Leveraging Designed Simulations and Machine Learning to Develop a Surrogate Model for Optimizing the Gas–Downhole Water Sink–Assisted Gravity Drainage (GDWS-AGD) Process to Improve Clean Oil Production

Abstract

The Gas and Downhole Water Sink–Assisted Gravity Drainage (GDWS-AGD) process addresses gas flooding limitations in reservoirs surrounded by infinite-acting aquifers, particularly water coning. The GDWS-AGD technique reduces water cut in oil production wells, improves gas injectivity, and optimizes oil recovery, especially in reservoirs with high water coning. The GDWS-AGD process installs two 7-inch production casings bilaterally. Then, two 2-3/8-inch horizontal tubings are completed. One tubing produces oil above the oil–water contact (OWC) area, while the other drains water below it. A hydraulic packer in the casing separates the two completions. The water sink completion uses a submersible pump to prevent water from traversing the oil column and entering the horizontal oil-producing perforations. To improve oil recovery in the heterogeneous upper sandstone pay zone of the South Rumaila oil field, which has a strong aquifer and a large edge water drive, the GDWS-AGD process evaluation was performed using a compositional reservoir flow model in a 10-year prediction period in comparison to the GAGD process. The results show that the GDWS-AGD method surpasses the GAGD by 275 million STB in cumulative oil production and 4.7% in recovery factor. Based on a 10-year projection, the GDWS-AGD process could produce the same amount of oil in 1.5 years. In addition, the net present value (NPV) given various oil prices (USD 10–USD 100 per STB) was calculated through the GAGD and GDWS-AGD processes. The GDWS-AGD approach outperforms GAGD in terms of NPV across the entire range of oil prices. The GAGD technique became uneconomical when oil prices dropped below USD 10 per STB. Design of Experiments–Latin Hypercube Sampling (DoE-LHS) and radial basis function neural networks (RBF-NNs) were used to determine the optimum operational decision variables that influence the GDWS-AGD process’s performance and build the proxy metamodel. Decision variables include well constraints that control injection and production. The optimum approach increased the recovery factor by 1.7525% over the GDWS-AGD process Base Case. With GDWS-AGD, water cut and coning tendency were significantly reduced, along with reservoir pressure, which all led to increasing gas injectivity and oil recovery. The GDWS-AGD technique increases the production of oil and NPV more than the GAGD process. Finally, the GDWS-AGD technique offers significant improvements in oil recovery and income compared to GAGD, especially in reservoirs with strong water aquifers.

1. Introduction

The utilization of the Gas and Downhole Water Sink–Assisted Gravity Drainage (GDWS-AGD) technique has been proposed as a means to enhance the recovery of oil in secondary and tertiary operations, particularly in the context of immiscible gas injection [1]. The GDWS-AGD procedure involves the placement of vertical wells at the uppermost section of a reservoir to inject gas in a gravity-stable mode that depends on gravity segregation of distinct fluid densities, with the objective of creating a gas cap. In the process of gravity drainage, both oil and water are directed towards the lower section of the reservoir, where a series of horizontal wells are strategically placed above the oil–water contact (OWC) area to facilitate the production of oil. Beneath the oil–water contact (OWC) area and directly adjacent to the oil producers, horizontal wells are deployed for water disposal. These wells are hydraulically separated from the overlying oil zone using the same production casing. The aforementioned design strategy guarantees optimal oil recovery, minimal water content, reduced occurrences of water coning or cresting, and improved gas injectivity as a consequence of declining reservoir pressure caused by water drainage. It is important to note that several methodologies have been employed to address the issue of water coning, including the utilization of partial penetration and chemical injection procedures. Nevertheless, the effectiveness of these approaches is constrained due to the rapid development of the water cone over time [2].

The GDWS-AGD process is a hybrid of Gas-Assisted Gravity Drainage (GAGD) technology and Downhole Water Sink technology (DWS). The GAGD process was devised to exploit the naturally occurring separation of fluids with varying densities by creating a gravity-stable mode that depends on gravity segregation of distinct fluid densities and subsequently enhancing oil recovery [3]. The GAGD process involves the injection of gas into vertical wells in order to form a gas cap. This gas cap exploits the phenomenon of gravity segregation, causing oil and water to migrate downward towards the lower regions of the reservoir. Horizontal producers are strategically placed in this lower area to facilitate the drainage of oil and water. The GAGD process has demonstrated significant efficiency in enhancing oil recovery when compared to alternative technologies, such as continuous gas injection (CGI) and water-alternating-gas (WAG) processes [4]. In contrast to CGI, the use of the WAG process offers superior mobility control and enhanced efficiency in exploiting carbon dioxide (CO₂) resources [5]. The GAGD process has been implemented at the South Rumaila oil field to enhance oil recovery in the mainpay reservoir, as documented in field-scale evaluations [6]. Furthermore, the efficiency of the Gas-Assisted Gravity Drainage (GAGD) process has been examined in relation to the continuous gas injection (CGI) and water-alternating-gas (WAG) methods to assess the application of CO₂ floods in an immiscible manner. These evaluations were conducted specifically on the South Rumaila oil field, as documented by the reference provided [4]. Downhole Water Sink (DWS) technology has emerged as an up-and-coming method for enhancing oil recovery in reservoirs characterized by a tendency for high water coning. DWS consists of two separate zones of oil and water that are isolated by a packer. The upper section is designed for oil production and is located above the oil–water contact (OWC) area. The lower section is specifically designed for water drainage and is located within the water zone [7]. The water generated from the lower completion can either be brought to the surface or reinjected into a designated disposal area [8].

