A Systemic Comparison of Physical Models for Simulating Surfactant–Polymer Flooding

: Three different reservoir simulators that utilize both two-phase and three-phase microemulsion phase behavior models are used to model surfactant–polymer ﬂooding to determine and compare their results. Different models are used in each simulator to describe the physical behavior of injected chemicals into the reservoir, which raises the need to benchmark their results. The physical behavior models of polymer and surfactant were constructed and veriﬁed on a 1D scale reservoir model and further veriﬁed in a 3D model. Finally, simulations were conducted in a ﬁeld-scale reservoir containing 680,400 grids, where results were compared and analyzed. The 1D and 3D model results suggest an excellent match between the different simulators in modeling surfactant–polymer ﬂoods. In the case of the ﬁeld-scale model, the simulators matched in terms of oil recovery and total volumes produced and injected, while having similar reservoir pressure proﬁles but with signiﬁcant discrepancies in terms of injected and produced chemicals. These results indicate that despite the differences in the calculated injected and produced chemicals due to the different models in the simulators, the effect of surfactant–polymer ﬂoods on oil recovery, total injected and produced ﬂuids, and average pressure proﬁles can be comparably modeled in all of the three simulators.


Introduction
Many oil reservoirs start production through primary recovery and transition to secondary oil recovery as the reservoir loses energy to produce alone.These methods, although economically viable, leave behind much untapped potential in oil recovery, with 55% to 75% of the original oil in place (OOIP) remaining in the reservoir after secondary recovery [1].In addition, steady growth in world energy demand over decades has made oil production increasingly difficult as oil reservoirs became depleted and transitioned to mature fields with declining oil production.Such challenges have led to innovative solutions that can improve oil recovery from existing mature fields, such as enhanced oil recovery (EOR), representing a wide range of advanced oil recovery methods.
When EOR methods are used, injected fluids interact with the reservoir strata and in situ fluids to increase oil production, improving its economic value and lifetime [2].EOR methods are categorized into chemical, gas/solvent, and thermal [3].These applications aim to increase oil production by reducing the residual oil saturation (Sor) or reducing oil viscosity.Oil residual saturation is reduced by leveraging two main properties: increasing the capillary number (Nc) and decreasing the mobility ratio (M) [4][5][6][7].Chemical EOR is characterized by individual or combined injection of polymer, surfactant, cosolvents, and alkali to improve oil recovery [3].Polymer flooding increases the viscosity of the injected fluid, thereby decreasing the mobility ratio and improving sweep efficiency.Surfactant flooding reduces the interfacial tension between oil and water in the reservoir, changes wettability, and can generate foam in specific cases.Such effects can increase the capillary number and improve the mobility ratio.
The difficulty in producing oil from mature fields comes from several factors, the most important of which are mobility control issues and natural capillary forces that trap the oil in the porous media.Surfactant-polymer flooding is designed to address those issues.Surfactant-polymer flooding increases oil production by decreasing the mobility ratio of the injected fluid and producing a low interfacial tension flood [2,[8][9][10][11][12].These effects aid in moving trapped or bypassed oil to the producer, thereby increasing recovery.However, the physical properties and processes of this type of flooding are complex and require careful investigation.That is, if not properly formulated, designed, or executed, the chemical flood will have an adverse effect on the reservoir.It might even cause permanent damage to the field's oil production capacities.Therefore, field tests, academic research, and extensive analyses are necessary before executing such a method.Numerical reservoir simulators are tools used to predict the performance of field-scale projects under certain conditions before deployment.Such a tool allows detailed analysis of enhanced oil recovery methods that minimize the risk involved in their development.
Reservoir simulators are computer programs that use reservoir engineering concepts to model the fluid flow and behavior in the reservoir.These models are constructed based on formulations derived from lab data and mathematical derivations that describe various physical behaviors in the field.Chemical EOR methods and physical properties have been studied extensively in recent decades.Subsequently, different simulators have been developed using various solution schemes to describe the reservoir characteristics during chemical EOR.While many approaches have been developed for modeling the fluid flow of black oil and compositional oils [13][14][15][16][17][18][19][20][21][22][23][24], modeling chemical EOR requires special phase behavior and fluid flow concepts, especially in cases where a microemulsion phase is present [25][26][27][28].
