# Applications of Machine Learning in Subsurface Reservoir Simulation—A Review—Part II

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## Abstract

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## 1. Introduction

_{2}injection for Enhanced Oil Recovery (EOR), fully compositional simulations are necessary to monitor detailed changes in fluid composition [9]. Compositional reservoir simulations involve stability and flash calculations using an Equation of State (EoS) model to determine the number and composition of fluid phases in each grid block. These calculations are computationally demanding, require high-performance systems to be executed successfully and, therefore, consume a significant portion of the simulation’s CPU time, as both problems need to be solved repeatedly for each discretization block, at each iteration of the non-linear solver and for each time step [10,11].

_{2}injection-related sweeping and recovery, and identifying optimal locations for new wells to enhance the future production.

## 2. Machine Learning Strategies for Production Forecast and Optimization Applications

_{2}injection into the reservoir for EOR purposes or injection well spacing optimization to improve recovery, respectively) using data obtained from the field (gauges, flow meters, etc.), sampling, logging, or experimental procedures. These methods can be adapted to obtain hydrocarbon predictions and optimize many reservoir- and production-related parameters, thus leading to an effective production optimization in a fraction of the time that would otherwise be needed using traditional reservoir simulators.

#### 2.1. Production Optimization of Conventional Oil Reservoirs

#### 2.1.1. Production Optimization Based on ANNs

#### 2.1.2. Production Optimization Based on Other Methods Other Than ANNs

#### 2.2. Production Forecasting of Conventional Reservoirs

#### 2.2.1. Static Machine Learning Models

#### 2.2.2. Dynamic Machine Learning Models

#### 2.3. Machine Learning Methods for PFO Applications in Unconventional Reservoirs

#### 2.3.1. Static Machine Learning Models

#### 2.3.2. Dynamic Machine Learning Models

#### 2.4. Machine Learning Methods for EOR/Sequestration Projects

#### 2.4.1. Machine Learning Models for the MMP Calculation

_{2}, since it can significantly affect the design of CO

_{2}injection operation through its impact on the injected gas sweep efficiency and, thus, the oil recovery factor. The methods currently used for MMP estimations are experimental measurements, the use of specific correlations, EoS, and computational techniques [110]. Experimental measurements are not always available since they are expensive and time-consuming; correlations can be restricted in the sense that they are usually applicable only to the parameter range they were created for, and EoS can sometimes suffer from numerical problems.

_{2}. The authors trained and validated the model using a training dataset of experimental CO

_{2}MMP values, their analogous oil and impurity compositions, reservoir temperature, Molecular Weights (MWs), etc. The results showed that the trained model surpasses all available methods, in terms of the accuracy of the predictions that are in good agreement with the experimental data. It is also shown that the model can predict the physical trend of CO

_{2}MMP values against reservoir temperature, the MW of the heavy fraction, and H

_{2}S/N

_{2}concentration. Ahmadi et al. [112] coupled LSSVM models with evolutionary algorithms (PSO, GA, and ICA) to predict the MMP using fluid parameters, such as reservoir temperature and the MW of C

_{5+}. It was shown that the LSSVM model, with all evolutionary algorithms, can be an efficient technique for estimating the MMP for pure and impure CO

_{2}streams. Nevertheless, it must be noted that there is a shortage of experimental data used for the training, thus the results can be questionable. Other studies also exist, such as in the works of Huang et al. [113] and Bian et al. [110], who created an ANN and an SVR-GA model, respectively, to predict the MMP of the pure and impure CO

_{2}in oil. The inputs to train the model were the MW of C

_{5+}, reservoir temperature, and oil composition. Moreover, Huang et al. predicted the impure CO

_{2}MMP factor by correlating the critical temperatures and concentrations of contaminants in the injected stream. Finally, Nezhad et al. [114] developed a Radial Basis Function Neural Network (RBFNN) model to determine the CO

_{2}-oil MMP using reservoir temperature, oil composition, C

_{5+}MW, and injected stream composition.

_{2}. The ANN was trained using the reservoir temperature and fluid composition, as well as the injected gas composition as input. In 2012, Ahmadi [116] developed an ANN optimized by hybrid genetic and PSO algorithms to predict the MMP of CO

_{2}. The model was trained, using as input data the reservoir temperature, injected gas composition, volatile and intermediate fractions, and the MW of C

_{5+}. Sayyad et al. [117] developed an ANN model coupled with a PSO algorithm to predict the MMP using reservoir temperature and fluid and injected gas composition, and Chen et al. [118] used a back-propagation ANN with a GA to predict the MMP for pure and impure CO

_{2}streams using reservoir temperature, mole fractions of volatile and intermediate oil components, MW of the C

_{7+}, and mole fractions of CO

_{2}and other impurities in the stream. All of the above ANN-based models coupled with efficient evolutionary algorithms present considerably better prediction results, compared with the simple ANN models, since they possess the capability of mitigating overfitting and local minima issues.