The optimization of oil recovery by gas-EOR flooding technologies retains great significance in the strategic planning of future field development. The optimization procedure involves adjusting the values of operational decision variables that govern the performance of reservoir flow. The operational decision variables refer to the constraints imposed on the injection and production wells, which directly impact the amount of fluid produced and injected into the reservoir. Optimal oil recovery relies heavily on the accurate identification and application of suitable operating variables. The Design of Experiments (DOE) is widely acknowledged as the primary optimization method used in reservoir engineering and enhanced oil recovery (EOR) processes [9,10]. The DoE principles provide a multiplicity of experiments or simulations (realizations) for a subject by combining several levels (values) for each parameter. The reservoir simulation is used to evaluate these realizations and compute the flow response factor. The statistical modeling incorporates the experiments and flow response components that were created to generate a relationship representing a proxy model [10]. Several DoE methodologies have been employed in several reservoir simulation studies for constructing proxy models. The prevalent Design of Experiments (DoE) methodologies include fractional factorial design [11], central composite (CC) designs [12,13], D-optimal design [14], Hammersley sequence sampling [15], and Latin Hypercube Design [10,16].

Developing a large and complicated reservoir flow simulation for assessing and improving CO₂-enhanced oil recovery, particularly in an actual oil field, is a costly and time-intensive action, particularly due to the requirement of executing numerous simulation scenarios during the optimization process. Thus, it is crucial to develop a simplified or reduced-order model, such as a metamodel or surrogate, as a substitute for complex flow simulation models. This reduced-order metamodel has the potential to deliver rapid and high-precision analysis of complex reservoir engineering problems. The potential drawbacks of these metamodels are associated with the precision of the methods employed to construct the proxy metamodels. Nevertheless, this issue has been resolved by employing powerful machine learning techniques that provide highly precise modeling and prediction, surpassing the results of complex models. More specifically, proxy modeling and Design of Experiments (DoE) are statistical techniques used to create a response surface methodology (RSM). The RSM serves as a simpler substitute or metamodel for complex models, allowing for the evaluation of multiple constructed experiments in the enhancement approach. This eliminates the need to evaluate the same simulator repeatedly [17]. The proxy model has been utilized in various reservoir studies and enhanced oil recovery (EOR) modeling applications, including in the optimization of the oil flow rate [18,19], waterflooding processes [20,21,22], gas flooding processes [23], steam injection [11,24,25,26], chemical flooding [14], foam flooding [27], and history matching [16,28,29]. Proxy models have been successfully utilized in reservoir studies, such as the application of a second-degree polynomial equation [24,30,31,32,33], Kriging algorithms [16,17,24,34], multivariate adaptive regression splines [35,36,37], response surface methodology [38,39], and artificial neural network algorithms [16,19,31,40].

This study examines the utilization of an immiscible CO₂ injection for the purpose of improving oil recovery and minimizing water content in the Gas and Downhole Water Sink–Assisted Gravity Drainage (GDWS-AGD) process. Carbon dioxide (CO₂) possesses several advantages in terms of its ability to decrease the surface tension of oil and water, enhance the mobility of oil, and consequently achieve high volumetric sweep efficiency and microscopic displacement. Additionally, CO₂ can also delay or reduce the tendency of CO₂ breakthrough in the production wells. In addition, it has been observed that carbon dioxide (CO₂) has the ability to decrease the viscosity of oil and induce oil swelling as a result of its solubility. This phenomenon facilitates the decomposition of heavy oil components, as documented by Mathiassen [41], Rao et al. [42]. Moreover, carbon dioxide (CO₂) exhibits greater suitability as a solvent compared to alternative solvents due to its economic feasibility in terms of sourcing from thermal power plants and refineries. The performance of the GDWS-AGD process was initially assessed by conducting compositional flow simulations for a 10-year prediction of future production. This evaluation sought to determine the method’s ability to enhance oil recovery, improve gas injectivity, reduce water cut, and mitigate cresting tendencies. Subsequently, the operational decision variables governing the production and injection operations were subjected to optimization using the Design of Experiments (DoE) and proxy metamodeling techniques. The objective was to ascertain the optimal flow response that would return the maximum oil recovery. The operating decision variables encompass several factors, such as the maximum injection rate and pressure in the injection wells, the maximum oil rate and minimum bottom hole pressure in the production wells, and the maximum water rates and minimum bottom hole pressure in the water sink wells. The Design of Experiments (DoE) methodology was utilized to create a sequence of computer simulations. These simulations were then evaluated using the compositional reservoir simulation technique to calculate the flow response of the reservoir. Subsequently, the entire dataset of the designed experiments and their associated flow responses was utilized to build the proxy model employing radial basis neural networks (RBF-NNs). The resulting proxy model serves as a simplified model (metamodel) alternative to the complex compositional flow simulation. The present study was conducted on the upper sandstone pay zone member (USM) of the Zubair formation, located within the South Rumaila oil field in southern Iraq. The USM reservoir has significant heterogeneity as a reservoir, with an extensive active edge-water aquifer in its vicinity. Based on the available information, it can be stated that the GDWS-AGD process represents a unique approach for enhanced oil recovery (EOR), exhibiting notable enhancements in oil production, the mitigation of water cut and water cresting, and improved gas injectivity. These improvements are particularly observed in reservoirs characterized by the presence of infinite active aquifers.

To the best of our knowledge, this research is the first to introduce the feasibility of the Gas and Downhole Water Sink–Assisted Gravity Draiange (GDWS-AGD) process to improve oil recovery and reduce water cut in reservoirs surrounded by strong aquifers. This paper also demonstrates the effectiveness of combining Design of Experiments and radial basis function neural networks (RBF-ANNs) to build a proxy model and rapidly optimize the Gas and Downhole Water Sink–Assisted Gravity Drainage (GDWS-AGD) process. The RBF-ANN approach has rarely been adopted in previous research for constructing proxy models, particularly for gas-EOR processes. The optimization is based on an extensive reservoir flow simulation of the heterogeneous upper sandstone reservoir in the South Rumaila oil field. Furthermore, the advanced DoE and RBF-NN-based proxy approaches can be utilized to rapidly assess and enhance other CO₂-EOR projects that have comparable reservoir characteristics. In addition, the resulting highly accurate proxy model can efficiently optimize CO₂ EOR in actual oil fields by rapidly executing hundreds or millions of specified simulations in a matter of seconds. Thus, in situations where there are insufficient data to construct simulation models, these precise proxy models can be effectively substituted for the computationally intensive compositional simulation used in other actual oil fields.