Pope and Nelson [29] developed a one-dimensional simulator that modeled the shear-thinning effect in polymer injection and the three-phase oil-brine-microemulsion phase behavior using an Implicit Pressure Explicit Composition (IMPEC) formulation.Delshad et al. [30] presented a three-dimensional, advection-diffusion, multiphase, multicomponent IMPEC reservoir simulator for chemical EOR considering dead crude oil (insignificant solution gas).Tong and Chen [31] developed an isothermal, fully implicit, three-phase, three-dimensional model to simulate polymer flooding with the black oil model.John et al. [32] and Han et al. [33] implemented Winsor Type I [34] microemulsion phase behavior using Hand's rule [35] in a fully implicit equation of state (EOS) compositional simulator (GPAS), which was further extended by Han et al. [36] to account for the Equivalent Alkane Carbon Number (EACN) and Najafabadi et al. [37] to account for the other Winsor microemulsion types.Another fully implicit four-phase simulator with similar capabilities was developed by Patacchini et al. [38].Yang et al. [39] presented an adaptive implicit method for surfactant-polymer flooding but considered only Winsor Type I microemulsion when a surfactant was injected.While the polymer's zero shear rate was assumed to change with the surfactant concentration, the interfacial tension was assumed to be a function of the surfactant concentration rather than the solubilization ratio.Mykkeltvedt et al. [40] implemented a fully implicit scheme using automatic differentiation and high-order discretization schemes for the polymer flooding simulation.Goudarzi et al. [41] conducted a benchmark study comparing various numerical reservoir simulators to assess the strengths and limitations of each simulator for specific chemical EOR processes, aiming to improve chemical design for field-scale studies and optimize field injection projects.
Nghiem et al. [42] presented an adaptive implicit compositional reservoir simulator capable of modeling the surfactant-polymer flooding that approximates the brine/oil/microemulsion three-phase system to a modified brine/oil system [43].Shi et al. [44] developed a new fully implicit chemical flooding formulation by mixing natural and global concentration variables and using total concentrations as primary unknowns for the components that only partition in the aqueous phase (polymer, anion, cation).The model considered the microemulsion phase and all Winsor phase environments.Such work was further improved by Han et al. [45] with the addition of cosolvents.Jia et al. [46] presented a two-phase, five-component, fully implicit reservoir simulator for polymer-surfactant flooding.Finally, Jia et al. [46] considered a variable substitution method that considered two sets of primary variables, but only the Type II(-) microemulsion type was considered in their work.The five components were water, oil, surfactant, polymer, and salt, and the implementation was performed using perpendicular bisector (PEBI) grid discretization.Their implementation was validated with the UTCHEM simulator [30].
Fernandes [47] and Fernandes et al. [48] presented advanced algorithms for solving partial differential equations in reservoir simulators, focusing on compositional miscible gas flooding and chemical EOR processes.The research develops adaptive implicit (AIM) methods, fully implicit (FI) approaches, and other novel techniques to improve simulation performance.The findings, implemented in the in-house simulators UTCOMPRS and UTCHEMRS, demonstrate increased robustness and computational performance compared to original IMPEC approaches and commercial simulators commonly used in the oil industry.An example of a field simulation case study conducted using different simulators was done by Guzman et al. [49], where different scenarios of polymer flooding and surfactant polymer flooding were evaluated using various simulators as part of a field case study on a Colombian oil field.In their study, a sector model was constructed and validated through history matching with the various simulators to determine the best approach for maximum oil recovery.
In this study, three different chemical EOR reservoir simulators were used to systematically investigate the differences using a three-phase microemulsion phase behavior model versus a two-phase model for SP flooding.Simulators A (UTCHEMRS [47,48]) and B (SLB-INTERSECT [50]) share some similarities, especially in terms of the three-phase microemulsion phase behavior model, but they use different relative permeability and adsorption reversibility models.On the other hand, simulator C (CMG-STARS [51]) can only simulate microemulsion phase behavior in Winsor Type I or Type II, with no capabilities to model Type III phase behavior.Additionally, simulator C uses fundamentally different methods to model polymer rheology, adsorption, and permeability reduction.To the best of our knowledge, this is the first time that commercial-grade reservoir simulators capable of modeling three-phase brine/oil/microemulsion systems for full-field simulation (INTERSECT and UTCHEMRS) are presented against a commercial simulator that models the surfactant flooding with a two-phase brine/oil model (CMG-STARS).It is important to consider that the simulations in this study serve as synthetic cases for comparing the physical models among the reservoir simulators, and the practicalities of realworld scenarios may differ.Notably, there have been significant debates regarding the inclusion of Type III microemulsion phase in the SP models (three phases of water/oil/microemulsion).CMG-STARS can only model Type I or Type II microemulsion systems, whereas UTCHEM-RS and INTERSECT both can model the salinity and phase behavior transition of Type I to Type III to Type II.This paper provides more insights into this aspect of SP modeling, making a valuable contribution to the ongoing discussions in the field.

