3 Lake, L.W., “Enhanced Oil Recovery”, Prentice-Hall (1989).
6
Process Manual - Polymer Flood
Revision 0I
Important Keywords for Modeling Polymer Adsorption:
Use keyword *ADSCOMP to specify components and fluid phase. Use keywords *ADSLANG or *ADSTABLE to specify the input option used for adsorption, as follows: *ADSLANG
Denotes that composition dependence is specified by Langmuir isotherm coefficients.
*ADSTABLE
Denotes that composition dependence is specified by a table of adsorption versus composition values.
To define the dependence of the adsorption data on rock type (permeability) for the component/phase specified by *ADSCOMP, use the following keywords: *ADMAXT
Specifies the maximum adsorption capacity.
*ADRT
Specifies the residual adsorption level.
*ADSROCK
Specifies the current rock type number.
*ADSTYPE
Used to assign multiple adsorption rock type numbers to grid blocks.
Permeability Reduction Many papers indicate a mobility reduction in the porous media after the polymer has flowed through. This phenomenon occurs due to increased water viscosity and reduction of permeability 4,5, caused in part by polymer adsorption, particularly if it is the chemical or mechanical (entrapment)4 type. The variation in rock permeability due to this process is given by:
(2)
k
Absolute rock permeability prior to polymer flooding
Rk
Permeability reduction factor
K =
where:
, a function of polymer adsorption and the residual resistance factor RRF , is given by:
=1+(
1) ×
(3)
4
Jennings, R. R., Rogers, J.H., and West, T. J., 1971. “Factors Influencing Mobility Control By Polymer Solutions”. J. Pet. Technol., 23(3): 391-401. SPE 2867-PA. 5 Bondor, P.L., Hirasaki, G.J., Tham, M.J., 1972. “Mathematical simulation of polymer flooding in complex reservoirs”. SPEJ (October), 369–382. SPE 3524-PA.
Revision 0I
Process Manual - Polymer Flood
7
where: AD
Cumulative adsorption of polymer per unit volume of reservoir rock
ADMAXT
Maximum adsorptive capacity of polymer per unit volume of reservoir rock
⁄⁄
Rk varies from 1.0 to a maximum of
, as adsorption level increases.
The residual resistance factor can be obtained from core flooding experiments and can be expressed as the water (or brine) mobility ratio before and after a polymer treatmen t4,6,7 .
=
,
=
,
where:
(
),
(
),
λw
Water mobility
k w
Effective water permeability
μw
Water viscosity
(4)
As the water viscosity does not change before or after the treatment, equation (4) can be reduced to:
∆ =
,
(5)
,
If the core flooding experiment is linear, the effective permeability can be calculated using the linear expression of Darcy’s equation:
=
×
×
(6)
×
If the core flooding experiment is radial, then the effective permeability should be calculated as follows:
ℎ⁄∆ =
×
(
2 ×
)×
×
(7)
If any of the above expressions are used to calculate the effective permeability before and after the polymer flood in a core flooding experiment and if the injection rate is the same in
6
Chang, H. L., “Polymer Flooding Technology – Yesterday, Today, and Tomorrow”, paper SPE 7043 presented at the 1978 SPE Symposium on Improved Methods for Oil Recovery, Tulsa, April 16-19. 7 Singleton, M. A., Sorbie, K. S., Shields, R. A., “Further Development of the Pore Scale Mechanism of Relative Permeability Modification by Partially Hydrolized Polyacrylamide”, paper SPE 75184, presented at the oil Recovery Symposium, Tulsa, Oklahoma, 2002.
8
Process Manual - Polymer Flood
Revision 0I
both tests, the residual resistance factor, RRF, can be expressed in terms of the pressure drops, as follows 8:
∆∆ � � ,
=
(8)
,
It is typically assumed that only single-phase flow paths are altered by polymers; therefore, the permeability reduction factor for each phase α can be expressed as:
=1+(
1) ×
(9)
which affects the effective permeability of phase α,
=
×
=
×
=
�
, as follows:
(10)
where:
�
α
,
Water, oil or gas phase Absolute permeability before and after the treatment, respectively.
Therefore, to account for permeability reduction in polymer flood simulations or in any other EOR process in which the adsorption of components plays an important role, it is necessary to input the residual resistance factor and the phase to which the resistance factor will be applied. Use the following keywords to model permeability reduction: *ADMAXT
Specifies the maximum adsorption capacity, as outlined in Polymer Adsorption.
*RRFT
Specifies the residual resistance factor for the adsorbing component “i” specified via *ADSCOMP. The value of *RRFT must be greater than or equal to 1. The default value is 1.
*ADSPHBLK
With sub-keyword phase_des, overrides the default phase to which the resistance factor calculation is applied, as follows: *W Water (aqueous) phase *O Oil (oleic) phase *G Gas (gaseous) phase *ALL All phases
8
Zaitoun, A. and Kohler, N., 1988, “Two-phase Flow Through Porous Media: Effect of an Adsorbed Polymer Layer”, paper SPE 18085 presented at the 1988 SPE Annual Technical Conference and Exhibition, Houston, TX, Oct. 2-5.
Revision 0I
Process Manual - Polymer Flood
9
DEFAULTS:
*RRFT
1 (no resistance effect)
*ADSPHBLK
If not specified, the resistance factor is applied to the phase that is the source of the adsorbing component (specified by *ADSCOMP).
Note: Some polymers reduce water permeability more than they reduce hydrocarbon permeability. The result of this phenomenon, referred to as disproportionate permeability 7,9,10 reduction (DPR ) is that the residual resistance factor is neither the same nor constant for all phases, so it should be calculated in core flooding experiments for each phase, as shown below:
From water-oil experiments:
=
=
;
;
;
;
(11)
(12)
From water-gas experiments:
where:
=
=
;
;
;
;
(13)
(14)
k
Effective permeability to the phase α, where α = w, o or g
S or
Residual oil saturation (water-oil experiment)
S gr
Residual gas saturation (water-gas experiment)
S wirr
Irreducible water saturation (water-oil and water-gas experiments)
α
In the current version of STARS, it is only possible to assign a single value of the residual resistance factor. For suggestions on how to simulate the DPR effect, refer to the workaround outlined in Disproportionate Permeability Reduction Effect on page 43.
Inaccessible Pore Volume (IPV) When the flow of polymer molecules through the porous media is restricted in small pore throats, only the passage of water or brine is possible. When these pores cannot be contacted by flowing polymer molecules, they are referred to as inaccessible pore volume (IPV). This
9
Botermans, C.W., van Batenburg, D.W., and Bruining, J., “Relative Permeability Modifiers: Myth or Reality?” in SPE European Formation Damage Conference. 2001, The Hague, Netherlands. 10 Elmkies, Ph., et al., “Polymer effect on gas/water flow in porous media”, SPE/DOE IOR Symposium, April 2002, SPE 75160.