#### 2.4.2. Machine Learning Models for EOR PFO Applications

_{2}sequestration into depleted, or partially depleted reservoirs to reduce CO

_{2}emissions into the atmosphere and, if combined with residual oil recovery, to increase oil production.

_{2}storage capacity co-optimization. The authors used a conventional simulator to simulate the CO

_{2}injection operation with the help of the LH sampling method. That way, the training dataset was obtained, which consisted of thickness, permeability, residual oil saturation, injection rate, producer BHPs, and porosity as input and cumulative oil production, cumulative CO

_{2}stored, and cumulative CO

_{2}as output. Ampomah et al. [120] developed an approach in which they proposed an ANN for oil recovery and CO

_{2}storage capacity co-optimization by maximizing both oil recovery and CO

_{2}storage. First, the authors performed the LH sampling method, a Monte Carlo simulation, and Sensitivity Analysis (SA) to examine the influence of several uncertain variables (e.g., injector BHPs, Water alternating gas-WAG cycle, injection/production rates, GOR) on the set OF. Then, the most influential parameters (e.g., vertical permeability anisotropy) were selected as inputs for the ANN model to perform the optimization. The results presented an improved oil recovery and CO

_{2}storage optimization when compared to a simple base case scenario.

_{2}/N

_{2}) by predicting oil rate, cumulative oil, and production time for each operation. The authors used a reservoir simulator to produce a training dataset for various operating strategies for each EOR method, consisting of reservoir fluid properties (e.g., oil gravity, viscosity, composition), rock parameters (permeability, porosity, thickness, water and oil saturation, etc.) and design characteristics (e.g., completion, well patterns and spacing, and well operating conditions such as production/injection pressures) as input. For the steam injection project, the input also incorporated the injection and saturation temperature, as well as enthalpy values of gas, liquid, and injection conditions. Therefore, a corresponding number of ANN models was generated, depending on a combination of the different EOR methods, fluid characteristics, and design parameters. As a result, the proposed methodology enables engineers to make predictions for many different inputs, depending on the operation design, providing a thorough screening of many depletion designs for each EOR method. Moreover, in her dissertation, Parada Minakowski C.H.P. [122] developed a similar study for screening different EOR methods using a forward and an inverse ANN. First, a traditional reservoir simulator is employed to produce the training dataset consisting of design parameters (e.g., well patterns with various operating conditions) and rock and fluid properties as inputs and the corresponding oil rate and cumulative oil production profiles as outputs. Different models are built for the different well patterns. The forward model predicts oil rate and cumulative production, given the rock, fluid and design parameters, while the inverse model predicts the design parameters, given the rock and fluid parameters and the desired oil rates and cumulative oil production. Both models provided accurate results. In another study, Surguchev et al. [123] built multi-criterion back-propagation and Scaled Conjugate Gradient (SCG) ANN models to screen different EOR schemes (gas injection, steam injection, and cyclic water-flooding) for different reservoir conditions (i.e., different input parameter ranges). The training dataset consisted of reservoir parameters (permeability, porosity, depth, fluid properties, heterogeneity, rock type, salinity, etc.) as input and the EOR methods for assessment as output, in the form of a scale that is between the interval of 0.7 and 1.0. As it was shown, in many cases the SCG approach presented more accurate results than the back-propagation one. The most crucial advantage of this method is that the ANN models allow the usability of various data, and they can act as screening tools for the efficiency of many EOR operations.

