Modeling and Simulation of Polymer-Enhanced Oil ...
Modeling and Simulation of Polymer–Enhanced Oil Production
Modeling and Simulation of Polymer-Enhanced Oil Production Chuangen Zheng, Bonnie L. Gall, Troy R. French, and Rebecca S. Bryant TRW Energy and Environment Systems Water-soluble polyacrylamide polymers have been used to reduce water production in oil wells and for mobility control in injection wells for decades. One of the attractive properties of polyacrylamides is their ability to reduce the relative permeability to water more than the relative permeability to oil, in porous media. Our work was to model the effect of polymer adsorption on oil-water two-phase relative permeabilities through experimentation. New models were incorporated into U.S. Department of Energy (DOE)-sponsored simulators to help field the design of polymer-related projects. Work was performed under a Managing and Operating contract for the DOE’s National Oil and Related Programs. Results from this work have been successfully applied to the design and prediction of an on-going Alkaline/Surfactant/Polymer pilot in the Sho-Vel-Tum Field, in Oklahoma, under the same U.S. DOE contract.
Introduction In oil wells, the oil remaining after the pressure energy of primary production is depleted, is the target of secondary recovery, which is most often by water flooding (except for heavy crudes). At the end of the economically productive life of a conventional water flood, some 50–70% of the oil originally in place typically remains as residual oil. Processes that attempt to recover oil beyond the conventional primary and secondary methods are referred to as “tertiary recovery” methods. Tertiary processes include such techniques as miscible fluid displacement, microemulsion flooding, and thermal and other chemical flooding methods. Application of tertiary processes usually entails substantial risk because of their technological sophistication and front-end financial requirements. The amount of residual oil after secondary recovery depends upon three factors: oil in place at the start of water flooding, reservoir sweep efficiency, and microscopic displacement efficiency. Reservoir sweep efficiency is a key factor in determining the final residual oil of water flooding within an economic limit. It is dependent upon the mobility ratio and reservoir heterogeneity. Polymers have been used in enhancing oil production in three modes: (1) as a near-well treatment to improve the performance of water injectors or water-out producers by blocking off high-conductivity zones; (2) as agents that may be cross-linked in situ to plug highconductivity zones at depth in the reservoir; and (3) as agents to increase aqueous viscosity, as well as decrease aqueous-phase permeability. All modes involve polymer adsorption.
Systems and Information Technology Review Journal • Fall/Winter 1998 © 1998 TRW. All rights reserved. Reprinted with permission.
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Modeling and Simulation of Polymer–Enhanced Oil Production
From the published field tests on well treatments in the 1970s and 1980s, only a few jobs were considered to be economically successful. Lessons-learned from those tests emphasize the importance of meticulous lab tests and simulation studies, which can dramatically reduce the risk and maximize the economy of polymer projects. The selective permeability reduction by polymer adsorption has been traditionally referred to as “permeability reduction” or the “residual resistance factor,” which is equivalent to the endpoint relative permeability. Most research was focused on the measurement of residual resistance alone. To model the effect of polymer adsorption, however, a measurement of the relative permeability is necessary, especially when residual saturation and the shape of the relative permeability curves change after polymer adsorption. On the other hand, as a polymer solution propagates through porous media, the solution will be diluted at the propagation front due to dispersion and adsorption, and the dilution could, in fact, extend to the entire polymer slug if the slug size is small. So far, few researchers have related the variations of the relative permeability curves as a function of polymer concentration or the amount of polymer adsorbed. Therefore, one of the objectives in the present study is to measure and correlate relative permeability curves as a function of polymer adsorption. The models of relative permeability as a function of polymer concentration developed during this study were incorporated into U.S. DOE-sponsored simulators. During field design, the amount of polymer injection is a sensitive factor in determining the economic impacts. Under- or over-estimating the amount of polymer injection will result in a failure or costincrease to projects. Our work will serve to optimize field design. Several cases were simulated, to compare incremental oil recovery predicted by the new models with previous models. A real three-layer reservoir model was used for comparative simulation runs. Polymer flooding and near-wellbore polymer treatments were also simulated. Results from these simulations should provide guidelines for future field strategies. Finally, the models were examined by several core flooding tests, obtaining excellent agreements with experimental data. Results were successfully applied to predict and optimize an ongoing alkaline/surfactant/polymer (ASP) pilot test.
Basis for Experimentation Although the final objective is to model the polymer process, the current state of development is based on experimental results. A schematic diagram of the flow system used for experimental studies is depicted in Figure 1. Cleaned cores were mounted horizontally in a Hassler-type core holder and placed in a convection oven. Polymer adsorption was determined from the breakthrough curves of two successive injections of the same polymer solution through the core. Results from this dynamic method are representative of the real polymer adsorption as opposed to the batch method. Both unsteady-state and steady-state imbibition and drainage relative permeability curves were measured. No significant difference was observed from the secondary relative permeability curves. Subsequent relative permeability curves were measured using the steady-state method, due to its simplicity.
