A Comprehensive Summary of the Application of Machine Learning Techniques for CO₂-EOR Projects

1. Introduction

Petroleum resources have been deemed as the principal source of fossil-fuel-based energy to meet the world’s energy demands since the early 20^th century. The importance of enhancing oil reservoir extraction efficiency has grown due to the restricted supply of reserves. Over two-thirds of the original oil in place (OOIP) remains trapped after primary and secondary recovery processes. Besides, extracting the remaining oil from mature reservoirs in complicated geological formations is more challenging. EOR methods are initiated to recover the remaining oil from reservoirs after both primary and secondary recovery methods are exhausted. Surfactant flooding, chemical flooding, polymer flooding, steam stimulation, microbial flooding, gas injection, and so forth (Green & Willhite, 1998; Yang et al., 2018) are the common EOR approaches. Carbon dioxide (CO₂) is very successful since it increases oil production by increasing mobility and reducing oil viscosity and saturation, which works well with both conventional and some unconventional formations. CO₂-EOR is one of the popular techniques, occupying around 20% of 1120 worldwide EOR projects (Figure 1). It may recover 15% to 25% of the OOIP of light or medium oil fields that are close to depletion due to flooding (Yongmao et al., 2004).

The utilization of CO₂ in EOR can significantly improve oil recovery; at the same time, it plays an essential role in environmental preservation. The importance of CO₂-EOR as part of carbon capture, use, and storage (CCUS) schemes becomes more vital as the petroleum industry works toward decarbonization to mitigate green house gas emissions. If reinjection is not considered, approximately 60% of injected CO₂ can be trapped in the reservoir at the CO₂ breakthrough (Gozalpour et al., 2005). This approach, efficiently utilizing CO₂ in oil recovery, aligns with an environmentally friendly protocol while simultaneously enhancing resource efficiency and contributing substantially to sustainability goals (Hasan et al., 2015).

Machine learning (ML) approaches have drawn considerable interest as emerging technologies in the oil and gas industry over the past 20 years. Applying the ML approaches to examine issues in the oilfield development process has acquired new life with the advent of intelligent oilfields and big data technology. Indeed, ML shows the feasibility of offering a more straightforward and quicker method than rigorous and numerous simulations or experiments. Many ML correlations have emerged with the development of computer tools, particularly in reservoir characterization, CO₂ storage, production, and drilling operations (Ghoraishy et al., 2008; Liu et al., 2023; Nait Amar & Zeraibi, 2020; You & Lee, 2022).

Many literature reviews have been conducted in the past to summarize the application of ML in the oil and gas industry (Ng et al., 2023). However, no study on global research trends analyzed the dominant input parameters and evaluated the research work on CO₂-EOR projects. The evaluations could help researchers get a preliminary idea about the current research trend on CO₂-EOR and whether their recent research impacts a particular field. Furthermore, few studies have systematically summarized and examined all the literature on ML for CO₂-EOR. Few reviews find the most critical topics, objectives, input parameters, evaluations, and research gaps in ML for CO₂-EOR. This study aims to offer insight into current trends and technological development indicators, which will help identify the viewpoint for the following research areas and prospects. Thus, data extraction analysis was carried out to ascertain the research advancement and trends in ML for CO₂-EOR, whereby a systematic review accomplishes the closure of research gaps on this subject.

This paper aims to summarize and evaluate the various ML models in CO₂-EOR and provide insightful analysis with 101 papers reviewed. The rest of the paper is organized as follows: Section 2 describes the mechanisms and processes of CO₂-EOR. Section 3 briefs the most popular ML and optimization methods employed in the literature. Section 4 summarizes the work that applied ML in the CO₂-EOR process, including MMP prediction, WAG, well placement optimization, oil production or recovery factor prediction, multiple objectives optimization, PVT properties estimation, and CO₂-foam. Section 5 outlines the benefits and limitations of the application of ML in the CO₂-EOR process before ending this survey paper with concluding remarks.

2. Mechanisms and process of CO₂-EOR

CO₂ is generally injected into the reservoir under the following conditions: (a) miscible injection; (b) immiscible front displacement after water flooding; (c) water alternating gas (WAG) displacement; and (d) CO₂ dissolved in brine flooding, also referred to as carbonated water injection (CWI) (Kumar et al., 2022). Miscible displacement has been successful over the years. It occurs at pressures above a minimum miscible pressure (MMP) of the oil, where the injected gas and the hydrocarbons are entirely miscible and form a single-phase fluid. The main advantages of miscible displacement are that it can promote oil swelling, reduce fluid viscosity, increase mobility, reduce remaining oil saturation, and improve oil production.

CO₂ has been historically favored over other gases due to its low MMP. Furthermore, CO₂ gas injection can potentially mitigate greenhouse gas emissions while improving oil recovery. CO₂ miscible flooding, whether initiated upon first contact or multiple contacts, the remaining oil and CO₂ become miscible, resulting in near zero interfacial tension (IFT), no capillary pressure, and improved volumetric sweep (Ev) and displacement efficiency (Ed) (Satter & Thakur, 1994). Conversely, in the case of CO₂ immiscible flooding, the IFT is not near zero, maintaining the capillary pressure and causing some residual oil saturation. The oil recovery efficacy is contingent upon the efficiency of fluid displacement, volumetric sweep, and CO₂ solubility in the oleic phase, consequently increasing oil mobility. These characteristics are influenced by various factors, including gravity, rock wettability, reservoir heterogeneity, crude oil phase behavior, and phenomena such as viscous fingering, etc. (Yang & Li, 2020; Kumar et al., 2022).

3. Summary of machine learning approaches

Machine learning (ML) involves the development of computational models and algorithms capable of learning patterns and making data-driven predictions or decisions without being explicitly programmed. ML algorithms employ data to automatically identify and generalize patterns, which may be applied for classification, regression, clustering, and more tasks. ML can be categorized into four main types: supervised learning, unsupervised learning, semi-supervised learning, and reinforcement learning. Figure 2 provides some examples of different ML algorithms. Among these various algorithms, supervised learning is most applied in the oil and gas industry (Ng et al., 2023).