_{2}sequestration in coal seam reservoirs is a widespread technology, since coal seams are among the most beneficial formations for CO

_{2}storage. The most important benefits of this operation in such reservoirs is that, as studies show, CO

_{2}shows a sorbing preferability in coal, replacing the coalbed methane that can be produced at the surface, and, furthermore, a very big CO

_{2}volume can be stored at low pressures, eventually cutting down the total storage cost that is usually necessary for constructing additional platforms for storage purposes [124]. For those reasons, Mohammadpoor et al. [125] developed a back-propagation ANN model to forecast two of the most important performance indicators for CO

_{2}storage projects in coal methane reservoirs, methane recovery, and the amount of CO

_{2}injected. As a first step, the authors run several conventional simulations to obtain the training dataset, consisting of porosity, permeability, pressure, thickness, temperature, and water saturation as input and CO

_{2}injected and methane production as output, normalizing the mean and standard deviation to improve the model’s accuracy. The authors also developed an RBFNN model for comparison reasons, which showed promising results; however, the ANN’s performance was of better quality. In a similar study in 2004, Odusote et al. [126] created a back-propagation ANN model to predict the crucial performance indicators for CO

_{2}storage projects in coal seams, such as cumulative CO

_{2}injected, amount of CO

_{2}sequestered, cumulative methane produced, and CO

_{2}breakthrough time. The authors run several simulation scenarios in a compositional coalbed methane simulator, to obtain the necessary input parameters for the ANN model, namely reservoir properties (e.g., porosity, permeability, water saturation, initial pressure, CO

_{2}and CH

_{4}sorption pressure and volume, etc.) and design parameters (e.g., injector orientation, pressure and length, etc.), normalized for more accurate results. The most important advantage of the proposed method is that it enables engineers to screen for the feasibility of CO

_{2}sequestration in such reservoir types. Later in 2005, Gorucu et al. [127] developed a similar ANN model to predict the same performance indicators as Odusote et al., except for cumulative CO

_{2}injected. Their training dataset consisted of reservoir (e.g., porosity, permeability, water saturation, etc.), design (e.g., well pattern, spacing) and operational parameters (e.g., injection/production pressures, skin factor) as input. The results of the aforementioned studies showed that the proposed models were very accurate in predicting critical CO

_{2}injection performance indicators.

_{2}stored as output. The ML model is then optimized by employing the StoSAG optimization algorithm. Kuk et al. [130] developed a novel auto-adaptive parameterized DT that is capable of automatically maximizing the NPV for a Carbon Capture Sequestration (CCS)—EOR process. The auto-adaptive DT is developed to replace the randomly selected limit values of the DT’s attributes with parameters whose optimum values are determined using the Sequential Model-based Algorithm Configuration (SMAC) optimization tool. In every DT iteration, the results are fed into the simulator to determine the NVP, which is then used by the SMAC which varies the limit values to obtain improved results that lead to the determination of the best NPV. When the model was applied to a real reservoir simulation of a CCS-EOR operation, it optimized the oil production during the CO

_{2}-EOR production stage, while also minimizing the amount of CO

_{2}injected.

_{2}and CO

_{2}in a depleted, naturally fractured reservoir. First, the authors run several reservoir compositional simulations based on various huff ‘n’ puff designs to obtain the input–output dataset that will train the models. To identify the cyclic, time-dependent nature of the operation, the dataset consisted of desired performance characteristics (e.g., peak oil rate and time, initial gas rate, final GOR, incremental oil production, stimulation ratio) as inputs and different design parameters (e.g., injection rate, injected gas amount, injection period in days and months) as outputs. Then, the inverse model is trained to predict the design parameters. After the model is validated using a blind dataset, its efficiency is assessed by comparing its output values with the reservoir simulation ones. It was shown that the model was not able to identify the underlying physics very well since the problem under investigation is an inverse one and there is not a unique solution. Because of that, the authors made several modifications to mitigate the presented issue, such as incorporating functional links to the output parameters (parameters that are functions of other parameters) to help the model better understand the connections and physics between them. Finally, another issue emerged: the difficulty of differentiating between the different cycles. While the model made precise predictions for the first cycle, as their number expanded, the precision was reduced, since at each cycle a certain gas volume is added, disturbing the reservoir system; thus, the design scheme of each period is altered based on the previous one. To mitigate this issue, the authors used a single-layered RNN model that identified the physics of the operation more easily. Mo et al. [132] developed an encoder-decoder CNN model to perform an image-to-image regression strategy to solve a CO

_{2}–water multiphase flow problem for a CO

_{2}CSS project with limited data. That way, the authors were able to extract multi-dimensional features from the input permeability field, which are then utilized by the decoder to reconstruct the output pressure and saturation images. Furthermore, they used a two-fold training procedure by integrating a regression loss with a segmentation loss function to efficiently describe the highly discontinuous saturation front. To accurately depict the high-dimensional and time-dependent outputs, time, in the form of injection duration, is incorporated in the training dataset as an additional scalar input. Even though the training dataset was of a limited capacity, the model was able to accurately predict the spatiotemporal development of pressure and CO

_{2}saturation fields.