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Both strongly water-wet and mildly oil-wet cores were chosen in order to study the influence of wettability on polymer adsorption, two-phase relative permeability, and polymer solution mobility. The mildly oil-wet medium is a Warden reservoir sandstone core (Core A) from the Santa Fe field, Stephens County, Oklahoma. Two strongly water-wet media are Berea sandstone cores (Cores B and C) with different permeabilities.
Figure 1. Schematic Diagram of Flow System Synthetic brines were prepared to represent reservoir brine (produced water) composition and makeup water (injection water) composition used in the Warden reservoir. Warden crude oil was used for the oil phase. The polymer used in this study is a high-molecular-weight hydrolyzed polyacrylamide Alcoflood 1275A polymer which is available in powder form, and is anionic. Polymer solutions were prepared in injection water with concentrations ranging between 250 and 5000 ppm and subsequently filtered through 8- and 2-µm filters prior to injection. Viscosities of the polymer solutions were measured over a wide range of shear rates.
Experimental Procedures Low-concentration polymer was injected at either 100% brine saturation (Core B) or at residual oil saturation (Cores A and C) until effluent concentration approached injected concentration. An initial polymer breakthrough curve (BTC) was measured. After displacement of all free polymer in the porous media, the same polymer solution was injected to determine the polymer excluded volume. Polymer adsorption was determined from the difference in breakthrough curves. Polymer solution mobility was then measured over a wide range of shear rates after reaching steady state. The polymer injection procedure was repeated with a series of increasing polymer concentration solutions. Relative permeability curves were determined for Cores A and C after each cycle of polymer injection, after flushing free polymer from the porous media.
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Modeling and Simulation of Polymer–Enhanced Oil Production
Modeling from Experimental Results Polymer Adsorption. The BTCs of two successive injections of the same polymer solution are S-shaped. The difference between the two polymer BTCs for each polymer concentration gives a measurement of polymer adsorption in porous media as described above. The adsorption isotherm follows Langmuir’s Law. Relative Permeability Curves. A principal focus of this study has been to model the effect of polymer concentration on the relative permeability curves, since polymer concentration varies throughout the reservoir due to adsorption and dispersion as polymer propagates through the reservoir. Figure 2 illustrates the variation of the relative permeability curves after polymer adsorption, at various polymer concentrations, for the reservoir core. Polymer adsorption has a greater effect on the relative permeability to water than on the relative permeability to oil. Irreducible water saturation was found to increase as polymer concentration increased in both strongly water-wet and mildly oil-wet cores. Residual oil saturation remained almost the same as in the absence of polymer. An exponential model can be used to fit the experimental data very well.
Figure 2. Variation of Relative Permeability Curves as a Function of Polymer Adsorption in Core A To compare the relative permeabilities over the entire range of water saturations, the relative permeability curves in the presence of polymer were extrapolated to the initial irreducible water saturation, as in the absence of polymer, for curve fitting. This treatment allowed comparison of the relative permeabilities at the same saturation. Results showed that the endpoint relative permeabilities varied with changing polymer concentration, whereas, the 58
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exponents were almost independent of polymer concentration for both reservoir and Berea cores. Therefore, the variations of the endpoint relative permeabilities are representative of the variations of the relative permeability curves by polymer adsorption. Both endpoint reductions were found to exhibit S-like curves. The reductions of the endpoint relative permeabilities to both water and oil phases increase exponentially as polymer concentration increases and eventually approach constants due to the full coverage of a mono-layer at the pore wall. These characteristics can be modeled by an equation of the following type, Rk o ,max − 1 Rk o = Rk o ,max − rα n rα rα S α 1+ S1 2 where, Rk o
rα
,max
= the maximum reduction of the endpoint relative permeability to phase α (water or oil), S1 2 = the amount of adsorbed polymer per gram of 1 rock when , Rk o = Rk o ,max nα = a constant rα 2 rα
Polymer Mobility. Polymer solutions reduce the mobility of the aqueous phase by two mechanisms — the increased viscosity of the polymer solution and the reduction of the relative permeability to the aqueous phase. The latter is usually referred to as the “residual resistance factor” in the absence of oil or at residual oil saturation. In our case, it also refers to Rk o in the presence of oil (at an arbitrary oil saturation, not necessarily at residual oil rw
saturation). Thus, the mobility of polymer solutions in porous media can be written as: * 1 krw λp = ⋅ µ p Rk o rw
* is the relative permeability to water in the absence of polymer, and where krw µ p is polymer solution viscosity in porous media.
Low-shear polymer solution viscosity measured in porous media is much lower than that observed in viscometer readings at the same shear rate. The shear-rate dependence of the polymer solution viscosity in tube flow was modeled by Meter’s equation, µ0 − µ∞ µ p = µ∞ + p −1 γ˙ 1+ γ˙1 2 where µ 0 is the zero-shear-rate viscosity, µ ∞ is the infinite-shear-rate viscosity, γ˙ is the shear rate, γ˙1 2 is the shear rate at which the viscosity is equal to half of µ 0 , and p is the shear-rate exponent. The shear rate can be modeled as (Model I):
γ˙ = 3.94C
u kkrwφSw
The correction factor C was taken as a unit value of 1.0 in previous simulation programs.
