Process Manual - Polymer Flood

Polymer Flood Process Manual

Revision 0I

By Computer Modelling Group Ltd.

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Revision 0I Process Manual - Polymer Flood • 1

Contents Introduction 3

Purpose ................................................................................................................................. 3 Organization ......................................................................................................................... 3 Polymer Flood Process ......................................................................................................... 3

Polymer Flood 5

Introduction .......................................................................................................................... 5 Theoretical Phenomena ........................................................................................................ 5

Polymer Adsorption......................................................................................................... 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 Viscosity Effects ............................................................................ 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 Reaction .................................................................................... 39 Polymer Adsorption....................................................................................................... 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 ........................................................................................................................ 45 General Formulas................................................................................................................ 45

2 • Process Manual - Polymer Flood Revision 0I

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


Introduction

Purpose The purpose of this manual is to provide users with the information 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.


Figure 1 shows a conceptual comparison of cumulative oil recovery for water, polymer, alkaline/polymer, and ASP flooding techniques.

CumulativeOil

Pore Volume Injected

ASP Flood

Alkaline/Polymer Flood

Polymer Flood

Continued Water Flood

Figure 1 Comparison of Chemical Flooding Techniques

Figure 2 illustrates the potential improvement from chemical flood EOR processes:

Water Flood

Chemical Flood EOR Potential to

Extend andEnhance

Production

Oil Rate

Time Figure 2 Improved Oil Recovery from Chemical Flood Processes1

1 Adapted from Cairn India brochure “Enhanced Oil Recovery”.


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.


Polymer Adsorption Adsorption is the adhesion of ions or molecules onto the surface of another phase2. 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:

( )i

i

cB1A

Ad×+

×=

c (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:

Figure 3 Typical Langmuir Isotherm Shapes3

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).

1.0

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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 permeability4,5, 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:

K�=𝑘𝑅𝑘

(2)

where:

k Absolute rock permeability prior to polymer flooding Rk Permeability reduction factor

𝑅𝑘, a function of polymer adsorption and the residual resistance factor RRF, is given by:

𝑅𝑘 = 1 + (𝑅𝑅𝐹 − 1) ×𝐴𝐷

𝐴𝐷𝑀𝐴𝑋𝑇 (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.

st201110en.chm::/WordDocuments/adsorbingcomponentfunctionsadscompadslangadstable.htm


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 𝑅𝑅𝐹, 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 treatment4,6,7.

𝑅𝑅𝐹 =𝜆𝑤,𝑏𝑒𝑓𝑜𝑟𝑒 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡

𝜆𝑤,𝑎𝑓𝑡𝑒𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡=

(𝑘𝑤 𝜇𝑤⁄ ),𝑏𝑒𝑓𝑜𝑟𝑒 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡

(𝑘𝑤 𝜇𝑤⁄ ),𝑎𝑓𝑡𝑒𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 (4)

where:

λw Water mobility kw Effective water permeability μw Water viscosity

As the water viscosity does not change before or after the treatment, equation (4) can be reduced to:

𝑅𝑅𝐹 =𝑘𝑤,𝑏𝑒𝑓𝑜𝑟𝑒 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡

𝑘𝑤,𝑎𝑓𝑡𝑒𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 (5)

If the core flooding experiment is linear, the effective permeability can be calculated using the linear expression of Darcy’s equation:

𝑘𝑤 =𝑄𝑤 × 𝐿 × 𝜇𝑤𝐴 × ∆𝑃

(6)

If the core flooding experiment is radial, then the effective permeability should be calculated as follows:

𝑘𝑤 =𝑄𝑤 × 𝐿𝑛(𝑟𝑒 𝑟𝑤⁄ ) × 𝜇𝑤

2𝜋 × ℎ × ∆𝑃 (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.


both tests, the residual resistance factor, RRF, can be expressed in terms of the pressure drops, as follows8:

𝑅𝑅𝐹 =∆𝑃,𝑎𝑓𝑡𝑒𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡

∆𝑃,𝑏𝑒𝑓𝑜𝑟𝑒 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 (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:

𝑅𝑘𝛼 = 1 + (𝑅𝑅𝐹 − 1) ×𝐴𝐷

𝐴𝐷𝑀𝐴𝑋𝑇 (9)

which affects the effective permeability of phase α, 𝑘�𝛼, as follows:

𝑘�𝛼 = 𝑘� × 𝑘𝑟𝛼 =𝑘 × 𝑘𝑟𝛼𝑅𝑘𝛼

=𝑘𝛼𝑅𝑘𝛼

(10)

where:

α Water, oil or gas phase 𝑘, 𝑘� 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.


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 reduction (DPR)7,9,10 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:

𝑅𝑅𝐹𝑤 =𝑘𝑤�𝑎𝑡 𝑆𝑜𝑟 ; 𝑝𝑟𝑒 − 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡�𝑘𝑤�𝑎𝑡 𝑆𝑜𝑟 ; 𝑝𝑜𝑠𝑡 − 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡�

(11)

𝑅𝑅𝐹𝑜 =𝑘𝑜�𝑎𝑡 𝑆𝑤𝑖𝑟𝑟 ; 𝑝𝑟𝑒 − 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡�𝑘𝑜�𝑎𝑡 𝑆𝑤𝑖𝑟𝑟; 𝑝𝑜𝑠𝑡 − 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡�

(12)

From water-gas experiments:

𝑅𝑅𝐹𝑤 =𝑘𝑤�𝑎𝑡 𝑆𝑔𝑟 ; 𝑝𝑟𝑒 − 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡�𝑘𝑤�𝑎𝑡 𝑆𝑔𝑟 ; 𝑝𝑜𝑠𝑡 − 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡�

(13)

𝑅𝑅𝐹𝑔 =𝑘𝑔�𝑎𝑡 𝑆𝑤𝑖𝑟𝑟 ; 𝑝𝑟𝑒 − 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡�𝑘𝑔�𝑎𝑡 𝑆𝑤𝑖𝑟𝑟; 𝑝𝑜𝑠𝑡 − 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡�

(14)

where:

kα Effective permeability to the phase α, where α = w, o or g Sor Residual oil saturation (water-oil experiment) Sgr Residual gas saturation (water-gas experiment) Swirr Irreducible water saturation (water-oil and water-gas experiments)

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.


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, 𝜙𝑝, can be used to represent the available pore volume to polymer solutions as follows:

𝜙𝑝 = (1 − 𝐼𝑃𝑉) × 𝜙 (15)

where 𝜙 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 − 𝐼𝑃𝑉) 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 oil13,14,15, 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, Society 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 Petroleum 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.


more quickly, while producing less water in the process. In more recent studies16,17,18, 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):

0 20 40 60 80 100

Water Saturation %

0

20

40

60

80

100

Rel

ativ

e P

erm

eabi

lity

%

KroKrwKrop

Krpfwfp

Figure 4 Comparison of kr-curves of Polymer/Oil and Water/Oil16

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ativ

e P

erm

eabi

lity

%

100

80

60

40

20

0

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0 20 40 60 80 100

500 mg/L

1500 mg/L

2000 mg/L

Figure 5 Influence of Different Polymer Concentration on kr-curves17

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.


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 flood19.

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, Malaysia, 19-21 July 2011.


*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 mechanical22:

• 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 Ca2+, Mg2+, Fe2+ in the water, and oxygen, which breaks down the polymer molecular chains23,24.

• 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.


• 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 in the vicinity of an injection well, where it is sheared by the high velocities4,25. Mechanical degradation of polymer is more severe at higher flow rates 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:

( ) ( )ww Water2StoPolymer1Sto → (16)

where:

1Sto Stoichiometric coefficient of reacting component

2Sto 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) Viscosity (cps)

Polymer 1 Polymer 2 Polymer 3 0 6.17 7.15 8.02 5 2.84 3.65 5.00

10 1.91 2.97 3.50 15 1.47 2.42 3.00 30 0.92 1.65 2.30 45 0.91 1.47 2.00 60 0.84 1.25 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.


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:

*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.


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 Ea = 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:

𝑀 = 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑖𝑛𝑔 𝑝ℎ𝑎𝑠𝑒 𝑚𝑜𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑 𝑝ℎ𝑎𝑠𝑒 𝑚𝑜𝑏𝑖𝑙𝑖𝑡𝑦

=𝑘𝑤/𝜇𝑤𝑘𝑜/𝜇𝑜

=𝑘𝑤𝑘𝑜

×𝜇𝑜𝜇𝑤

(17)


where: kw Effective permeability to water μw Water viscosity ko 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 Effects26

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 Polymer26

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”.


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



…

Tn μw,Tn μo,T4 μg,Tn μP,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 follows:

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:

𝜇𝑖 = 𝑎𝑣𝑖𝑠𝑐𝑖 × exp (𝑏𝑣𝑖𝑠𝑐𝑖/Tabs) (18)

where:

avisc1, bvisc1 Coefficients of the correlation for the temperature-dependence of a component viscosity in the liquid phase

Tabs 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:

𝐿𝑛(𝜇𝛼) = �𝑓𝛼𝑖

𝑛𝑐

𝑖=1

× 𝐿𝑛�𝜇𝛼𝑖� (19)


where:

𝜇𝛼 Viscosity of mixture

𝑓𝛼𝑖 Weighting factor of component “i” in the aqueous (α = w) or oleic (α = o) phase viscosity in the linear mixing rule.

𝜇𝛼𝑖 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 𝑓𝑜𝑖 = 𝑥𝑖 (oil mole fractions) and 𝑓𝑤𝑖 = 𝑤𝑖 (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 𝑓𝑜𝑖and 𝑓𝑤𝑖 are different from the mole (mass) fractions 𝑥𝑖 and 𝑤𝑖 respectively, for the key component.