Furthermore, the enhancement of the ML process involves the optimization techniques to determine optimal values for control parameters, including the spreading coefficient, number of neurons, biases, and weights. Several optimization methods, such as the Levenberg-Marquardt (LM) algorithm, genetic algorithm (GA), and smart nature-inspired swarm algorithms like particle swarm optimization (PSO), grey wolf optimization (GWO), and ant colony optimization (ACO), have demonstrated their efficacy in achieving significant improvements in these tasks. There are two categories in intelligent optimization algorithms: single-objective optimization and multi-objective optimization (Figure 3).

4. Application of ML in CO₂-EOR

4.1. Minimum miscibility pressure (MMP)

In miscible gas injection, MMP is one of the most important parameters to determine the accuracy of miscible CO₂ flooding into the reservoir. Traditionally, MMP is defined as the pressure at which 80% of the OOIP is extracted from the reservoir upon the breakthrough of CO₂ (Holm & Josendal, 1974). Because CO₂ flooding is more expensive than waterflooding, an accurate estimation of MMP can help better design miscible CO₂ flooding, ultimately leading to cost savings. In the literature, researchers have proposed various MMP estimation approaches, including:

a)

experimental methods such as slim-tube tests (Yellig & Metcalfe, 1980), rising-bubble apparatus (Christiansen & Haines, 1987), vanishing interfacial tension (Rao & Lee, 2002);

b)

empirical correlations (Alston et al., 1985; Orr & Jensen, 1984; Shokir, 2007; Yellig & Metcalfe, 1980) and computational techniques such as single mixing-cell and multiple mixing-cell approaches (Ahmadi & Johns, 2011).

However, though accurate and reliable, experimental methods are time-consuming and expensive. Most empirical correlations and computation techniques do not consider different thermodynamic and reservoir properties. Moreover, they exhibit limitations in accurately estimating the trend of MMP concerning their input parameters (Lv et al., 2023). In contrast, the advent of ML has provided various robust algorithms in problems involving regression/classification. Consequently, considerable research studies dedicated to the precise modeling of MMP and the successful application of ML in this domain have been well-documented.

The earliest application of ML on CO₂-EOR MMP can be traced back to 2003, when Huang et al. first introduced ANN into this field. Subsequently, Emera and Sarma (2005) employed the GA to optimize the MMP prediction processes. Following the year 2010, there has been a gradual increase in the adoption of ML algorithms and optimization techniques, accompanied by a significant expansion of the available dataset. Nowadays, the application of ML in predicting MMP has evolved into a more mature state. A comprehensive survey of the literature review in the field of CO₂-oil MMP estimation applying ML, spanning the period from 2003 to the present, is summarized in Table 1. Each reviewed paper is scrutinized and synthesized with respect to the employed algorithms, dataset size, data splitting methods, input variables, outcomes, our assessment, and a rating score. The rating score is determined through an evaluation encompassing criteria that consider the quality of data, the ML process, and the depth of results analysis.

Figure 5 presents a statistical analysis from 56 research papers. The reveals a remarkable surge in the adoption of ML methodologies within this domain. ANN and GA have emerged as the most favored choices among many ML and optimization algorithms. ANNs, particularly RBFNN and MLP, are prominently employed. We have provided a separate categorization for RBFNN and MLP to afford a more detailed perspective on their individual utilization patterns.

Furthermore, an essential factor impacting the efficacy of ML models in MMP predictions is the size of the dataset. It is widely recognized that an inadequately sized dataset can lead to overfitting, potentially compromising the model's generalizability. A substantial proportion of the examined papers (64%) have datasets with fewer than 200 data points, with a noteworthy subset (21%) relying on datasets with fewer than 100 data points. This stark discrepancy in dataset size necessitates critically examining the quality and robustness of models trained on such limited data. Therefore, it becomes paramount to consider the trade-offs between the advantages of ML applications and the constraints posed by data scarcity in the context of MMP prediction.

As summarized in Table 1, the most dominant parameters affecting pure CO₂ MMP are reservoir temperature, molecular weight of C₅₊ or C₇₊, mole fraction of volatile oil elements, and mole fraction of intermediate oil elements. While for impure CO₂ MMP, additional parameters such as mole fraction of gas, including C₁ to C₄, CO₂, N₂, and H₂S, are also considered. Some studies included volatile oil components (C₁ and N₂) as well.

Figure 4. (a) Rise of ML application papers in MMP prediction; (b) Occurrence of different ML algorithms; (c) Distribution of dataset size.

Figure 4. (a) Rise of ML application papers in MMP prediction; (b) Occurrence of different ML algorithms; (c) Distribution of dataset size.

4.2. Water-alternating-gas (WAG)

WAG injection, a widely adopted method in EOR techniques, cyclically injects water and gas, typically CO₂ or CO₂-hydrocarbon blends, to increase sweep efficiency and maximize oil recovery. Optimizing parameters such as WAG ratio, duration of each cycle, and reservoir properties is pivotal for achieving favorable economic outcomes. The application of ML methods on WAG has been developed more recently. The earliest application of ML in WAG started in 2016, Hosseinzadeh Helaleh & Alizadeh employed SVM together with three optimization methods, ACO, PSO, and GA, to predict fractional oil recovery. In 2018, Nait Amar et al. used time-dependent multi-ANN to predict the total field oil production. Later on, Nait Amar & Zeraibi (2020) successfully applied SVR to construct a dynamic proxy of a field in Algeria, complemented by Genetic Algorithms (GA) for optimizing water-alternating-CO₂ gas parameters. A more detailed summary is listed in Table 2. Figure 5 provides statistical analysis based on 26 papers. Similar to MMP, the most popular ML algorithm is ANN, and the most preferred optimization is GA.

4.3. Well placement optimization (WPO)

WPO plays an essential role in reservoir management and development for many reasons. It can help maximize oil recovery and economic considerations (because drilling and maintaining wells are expensive). However, it has been considered one of the most challenging tasks due to the necessity of evaluating numerous computation scenarios to identify the optimal location for wells and achieve maximum production. The complexity of geological heterogeneities, such as variations in permeability and porosity, the existence of multiple facies, and stratigraphic and structural boundary conditions, requires extensive computational efforts. Besides, small changes in well locations can lead to significant changes in oil recovery prediction, making the optimization more challenging. Numerous simulations for hundreds or thousands of scenarios need to be run to make the best decision.