The complete assessment and optimization process can be concisely described by the subsequent stages, as illustrated in Figure 1:

• Develop a comprehensive and detailed compositional reservoir flow simulation to evaluate the reservoir production using the immiscible GDWS-AGD process for a prediction period of 10 years.
• The Design of Experiments–Latin Hypercube Sampling (DoE-LHS) approach was used to create many computer experiments (realizations) that were included in the compositional reservoir simulation to calculate the flow response factor, which is the recovery factor. More specifically, the DoE-LHS technique was employed to generate several simulation runs by varying the values of each controlling parameter on the gas injection, oil, and water production activities.
• The controlling parameters were adjusted systematically to minimize the number of simulation runs needed to obtain the optimal scenarios for implementing CO₂ injection.
• Subsequently, following the implementation of numerous simulation scenarios, the DoE-LHS method was integrated to produce a simplified surrogate approach (metamodel) as an alternative to the compositional reservoir model.
• The radial basis function neural networks (RBF-ANNs) were effectively utilized to construct a proxy model that acts as a computationally efficient alternative to the complex compositional reservoir simulation.

2. Gas and Downhole Water Sink–Assisted Gravity Drainage (GDWS-AGD) Process

The GDWS-AGD process has been hypothesized as a means to improve the recovery of oil in reservoirs that have strong water drive from aquifers. The main pay reservoir in the South Rumaila oil field is surrounded by strong edge and boundary aquifers. The reservoir initially consisted of 60 vertical wells, with 40 producers and 20 water injectors. The producers were primarily situated at the crest of the reservoir. However, the 20 injectors were specifically positioned on the eastern flank to maintain reservoir pressure due to the presence of a very active aquifer on the western flank. In the GAGD and GDWS-AGD processes, the existing wells have been closed, and new wells have been strategically positioned in areas with high permeability. These new wells are used for injecting gas and producing oil and water.

In the GDWS-AGD process, gas injection is implemented in immiscible mode and below the minimum miscibility pressure in the upper section of the reservoir of the South Rumaila oil field using vertical injectors in a gravity-stable mode. Due to the gravity segregation resulting from the different fluid densities in the reservoir conditions, the injected gas moves to the top of the reservoir to form a gas cap. This phenomenon should be providing a gravity-stable displacement that causes oil and water to drain down towards the bottom of the reservoir, where a series of horizontal wells are placed in the oil and water zones for simultaneous production. Specifically, oil and water are subsequently produced via a sequence of horizontal producers placed both above and below the oil–water contact (OWC) area inside the corresponding oil and water zones. In the GDWS-AGD process, the fluids’ gravity segregation and the oil drainage towards the bottom of the payzone lead to better sweep efficiency and higher oil recovery.

All the characteristics of these horizontal wells, including their position, length, and diameter, are identical. In order to mitigate the occurrence of water cresting and coning, it is advisable to produce water through horizontal wells that are precisely placed beneath the oil–water contact area and situated below the oil producers. Two 7-inch production casing strings are fitted in a bilateral manner and are furnished with two 2-3/8 inch horizontal tubings. These tubings are effectively segregated from one another within the well through the use of a packer. The concept of the GDWS-AGD process is illustrated in Figure 2, which attempts to facilitate effective global water drainage in order to regulate the proliferation of water cresting. Localized drainage refers to the phenomenon where oil and water are created by vertical DWS wells [7].

3. Compositional Reservoir Simulation of the GDWS-AGD Process

The reservoir in the South Rumaila oil field in the USM has three distinct lithotypes, namely sand, shaly sand, and shale, each characterized by unique spatial permeability distributions. The construction of a fine-scale geostatistical reservoir model was carried out to facilitate lithological and petrophysical modeling. Multiple-point geostatistics and sequential Gaussian simulation techniques were employed for this purpose. The fine-scale geomodel consists of around 2 million grid cells, with each cell measuring 50 m × 50 m. The grid is defined by the cell numbers 210, 202, and 45 in the I, J, and K directions, respectively. The reconstruction of the fine-scale geomodel was undertaken with the objective of preserving the variability of the reservoir, facilitating efficient history matching, and obtaining a realistic prediction of the future performance of the GDWS-AGD process. The high-resolution geomodel was subsequently transformed into a grid system with regular grid cells of 150 m × 150 m in order to decrease computational requirements during the compositional reservoir flow simulation (CMG-GEM) [43]. The upscaled model consists of a total of 54,648 grid cells, with 69 grid cells in the I direction, 66 grid cells in the J direction, and 12 grid cells in the K direction. The 3D coarse-scale reservoir models depicted in Figure 3 showcase the incorporation of 3D spatial variations in lithofacies, porosity, and horizontal and vertical permeability. More specifically, Figure 3 provides insights about the highly permeable zones that the vertical gas injectors along with the horizontal oil and water producers should be placed in. The highly permeable zones are represented by the yellow and orange colors in the top-left figure, which represent sand and shaly sand regions. These regions correspond to the highly porous and permeable regions in the reservoir, as depicted in the other three subfigures.

As shown in Figure 3, the USM reservoir consists of three primary lithotypes or rock types that control the movement of fluids in porous media throughout the entire reservoir. Considering the significant impact of oil’s relative permeability on the gravity-drainage process [44], it is essential to include three distinct relative permeability and capillary curves in the reservoir simulation model to precisely quantify fluid movement in multiphase flow and to rapidly achieve history matching. These curves should be based on the permeability ranges of the three lithotypes: sand, shaly sand, and shale. Figure 4 illustrates these lithotypes.