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Modeling and Simulation of Polymer–Enhanced Oil Production
In the presence of polymer adsorption, the polymer solution viscosity was found to be much lower than predicted using the previous model (Model I) as shown in Figure 3. In this work, the correction factor was modeled as (Model II):
(
C = 4.8 Nv1 6
)
1 1− P θ
This leads to a greater value for the correction factor required by the reservoir core with respect to Berea core at the same conditions, revealing that this polymer as a mobility control agent is less effective in the reservoir core than in the Berea core. A significant improvement of the model prediction is indicated after applying the correction factor (Model II).
Figure 3. Comparison of the Mobility Curves Predicted from Model I with the Experimental Data for Core A Viscoelastic characteristics induce increased flow resistance at high flow rate. Although it exists infrequently under reservoir flow conditions, a simple model can be used to account for this feature, * 1 k rw 1 λp = ⋅ ⋅ µ p Rk o (1 + ψv) rw
where ψ is a constant associated with the porous media, polymer characteristics, and concentration. The final improvement is shown in Figure 4 (Model III).
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Figure 4. Comparison of the Mobility Curves Predicted from Model III with the Experimental Data for Core A
Simulation — Model Comparison, Case, and Application Study The models of relative permeability and shear rate as a function of polymer concentration developed above were incorporated into the U.S. DOE-sponsored contract. Except where specified, simulation studies were performed on one-quarter of an injection-well-centered five-spot, three-layer 330 x 330 x 15.75-foot Warden reservoir model as shown in Figure 5. Layer thicknesses were 8.75, 4, and 3 feet from the top to the bottom layers, respectively. Horizontal permeabilities were 100, 1300 and 25 millidarcies (md) in the same order. The ratio of vertical to horizontal permeabilities is 0.8. Before performing a case study and applying the results to real-world problems, a comparison of the discrepancy between the new models and previous models was made by simulating a polymer flooding process.
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Figure 5. Three-Layer Reservoir Model Model Comparison. The simulation was performed with the injection sequence of 1.0 pore volume (PV) water flooding, 0.5-PV 1500-ppm polymer flooding, followed by additional 3.5-PV water flooding. Figure 6 demonstrates an overall comparison of oil recovery predicted by new models, to other existing models. Results from continuous water flooding are also shown in the figure as a base case, as the bottommost line.
Figure 6. Comparison of Oil Recovery Predicted by the New Model with Other Models (1 PV = 254 days; %OOIP = Percent of Original Oil In-Place)
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Incremental oil recovery by polymer flooding was predicted by all models. As described above, the effective polymer viscosity is directly obtained from the mobility measurement. By using the effective viscosity in simulation instead of the real polymer viscosity and relative permeability reduction, the oil recovery without considering polymer adsorption can be predicted. However, the new relative permeability model was found to predict a higher oil recovery than the effective viscosity model. Although, on one hand, the loss of polymer due to adsorption reduces the actual amount of polymer sweeping through the reservoir, on the other, adsorbed polymer results in a long-lasting reduction of relative permeability to water even when water flooding resumes after polymer flooding, as shown as the middlemost line (Figure 6). Therefore, the loss of polymer by adsorption is offset by the reduction of relative permeability. What started with an anticipation of polymer loss by adsorption turns into an advantage through better oil recovery. However, this conclusion should be carefully extended to low-tension chemical flooding processes, because the reduction of relative permeability decreases as residual oil saturation decreases. The concept of permeability reduction stemmed from the residual resistance factor in a full water saturation medium. Some simulators used the value measured in a 100% watersaturated medium. Recent studies have shown that this factor is increased by the presence of oil. Therefore, by using the permeability reduction, one will predict a lower oil recovery than with the new model, as shown by the second line from the bottom. An interpolation can be made to easily evaluate the situation, at the point of water saturation, between the older and newer models. This enables the simulation to cover the whole range of saturation.