10
Process Manual - Polymer Flood
Revision 0I
phenomenon was first reported by Dawson and Lautz (1972) 11, who showed that some pore spaces may not be accessible to polymer molecules and that this allows polymer solutions to advance and displace oil at a faster rate than predicted on the basis of total porosity. They concluded that about 30% of the total pore volume may not be accessible to polymer molecules, and this has been corroborated in recent experiments by Pancharoen, Thiele and Kovscek (2010) 12. As a result, the effective porosity for a polymer solution is less than the actual reservoir porosity. A reduced polymer porosity, , can be used to represent the available pore volume to polymer solutions as follows:
= (1
where
)×
(15)
is the original porosity, adjusted for pressure and temperature of the block.
IPV can have beneficial effects on field performance. The rock surface in contact with the polymer solution will be less than the total pore volume, thus decreasing polymer adsorption. More importantly, if connate water is present in the smaller pores that are inaccessible to the polymer, the bank of connate water and polymer-depleted injection water that precedes the polymer bank is reduced by the amount of the inaccessible pore volume. One drawback, however, is that movable oil located in the smaller pores will not be contacted by the polymer and therefore may not be displaced.
In STARS, the difference (1 ) is requested directly, to update the porosity that will be used for the adsorbing component “i” and the adsorption rock type. In the simulator, it is denoted as the accessible pore volume or fraction of available pore volume to polymers or any similar component, and it should be specified by keyword *PORFT. The default value of *PORFT is 1, which means that there is no inaccessible pore volume.
Relative Permeability/Wettability Alteration Effects The effect of the modification of relative permeability by polymer adsorption has been intensively studied by many authors in the past and although they have found evidence of a selective reduction of the relative permeability to water with respect to relative permeability to oil 13,14,15, the conventional belief is that polymer flooding does not reduce residual oil saturation on a micro-scale; rather, it allows the undisplaced oil to approach this low level
11
Dawson, R. and Lautz, R., “Inaccessible Pore Volume in Polymer Flooding”, SPE Journal, October 1972. 12 Pancharoen, M., Thiele, M.R., and Kovscek, A.R., “Inaccessible Pore Volume of Associative Polymer Floods”, paper SPE 129910, SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, 2010. 13 Schneider, N. and Owens, W.W., 1982, “Steady-state measurements of relative permeability for polymer/oil systems”, paper SPE 9408-PA, Societ y of Petroleum Engineers Journal, 79-86. 14 Barrufet, A., and Ali, L., “Modification of Relative Permeability Curves by Polymer Adsorption”, paper SPE 27015 presented at the 1994 Latin American/Caribbean Petrol eum Engineering Conference, Buenos Aires, Argentina, April 27-29. 15 Zheng, C. G., Gall, B. L., Gao, H. W., Miller, A. E., and Bryant, R. S., “Effects of Polymer Adsorption and Flow Behavior on Two-Phase Flow in Porous Media”, paper SPE 39632 presented at the 1998 SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, U.S.A, 19-22 April 1998.
Revision 0I
Process Manual - Polymer Flood
11
more quickly, while producing less water in the process. In more recent studies 16,17,18, however, it can be seen that all types of micro-scale residual oil were reduced after flooding with viscous-elastic polymers, increasing micro-scale displacement efficiency in the cores. Figure 4 and Figure 5 show typical relative permeability curves for water flooding and polymer flooding obtained from previous studies (Wang et al): 100 Kro Krw
80 % y t i l i b a 60 e m r e P e 40 v i t a l e R
Krop Krp fw fp
20
0 0
20
40
60
80
100
WaterSaturation%
Figure 4 Comparison of kr-curves of Polymer/Oil and Water/Oil 16 100 500mg/L 1500mg/L
% 80 y t i l i b a e 60 m r e P e v i t a 40 l e R
2000mg/L
20
0 0
20
40
60
80
100
WaterSaturation%
Figure 5 Influence of Different Polymer Concentration on kr-curve s17
16
Wang, D., Cheng, J., Yang, Q., Gong, W., and Li, Q., “Viscous-Elastic Polymer Can Increase Microscale Displacement Efficiency in Cores”, paper SPE 63227-MS presented at the 2000 SPE Annual technical and Exhibition held in Dallas, Texas, U.S.A, 1-4 October 2000. 17 Wang, D., Wang, G., Wu, W., Xia, H., and Yin, H., “The Influence of Viscoelasticity on Displacement Efficiency – From Micro- to Macroscale”, paper SPE 109016-MS presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California, U.S.A, 11-14 November 2007. 18 Xia, H., Wang, D., Ma, W., and Liu, J., “Mechanism of the Effect of Micro-Forces on Residual Oil In Chemical Flooding”, paper SPE 114335 presented at the 2008 SPE/DPE Improved Oil Symposium Held in Tulsa, Oklahoma, U.S.A, 19-23 April 2008.
12
Process Manual - Polymer Flood
Revision 0I
Chun and Pope (2008)19 reported that while a tertiary polymer flood did not mobilize the water flood residual oil saturation, a secondary polymer flood did cause a displacement of oil saturation below the water flood residual oil saturation in the same core. Also, the authors indicate that the water flood and secondary polymer flood results could not be matched in the simulations conducted if the same residual oil saturation value is used for both floods. The core flood data could be only matched when the residual oil saturation value for the polymer flood was lower than that for the water flood 19. Although it is known that polymer flooding will not be applied as an enhanced secondary recovery, this is precisely what happens when the oil that was bypassed by a previous water flood process and that is trapped in the low-permeable zone is mobilized by the polymer; therefore, if the reduction in oil residual saturation in the simulations is neglected, the oil recovery might be underestimated, resulting in large errors and improperly forecasted results20,21. To simulate this modification, STARS can optionally interpolate basic relative permeability and capillary pressure data as functions of concentration. With this option, the curvature and endpoints of the curves can be modified based on laboratory experimental data, and used for each grid block depending on the polymer adsorption or concentration level. Enabling this option in STARS requires the following keywords: *INTCOMP
With sub-keywords comp_name and phase, indicates respectively, the name of the component upon whose composition the rock-fluid interpolation will depend, and the phase from which the component’s composition will be taken: *WATER Water (aqueous) mole fraction *OIL Oil (oleic) mole fraction *GAS Gas mole fraction *GLOBAL Global mole fraction *MAX Maximum of water, oil and gas mole fractions *ADS Adsorption phase, fraction of maximum
*KRINTRP
Indicates the interpolation set number, local to the current rock-fluid rock type. Values start at 1 for each new rock type and increase by 1 for each additional interpolation set. For example, rock type #1 might have local set numbers 1 and 2 while rock type #2 might have local set numbers 1, 2 and 3.
