1. Introduction

2. Materials and Methods

Figure 1. Model Building Workflow.

Figure 1. Model Building Workflow.

2.2. Dynamic Reservoir Model

The reservoir is initialized using the enumeration method to import saturation, composition and pressure values from the previous model which was history-matched to primary (1955 to 1964) and secondary (1964 to 2010) recovery phases. The average water saturation at the start of the history match period is approximately 31% with 93 MMSTB of oil in place. The average reservoir pressure ranges from 4,200 psi to 4,500 psi.

Figure 3. (a) Scaled Dynamic Grid; (b) Dynamic Grid showing water saturation distribution; (c) Dynamic Grid showing pressure distribution.

Figure 3. (a) Scaled Dynamic Grid; (b) Dynamic Grid showing water saturation distribution; (c) Dynamic Grid showing pressure distribution.

Figure 4. (a) Reservoir Grid of Left Range showing Water Saturation Distribution; (b) Reservoir Grid of Right Range showing Water Saturation Distribution.

Figure 4. (a) Reservoir Grid of Left Range showing Water Saturation Distribution; (b) Reservoir Grid of Right Range showing Water Saturation Distribution.

The initial relative permeability curves proved unreliable for this work. Relative permeability lab data acquired is tested on dead oil, and hence, is not conclusively representative of the relative permeability at field condition. Relative permeability of a reservoir is known to evolve with time as recovery continues. There have been two recovery stages, primary and secondary, that have taken place. The history-matching in this work focuses on the tertiary phase of production. Two relative permeability curves are used. The reservoir was divided into two—left side and right side. The left side has seen a prolonged period of CO₂ injection and is in the tertiary recovery phase compared to the right side which is still in the secondary recovery phase.

Figure 5. (a) Oil-Water Relative Permeability Curve for Right Range; (b) Gas-Liquid Relative Permeability Curve for Right Range; (c) Oil-Water Relative Permeability Curve for Left Range; (d) Gas-Liquid Relative Permeability Curve for Left Range.

Figure 5. (a) Oil-Water Relative Permeability Curve for Right Range; (b) Gas-Liquid Relative Permeability Curve for Right Range; (c) Oil-Water Relative Permeability Curve for Left Range; (d) Gas-Liquid Relative Permeability Curve for Left Range.

2.8. Optimization of Development Strategy

The development scenario starts with all wells reopened. There are 31 producers and 20 injectors. All injectors are on WAG cycles and to be optimized. The maximum average reservoir pressure is capped 4,500 psia with a minimum of 4,200 psia so that is remains above the minimum miscibility pressure. A watercut percentage of 90% and gas-oil ratio constraint of 50,000 SCF/STB is applied to the producers. Below is table summarizing the operating conditions and WAG cycles of the base developed case.

Table 2. Summary of Operating Conditions of Base Developed Strategy.

Table 2. Summary of Operating Conditions of Base Developed Strategy.

Parameters	Default
Pressure on Production Manifold, psi	90
Injection Group 1 (gas/water), months	2/2
Injection Group 2 (gas/water), months	3/1
Injection Group 3 (gas/water), months	9/1
Injection Group 4 (gas/water), months	3/3
Compressor Rate, MMSCF/Day	34
High Separator Pressure, psi	62

Analogous to the process in the history matching stage, a set of variables representing the operating conditions of components in the surface facility are selected and a sensitivity analysis is run on these parameters to determine the degree of impact each component has.

In this stage, a Radial Basis Function Neural Network (RBFNN) is trained using the Response Surface Methodology to build a proxy model. This proxy model would substitute complex surface-coupled flow physics and be used in determining the sensitivity of each parameter. The most impactful and sensitive parameters are selected and fed into the particle swarm optimization algorithm to give us the best possible output. Using the PSO, the selected parameters would continue to vary within the ranges they are assigned until each is an optimum position that is closest to the objective function. Below is a table summarizing the selected uncertainty parameters and the bounds within which they would be varied.

Table 3. Optimization Parameters.

Table 3. Optimization Parameters.