In order to verify the accuracy of the reservoir model in assessing fluid flow through porous medium and to obtain reliable predictions of future reservoir performance, history matching was successfully accomplished considering the upscaling of geostatistical reservoir models, focusing on the cumulative field production rates of oil and water injection. The correlation between the production and injection history serves as a reliable predictor of reservoir and fluid behavior, as it accurately replicates the alignment of water cut and saturation distributions. The accessibility of the production and injection flow rates was available until February 2010. The process of history matching was successfully conducted between the years 1954 and 2010. The matching between the field production rates and the cumulative oil output is depicted in Figure 5. Figure 6 illustrates the matching between the production rates and cumulative oil for a sample of four wells. The matching between the field injection rates and the cumulative water injection is illustrated in Figure 7. Figure 8 depicts the matching between the injection rates and cumulative water for a sample of four wells.

To comprehensively assess the future performance of the GDWS-AGD process, a satisfactory match was successfully conducted between the observed and calculated cumulatives and rates of oil production for the entire field and individual wells, as depicted in Figure 8. Nevertheless, there was a discrepancy between the observed and predicted injection rates at certain intervals, resulting in improper matching due to imprecise recorded rate data in specific injection wells, as depicted in Figure 8.

Figure 7 and Figure 8 illustrate a discrepancy between the actual field data of water injection rates and the cumulative values at specific intervals, resulting from inconsistencies in certain injection wells. The main reason for this difference is the inaccurate quantification of water injection rates in certain wells, which results from the utilization of substandard measurement instruments. This resulted in inaccuracies in the recorded cumulative water injection data.

The Equation of State (EOS)-compositional reservoir simulation model was then adopted to predict future reservoir performance through the GDWS-AGD process over a 10-year prediction period. The compositional simulation is essential to model the fluid flow and track the chemical interaction in terms of the components of injected solvents and reservoir fluids. Consequently, a comprehensive PVT model was constructed to accurately measure the interplay between the primary components of the oil phase and the secondary component of the injection solvent. More precisely, the fluids were classified according to their components in order to deal with the compositional interaction within the reservoir. The main constituents consisted of carbon dioxide (CO₂), nitrogen (N2), methane (C1), ethane (C2), n-butane (NC4), isopentane (IC5), hexane (C6), and heptane and higher hydrocarbons (C7+).

In accordance with the GDWS-AGD process, a total of twenty vertical injectors were deployed for CO₂ injection, while eleven horizontal producers were utilized for oil production. Additionally, six water sinkers were strategically placed within the highly permeable zones to facilitate Downhole Water Sinks. Specifically, carbon dioxide (CO₂) was injected into the uppermost two layers of the reservoir in order to create a gas cap. The subsequent three layers were intentionally maintained as a transition zone, with the purpose of establishing a fluid column that was stable under the influence of gravity. The oil horizontal producers were placed in the sixth, seventh, and eighth layers, while the six water sinkers were located in the twelve layer, which was completely saturated with water from the unlimited edge-water aquifer. The six water sink wells were positioned precisely beneath the six horizontally aligned oil wells. The horizontal producers for oil and water have a length ranging from 2000 to 3000 m, extending in the J-direction of the reservoir. Figure 9 and Figure 10 depict the spatial distribution of CO₂ injection locations, as well as the locations of oil and water production wells. The reservoir body shown in Figure 9 is represented with a red color, referring to the shale zone. However, the perforations of producers and injectors were mainly located in sand zones (referred to as index 2) and shaly sand zones (referred to as index 1) that have high permeability ranges. To provide more explanation, Figure 10 depicts the precise positions of the horizontal well trajectories for oil and water within the oil and water zones in the 3D slab permeability map. The Carter-Tracy method was employed to model the edge aquifer of the infinite water drive, which is situated along the eastern and western margins and bottom of the reservoir. This method was selected rather than the van Everdingen and Hurst technique because it assumes constant water influx rates over time, and this takes place in infinite active aquifers [45].

It is important to note that the reservoir simulation configuration of the GAGD process closely resembles that of the GDWS-AGD process, except for the removal of the six horizontal water sinks. Furthermore, these processes maintain identical values for the operational decision variables that govern the injection and production operations.

In order to showcase a full evaluation of the GDWS-AGD process in comparison to the GAGD process, two distinct scenarios were simulated to determine the reservoir flow response, namely the oil recovery factor, during a 10-year period from 2016 to 2026. It should be noted that the history matching process was performed to align the production history from 1954 to 2010, taking into account the availability of observed oil production and water injection rates. This period encompassed both the primary and secondary recovery stages, which involved the injection of water. During the period between 2010 and 2016, we operated the reservoir under the same conditions as the secondary recovery phase that occurred before 2010. Hence, the forecast is for a decade-long projection period from 2016 to 2026 for the evaluation and optimization of the GDWS-AGD process.

The two scenarios of the GAGD process and the GDWS-AGD process (Base Case) were set to have similar configurations for the operational decision variables (well constraints) that govern the injection and production activities. The values of the operational decision variables obtained from the GAGD and GDWS-AGD (Base Case) processes are presented in

Table 1. Operational decision factors of the GAGD and GDWS-AGD (Base Case) processes.

Response	GAGD	GDWS-AGD (Base Case)
Oil Recovery	71.6744%	76.3675%
Parameters
MAXSTO, STB/DAY	500,000	500,000
MINBHP, PSI	2000	2660
MAXBHG, SCF/DAY	5,000,000	5,000,000
MAXBHP, PSI	3200	4000
MAXSTW, STB/DAY $f{t}^3/DAY$		400,000
MINBHPw, PSI		1000

. Figure 11 presents a comparison of the GAGD and GDWS-AGD (Base Case) processes in relation to the field oil recovery factor and average reservoir pressure. It can be noticed from Table 1 and Figure 11 that the GDWS-AGD (Base Case) process led to a recovery factor of 76.3675%, higher than the GAGD process of 71.6744%, both at the end of the 10-year prediction period. Additionally, the GDWS-AGD scenario resulted in a notable decrease in the average reservoir pressure when compared to the GAGD process, as depicted in Figure 11. In addition, the comparison between the GAGD and GDWS-AGD processes was further evaluated based on the field oil rates and cumulative oil production by the end of the prediction period, as depicted in Figure 12. The reduction in reservoir pressure has the advantage of improving gas injectivity by reducing the need for a high injection pressure and facilitating the injection of large amounts of gas.