To accomplish nonlinear mixing with alternate weighting factors, 𝑓𝛼𝑖 is replaced with the nonlinear mixing function 𝑓�𝑓𝛼𝑖� for each component i ∈ S and with 𝑁 × 𝑓𝛼𝑖 for each component i ∉ S, where S denotes the set of key components. The nonlinear mixing rule for the liquid viscosity is calculated as:

𝐿𝑛(𝜇𝛼) = � 𝑓�𝑓𝛼𝑖�𝑛𝐶∈𝑆

𝑖=1

× 𝐿𝑛�𝜇𝛼𝑖� + 𝑁 × � 𝑓𝛼𝑖 × 𝐿𝑛�𝜇𝛼𝑖�

𝑛𝑐∉𝑆

𝑖=1

(20)

where:

𝜇𝛼 Viscosity of mixture aqueous (α = w) or oleic (α = o). 𝜇𝛼𝑖 Viscosity of component “i” in the aqueous (α = w) or oleic (α = o) phase.

𝑓𝛼𝑖 Weighting factor of the non-key component “i” in the aqueous (α = w) or oleic (α = o) phase viscosity in the nonlinear mixing rule.

𝑓�𝑓𝛼𝑖� Weighting factor of the key component “i” in the aqueous (α = w) or oleic (α = o) phase viscosity in the nonlinear mixing rule.

𝑛𝑐∈𝑆 Number of key components in the liquid phase. 𝑛𝑐∉𝑆 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 𝑓�𝑓𝛼𝑖� depends only on the mass or mole fraction (𝑥𝑖 or 𝑤𝑖). This implies that the function data entries must be generated assuming the absence of other key components.


The format for specifying the nonlinear mixing rule for liquid viscosities is as follows:

VSMIXCOMP comp_name Specifies the component that is exhibiting nonlinear viscosity mixing

VSMIXENDP xlow xhigh Specifies the minimum and maximum compositions of the specified comp_name

VSMIXFUNC f1 . . .f11 Nonlinear mixing function corresponding to the 11 intervals between xlow and xhigh

DEFAULTS:

If *VSMIXCOMP is absent, linear mixing is assumed for all components.

If *VSMIXENDP is absent, xlow = 0 and xhigh = 1 are assumed.

If *VSMIXFUNC is absent, entries 𝑓𝑖 = (𝑖 − 1)/10, for i = 1 to 11, corresponding to linear spacing from 0 to 1.

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 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 f1...f11 values. Inside STARS, the table will appear as shown in the following example:


Composition (wp)

Mixing Function f(wp)

0.0000 0.0000 0.0001 0.0759 0.0002 0.1598 0.0003 0.2514 0.0004 0.3498 0.0005 0.4534 0.0006 0.5608 0.0007 0.6704 0.0008 0.7808 0.0009 0.8910 0.0010 1.0000

At any composition wp, a corresponding mixing function f(wp) will be determined either directly from the table or through interpolation. This function will be used to calculate the viscosity of the solution. As the composition 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.

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 fluid.

Generally, a fluid can be classified as Newtonian or non-Newtonian depending on its flow behavior; that is, how its viscosity changes in the presence of shear stress and the rate of shear applied. If the shear stress (𝜏) 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 𝜇, passing through the origin. The constant of proportionality, 𝜇, 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 (𝜏) and the shear rate (�̇�). The coefficient of viscosity is not constant and is a function of 𝜏 and �̇�.

The relationship between shear stress τ and shear rate �̇� is as follows:

𝜏 = 𝜇 × �̇� (21)


where: 𝜏 Shear stress �̇� Shear rate 𝜇 Apparent viscosity of the fluid

A typical shear stress versus shear rate plot for a non-Newtonian fluid is shown in Figure 9:

Shear Rate (s-1)

She

ar S

tres

s (γ

)

Newtonian Fluid

Dilatant Fluid(Shear Thickening)

Pseudoplastic Fluid(Shear Thinning)

Figure 9 Typical Plot of Shear Stress vs. Shear Rate for Newtonian and non-Newtonian Fluids27

Often the relationship between shear stress (𝜏) 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:

𝜏 = 𝐾 × �̇�𝑛 (22)

where: 𝜏 Shear stress �̇� Shear rate 𝐾 Fluid consistency coefficient or index. 𝑛 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 shear-thickening. Shear-thinning fluids are also referred to as pseudoplastic fluids, while shear-thickening 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.


Shear-Thickening Fluid

App

aren

t Vis

cosi

ty

Shear RateShear Rate

Shear-Thinning Fluid

App

aren

t Vis

cosi

ty

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:

Newtonian Region

Newtonian Region

Power-Law Region

Shear-ThinningFluid

log

App

aren

t Vis

cosi

ty

log Shear Rate Figure 11 Apparent Viscosity vs. Shear Rate for a Shear-Thinning Fluid28

28 Subramanian, R. Shankar, “Non-Newtonian Flows”, Department of Chemical and Biomolecular Engineering, Clarkson University.


Newtonian Region

Newtonian Region

Power-Law Region

Shear-ThickeningFluid

log Shear Rate

log

App

aren

t Vis

cosi

ty

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:

𝐿𝑛�𝜇𝑎𝑝𝑝� = 𝑎 + 𝑏 × 𝐿𝑛(�̇�) (23)

This can be rewritten as:

𝜇𝑎𝑝𝑝 = 𝑒𝑥𝑝(𝑎) × �̇�𝑏 (24)

Equation (24) can be replaced by one more commonly used in the literature, which comes from combining equations (21) and (22):

𝜇𝑎𝑝𝑝 = 𝐾 × �̇�𝑛−1 (25)

K represents the fluid consistency index and is equal to “𝑒𝑥𝑝(𝑎)” in equation (24). 𝑛 represents the power-law exponent, and the expression (𝑛 − 1) is equal to “b” in equation (24). Note the following:

• 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.


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 shear-thinning effect as follows:

*SHEARTHIN 𝑛𝑡ℎ𝑖𝑛 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟

DEFINITIONS: 𝑛𝑡ℎ𝑖𝑛 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.

𝑢𝑙,𝑙𝑜𝑤𝑒𝑟 The meaning of 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟 depends on *SHEAREFFEC (*SHV | *SHR). *SHV: Reference Darcy velocity (m/day | ft/day | cm/min) in viscosity shear thinning equation. The allowed range is 10-10 to 1010 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 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 𝜇𝑎𝑝𝑝 and the Darcy fluid velocity 𝑢𝑙 is:

𝜇𝑎𝑝𝑝 =

⎩⎪⎨

⎪⎧

𝜇𝑙,𝑝 for 𝑢𝑙 ≤ 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟

𝜇𝑙,𝑝 × �𝑢𝑙

𝑢𝑙,𝑙𝑜𝑤𝑒𝑟�𝑛𝑡ℎ𝑖𝑛−1

for 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟 < 𝑢𝑙 < 𝑢𝑙,𝑢𝑝𝑝𝑒𝑟

𝜇𝑙,0 for 𝑢𝑙 ≥ 𝑢𝑙,𝑢𝑝𝑝𝑒𝑟

(26)

The upper velocity boundary of the shear thinning regime, 𝑢𝑙,𝑢𝑝𝑝𝑒𝑟 , is defined by the point on the power-law curve where the apparent viscosity, 𝜇𝑎𝑝𝑝, equals the phase fluid viscosity in the absence of polymer (𝜇𝑙,0). The lower velocity boundary of the shear thinning regime, 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟 , is defined by the point on the power-law curve where the apparent viscosity, 𝜇𝑎𝑝𝑝, equals the fluid phase viscosity in the absence of thinning (𝜇𝑙,𝑝). 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 (𝑛𝑡ℎ𝑖𝑛 − 1).


log (Darcy Velocity)

ul = ul,lower ul = ul,upper

µapp = µl,0

µapp = µl,p

log (Apparent Viscosity)

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 shear-thickening effect as follows:

*SHEARTHICK 𝑛𝑡ℎ𝑖𝑐𝑘 𝑢𝑙,𝑚𝑎𝑥 𝜇𝑙,𝑚𝑎𝑥

DEFINITIONS: 𝑛𝑡ℎ𝑖𝑐𝑘 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.

𝑢𝑙,𝑚𝑎𝑥 The meaning of 𝑢𝑙,𝑚𝑎𝑥 depends on *SHEAREFFEC (*SHV | *SHR). *SHV: Reference Darcy velocity (m/day | ft/day | cm/min) in viscosity shear thickening equation. The allowed range is 10-10 to 1010 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).

𝜇𝑙,𝑚𝑎𝑥 Maximum viscosity (cp) in viscosity shear thickening equation. The allowed range is 10-5 to 106 cp.


The power-law relation between apparent fluid viscosity 𝜇𝑎𝑝𝑝 and Darcy fluid velocity 𝑢𝑖 is:

𝜇𝑎𝑝𝑝 =

⎩⎪⎨

⎪⎧

𝜇𝑙,𝑝 for 𝑢𝑙 ≤ 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟

𝜇𝑙,𝑚𝑎𝑥 × �𝑢𝑙

𝑢𝑙,𝑚𝑎𝑥

�𝑛𝑡ℎ𝑖𝑐𝑘−1

for 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟 < 𝑢𝑙 < 𝑢𝑙,𝑚𝑎𝑥

𝜇𝑙,𝑚𝑎𝑥 for 𝑢𝑙 ≥ 𝑢𝑙,𝑚𝑎𝑥

(27)

The lower velocity boundary of the shear thickening regime, 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟 , is defined by the point on the power law curve when the apparent viscosity, 𝜇𝑎𝑝𝑝, equals the phase fluid viscosity in the absence of thickening (𝜇𝑙,𝑝). 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, 𝑢𝑙,𝑚𝑎𝑥 , is defined by the point on the power-law curve where the apparent viscosity, 𝜇𝑎𝑝𝑝, equals the user-defined maximum viscosity (𝜇𝑙,𝑚𝑎𝑥).

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 (𝑛𝑡ℎ𝑖𝑐𝑘 − 1).