19
Chun, H., and Pope, G. A., “Residual Oil Saturation From Polymer Floods: Laboratory Measurements and Theoretical Interpretation”, paper SPE 113417 presented at the 2008 SPE/DPE Improved Oil Symposium Held in Tulsa, Oklahoma, U.S.A, 19-23 April 2008. 20 Kamaraj, K., Zhang, G., and Seright, R., “Effect of Residual Oil Saturation on Recovery Efficiency during Polymer Flooding of Viscous Oils”, paper OTC 22040 presented at the Arctic Technology Conference Held in Houston, Texas, U.S.A, 7-9 February 2011. 21 Chen, G., Han, P., Shao, Z., Zhang, X., Ma, M., Lu, K., and Wei, C., “History Matching Method for High Concentration Viscoelasticity Polymer Flood Pilot in Daqing Oilfield”, paper SPE 144538 presented at the SPE Enhanced Oil Recovery Conference held in Kuala Lumpur, Mala ysia, 19-21 July 2011.
Revision 0I
Process Manual - Polymer Flood
13
*DTRAPW
Indicates the value of the wetting phase interpolation parameter (mole fraction) for the current rock-fluid data set.
*DTRAPN
Indicates the value of the non-wetting phase interpolation parameter (mole fraction) for the current rock-fluid data set.
*WCRV
Indicates the curvature change parameter for water relative permeability.
*OCRV
Indicates the curvature change parameter for oil relative permeability.
*GCRV
Indicates the curvature change parameter for gas relative permeability.
*SCRV
Indicates the curvature change parameter for liquid relative permeability.
DEFAULTS:
•
If *INTCOMP is absent, interpolation will not be enabled.
•
For a rock type, if *KRINTRP is absent then there is no rock-fluid interpolation.
•
At least one of *DTRAPW and *DTRAPN must be present to enable interpolation. If only one is present, its value is applied to the absent keyword.
•
Each of *WCRV, *OCRV, *GCRV and *SCRV default to 1 if absent.
For more detail, refer to the STARS User’s Guide.
Polymer Degradation Polymer degradation refers to any process that breaks down the molecular structure of polymer macromolecules. The main degradation mechanisms that may be of concern in an EOR process are chemical, thermal, biological and mechanical 22: •
Chemical degradation of polymer, or polymer chemical stability, is mainly controlled by oxidation-reduction reactions and hydrolysis, which are due to the presence of divalent cations such as Ca 2+, Mg2+, Fe2+ in the water, and oxygen, 23,24 which breaks down the polymer molecular chains .
•
Thermal degradation of polymers is commonly associated with chemical degradation and is defined as molecular deterioration resulting from overheating. At high temperatures, the components of the long-chain backbone of the polymer can separate (molecular scission) and react with one another to change the properties of the polymer rheology and phase behavior. Thermal degradation generally involves changes to the molecular weight and it can occur at temperatures which are much lower than those at which mechanical failure is likely to occur.
•
Biological degradation is more prevalent for biopolymers than it is for synthetic polymers, however it can occur in both. Biological degradation, the microbial breakdown of polymer macromolecules in the presence of bacteria in the reservoir, occurs more often at lower temperatures and salinities23,24.
22
Chang, H. L., “Polymer Flooding Technology – Yesterday, Today, and Tomorrow”, paper SPE 7043 presented at the 1978 SPE Symposium on Improved Methods for Oil Recovery, Tulsa, April 16-19. 23 Littmann, W., “Polymer Flooding”, Developments in Petroleum Science, Vol. 24, Elsevier, Amsterdam (1988), pp 32-34. 24 Sheng, J.J.: “Modern Chemical Enhanced Oil Recovery: Theory and Practice”, Elsevier, 2011.
14
Process Manual - Polymer Flood
Revision 0I
•
Mechanical degradation occurs when a polymer solution is exposed to high shear conditions, which fragment/break the polymer molecular chains, resulting in loss of viscosity and mobility control. This may happen when a polymer solution is forced at high flow rates through a porous medium or is i n the vicinity of an injection well, where it is sheared by the high velocities 4,25. Mechanical degradation of polymer is more severe at higher flow r ates and longer flow distances, and with lower permeability porous media. The behavior of the polymer as a non-Newtonian fluid in the presence of shear conditions and the effects of shear-thinning and shear-thickening can be modeled by STARS as explained in Shear-Dependent Viscosity Effects.
All of the above degradation mechanisms, if applicable, should be considered in an EOR process. To be effective, polymer solutions must remain stable for a long time at reservoir conditions. These degradations are often neglected at the simulation level because the processes are quite complex. A simple approximation for predicting these phenomena is to use a first-order reaction where the polymer is degraded to water. In this case, the polymer concentration is reduced in each grid cell over time, which results in a reduced viscosity that can be calculated with the same nonlinear mixing rule used to account for the behavior of the aqueous phase viscosity with polymer concentration. For the simple case of polymer consumption, the first-order reaction can be expressed as follows:
Sto1 Polymer (w ) → Sto2 Water ( w )
(16)
where:
Sto1
Stoichiometric coefficient of reacting component
Sto2
Stoichiometric coefficient of produced component
Typical values of polymer viscosity stability over time are shown in Table 1 and Figure 6 : Table 1 Polymer Viscosity Specifications
Time (Days)
0 5 10 15 30 45 60
Viscosity (cps) Polymer 1
Polymer 2
Polymer 3
6.17 2.84 1.91 1.47 0.92 0.91 0.84
7.15 3.65 2.97 2.42 1.65 1.47 1.25
8.02 5.00 3.50 3.00 2.30 2.00 1.80
25
Seright, R.S., “The Effects of Mechanical Degradation and Viscoelastic Behavior on Injectivity of Polyacrylamide Solutions”, paper SPE 9297 presented at the 55th Annual Fall Technical Conference, Society Petroleum Engineers, Dallas, Sept. 1980.
Revision 0I
Process Manual - Polymer Flood
15
Figure 6 Viscosity Stability of Sample Polymers
The STARS reaction modeling capability is quite robust and can be used to model more complex reactions if desired. The STARS simulator allows the user to model kinetic reactions in the formation and/or the breaking of any component as a function of fluid flow velocity, temperature, concentration and type of process. The mandatory keywords for the chemical reaction data are: *STOREAC
Used to specify the stoichiometric coefficient of reacting component
*STOPROD
Used to specify the stoichiometric coefficient of produced component
*FREQFAC
Used to specify the reaction frequency factor
If the reaction is different from the first-order reaction and the components are reacting in a different phase than they were originally part of, *RPHASE and *RORDER must also be specified:
16
*RPHASE
Used to specify a flag defining the phase of the reacting component. The allowed values of this flag are as follows: 0 = non-reacting components, 1 = water phase (fluid components only) 2 = oil phase (fluid components only) 3 = gas phase (fluid components only) 4 = solid phase (solid components only) Note: An adsorbing component may not react in the adsorbed phase.
*RORDER
Used to specify the order of the reaction with respect to each reacting component’s concentration factor. It must be non-negative. Enter zero for non-reacting components. Normally, you would use a value of one (1); however, if the value is zero (0), the reaction rate will be independent of that component’s concentration.