Materials and Methods
Surfactant-polymer flooding was modeled using various simulation cases for three reservoir models.The methodology used to construct and validate the simulation cases is explained here.

Modeling Approach
In this study, 27 simulation cases are presented based on three reservoir models and three different flooding designs using three simulators.The reservoir models are 1D, 3D, and field reservoir models (Figure 1).The flooding scenarios comprise waterflood, polymer flood, and SP flood.Initially, 1D waterflooding was modeled to validate the physical property models before polymer or SP simulations.Next, a simple 3D model with one injector and one producer and, finally, a field-scale model with 680,400 grids with 12 injectors and six producers were simulated.

One-Dimensional Model
The reservoir parameters, injection well constraint, production well constraint, and initial conditions are summarized in Table 1.The 1D cases are conducted first to ensure the input parameters among different reservoir simulators are calibrated before conducting the more complex and CPU-intensive 3D cases.

Field-Scale Model
The field-scale reservoir model considers a geological model with 680,400 gridblocks based on the publicly available data set of the Volve field in the Norwegian North Sea [52].This model is constructed using a corner point grid with 215,114 active blocks.The reservoir is highly heterogeneous and faulted.
The reservoir was initialized using the equilibrium model in Simulator B and subsequently applied to the other simulators.The water-oil contact was at a depth of 9800 ft. Figure 2 shows the porosity distribution, permeability in the X direction, the initial reservoir pressure, and the well locations.The model was constructed with 18 wells in a 5-spot pattern, with twelve injectors and six producers (Figure 2d).A summary of the properties of the model is compiled in Table 3.

Summary of Physical Properties
Physical properties are presented based on the type of flood simulated.

Waterflood
The first scenario is a waterflood with input parameters summarized in Table 4, and the oil/water relative permeability curves are illustrated in Figure 3.

Polymer Flood
Polymer is injected after an initial waterflood.Simulating separate cases for polymer and SP is necessary to distinguish between the effects of polymer and surfactant on oil recovery, volumetric and displacement sweep efficiencies, and other results.Table 5 summarizes the polymer property models included, where simulators A and B share the same models (denoted as 1), while simulator C uses different models (denoted as 2).Table 6 summarizes the polymer model input parameters in simulators A and B. The polymer viscosity as a function of polymer concentration is illustrated in Figure 4a.In simulator C, polymer viscosity is modeled using the non-linear mixing function shown in Figure 4b.Polymer adsorption and permeability reduction parameters for simulators A and B are shown in Table 6. Figure 5 illustrates the adsorption model as a function of polymer concentration.