Case Study: Polymer Flooding, Profile Modification, and Well Treatment Case 1 — Polymer Flooding. In addition to mobility control, polymer will build up flow resistance in the portions of the reservoir it penetrates, through selective reduction of relative permeability and viscosity increase, as discussed above. The increased resistance to flow will divert subsequently injected water into poorly swept areas. Figure 7 demonstrates a significant sweeping improvement in the vertical direction by polymer flooding over water flooding. In highly heterogeneous reservoirs, this benefit is much more significant than that of fractional flow or an improvement in the mobility ratio. Maximum benefits are likely be achieved by polymer adsorption as opposed to viscosity increase alone, as demonstrated in the oil production predictions shown in Figure 6. Case 2 — Profile Modification. Initially, the injected polymer preferentially enters high-permeability “thief” zones due to low flow resistance. Polymer adsorption in these zones leads to a long-lasting profile modification throughout the reservoir. How well polymer selectively adsorbs in high-permeability zones is dependent upon permeability contrast and cross-flow between layers. Figure 8 demonstrates a comparison of the selective placement of a polymer layer in Warden reservoir with and without cross-flow, using different injection strategies. In the case of no cross-flow, the deep emplacement of the polymer layer inside the high-permeability zone is associated with the formation of a secondary polymer layer in the low-permeability zones. Nevertheless, this does not cause a dramatic reduction in injectivity because fluids enter the reservoir through the high-permeability entrance, and are subsequently diverted into the low-permeability zones. Systems and Information Technology Review Journal • Fall/Winter 1998
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Modeling and Simulation of Polymer–Enhanced Oil Production
Figure 7. Comparison of Vertical Sweeping Between Water- and Polymer Flooding after 0.2-PV Fluid Injection
Figure 8. Comparison of Relative Permeability Reduction over Reservoir after 0.2-PV Polymer Injection with and without Cross-Flow, and Using Different Injection Strategies However, selective placement of a polymer layer in the high-permeability zones will be seriously hindered by side growth due to cross-flow, as shown in Figure 8. A selective injection strategy of injecting the polymer only into the high-permeability zone is of no help in preventing the spread of the polymer layer. Dual injection, low viscosity
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surfactant precipitation, and colloidal dispersion gels are likely to be promising technologies to overcome the difficulty caused by cross-flow. Case 3 — Well Treatment. Polymer adsorption for profile modification as described above is actually a case of deep-well treatment, whereas many field practices involve near-wellbore treatment. The mechanism again is to build flow resistance in watered-out zones and divert the subsequently injected fluid to poorly swept zones. Two factors are extremely important for the success of the well treatment. They are cross-flow and relative permeability reduction. In addition to causing side growth of the polymer layer, cross-flow will also lead the fluids, which have been already diverted into the poorly swept layers near the wellbore, to return to the high-permeability layers again. Therefore, if cross-flow is significant, minimum benefits from near-well treatment is expected. The maximum allowed cross-flow was explored by Gao and Burchfield in polymer gel treatments. Even in the case of no cross-flow, the buildup of enough flow resistance in the highpermeability layers is a major concern relative to the redistribution of fluids near the well. Polymer adsorption alone may not build enough flow resistance. Cross-linking or swelling agents are good candidates to enhance this effect. Applications to Real-World Problems. A simulation highlighted the discrepancy between the new models and other existing models. Here, the new models were incorporated into the UTCHEM simulator for simulating an on-going lab and field ASP project. A lab test has been done by injecting 0.1-PV alkaline, followed by a 0.3-PV ASP slug, a 0.8-PV chase polymer, and 2.3-PV water. Simulation was done by setting the other parameters using reasonable values from previous measurements. Oil production history is shown as having an excellent agreement with experimental data (Figure 9).
Figure 9. Oil Production History of ASP Flooding in a Warden Reservoir Core (%ROIP = Percent of Remaining Oil In-Place) Systems and Information Technology Review Journal • Fall/Winter 1998
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Modeling and Simulation of Polymer–Enhanced Oil Production
A simulation was then performed for making predictions for the on-going field ASP project. The field has been water flooded since the mid-1930s. The final residual saturation has been reached according to the core analysis data, although the reservoir is highly heterogeneous. As expected, this kind of reservoir is not favorable to any further ASP flooding. However, results from this field test can provide valuable information for examining simulation predictions and designing future field projects. From the test results obtained so far, it has been found that a significant increase in oil production has occurred, as was predicted by the simulation.
Summary The effects of polymer adsorption on oil-water, two-phase relative permeability curves, and the rheology of polymer solutions were studied and modeled. The new models were successfully incorporated into U.S. DOE-sponsored simulators. The discrepancy between the new models and previous models is perceivable. Applications to the real-world lab and field tests showed that the new models can provide accurate predictions. This should provide dependable tools for future field design.
Chuangen Zheng is a staff engineer in the Production Technology group at TRW’s Energy and Environment Systems. His specialties include reservoir engineering and simulation, chemical process engineering, process development and scale-up, and software development. He holds a Bachelor of Science degree from East China University of Chemical Technology, a Master of Science degree from the Chinese Academy of Sciences, and a PhD from the University of Houston, all in Chemical Engineering.
Bonnie L. Gall is retired from TRW’s Energy and Environment Systems. Prior to her retirement, she was a leader in Chemical Enhanced Oil Recovery. Her specialties include surfactant systems for improved oil production, formation damage and low permeability gas formations. She holds a Bachelor of Arts degree in Chemistry from Mount Holyoke College, and a PhD in Physical Chemistry from Ohio State University.
Troy R. French is a senior chemist in Production Technology group at TRW’s Energy and Environment Systems. His specialties include the design and application of Alkaline/Surfactant/Polymer chemical systems. He also conducted research on the use of biopolymer gel systems and emulsions for conformance improvement. He holds a Bachelor of Science degree in Chemistry from the University of Oklahoma.
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Rebecca S. Bryant is the Director of the Production Technology group at TRW’s Energy and Environment Systems, responsible for program management. Her specialties include biotechnology for enhanced oil recovery and bio-remediation. She holds Bachelor of Science, Master of Science, and PhD degrees from Oklahoma State University, all in Microbiology.