Figure 12 clearly illustrates that the cumulative oil production in the GDWS-AGD process outperforms that of the GAGD process by the end of the 10-year prediction period. The field cumulative oil production at the end of the prediction period through the GAGD and GDWS-AGD processes was 4.3887E09 STB and 4.6635E09 STB, respectively, with 275 million more STB in the GDWS-AGD process than the GAGD process. Specifically, the quantity of oil produced by the GAGD process within a 10-year prediction may be achieved in around 1.5 years using the GDWS-AGD process. This demonstrates the effectiveness of the GDWS-AGD technique in significantly enhancing oil recovery. Along with improving oil recovery, the GDWS-AGD process also effectively minimizes water cut to nearly significant low levels and mitigates water cresting tendencies.

Figure 13 presents the water cut levels in the six horizontal water sink wells over a 10-year period in the GDWS-AGD process. Based on Figure 13, significant amounts of water were produced from the six Downhole Water Sink wells, which were placed exactly below horizontal oil wells in the bottom layer (the twelve layer). The water sink reduced the tendency of water cresting from the bottom water zone and then significantly reduced the water cut. This can also be noticed from the 2D water saturation map of the sixth, seventh, and eighth layers, where the 11 horizontal oil producers were placed. The water saturation was reduced to less than 0.1 in the well regions through the GDWS-AGD process. However, the same three layers had high levels of water saturation in the GAGD process at the end of the pedicition period, which reached 0.8, as depicted in Figure 14.

In the context of discussing the oscillations observed in the simulation runs, especially Figure 12 and Figure 13, this phenomenon primarily occurs in the compositional reservoir simulation modeling of CMG-GEM due to numerical instabilities, particularly when well limitations are specified for minimal bottom hole pressure and maximum oil rate. While the simulation was in progress, it was seen that the failure to converge resulted in this oscillation. CMG has addressed this issue in the latest iterations of their software, including version 2021. Although it is theoretically achievable to mitigate these oscillations by substantially reducing the timestep and grid size [46], this cannot be achieved due to the constraints of the computer processor. To be more precise, the current model comprises a substantial quantity of grid blocks, amounting to a total of 55,000. Consequently, each iteration of the model presently necessitates over 10 h to conclude. Liu et al. [47] conducted a thorough investigation of this issue in CMG reservoir modeling. They presented numerous case studies demonstrating that the relative error caused by oscillation is consistently around 0.05%, making it insignificant.

Given the large difference between cumulative oil productions between the two processes, which reached 275 MMSTB with a difference in recovery factor (approximately 4.7%), one can expect the net present value (NPV) obtained by the GDWS-AGD process to be higher than that by the GAGD process because the main extra expenses in the GDWS-AGD process are related to drilling the six Downhole Water Sink wells and injecting larger amounts of gas. Therefore, the NPV value was calculated for the two processes given various oil prices (USD 10–100). The decision parameters in the NPV formula through the two processes represent field output parameters, which include cumulative oil, water, and gas production and cumulative gas injection, all at the end of the 10-year prediction period. In the NPV calculation, revenues are obtained from oil and gas sales, and expenses are concluded from capital expenditures (CAPEX), operational expenses (OPEX), water handling, and injection costs [48,49]. The interest rate is also incorporated to estimate the discounted factor. The adopted NPV formula is formulated in Equation (1):

$$\begin{array}{c}\hfill NPV={\displaystyle \sum _t}\frac{OilProd. \times {\$}_o + GasProd. \times {\$}_g - WaterProd. \times {\$}_{whc} - GasInj. \times {\$}_{gic} - OPEX}{{(1 + i)}^t}-CAPEX\end{array}$$

(1)

where the variables are as follows:

• NPV: net present value, USD.
• Oil price (${\$}_o$): USD per STB.
• Gas price (${\$}_g$): USD 3.0 per MSCf.
• Water handling cost (${\$}_{whc}$): USD 1 per STB.
• Gas injection cost (${\$}_{gic}$): USD 2.15 per MSCF.
• OPEX: the operational expenditures (USD 1.25–1.5/STB of oil), which include staff salaries, daily energy requirements, fuel and transportation, well workover, maintenance, and other facility improvements.
• CAPEX: the capital expenditures for drilling, completion, cementing, perforation, stimulation, and rig movement. In this paper, the CAPEX was set based on the costs of drilling vertical and horizontal wells in addition to the surface facilities for gas injection. According to the current average cost ranges in the Rumaila field, the drilling cost of one vertical well is USD 5 million, and for a horizontal well, it is USD 10 million. There was USD 35 million for the gas injection facilities.
• i: the interest rate.

In this research, the NPV was considered to further demonstrate the feasibility of the GDWS-AGD process (Base Case) in comparison with the GAGD process. The two processes were economically evaluated by calculating the NPV given a range of oil prices from 10–100/STB of oil, as depicted in Figure 15.

It can be identified from Figure 15 that the GDWS-AGD process outperforms the GAGD process by achieving a higher NPV along the different oil prices (USD 10–USD 100 per STB of oil). However, the GAGD process was not economically feasible when the oil price became lower than USD 10 per STB of oil.