Parameters	Default	Minimum	Maximum
Pressure on Production Manifold, psi	90	60	120
Injection Group 1 (gas/water), months	2/2	(1:1)	(12:3)
Injection Group 2 (gas/water), months	3/1	(1:1)	(12:3)
Injection Group 3 (gas/water), months	9/1	(1:1)	(12:3)
Injection Group 4 (gas/water), months	3/3	(1:1)	(12:3)
Compressor Rate, MMSCF/Day	34	17	34
High Separator Pressure, psi	62	30	70

After viewing the impact of parameters on the cumulative oil recovered and mass of CO₂ stored, the resulting impact of these parameters on the Net Present Value (NPV) is ascertained. For each objective, there are four plots that would be highlighted and used to address the sensitivity analysis. These four plots are the qq-plot, Monte Carlo Simulation plot, Morris Analysis, and Sobol Analysis Tornado Chart.

Looking at the impact of each parameter on the selected objective functions, a new term, Field NPV, is defined to include both objective functions, cumulative oil recovery and CO₂ stored, by summing the local NPVs which are the two objective functions. The Field NPV was calculated by summing two local NPVs. These NPVs are the revenue generated from the daily oil production and the tax benefits generated from CO₂ stored. The oil revenue local NPV considers gains from oil sales at $60/bbl. Losses are estimated due to facility maintenance and water management. The impact of water management and its recycling is estimated at $2.64/bbl of water. Facility maintenance and well workover is also estimated to result in approximately $20.92/bbl of oil produced. This is a simplified economic analysis which does not account for royalties and taxes. Capital expenditure is also left out since the field is mature and the facilities needed for this development are already in place. Other operating costs such as staff or labor and well workover costs are not included since this not the main focus of the study. In the second local NPV, CO₂ stored, the tax benefit from CO₂ sequestered is considered to be $24/t [29]. The cost of recycling and compressing CO₂ is estimated at $0.4/MSCF. Smith et al. [30] estimates from analysis of various literature that the cost of transport and storage of CO₂ is approximately $11.2/t via pipeline. The two local NPVs are combined in an arithmetic sum in the Field NPV.

Table 4. Factors Considered in Calculating NPV.

Table 4. Factors Considered in Calculating NPV.

Parameters	Cost
Price of CO2 transport and storage, $/t	11.2
Recycle Compression, $/MCF	0.4
Surface Facility Maintenance and Well Workover, $/bbl	20.92
Water Management Cost, $/bbl	2.64
Price of oil, $/bbl	60
Tax Benefit for CO2 stored, $/t	24

3. Results and Discussion

3.3. Simulation and Forecast

3.3.1. Do-Nothing Forecast

The results of the Do-Nothing case are shown below. The dashed blue line indicates the end of the historical period. The cumulative oil production at the end of forecast is 9.57 MMSTB. The oil production shows minimal decline, maintaining relatively stable production rates. This stability can be attributed to the high-pressure maintenance in the reservoir due to extensive water injection during the historical period (Figure 10).

Water production remains steady throughout the forecast period, without significant fluctuations. The cumulative water production reaches 50.438 MMSTB by the end of the forecast (Figure 11). The consistent water production rate suggests that the reservoir’s water handling capabilities are sufficient to support ongoing production without significant changes in water cut.

The gas production rate does not rise past 20MMSCF/D which is the injection limit for the recycling plant on the field. For the purpose of this study, gas production rate is to be controlled and keep GOR within field capacity. This knowledge is learned and implemented in the development strategy. Gas production continues to increase steadily, with periodic fluctuations due to operational constraints and gas recycling efforts. Wells producing excess gas are strategically shut-in to manage the GOR effectively (Figure 12).

Figure 12. Do-Nothing Forecasted Gas Production Rate.

Figure 12. Do-Nothing Forecasted Gas Production Rate.

Figure 13. Do-Nothing Forecasted Cumulative CO₂ Storage.

Figure 13. Do-Nothing Forecasted Cumulative CO₂ Storage.

The cumulative CO₂ stored at the end of the forecast period is 2,822.7 MMlbs. This amounts to 1,411,350 tons of CO₂ stored. The amount of CO₂ stored stalls at the end of history since no gas is injection for the do- nothing scenario.

Below is a table summarizing the cumulative values of the “Do-Nothing” forecast.

Table 5. Summary of Do-Nothing Forecast Results.