Surfactant-Polymer Flood
The SP flood was designed in four stages, starting with water, followed by a surfactant-polymer slug; then a polymer drive is injected, and finally, a second waterflood is injected.
Additional physical properties were added to previous water and polymer data to model surfactant-polymer behavior in the reservoir.Table 7 compares the surfactant models in three simulators.First, the presence of a microemulsion phase necessitates an additional viscosity model.Figure 6a displays the microemulsion viscosity behavior as a function of oil concentration in the microemulsion phase for Simulators A and B. A non-linear mixing function is used to model microemulsion viscosity for simulator C.
The surfactant model parameters are detailed in Table 8. Figure 6b shows the adsorption model's behavior as a function of surfactant concentration.Next, simulators A and B require input parameters to construct the binodal curve for microemulsion phase behavior.Figure 7 shows the solubilization plot for the surfactant formulation used in the simulations.Simulator C lacks this capability and models surfactant as a tracer that can solubilize oil and is provided by a table entry of K-values.The user provides the K-values as a function of temperature, pressure, and surfactant concentration.We generated the Kvalues using Hand's rule in Equation (A69) in Appendix A.
The Capillary Desaturation Curve (CDC) parameters are given in Table 8.The CDC describes how residual saturation changes as a function of the capillary/trapping number (Figure 8).These parameters were used in simulators A and B. Simulator C generates residual oil data based on input capillary number for the start and end of the desaturation.Finally, the parameters to model IFT are provided in Table 8.Simulators A and B use Equations (A16)-(A19) in Appendix A and simulator C uses a table of IFT values as a function of oil mole fraction.The oil/microemulsion IFT behavior as a function of oil concentration in the microemulsion phase is given in Figure 9.

1D Model Simulation Cases
In this subsection, simulation results of waterflood, polymer flood, and surfactantpolymer flood in the 1D model are compared among the three simulators.

Waterflood
This simulation was set to run for 1000 days using waterflooding, with parameters specified in Section 2 (Table 1).Table 9 summarizes the results from these three simulations with very similar results (Figure 10).

Polymer Flood
Waterflood is conducted for the first 200 days, followed by polymer injection for 600 days with 0.25 wt % polymer concentration, and another waterflood for 200 days.The results in Figure 11 confirm an excellent agreement among the simulators for polymer flood.Further details of the comparison are presented in Table 10, from which can be observed an excellent agreement between the simulators.0.003% 0.004% 0.001%

Surfactant-Polymer Flood
For this case, the reservoir was initiated in simulators A and B at a brine salinity of 0.325 , which is 25% higher than the optimum salinity of 0.26 .The flood started with a waterflood at 0.325 , followed by a 200-day SP slug with a 0.25 wt % polymer concentration and 0.02 volume fraction of surfactant concentration at a salinity of 0.26 .
Then, a polymer drive was injected for 400 days at 0.25 wt % concentration at salinity 0.26 . Finally, a water flush was injected for 200 days at 0.26 salinity.The salinity profile of this flood enables the surfactant to operate in Type III microemulsion phase behavior, thereby significantly increasing oil production.
Figure 12a-c favorably compare the cumulative produced volumes with a close match across the simulators.Furthermore, Figure 12d indicates similar pressure histories between Simulators A and B but some differences when compared to Simulator C. For Simulator B, the default settings gave a very different pressure history, indicating a different model compared to the other simulators, which is explained in detail in Appendix A. However, the results matched well after modifying the default settings to one similar to Simulator A. However, it showcases a different history match.This is explained by how Simulator C models relative permeability when surfactant is present, as described in Appendix A. Table 11 summarizes the results with good agreement in the overall results.However, it is important to note that there is a difference of about 1% between simulator C and the other two simulators for produced polymer volumes since it uses a different polymer adsorption model from the other simulators.Nevertheless, this 1D base case establishes that the results from the SP models are comparable for the three simulators.

3D Simulation Cases
This subsection discusses the 3D simulation results of waterflood, polymer flood, and surfactant-polymer flood.

Waterflood
Waterflood is conducted for 6000 days.Figure 13 shows good agreements among the simulators.Table 12 summarizes the results and establishes a solid base to model polymer and surfactant flooding.−0.002% 0.000% 0.002%

Polymer Flood
A waterflood is modeled for the first 1000 days, followed by polymer injection for 5000 days at 0.25 wt % concentration, and finally, a waterflood flush for another 1000 days.Figure 14a,b show a close match of the results for all three simulators.However, there are some discrepancies in reservoir pressure during polymer flood (Figure 14c).
Finally, Table 13 summarizes the results of this simulation case.The results obtained show an agreement between the simulators in this study in terms of polymer flood in the 3D model.However, discrepancies exist in pressure history, as shown in Figure 14c, due to model implementation differences.−0.008% 0.001% 0.009%

Surfactant-Polymer Flood
The 3D flood design is the same as the 1D SP case, except the waterflood was done for 1000 days, followed by a 1000-day SP slug, a 2000-day polymer drive, and a final water post flush for 1000 days.Similarly to the 1D case, all results agree (Figure 15a-c), except for the average reservoir pressure, which shows significant discrepancies (Figure 15d).The difference in pressure histories is similar to the 1D case, where the source of such differences is the relative permeability models being different between the different simulators.Table 14 summarizes the results presented in this case, which establishes high accuracy in volumetric matches, with discrepancies in pressure results due to relative permeability models when the microemulsion phase is present.

