Five-spot Pattern Research Articles

Water injection in single well model case study

This study compares two water injection patterns (line drive and five-spot) using CMG software in a cubic reservoir model based on Buzergan field data. Line drive injection showed higher water cut rates due to direct water flow, while the five-spot pattern distributes water flow across the area, resulting in lower water cuts. Economic analysis favors the line drive pattern for its lower setup cost and reduced water injection requirements. These findings offer insights for optimizing injection patterns and maximizing oil production in reservoir management. Highligt: Injection Pattern Comparison: Direct vs. Distributed Water Flow Analysis. CMG Software Simulation: Accurate Reservoir Modeling and Analysis Tool. Cost-Effective Optimization: Maximizing Oil Production with Economical Injection Strategies. Keyword: Water Injection Patterns, CMG Software, Reservoir Management, Oil Production Optimization, Economic Analysis

Machine learning insights to CO2-EOR and storage simulations through a five-spot pattern – a theoretical study

The utilization of CO2 flooding is a widely applied enhanced oil recovery (EOR) technique in mature onshore oil fields. As well as being able to increase oil production and recovery it offers the potential to provide long-term, geological storage for carbon in subsurface reservoirs, thereby contributing to the mitigation of carbon emissions originating from human activities. Substantial research efforts have provided some insight into the uncertainties associated with CO2-EOR projects, but further understanding and the development of more reliable methods are required to accurately predict the outcomes of the complex processes involved in CO2 reservoir flooding. In this study, four machine learning (ML) algorithms were developed to predict CO2 storage mass and cumulative oil production, using the CMG-GEM three-phase flow compositional reservoir simulator with nine reservoir input variables covering a range of uncertainties associated with oil zones. The Mahalanobis distance technique was applied for identifying and excluding outlier data points from the target variable distributions of training data groups. 520 and 439 data records were excluded from the CO2 storage quantity and cumulative oil production dataset, respectively, to generate more reliable predictions. Meticulous training and testing of the ML models revealed that, of the models evaluated, the LSSVM model generated the lowest prediction errors with the test dataset (RMSE = 0.7811 million mt for CO2 storage mass; RMSE = 10.1245 million barrels for cumulative oil production) demonstrating excellent generalization capabilities.

Effect of reservoir heterogeneity on well placement prediction in CO2-EOR projects using machine learning surrogate models: Benchmarking of boosting-based algorithms

Rising Carbon Dioxide (CO2) levels from human activities are driving climate change. Carbon capture and storage (CCS) during enhanced oil recovery (EOR) in underground reservoirs offer both environmental and economic benefits. This method boosts oil production, cuts greenhouse gas emissions, and supports sustainable energy. Precise well placement in CO2-EOR is a crucial task for effective oil displacement, but traditional reservoir simulators are costly. This study explores and compares boosting algorithms, as fast surrogate models, to achieve accurate well placement during CO2-EOR in light oil carbonate reservoirs. The research considers various reservoir scenarios with different geological heterogeneity levels (i.e., homogeneous, moderately heterogeneous, and highly heterogeneous reservoirs). Various parameters, such as injection and production well locations, the distance between production and injection wells in an inverted five-spot pattern, pattern angle, and injection and production rates are explored using a compositional reservoir simulator to assess their impact on the well placement problem. A comprehensive analysis of various boosting algorithms, including AdaBoost, CatBoost, Gradient Boosting, LightGBM, and XGBoost is performed using the simulated dataset to assess their efficacy. The results demonstrate that LightGBM outperformed the other algorithms with the lowest Mean Absolute Error and Root Mean Square Error of 115.3 × 106 $ and 188.2 × 106 $, respectively. Additionally, it demonstrates exceptional speed, averaging 3 to 8 times faster than other boosting algorithms in the three reservoir scenarios. This superior performance coupled with its efficient runtime makes LightGBM the ideal choice for the study objectives. Moreover, the mass balance approach highlights the significant CO2 storage efficiency, emphasizing the effectiveness of CO2-EOR in storing CO2 in underground heterogeneous reservoirs.