µapp = µl,p

µapp = µl,max

ul = ul,lower ul = ul,max

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:

𝜇𝑎𝑝𝑝 = 𝜇𝑎𝑝𝑝,𝑡ℎ𝑖𝑛 + 𝜇𝑎𝑝𝑝,𝑡ℎ𝑖𝑐𝑘 (28)


The summed power-law relation between apparent fluid viscosity, 𝜇𝑎𝑝𝑝, and Darcy fluid velocity, 𝑢𝑖, is:

𝜇𝑎𝑝𝑝 = � 𝜇𝑙,𝑝 for 𝑢𝑙 ≤ 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟

𝜇𝑎𝑝𝑝,𝑡ℎ𝑖𝑛 + 𝜇𝑎𝑝𝑝,𝑡ℎ𝑖𝑐𝑘 for 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟 < 𝑢𝑙 < 𝑢𝑙,𝑚𝑎𝑥

𝜇𝑙,𝑚𝑎𝑥 for 𝑢𝑙 ≥ 𝑢𝑙,𝑚𝑎𝑥

(29)

The lower velocity boundary of the shear thinning and thickening regime, 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟 , is defined by the point on the thinning power-law curve where the apparent viscosity, 𝜇𝑎𝑝𝑝, equals the fluid phase viscosity in the absence of thinning (𝜇𝑙,𝑝). The upper velocity boundary of the shear thinning and thickening regime, 𝑢𝑙,𝑚𝑎𝑥, is defined by the point on the thickening power-law curve where the apparent viscosity, 𝜇𝑎𝑝𝑝, equals the user-defined maximum viscosity (𝜇𝑙,𝑚𝑎𝑥).

The summed power-law relation of apparent viscosity versus velocity is depicted in the log/log plot of Figure 15.



µapp = µl,max

µapp = µl,p

ul = ul,lower ul = ul,max

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-rate-dependent viscosity option, the *SHEAREFFEC keyword must be used. The format of this keyword is as follows:

*SHEAREFFEC (*SHV | *SHR)


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 velocity-dependent viscosity or shear-rate-dependent viscosity, which is useful when the viscosity-versus-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 | cm/min). The allowed range is 10-10 to 1010 m/day (3.28×∙10-10 to 3.28×1010 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.


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, 𝑟𝑒, 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, 𝑃𝑘, can be represented by:

𝑃𝑤𝑓𝑘 − 𝑃𝑘 = �𝜇𝑘�× �

𝑞𝑗𝑘2𝜋 ∙ ℎ

� × �𝐿𝑛 �𝑟𝑒𝑟𝑤�+ 𝑆� (30)

A similar equation can be written for a velocity-dependent viscosity and non-Newtonian flow29:

𝑃𝑤𝑓𝑘 − 𝑃𝑘 = �𝜇𝑟𝑒𝑓

𝑘 ∙ 𝑢𝑟𝑒𝑓𝑛−1�× �𝑞𝑗𝑘

2𝜋 ∙ ℎ� × �

11 − 𝑛

� × [𝑟𝑒1−𝑛 − 𝑟𝑤1−𝑛] (31)

where 𝑛, 𝜇𝑟𝑒𝑓 and 𝑢𝑟𝑒𝑓 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 𝑛 = 𝑛𝑡ℎ𝑖𝑛, 𝑢𝑟𝑒𝑓 = 𝑢𝑙,𝑙𝑜𝑤𝑒𝑟, and 𝜇𝑟𝑒𝑓=𝜇𝑙,𝑝.

A skin factor to account for the pressure drop difference between Newtonian and non-Newtonian flow can be determined by equating the above equations:

𝑆 = �1

1 − 𝑛� × �1 − �

𝑟𝑤𝑟𝑒�1−𝑛

� + 𝐿𝑛 �𝑟𝑤𝑟𝑒� (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.


where:

𝜇 = 𝜇𝑟𝑒𝑓 × �𝑢𝑙𝑢𝑟𝑒𝑓

�𝑛−1

(33)

and:

𝑢𝑙 =𝑞𝑗𝑘

2𝜋 × ℎ × 𝑟𝑒 (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 Peaceman30.

Convert Shear Rates to Velocities The information for converting shear rate data from 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:

�̇� =𝛾𝑓𝑎𝑐 × |𝑢𝑙|

�𝑘𝑎𝑏𝑠 × 𝑘𝑟𝑙 × φ × 𝑆𝑙 (35)

where 𝑘𝑎𝑏𝑠 and φ are the absolute permeability and porosity, and 𝑢𝑙, 𝑘𝑟𝑙, and 𝑆𝑙 are the phase Darcy velocity, relative permeability, and saturation respectively.

The shear rate factor is given by:

𝛾𝑓𝑎𝑐 = 𝐶 × �3𝑛 + 1

4𝑛 �𝑛

𝑛−1 (36)

where 𝑛 is the shear thinning power exponent and 𝐶 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 𝛾𝑓𝑎𝑐 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 Permeability”, 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.


DEFAULTS:

If *SHEAR_FAC is absent then 𝛾𝑓𝑎𝑐 = 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:

𝜇𝑝 =

⎩⎨

⎧ 𝜇𝑝0 for 𝑥𝑠𝑎𝑙𝑡 ≤ 𝑥𝑚𝑖𝑛

𝜇𝑝0 × �𝑥𝑠𝑎𝑙𝑡𝑥𝑚𝑖𝑛

�𝑠𝑝

for 𝑥𝑠𝑎𝑙𝑡 > 𝑥𝑚𝑖𝑛

(37)

where:

𝑥𝑚𝑖𝑛 Salinity component mole/mass fraction below which the nonlinear mixing component viscosity is considered independent of salinity. In other words, 𝑥𝑚𝑖𝑛 is the enforced minimum salinity of the phase. The allowed range is 10-5 to 10-1.

𝑥𝑠𝑎𝑙𝑡 Salinity component mole/mass fraction.

𝜇𝑝0 Polymer viscosity as pure component (for information about the *AVISC or *VISCTABLE keywords, refer to the STARS User’s Guide).

𝜇𝑝 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.

𝑠𝑝 Slope on a log-log plot of polymer component viscosity versus ratio of salinity, �𝑥𝑠𝑎𝑙𝑡

𝑥𝑚𝑖𝑛�. The allowed range is -100 to 100.


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 field testing will include injectivity, biological stability, and in-situ viscosity measurements32.

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 time33.

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.


▪ 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:


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:


5. Select the Polymer flood (add 1 component) model:

Type and/or density of rock for the adsorption

conversion

Polymer adsorption

Fraction of the pore volume accessible to the

polymer molecules

Residual resistance factor from lab

Polymer consumption and/or degradation with time

Enter polymer half life

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.


7. If necessary, add components then click Next. The Step 4 - Set Adsorption Values dialog box is displayed:

Porosity used in the adsorption lab experiment

Polymer adsorption reported by lab(mg / 100g of rock)

Polymer concentration in

weight %

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 solution viscosity (cps)

Polymer concentration in

weight %

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.


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:

Polymerdefinition

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 reaction rate

Stoichiometric coefficients

Reaction orders

Phase of the reaction

Summary of the 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.


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:

Modify adsorption settings

Phase where component “i” is encountered

Adsorption ranges

Adsorption rock types

Maximum adsorption

Fraction of pore volume accessible

Residual resistance factor

Component “i”

Component ranges

Phase to apply the permeability reduction

Residual adsorption1. Totally reversible (ADRT = 0)2. Partially reversible (0 < ADRT < ADMAXT)3. Totally irreversible

(ADRT = ADMAXT)

For information about the calculations used to produce the polymer adsorption table, refer to Polymer Adsorption Table on page 49.

Langmuir Isotherm Option Click the Change Adsorption Options button to change the adsorption dependence to Langmuir isotherm coefficients. The Component Adsorption dialog box will change as shown below, with a table for entering the Langmuir isotherm coefficients:

Component “i”

Component ranges

Phase to apply the permeability reduction

Residual adsorption1. Totally reversible (ADRT = 0)2. Partially reversible (0 < ADRT < ADMAXT)3. Totally irreversible

(ADRT = ADMAXT)

Modify adsorption settings

Phase where component “i” is encountered

Adsorption rock types

Maximum adsorption

Fraction of pore volume accessible

Residual resistance factor

tad1

tad2

tad3

For information about the Langmuir isotherm calculations, refer to Langmuir Isotherm Option on page 50.

Note: When one value of adsorption is used, Builder calculates the corresponding adsorption values for intermediate concentrations using a linear interpolation, which will not follow a Langmuir shape.


For information about the adsorption equations used in the Permeability Reduction calculations, refer to Permeability Reduction on page 52.

Polymer Viscosity To view the polymer viscosity results, click Component | Add/Edit Components in the menu bar then select the Liquid phase viscosities tab:

Polymer viscosity(as pure component) calculated by the Wizard

Non-linear mixing rule for the viscosity

Note: A value of 0 for BVISC indicates that the component’s viscosity does not change with temperature.

To specify the nonlinear viscosity mixing rule, click Specify. The Nonlinear Mixing dialog box is displayed:

Maximum polymer concentration is extrapolated to consider future optimizations

Viscosity function calculated by the Wizard

For information about the calculations used to model polymer viscosity, refer to Polymer Viscosity on page 53.


Other Considerations and Troubleshooting Information This section includes considerations that you may need to make, and information to help you troubleshoot problems with polymer flood models.

High Molecular Weight (or Low Mole Fractions) STARS uses numerical derivatives with a default concentration shift of 10e-7 instead of algebraic derivatives to form the flow equations. As a result, the use of polymers of high molecular weight (for example 10e+6) might reduce the numerical performance of the simulator. This is because, in a mole-fraction-based model, the polymer concentration values are expected to be very low (for example 10e-9). Refer to Polymer Flood Calculations on page 46 for information about the mole fraction calculation.

If numerical shifts are larger than the injected mole fractions, inexact derivatives may occur, which will interfere with convergence. As well, numerical performance may degrade as the chase water pushes the polymer out of the reservoir at the end of the simulation and polymer concentrations are reduced further, resulting in poorer derivative estimates.