Field Model Simulations
This subsection discusses the results for water, polymer, and surfactant-polymer flooding simulations based on the Volve field reservoir model.

Waterflood
Waterflooding was simulated for 6000 days using 12 injectors and 6 producers.Figure 16a,b show the three simulators' total oil production and average reservoir pressure.Table 15 summarizes the quality of the results.All volumetric rates and the pressure history show good agreement among the simulators.−0.675% −0.660% 0.014%

Polymer Flood
The polymer flood was designed in the same manner as the previously discussed case, with a waterflood for the first 1000 days followed by a polymer injection in all 12 injectors for 5000 days at 0.25 wt % concentration and water salinity of 0.26 . Finally, water was injected for 1000 days.
The results are illustrated in Figure 17, where the total volumetric rates indicate consistent agreement among the simulators.On the other hand, compared with the previous smaller simulation models, the result for the field simulation has a more significant discrepancy in the produced polymer (Figure 17b).There are several reasons for this difference, the first of which is that Simulator B models irreversible adsorption and can negatively affect the produced quantities of polymer compared with Simulator A. In Simulator C's case, adsorption and permeability reduction use different models.These were also present in the smaller cases; however, their effect was magnified due to the size and complexity of the reservoir model.Table 16 summarizes the results.Additionally, Figure 17c showcases the average reservoir pressure with good agreement among simulators.−0.125% −0.204% −0.079%

Surfactant-Polymer Flood
The same chemical injection designed for the previous 3D model is used in this fieldscale simulation of a surfactant-polymer flood.Simulators A and B model a salinity gradient design to achieve the Type III microemulsion phase behavior with ultralow interfacial tension.
Figure 18 compares the total volumes of produced oil and average reservoir pressure results, with a good agreement among the three simulators.Figures 19 and 20 show the injected and produced volumes of polymer and surfactant, respectively.Table 17 summarizes the key results indicating that all three simulators can closely match oil recovery, and total injected and produced water.In addition, the average reservoir pressure history has similar trends but with some variations in the range of 100 psi.Finally, the produced surfactant and polymer volumes differ significantly, although the cumulative injected volumes are similar.

Comparing Results with Previous Work
Despite the prevalence of simulation studies in the existing literature, as highlighted in the introduction, there is a scarcity of research directly analogous to the present study.Such analogues would permit a side-by-side evaluation of outcomes, which can clarify potential similarities and disparities.Nonetheless, a handful of studies do permit a broad level of comparison.
Patacchini et al. [38] compared their new four-fluid-phase, fully implicit in-house research reservoir simulator (IHRRS) with UTCHEM on a 1D, three-fluid-phase (oil/water/microemulsion) synthetic coreflood.They also considered scenarios where it is necessary to account for four phases in equilibrium, such as a scenario where the chemical flood is preceded by a vaporizing gas drive, as well as a case where solution gas is evolved during the flooding.They discussed some aspects of their implementation, such as numerical dispersion vs. timestep length and nonlinear convergence.They showed that numerical performance is not degraded by the four-phase equilibrium.In Figure 6 in their paper, they also showed a close match of oil production and oil recovery factor between the simulators.Khorsandi et al. [27] use 1D and 2D simulations to compare PennSim reservoir simulator to UTCHEM (2000) for surfactant/polymer floods.Their study compared the two simulators in term of compositions and oil, water, and surfactant volumes, which shows a close match.Druetta et al. [53] conducted a similar comparison of UTCHEM to a novel two-dimensional surfactant flooding simulator for a four-component, two-phase system in porous media, where they found the oil recovery to be comparable in Figure 2 of their paper.Additionally, Lashgari et al. [54] compared the UTCHEM four-phase model for oil/water/microemulsion/gas to CMG-IMEX in terms of average pressure, water rate, gas rate, and cumulative oil production (Figure 8 in that paper) with a close match.
A particularly noteworthy example is the work of Goudarzi et al. [41], in which a comparative analysis of UTCHEM, ECLIPSE-E100, and CMG-STARS is conducted in the context of polymer, surfactant/polymer, and alkaline/surfactant/polymer flooding.The pressure results in Figures 7b and 9b in their study reveal similar discrepancies when compared with the results obtained for the 3D polymer simulations in the present paper.It is important to acknowledge that the versions of the simulators utilized are not identical, and one of the simulators is completely different, but the differences are still present.Further agreement is observed when comparing cumulative oil production, as depicted in Figures 16b and 22a, as well as the total surfactant injected (Figure 22) in their study compared to the results of our paper.
In addition to the above comparisons, it is pertinent to note that the present study encompasses a more comprehensive set of data and details that could not be compared against the study by Goudarzi et al. [41].This is primarily because their study does not delve into certain aspects and parameters that our paper extensively examines.The inclusion of these additional facets in our research not only amplifies the scope but also lends a deeper insight into the complexities and nuances of the simulations.This expanded analysis could be instrumental for researchers and practitioners aiming for a more in-depth understanding and application of these simulations.