Data-driven modeling for forecasting oil recovery: A timeseries neural network approach for tertiary CO2 WAG EOR

Attaining reliable forecasts in the petroleum industry is a constant challenge, prompting ongoing research into models that empower engineers to make informed decisions. The conventional approach suffers from high uncertainties with complex input parameters resulting in convergence issues and high computational costs. The emergence of timeseries machine-learning models has shown to leverage trends and pattern recognition to achieve tractable, robust and cost-effective solutions. While previous research primarily focused on predicting existing production trends, this study uses timeseries analysis to forecast oil recovery in a CO2-EOR reservoir, focusing on an inverted five-spot pattern. Dynamic data encompassing pressures, WAG cycles, and injection volumes undergo preprocessing and chronological division to facilitate training and testing of an LSTM model. The analysis of field history calibration through the loss iteration of the training dataset shows promising results reflected in low mean-squared-error of 6.65. Model validation, including the test and blind datasets, demonstrates an approximate R-squared value of 0.88. The forecasted results unveil mounting uncertainty over time, and sensitivity analysis shows the significance of WAG cycle adjustments. This study introduces an economical oil recovery forecasting approach, devoid of complex physical models, offering a versatile framework applicable across disciplines, especially for scenarios influenced by past decisions.

The influence of irreducible water for enhancing CH4 recovery in combination of CO2 storage with CO2 injection in gas reservoirs

CO2 flooding to enhance gas recovery (CO2-EGR) with CO2 storage offers the prospects of significant environmental and economic benefits by increasing CH4 recovery while simultaneously storing CO2. Most studies ignored the interaction of water with CO2 and the formation rocks and the influence of irreducible water to enhance CH4 recovery combined with CO2 storage were poorly understood by core-flooding experiments. In this research, a numerical model of a five-spot well pattern was developed by benchmarking against the existing literature, and the model was further modified to investigate the effects of irreducible water on CO2-EGR and CO2 storage in gas reservoirs. The injected CO2 preferentially moved horizontally and gradually flowed vertically to flood CH4, making the displacement front an inclined CO2-CH4 mixing zone. The model with irreducible water changed from 0% to 40%, the CO2 sweep efficiency improved and the CH4 recovery increased by 4.37%. This could be attributed to the narrowing of the CO2-CH4 mixing zone and the change in displacement front from an inclined horizontal plane to a near arc plane with better stability. The cumulatively stored CO2 decreased by 21.24%, due to the early CO2 breakthrough and shut-in times. However, because more CO2 was dissolved in water and trapped in residual gas, the contribution of CO2 solubility trapping and CO2 residual trapping increased by 12.01% and 10.34% respectively, while CO2 structural trapping decreased by 22.86%, resulting in a significant increase in long-term storage security. Mineral reactions had a negligible influence on CO2-EGR and CO2 sequestration in the CO2 flooding process. The higher the salinity, the lower the amount of dissolved CO2, and the lower the CH4 recovery and cumulatively stored CO2, with decreased security of CO2 storage with limited impact. The higher the irreducible water saturation (Swi), the more CO2 dissolved, and the CH4 recovery and long-term storage security of CO2 improved with a reduction of cumulatively stored CO2. Changing the gas relative permeability (Krg) has a small effect for CH4 recovery and CO2 storage. This research may provide new insights into analyzing the mechanism of irreducible water on the influence of CO2-EGR and CO2 storage, laying a foundation for the optimization of CO2-EGR schemes and the implementation of field applications in water-bearing gas reservoirs with CO2 injection in the future.