In recent years, studies suggest the integration of ML approaches has been proposed in the literature as the potential solution. It holds the potential to accelerate computation processes, enabling quicker attainment of accurate scenarios within numerical simulations. Despite the recognized importance of optimizing well placement, the investigations of CO₂ injector locations for optimal oil recovery and storage are relatively infrequent (Table 3). Most research is focused on waterflood injector selection (Xiong & Lee, 2020).

Table 2. Summary for ML applications on WAG.

Authors	Methods	Dataset	Train/Test/Validate	Objectives	Inputs	Results	Evaluation	Limitations	Rating*
Hosseinzadeh Helaleh & Alizadeh (2016)	SVM (ACO, GA, PSO)	200	80% train + 20% test	Fractional oil recovery	RLC, RLD, NgAO, NgGO, MSWAG, NC, SGR, NPe, NSCon, NB, Nα, Nσ, λ*Dx, Nn, He	ACO has high accuracy and low computational time compared to ANN, GA, and PSO.	Evaluate with both experiments and simulations. Limited to a similar geological model.	Only has SVM model.	8
Le Van & Chon (2017)	ANN	223 (simulation)	45% train + 20% test + 35% validation	Oil recovery factor, oil rate, GOR, accumulative CO2 production, net CO2 storage	Swi, kv/kh, WAG ratio, duration of each cycle	ANN models can support numerical simulation of CO2-EOR projects. WAG ratio less than 1.5 is best.	Evaluated multiple objectives but only limited to ANN.	Only have simulation results as trained data.	8
Van & Chon (2018)	ANN	263 (simulation)	50% train + 20% test + 30% validation	Oil recovery + net CO2 storage + cumulative gaseous CO2 production	Kv/Kh, WAG ratio, Sw, well distance between each injector, T	ANN can help estimate oil recovery and CO2 storage. 25 injection cycle is best.	Evaluate different WAG ratios but limited to ANN models only.	Only have simulation results as trained data.	7
Mohagheghian et al. (2018)	GA, PSO	2000 (simulation)	NA	NPV + incremental recovery factor	Water and gas injection rates, BHP of producers, cycle ratio, cycle time, injected gas composition, total WAG period.	PSO is capable of optimizing WAG variables and projects at field scale.	First used GA in WAG at field scale. Evaluated with three case studies. Limited to specific geological models.	Only GA and PSO are evaluated. Specific to E-segment.	9
Nwachukwu, Jeong, Sun, et al. (2018)	XGBoost, MADS	1000 (simulation)	50% train + 50% test	Oil/water/gas production rates, well locations, NPV	Well x-coordinates, well y-coordinates, water/gas injection rates, well block ϕ/k, well block Swi	The new model combined XGBoost and MADS provided high accuracy.	Demonstrated with a case study in which underlying geology is uncertain. Limited to one model.	Only XGBoost is employed.	8
Nait Amar et al. (2018)	ANN/GA, ACO	85	88% train + 12% test	Field oil production total	Gas/water injection rates, gas/water injection half-cycle, WAG ratio, and slug size.	Both GA and ACO are highly effective in the optimization of the WAG process.	Demonstrated the application of a time-dependent proxy model for the WAG process. Without further application of the case study.	Restricted to specific geological models. Limited simulation runs	8
Belazreg et al. (2019)	Regression, GDMH	4290	70% train + 30% test	Incremental recovery factor	kh, kv, API, gas gravity, water viscosity, solution GOR, WAG ratio, WAG cycle, land coefficient, reservoir pressure, PV of injected water, PV of injected gas.	GMDH performed better in selecting effective input parameters and optimizing the model structure.	Novel approach but didn’t apply real field WAG pilot data to validate.	Limited to two ML methods.	8
Jaber et al. (2019)	CCD	81	NA	Oil recovery	k, ϕ, kv/kh, cyclic length, BHP, WAG ratio, CO2 slug size	The new proxy model can predict oil recovery. The optimum WAG ratio is 1.5.	Developed a new proxy model based on CCD, But limited to one model.	Limited data points and only from simulation runs.	7
Menad & Noureddine (2019)	MLP (LMA, BR, SCG) + NSGA-II	From 2010 to 2018	NA	FOPR, FWPR	Time, FWIR, FGIR, the value of the needed parameter at the previous time step	MLP-LMA has the highest accuracy and lowest computation time.	Developed a dynamic proxy model for multiple objectives. But limited to one geological model.	The database was generated based on multiple runs of the simulation.	8
Nait Amar & Zeraibi (2020)	SVR, GA	75	NA	Field oil production total	Injection rates of water and gas, half-cycle injection time, WAG ratio, slug size, initialization time of the process	SVR-GA provides high accuracy and reasonable CPU time.	Established a dynamic proxy model based on SVR-GA, but no comparison with other algorithms.	Limited data points and only one model evaluated.	7
Yousef et al. (2020)	ANN	8 years * 37 wells	85% train + 15% test	Oil/gas/water production rate, GOR, infill well location	Well trajectory data, well logs, seismic data, production and injection history, reservoir pressure, choke opening, and WHP history.	Implementing ANNfor top-downmodeling can predictreservoir performanceunder WAG.	Can predict the reservoir performance 3 months ahead. But simplify the data gathering, modeling, and validation process.	Unknown about specific input data. No comparison with other models or field case studies.	6
Belazreg & Mahmood (2020)	GDMH	177	70% train + 30% test	Incremental oil recovery factor	Rock type, WAG process type, reservoir horizontal permeability, API, oil viscosity, reservoir pressure and temperature, and hydrocarbon pore volume of injected gas.	GDMH models can predict three WAG incremental recovery factors: sandstone immiscible gas injection, sandstone miscible gas injection, and carbonate miscible gas injection	Proved GDMH can model the WAG process and has good potential. More data and validation are needed to improve model robustness and applicability.	Limited published WAG pilot data.	8