Process Manual - Polymer Flood
Revision 0I
DEFAULTS:
If *RPHASE is absent, the assumption is: iphas = 0 for non-reacting components iphas = 1 for aqueous components 1 to numw iphas = 2 for oleic components numw+1 to numx iphas = 3 for noncondensable components numx+1 to numy iphas = 4 for solid components numy+1 to ncomp If *RORDER is absent, the assumption is: enrr = 0 for non-reacting components enrr = 1 for reacting components If the process you are simulating is thermal (i.e., the polymer degradation rate depends on the temperature and activation energy [Ea]), the first-order reaction may be rewritten to depend on the absolute temperature in the grid cells according to the Arrhenius equation. In this case, new keywords *RENTH and *EACT are required: *RENTH
Used to specify the reaction enthalpy (J/gmol | Btu/lbmol). It is positive for exothermic reactions and negative for endothermic reactions. The default is 0.
*EACT
Used to specify the single activation energy (J/gmol | Btu/lbmol). Defines the dependence of reaction rate on grid block temperature. If absent, the reaction is independent of temperature (equivalent to *EACT with E a = 0).
For information about the formulas used in determining the volumetric reaction rate, refer to Volumetric Reaction Rate on page 46. For information about the formulas used to calculate the stoichiometric coefficients, refer to Stoichiometric Coefficients on page 48. For more details refer to the STARS User’s Guide.
Composition-Dependent Viscosity Effects The main purpose of using a polymer is to achieve a favorable mobility ratio. The efficiency of a waterflood is heavily dependent on the mobility ratio of the displacing and displaced fluids. The mobility ratio is defined as follows:
ℎ ℎ =
Revision 0I
=
/
/
=
×
(17)
Process Manual - Polymer Flood
17
where: k w
Effective permeability to water
μw
Water viscosity
k o
Effective permeability to oil
μo
Oil viscosity
With a high mobility ratio, the displacing fluid moves much faster than the displaced fluid. As a result, a phenomenon called viscous fingering occurs in which the displacing fluid bypasses the displaced fluid and channels towards the producer. Figure 7 illustrates this effect. The fingering of the water leaves behind large areas of oil that are unswept by the water. The water also channels itself towards the producer (upper left). Once this communication has been established, water will go straight from the injector to the producer, bypassing the remaining oil in the reservoir.
Figure 7 Water Fingers through Oil due to Adverse Viscosity Effects 26
If polymer is added to the injected water, the mobility ratio is lowered (more favorable). The polymer increases the viscosity of the injected water, thus reducing its mobility. The flood front is more uniform, and there is very little evidence of viscous fingering. The displacement is more piston-like and leaves very little trapped oil behind. This is illustrated in Figure 8.
Figure 8 Improved Sweep Efficiency and Oil Recovery through Use of Polymer 26
Component viscosity can be entered in two ways. The first way is to enter a viscosity versus temperature table using the keyword *VISCTABLE, which contains a temperature column 26
Adapted from Cairn India brochure “Enhanced Oil Recovery”.
18
Process Manual - Polymer Flood
Revision 0I
followed by columns corresponding to the number and order of the non-solid components listed under the *MODEL keyword. For example, consider a fluid model containing water, oil, gas and polymer. The *VISCTABLE will appear similar to that shown below: VISCTABLE T1
μw,T1
μo,T1
μg,T1
μP,T1
T2
μw,T2
μo,T2
μg,T2
μP,T2
T3
μw,T3
μo,T3
μg,T3
μP,T3
μw,Tn
μo,T4
μg,Tn
μP,Tn
… Tn
Different VISCTABLEs can be defined at different pressures, allowing temperature and pressure dependency to be modeled. The *ATPRES keyword can be used to specify a *VISCTABLE at different pressures, as f ollows: ATPRES pres_1 VISCTABLE ATPRES pres_2 VISCTABLE ATPRES pres_n VISCTABLE The second way to define component viscosity is to enter the coefficients and use a correlation to calculate the viscosity at different temperatures. The correlation uses the following equation:
abs =
× exp(
/T
)
(18)
where:
avisc1, bvisc1
Coefficients of the correlation for the temperature-dependence of a component viscosity in the liquid phase
T abs
Absolute temperature
Within STARS, the viscosity of a liquid phase is modeled using either a linear mixing rule or a nonlinear mixing rule. The default method in STARS is the linear mixing rule, which uses the following equation to calculate the viscosity of a multi-component mixture:
=1 (
Revision 0I
)=
×
(19)
Process Manual - Polymer Flood
19
where:
Viscosity of mixture
Weighting factor of component “i” in the aqueous (α = w) or oleic (α = o) phase viscosity in the linear mixing rule. Viscosity of component “i” in the aqueous (α = w) or oleic (α = o) phase.
nc
Number of components in the oleic or aqueous phase.
Factors = (oil mole fractions) and = (water mole fractions) are used for linear mixing. To specify nonlinear mixing (for example, solution gas in the oleic phase or polymer in the aqueous phase), use keywords *VSMIXCOMP, *VSMIXENDP and *VSMIXFUNC (one instance for each key component), where factors and are different from the mole (mass) fractions and respectively, for the key component.
∉ ∈ =1 =1 ∈∉
To accomplish nonlinear mixing with alternate weighting factors,
is replaced with the
nonlinear mixing function for each component i ∈ S and with × for each component i ∉ S, where S denotes the set of key components. The nonlinear mixing rule for the liquid viscosity is calculated as:
(
)=
×
+
×
×
(20)
where:
Viscosity of mixture aqueous (α = w) or oleic (α = o).
Viscosity of component “i” in the aqueous (α = w) or oleic (α = o) phase. Weighting factor of the non-key component “i” in the aqueous (α = w) or oleic (α = o) phase viscosity in the nonlinear mixing rule.
Weighting factor of the key component “ i” in the aqueous (α = w) or oleic (α = o) phase viscosity in the nonlinear mixing rule.
Number of key components in the liquid phase.
Number of components in the liquid phase that are not key components.
In the determination of the weighting factors for the nonlinear mixing rule, each key component acts independent of other key components, which is reflected in the fact that the nonlinear mixing function depends only on the mass or mole fraction ( or ). This implies that the function data entries must be generated assuming the absence of other key components.
20
Process Manual - Polymer Flood
Revision 0I
The format for specifying the nonlinear mixing rule for liquid viscosities viscosities is as follows: VSMIXCOMP comp_name
Specifies the component that is exhibiting nonlinear viscosity mixing
VSMIXENDP x VSMIXENDP xlow xhigh
Specifies the minimum and maximum compositions of the specified comp_name
VSMIXFUNC f VSMIXFUNC f 1 . . .f 11 11
Nonlinear mixing mixing function corresponding to the 11 intervals between x between xlow and x and xhigh
DEFAULTS:
If *VSMIXCOMP is absent, linear mixing is assumed for all components. If *VSMIXENDP is absent, x absent, xlow = 0 and x and xhigh = 1 are assumed.
If *VSMIXFUNC is absent, entries linear spacing from 0 to 1.