Coupled Hydromechanical Modeling and Assessment of Induced Seismicity at FWU: Utilizing Time-Lapse VSP and Microseismic Data

The objective of this work is to utilize integrated geomechanics, field vertical seismic profile (VSP) and microseismic data to characterize the complex subsurface stress conditions at the Farnsworth Unit (FWU). The model is based on a five-spot sector model extracted from a primary geomechanical model. The five-spot well injection pattern is characterized by extensive reservoir characterization data, such well logs, extracted cores and borehole geophone data, to facilitate the detailed examination of stress changes and microseismic event occurrences. The study utilizes field vertical seismic volumes acquired from the injection well 13-10A. The seismic volumes successfully provided snapshots of the behavior of the reservoir at distinct times. The use of VSP and microseismic data provided direct and indirect estimates of the dynamic stress changes occurring in the overburden, reservoir and underburden rock formations. In order to illuminate the stress regions and identify rocks that have undergone inelastic failure, microseismic event occurrences were utilized. Microseismic activity has been detected at the FWU; further study of its locations, timing, and magnitude was needed to deduce the nature of the changing stress state. The results of the study revealed that microseismic events were successfully modeled within the Morrow B formation. Moment magnitudes of seismic events were within the same magnitudes for events in the reservoir, suggesting the suitability of the model. The results of the study showed that the computed moment magnitudes for seismic events were insignificant to warrant safety concerns. The study findings showed the usefulness of coupled hydromechanical models in predicting the subsurface stress changes associated with CO2 injection. The knowledge gained from this study will serve as a guideline for industries planning to undertake underground CO2 storage, and characterize the subsurface stress changes.

Application of Inter-Well Connectivity Analysis with a Data-Driven Method in the SAGD Development of Heavy Oil Reservoirs

The development of heavy oil reservoirs in China is of great significance to safeguard national energy security, but great challenges are faced due to the complex and heterogeneous reservoir properties. Inter-well connectivity analysis is critical to enhancing the development performance, as it is a good way to interpret fluid flow and provides a theoretical basis for injection-production optimization. Data-driven deep learning methods have been widely used in reservoir development and can be employed to develop surrogate models of injection and production and to infer inter-well connectivity. In this study, the model performance of a recurrent neural network (RNN) and its four variants were evaluated and compared in a temporal production prediction. The comparison results showed that bidirectional gated recurrent unit (Bi-GRU) is the optimal algorithm with the highest accuracy of 0.94. A surrogate model was established to simulate the inter-well connectivity of steam-assisted gravity drainage (SAGD) in the research area by utilizing the Bi-GRU algorithm. A global sensitivity analysis method, Fourier amplitude sensitivity testing (FAST), was introduced and combined with the surrogate model to explain the influence of the input variables on the output variables by quantitatively calculating the sensitivity of each variable. Quantitative results for the inter-well connectivity of SAGD were derived from the sensitivity analysis of the proposed method, which was effectively applied to typical linear patterns and five-spot patterns. Inter-well connectivity varied from 0.1 to 0.58 in test applications, and mutual corroboration with previous geological knowledge can further determine the distribution of the interlayer in the reservoir. The workflow proposed in this study provides a new direction for analyzing and inferring the inter-well connectivity of SAGD in Northeast China heavy oil reservoirs.

Numerical evaluation of refracturing fracture deflection behavior under non-uniform pore pressure using XFEM

Refracturing has become an important technique for tapping old wells to stabilize and improve well performance. However, due to inaccurate well selection and formation selection for refracturing and inadequate prediction of refracturing fracture propagation, refracturing effectiveness sometimes may be diminished. Hence, the objective of this paper is to establish a numerical model to efficiently simulate the processes of first fracturing, injection and production, and hydraulic refracturing. The extended finite element method (XFEM) is first applied. Then, a five-spot well pattern is considered, which couples the angle of the well array to the maximum horizontal principal stress with the angle of the perforation orientation. Afterward, we optimize the refracturing orientation under non-uniform pore pressure conditions. Fracture length and fracture deflection angle are utilized as evaluation indicators. Results indicate that the orientation of refracturing is not recommended to follow the injection well and the optimal perforation area exists when the direction is along the middle of the two injection wells. Long fractures with large deflection angles can be obtained along the mid-line of the well array in a clockwise as well as a counter-clockwise direction of 15°, leading to a higher reservoir modification area. In addition, fractures tend to propagate into areas of high pore pressure. This work provides a useful model including the dynamic propagation of fractures during refracturing after initial fracturing and production operations, which can assist operators optimize the fracturing process.