You et al. (2020)	ANN	820	80% train + 10% test + 10% validation	Oil recovery, CO2 storage, and project NPV	Water injection time, CO2 injection time, producer BHP, water injection rate.	The ANN proxy model can help improve the prediction performance.	Could handle two or three objectives very well when a limited number of control parameters	Only suitable for limited input parameters.	8
You et al. (2021)	Gaussian SVR - PSO	217	NA	Hydrocarbon recovery + CO2 sequestration volume + NPV	FOPR*2, gas cycle*5, water cycle *5	The proposed method can optimize the WAG process with high accuracy.	Nice sensitivity studies of CO2 price and oil price on NPV. Limited comparison with other ML models.	Restricted to specific geological models.	8
Enab & Ertekin (2021)	ANN	2000	80% train + 10% test + 10% validation	Production prediction, production schemes design, history matching	25 inputs including reservoir rock characteristics, initial conditions, oil composition, well design parameters, and injection strategy parameters.	ANN provides a faster prediction for fish-bone structure in low permeability reservoirs.	Nice project design and economic analysis, but limited to ANN model only.	Limitations wereimposed by defining the range of each variable.	8
Afzali et al. (2021)	GEP	96	67% train + 33% test	Recovery factor	Oil viscosity, gas/water injection rates, k, PVI, number of cycles	The developed model is successful when compared with experimental results.	Novelty in using GEP. The dataset is from mathematical correlation.	Limited and less supportive dataset.	8
Lv et al. (2021)	ANN-PSO	2100	70% train + 15% test + 15% validation	Oil production	So, Pi, k, ϕ, h, Pwf, water injection rate, water cut before gas flooding, gas injection rate, water injection volume, cycle time, water injection time, production rate, grid size	ANN-PSO provides a good model for parameter optimization of CO2 WAG-EOR.	Routine procedures, not too much novelty in applying ANN-PSO.	No comparison with other ML models.	7
Nait Amar et al. (2021)	MLP-LM, RBFNN-ACO/GWO	82	88% train + 12% test	Field oil production total	Water/gas injection rates, injection half-cycle, downtime, WAG ratio, gas slug size	MLP-LMA is best. The proxy model can significantly reduce simulation time and conserve high accuracy.	The application of GWO is novel. Limited runs and may have overfitting problems.	Water cut is limited to 50%. Reservoir pressure must be higher than MMP.	8
Junyu et al., (2021)	Gaussian-SVR	1400	NA	Cumulative oil production and cumulative CO2 storage.	Water/gas cycle, producer BHP, water injection rate, etc. (91 variables in total)	Gaussian-SVR performs best.	Showed the possibility to design a CO2-WAGproject using as many inputs as possible.	Given the large number of input parameters, the dataset may not be large enough.	7
Sun et al. (2021)	SVR, MLNN, RSM	600	83% train + 17% test	Oil production, CO2 storage, NPV.	Duration of CO2 and water injection cycles, water injection rate, production well specifications, oil price, CO2 price, etc. (62 parameters)	The MLNN model can handle problems with large input and output dimensions.	Compared three different methods. But only suitable for specific geological models.	The average reservoir pressure must be between 3700 – 5400 psi.	8
Huang et al. (2021)	LSTM	5404	90% train + 10% test	Oil production, GOR, water cut	Daily liquid rate, daily oil/gas/water rate, GIR, WIR, reservoir pressure, WHFP, choke size of producers.	The calculation time of LSTM is 864% less than the simulation, while the prediction error of the LSTM method is 261% less than the simulation.	The model is based on real reservoir data over 15 years. But limited to one ML model.	Only one ML model is considered. No comparison with other models.	7
H. Li et al. (2022)	RF	216	70% train + 30% test	Cumulative oil production, CO2 storage amount, CO2 storage efficiency	CO2-WAG period, CO2 injection rate, water-gas ratio, reservoir properties, oil properties, depth, layer thickness, Soi, well operation	CO2-WAG cycle time has a slight influence on oil production. Random forest can predict oil production and CO2 storage.	Proved RF has high computation efficiency and accuracy in CO2-WAG projects. But no comparison of different ML models.	Small dataset and only one ML model is studied.	7
Andersen et al. (2022)	LSSVM – PSO/GA/GWO/GSA	2500	70% train + 15% test + 15% validation	Oil recovery factor	Water-oil and gas-oil mobility ratios, water-oil and gas-oil gravity numbers, reservoir heterogeneity factor, two hysteresis parameters, and water fraction.	LSSVM with GWO or PSO performed better than GA or GSA.	Very detailed and thorough study. The dataset is relatively large. Some limitations of input parameters.	Several important parameters were not varied much.	9
Singh et al. (2023)	DNN - GA	2200	70/80% train + 30/20% test	Maximize oil recovery	Water injection rates, gas-to-water ratio, slug size.	DNN-GA workflow can identify improved WAG parameters over the baseline recovery, with incremental increases of 0.5-2%.	Presents a novel workflow for WAG optimization using ML. Requires a large number of simulation runs (2200 here) to initially train DNN.	Limited to optimizing WAG parameters.	7
Asante et al. (2023)	LSTM	2345*3	80% train + 20% test	Oil production rate, oil recovery factor	Bottom-hole pressure at injector and producer, water and gas injection volumes, WAG cycle.	LSTM can model complex time-series data without the use of the geological model.	Shows the ability of LSTM to perform time series analysis. But the input parameters are restricted.	Requires large amounts of quality field data.	7
Matthew et al. (2023)	ANN-NSGA-II	68 + 97	NA	Maximize oil produced and CO2 storage	Water and gas injection rate, half-cycle length, time step.	The developed proxy model can predict both simple and complex models.	Developed a dynamic proxy model for multiple objectives. But the dataset size is limited.	Limited simulation runs. Has a high possibility of overfitting.	7

*: The rating for each paper is from the author’s perspective.

Table 2. Summary for ML applications on WAG.