There are four ways to address this problem. The first way is to change (decrease) the default convergence tolerance for *ZAQ, which ties the numerical shift level to the convergence tolerance, so that decreasing one decreases the other. By making this modification in the numerical section, along with reducing the maximum time step size *DTMAX and limiting the number of wasted Newton iterations by setting *NEWTONCYC < default value, it is possible to improve the run. A good approximation can be obtained by using the following numerical parameters:

*NUMERICAL

*NORM *ZAQ 0.075

*CONVERGE *ZAQ 5.0e-4

*DTMAX 15.0

*NEWTONCYC 8

The second way is to define a “pseudo-polymer” of reduced molecular weight but with the same viscosity and adsorption effects as for a higher mole fraction. This “pseudo-polymer” mole fraction approach will preserve the mass fraction used by the true polymer mole fraction model. Refer to Using the Process Wizard to Model a Polymer Flood starting on page 35 for information about defining the recommended “pseudo-polymer” molecular weight.

The third way to address this problem is to run the model with mass fraction concentrations by using the *MASSBASIS option. If the laboratory simulations are run this way, we recommend that the field model also be run this way, particularly if no gas phase is generated and the field GOR stays at its initial value, in which case there is little motivation for mole fraction representation. Note that using *MASSBASIS will require converting the solution gas oil mole fraction composition to mass fraction, and also conversion of the solution gas k-values.

The fourth way is to use the *SHIFT MWT keyword (refer to the latest STARS User’s Guide for information about this keyword).


Disproportionate Permeability Reduction Effect As mentioned in previous sections, some polymers have the ability to reduce the permeability to water more than that to hydrocarbons. This phenomenon is known as the disproportionate permeability reduction or DPR effect.

STARS does not explicitly handle this effect by using residual resistance factors for each phase. This section provides options and tools for simulating the permeability reduction of the phases by using different blockage alternatives. The four options are described below.

The first option is to obtain “pseudo” residual resistance factors for the each of the phases by dividing the values obtained from coreflooding experiments by one of them, i.e., a reference residual resistance factor. Normally, the reference residual resistance factor would be that of the oil because the oleic phase is not altered as much as the aqueous phase is, in which case:

𝑅𝑅𝐹𝑤′ =𝑅𝑅𝐹𝑤𝑅𝑅𝐹𝑜

> 1 → because normally 𝑅𝑅𝐹𝑤 > 𝑅𝑅𝐹𝑜 (38)

𝑅𝑅𝐹𝑜′ =𝑅𝑅𝐹𝑜𝑅𝑅𝐹𝑜

= 1

→ no resistance effect, and it is not necessary to assign it to the simulator (39)

The second alternative is to reduce the absolute permeability of all phases by first using the STARS variable permeability option and then further modifying the water mobility with the residual resistance factor. Here, the absolute permeability is a function of porosity. As the porosity is reduced by the adsorbed polymer, the permeability should be reduced as follows:

• Carmen-Kozeny type formula using keyword *PERMCK • A permeability multiplier obtained from table look-up through the keyword

*PERMTAB • A user-defined multiplier factor specified by keywords *PERMULI, *PERMULJ

or *PERMULK

The third option is to use the relative permeability interpolation method to modify only the relative permeability curve to oil, considering the effect in this phase. The residual resistance factor to water is then used as the default for modifying the mobility to water.

The fourth option involves the creation of a first-order reaction where the polymer is divided into two new components or “pseudo-polymers”. One of these components will reduce the mobility to water (by using the water residual resistance factor) and the other will reduce the mobility to oil (by using the oil residual resistance factor).

𝑃𝑜𝑙𝑦𝑚𝑒𝑟 → 𝑎𝑃𝑜𝑙𝑦𝑚𝑒𝑟𝑤 + 𝑏𝑃𝑜𝑙𝑦𝑚𝑒𝑟𝑜 (40)

The stoichiometric coefficients for balancing the reaction can be obtained from the residual resistance factor information using the following equations:

𝑅𝑅𝐹𝑇 = 𝑅𝑅𝐹𝑤 + 𝑅𝑅𝐹𝑜 (41)


𝑎 =𝑅𝑅𝐹𝑤𝑅𝑅𝐹𝑇

< 1 (42)

𝑏 =𝑅𝑅𝐹𝑜𝑅𝑅𝐹𝑇

< 1 (43)

The adsorption must be adjusted and care should be taken in the water viscosity calculation with polymer concentration.

Interpreting Polymer Flood Model Outputs To interpret the chemical flood results in Results 3D, first add the following grid outputs through IO Control | Simulation Results Output:

• ADSORP: Component adsorbed • ADSPCMP: Composition of key component used in the calculation of adsorbing

component • KRINTER: Relative perm interpolation value • SHEARO: Shear rate of oil phase • SHEARW: Shear rate of water phase • SHEARG: Shear rate of gas phase • SHEARSTRG: Shear stress (viscosity times shear rate) of gas phase • SHEARSTRW: Shear stress (viscosity times shear rate) of water phase • SHEARSTRO: Shear stress (viscosity times shear rate) of oil phase • VISCVELW: Magnitude of Darcy velocity of water phase • VISCVELO: Magnitude of Darcy velocity of oil phase • VISCVELG: Magnitude of Darcy velocity of gas phase • VISWCOM: Component composition of the key component in the nonlinear

mixing of water viscosity given by *VSMIXCOMP

After you have output the above grid variables, the following plots are required, on a grid-block basis, wherever there is chemical concentration and are relatively significant for analyzing the chemical flood results:

• ADSORP vs. time: The mole fraction of component that has been adsorbed in rock as a function of time.

• KRINTERP vs. time: Used to analyze how the relative permeability interpolation parameter is changing with time, and the set of relative permeability to which STARS is referring.

• Output Mole Fraction vs. time: To show what is happening inside the reservoir. • VISCVELW vs. SHEARW: To analyze shearing in the water phase at respective

Darcy velocities.


Appendix A – Equations

Introduction This chapter provides additional information about the equations used by the Process Wizard, including descriptions of the variables and constants used.

Note: To avoid confusion, all windows and calculations in this manual have been shown or made in *Field Units. For further information about the specific units used, refer to the STARS User’s Guide.

General Formulas The following general formulas are used by the Process Wizard:

Parts-per-million (ppm)

mg/l1ppm1 =

Weight Percentage

4101ppmwt%×

=

Mass Fraction (wt)

100wt%

101ppmwt 6 =×

=

Mole Fraction (dim)

∑=

=cn

1i i/Mwiwt

)i/Mwi(wt ix

(44)


where:

wti Mass fraction of component “i” Mwi Molecular Weight of component “i” nc Number of components in the solution

Polymer Flood Calculations Assuming a polymer solution (water + polymer) with a polymer concentration of 0.1 wt% and a molecular weight of 8000 lb/lbmol, the mass and mole fraction of the polymer are calculated as follows:

Polymer Mass Fraction

0.0011000.1wt ==

Polymer Mole Fraction

( )

( )6

i 102.25412

18.0150.0011

80000.001

0.001/8000 x −×=−

+=

To simulate the polymer degradation and/or consumption in STARS, use the reaction module and input the properties required to express the volumetric reaction rate.

Volumetric Reaction Rate A kinetic reaction provides information about the speed with which the reaction proceeds. The expression for the volumetric reaction rate in STARS is as follows:

×−××∏

= TREaexpCrrf

ci

n

1i

ai (45)

The concentration factor for component “i” in the liquid phase is usually based on density, as shown in the following formulas:

ifi xSC ×××= αα ρφ (46)

( )

−×= ∑

=

n

k sk

skvf TP

C1 ,

1ρ

φφ (47)

In the above equations, void porosity, ϕv, is corrected for pore pressure and temperature, and the effective porosity to fluids, ϕf, is corrected for the volume of the solid phase in the pore space. Each component “k” in the solid phase has concentration 𝐶𝑠𝑘and density 𝜌𝑠𝑘(𝑃,𝑇). For further information, refer to keyword *SOLID_DEN in the STARS User’s Guide.


The concentration factor for component “i” in the solid phase, if one exists, is:

isvi CC ×= φ (48)

The following constants and variables are used in the above formulas:

rrf Constant factor in the expression, known as the “kinetic constant” Ea Activation energy, gives the dependence of reaction rate on temperature T Temperature R Universal gas constant Ci Concentration factor contributed by reactant component “i” ai Order of reaction with respect to component “i”

fφ Effective porosity to fluids

αS Saturation of the phase α where component “i” is reacting

αρ Molar density of the phase α where component “i” is reacting

xi Mole fraction of the component “i” from the phase where it is reacting

vφ Void porosity

skC Concentration of component “k” in the solid phase

( )TPsk ,ρ Density of component “k” in the solid phase

isC Concentration of component “i” in the solid phase

iC Actual concentration of component “i” in the porous space

For the simple case of polymer consumption, the reaction is:

( ) ( )ww Water2StoPolymer1Sto → (49)

where:

1Sto Stoichiometric coefficient of reacting component

2Sto Stoichiometric coefficient of produced component

The kinetic rate for this first-order reaction is typically expressed as:

( )1/21/2 tt

2Lnrfr 69315.0==

(50)


where:

rrf Reaction frequency factor (day-1)

2/1t Half-life (days)

If the half-life of the polymer uses the Process Wizard default value of 180 days, the reaction frequency factor will have the following value:

1day0.0038518069315.0rfr −==

(51)

Stoichiometric Coefficients Typically, the stoichiometric coefficients are based on 1 mole of one of the reactive components. The user is responsible for ensuring that the stoichiometric coefficients entered as data represent a mass-conserving set. A set of mass-conserving coefficients will satisfy:

i

n

1iii

n

1ii Sto2MwSto1Mw

cc

×=× ∑∑==

(52)

where:

iMw Molecular weight of component “i”

iSto1 Stoichiometric coefficient of component “i” as reactant

iSto2 Stoichiometric coefficient of component “i” as product

Assuming the following reaction:

cC bB aA ⇔+ (53)

The stoichiometric coefficients can be calculated as follows:

mbMwb

Mwama

ba

×=

(54)

mcMwc

Mwama

ca

×=

(55)

where:

cba ,, Moles of components A, B, and C respectively

mcmbma ,, Mass of components A, B, and C respectively

The stoichiometric coefficients for the first-order reaction:

( ) ( )ww Water Sto2Polymer1toS → (56)


are as follows:

W

W

p

P

mMw

Mwm

2Sto1Sto

×=

(57)

Reorganizing:

×

×=

P

W

W

P

mm

MwMw1Sto2Sto

(58)

The mass fraction is used more often than the mass of the components for this type of simulation, so the expression is reorganized using:

=

P

W

P

W

wtwt

mm

(59)

Substituting into equation (58):

×

×=

P

W

W

P

wtwt

MwMw1Sto2Sto

(60)

Usually the stoichiometric coefficient for the main reacting component is chosen to be equal to 1, as follows:

444.07411

18.01580001toS =

×

×=2

(61)

The final expression for this example is:

( ) ( )ww Water074.444Polymer → (62)

Polymer Adsorption Table The form of the adsorption term in flow equations is generally expressed as:

[ ]iAdtφ

∂∂

(63)

For this reason, the adsorption levels in the simulator are described as moles (or mass) of component “i” adsorbed per unit volume; however, other measures of adsorption level can be used and these need to be converted to meet the simulator input requirements:

( )φ

φ−××=

1ρAdAd rii labStars

(64)


where:

StarsiAd Adsorption of component “i”, to be used in STARS (gmol/m3, lbmol/ft3, or gmol/cm3)

labiAd Adsorption obtained in laboratory (mg polymer/100 gr-rock)

rρ Rock density (gr/cm)

φ Porosity

Using the data assigned to the Process Wizard, the appropriate conversion is as follows:

( )Cf

0.2494

0.24941cm

g2.65

100grmg

50Ad3

rock

PolymeriStars

×−×

×=

(65)

where:

Cf Unit conversion factor

In the following example, Cf is used to convert to lbmol/ft3:

( )

3

36

3

33

ftmgcmlbmol107.8

lb8000lbmol1

ft1cm30.48

mg453592.37lb1Cf

⋅⋅

×=

×

×

= −

Substituting:

35i lbmol/ft103.11184AdStars

−×=

Langmuir Isotherm Option The Langmuir adsorption isotherm gives the adsorbed moles of component “i” per unit pore volume, as follows:

( )( )i

ii c tad31

cxnacl tad2tad1AdStars ×+

××+=

(66)


where:

tad1 1st parameter in the Langmuir expression (gmol/m3, lbmol/ft3, or gmol/cm3)

tad2 2nd parameter in the expression associated with salt effects (gmol/m3, lbmol/ft3, or gmol/cm3)

tad3 3rd parameter in the Langmuir expression (dim) xnacl Salinity of the brine

ic Mole fraction of component “i”

The Langmuir isotherm equation can be rewritten as:

( )( )i

ii ctad31

ctadtad

xnacltad2tad1AdStars ⋅+

××+=

33

(67)

At high concentrations (large ci), the maximum adsorption, obtained using the above conversion, is:

( )tad3

xnacltad2tad1 ×+

(68)

In addition to the maximum adsorption, the rate of increase of adsorption with fluid composition should be known in order to fit the Langmuir parameters tad1 and tad3. If this is not reported, as is often the case, you can use the fluid composition at the adsorption maximum to indirectly determine this second factor.

Assuming tad2 is negligible, the equation can be rewritten as:

( )i

ii ctad31

ctad3tad3tad1Ad

Stars ×+×

×

=

(69)

The first factor in the above expression is the maximum adsorption and the second factor is of order one (1) when 10ctad3 i ≥× . In the above example, the maximum adsorption level occurs at 0.1 wt% of polymer which is equivalent to a mole fraction concentration of ci = 2.25412×10-6. In this case, tad3 can be calculated as follows:

ic

10tad3 =

Substituting for ci:

4436321.05102.25412

10tad3 6- =×

=


With the value of tad3 established, the adsorption maximum level can be used to determine tad1:

335

i ftlbmol138.054436321.05

ftlbmol103.11184tad3Adtad1

Stars=××=×= −

If lStarsiAd is the maximum adsorption that can be obtained, then it should be used as

*ADMAXT. Maximum adsorption levels *ADMAXT and residual adsorption levels *ADRT can be made region-dependent, so that these properties can be varied from grid block to grid block. Specification of residual adsorption levels provides flexibility for modeling both reversible (chemical, adsorption ADRT = 0.0) and irreversible (mechanical, ADRT = ADMAXT) processes, as well as partially reversible processes (0 < ADRT < ADMAXT).

Permeability Reduction Permeability alteration often accompanies adsorption, especially if adsorption is of the mechanical blockage type. The simulator accounts for this through the use of resistance factors, RRF, and region dependence, which allow for the correlation of local permeability with local adsorption levels (Adcell). It is assumed that only single-phase flow paths are altered. When this is the case, for each phase, the permeability reduction (equilibrium blockage) is calculated as follows:

( )ADMAXT

Ad1RRF1R cell

αkα ×−+=

(70)

where:

kαR Permeability reduction factor of phase α

αRRF Residual resistance factor of phase α

Rka varies between 1.0 and a maximum of RRFα, as adsorption level increases. The mobility of the each phase is divided by Rkα , so accounting for blockage:

α

αα

k

absref R

kkk

×=

(71)

where:

αefk Effective permeability of phase α

absk Absolute permeability of the rock

αrk Relative permeability of phase α


Polymer Viscosity The viscosities of the liquid phases are obtained by applying the following linear mixing rule:

( ) ( )∑=

×=c

ii

n

iLnfLn

1ααα µµ

(72)

where:

𝜇𝛼 Viscosity of aqueous (α = w) or oleic (α = o) phase. 𝑓𝛼𝑖 Weighting factor of component “i” in the aqueous (α = w) or oleic (α = o)

phase viscosity in the linear mixing rule. 𝜇𝛼𝑖 Viscosity of component “i” in the aqueous (α = w) or oleic (α = o) phase,

obtained from the correlation of viscosity or from the table assigned to simulator. For further information, refer to the keywords *AVISC, *BVISC or *VISCTABLE in the STARS User’s Guide.

nc Number of components in the oleic or aqueous phase.

The weighting factors, 𝑓𝛼𝑖, in the linear mixing rule expression are normally expressed as mole (mass) fractions of the components in the respective phases, i.e., wi in the aqueous phase and xi in the oleic phase.

In the case where the viscosity of the phase is nonlinear (for example, in the presence of solution gas or polymers), the simulator uses a modified mixing rule to represent these changes in viscosity. This nonlinear mixing option partitions all the components into two groups: those that are key components specified by *VSMIXCOMP (call it set S), and those are that are not. The mole (mass) fractions ( 𝑥𝑖 or 𝑤𝑖) of the two groups sum to 1:

� 𝑥𝑖

𝑛𝑐∈𝑆

𝑖=1

+ � 𝑥𝑖

𝑛𝑐∉𝑆

𝑖=1

= 1 𝑜𝑟 �𝑤𝑖

𝑛𝑐∈𝑆

𝑖=1

+ �𝑤𝑖

𝑛𝑐∉𝑆

𝑖=1

= 1 (73)

where: 𝑛𝑐∈𝑆 Number of key components in the liquid phase. 𝑛𝑐∉𝑆 Number of components in the liquid phase that are not key components.

In the modified mixing rule the weighting factors of the linear expression, 𝑓𝛼𝑖 are replaced with alternate weighting factors: a nonlinear mixing function 𝑓�𝑓𝛼𝑖� for each component i=S and with 𝑁 ∙ 𝑓𝛼𝑖 for each component i≠S, where N is a normalizing factor that comes from the requirement that the alternate weighting factors still sum to 1 and are derived as follows:

� 𝑓�𝑓𝛼𝑖�𝑛𝑐∈𝑆

𝑖=1

+ �𝑁 × 𝑓𝛼𝑖

𝑛𝑐∉𝑆

𝑖=1

= 1 → � 𝑓�𝑓𝛼𝑖�𝑛𝑐∈𝑆

𝑖=1

+𝑁 × � 𝑓𝛼𝑖

𝑛𝑐∉𝑆

𝑖=1

= 1 (74)


𝑁 = �1− � 𝑓�𝑓𝛼𝑖�𝑛𝑐∈𝑆

𝑖=1

�× �� 𝑓𝛼𝑖

𝑛𝑐∉𝑆

𝑖=1

�

−1

(75)

Therefore the nonlinear mixing rule for the liquid viscosity has the following expression:

𝐿𝑛(𝜇𝛼) = � 𝑓�𝑓𝛼𝑖�𝑛𝑐∈𝑆

𝑖=1

× 𝐿𝑛�𝜇𝛼𝑖� +𝑁 × � 𝑓𝛼𝑖 × 𝐿𝑛�𝜇𝛼𝑖�

𝑛𝑐∉𝑆

𝑖=1

(76)

where: 𝜇𝛼 Viscosity of mixture aqueous (α = w) or oleic (α = o). 𝜇𝛼𝑖 Viscosity of component “i” in the aqueous (α = w) or oleic (α = o) phase. 𝑓𝛼𝑖 Weighting factor of the non-key component “i” in the aqueous (α = w) or oleic (α =

o) phase viscosity in the nonlinear mixing rule. 𝑓�𝑓𝛼𝑖� Weighting factor of the key component “i” in the aqueous (α = w) or oleic (α = o)

phase viscosity in the nonlinear mixing rule. 𝑛𝑐∈𝑆 Number of key components in the liquid phase. 𝑛𝑐∉𝑆 Number of components in the liquid phase that are not key components. N Normalizing factor.