Should readers be interested in more information, they may contact the Energy and Environment Systems office via E-mail: [email protected]
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Modeling and Simulation of Polymer-Enhanced Oil Production Chuangen Zheng, Bonnie L. Gall, Troy R. French, and Rebecca S. Bryant TRW Energy and Environment Systems Water-soluble polyacrylamide polymers have been used to reduce water production in oil wells and for mobility control in injection wells for decades. One of the attractive properties of polyacrylamides is their ability to reduce the relative permeability to water more than the relative permeability to oil, in porous media. Our work was to model the effect of polymer adsorption on oil-water two-phase relative permeabilities through experimentation. New models were incorporated into U.S. Department of Energy (DOE)-sponsored simulators to help field the design of polymer-related projects. Work was performed under a Managing and Operating contract for the DOE’s National Oil and Related Programs. Results from this work have been successfully applied to the design and prediction of an on-going Alkaline/Surfactant/Polymer pilot in the Sho-Vel-Tum Field, in Oklahoma, under the same U.S. DOE contract.
Introduction In oil wells, the oil remaining after the pressure energy of primary production is depleted, is the target of secondary recovery, which is most often by water flooding (except for heavy crudes). At the end of the economically productive life of a conventional water flood, some 50–70% of the oil originally in place typically remains as residual oil. Processes that attempt to recover oil beyond the conventional primary and secondary methods are referred to as “tertiary recovery” methods. Tertiary processes include such techniques as miscible fluid displacement, microemulsion flooding, and thermal and other chemical flooding methods. Application of tertiary processes usually entails substantial risk because of their technological sophistication and front-end financial requirements. The amount of residual oil after secondary recovery depends upon three factors: oil in place at the start of water flooding, reservoir sweep efficiency, and microscopic displacement efficiency. Reservoir sweep efficiency is a key factor in determining the final residual oil of water flooding within an economic limit. It is dependent upon the mobility ratio and reservoir heterogeneity. Polymers have been used in enhancing oil production in three modes: (1) as a near-well treatment to improve the performance of water injectors or water-out producers by blocking off high-conductivity zones; (2) as agents that may be cross-linked in situ to plug highconductivity zones at depth in the reservoir; and (3) as agents to increase aqueous viscosity, as well as decrease aqueous-phase permeability. All modes involve polymer adsorption.
Systems and Information Technology Review Journal • Fall/Winter 1998 © 1998 TRW. All rights reserved. Reprinted with permission.
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Modeling and Simulation of Polymer–Enhanced Oil Production
From the published field tests on well treatments in the 1970s and 1980s, only a few jobs were considered to be economically successful. Lessons-learned from those tests emphasize the importance of meticulous lab tests and simulation studies, which can dramatically reduce the risk and maximize the economy of polymer projects. The selective permeability reduction by polymer adsorption has been traditionally referred to as “permeability reduction” or the “residual resistance factor,” which is equivalent to the endpoint relative permeability. Most research was focused on the measurement of residual resistance alone. To model the effect of polymer adsorption, however, a measurement of the relative permeability is necessary, especially when residual saturation and the shape of the relative permeability curves change after polymer adsorption. On the other hand, as a polymer solution propagates through porous media, the solution will be diluted at the propagation front due to dispersion and adsorption, and the dilution could, in fact, extend to the entire polymer slug if the slug size is small. So far, few researchers have related the variations of the relative permeability curves as a function of polymer concentration or the amount of polymer adsorbed. Therefore, one of the objectives in the present study is to measure and correlate relative permeability curves as a function of polymer adsorption. The models of relative permeability as a function of polymer concentration developed during this study were incorporated into U.S. DOE-sponsored simulators. During field design, the amount of polymer injection is a sensitive factor in determining the economic impacts. Under- or over-estimating the amount of polymer injection will result in a failure or costincrease to projects. Our work will serve to optimize field design. Several cases were simulated, to compare incremental oil recovery predicted by the new models with previous models. A real three-layer reservoir model was used for comparative simulation runs. Polymer flooding and near-wellbore polymer treatments were also simulated. Results from these simulations should provide guidelines for future field strategies. Finally, the models were examined by several core flooding tests, obtaining excellent agreements with experimental data. Results were successfully applied to predict and optimize an ongoing alkaline/surfactant/polymer (ASP) pilot test.
Basis for Experimentation Although the final objective is to model the polymer process, the current state of development is based on experimental results. A schematic diagram of the flow system used for experimental studies is depicted in Figure 1. Cleaned cores were mounted horizontally in a Hassler-type core holder and placed in a convection oven. Polymer adsorption was determined from the breakthrough curves of two successive injections of the same polymer solution through the core. Results from this dynamic method are representative of the real polymer adsorption as opposed to the batch method. Both unsteady-state and steady-state imbibition and drainage relative permeability curves were measured. No significant difference was observed from the secondary relative permeability curves. Subsequent relative permeability curves were measured using the steady-state method, due to its simplicity.