4. Recovery Optimization of the GDWS-AGD Process

Design of Experiments (DoE) and proxy metamodeling techniques were employed to optimize the performance of the GDWS-AGD process. This was achieved by modifying the operational decision factors that govern the gas injection as well as the production of oil and water. Specifically, the optimum design for the GDWS-AGD process was determined by manipulating the controllable operational decision parameters, including the maximum oil rate, maximum injection pressure, and bottom hole pressure. Unlike sensitivity analysis, which identifies the most relevant uncontrolled characteristics affecting reservoir flow performance, such as permeability and porosity, this is a distinct process. Permeability is fundamentally more influential than porosity because it influences the flow of fluids through porous media according to Darcy’s law. In a previous study, we analyzed how permeability and porosity affect the effectiveness of the GAGD process. Our findings showed that permeability has a stronger impact compared to porosity [50].

The Latin Hypercube Sampling (LHS) methodology was employed as a Design of Experiments (DoE) technique, while the radial basis function neural networks (RBF-ANNs) were selected as the modeling strategy for constructing the proxy model. The Design of Experiments (DoE) is an initial step in solving the optimization problem. It involves creating multiple experiments or simulation runs for the reservoir simulation model. These experiments are used to evaluate the model. Subsequently, the RBFNN is employed as a simplified proxy model to replace the complex reservoir simulation. This allows for quick evaluation and optimization of recovery predictions.

4.1. Optimization Approaches

The Design of Experiments (DoE) is a methodical statistical technique that facilitates the creation of a well-structured series of experiments in order to ascertain the parameters that exert the greatest influence on the response variable, hence enabling sensitivity analysis. Moreover, Design of Experiments (DoE) is employed in the fields of optimization and uncertainty assessment to determine the most probable scenario that delivers the ideal solution through a systematic procedure, as well as to quantify the analysis of risk [51,52]. Given its advantages in terms of speed, cost, and flexibility compared to physical or lab experiments, it is imperative to obtain the most precise model that accurately replicates the physical model or process. In order to accomplish this objective, it is vital to conduct a thorough analysis of the necessary parameters and interactions. This analysis is crucial for ensuring the accuracy and dependability of both the application and interpretation of the results [33].

The present work employed Latin Hypercube Sampling (LHS) as a space-filling Design of Experiments (DoE) and sampling technique that divides the range of possible values into equally sized intervals, reducing the number of experiments or simulations needed to measure uncertainty in responses [53,54]. More specifically, the LHS technique is employed to generate experiments for a given number of parameters that are effective in thoroughly analyzing a physical process, which lacks a precise technique [55,56]. This method also ensures a regular dispersion of points by maximizing the distance between each point and all other points, as in Stocki [57]. Using Latin Hypercube Sampling techniques and considering the limitations of the computer, we conducted 100 experiments. These experiments involved mixing the values of six operational decision variables at the beginning of the prediction period. As a result, we performed 100 compositional simulation runs to calculate the field oil recovery factor at the end of the 10-year prediction period. The compositional flow model was then utilized to evaluate the performance of these designed experiments and predict the reservoir’s flow response, namely the oil recovery factor. The generated datasets and the corresponding flow response factor were then used to determine the most effective solution and subsequently create the proxy model. The proxy metamodel provides results that are equivalent to those obtained by the complex model but with significantly reduced computational time, often in the range of a few seconds for millions of iterations. However, the complex model necessitates a substantial duration, which generally extends over several days, to provide the results of a limited number of iterations. The proxy model is obtained by completing a regression analysis on the experimental data of operational decision variables and their related flow response, as shown in the following equation:

$$y=f(X_1,X_2,...,X_k)+{ϵ}_i$$

(2)

where $X_1,X_2,...,X_k$ are the input parameters, and y is the expected response factor.

This study utilized radial basis function neural networks (RBF-ANNs) as a proficient method of supervised machine learning to construct a proxy model, which serves as a viable substitute for compositional reservoir flow simulation [58]. The radial basis function-neural network (RBF-NN) is an effective approach for accurately representing the complex nonlinear interactions between the input variables and the corresponding response factor [59]. The weights of the RBF-NN function are calculated during the training process, and the network variables are tuned to match the network’s outputs with the specified inputs. A cost function, usually the mean square error, is employed to evaluate the accuracy of the fit. Following the completion of the training procedure, the created RBF-NN model can be applied to test data that were not included during the training phase [58]. The RBF-NN consists of three layers: the input layer, the hidden layer, and the output layer. Every node, or neuron, serves as a nonlinear activation function and utilizes a radial basis function (RBF) in the hidden layer. The input layer consists of an input vector that undergoes a nonlinear transformation in the hidden layer, which is constructed of radial basis functions (RBFs). The net input for the radial basis function (RBF) activation function is calculated by taking the vector distance between the weight vector and the input vector and then multiplying it by the corresponding bias value. The output layer, which is a linear combiner, transforms the nonlinearity into a different space. By incorporating an extra neuron into the hidden layer, it is possible to accurately represent the biases of the neurons in the output layer. The RBF can utilize the linear optimization method to obtain a globally optimal solution for adjusting the weights in the minimum mean squared error (MSE) context [60].

In addition to constructing the proxy model, the other objective is to determine the key factors that have a significant impact on the reservoir flow performance during the GDWS-AGD process. This was achieved through the application of Sobol analysis and the examination of response–parameter cross-plots. More specifically, Sobol analysis is used to identify the most influential parameters affecting the proxy predictive modeling of the GDWS-AGD process. The evaluation of the correctness of the proxy model involved the calculation of the discrepancy between the flow response obtained from the proxy model and the flow response obtained from the simulator. The discrepancy was measured by calculating the adjusted R-squared ($Adj.R^2$). $Adj.R^2$ is a variant of the R-squared statistic that accounts for the number of predictors (parameters) included in a model. It quantifies the proportion of variance in the dependent variable that can be explained by the model, taking into consideration the complexity of the model [36].

$$adj.R^2=1-\frac{(1-R^2)(n-1)}{n-k-1}$$

(3)

where n is the number of experiments, and k is the number of predictors (operational decision variables).