Table 5. Summary of Do-Nothing Forecast Results.

Parameters	Cumulative Value
Oil Production, MMSTB	9.57
Water Production, MMSTB	50.44
Gas Production, MMSCF	94,669.58
CO2 Stored, MMIbs	2,822.70

3.3.2. Development Scenario Forecast

The results from the development scenario forecast are depicted below. There is an increase in the cumulative oil produced at the end of forecast using the improved development strategy. This is due to shutting in wells with high watercut and high GOR. Opening the already-closed wells also contributes to the increased production. A cumulative 13.95 MMSTB of oil was recovered which is about 4 MMSTB more oil than the Do-Nothing case.

Figure 14. Cumulative Oil Recovered for Development Strategy.

Figure 14. Cumulative Oil Recovered for Development Strategy.

The cumulative water production for the development strategy scenario remains steady throughout the forecast period, mirroring the trends observed in the Do-Nothing case. The total cumulative water production is 38.39 MMSTB (Figure 15). The stability in water production rates suggests that the reservoir’s water management strategies are effective and consistent with the baseline scenario, ensuring efficient handling of produced water.

Gas production under the development strategy scenario follows a trend similar to the Do-Nothing case, but with noticeable improvements due to the extended period of CO₂ injection (Figure 16). The gas production rate peaks higher in this scenario, reaching the injection limit of 20 MMSCF/D. This higher gas production rate is a result of increased oil recovery, leading to more associated gas being produced and subsequently recycled. The effective management of gas production ensures that the GOR remains within optimal field capacity, further supporting enhanced oil recovery efforts.

The cumulative CO2 storage in the development strategy scenario is 5,061.68 MMlbs, which is more than the Do-Nothing case (Figure 17). This increase is attributed to the shutting-in of wells with high water cut, resulting in increased oil recovery and, consequently, more dissolved gas being evolved and recycled at the surface. CO₂ is purchased and injected until the injection target of 20 MMSCF/D can be reached from recycled gas. This would eliminate the need for additional CO₂ purchase from external sources. This efficient recycling process ensures that the development strategy remains economically viable while maximizing oil recovery and CO₂ storage.

The summarized results of the development scenario forecast are presented in Table 6.

Based on the forecast results for the two cases, the development strategy scenario demonstrates significant improvements in oil recovery and gas management compared to the Do-Nothing scenario. The strategic interventions, such as shutting-in wells with unfavorable production characteristics contribute to the overall success of the development plan. This comprehensive analysis provides valuable insights for optimizing production strategies and enhancing the efficiency of CO₂-EOR processes in the FWU field.

3.4. Optimization

3.4.1. Parameterization and Sensitivity Analysis

The results of the sensitivity analysis below show the effect of each parameter on the two main objectives of this study—cumulative oil recovered, and mass of CO₂ stored. It can be inferred from the qq-plot of the simulated cumulative oil recovered versus proxy cumulative oil recovered that the proxy matches the high-physics calculations enough to be used suitably as a substitute in prediction.

Figure 18. Q-Q Plot of Simulated Cumulative Oil Produced vs. Proxy Predicted Cumulative Oil Produced.

Figure 18. Q-Q Plot of Simulated Cumulative Oil Produced vs. Proxy Predicted Cumulative Oil Produced.

The results of the Monte Carlo plot demonstrate the robustness of the development strategy with a percentage difference of 0.587% between estimated P10 and estimated P90. With P90 standing at 1.30258 × 107STB and P10 at 1.29494 × 107STB, there is only a difference of 76, 400 STB.

Figure 19. Monte Carlo Simulation Plot of Cumulative Oil Sensitivity Analysis.

Figure 19. Monte Carlo Simulation Plot of Cumulative Oil Sensitivity Analysis.

The next plot to be viewed is the results of the Morris Analysis. This plots the standard deviation which represents the non-linearity effect of each sensitive parameter against the Absolute Elementary Effect Mean (AEEM) which is quantifies the impact it has on the objective function. This uses a one-at-a-time approach to determining local sensitivity of the parameter and the impact it has on the cumulative oil produced.

Figure 20. Plot of Morris Analysis for Cumulative Oil Produced.