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Both strongly water-wet and mildly oil-wet cores were chosen in order to study the influence of wettability on polymer adsorption, two-phase relative permeability, and polymer solution mobility. The mildly oil-wet medium is a Warden reservoir sandstone core (Core A) from the Santa Fe field, Stephens County, Oklahoma. Two strongly water-wet media are Berea sandstone cores (Cores B and C) with different permeabilities.
Figure 1. Schematic Diagram of Flow System Synthetic brines were prepared to represent reservoir brine (produced water) composition and makeup water (injection water) composition used in the Warden reservoir. Warden crude oil was used for the oil phase. The polymer used in this study is a high-molecular-weight hydrolyzed polyacrylamide Alcoflood 1275A polymer which is available in powder form, and is anionic. Polymer solutions were prepared in injection water with concentrations ranging between 250 and 5000 ppm and subsequently filtered through 8- and 2-µm filters prior to injection. Viscosities of the polymer solutions were measured over a wide range of shear rates.
Experimental Procedures Low-concentration polymer was injected at either 100% brine saturation (Core B) or at residual oil saturation (Cores A and C) until effluent concentration approached injected concentration. An initial polymer breakthrough curve (BTC) was measured. After displacement of all free polymer in the porous media, the same polymer solution was injected to determine the polymer excluded volume. Polymer adsorption was determined from the difference in breakthrough curves. Polymer solution mobility was then measured over a wide range of shear rates after reaching steady state. The polymer injection procedure was repeated with a series of increasing polymer concentration solutions. Relative permeability curves were determined for Cores A and C after each cycle of polymer injection, after flushing free polymer from the porous media.
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Modeling from Experimental Results Polymer Adsorption. The BTCs of two successive injections of the same polymer solution are S-shaped. The difference between the two polymer BTCs for each polymer concentration gives a measurement of polymer adsorption in porous media as described above. The adsorption isotherm follows Langmuir’s Law. Relative Permeability Curves. A principal focus of this study has been to model the effect of polymer concentration on the relative permeability curves, since polymer concentration varies throughout the reservoir due to adsorption and dispersion as polymer propagates through the reservoir. Figure 2 illustrates the variation of the relative permeability curves after polymer adsorption, at various polymer concentrations, for the reservoir core. Polymer adsorption has a greater effect on the relative permeability to water than on the relative permeability to oil. Irreducible water saturation was found to increase as polymer concentration increased in both strongly water-wet and mildly oil-wet cores. Residual oil saturation remained almost the same as in the absence of polymer. An exponential model can be used to fit the experimental data very well.
Figure 2. Variation of Relative Permeability Curves as a Function of Polymer Adsorption in Core A To compare the relative permeabilities over the entire range of water saturations, the relative permeability curves in the presence of polymer were extrapolated to the initial irreducible water saturation, as in the absence of polymer, for curve fitting. This treatment allowed comparison of the relative permeabilities at the same saturation. Results showed that the endpoint relative permeabilities varied with changing polymer concentration, whereas, the 58
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exponents were almost independent of polymer concentration for both reservoir and Berea cores. Therefore, the variations of the endpoint relative permeabilities are representative of the variations of the relative permeability curves by polymer adsorption. Both endpoint reductions were found to exhibit S-like curves. The reductions of the endpoint relative permeabilities to both water and oil phases increase exponentially as polymer concentration increases and eventually approach constants due to the full coverage of a mono-layer at the pore wall. These characteristics can be modeled by an equation of the following type, Rk o ,max − 1 Rk o = Rk o ,max − rα n rα rα S α 1+ S1 2 where, Rk o
rα
,max
= the maximum reduction of the endpoint relative permeability to phase α (water or oil), S1 2 = the amount of adsorbed polymer per gram of 1 rock when , Rk o = Rk o ,max nα = a constant rα 2 rα
Polymer Mobility. Polymer solutions reduce the mobility of the aqueous phase by two mechanisms — the increased viscosity of the polymer solution and the reduction of the relative permeability to the aqueous phase. The latter is usually referred to as the “residual resistance factor” in the absence of oil or at residual oil saturation. In our case, it also refers to Rk o in the presence of oil (at an arbitrary oil saturation, not necessarily at residual oil rw
saturation). Thus, the mobility of polymer solutions in porous media can be written as: * 1 krw λp = ⋅ µ p Rk o rw
* is the relative permeability to water in the absence of polymer, and where krw µ p is polymer solution viscosity in porous media.
Low-shear polymer solution viscosity measured in porous media is much lower than that observed in viscometer readings at the same shear rate. The shear-rate dependence of the polymer solution viscosity in tube flow was modeled by Meter’s equation, µ0 − µ∞ µ p = µ∞ + p −1 γ˙ 1+ γ˙1 2 where µ 0 is the zero-shear-rate viscosity, µ ∞ is the infinite-shear-rate viscosity, γ˙ is the shear rate, γ˙1 2 is the shear rate at which the viscosity is equal to half of µ 0 , and p is the shear-rate exponent. The shear rate can be modeled as (Model I):
γ˙ = 3.94C
u kkrwφSw
The correction factor C was taken as a unit value of 1.0 in previous simulation programs.