Authors	Methods	Dataset	Train/Test/Validate	Objectives	Inputs	Results	Evaluation	Limitations	Rating*
Hosseinzadeh Helaleh & Alizadeh (2016)	SVM (ACO, GA, PSO)	200	80% train + 20% test	Fractional oil recovery	RLC, RLD, NgAO, NgGO, MSWAG, NC, SGR, NPe, NSCon, NB, Nα, Nσ, λ*Dx, Nn, He	ACO has high accuracy and low computational time compared to ANN, GA, and PSO.	Evaluate with both experiments and simulations. Limited to a similar geological model.	Only has SVM model.	8
Le Van & Chon (2017)	ANN	223 (simulation)	45% train + 20% test + 35% validation	Oil recovery factor, oil rate, GOR, accumulative CO2 production, net CO2 storage	Swi, kv/kh, WAG ratio, duration of each cycle	ANN models can support numerical simulation of CO2-EOR projects. WAG ratio less than 1.5 is best.	Evaluated multiple objectives but only limited to ANN.	Only have simulation results as trained data.	8
Van & Chon (2018)	ANN	263 (simulation)	50% train + 20% test + 30% validation	Oil recovery + net CO2 storage + cumulative gaseous CO2 production	Kv/Kh, WAG ratio, Sw, well distance between each injector, T	ANN can help estimate oil recovery and CO2 storage. 25 injection cycle is best.	Evaluate different WAG ratios but limited to ANN models only.	Only have simulation results as trained data.	7
Mohagheghian et al. (2018)	GA, PSO	2000 (simulation)	NA	NPV + incremental recovery factor	Water and gas injection rates, BHP of producers, cycle ratio, cycle time, injected gas composition, total WAG period.	PSO is capable of optimizing WAG variables and projects at field scale.	First used GA in WAG at field scale. Evaluated with three case studies. Limited to specific geological models.	Only GA and PSO are evaluated. Specific to E-segment.	9
Nwachukwu, Jeong, Sun, et al. (2018)	XGBoost, MADS	1000 (simulation)	50% train + 50% test	Oil/water/gas production rates, well locations, NPV	Well x-coordinates, well y-coordinates, water/gas injection rates, well block ϕ/k, well block Swi	The new model combined XGBoost and MADS provided high accuracy.	Demonstrated with a case study in which underlying geology is uncertain. Limited to one model.	Only XGBoost is employed.	8
Nait Amar et al. (2018)	ANN/GA, ACO	85	88% train + 12% test	Field oil production total	Gas/water injection rates, gas/water injection half-cycle, WAG ratio, and slug size.	Both GA and ACO are highly effective in the optimization of the WAG process.	Demonstrated the application of a time-dependent proxy model for the WAG process. Without further application of the case study.	Restricted to specific geological models. Limited simulation runs	8
Belazreg et al. (2019)	Regression, GDMH	4290	70% train + 30% test	Incremental recovery factor	kh, kv, API, gas gravity, water viscosity, solution GOR, WAG ratio, WAG cycle, land coefficient, reservoir pressure, PV of injected water, PV of injected gas.	GMDH performed better in selecting effective input parameters and optimizing the model structure.	Novel approach but didn’t apply real field WAG pilot data to validate.	Limited to two ML methods.	8
Jaber et al. (2019)	CCD	81	NA	Oil recovery	k, ϕ, kv/kh, cyclic length, BHP, WAG ratio, CO2 slug size	The new proxy model can predict oil recovery. The optimum WAG ratio is 1.5.	Developed a new proxy model based on CCD, But limited to one model.	Limited data points and only from simulation runs.	7
Menad & Noureddine (2019)	MLP (LMA, BR, SCG) + NSGA-II	From 2010 to 2018	NA	FOPR, FWPR	Time, FWIR, FGIR, the value of the needed parameter at the previous time step	MLP-LMA has the highest accuracy and lowest computation time.	Developed a dynamic proxy model for multiple objectives. But limited to one geological model.	The database was generated based on multiple runs of the simulation.	8
Nait Amar & Zeraibi (2020)	SVR, GA	75	NA	Field oil production total	Injection rates of water and gas, half-cycle injection time, WAG ratio, slug size, initialization time of the process	SVR-GA provides high accuracy and reasonable CPU time.	Established a dynamic proxy model based on SVR-GA, but no comparison with other algorithms.	Limited data points and only one model evaluated.	7
Yousef et al. (2020)	ANN	8 years * 37 wells	85% train + 15% test	Oil/gas/water production rate, GOR, infill well location	Well trajectory data, well logs, seismic data, production and injection history, reservoir pressure, choke opening, and WHP history.	Implementing ANNfor top-downmodeling can predictreservoir performanceunder WAG.	Can predict the reservoir performance 3 months ahead. But simplify the data gathering, modeling, and validation process.	Unknown about specific input data. No comparison with other models or field case studies.	6
Belazreg & Mahmood (2020)	GDMH	177	70% train + 30% test	Incremental oil recovery factor	Rock type, WAG process type, reservoir horizontal permeability, API, oil viscosity, reservoir pressure and temperature, and hydrocarbon pore volume of injected gas.	GDMH models can predict three WAG incremental recovery factors: sandstone immiscible gas injection, sandstone miscible gas injection, and carbonate miscible gas injection	Proved GDMH can model the WAG process and has good potential. More data and validation are needed to improve model robustness and applicability.	Limited published WAG pilot data.	8
You et al. (2020)	ANN	820	80% train + 10% test + 10% validation	Oil recovery, CO2 storage, and project NPV	Water injection time, CO2 injection time, producer BHP, water injection rate.	The ANN proxy model can help improve the prediction performance.	Could handle two or three objectives very well when a limited number of control parameters	Only suitable for limited input parameters.	8
You et al. (2021)	Gaussian SVR - PSO	217	NA	Hydrocarbon recovery + CO2 sequestration volume + NPV	FOPR*2, gas cycle*5, water cycle *5	The proposed method can optimize the WAG process with high accuracy.	Nice sensitivity studies of CO2 price and oil price on NPV. Limited comparison with other ML models.	Restricted to specific geological models.	8
Enab & Ertekin (2021)	ANN	2000	80% train + 10% test + 10% validation	Production prediction, production schemes design, history matching	25 inputs including reservoir rock characteristics, initial conditions, oil composition, well design parameters, and injection strategy parameters.	ANN provides a faster prediction for fish-bone structure in low permeability reservoirs.	Nice project design and economic analysis, but limited to ANN model only.	Limitations wereimposed by defining the range of each variable.	8
Afzali et al. (2021)	GEP	96	67% train + 33% test	Recovery factor	Oil viscosity, gas/water injection rates, k, PVI, number of cycles	The developed model is successful when compared with experimental results.	Novelty in using GEP. The dataset is from mathematical correlation.	Limited and less supportive dataset.	8
Lv et al. (2021)	ANN-PSO	2100	70% train + 15% test + 15% validation	Oil production	So, Pi, k, ϕ, h, Pwf, water injection rate, water cut before gas flooding, gas injection rate, water injection volume, cycle time, water injection time, production rate, grid size	ANN-PSO provides a good model for parameter optimization of CO2 WAG-EOR.	Routine procedures, not too much novelty in applying ANN-PSO.	No comparison with other ML models.	7
Nait Amar et al. (2021)	MLP-LM, RBFNN-ACO/GWO	82	88% train + 12% test	Field oil production total	Water/gas injection rates, injection half-cycle, downtime, WAG ratio, gas slug size	MLP-LMA is best. The proxy model can significantly reduce simulation time and conserve high accuracy.	The application of GWO is novel. Limited runs and may have overfitting problems.	Water cut is limited to 50%. Reservoir pressure must be higher than MMP.	8
Junyu et al., (2021)	Gaussian-SVR	1400	NA	Cumulative oil production and cumulative CO2 storage.	Water/gas cycle, producer BHP, water injection rate, etc. (91 variables in total)	Gaussian-SVR performs best.	Showed the possibility to design a CO2-WAGproject using as many inputs as possible.	Given the large number of input parameters, the dataset may not be large enough.	7
Sun et al. (2021)	SVR, MLNN, RSM	600	83% train + 17% test	Oil production, CO2 storage, NPV.	Duration of CO2 and water injection cycles, water injection rate, production well specifications, oil price, CO2 price, etc. (62 parameters)	The MLNN model can handle problems with large input and output dimensions.	Compared three different methods. But only suitable for specific geological models.	The average reservoir pressure must be between 3700 – 5400 psi.	8
Huang et al. (2021)	LSTM	5404	90% train + 10% test	Oil production, GOR, water cut	Daily liquid rate, daily oil/gas/water rate, GIR, WIR, reservoir pressure, WHFP, choke size of producers.	The calculation time of LSTM is 864% less than the simulation, while the prediction error of the LSTM method is 261% less than the simulation.	The model is based on real reservoir data over 15 years. But limited to one ML model.	Only one ML model is considered. No comparison with other models.	7
H. Li et al. (2022)	RF	216	70% train + 30% test	Cumulative oil production, CO2 storage amount, CO2 storage efficiency	CO2-WAG period, CO2 injection rate, water-gas ratio, reservoir properties, oil properties, depth, layer thickness, Soi, well operation	CO2-WAG cycle time has a slight influence on oil production. Random forest can predict oil production and CO2 storage.	Proved RF has high computation efficiency and accuracy in CO2-WAG projects. But no comparison of different ML models.	Small dataset and only one ML model is studied.	7
Andersen et al. (2022)	LSSVM – PSO/GA/GWO/GSA	2500	70% train + 15% test + 15% validation	Oil recovery factor	Water-oil and gas-oil mobility ratios, water-oil and gas-oil gravity numbers, reservoir heterogeneity factor, two hysteresis parameters, and water fraction.	LSSVM with GWO or PSO performed better than GA or GSA.	Very detailed and thorough study. The dataset is relatively large. Some limitations of input parameters.	Several important parameters were not varied much.	9
Singh et al. (2023)	DNN - GA	2200	70/80% train + 30/20% test	Maximize oil recovery	Water injection rates, gas-to-water ratio, slug size.	DNN-GA workflow can identify improved WAG parameters over the baseline recovery, with incremental increases of 0.5-2%.	Presents a novel workflow for WAG optimization using ML. Requires a large number of simulation runs (2200 here) to initially train DNN.	Limited to optimizing WAG parameters.	7
Asante et al. (2023)	LSTM	2345*3	80% train + 20% test	Oil production rate, oil recovery factor	Bottom-hole pressure at injector and producer, water and gas injection volumes, WAG cycle.	LSTM can model complex time-series data without the use of the geological model.	Shows the ability of LSTM to perform time series analysis. But the input parameters are restricted.	Requires large amounts of quality field data.	7
Matthew et al. (2023)	ANN-NSGA-II	68 + 97	NA	Maximize oil produced and CO2 storage	Water and gas injection rate, half-cycle length, time step.	The developed proxy model can predict both simple and complex models.	Developed a dynamic proxy model for multiple objectives. But the dataset size is limited.	Limited simulation runs. Has a high possibility of overfitting.	7