4.2. GDWS-AGD Process Optimization

The GDWS-AGD process (Base Case) was established as a foundation for the subsequent scenarios involving more advanced parameter levels in the optimization step. The GDWS-AGD process optimization was accomplished by systemically changing the values of the operational decision variables in order to attain the optimal solution based on the optimal values of these variables. These parameters include the maximum injection rate and pressure applied to the injection wells, the maximum oil rate and minimum bottom hole pressure in the production wells, and the maximum water rates and minimum bottom hole pressure in the water sink wells.

Table 2. Levels of the GDWS-AGD recovery optimization’s parameters.

Parameters	Min	Base Case	Max
MAXSTO, STB/DAY	300,000	500,000	700,000
MINBHP, PSI	2000	2660	3000
MAXBHG, SCF/DAY	2,000,000	5,000,000	8,000,000
MAXBHP, PSI	3000	4000	5000
MAXSTW, STB/DAY	25,000	400,000	700,000
MINBHPw, PSI	250	1000	2000

depicts the levels (values) of the operational variables in the Base Case GDWS-AGD process and the ranges of each parameter (lowest and maximum levels) throughout the optimization process. The Design of Experiments (DoE)–Latin Hypercube Sampling (LHS) method was employed to combine the levels (values) of each parameter presented in Table 2. Specifically, the values of each parameter were adjusted systematically and mixed with other variables’ levels to minimize the number of simulation runs needed to obtain the optimal scenarios for implementing CO₂ injection. Then, multiple simulation runs were evaluated using the compositional reservoir simulator to calculate the oil recovery factor at the end of a 10-year prediction period. Then, following the implementation of numerous simulation scenarios, the DoE-LHS method was integrated to produce a simplified surrogate approach (metamodel) as an alternative to the compositional reservoir model using radial basis function neural network (RBF-ANN) machine learning.

The term “optimal solution” pertains to the simulation job that achieves the highest oil recovery factor after a 10-year prediction period, as depicted in Figure 16. This figure also showcases the oil recovery factor for the advanced GDWS-AGD case and the general solutions that represent suboptimal scenarios. The general solutions seen in Figure 16, denoted by the green curves, pertain to the minimum flow response achieved by utilizing suboptimal combinations of parameter levels. Figure 17 provides an additional illustration of the progress of the LHS-based optimization technique. Specifically, it shows how frequently the oil recovery factor was obtained as a function of the 100 simulation runs by illustrating the frequency percentage.

Table 3. Levels of the GDWS-AGD recovery optimization’s parameters.

Response	Base Case	Optimal
Recovery factor	76.3675%	78.120033%
Parameters	Advanced Case	Optimal
MAXSTO, STB/DAY	500,000	580,000
MINBHP, Psia	2660	2000
MAXBHG, SCF/DAY	5,000,000	2,600,000
MAXBHP, Psia	4000	4800
MAXSTW, STB/DAY	400,000	92,500
MINBHPw, Psia	1000	1650

depicts the levels of the operational variables in the advanced and optimal GDWS-AGD scenarios, together with their corresponding oil recovery factor. These values were calculated after a 10-year prediction period.

The oil recovery achieved by the conclusion of the prediction period using the advanced case GDWS-AGD method amounted to 76.3675%. However, by utilizing LHS-based proxy optimization, the ideal solution was determined, resulting in an enhanced recovery rate of 78.120033%. This improvement is visually depicted in Figure 18.

Following the acquisition of the reservoir flow response that best represents the maximum oil recovery after a 10-year prediction period, the RBF neural networks were developed using the aforementioned six variables and the computed flow response. The objective was to identify the parameter(s) with the greatest influence on flow performance through the GDWS-AGD process. Initially, the validation of the proxy model was conducted by quantifying the discrepancy between the oil recovery obtained from the simulator and the proxy model, as depicted in Figure 19.

The Sobol analysis and response–parameter cross-plots were utilized in order to determine the parameter(s) that had the greatest impact on the flow performance in the GDWS-AGD process. The Sobol analysis method is a variance-based sensitivity analysis that is employed to assess the influence of individual input variables on the variance of the output model [61]. More specifically, the Sobol analysis method utilizes variance decomposition techniques to quantitatively assess the contributions of the input variables to the variance in the output. In other words, Sobol sensitivity analysis quantifies the extent to which the variability in the model output is influenced by each individual input parameter [61]. In this research, the Sobol sensitivity analysis was used to identify the most influential variables affecting the proxy predictive modeling of the GDWS-AGD process. The parameter that delivers the greatest influence, as determined by the Sobol analysis, is the maximum bottom hole injection pressure in the gas injectors. The other influential criteria, in descending order, include the minimum bottom hole pressure, the maximum oil rate in oil producers, the minimum bottom hole pressure in water producers, and the maximum bottom hole gas injection rate. The field oil recovery was not significantly affected by the maximum water sink rate. The influence of various factors on oil recovery in the GDWS-AGD process was analyzed using the Sobol analysis, as depicted in Figure 20.

The Sobol analysis reveals that the performance of the GDWS-AGD process is most significantly influenced by the maximum bottom hole injection pressure in the gas injectors. It has a substantial impact compared to other factors because it can effectively manage the amount of gas injected into the reservoir, greatly increase the reservoir pressure, and consequently regulate other variables, such as the minimum bottom hole flowing pressure and the rates of oil and water production in the wells. Consequently, the impact of other factors relies on alterations in the bottom hole gas injection pressure. Moreover, pressure is a crucial factor that decides whether gas injection is immiscible or miscible. This determination is based on whether the pressure is below or over the minimum miscibility pressure. Furthermore, the injection pressure has a direct influence on several properties of the reservoir fluids, such as the oil viscosity, solution gas–oil ratio, oil formation volume factor, interfacial tension, gas solubility, oil swelling, and mobility ratio [62,63]. Hence, it regulates the complete fluid movement within the reservoir. This research is the first extensive study on optimizing the GDWS-AGD process in the existing literature, as far as we know.