Numerical investigations of the PUGA geothermal reservoir with multistage hydraulic fractures and well patterns using fully coupled thermo-hydro-geomechanical modeling

The Puga geothermal reservoir is located in the south-eastern part of Ladakh (Himalayan region, India), and it is providing encouraging results towards heat production. We proposed an improved mathematical model for the fully coupled thermo-hydro-geomechanical model to examine the variations in the Puga geothermal reservoir at between 4500 m from the surface with three, four, and seven hydraulic fractures in the reservoir along with four-spot, five-spot, seven-spot, and nine-spot well patterns. The distribution of low-temperature region is found in each fracture, and it is low in the reservoir with seven hydraulic fractures. The changes in the rock and fluid properties are examined effectively. Thermal strain is dominated in the fractures, and mechanical strain is impressive in the rock matrix; it is dependent on the number of hydraulic fractures and well patterns. The thermal performance of the Puga reservoir is examined with the geothermal life, reservoir impedance, and heat power and found that the number of hydraulic fractures and well patterns are influenced significantly in the multistage modeling of the Puga geothermal reservoir. Thus, the proposed mathematical model can effectively evaluate and predict the variations that occur in the Puga geothermal reservoir with dynamic rock, fracture, and fluid properties.

Production Splitting Method for Commingled Production Reservoir Based on Automatic History Matching of Single Well

Abstract The interlayer interference is very serious in the process of water flooding development, especially when the reservoir adopts commingling production. The implementation of various interlayer interference mitigation measures requires that the production performance parameters and remaining oil distribution of each layer of the reservoir should be clearly defined, and the accurate production splitting of oil wells is the key. In this paper, the five-spot pattern is simplified to a single well production model of commingled production centered on oil well. The accurate production splitting results are obtained through automatic history matching of single well production performance. The comparison between the calculation results of this method and that of reservoir numerical simulation shows that the method is simple, accurate, and practical. In the field application, for the multilayer commingled production reservoir without accurate numerical simulation, this method can quickly and accurately realize the production splitting of the reservoir according to the development performance data.

Influence of Gas Flooding Pressure on Groundwater Flow during Oil Shale In Situ Exploitation

In order to weaken the influence of external groundwater on in situ pyrolysis exploitation, the flow characteristics of groundwater were studied according to the oil shale reservoir characteristics of Qingshankou Formation in Songliao Basin, China. In addition, the parameters of marginal gas flooding for water-stopping were optimized. Taking a one-to-one pattern and a five-spot pattern as examples, the characteristics of groundwater flow under the in situ process were studied. Under the one-to-one pattern, the external groundwater flows into the production well from the low-pressure side, and the water yield was basically stable at 1000 kg/d. In the five-spot pattern, the groundwater can flow into the production wells directly from the windward side, and the water yield of the production well on the leeward side mainly comes from the desaturated zone; the water yield of each production well remains at a high level. By setting water-stopping wells around the production well and keeping the gas flooding pressure slightly higher than the production well, the water yield of the production well can be reduced and stabilized within 100 kg/d under gas flooding pressures of 3 and 5 MPa. However, the gas yield of the production well slightly decreased when the gas flooding pressure reduced from 5 to 3 MPa. Therefore, the gas flooding pressure of water-stopping wells shall be determined in combination with the water yield and gas yield, so as to achieve the best process effect. It is expected that the results will provide technical support for large-scale oil shale in situ pyrolysis exploitation.