*: The rating for each paper is from the author’s perspective.

Table 3. Summary of ML applications in well location optimization.

Authors	Methods	Dataset	Train/Test/Validate	Objectives	Inputs	Results	Evaluation	Limitations	Rating*
Nwachukwu et al. (2018)	XGBoost	200, 500, 1000	NA	Total profit, cumulative oil/gas produced, net CO2 stored	Well-to-well pairwise connectivity, injector block k and ϕ, initial injector block saturations	Quick evaluation of well placement using well-to-well connectivity was successful with 1000 simulation runs and R2 = 0.92.	No co-optimization of oil recovery and CO2 storage, only ML proxy usage.	The dataset is from simulation runs. Only suitable for one geological model.	8
Selveindran et al. (2021)	AdaBoost, RF, ANN	3000, 2000, 1000	70% train + 30% test	Incremental oil production	K, ϕ, PV, initial fluid saturation, pressure, time of flight, well-to-well distances, distance to the injector, injection rate, and injection depth.	Stacked learner is better than an individual learner. ML helps rapidly identify the areas that are optimal for injection.	Detailed and comprehensive analysis, including posterior sampling.	Heavily rely on the geological model.	8

*: The rating for each paper is from the authors’ perspective.

Table 3. Summary of ML applications in well location optimization.