Figure 20. Plot of Morris Analysis for Cumulative Oil Produced.

where;

• PMO_Pressure = Pressure on Production Manifold
• HPS_Inlet Pressure = High Separator Pressure
• Gas_Injection_Rate = Compressor Rate
• IG1_GI = Injection Group 1—Gas Injection Cycle Duration
• IG1_WI = Injection Group 1—Water Injection Cycle Duration
• IG2_GI = Injection Group 2—Gas Injection Cycle Duration
• IG2_WI = Injection Group 2—Water Injection Cycle Duration
• IG3_GI = Injection Group 3—Gas Injection Cycle Duration
• IG3_WI = Injection Group 3—Water Injection Cycle Duration
• IG4_GI = Injection Group 4—Gas Injection Cycle Duration
• IG4_WI = Injection Group 4—Water Injection Cycle Duration

According to the Morris analysis, the most sensitive parameter is the Inlet Pressure of the high-pressure separator, which exhibits the highest AEEM and standard deviation. This is followed by the gas injection cycle of group 3 (IG3_GI) and water injection cycle of group 2 respectively (IG2_WI). Following at a distance are gas injection cycle of group 2, pressure on production manifold outlet and gas injection rate. However, the effect of pressure on the production manifold outlet exhibits less non-linearity than the other 2.

The Sobol Analysis (Figure 21) further supports the Morris Analysis findings, showing that the gas injection rate has the highest total effect at approximately 63%, followed by HPSIP at 61%. The distinction between these two is that HPSIP directly impacts cumulative oil produced, whereas the gas injection rate influences other parameters, thereby affecting the cumulative oil.

For CO₂ storage, the qq-plot (Figure 22) indicates a close match between the proxy and the high-physics model, suggesting the proxy’s reliability for further analysis. Using this proxy, a plot of the Monte Carlo simulation shows a difference of 3.74% between the P90 and P10 of estimated CO₂ stored. This shows a wider range in percentage than in the case of cumulative oil produced. However, this range is quantitatively small and also shows the robustness of the model. With P90 at 4452.31 × 106 and P10 at 4285.95 × 106, a difference of 166MMlb of CO₂ is stored.

The Morris Analysis (Figure 24) reveals that the injection group cycles of gas and water have a more significant impact on CO₂ storage than surface components such as HPSIP, Production Manifold Outlet Pressure (PMOP) and gas injection rate. This is likely due to the fact that the amount of CO₂ stored depends on how much anthropogenic CO₂ is purchased which in turn depends on the gas production rate. The gas production rate is heavily dependent on pressure distribution in the reservoir, gas channels and pathways and rate of oil production. These are influenced more by the amount of water (for pressure maintenance) and gas injected (for miscible flood but excess injection can lead to early gas breakthrough). An effective miscible flood would slow down the gas production and increase sweep efficiency. This would allow more CO₂ to be stored since more would be purchased.

The Sobol Analysis (Figure 25) corroborates the Morris Analysis, indicating that injection group cycles have a greater influence on CO₂ storage than surface components operating conditions. This analysis highlights the importance of optimizing injection strategies to maximize CO₂ storage.

Despite this proxy model of the Field NPV showing a greater deviation than the previous two, the maximum absolute error is 3.4%. This affirms that our proxy is suitable for the investigations ahead.

Figure 26. QQ-Plot of Proxy for Field NPV.

Figure 26. QQ-Plot of Proxy for Field NPV.

The Monte Carlo plot shows that this proxy estimates a difference of 9.87% between the P90 and P10. This wider range suggests a higher uncertainty in NPV predictions compared to oil production and CO₂ storage. With P90 at 1.08612 × 1010 and P10 at 1.20509 × 10¹⁰, a resulting in a difference of 1.1897 × 10⁹.

Figure 27. Monte Carlo Simulation for Field NPV.

Figure 27. Monte Carlo Simulation for Field NPV.

The Morris analysis clearly shows injection group 4 as being the most impactful despite all parameters having a similar degree of non-linearity. Following closely is the gas injection cycle of injection group 2 and at a distance is the gas injection of injection group 3. Parameters cluster together on the lower left side, including the surface components. This is due to limiting the range for sensitivity to existing field conditions.

Figure 28. Morris Analysis for Field NPV.

Figure 28. Morris Analysis for Field NPV.