The impact of individual operational decision variables on field oil recovery can be determined through the use of parameter–oil recovery cross-plots, as depicted in Figure 21. This figure also illustrates the optimum setting of each parameter that resulted in the attainment of the highest oil recovery. It is seen in Figure 21 that the attainment of the global optimal oil recovery is not achieved by maximizing each individual parameter, as the proposed experiments combined the effects of the six variables to obtain the optimal oil recovery. The recovery increases and the design process in the gas injection wells appears to be mostly influenced by the parameter of maximum bottom hole injection pressure parameter, as indicated by Figure 20 and Figure 21.

Figure 21 depicts the optimal level (represented by a red dot) of each operational decision parameter that results in the highest oil recovery, as compared to the Base Case (shown as a black dot). The objective function is defined as the maximum field oil recovery (OilR). We next utilized the RBF-NN method to fit the DoE-based planned simulations (experiments) to the calculated objective function. The optimum level of each of the six operational decision parameters was determined by a single experiment that achieved the maximum oil recovery. This process offers a comprehensive understanding of how each parameter’s value (whether it is at its minimum, such as maximum BHG, or at its maximum, such as maximum BHP) contributes to achieving the highest possible oil recovery. Furthermore, it was determined that the most efficient oil recovery on a worldwide scale is attained by maximizing all six factors. Each parameter has a varying impact on the performance of the GDWS-AGD process.

5. Summary and Conclusions

The present study involved the evaluation, development, and optimization of a novel process that utilizes gravity drainage-based gas injection and a Downhole Water Sink. The objective of this process is to improve oil recovery while simultaneously reducing the water cut in reservoirs that are characterized by the presence of strong edge and/or bottom water aquifers. This study involved the utilization of a compositional reservoir simulator to undertake a simulation of the Gas and Downhole Water Sink–Assisted Gravity Drainage (GDWS-AGD) process in the heterogeneous upper sandstone area of the South Rumaila oil field. Once satisfactory history matching was achieved, the performance of the GDWS-AGD process was evaluated for a 10-year future production period. Consequently, a total of 20 carbon dioxide injectors, 11 oil producers, and 6 water sinkers were implemented in order to simulate the GDWS-AGD procedure. This study examined the evaluation of the GDWS-AGD process in comparison to the GAGD process by the end of a 10-year prediction period. The two scenarios of the GAGD and GDWS-AGD processes have similar settings for the operational decision variables that control the injection and production activities. It was concluded that the GDWS-AGD process outperforms the GAGD process by achieving a much higher cumulative oil production and field recovery factor than the GAGD process. Specifically, the field cumulative oil production obtained by the GAGD and GDWS-AGD processes was 4.3887E09 STB and 4.6635E09 STB, respectively, with 275 million more STB in the GDWS-AGD process than the GAGD process. More specifically, the quantity of oil produced by the GAGD process within a 10-year prediction may be achieved in around 1.5 years using the GDWS-AGD process. Additionally, the GDWS-AGD process led to a recovery factor of 76.3675%, higher than the GAGD process of 71.6744%, with an increase of approximately 4.7%.

Furthermore, significant amounts of water were produced from the six Downhole Water Sink wells in the GDWS-AGD process. The water sink reduced the tendency of water cresting from the bottom water zone and then significantly reduced the water cut in the oil producers. This was noticed in the water saturation distribution, which was reduced to less than 0.1 in the oil well layers through the GDWS-AGD process. However, the same layers had high levels of water saturation in the GAGD process at the end of the prediction period, which reached 0.8. This demonstrates the effectiveness of the GDWS-AGD technique in significantly enhancing oil recovery and mitigating water cresting tendencies.

For further evaluating the comparison between the GAGD and GDWS-AGD processes, an economic analysis was conducted by calculating the net present value (NPV) given various oil prices (USD 10–100). The decision variables in the NPV formula through the two processes represent field output parameters, which include cumulative oil, water, and gas production and cumulative gas injection, all at the end of the 10-year prediction period. In the NPV calculation, it was identified that the GDWS-AGD process outperforms the GAGD process by achieving a higher NPV along the different oil prices (USD 10–USD 100 per STB of oil). However, the GAGD process was not economically feasible when the oil price became lower than USD 10 per STB of oil.

In the GDWS-AGD process, this research also involved investigating the optimal setting of the operational decision variables, which control the injection and production activities, to attain optimal oil recovery within a 10-year prediction period. Design of Experiments–Latin Hypercube Sampling (DoE-LHS) was employed as a systematic strategy to create a set of experiments that were subsequently evaluated by the compositonal reservoir simulator to determine the optimal oil recovery and to construct the proxy model. In addition, the optimal setting of the operational decision variables resulted in a higher oil recovery rate compared to the Base Case setting. Specifically, the optimal GDWS-AGD process led to a substantial improvement in oil recovery of 78.12%.

Additionally, the proxy model analysis revealed that the maximum bottom hole injection pressure is the parameter with the highest influence on the performance of the GDWS-AGD process. This is because the injection pressure not only governs the quantity of gas injected but also affects the overall reservoir pressure. Furthermore, the attainment of the most favorable oil recovery was observed when the maximum bottom hole injection pressure, maximum oil rate, and minimum bottom hole pressure were at their highest levels in sink wells, while the maximum bottom hole injection pressure, maximum water sink rate, and minimum bottom hole pressure were at their lowest levels in oil wells. The occurrence of water cut and coning (cresting) has experienced a notable decrease, as evidenced by the evaluation of the GDWS-AGD procedure. This finding illustrates the efficacy of the GDWS-AGD process in augmenting oil recovery and mitigating water production in reservoirs characterized by strong aquifers.