Authors	Methods	Dataset	Train/Test/Validate	Objectives	Inputs	Results	Evaluation	Limitations	Rating*
Nwachukwu et al. (2018)	XGBoost	200, 500, 1000	NA	Total profit, cumulative oil/gas produced, net CO2 stored	Well-to-well pairwise connectivity, injector block k and ϕ, initial injector block saturations	Quick evaluation of well placement using well-to-well connectivity was successful with 1000 simulation runs and R2 = 0.92.	No co-optimization of oil recovery and CO2 storage, only ML proxy usage.	The dataset is from simulation runs. Only suitable for one geological model.	8
Selveindran et al. (2021)	AdaBoost, RF, ANN	3000, 2000, 1000	70% train + 30% test	Incremental oil production	K, ϕ, PV, initial fluid saturation, pressure, time of flight, well-to-well distances, distance to the injector, injection rate, and injection depth.	Stacked learner is better than an individual learner. ML helps rapidly identify the areas that are optimal for injection.	Detailed and comprehensive analysis, including posterior sampling.	Heavily rely on the geological model.	8

*: The rating for each paper is from the authors’ perspective.

4.4. Oil production/recovery factor

The recovery factor, defined as the ratio of produced oil to OOIP, is one of the most crucial success metrics for evaluating all EOR projects, as it determines how much incremental oil or ultimate oil is produced. Accurately predicting the recovery factor is challenging because it depends on diverse factors, including reservoir characteristics and heterogeneity, fluid properties, well design, injection condition, and composition of injected fluid. Reservoir simulations, together with laboratory experiments at reservoir conditions, can help predict recovery factor. After that, a small-scale pilot test is conducted before undertaking larger-scale operations (Ding et al., 2017). Although this approach may provide solutions to numerous problems, it is costly and time-consuming. Therefore, ML methods emerge as more practical, affordable, rapid, and accurate alternatives.

Alternatively, ML methods have obtained popularity in predicting oil recovery. For example, Ahmadi et al. (2018) applied LSSVM to predict the ultimate oil recovery factor of the miscible CO₂-EOR injection operations at the different rock, fluids, and process conditions. Karacan (2020) employed fuzzy logic to predict recovery factors of the major past and existing U.S. field applications of miscible CO₂-EOR. Table 4 provides further information on ML applications on the CO₂-EOR recovery factor.

4.5. Multi-objective optimization

As the name indicates, multi-objective optimization optimizes multiple objections simultaneously, such as oil recovery factor or cumulative oil production, CO₂ storage, and net present value (NPV). For each objective, running high-fidelity numerical models provides possible solutions to figure out the optimum. However, finding optimal solutions to all objectives simultaneously is not always guaranteed since objectives can compete with each other. For example, to maximize oil recovery, more CO₂ may be needed, leading to higher oil production. However, this might also mean more CO₂ is used, potentially increasing the project's cost, which will also adversely affect the project NPV (You, Ampomah, Sun, et al., 2020). It requires sophisticated optimization techniques to identify solutions that balance these objectives, considering all the constraints involved in the problem. Therefore, ML techniques outperform other methods as an effective, reliable, and stable workflow to co-optimize crude oil recovery, CO₂ sequestration, NPV, and related factors.

Given the complexity of multi-objective optimization, the application of ML on CO₂-EOR is very limited (Table 5 and Table 6) and is strongly restricted by the geological model. Once the reservoir characteristics change, the model must be rebuilt and retrained. The development of ML and optimization workflow is challenging and requires more effort in different oil and gas fields.

Table 4. Summary of ML applications on oil production/recovery factor.

Authors	Methods	Dataset	Train/Test/Validate	Objectives	Inputs	Results	Evaluation	Limitations	Rating*
Ahmadi et al. (2018)	LSSVM	46	80% train + 20% test	Oil recovery factor	BHP of injection well, CO2 injection rate, CO2 injection concentration, BHP of production well, oil production rate	The hybridization of LSSVM and BBD is statistically correct for predicting RF.	Provided the possibility of using ML and comparing it with commercial software. But limited dataset.	Small dataset and only suitable for similar oil reservoirs. Only valid for the same input parameters range.	7
Chen & Pawar (2019)	MARS, SVR, RF	500, 250, 100	NA	Recovery factor	Thickness, depth, k, Sor, CO2 injection rate, BHP of production well	MARS has the best performance.	Applied to 5 fields in Permian Basin and had good matches. Heavily relies on a base model and may not fully represent diverse ROZs.	Significant assumptions are made regarding uncertain parameters like residual oil saturation.	8
Karacan (2020)	FL	24	83% train + 17% test	Recovery factor	Lithology, API, ϕ, k, HCPV, depth, net pay, Pi, well spacing, Sorw	FL provided a reasonably accurate prediction.	Though a small dataset, but provides the possibility of using ML in recovery factor prediction.	Too difficult to draw statistical conclusions from such a small dataset.	7
Iskandar & Kurihara (2022)	AR, MLP, LSVM	3653 * 8 wells	40% train + 20% test + 40% validation	Oil, gas, and water production	ϕ, k, formation thickness, BHP, flow capacity, storage capacity	The AR model is best, with long and consistent forecast horizons across wells. LSTM performs well but has shorter forecast horizons. MLP has high variability and short forecast horizons.	First time series forecasting study. No model updating/retraining over time. Overall, it is a solid study.	Limited hyperparameter tuning is done. Only three models were tested.	9

*: The rating for each paper is from the authors’ perspective.

Table 4. Summary of ML applications on oil production/recovery factor.