=(
1)/10, for i = 1 to 11, corresponding to
CONDITIONS:
The phase to which this data will be assigned depends on which of *LIQPHASE, *WATPHASE and *OILPHASE is in force. A nonlinear function may be specified for more than one component in each of the water and oil phases. At least one component in each liquid phase must not be a key component, since the algorithm involves adjusting the weighting factors of the non-key components. Keywords *VSMIXENDP and *VSMIXFUNC are applied to the last key component defined via *VSMIXCOMP. A key component may not be specified more than once in each liquid phase. An example of how these keywords should be entered in the simulation dataset to model the nonlinear mixing rule of the water viscosity with the presence of a polymer in the aqueous phase is shown shown below: VSMIXCOMP 'Polymer' VSMIXENDP 0 0.001 VSMIXFUNC 0 0.0 0.0759 0.1598 0.2514 0.3498 0.4534 0.5608 0.6704 0.7808 0.891 1.0 Internally, STARS will divide the composition interval ( xhigh - xlow) into 11 equal subintervals, corresponding to the f the f 1... f f 11 11 values. Inside STARS, the table will appear as shown in the following example:
Revision 0I
Process Manual - Polymer Flood
21
Composition (w p)
Mixing Function f (w p)
0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.0010
0.0000 0.0759 0.1598 0.2514 0.3498 0.4534 0.5608 0.6704 0.7808 0.8910 1.0000
At any composition w p, a corresponding mixing function f function f (w p) will be determined either directly from the table or through interpolation. interpolation. This function will be used to calculate the viscosity of the solution. As the composition changes changes due to injection, decomposition or adsorption, the mixing function will change accordingly, resulting in a change of water viscosity. For further information and a calculation example, refer to the Polymer Viscosity section of Polymer Flood Calculations in Appendix A – Equations. Equations .
Shear-Dependent Viscosity Effects Flow in a porous medium is affected by the morphology of the medium and the rheology of the fluid. Many applications of flow in porous media involve Newtonian fluids, in which the viscosity is independent of shear rate. Any fluid that does not obey Newton’s law of viscosity is a non-Newtonian non-Newtonian fluid. Generally, a fluid can be classified as Newtonian or non-Newtonian depending on its flow behavior; that that is, how how its viscosity viscosity changes changes in the presence of shear stress stress and the the rate of of shear applied. If the shear stress ( ) is plotted against shear rate ( ) at constant temperature and pressure, the so-called “flow curve” or “rheogram” (the response of a Newtonian fluid) is a straight line with slope , passing through the origin. The constant of proportionality, , referred to as the Newtonian or dynamic viscosity is, by definition, independent of shear rate and shear stress and depends only on the material, its temperature, and its pressure.
̇
̇
On the other hand, for a non-Newtonian fluid, the curve does not pass through the origin and/or does not result in a linear relationship between the shear stress ( ) and the shear rate ( ). ). The coefficient of viscosity is not constant and is a function of and .
̇
̇
The relationship between shear stress τ and shear rate is is as follows: f ollows:
̇ =
22
×
(21)
Process Manual - Polymer Flood
Revision 0I
̇
where: Shear stress Shear rate Apparent viscosity of the fluid
A typical shear stress versus shear rate plot for a non-Newtonian fluid is shown in Figure in Figure 9:
PseudoplasticFluid (ShearThinning)
Newtonian Fluid
) γ ( s s e r t S r a e h S
DilatantFluid (ShearThickening) -1
ShearRate(s ) Figure 9 Typical Plot of Shear Stress vs. Shear Rate for Newtonian and non-Newtonian non-Newtonian Fluids27
̇
Often the relationship between shear stress ( ) and shear rate ( ) for these fluids is plotted on log-log coordinates, and the relationship can be approximated as a straight line over a limited range of shear rate ( or stress), that is:
̇ ̇ =
×
(22)
where:
Shear stress Shear rate Fluid consistency coefficient or index. Flow behavior index or power-law exponent.
When viscosity decreases with increasing shear rate, the fluid is called shear-thinning. In the opposite case, where viscosity increases as the fluid is subjected to a higher shear rate, the fluid is called shear-thickening. Shear-thinning behavior is more common than shearthickening. Shear-thinning Shear-thinning fluids are also referred to as pseudoplastic fluids, while shearthickening fluids are referred to as dilatant fluids. The behavior of these fluids is illustrated in the following figures. 27
Derived from figure “Rheology_of_time_independent_fluids.png”, Wikimedia Commons.
Revision 0I
Process Manual - Polymer Flood
23
y t i s o c s i V t n e r a p p A
Shear-ThinningFluid
y t i s o c s i V t n e r a p p A
Shear-ThickeningFluid
ShearRate
ShearRate
Figure 10 Apparent Viscosity vs. Shear Rate for Shear-Thinning and Shear-Thickening Fluids28
Many shear-thinning and shear-thickening fluids exhibit Newtonian behavior at extreme shear rates, both low and high. For such fluids, when the apparent viscosity is plotted against log shear rate, the curve appears as follows: NewtonianRegion y t i s o c s i V t n e r a p p A g o l
Power-LawRegion
Shear-Thinning Fluid
NewtonianRegion
logShearRate Figure 11 Apparent Viscosity vs. Shear Rate for a Shear-Thinning Fluid 28
28
Subramanian, R. Shankar, “Non-Newtonian Flows”, Department of Chemical and Biomolecular Engineering, Clarkson University.
24
Process Manual - Polymer Flood
Revision 0I
NewtonianRegion y t i s o c s i V t n e r a p p A g o l
Power-LawRegion
Shear-Thickening Fluid
NewtonianRegion
logShearRate Figure 12 Apparent Viscosity vs. Shear Rate for a Shear-Thickening Fluid
The regions where the apparent viscosity is approximately constant are known as Newtonian regions. The behavior between these regions can usually be approximated by a straight line on these axes. In this region, which is known as the power-law region, the behavior can be approximated by the following expression:
̇ ̇ ̇−1 =
+
×
( )
(23)
This can be rewritten as:
=
( )×
(24)
Equation (24) can be replaced by one more commonly used in the literature, which comes from combining equations (21) and (22):
=
×
(25)
K represents the fluid consistency index and is equal to “ represents the power-law exponent, and the expression ( (24). Note the following:
( )” in equation (24). 1) is equal to “b” in equation
•
When n < 1, the fluid exhibits shear-thinning properties.
•
When n = 1, the fluid shows Newtonian behavior.
•
When n > 1, the fluid shows shear-thickening behavior.
The above shows that rheology in porous media has an important impact on enhanced oil recovery projects where polymer solutions are used, because if the effective viscosity of the polymer solution is high at the high velocities experienced near an injection well, the polymer injection rate and/or the oil production rate (at the producer well) may be decreased. On the other hand, if the effective viscosity of the polymer solution is too low at the low velocities experienced away from the injection well or deep into the reservoir, oil displacement may be inefficient.