The Sobol analysis supports the results of the Morris analysis with injection group 4 being the most influential sensitive parameter at 52% and 25%, and gas injection of injection groups 2 and 3 following 12% and 4.2%. The parameters do not seem to show much interaction with each other in the outcome of the Field NPV.

Figure 29. Sobol Analysis for field NPV.

Figure 29. Sobol Analysis for field NPV.

Following the results of the sensitivity analysis, 7 of the 11 sensitivity parameters are selected for optimization using the particle swarm optimizer. Since our study focuses on the surface facility, all 3 of the surface component operation conditions are selected. These are the HPSIP, gas injection rate and Production Manifold Outlet Pressure (PMOP). The additional 4 parameters that are selected are the gas and water injection cycles for injection group 4, and gas injection cycles for injection groups 2 and 3.

3.4.2. Optimized Operating Conditions

The application of the particle swarm optimizer yielded optimum operating conditions for the selected sensitive parameters. The results of this optimization are depicted in the plots below, which demonstrate the improvements achieved through the optimization process.

Based on the cumulative oil produced, the optimal experiment ID is 31, as shown in Figure 30. This experiment resulted in the highest incremental oil production. The optimal strategy produced a cumulative oil volume of 14,043,372 STB, which is an incremental increase of 96,804 STB over the base development strategy, translating to a 0.694% improvement (Figure 31 and Table 8).

Table 7. Percentage Increase in Cumulative Oil Production.

Table 7. Percentage Increase in Cumulative Oil Production.

Experiment ID	Cumulative Oil Produced (STB)	Incremental Oil Recovered (STB)	Percentage Increment
Development Case	13,946,568
Optimal Strategy	14,043,372	96,804	0.694

The optimized operating conditions not only enhanced oil recovery but also significantly reduced the amount of CO₂ purchased. As illustrated in Figure 32, the optimal strategy utilized approximately 10% less purchased gas (1,984 MMSCF) to achieve a slightly higher cumulative oil production. This is the benefit of having the right operating conditions in the surface facility components and optimal scheduling of water and gas injection cycles. The savings involved in CO₂ purchased is the driving force in raising NPV of experiment 31 above the others.

The economic benefits of the optimized strategy are evident in the Field NPV results (Figure 33). The optimal strategy yielded a field NPV of $114,871,730, which is a 25.84% increase over the base development strategy (Table 10). The reduced CO₂ purchase costs and the efficient utilization of injected CO₂ are the primary drivers behind this substantial increase in NPV. However, it is important to note that the reduction in CO₂ purchase also results in less CO₂ being stored subsurface.

Figure 33. Field NPV at the end of forecast period.

Figure 33. Field NPV at the end of forecast period.

Table 9. Percentage Increase in Field NPV.

Table 9. Percentage Increase in Field NPV.

Experiment ID	Field NPV ($)	Incremental Field NPV ($)	Percentage of Incremental Field NPV
Development Case	91,281,921
Optimal Strategy	114,871,730	23,589,809	25.84

Table 10. Incremental CO₂ Stored per Experimental ID.

Table 10. Incremental CO₂ Stored per Experimental ID.

Experiment ID	Cumulative CO2 stored (MMIbs)	Incremental Storage (MMIbs)	Percentage Decrement
Development Case	5,061.68
Optimal Strategy	4,832.18	-229.5	4.53

Figure 34. Plot of CO₂ Stored per Experimental ID.

Figure 34. Plot of CO₂ Stored per Experimental ID.

The cumulative CO₂ stored for the optimal strategy is 4,832.18 MMlbs, compared to 5,061.68 MMIbs in the base development strategy (Figure 35). This discrepancy is due to the decreased need for external CO₂, as the optimized strategy maximizes the use of recycled CO₂ from produced gas. Based on these results. Experiment 31 is selected as our ideal optimized case.

The amount of CO₂ stored is equal to the amount of purchased CO₂ because all CO₂ remains trapped in the closed system. This would not have huge economic significance since the financial gains and tax reliefs of CO₂ storage last only 12 years. This simulation goes for 15 years and thus, the last 3 years of extra purchased CO₂ does not contribute economic benefits to the strategy.

4. Recommendation and Conclusion

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