Generating Data for the Polymer Case in the Aqueous Phase

Let “polymer (p)” be the key component in an aqueous mixture whose function data 𝑓(𝑓𝑤𝑝) is to be generated. That component has mole (or mass) fraction wp and pure-component viscosity μp. It is the only key component in the mixture of current interest, so:

� 𝑓�𝑓𝛼𝑖�𝑛𝑐∈𝑆

𝑖=1

+ 𝑁 × � 𝑓𝛼𝑖

𝑛𝑐∉𝑆

𝑖=1

= 1 → � 𝑓(𝑤𝑖)𝑛𝑐∈𝑆

𝑖=1

+ 𝑁 × �𝑤𝑖

𝑛𝑐∉𝑆

𝑖=1

= 1 (77)

where:

� 𝑓(𝑤𝑖)𝑛𝑐∈𝑆

𝑖=1

= 𝑓�𝑤𝑝� 𝑎𝑛𝑑 �𝑤𝑖

𝑛𝑐∉𝑆

𝑖=1

= 1 −𝑤𝑝 (78)

Therefore, the normalizing factor N is:

𝑁 =1 − 𝑓�𝑤𝑝�

1 −𝑤𝑝 (79)


Substitute the expression for N, into the mixing rule equation and solve for 𝑓(𝑤𝑝):

𝐿𝑛�𝜇𝑎𝑞� = 𝑓�𝑤𝑝� × 𝐿𝑛�𝜇𝑝� + �1− 𝑓�𝑤𝑝�

1−𝑤𝑝�× �𝑤𝑖 × 𝐿𝑛(𝜇𝑖)

𝑛𝑐∉𝑆

𝑖=1

(80)

Now solving for 𝑓(𝑤𝑝):

𝑓�𝑤𝑝� =𝐿𝑛(𝜇𝑤) −𝑀𝐿𝑛�𝜇𝑝� −𝑀

(81)

where:

𝑀 = �1

1−𝑤𝑝� × �𝑤𝑖 × 𝐿𝑛(𝜇𝑖)

𝑛𝑐∉𝑆

𝑖=1

(82)

This calculation is done for each of the 11 (xlow, xhigh and 9 intermediate) 𝑤𝑝 values specified by *VSMIXENDP, and the result 𝑓�𝑤𝑝� is entered for the 11 values f1 ... f11 required by *VSMIXFUNC. This entire process must be done for each different key component comp_name specified by *VSMIXCOMP.

Keywords *VSMIXENDP and *VSMIXFUNC cause function 𝑓(𝑤𝑝) to be continuous and piecewise linear in the 𝑤𝑝 domain [0,1] and 𝑓�𝑤𝑝� range [0,1]. Beyond these constraints, any function can be matched at the 11 points. If 𝑓�𝑤𝑝� = 𝑤𝑝, the nonlinear mixing option reduces to the linear mixing rule.

Example:

Consider the following table in which the aqueous phase viscosity (µaq) is a function of polymer concentration (Cp), and the linear mixing rule is less appropriate for modeling the changes of the liquid viscosity. Therefore, the key component in the mixing rule of the viscosity will be the polymer and this needs to be specified by the *VSMIXCOMP keyword.

Cp (%) µaq (cp) 0.00 1.000 0.03 1.417 0.05 1.875 0.10 4.000

In the aqueous phase, only the water and polymer components will be present. It can be inferred from the above table that the water component viscosity (µw) is equal to 1 cp and the polymer viscosity, as “pure” component, is 4 cp.


The nonlinear viscosity function will depend upon mole (mass) fraction of polymer component. The next step involves converting the weight percent of polymer to mass fraction 𝑤𝑝 = 𝐶𝑝/100 then determining the nonlinear viscosity, as shown in the following table:

wp (mass frac) µaq (cp) 0.0000 1.000 0.0003 1.417 0.0005 1.875 0.0010 4.000

Assuming the *MASSBASIS keyword is activated (which means the component property data is based on mass instead of mole), this data can be plotted directly to obtain the equation that represent the aqueous viscosity as a polymer concentration function:

The aqueous viscosity equation for this example will be:

𝜇𝑎𝑞 = 𝜇𝑤 × �1 + 1 × 103 × 𝑤𝑝 + 1 × 106 × 𝑤𝑝2 + 1 × 109 × 𝑤𝑝3�

If the polymer injection concentration is assumed to be 1000 ppm (0.1 %wt) then the values of xlow and xhigh will be 0 and 0.1 respectively. The nine intermediate values will be calculated internally in STARS using the following expression:

𝑥𝑗+1 = 𝑥𝑗 + �𝑥ℎ𝑖𝑔ℎ − 𝑥𝑙𝑜𝑤� 10 (𝑓𝑜𝑟 𝑗 = 2 𝑡𝑜 10)⁄ (83)

where 𝑥1 = 𝑥𝑙𝑜𝑤 𝑎𝑛𝑑 𝑥11 = 𝑥ℎ𝑖𝑔ℎ.

The corresponding viscosity values for the nine intermediate points of mass fraction are obtained from the above aqueous viscosity equation:

j wp (mass frac) µaq (cp) 1 0.0000 1.000 2 0.0001 1.111


j wp (mass frac) µaq (cp) 3 0.0002 1.248 4 0.0003 1.417 5 0.0004 1.624 6 0.0005 1.875 7 0.0006 2.176 8 0.0007 2.533 9 0.0008 2.952

10 0.0009 3.439 11 0.0010 4.000

The last step is to determine the values of the nonlinear function for j = 2, as shown below:

𝑓�𝑤𝑝� =𝐿𝑛�𝜇𝑎𝑞� −𝑀𝐿𝑛�𝜇𝑝� − 𝑀

→ 𝑀 = �1

1 −𝑤𝑝�× �𝑤𝑖 × 𝐿𝑛(𝜇𝑖)

𝑛∉𝑆

𝑖=1

(84)

where water is the common component and the polymer is the key component. Further:

𝑀 = �1

1 − 0.001�× (0.9999) × 𝐿𝑛(1) = 0 → 𝑓�𝑤𝑝� =

𝐿𝑛(1.111)𝐿𝑛(4) (85)

Proceeding in the same way, the remaining cells in the table can be calculated: wp (mass frac) µaq (cp) f(wp)

0.0000 1.000 0.0000 0.0001 1.111 0.0759 0.0002 1.248 0.1598 0.0003 1.417 0.2514 0.0004 1.624 0.3498 0.0005 1.875 0.4534 0.0006 2.176 0.5608 0.0007 2.533 0.6704 0.0008 2.952 0.7808 0.0009 3.439 0.8910 0.0010 4.000 1.0000

The keywords for representing the nonlinear mixing rule should appear as follows:

*VSMIXCOMP 'Polymer'

*VSMIXENDP 0 0.001

*VSMIXFUNC 0.0 0.0759 0.1598 0.2514 0.3498 0.4534 0.5608 0.6704 0.7808 0.891 1.0


Shear Effect on Polymer Viscosity

The following figure shows an example of polymer viscosity at different shear rates. The data for generating this figure will be used to illustrate the Darcy velocity calculation using the study of Cannella et al.31, mentioned earlier:

Figure 16 Polymer Viscosity at Different Shear Rates

For this example, assume the following coreflood experimental and rheological data:

kabs = 1 Darcy krw = 0.15 Sw = 0.78 φ = 0.35

Table 2 Polymer Viscosity vs. Shear Rate

SR (1/sec) Aqueous Phase Viscosity (cps)

0.05 wt% Polymer 0.1 wt% Polymer 0.01 1.875 4.000 0.1 1.836 3.865 1 1.507 2.737

10 1.253 1.868 100 1.126 1.432

1000 1.063 1.215

The first step is to use the expression in Cannella et al.31 to convert shear rate to Darcy velocity:

𝑢𝑙 =�̇� ×�𝑘𝑎𝑏𝑠 × 𝑘𝑟𝑙 × φ × 𝑆𝑙

𝛾𝑓𝑎𝑐=

0.01 × √1 × 0.15 × 0.35 × 0.784.8 × 10066

= 4.18 × 10−8𝑐𝑚/𝑠𝑒𝑐


where 4.8 is the default shear rate factor and 10066 is a conversion factor to obtain cm/sec as the units of velocity.

Proceeding in the same way, the following table can be generated:

SR (1/sec) Darcy velocity (cm/sec) 0.01 4.188E-08 0.1 4.188E-07 1 4.188E-06 10 4.188E-05

100 4.188E-04 1000 4.188E-03

The shearing applies to the component and not to the phase, so the second step is to calculate the pure component viscosity by using the non-linear mixing rule expression. For this example the data used in Generating Data for the Polymer Case in the Aqueous Phase, will be used. Assuming a polymer injection concentration of 500 ppm (𝑤𝑝 = 0.0005), the function 𝑓�𝑤𝑝� will be equal to 0.4534 and the aqueous phase viscosity, 1.875 cps, based on which the polymer viscosity as pure component will be:

𝐿𝑛�𝜇𝑝� =𝐿𝑛�𝜇𝑎𝑞� − �

1− 𝑓�𝑤𝑝�1−𝑤𝑝

�× 𝑤𝑤 × 𝐿𝑛(𝜇𝑤)

𝑓�𝑤𝑝�

(86)

𝜇𝑝 = 𝑒𝑥𝑝�𝐿𝑛(1.875) − �1 − 0.4534

1 − 0.0005�× 0.9995 × 𝐿𝑛(1)

0.4534� = 4 𝑐𝑝𝑠

Proceeding in the same way, all the polymer viscosity values as pure component can be calculated and the table of *SHEARTAB will appear as follows:

*SHEARTAB **Darcy Velocity (cm/sec) Polymer Viscosity (cps)

4.188E-08 4.0000 4.188E-07 3.8172 4.188E-06 2.4695 4.188E-05 1.6455 4.188E-04 1.2998 4.188E-03 1.1441

If 𝑓�𝑤𝑝� = 1 at the injection concentration, then the pure polymer viscosity will equal the aqueous phase viscosity. For polymer concentrations at the grid blocks in the simulation which are lower than the injection concentration, SHEARTAB is scaled down on the basis of log (viscosity) versus log (velocity).


In brief, STARS performs the following calculations:

1. STARS calculates the Darcy velocity for each grid cell. From the example, take the value 4.188E-06 cm/sec.

2. STARS looks up the shear table with the calculated velocity to obtain the “pure” component viscosity (polymer); in our example, 2.4695 cps.