Revision 0I
Process Manual - Polymer Flood
25
To simulate the behavior of the pseudoplastic or dilatant fluids used in enhanced oil recovery (foam, high molecular weight liquids which include solutions of polymers, as well as liquids in which fine particles are suspended [suspensions]), STARS uses the power-law or Ostwald de Waele model, as described below.
Power-Law Expression for Shear-Thinning or Pseudoplastic Fluids The *SHEARTHIN keyword is used to represent the pseudoplastic behavior or the shearthinning effect as follows: *SHEARTHIN
DEFINITIONS:
,
Power-law index or exponent in the viscosity shear thinning equation (dimensionless). The allowed range is from 0.1 to 0.99, inclusive. Values below 0.3 can result in unacceptable numerical performance and so are not recommended. Values close to 1 approximate Newtonian behavior. The meaning of
,
,
depends on *SHEAREFFEC (*SHV | *SHR).
*SHV: Reference Darcy velocity (m/day | ft/day | cm/min) in viscosity -10 10 shear thinning equation. The allowed range is 10 to 10 m/day (3.28×10-10 ft/day to 3.28×10 10 ft/day | 6.94×10-12 to 6.94×108 cm/min). *SHR: Reference shear rate (1/day | 1/day | 1/min) in viscosity shear thinning equation. The allowed range is 10 -10 to 1010 1/day (6.94×10-14 to 6.94×106 1/min).
⎩
The bounded power-law relation between the apparent fluid viscosity fluid velocity is:
=
,
−1 ≤ ≥ ,
×
for
for
,
,
for
and the Darcy
,
,
<
<
(26)
,
,
The upper velocity boundary of the shear thinning regime,
,
, is defined by the point on
the power-law curve where the apparent viscosity, , equals the phase fluid viscosity in the absence of polymer ( , ). The lower velocity boundary of the shear thinning regime, , is defined by the point on the power-law curve where the apparent viscosity, , , equals the fluid phase viscosity in the absence of thinning ( , ). For further discussion on the
calculation of phase viscosities for Newtonian flow, refer to the STARS User’s Guide for information on *AVISC and *BVISC. The bounded power law relation of apparent viscosity versus velocity for shear thinning is depicted in the log/log plot of Figure 13. The shear thinning regime is represented by a linear relation of slope ( 1).
26
Process Manual - Polymer Flood
Revision 0I
µapp=µl,p
log(Apparent Viscosity)
µapp=µl,0 ul=ul,lower
ul=ul,upper
log(DarcyVelocity)
Figure 13 Shear Thinning Power Law - Apparent Viscosity vs. Darcy Velocity
Power-Law Expression for Shear-Thickening or Dilatant Fluids The *SHEARTHICK keyword is used to represent the dilatant’s behavior or the shearthickening effect as follows: *SHEARTHICK
DEFINITIONS:
,
,
Revision 0I
,
,
Power-law index or exponent in the viscosity shear thickening equation (dimensionless). The allowed range is from 1.01 to 5, inclusive. Values above 2.5 can result in unacceptable numerical performance and so are not recommended. Values close to 1 approximate Newtonian behavior. The meaning of
,
depends on *SHEAREFFEC (*SHV | *SHR).
*SHV: Reference Darcy velocity (m/day | ft/day | cm/min) in viscosity -10 10 shear thickening equation. The allowed range is 10 to 10 m/day (3.28×10-10 ft/day to 3.28×1010 ft/day | 6.94×10-12 to 6.94×108 cm/min). *SHR: Reference shear rate (1/day | 1/day | 1/min) in viscosity shear thickening equation. The allowed range is 10 -10 to 1010 1/day (6.94×10-14 to 6.94×106 1/min). Maximum viscosity (cp) in viscosity shear thickening equation. The -5 6 allowed range is 10 to 10 cp.
Process Manual - Polymer Flood
27
≤ ≥
The power-law relation between apparent fluid viscosity
−1 ⎩ ,
=
×
,
for for
,
,
for
and Darcy fluid velocity
is:
,
,
<
<
,
(27)
,
The lower velocity boundary of the shear thickening regime, , , is defined by the point on the power law curve when the apparent viscosity, , equals the phase fluid viscosity in the absence of thickening ( , ). For further discussion on the calculation of phase viscosities for Newtonian flow, refer to the STARS User’s Guide for information about *AVISC and *BVISC.
The upper velocity boundary of the shear thickening regime, , , is defined by the point on the power-law curve where the apparent viscosity, , equals the user-defined maximum viscosity ( , ).
The bounded power-law relation of apparent viscosity versus velocity for shear thickening is depicted in the log/log plot of Figure 14. The shear thickening regime is represented by a linear relation of slope ( 1).
µapp =µl,max
log(Apparent Viscosity)
µapp =µl,p
ul=ul,lower
ul=ul,max
log(DarcyVelocity)
Figure 14 Shear Thickening Power Law - Apparent Viscosity vs. Darcy Velocity
In cases where fluids exhibit both behaviors (shear-thinning and shear thickening), the keywords can be used together. The apparent viscosity of the combined effect is the sum of the shear thinning and thickening apparent viscosities defined in the above sections:
=
28
,
+
,
Process Manual - Polymer Flood
(28)
Revision 0I
The summed power-law relation between apparent fluid viscosity, velocity, , is:
≤ ≥ for
,
=
,
+
,
,
, and Darcy fluid
,
for for
,
<
<
(29)
,
,
The lower velocity boundary of the shear thinning and thickening regime, , , is defined by the point on the thinning power-law curve where the apparent viscosity, , equals the fluid phase viscosity in the absence of thinning ( , ). The upper velocity boundary of the shear thinning and thickening regime, law curve where the apparent viscosity, ( , ).
,
, is defined by the point on the thickening power, equals the user-defined maximum viscosity
The summed power-law relation of apparent viscosity versus velocity is depicted in the log/log plot of Figure 15.
µapp=µl,max
log(Apparent Viscosity)
µapp=µl,p
ul=ul,lower
ul=ul,max
log(DarcyVelocity)
Figure 15 Shear Thinning and Thickening Power Laws - Apparent Viscosity vs. Darcy Velocity
The above explanations are for velocity-dependent viscosity, which is the default option implemented in STARS. For the shear-rate-dependent viscosity option, the same logic applies, with the term “shear rate” replacing “velocity” throughout. If you need to replace the default option (velocity-dependent viscosity) with the shear-ratedependent viscosity option, the *SHEAREFFEC keyword must be used. The format of this keyword is as follows: *SHEAREFFEC (*SHV | *SHR)
Revision 0I
Process Manual - Polymer Flood
29
DEFINITIONS:
*SHV
Viscosity shear depends on Darcy velocity.
*SHR
Viscosity shear depends on shear rate.
DEFAULTS:
If *SHEAREFFEC is absent, *SHEAREFFEC *SHV is assumed.