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Modeling and Simulation of Polymer–Enhanced Oil Production
In the presence of polymer adsorption, the polymer solution viscosity was found to be much lower than predicted using the previous model (Model I) as shown in Figure 3. In this work, the correction factor was modeled as (Model II):
(
C = 4.8 Nv1 6
)
1 1− P θ
This leads to a greater value for the correction factor required by the reservoir core with respect to Berea core at the same conditions, revealing that this polymer as a mobility control agent is less effective in the reservoir core than in the Berea core. A significant improvement of the model prediction is indicated after applying the correction factor (Model II).
Figure 3. Comparison of the Mobility Curves Predicted from Model I with the Experimental Data for Core A Viscoelastic characteristics induce increased flow resistance at high flow rate. Although it exists infrequently under reservoir flow conditions, a simple model can be used to account for this feature, * 1 k rw 1 λp = ⋅ ⋅ µ p Rk o (1 + ψv) rw
where ψ is a constant associated with the porous media, polymer characteristics, and concentration. The final improvement is shown in Figure 4 (Model III).
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Figure 4. Comparison of the Mobility Curves Predicted from Model III with the Experimental Data for Core A
Simulation — Model Comparison, Case, and Application Study The models of relative permeability and shear rate as a function of polymer concentration developed above were incorporated into the U.S. DOE-sponsored contract. Except where specified, simulation studies were performed on one-quarter of an injection-well-centered five-spot, three-layer 330 x 330 x 15.75-foot Warden reservoir model as shown in Figure 5. Layer thicknesses were 8.75, 4, and 3 feet from the top to the bottom layers, respectively. Horizontal permeabilities were 100, 1300 and 25 millidarcies (md) in the same order. The ratio of vertical to horizontal permeabilities is 0.8. Before performing a case study and applying the results to real-world problems, a comparison of the discrepancy between the new models and previous models was made by simulating a polymer flooding process.
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Figure 5. Three-Layer Reservoir Model Model Comparison. The simulation was performed with the injection sequence of 1.0 pore volume (PV) water flooding, 0.5-PV 1500-ppm polymer flooding, followed by additional 3.5-PV water flooding. Figure 6 demonstrates an overall comparison of oil recovery predicted by new models, to other existing models. Results from continuous water flooding are also shown in the figure as a base case, as the bottommost line.
Figure 6. Comparison of Oil Recovery Predicted by the New Model with Other Models (1 PV = 254 days; %OOIP = Percent of Original Oil In-Place)
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Incremental oil recovery by polymer flooding was predicted by all models. As described above, the effective polymer viscosity is directly obtained from the mobility measurement. By using the effective viscosity in simulation instead of the real polymer viscosity and relative permeability reduction, the oil recovery without considering polymer adsorption can be predicted. However, the new relative permeability model was found to predict a higher oil recovery than the effective viscosity model. Although, on one hand, the loss of polymer due to adsorption reduces the actual amount of polymer sweeping through the reservoir, on the other, adsorbed polymer results in a long-lasting reduction of relative permeability to water even when water flooding resumes after polymer flooding, as shown as the middlemost line (Figure 6). Therefore, the loss of polymer by adsorption is offset by the reduction of relative permeability. What started with an anticipation of polymer loss by adsorption turns into an advantage through better oil recovery. However, this conclusion should be carefully extended to low-tension chemical flooding processes, because the reduction of relative permeability decreases as residual oil saturation decreases. The concept of permeability reduction stemmed from the residual resistance factor in a full water saturation medium. Some simulators used the value measured in a 100% watersaturated medium. Recent studies have shown that this factor is increased by the presence of oil. Therefore, by using the permeability reduction, one will predict a lower oil recovery than with the new model, as shown by the second line from the bottom. An interpolation can be made to easily evaluate the situation, at the point of water saturation, between the older and newer models. This enables the simulation to cover the whole range of saturation.