#### 2.4.3. Machine Learning Models for EOR Trapping Performance Metrics

_{2}trapping mechanism in saline aquifers. To obtain the training dataset for the models, the authors run a large number of simulations obtaining several useful CO

_{2}trapping-related parameters as inputs (geologic parameters, petrophysical properties, and other physical characteristics data) and the corresponding residual trapping, solubility trapping, and cumulative CO

_{2}injection as outputs. The results showed that all ML models can be good candidates for predicting the CO

_{2}trapping performance; however, the GPR model, followed by the SVM one, exhibited the highest performance, demonstrating that they can successfully and robustly assist in numerical simulation for sequestration applications. Kim et al. [134] used a simple ANN model to predict only the CO

_{2}storage efficiency in saline aquifers, i.e., trapping indices of the residual CO

_{2}and solubility trapping mechanisms. The authors created the training data with a reservoir simulator using a parameter SA, where the parameters that mostly affect the CO

_{2}sequestration (porosity, permeability, thickness, depth, and residual gas saturation) were identified. The results showed that the model’s accuracy is excellent and, hence, it can be used as a potent tool for predicting the practicability of CO

_{2}sequestration. In his Dissertation, Al-Nuaimi M. [135] developed an ANN model to make pressure and saturation (CO

_{2}plume) time-series distribution predictions for a CO

_{2}injection process into a saline aquifer. The author used reservoir static and dynamic data as input. The results showed that the model is capable of effectively predicting the pressure and CO

_{2}distributions.

_{2}plume migration in highly heterogeneous reservoirs. The authors run several reservoir simulations to obtain the training dataset which consisted of input parameters such as permeability, injection duration, rate, and location. Furthermore, they were able to take into consideration the buoyancy so that the model could establish the effect of gravity, viscous, and capillary forces, which are crucial parameters when predicting CO

_{2}plume migration. After the model was trained and validated, it was shown that it was able to generalize to a limited extent, by extrapolating beyond the bounds of the training set. In order to further improve the generalization efficiency, the authors proposed a fine-tuning process to transfer new information to the model without any retraining. In another study, Zhong et al. [137] used a conditional deep convolutional GAN model to predict the migration of the CO

_{2}plume in heterogeneous storage reservoirs. This specific model, as the classic GAN, is a semi-supervised one, in the sense that it self-trains to boost its overall quality without the need for major assumptions about the input distributions. The model was developed to identify the dynamic functional mappings among high-dimensional inputs and outputs (permeability and phase saturations, respectively) by also incorporating the injection duration as conditional information. The results of both studies by Wen et al. [136] and Zhong et al. [137] showed that the proposed models can accomplish high accuracy for forecasting CO

_{2}plume spatiotemporal evolution patterns, as compared to the results of traditional compositional reservoir simulators.

#### 2.4.4. Machine Learning Models for WAG-EOR Applications

#### Static Machine Learning Models

_{2}inside a partially depleted reservoir using the CO

_{2}-WAG process. Thus, ANN models are trained with geological, geophysical, and engineering data as inputs to forecast hydrocarbon production, CO

_{2}storage, and reservoir pressure responses. These outputs can help assess the problem’s specific OF, expressed by cumulative oil production and CO

_{2}sequestration volume. Furthermore, the NPV and reservoir pressure are utilized to scan for the best solutions. The results show that the proposed approach is more potent for CO

_{2}-EOR optimization projects, leading to an increased production and CO

_{2}storage amount. In particular, those improvements led to an increased NPV, validating the benefits of the proposed approach for CO

_{2}EOR/sequestration applications. Van et al. [140] developed an ANN model to predict the recovery factor, oil rate, GOR, cumulative CO

_{2}production, and storage for a multi-cycle WAG process. The model was trained using initial water saturation, vertical-to-horizontal permeability and WAG ratios, and the duration of each cycle as input. The results showed a very good oil recovery factor, cumulative CO

_{2}production, and storage accuracy; however, oil rate and GOR predictions presented significantly less accurate results. By using the proposed model, engineers can make economic assessments and identify the optimum WAG design.