3. STARS substitutes the new viscosity in the *AVISC/*BVISC keywords table. 4. STARS calculates the phase viscosity using the polymer mole fraction in each grid

cell, the polymer viscosity from the previous step, and the nonlinear mixing rule. Assuming a polymer mole fraction of 0.0005, the viscosity of the aqueous phase or

polymer solution will be:

𝐿𝑛�𝜇𝑎𝑞� = 𝑓�𝑤𝑝� × 𝐿𝑛�𝜇𝑝� + �1− 𝑓�𝑤𝑝�

1−𝑤𝑝�× 𝐿𝑛(𝜇𝑤) × 𝑤𝑤 (87)

𝐿𝑛�𝜇𝑎𝑞� = 0.4534 × 𝐿𝑛(2.4695) + �1 − 0.45341 − 0.0005

�× 𝐿𝑛(1) × (0.9995)

= 0.40988

𝜇𝑎𝑞 = 1.507 𝑐𝑝𝑠

This last value means that the equations reproduce the viscosity values of the polymer solution reported from the laboratory at different velocities or shear rates.

Salinity Effect on Polymer Viscosity An example of the effect of salt concentration on polymer solution viscosity is shown in Figure 17. The values used to build this plot are shown in Table 3.

Figure 17 Salinity Effect on Polymer Solution Viscosity


Table 3 Salinity Effect on Polymer Solution Viscosity

Salt Concentration wt%

Polymer Solution Viscosity, cps @ 0.05 wt% 0.1 wt% 0.15 wt%

3 1.875 4 8.125 6 1.125 2.3 5.6875

10 0.75 1.6 4.0625

The keyword format requested by STARS to account for the salinity effect on the polymer viscosity is as follows:

*VSSALTCMP 𝑐𝑜𝑚𝑝_𝑛𝑎𝑚𝑒 𝑥𝑚𝑖𝑛 𝑠𝑝

where 𝑐𝑜𝑚𝑝_𝑛𝑎𝑚𝑒 is the component (e.g. salt or alkaline) affecting the viscosity of the nonlinear mixing component (e.g. polymer). This must be one of the component names specified by *COMPNAME. 𝑥𝑚𝑖𝑛 is the minimum salinity of the phase and 𝑠𝑝 is the slope of the log-log plot of polymer component viscosity versus ratio of salinity over minimum salinity (𝑥𝑠𝑎𝑙𝑡 𝑥𝑚𝑖𝑛⁄ ).

To build the log-log plot, first calculate the polymer viscosity as a pure-component using the non-linear mixing rule for phase viscosity, as outlined in Generating Data for the Polymer Case in the Aqueous Phase:

*VSMIXCOMP 'Polymer'

*VSMIXENDP 0 0.001

*VSMIXFUNC 0.0 0.0759 0.1598 0.2514 0.3498 0.4534 0.5608 0.6704 0.7808 0.891 1.0

With a water component viscosity of 1 cps and a polymer component viscosity of 4 cps at 1 wt% Polymer, *AVISC = 4, and *BVISC = 0. In the above non-linear mixing rule, the rule of mixture was made based on a maximum concentration of 1 wt% polymer with f�𝑤𝑝� = 1 at this maximum concentration. At this point, the polymer viscosity as pure component is equal to that of the phase. For this example, however, we will assume the injection concentration is 500 ppm (0.05 wt%). At this concentration, 𝑓�𝑤𝑝� = 0.4534.

To illustrate, calculate the pure component viscosity at 0.05 wt% polymer concentration using the following formula and the values of polymer solution or aqueous viscosity from Table 3:

𝐿𝑛�𝜇𝑝� =𝐿𝑛�𝜇𝑎𝑞� − �

1− 𝑓�𝑤𝑝�1−𝑤𝑝

�× 𝑤𝑤 × 𝐿𝑛(𝜇𝑤)

𝑓�𝑤𝑝�

(88)

The viscosity of the water component is 1 cp, so the above equation can be reduced to:

𝜇𝑝 = 𝑒𝑥𝑝 �𝐿𝑛�𝜇𝑎𝑞�𝑓�𝑤𝑝�

� = 𝑒𝑥𝑝�𝐿𝑛(1.125)

0.4534 � = 1.297 𝑐𝑝𝑠 (89)


Repeat the calculation for the remaining polymer viscosity values as pure component, as shown in Table 4. Table 4 Polymer Solution and Component Viscosities vs. Salt Concentration

Salt Conc. (wt%) Viscosity @ 0.05 wt% (cps) Solution Component

3 1.875 4.000 6 1.125 1.297 10 0.75 0.530

The second step is to calculate the ratio of the salinities (𝑥𝑠𝑎𝑙𝑡 𝑥𝑚𝑖𝑛⁄ ). For this, assume that the brine salinity (or minimum salinity) is 30,000 ppm (3 wt%). The results are shown below:

(xsalt /xmin) Component Viscosity (cps),

@ 0.05 wt%

1 4.000 2 1.297

3.33 0.530

The third step consists of plotting the viscosity of the component versus the salinity ratio in a log-log graphic and calculating the slope of this curve, as shown in Figure 18:

Figure 18 Component Viscosity vs. Salinity Ratio

From Figure 18, 𝑠𝑝 = −1.6754 and 𝑥𝑚𝑖𝑛 = 0.03 in mass fraction. The keywords can be added to STARS as follows:

*VSSALTCMP 'Salt' 0.03 -1.6754


Using this information and the STARS power-law equation, the most updated viscosity (final or resultant) of polymer (as pure component) in the saline solution will be obtained and used with the nonlinear mixing function to determine the phase viscosities. To verify this, assume the salinity in the system increases to 6 wt%. Since *AVISC = 4, 𝜇𝑝0 = 4 𝑐𝑝𝑠. Therefore:

𝜇𝑝 = 𝜇𝑝0 × �𝑥𝑠𝑎𝑙𝑡𝑥𝑚𝑖𝑛

�𝑠𝑝

= 4 × �0.060.03

�−1.6754

= 1.2523 𝑐𝑝𝑠 (90)

and the aqueous phase viscosity is:

𝜇𝑎𝑞 = 𝑒𝑥𝑝 �𝑓�𝑤𝑝� × 𝐿𝑛�𝜇𝑝�� = 𝑒𝑥𝑝�0.4534 × 𝐿𝑛(1.2523)� = 1.107 𝑐𝑝𝑠 (91)

This value of 1.107 cps of the phase viscosity at 6 wt% of salt is comparable with that in Figure 18, 1.125 cps obtained for example from laboratory. Therefore, the equations and the calculations made can reproduce the effect observed in laboratory.

If both effects (shear rate and salinity) are considered in the simulation, then the polymer viscosity as pure component is updated first by the velocity (or shear rate), then used in the equation of salinity as 𝜇𝑝0, to be updated by the salt concentration, and finally is used in the non-linear mixing rule to calculate the phase viscosity.


Appendix B – Conversion of Eclipse Polymer Option to IMEX

Example of Eclipse Data --polymer solution viscosity function --column 1: polymer concentration in solution kg/m³ = ppm/1000 --column 2: corresponding factor by which water viscosity in PVTW has to be multiplied PLYVISC 0.0000 1.00000 0.5000 3.3333 1.0000 6.0 1.125 6.666 1.250 8 / PLYSHEAR --shear thickening 0.0 1.000 0.05 1.001 0.5 1.300 0.7 1.380 0.9 1.400 1.5 1.420 4.0 1.500 / PLYROCK --column 1: inaccessible PV, should change with rock type (more IPV for bad rock) --column 2: RRF = decrease in krw when max amount of poly has been adsorbed --column 3: mass density of rock [kg/m³] --column 4: adsorption index 2= no desorption --column 5: max polymer adsorption [kg/kg] for max. RRF 0.07 1.5 1.9 2 5.0E-5 / --polymer adsorption function, units in Eclipse: column 1: g/cm³ column 2: g/g PLYADS --column 1: concentration of polymer in solution around the rock [kg/m³] --column 2: corresponding saturated concentration of polymer adsorbed by the rock [kg/kg] 0.000 0.0000000 0.500 0.0000250 1.000 0.0000500 1.500 0.0000750 /


PLYVISC and PLYSHEAR Conversion to IMEX Eclipse PLYVISC converts to IMEX *PMIX keyword plus the use of *PREFCONC. If the Eclipse keyword PLYSHEAR is present, then the subkeyword for *PMIX should be *VELTABLE, otherwise if PLYSHEAR is not present the subkeyword for *PMIX should be *TABLE.

Polymer Concentration Values The IMEX keyword *PREFCONC should be set to the maximum value of the polymer concentration given in the Eclipse keyword PLYVISC, and all concentration values in the table for PLYVISC should be divided by this maximum value.

Viscosity Multipliers The viscosity multipliers given in the second column in the table for PLYVISC can be used without any changes for the second column of values for *PMIX in IMEX. If PLYSHEAR is present, then a table must be generated for each velocity under this keyword. The table will consist of the same values of polymer concentration and viscosity multipliers that were converted from PLYVISC, except the second column of values will be multiplied by the values corresponding to the velocity in the table.

The converted keywords PLYVISC and PLYSHEAR for the example on the first page are as follows:

PREFCONC 1.25 **kg/m3 PMIX VELTABLE VWT 0.0 **velocity=0.0 m/day 0.0000 1.00000 0.4000 3.3333 0.8000 6.0000 0.9000 6.6660 1.0000 8.0000 VWT 0.05 **velocity=0.05 m/day. 0.00 1.0000 0.40 3.3366 0.80 6.0060 0.90 6.6727 1.00 8.0080 VWT 0.5 **velocity=0.5 m/day 0.00 1.0000 0.40 4.3333 0.80 7.8000 0.90 8.6658 1.00 10.4000 VWT 0.7 **velocity=0.7 m/day 0.00 1.0000 0.40 4.6000 0.80 8.2800


0.90 9.1991 1.00 11.0400 VWT 0.9 **velocity=0.9 m/day. 0.00 1.0000 0.40 4.6666 0.80 8.4000 0.90 9.3324 1.00 11.2000 VWT 1.5 **velocity=1.5 m/day. 0.00 1.0000 0.40 4.7333 0.80 8.5200 0.90 9.4657 1.00 11.3600 VWT 4.0 **velocity=4.0 m/day. 0.00 1.0000 0.40 5.0000 0.80 9.0000 0.90 9.9990 1.00 12.0000

PLYROCK Conversion to IMEX Eclipse keyword PLYROCK converts to the IMEX keyword *PPERM. The first entry on PLYROCK converts to the fourth table column on *PPERM via the formula “p_pore = 1.0 – IPV”. The 2nd entry on PLYROCK is used directly for entry as the 5th column on *PPERM (RRF). The 3rd entry on PLYROCK is used for calculation of IMEX adsorption. The 4th entry on PLYROCK is used to indicate whether the 3rd column on *PPERM (res_ad) is set equal to the 2nd column (i.e. for no desorption, set res_ad = max_ad, for desorption set res_ad=0). The 5th entry on PLYROCK is used directly for entry in the 2nd column of *PPERM (max_ad).