Optimizing Water Injection Performance by Using Sector Modeling of the Mishrif Formation in West Qurna-1 Oil Field, Southern Iraq

The regular job of a reservoir engineer is to put a development plan to increase hydrocarbon production as possible and within economic and technical considerations. The development strategy for the giant reservoir is a complex and challenging task through the decision-making analysis process. Due to the limited surface water treatment facility, the reservoir management team focuses on minimizing water cut as low as possible by check the flow of formation and injected water movement through the Mishrif reservoir. In this research, a representative sector was used to make the review of water injection configuration, which is considered an efficient tool to make study in a particular area of the entire field when compared with the full-field model on the basis of time-consuming and computational analysis. The sector model was neighboring by extra grid blocks and three pseudo wells as injector wells to realize the pressure on the sector boundary, which attained an acceptable history matching. The fluid model and physics model were introduced by using Pressure Volume Temperature data of well involved in the study area and two relative permeability curves. Fourteen wells were utilized in this work, four wells are injectors, and the rest are producer. The development scenarios were implemented by setting various targets of oil production and different water injection rates required for pressure maintenance operations. Optimization of water cut has been applied by adjustment of production and injection rates and shut off the high water cut intervals. The results obtained from this study showed that the inverted 9-spot has a good recovery which is illustrated in the case_2C, the production rate was (49,000 STB/D) with minimum water cut (27.5%) as compared with a five-spot pattern.

Using cyclic alternating water injection to enhance oil recovery for carbonate reservoirs developed by linear horizontal well pattern

In view of high water cut and low oil recovery caused by the unidirectional flow in linear pattern of horizontal wells for the carbonate reservoirs in the Middle East, this paper provides a novel approach to improve oil recovery by converting linear water injection to cyclic alternating water injection patterns including cyclic alternating water injection with apparent inverted seven-spot pattern or apparent five-spot pattern and cyclic differential alternating water injection. The main advantage of using this strategy is that the swept efficiency is improved by changing injection-production streamlines and displacement directions, which means displacement from two different direction for the same region during a complete cycle. This technology is effective in increasing the swept efficiency and tapping the remaining oil, thus resulting in higher oil recovery. Field application with three new patterns in a carbonate reservoir in the Middle East is successful. By optimizing injection and production parameters based on the cyclic alternating well pattern, the test well group had a maximum increase of daily oil production per well of 23.84 m 3 and maximum water cut drop of 18%. By further optimizing the distance (keep a long distance) between the heels of injection and production wells, the waterflooding performance could be better with water cut decreasing and oil production increasing.

Numerical Modeling of CO2 Sequestration within a Five-Spot Well Pattern in the Morrow B Sandstone of the Farnsworth Hydrocarbon Field: Comparison of the TOUGHREACT, STOMP-EOR, and GEM Simulators

The objectives of this study were (1) to assess the fate and impact of CO2 injected into the Morrow B Sandstone in the Farnsworth Unit (FWU) through numerical non-isothermal reactive transport modeling, and (2) to compare the performance of three major reactive solute transport simulators, TOUGHREACT, STOMP-EOR, and GEM, under the same input conditions. The models were based on a quarter of a five-spot well pattern where CO2 was injected on a water-alternating-gas schedule for the first 25 years of the 1000 year simulation. The reservoir pore fluid consisted of water with or without petroleum. The results of the models have numerous broad similarities, such as the pattern of reservoir cooling caused by the injected fluids, a large initial pH drop followed by gradual pH neutralization, the long-term persistence of an immiscible CO2 gas phase, the continuous dissolution of calcite, very small decreases in porosity, and the increasing importance over time of carbonate mineral CO2 sequestration. The models differed in their predicted fluid pressure evolutions; amounts of mineral precipitation and dissolution; and distribution of CO2 among immiscible gas, petroleum, formation water, and carbonate minerals. The results of the study show the usefulness of numerical simulations in identifying broad patterns of behavior associated with CO2 injection, but also point to significant uncertainties in the numerical values of many model output parameters.