Tabular Input Option for Velocity/Shear-Rate-Dependent Viscosity In addition to the keywords described above, STARS has a tabular input option for velocitydependent viscosity or shear-rate-dependent viscosity, which is useful when the viscosityversus-velocity relation or viscosity-versus-shear-rate relation is specified by laboratory data, or when a simple power-law relation is not sufficient. The format is as follows: FORMAT:
*SHEARTAB { velocity viscosity } or *SHEARTAB { shear-rate viscosity } DEFINITIONS:
*SHEARTAB
A viscosity-versus-velocity table follows. The maximum allowed number of table rows is 40. The first column is either velocity or shear rate, depending on *SHEAREFFEC.
Velocity
*SHEAREFFEC 0: The first column is phase velocity (m/day | ft/day | -10 10 -10 10 cm/min). The allowed range is 10 to 10 m/day (3.28×∙10 to 3.28×10 ft/day | 6.94×10-12 to 6.94×108 cm/min).
shear-rate
*SHEAREFFEC 1: The first column is phase shear-rate (1/day | 1/day | 1/min). The allowed range is 10 -10 to 1010 1/day (6.94×10-14 to 6.94×106 1/min).
viscosity
Viscosity (cp) of the component at corresponding velocity. The allowed range is 10 -5 to 106 cp.
The following conditions apply to these keywords: a) *SHEARTAB is applied to the component and phase specified by the immediately preceding *VSMIXCOMP, so *VSMIXCOMP must be present before *SHEARTAB. b) *SHEARTAB may not be used together with *SHEARTHICK and *SHEARTHIN. c) The first column is either velocity or shear rate, depending on *SHEAREFFEC. d) For phase velocity/shear-rate outside the velocity/shear-rate table range, the nearest viscosity table entry is used.
30
Process Manual - Polymer Flood
Revision 0I
Velocity Dependent Skin Factor In many cases, much of the shear thinning or thickening occurs within the injection well grid block. Although non-Newtonian flow between grid blocks is accounted for, modeling of non Newtonian flow within the well grid block requires a user-input skin factor. The following is a discussion of the standard radial inflow well model based on Newtonian flow and a derivation of the recommended skin factor that can be used to correct for actual non Newtonian flow within the well grid block. For model input protocol and a detailed discussion of well skin factors, refer to “Well Element Geometry (Conditional)” of section “Well and Recurrent Data” and “Radial Inflow Well Model” of section “Appendix A: Well Model Details” in the STARS User’s Guide. The Radial Inflow Well Model is based on a steady-state Newtonian flow which incorporates a dimensionless pressure-drop skin factor. This equation uses an equivalent well block radius, , defined as the radius at which the steady-state flowing pressure of the actual well is equal to the numerically calculated pressure for the well block.
The pressure drop between the well bottom-hole pressure and the well block pressure, be represented by:
∙ℎ ∙−1 ∙ℎ 1− 1− = 1− =
×
×
2
+
, can
(30)
A similar equation can be written for a velocity-dependent viscosity and non-Newtonian flow29:
=
where ,
×
and
×
2
1
1
×[
]
(31)
are the power index, reference viscosity and reference velocity.
The user must determine whether shear thinning or shear thickening is dominating in the well grid block and use the appropriate power index and reference parameters from the power law relations. For example, if thinning is the dominant (or only) velocity-dependent viscosity effect, then = , , and = , , . A skin factor to account for the pressure drop difference between Newtonian and non Newtonian flow can be determined by equating the above equations:
=
1
1
× 1
+
(32)
29
Odeh, A.S., and Yang, H.T., “Flow of Non-Newtonian Power-Law Fluids Through Porous Media”, SPEJ, June 1979, pp. 155-163.
Revision 0I
Process Manual - Polymer Flood
31
where:
−1 ℎ =
(33)
×
and:
=
2 ×
(34)
×
This skin factor should provide the necessary correction to the Newtonian Radial Inflow Well Model to account for non-Newtonian flow within the well grid block. The equation can be solved by assuming that the equivalent well block radius for Newtonian and non-Newtonian flow is similar. However, technically these values will be different and a more accurate determination of the well block radius for non-Newtonian flow can be done using the velocity-dependent power law for viscosity and a derivation similar to the one outlined in Peaceman 30.
Convert Shear Rates to Velocities The information for converting shear rate data f rom laboratory measurements to Darcy velocities comes from a study by Cannella et al. 31 The equation relating the effective porous media shear rate and the fluid Darcy velocity is as follows:
̇ −1 ×| |
=
×
(35)
× φ ×
where and φ are the absolute permeability and porosity, and , Darcy velocity, relative permeability, and saturation respectively.
, and
are the phase
The shear rate factor is given by:
=
×
3 +1
(36)
4
where is the shear thinning power exponent and is a constant value, usually equal to 6 and related to the tortuosity of the porous medium. The default shear rate factor of 4.8 corresponds to C = 6 and n = 0.5; however, the user can adjust this conversion via the *SHEAR_FAC keyword as follows: FORMAT:
*SHEAR_FAC factor DEFINITIONS:
factor
Factor
in the shear rate equation described above.
30
Peaceman, D.W., “Interpretation of Well-Block Pressures in Numerical Reservoir Simulation with Non-Square Grid Blocks and Anisotropic Permeabilit y”, SPEJ, June 1983, pp. 531. 31 Cannella, W., Huh, C., and Seright, R.S., “Prediction of Xanthan Rheology in Porous Media”, paper SPE 18089, presented at the 63rd Annual Tech. Conference SPE, Houston, Texas, October 1988.
32
Process Manual - Polymer Flood
Revision 0I
DEFAULTS:
If *SHEAR_FAC is absent then
= 4.8 is assumed.
If velocity-dependent viscosity is used, the reference velocity applies to a reference permeability. Thus, the relevant parts of the reservoir should be adequately represented by an average permeability. If the reservoir is highly non-uniform in permeability, the use of a shear-rate dependent viscosity model is recommended. An example of Darcy velocity calculation using the *SHEARTAB keyword is shown in Shear Effect on Polymer Viscosity in Appendix A – Equations on page 58.
Salinity-Dependent Viscosity Effects Consideration for brine salinity is important for polymer selection. For example, hydrolyzed polyacrylamide (HPAM) is very sensitive to salinity and hardness, so the viscosity improvement property will be significantly reduced when it dissolves in water with high salinity or hardness. This characteristic represents the disadvantage of using this polymer. On the contrary, the biopolymer Xanthan is more tolerant to salinity or hardness than HPAM, which is its main advantage. If the formation water is of high salinity, the polymer should be stable to salt concentration or else a preflush of fresh water must be injected to precondition the reservoir and prevent the polymer from losing most of its viscosity. To simulate this effect, the STARS simulator has a power-law equation that uses the viscosity of the key component in the non-linear mixing rule (*AVISC, *BVISC or *VISCTABLE). The ratio of salt concentration is as follows:
0 ≤ 0 ⎩
for
=
×
for
(37)
>
where:
0
Salinity component mole/mass fraction below which the nonlinear mixing component viscosity is considered independent of salinity. In other words, is the enforced minimum salinity of the phase. The allowed range is -5 10 to 10-1. Salinity component mole/mass fraction. Polymer viscosity as pure component (for information about the *AVISC or *VISCTABLE keywords, refer to the STARS User’s Guide).