PLYADS Conversion to IMEX Eclipse keyword PLYADS converts to the IMEX keyword *PADSORP. The first column on PLYADS is used directly for the 1st column in *PADSORP. The 2nd column on PLYADS converts to the 2nd column in *PADSORP via the formula: PADSORP(2nd col) = PLYADS(2nd col) * rock_density * (1.0 – porosity)/porosity. Rock_density is input as the 3rd parameter in PLYROCK.


The converted keywords PLYROCK and PLYADS for the example shown on page 64 are as follows:

PPERM ** perm max_ad res_ad p_pore rrf 10.0 0.530 0.530 0.93 1.5 10000.0 0.530 0.530 0.93 1.5 PADSORP **col 1: Polymer concentration kg/m3 **col 2: adsorption level (kg/m3) = kg_polymer/kg_rock*rock_density*(1-porosity)/porosity ** use: rock_density=sandstone=2650.0 kg/m3 and porosity = 0.2. Factor=10600. ** p_con adsorp_level 0.000 0.000 0.500 0.265 ** =0.0000250 * 10600 1.000 0.530 ** =0.0000500 * 10600 1.500 0.795 ** =0.0000750 * 10600


Appendix C – Conversion of IMEX Polymer Option to STARS

Step 1: Builder Convert Simulator Type Open the IMEX data set in Builder and select the menu item File | Convert Simulator Type For Data Set | To STARS. Enter a new data set name and select the option for fluid model conversion “Convert from Black oil model”. Enter reservoir temperature and bubble point as required to convert the PVT data into a STARS fluid model. This PVT conversion is explained in more detail in the user manual for Builder (press F1 in Builder) under the heading “Using the STARS Import Black Oil PVT Wizard”.

Step 2: Process Wizard Open the STARS data set created in Step 1 in Builder and select the menu item Components | Process Wizard. From the drop-down box, select Alkaline, surfactant, foam and/or polymer model and then click Next. Choose model Polymer flood (add 1 component).

Input Polymer Data Obtain the polymer resistance factor from column 5 of the IMEX keyword *PPERM and enter this number in the wizard. Similarly, obtain the accessible pore volume from column 4 of *PPERM and enter this number in the wizard. Cancel Polymer quantity decreases with time and enter the rock density appropriate for the reservoir to be modeled (if this file was converted from Eclipse, then enter the rock density input from the 3rd parameter on Eclipse keyword PLYROCK). Now click Next and Next again on the Component Selection dialog box.

Input Adsorption Data For adsorption, enter the porosity of the laboratory sample used for adsorption measurements or if this file was converted from Eclipse, enter the porosity used for conversion of adsorption from Eclipse (PLYADS) to IMEX (PADSORP). Locate the adsorption table in the IMEX data file (*PADSORP) and determine the number of rows used for the table. In the process wizard, right click on the adsorption table and insert rows until the number of rows in the table equals the number of rows in *PADSORP. Calculate the 1st column for the wizard (poly_wt%) from the 1st column of *PADSORP (p_con) with:

poly_wt% = p_con * 100 / water_density


Calculate the 2nd column for the wizard (poly_ads, mg/100 gm rock) from the 2nd column of *PADSORP (ads_level) with the equation below, then click Next.

poly_ads = ads_level / rock_density * porosity/(1–porosity) * 1.0e5

Input Polymer Viscosity Locate the polymer viscosity data in the IMEX data file under the keyword *PMIX. Determine the number of rows of data used on this keyword (first table at velocity=0 if PMIX VELTABLE is used). Make the number of rows on the process wizard equal to this number of rows by right clicking on the table of viscosity vs. weight % polymer. Calculate the 1st column of data for the wizard (poly_weight%) from the 1st column of PMIX (poly_conc, kg/m3) and the value input in IMEX on keyword *PREFCONC using:

Poly_weight% = poly_conc * prefconc * 100 / water_density

Calculate the 2nd column of data for the wizard (poly_visc) from the 2nd column of PMIX (visc_mult) using the equation below (note that the water viscosity with no polymer is shown in the wizard on row 1 of the viscosity table). Click Finish when done with this table and save the data set.

Poly_visc = visc_mult * water_viscosity(no polymer)

Step 3: Shear Dependent Viscosity If the IMEX keyword *PMIX *VELTABLE is used, then the shear dependent viscosity option must be used in STARS. With STARS versions 2012.10 or earlier, *VISCTABLE cannot be used with SHEARTAB, so with these versions of STARS the *VISCTABLE data must be converted into the *AVISC and *BVISC format. This can be done easily for isothermal simulations by locating the *VISCTABLE entries at reservoir temperature and entering these values on *AVISC, while setting all *BVISC values to zero.

To enable the input of velocity vs. viscosity (instead of shear rate vs. viscosity), open the STARS data file in a text editor and add the keyword *SHEAREFFEC *SHV in the I/O section of the data set (i.e. at the top).

Plot the values of polymer viscosity vs. velocity at different concentrations of polymer from the IMEX data on PMIX. The Eclipse example data given at the beginning of this section is plotted as shown below.


From this plot, select the polymer concentration line that most represents the polymer versus velocity behavior at the polymer concentrations and velocities expected to be dominant in the simulation. This selection needs to be done because STARS will calculate the velocity dependent viscosity at different polymer concentrations using the viscosity mixing rule (see the discussion in the Shear-Dependent Viscosity Effects section of this manual). For the example plot of viscosity versus velocity above, the STARS calculations of velocity dependent viscosities will be as shown in the following figure. Some small differences can be noted.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 0.5 1 1.5 2 2.5 3 3.5 4

Visc

osity

, cp

Velocity, m/day

Viscosity vs. Velocity vs. Polymer Concentration

Viscosity at 0 wt% PolymerViscosity at 0.05 wt% PolymerViscosity at 0.1 wt% PolymerViscosity at 0.1125 wt% PolymerViscosity at 0.125 wt% Polymer

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 0.5 1 1.5 2 2.5 3 3.5 4

Visc

osity

, cp

Velocity, m/day

STARS Calculation of Viscosity vs. Velocity vs. Polymer Concentration

Viscosity at 0.000 wt% PolymerViscosity at 0.050 wt% PolymerViscosity at 0.100 wt% PolymerViscosity at 0.1125 wt% PolymerViscosity at 0.1250 wt% Polymer


Using a text editor with the STARS data file, insert the *SHEARTAB keyword after the *VSMIXFUNC keyword corresponding to “Polymer”. Then, with the table of velocity vs. viscosity selected above, enter the velocity values directly into the first column in the table following *SHEARTAB. Locate the value corresponding to the component “Polymer” on the STARS keyword *AVISC (avisc_poly). Use this value together with the viscosity values (visc_selected) from the table of velocity versus viscosity selected above to calculate the values for the 2nd column of data following *SHEARTAB using the following formula:

SHEARTAB(2nd col) = visc_selected * avisc_poly / visc_selected(first_row)

The equivalent STARS keywords that were converted from the example Eclipse data are as follows:

MODEL 4 4 4 2 COMPNAME 'Water' 'Polymer' 'Dead_Oil' 'Soln_Gas' CMM 0 8 0.281591 0.017346 . . AVISC 0.4837 4.64398 52.2 1.26719 BVISC 0.0 0.0 0.0 0.0 VSMIXCOMP 'Polymer' VSMIXENDP 0 3.10137e-006 VSMIXFUNC 0 0.1465 0.2930 0.43951 0.55849 0.62995 0.7014 0.77286 0.82949 0.91137 1 SHEARTAB 0.05 4.64398 0.5 6.031142857 0.7 6.40229011 0.9 6.495076923 1.5 6.587863736 4 6.959010989


Appendix D – Example IMEX and STARS Simulations of Polymer

Comparisons of IMEX and STARS To make sure that IMEX and STARS are predicting the same for both a normal waterflood and a polymer flood with no velocity dependence, simulation runs should be done to compare the results. A sample comparison, shown below, compares oil and water rates and well block pressure.

Time (Date)

Oil

Ra

te S

C (

m3

/da

y)

2012 2014 2016 2018 2020 20220.0

0.1

1.0

10.0

IMEX_BaseWF.irfIMEX_Polymer_NoVelocityDep.irfStars_BaseWF.irfStars_Polymer_NoVelocity.irf

Time (Date)

Wa

ter

Ra

te S

C (

m3

/da

y)

2012 2014 2016 2018 2020 20220.00

0.50

1.00

1.50

2.00


Time (Date)

We

ll B

loc

k P

res

su

re (

kP

a)

2012 2014 2016 2018 2020 202210,500

11,000

11,500

12,000

12,500

13,000

13,500



STARS Options For Real Polymer Phenomena Simulations using STARS polymer injection options to determine the effects of various real phenonena are given in the following plot. As shown, the effects of using polymer degradation [see section Polymer Degradation] results in a lower amount of incremental oil. Adding wettability effects (see section Relative Permeability/Wettability Alteration Effects) that cause the rock to shift towards water wet results in additional incremental oil.

Time (Date)

Cum

ulat

ive

Oil

SC (m

3)

2012 2014 2016 2018 2020 20220

200

400

600

800

Stars_BaseWF.irfStars_Polymer.irfStars_Polymer_Degradation.irfStars_Polymer_Degradation_Wettability.irf