Modelling of CO2-foam Core Flooding Experiments

This work presents results from simulation of core-flooding experiments with several commercially available surfactants for CO2-foam stabilisation, potentially applicable for CO2 mobility control in CO2 storage operations. The simulations are run with a CO2 foam module for MRST, based on a foam effect model developed by Vassenden and Holt. Efficient use of mobility control for CO2 at field scale could give a significant increase in storage capacity. It could counter the negative effects of the mobility contrast between injected CO2 and the resident formation brine, enabling more optimal filling of structural traps and delaying breakthrough of injected CO2 at wells where formation brine is extracted for pressure management purposes. Efficient mobility control and the associated sweep improvement can more than double the storage efficiency in a developed five-spot pattern of injection and pressure control wells. Partitioning of surfactant between the CO2 and brine phases will lead to gradually reduced surfactant concentration and eventually loss of foam-generation as the CO2 penetrated deeper into the reservoir. Adsorption of surfactant to mineral surfaces will also contribute to the reduced concentration. Investigation of realistic field-scale effects of mobility control by foam requires both careful measurement of partitioning and adsorption properties in laboratory experiments and a reservoir simulator capable of including such effects.

Numerical Simulation of the Combined Effects of Low Salinity Water and Alkaline-Surfactant-Polymer Flooding

Low Salinity Water (LSW) and Alkaline-Surfactant-Polymer (ASP) flooding are emerging enhanced oil recovery methods that help recover oil from the reservoir after primary and secondary recovery processes. Experimental studies on LSW and ASP flooding have indicated potential in additional oil recovery. In this paper, numerical simulation was performed to study the combined effects of LSW and ASP flooding. A heterogenous reservoir initially saturated with oil and water was modelled using Eclipse. The wells were completed with an inverse five-spot pattern and the production life of the reservoir was taken to be five years. The results showed that LSW flooding using a salt concentration of 1 000 ppm achieved a higher oil recovery than conventional (high salinity) water flooding with a salt concentration of 35 000 ppm. The oil recovery for conventional water flooding was 59.5% and that of low salinity flooding was 64.1%. The overall oil recovery for LSW combined with alkaline, surfactant and polymer flooding were 64.1%, 70.5% and 62.6%, respectively. The model indicated an increase in overall oil recovery of 91% when alkaline, surfactant and polymer were combined and injected as the same slug as opposed to the injection of the chemicals individually. This was attributed to the synergy of the chemicals. The alkaline and the surfactant reduce the interfacial tension between the oil and water and the polymer improves the mobility ratio thereby increasing sweep efficiency.

Model-based water-flooding optimization using multi-objective approach for efficient reservoir management

The efficient development of an oil field mostly depends on a comprehensive optimization of subsurface flow. To account for several discrete or even contradicting objectives, multi-objective optimization (MOO) approach presents multiple optimum solutions for decision-making processes. There are excessive degrees of freedom in any optimization problem of the life-cycle of water-flooding to optimize the short-term performance during the process. Choosing each strategy has a different impact on the long-term reservoir performance. Thus, in this study, we have utilized two different model-based algorithms based on multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II) methods with some modifications to plan the short- and long-term production strategies simultaneously in water-flooded reservoirs. These algorithms are both population-based techniques, in which the Pareto-ranking approach is combined with the inherent search towards the optimal solution for a multi-criterion optimization problem. Maximizing the long-term Net Present Value (LNPV) and short-term (discounted) NPV (SNPV) are the objectives to be met in the investigated MOO problems. To address the imperfect Pareto front obtained in MOO problems, some modifications have been added to the utilized algorithms, including using a modified comparison operator in the NSGA-II method and employing the crowding distance parameter in the leader selection process together with a revised archive controller as well as a dynamic boundary search to MOPSO algorithm. By these means, the entire Pareto fronts are actively generated, which covers the complete solutions area through both algorithms. To validate the developed approaches, two benchmark water-flooded reservoir models have been employed. In the first case, the optimization parameters are the wells injection rates in the Egg benchmark reservoir model. In the second one, we have adjusted the opening values of the inflow control valves (ICV) of smart wells in the water-flooding process of a layered reservoir with a five-spot pattern. The effect of the trading-off between Pareto elitism and diversity on the final results is investigated for both algorithms. Results illustrate that the competitive values of the NPV functions, LNPV and SNPV pairs, lying on the obtained Pareto front, provide a promising criterion to improve the decision-making process. A comparison of various methods shows that for both case-studies, MOPSO can strongly propose a production strategy that more appropriately optimizes SNPV and LNPV compared to the NSGA-II as well as compared to some previous efforts published in the literature. A high rate of convergence, together with the logical Pareto front having enough diversity and uniformity, and also the independency of the final solution on the initial guess, are the main advantages of MOPSO in comparison with other approaches.