Authors	Methods	Dataset	Train/Test/Validate	Objectives	Inputs	Results	Evaluation	Limitations	Rating*
Ahmadi et al. (2018)	LSSVM	46	80% train + 20% test	Oil recovery factor	BHP of injection well, CO2 injection rate, CO2 injection concentration, BHP of production well, oil production rate	The hybridization of LSSVM and BBD is statistically correct for predicting RF.	Provided the possibility of using ML and comparing it with commercial software. But limited dataset.	Small dataset and only suitable for similar oil reservoirs. Only valid for the same input parameters range.	7
Chen & Pawar (2019)	MARS, SVR, RF	500, 250, 100	NA	Recovery factor	Thickness, depth, k, Sor, CO2 injection rate, BHP of production well	MARS has the best performance.	Applied to 5 fields in Permian Basin and had good matches. Heavily relies on a base model and may not fully represent diverse ROZs.	Significant assumptions are made regarding uncertain parameters like residual oil saturation.	8
Karacan (2020)	FL	24	83% train + 17% test	Recovery factor	Lithology, API, ϕ, k, HCPV, depth, net pay, Pi, well spacing, Sorw	FL provided a reasonably accurate prediction.	Though a small dataset, but provides the possibility of using ML in recovery factor prediction.	Too difficult to draw statistical conclusions from such a small dataset.	7
Iskandar & Kurihara (2022)	AR, MLP, LSVM	3653 * 8 wells	40% train + 20% test + 40% validation	Oil, gas, and water production	ϕ, k, formation thickness, BHP, flow capacity, storage capacity	The AR model is best, with long and consistent forecast horizons across wells. LSTM performs well but has shorter forecast horizons. MLP has high variability and short forecast horizons.	First time series forecasting study. No model updating/retraining over time. Overall, it is a solid study.	Limited hyperparameter tuning is done. Only three models were tested.	9

*: The rating for each paper is from the authors’ perspective.

4.6. PVT Properties

For any CO₂ flooding project, it is imperative to comprehend the intricate physical and chemical interactions between CO₂ and the reservoir oil, even when primarily exploring recovery potential. Laboratory investigations and the utilization of available modeling or correlation packages serve as viable methods for analyzing the influence of CO₂ on the physical properties of oil. Nonetheless, conducting a comprehensive laboratory study to obtain an extensive dataset is costly and time-consuming. Furthermore, the available correlation packages are limited in their applicability, rendering them unsuitable for many scenarios.

ML is being increasingly harnessed for tasks such as predicting CO₂ solubility and Interfacial Tension (IFT), as briefly presented in Table 6. Intriguingly, a majority of the studies incorporated the same dataset sourced from Emera & Sarma (2008). Given the relatively small dataset size comprising only 106 data points, the risk of overfitting looms large, casting doubt on the accuracy and generalizability of their ML models. It is evident that a larger and more diverse dataset is required to facilitate a deeper comprehension of the performance of ML techniques in this context.

4.7. CO₂-foam flooding

The implementation of CO₂ injection in Enhanced Oil Recovery (EOR) demonstrates significant potential, but it is accompanied by inherent limitations, including suboptimal sweep efficiency, asphaltenes precipitation, and corrosion of well infrastructure. In response to these challenges, the utilization of CO₂ foam has emerged as a promising strategy to enhance the effectiveness of CO₂-EOR flooding. Foams offer distinct advantages, primarily due to their elevated viscosities compared to pure gases, a property that equips foams with the capability to displace oil from reservoir formations more efficiently (Iskandarov et al., 2022). Furthermore, by obstructing highly permeable pore pathways, foams redirect displaced fluids towards unswept reservoir regions, thereby improving both sweep efficiency and the storage capacity of CO₂ within the reservoir matrix. While ML models have found extensive applications in EOR research, their application in the context of CO₂-foam is still in its nascent stages, and the existing body of literature on this subject remains limited, as evidenced in Table 7.

5. Benefits and limitations of ML

ML exhibits high efficiency when compared with conventional reservoir simulators. Typically, these simulators are performed on 3-D grids comprising one million to several billion cells. The computations tend to be time-consuming, imposing constraints on the feasibility of conducting multiple iterations. Consequently, this limitation reduces the optimization potential for meticulous field development planning. A pivotal role of ML techniques is their capacity to speed up reservoir modeling computations. These models can predict time-dependent variables at 100 to 1000 times faster speeds than traditional simulators. This acceleration in computation velocity via ML methods maintains an equivalent level of functionality (Ng et al., 2023).

Furthermore, extensive research findings have proved the impressive performance of ML methods, consistently yielding accuracy levels exceeding 90% based on statistical quality assessments. This high degree of accuracy demonstrates the confidence in ML's reliability and portends a promising future within the oil and gas industry.

While the advantages of employing ML are widely acknowledged, it is imperative to recognize the associated limitations inherent in ML-based methodologies. A central challenge confronting researchers is obtaining authentic data from experimental and/or field sources. The limited availability of large datasets is also a concern, impacting both the training accuracy and the overall efficacy of the ML models. When faced with restricted data, researchers often use single-shot learning strategies, wherein models are pre-trained on similar datasets and subsequently refined through experience.

Overfitting is a prevalent issue in ML applications, primarily driven by insufficient training data and the absence of well-defined stopping criteria during training. 12% of reviewed research papers contain datasets with fewer than 100 data points, heightening the risk of overfitting. Addressing this problem may involve adjusting the model's structure, including weight modifications. However, it is important to recognize that such alterations can increase model complexity, potentially limiting its generalization beyond the specific dataset.

6. Conclusions

In this work, we have investigated and summarized the employment of ML methods in the application of CO₂-EOR from several areas: MMP, WAG, well location placement, oil production/recovery factor, multi-objective optimization, PVT properties, and CO₂-foam. We list the input parameters, objectives, data sources, results, evaluation, and rating for each area based on the data quality, ML process, and results analysis. The key highlights of this work are as follows:

• Our literature review showed that most reports on model performance indicators are limited to the size of the data bank, making it difficult to accurately assess the quality of the model over time or track its drift with new data.
• Regarding validation and verification, the CO₂-EOR has many reliable, dependable, and well-established techniques for verification and validation procedures for ML models. The research highlights several issues with current machine learning models, including model scalability, validation and verification deficiencies, and an absence of published data regarding the establishment costs of ML models.
• Most CO₂-EOR research focused on MMP predictions and WAG design. The applications in recovery factor, well placement optimization, and PVT properties are limited.
• We also found that ANN is the most employed ML algorithm, and GA is the most popular optimization algorithm based on 101 reviewed papers. ANN has been proven to be flexible enough to be implemented to build intelligent proxies.
• ML algorithms can greatly reduce the computational cost and time to perform compositional simulation runs. However, ML applications for well placement optimization in CO₂-EOR are very limited.
• The reliability of coupled ML-metaheuristic paradigms based on reservoir simulation results needs further investigation.