Case Study: Polymer Flooding, Profile Modification, and Well Treatment Case 1 — Polymer Flooding. In addition to mobility control, polymer will build up flow resistance in the portions of the reservoir it penetrates, through selective reduction of relative permeability and viscosity increase, as discussed above. The increased resistance to flow will divert subsequently injected water into poorly swept areas. Figure 7 demonstrates a significant sweeping improvement in the vertical direction by polymer flooding over water flooding. In highly heterogeneous reservoirs, this benefit is much more significant than that of fractional flow or an improvement in the mobility ratio. Maximum benefits are likely be achieved by polymer adsorption as opposed to viscosity increase alone, as demonstrated in the oil production predictions shown in Figure 6. Case 2 — Profile Modification. Initially, the injected polymer preferentially enters high-permeability “thief” zones due to low flow resistance. Polymer adsorption in these zones leads to a long-lasting profile modification throughout the reservoir. How well polymer selectively adsorbs in high-permeability zones is dependent upon permeability contrast and cross-flow between layers. Figure 8 demonstrates a comparison of the selective placement of a polymer layer in Warden reservoir with and without cross-flow, using different injection strategies. In the case of no cross-flow, the deep emplacement of the polymer layer inside the high-permeability zone is associated with the formation of a secondary polymer layer in the low-permeability zones. Nevertheless, this does not cause a dramatic reduction in injectivity because fluids enter the reservoir through the high-permeability entrance, and are subsequently diverted into the low-permeability zones. Systems and Information Technology Review Journal • Fall/Winter 1998
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Figure 7. Comparison of Vertical Sweeping Between Water- and Polymer Flooding after 0.2-PV Fluid Injection
Figure 8. Comparison of Relative Permeability Reduction over Reservoir after 0.2-PV Polymer Injection with and without Cross-Flow, and Using Different Injection Strategies However, selective placement of a polymer layer in the high-permeability zones will be seriously hindered by side growth due to cross-flow, as shown in Figure 8. A selective injection strategy of injecting the polymer only into the high-permeability zone is of no help in preventing the spread of the polymer layer. Dual injection, low viscosity
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surfactant precipitation, and colloidal dispersion gels are likely to be promising technologies to overcome the difficulty caused by cross-flow. Case 3 — Well Treatment. Polymer adsorption for profile modification as described above is actually a case of deep-well treatment, whereas many field practices involve near-wellbore treatment. The mechanism again is to build flow resistance in watered-out zones and divert the subsequently injected fluid to poorly swept zones. Two factors are extremely important for the success of the well treatment. They are cross-flow and relative permeability reduction. In addition to causing side growth of the polymer layer, cross-flow will also lead the fluids, which have been already diverted into the poorly swept layers near the wellbore, to return to the high-permeability layers again. Therefore, if cross-flow is significant, minimum benefits from near-well treatment is expected. The maximum allowed cross-flow was explored by Gao and Burchfield in polymer gel treatments. Even in the case of no cross-flow, the buildup of enough flow resistance in the highpermeability layers is a major concern relative to the redistribution of fluids near the well. Polymer adsorption alone may not build enough flow resistance. Cross-linking or swelling agents are good candidates to enhance this effect. Applications to Real-World Problems. A simulation highlighted the discrepancy between the new models and other existing models. Here, the new models were incorporated into the UTCHEM simulator for simulating an on-going lab and field ASP project. A lab test has been done by injecting 0.1-PV alkaline, followed by a 0.3-PV ASP slug, a 0.8-PV chase polymer, and 2.3-PV water. Simulation was done by setting the other parameters using reasonable values from previous measurements. Oil production history is shown as having an excellent agreement with experimental data (Figure 9).
Figure 9. Oil Production History of ASP Flooding in a Warden Reservoir Core (%ROIP = Percent of Remaining Oil In-Place) Systems and Information Technology Review Journal • Fall/Winter 1998
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A simulation was then performed for making predictions for the on-going field ASP project. The field has been water flooded since the mid-1930s. The final residual saturation has been reached according to the core analysis data, although the reservoir is highly heterogeneous. As expected, this kind of reservoir is not favorable to any further ASP flooding. However, results from this field test can provide valuable information for examining simulation predictions and designing future field projects. From the test results obtained so far, it has been found that a significant increase in oil production has occurred, as was predicted by the simulation.
Summary The effects of polymer adsorption on oil-water, two-phase relative permeability curves, and the rheology of polymer solutions were studied and modeled. The new models were successfully incorporated into U.S. DOE-sponsored simulators. The discrepancy between the new models and previous models is perceivable. Applications to the real-world lab and field tests showed that the new models can provide accurate predictions. This should provide dependable tools for future field design.
Chuangen Zheng is a staff engineer in the Production Technology group at TRW’s Energy and Environment Systems. His specialties include reservoir engineering and simulation, chemical process engineering, process development and scale-up, and software development. He holds a Bachelor of Science degree from East China University of Chemical Technology, a Master of Science degree from the Chinese Academy of Sciences, and a PhD from the University of Houston, all in Chemical Engineering.
Bonnie L. Gall is retired from TRW’s Energy and Environment Systems. Prior to her retirement, she was a leader in Chemical Enhanced Oil Recovery. Her specialties include surfactant systems for improved oil production, formation damage and low permeability gas formations. She holds a Bachelor of Arts degree in Chemistry from Mount Holyoke College, and a PhD in Physical Chemistry from Ohio State University.
Troy R. French is a senior chemist in Production Technology group at TRW’s Energy and Environment Systems. His specialties include the design and application of Alkaline/Surfactant/Polymer chemical systems. He also conducted research on the use of biopolymer gel systems and emulsions for conformance improvement. He holds a Bachelor of Science degree in Chemistry from the University of Oklahoma.
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Rebecca S. Bryant is the Director of the Production Technology group at TRW’s Energy and Environment Systems, responsible for program management. Her specialties include biotechnology for enhanced oil recovery and bio-remediation. She holds Bachelor of Science, Master of Science, and PhD degrees from Oklahoma State University, all in Microbiology.
Should readers be interested in more information, they may contact the Energy and Environment Systems office via E-mail: [email protected]
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