OPTIMIZATION OF SURFACTANT FLOODING ON BJG FIELD USING DYNAMIC PATTERN

Mature fields, also known as brownfields, are fields that are in a state of declining production or reaching the end of their production lives. Development of mature oil fields has been, and will increasingly be, an exciting subject (Babadagli, 2007). New studies already discovered innovative ways of finding, developing, and producing hydrocarbons that are efficient and cost-effective and minimize harm to the environment. BJG Field is one of the mature fields which is produced in 1927, one of the efforts for enhancing the production is using waterflood at the beginning of 2001. To increase production further, then we need to conducted studies as an application of the second recovery from BJG Field. The oil recovery factor BJG field can be increased using a surfactant flooding scenario. This research aimed to conduct a study of dynamic pattern surfactant flooding using simulations as applicable for the mature field. The research is expected to obtain an optimum surfactant injection scenario using IMEX and STARS simulator. Simulation is done with real data from the BJG field, and the result has shown the scenario which has the most significant oil production. The highest recovery factor is the chosen scenario. From the results of studies and simulation shown that dynamic pattern inverted five-spot pattern can be used. The increment of oil recovery factor is 32.29% from the waterflood case.

Application of Polynomial Chaos Expansion to Optimize Injection-Production Parameters under Uncertainty

The optimization of oil field development scheme considering the uncertainty of reservoir model is a challenging and difficult problem in reservoir engineering design. The most common method used in this regard is to generate multiple models based on statistical analysis of uncertain reservoir parameters and requires a large number of simulations to efficiently handle all uncertainties, thus requiring a huge amount of computational power. In order to reduce the computational burden, a method which combines reservoir simulation, an economic model, polynomial chaos expansion with response surface methodology, and Levy flight particle swarm optimization (LFPSO) algorithm is proposed to determine the optimal injection-production parameters with reservoir uncertainties at a reasonable computational cost. This approach is applied to a five-spot well pattern optimization design for obtaining the optimal parameters, including oil-water well distance, injection rate, and bottom hole pressure, while considering the uncertainties of porosity, permeability, and relative permeability. The results of the case study indicated that the integrated approach is practical and efficient for performing reservoir optimization with uncertain reservoir parameters.

Evaluation of Intelligent Wells Performance in a Five-Spot Arrangement

The efficiency of water flooding processes can be improved by installing intelligent wells which are good candidates for control and optimization. Optimal control theory based on adjoint formulations was found to be efficient for reservoir optimization. However, this solution approach is local and may not be suitable for comparing design alternatives. In this work, an approach for determining an optimal starting point for optimal control theory procedure was developed to give near global optima. The performance in terms of net present value (NPV) of two forms of five-spot pattern was compared. The method results to similar performances of the two alternatives because it was formulated to give true optimal solution trajectories. It was found that regular five-spot pattern results to a NPV in excess of $4,900 over inverted design. Respective increase in oil and water productions of 0.23% and 0.22% were recorded for former design against the later.Keywords: intelligent wells; adjoint; optimal control theory; global optimum; water flooding.