Summary and Conclusions
This study uses three chemical flooding reservoir simulators to systematically compare the models' impact on the field scale results, specifically the impact of modeling middle-phase microemulsion in a three-phase (oil, microemulsion, water) system against the two-phase system.
The surfactant-polymer floods were designed in Winsor Type III phase behavior at an optimum salinity in simulators A and B. Simulator C lacks the capabilities to model salinity gradient and the middle-phase microemulsion.However, the effects of surfactant can be approximated by solubilization and IFT tables.
The water, polymer, and SP flood results for the 1D and 3D cases were similar.The results for the field model showed close results for produced water and oil.However, significant discrepancies were observed in injected and produced chemical volumes.These results indicate that despite the different formulations, the effect of surfactant polymer floods on oil recovery, total injected and produced fluids, and average pressure profiles can be comparably modeled in these simulators.Data Availability Statement: All data generated or analyzed during this study are encompassed within the manuscript.This study is entirely based on modeling and simulation, with sufficient details provided in the paper and the appendix to replicate the reported results.These results can be reproduced using any of the commercial reservoir simulators discussed in the manuscript.

Acknowledgments:
The first author acknowledges support from Saudi Aramco for sponsoring his studies at the University of Texas at Austin.The authors would like to acknowledge the sponsors of the RSJIP from the University of Texas at Austin for their financial support.The authors thank CMG, SLB, Chevron Corp., and ScienceSoft Inc, for providing the software licenses.

Conflicts of Interest:
The authors declare no conflicts of interest.

𝛁 ⃗ 𝚽 𝒍
The hydraulic potential gradient of the conjugate phase of phase The permeability reduction factor in Simulator A and B is modeled as follows: where  refers to the phase with the highest polymer concentration (either aqueous or phase or microemulsion phase),  is the polymer concentration in phase l,  is an input parameter, and the maximum permeability reduction ( , ) is defined as follows: where  is a calibration parameter and  , is a cutoff value for the permeability reduction defined by the user corresponding to the maximum permeability reduction limit.The permeability reduction is assumed to be irreversible.
For simulator C, permeability reduction is modeled as a function of polymer adsorption.That is, polymer effects on permeability are modeled such that polymer injection can cause blockage in the porous media through adsorption.The permeability reduction is modeled as follows: where  is the residual resistance factor of phase l,  is the polymer's adsorbed concentration obtained from the adsorption isotherm,  , is the permeability reduction factor from phase l, and  is the maximum adsorption capacity of the rock.

Figure 3 .
Figure 3. Two-phase oil and water relative permeability curves.

Figure 4 .Figure 5 .
Figure 4. Polymer viscosity model.(a) Simulators A and B and (b) non-linear mixing rule for simulator C.