_{2}-WAG procedure and, also, can rank the most important parameters with the highest effect on the WAG process. The training dataset contains many WAG-related real data, such as the WAG scheme (miscible; immiscible), permeability, oil gravity and viscosity, reservoir temperature and pressure, and hydrocarbon pore volume of gas injected. The benefit of the proposed method is that it can be used by engineers to predict the WAG incremental recovery factor ahead of any expensive laboratory and technical studies, giving prior fast and accurate information about the WAG process. In a recent study, Li et al. [145] developed an RF regression algorithm to predict oil production, CO

_{2}storage amount, and CO

_{2}storage efficiency for a CO

_{2}-WAG operation. The authors run several simulations to represent CO

_{2}-WAG development schemes and obtain the training set which consisted of the CO

_{2}-WAG period, CO

_{2}injection rate, and water–gas ratio as the input parameters. Then, the bagging method was used to sample several sub-sets from the training set to train each DT. It was shown that the proposed model could efficiently predict CO

_{2}-WAG performance, since it presented high-accuracy results under computational efficiency.

_{2}-WAG injection, represented by defined OFs and based on injector well locations (input) since they greatly affect the responses. Furthermore, the authors included well-to-well connectivities, injector block permeabilities and porosities, and initial injector block saturations as inputs. The defined OFs are based on NPV, cumulative oil/gas production, and CO

_{2}stored. The authors extended their previous ML method and developed [147] an additional XGB method to determine reservoir responses, represented by a defined OF based on NPV, for changes in well placement, WAG ratio, and slug size. Furthermore, the authors performed an optimization of well locations and controls, using the Mesh Adaptive Direct Search (MADS) technique, providing improvements without increasing the computational cost. Alizadeh et al. [148] built two models, a mathematical-based one and an ANN one, to predict oil recovery using dimensionless scaling groups, based on geological, reservoir, and fluid properties, whose effect on the WAG displacement procedure is determined by an SA. Their results confirmed the ANN’s suitability for predicting oil recoveries. You et al. [149] developed Gaussian kernel SVR (Gaussian-SVR) models integrated with a multi-objective PSO algorithm to obtain optimal results for multi-objective optimization problems in the context of a CO

_{2}-WAG project. For the optimization, various operational parameters that affect the CO

_{2}-WAG operation (e.g., water/gas injection duration, producer BHP, water injection rate) were used. The hyperparameters of the models were adjusted with Bayesian optimization to accomplish the best possible generalization. The study exhibited very good results that were validated by performing simulations using the obtained optimized parameters. The advantage of this study is that it provides engineers with the capability to optimally design a CO

_{2}-WAG process. Additionally, it can apply to the optimization of numerous operational parameters of the CO

_{2}-WAG procedure, expanding the solving capability of large-scale optimization problems.

#### Dynamic Machine Learning Models

_{2}-WAG procedure with time-dependent constraints. The authors first used the LH sampling method to select the most appropriate dataset to train the models. Their main goal was to determine the most suitable hyperparameters of the SVR models and, when the training and validation are complete, to couple the GA for identifying the optimum WAG parameters that maximize cumulative oil production, with time-dependent water-cut constraints. The results showed that the proposed model is very efficient and capable of optimizing a WAG process in real-time. Finally, in 2021, Amar et al. [153] extended their research and developed Multi-Layer Perceptron (MLP) (i.e., a DL ANN) and RBFNN models, with the same training dataset as before, to determine the parameters needed (oil/water production rates—real-time) to optimize the WAG design parameters, such as water and gas injection rate, half-cycle time and downtime, and based on several constraints (a limit for the water cut value and reservoir pressure). Once developed, these models were optimized using the Levenberg–Marquardt (LM) algorithm [154] for the MLP, and the ACO and Grey Wolf Optimization (GWO) [155] algorithms for the RBFNN to enhance their accuracy. The results showed that the coupled MLP-LM model presents a better efficiency than the other two coupled methods.