Resultant polymer component viscosity in the saline solution. This new polymer component viscosity is then used with the nonlinear mixing function to determine the phase viscosities. Slope on a log-log plot of polymer component viscosity versus ratio of salinity,
Revision 0I
. The allowed range is -100 to 100.
Process Manual - Polymer Flood
33
For further information, refer to the *VSSALTCMP keyword in the STARS User’s Guide. For an example of the calculation, refer to the Polymer Viscosity subsection of the Polymer Flood Calculations section in Appendix A – Equations of this manual.
Lab and Field Information Before an EOR method can be applied to a particular well or reservoir, laboratory and field measurements must be carried out to determine the optimal method and formulation. For a polymer flood process, for example, the laboratory tests will consist of polymer injectivity, retention, stability, fluid compatibility, and effective viscosity measurements, while fi eld testing will include injectivity, biological stability, and in-situ viscosity measurements 32. The main objective in a polymer flood process is the selection of the polymer most suitable for the reservoir conditions, based on temperature stability, salinity tolerance, quality of the mixing water, and economic conditions. To correctly choose the polymer, a detailed screening program should be performed to evaluate the basic fluid rheological properties and quality, such as screen factor tests, filtration ratio, and viscosity measurement. Once the polymer is selected, core-flooding experiments should be performed as the second stage of the experimental program. The measured displacements are used to describe the rock-polymer interactions, based on polymer adsorption, resistance factor and residual resistance factor. With this information, polymer concentration in the effluents can be determined, as well as the water and/or oil volumes produced. Finally, a thermal aging study may be needed to verify that the selected polymer does not degrade significantly at reservoir temperature over time 33. In summary, the parameters needed to model a polymer flood simulation at the laboratory and/or field scale are as follows:
•
Polymer Screening -
Viscosity (dependent on shear rate and concentration)
-
Molecular weight
-
Polymer stability (thermal, biological, mechanical, and/or chemical) ▪
•
Polymer screening is used to determine the polymer half-life, which in turn, is used to generate the degradation reactions explained in Polymer Degradation on page 14.
Core flooding -
SCAL for understanding rock and fluid properties: ▪
Porosity
▪
Permeability
▪
Relative permeability curves (initial and residual saturations)
32
Castagno, R.E., Shupe, R. D., Gregory, M. D. and Lescarboura, J. A., “A Method for Laboratory and Field Evaluation of a Proposed Polymer Flood”, SPE 13124, presented at the 59th Annual technical Conference and Exhibition, Houston, Texas, September 16-19, 1984. 33 Saavedra, N.F., Gaviria, W, and Davitt, H.J., “Laboratory Testing of Polymer Flood Candidates: San Francisco Field”, prepared for the SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, April 13-14, 2002 SPE 75182.
34
Process Manual - Polymer Flood
Revision 0I
▪
Oil and water properties (densities, viscosities, and so on)
-
Pressure taps on core
-
Polymer concentration and slug size
-
Flow rates
-
Polymer adsorption (static or dynamic)
-
Polymer concentration of effluent
-
Viscosity of effluent over the range of injection rates (shear rates) ▪
To be compared and matched with those measured in the rheometer.
-
Residual resistance factor and permeability reduction
-
Oil and water produced volumes
Using the Process Wizard to Model a Polymer Flood To use the Process Wizard to build a model for a polymer flood:
1. Open the dataset in Builder. 2. Click Components in the menu bar then select Process Wizard. The Process Wizard Step 1 - Choose Process dialog box is displayed:
Revision 0I
Process Manual - Polymer Flood
35
3. Select Alkaline, surfactant, foam and/or polymer model :
4. Click Next. The Step 2 - Input Specific Data For A.S.P. Models dialog box is displayed:
36
Process Manual - Polymer Flood
Revision 0I
5. Select the Polymer flood (add 1 component) model:
Polymeradsorption Fractionofthepore volumeaccessibletothe polymermolecules Typeand/ordensityof rockfortheadsorption conversion
Residualresistance factorfromlab Polymerconsumption and/ordegradationwith time Enterpolymerhalflife
6. Configure the model options as directed above then click Next. The Step 3 Component Selection dialog box is displayed:
Step 3 of the Process Wizard allows you to either add a new polymer component if one has not been defined, as shown below:
or to select or update the polymer component that has already been defined, as shown below:
If you select the check box, a new component will be added. If you leave the check box blank, you can use the drop-down menu below it to select the component whose properties you want to change or update.
Revision 0I
Process Manual - Polymer Flood
37
7. If necessary, add components then click Next. The Step 4 - Set Adsorption Values dialog box is displayed: Porosityusedinthe adsorptionlab experiment Polymer concentrationin weight%
Polymeradsorption reportedbylab (mg/100gofrock)
8. As necessary, enter the polymer adsorption values as directed above then click Next. The Step 5 - Set Polymer Values dialog box is displayed:
Polymer concentrationin weight%
Polymersolution viscosity(cps)
9. Enter the polymer viscosity values as shown above then click Finish. If, in Step 3 – Component Selection, you changed or updated the polymer component that was already defined and the polymer molecular weight is now greater than 8 kg/gmmole (or 8000 lb/lbmole), the following message will be displayed:
10. As stated in the message, click Yes to use the recommended polymer weight of 8 kg/gmmole (8000 lb/lbmole), or click No to continue with the current value. The Process Wizard calculations are performed, the dataset is updated, and the main Builder window becomes active.
38
Process Manual - Polymer Flood
Revision 0I
Viewing and Adjusting the Process Wizard Results Components Generation To check (and if necessary, edit) the polymer components that have been generated by the Process Wizard, click Component | Add/Edit Components in the menu bar. The Components and Phase Properties dialog box is displayed:
Polymer definition
Polymer Consumption Reaction To view details of the polymer consumption reaction, click Component | Reactions in the menu bar. The Reactions dialog box is displayed, as shown in the following example:
Kinetic reactionrate
Stoichiometric coefficients Reactionorders Phaseofthe reaction Summaryofthe reaction
For information about the formulas used in determining the volumetric reaction rate, refer to Volumetric Reaction Rate on page 46. For information about the formulas used to calculate the stoichiometric coefficients, refer to Stoichiometric Coefficients on page 48.
Revision 0I
Process Manual - Polymer Flood
39
Polymer Adsorption Polymer Adsorption Table To view the details of the polymer adsorption table, click Rock-Fluid | Components in the menu bar. The Component Adsorption dialog box is displayed: Modifyadsorption settings
Component“i”
Phasewhere component“i”is encountered
Componentranges
Adsorptionranges Phasetoapplythe permeabilityreduction
Adsorptionrock types Maximum adsorption
Residualadsorption 1.Totallyreversible (ADRT=0) 2.Partiallyreversible (0