Figure 6 .Figure 7 .
Figure 6.Surfactant flood properties.(a) Microemulsion viscosity as a function of oil concentration in microemulsion phase, and (b) Langmuir surfactant adsorption as a function of surfactant concentration.

Figure 10 .
Figure 10.Waterflood results in the 1D model.(a) Cumulative produced oil and (b) average reservoir pressure.

Figure 11 .
Figure 11.Polymer flood results in the 1D model.(a) Cumulative produced oil, (b) Cumulative produced polymer solution volume, and (c) Average reservoir pressure.

Figure 13 .
Figure 13.Waterflood in the 3D model results.(a) Cumulative produced oil and (b) Average reservoir pressure.

Figure 14 .
Figure 14.Polymer flood in the 3D model results.(a) Cumulative injected fluid, (b) Cumulative produced oil, and (c) Average reservoir pressure.

Figure 16 .
Figure 16.Waterflood in the field-scale model results.(a) Cumulative volume of oil produced and (b) average reservoir pressure.

Figure 17 .
Figure 17.Polymer flood in the field-scale model results.(a) Cumulative produced oil, (b) Cumulative produced polymer solution volume, and (c) Average reservoir pressure.

Figure 18 .
Figure 18.Surfactant-polymer flood in the field-scale model (a) cumulative produced oil and (b) average reservoir pressure.

Figure 19 .
Figure 19.Surfactant-polymer flood in the field-scale model (a) cumulative injected polymer and (b) cumulative produced polymer volume.

Figure 20 .
Figure 20.Surfactant-polymer flood in the field-scale model (a) cumulative volume of surfactant injected and (b) cumulative volume of surfactant produced.

Author
Contributions: Methodology, software, validation, analysis, investigation, data curation, writing-original draft preparation, visualization, M.M.A.; Methodology, software, validation, supervision, writing-review and editing, B.R.B.F.; Conceptualization, resources, writing-review and editing, supervision, project administration, M.D.; Conceptualization, resources, writing-review and editing, supervision, project administration, K.S.All authors have read and agreed to the published version of the manuscript.

Funding:
This research received no external funding.

Table 2 .
Properties for the three-dimensional model.

Table 3 .
Properties for field reservoir model.

Table 4 .
Basic physical parameters for waterflood cases.

Table 5 .
Polymer property model in each simulator.
1Simulator B uses the same model as simulator A but with irreversible adsorption.

Table 7 .
Surfactant model comparison in each reservoir simulator.
1Simulator B uses the same model as simulator A but with irreversible adsorption.

Table 8 .
Parameters used in microemulsion viscosity model in simulators A and B.   ) 500 Lower Limit of Effective Salinity (  ), meq/mL 0.177 Upper Limit of Effective Salinity (  ), meq/mL 0.344 Height of Binodal Curve at Zero Effective Salinity 0.131 Height of Binodal Curve at Optimum Effective Salinity 0.026 Height of Binodal Curve at Twice Optimum Effective Salinity 0.028 Water Trapping Parameter (  ) 1600 Oil Trapping Parameter (  ) 4000 Microemulsion Trapping Parameter (  ) 2600 Swr at High Trapping Number (water phase) 0 Sor at High Trapping Number (oil phase) 0 Smr at High Trapping Number (microemulsion phase) 0 Huh Interfacial Tension Constant () 0.35 Huh Interfacial Tension Constant () 10

Table 9 .
Summary of simulation results for 1D waterflood case.

Table 10 .
Summary of simulation results for 1D polymer flood case.

Table 11 .
Summary of simulation results for 1D surfactant-polymer flood case.

Table 12 .
Summary of simulation results for 3D waterflood.

Table 13 .
Summary of simulation results for 3D polymer flood case.

Table 14 .
Summary of simulation results for 3D surfactant-polymer flood case.

Table 15 .
Summary of simulation results for field-scale waterflood.

Table 16 .
Summary of simulation results for field polymer flood.

Table 17 .
Summary of simulation results for field surfactant-polymer flood.
The shear rate at which the polymer viscosity is equal to the average of  and     The mass density of conjugate phase l ( = , , ) _The mass density of phase l ( = , , ) The interfacial tension between the phase l ( = , , ) and its conjugate phase The interfacial tension between the displacing phase and the displaced phase ( = , , )