#### 2.5. Machine Learning Methods for Heavy Oil Production Applications

#### 2.5.1. Machine Learning Models for Thermal EOR Applications

#### Static Machine Learning Models

**Figure 14.**Reinforcement Learning [168].

#### Dynamic Machine Learning Models

#### 2.5.2. Machine Learning Models for Non-Thermal (Chemical) EOR Applications

#### Static Machine Learning Models

#### Dynamic Machine Learning Models

#### 2.6. Machine Learning Methods for Gas Condensate Reservoirs

#### 2.7. Machine Learning Methods for Flow Assurance Problems

## 3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Abbreviations | Meaning |

ML | Machine Learning |

EOR | Enhanced Oil Recovery |

EoS | Equation of State |

HM | History Matching |

PFO | Production Forecast and Optimization |

SL | Supervised Learning |

UL | Unsupervised Learning |

RL | Reinforcement Learning |

NPV | Net Present Value |

DCA | Decline Curve Analysis |

BHP | Bottom Hole Pressure |

ANN | Artificial Neural Network |

GA | Genetic Algorithm |

XGB | Extreme Gradient Boosting |

MVR | MultiVariate Regression |

PSO | Particle Swarm Optimization |

GSO | Genetical Swarm Optimization |

LSSVR | Least Square Support Vector Regression |

LH | Latin Hypercube |

StoSAG | Stochastic Simplex Approximate Gradient |

SVR | Support Vector Regression |

GOR | Gas to Oil Ratio |

RF | Random Forest |

GBR | Gradient Boosting Regressor |

SVM | Support Vector Machine |

CNN | Convolutional Neural Network |

DL | Deep Learning |

RNN | Recurrent Neural Network |

PCA | Principal Component Analysis |

GAN | Generative Adversarial Network |

TgNN | Theory-guided Neural Network |

LSTM | Long Short-Term Memory |

EMD | Empirical-Mode Decomposition |

MDI | Mean Decrease Impurity |

ARIMA | Autoregressive Integrated Moving Average |

EnKF | Ensemble Kalman Filter |

ICA | Imperialist Competitive Algorithm |

MTS | Multivariate Time Series |

VAR | Vector Auto-Regressive |

HONN | Higher Order Neural Network |

ACF | Auto-Correlation Function |

CCF | Cross-Correlation Function |

MLMVN | MultiLayer network with Multi-Valued Neurons |

FNN | Fuzzy Neural Network |

DT | Decision Tree |

AdaBoost | Adaptive Boosting |

LSSVM | Least Square Support Vector Machines |

HFK | Hybrid Fuzzy Kalman filter |

ROM | Reduced Order Model |

MMP | Minimum Miscibility Pressure |

MW | Molecular Weight |

RBFNN | Radial Basis Function Neural Network |

SA | Sensitivity Analysis |

WAG | Water alternating gas |

SCG | Scaled Conjugate Gradient |

MARS | Multivariate Adaptive Regression Splines |

CCS | Carbon Capture Sequestration |

SMAC | Sequential Model-based Algorithm Configuration |

GPR | Gaussian Process Regression |

GMDH | Group Method of Data Handling |

MADS | Mesh Adaptive Direct Search |

ACO | Ant Colony Optimization |

MLP | Multi-Layer Perceptron |

LM | Levenberg–Marquardt |

GWO | Grey Wolf Optimization |

SAGD | Steam-Assisted Gravity Drainage |

CSS | Cyclic Steam Stimulation |

DACE | Design and Analysis of Computer Experiment |

SP | Surfactant–Polymer |

WAT | Wax Appearance Temperature |

ABC | Artificial Bee Colony |

CSA | Coupled Simulated Annealing |

ANFIS | Adaptive Neuro-Fuzzy Inference System |

ERT | Extremely Randomized Tree |

GP | Genetic Programming |

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**Figure 4.**Structure of XGB algorithm [32].

**Figure 6.**Random Forest architecture [52].

**Figure 9.**Architecture of an LSTM cell [65].

**Figure 10.**Adaptive Boosting architecture [98].

**Figure 12.**Multivariate Adaptive Regression Splines algorithm [128].

**Figure 15.**Adaptive Neuro-Fuzzy Inference System architecture [206].

ML Application | ML Training Scheme | Main Objective | ML Method | Reviewed Studies (Reference List Number) |
---|---|---|---|---|

Optimization | Supervised | Production optimization | ANNs or ANNs with optimization techniques | [23,24,25,31,33,93,101] |

DTs and Ensemble methods (e.g., XGB, GBR, RF) | [33,40,101] | |||

SVMs and their variations (e.g., LSSVMs, SVRs) | [36] | |||

Well placement optimization | ANNs or ANNs with optimization techniques | [28,30,92,162] | ||

DTs and Ensemble methods (e.g., XGB, GBR, RF) | [99] | |||

Unsupervised | Production optimization | Clustering techniques | [38,39] | |

Forecasting | Supervised | Static predictions | ANNs or ANNs with optimization techniques | [45,46,48,49,50,51,91,94,100,102,104,113,115,116,117,118,119,120,121,122,123,125,126,127,131,134,140,148,158,159,160,161,163,165,173,174,175,176,177,180,181,189,190,191,192,194,202,210,211] |

RBFNN | [114,180,199,207] | |||

DTs and Ensemble methods (e.g., XGB, GBR, RF) | [43,54,96,100,130,133,145,146,147,180,208,210,212] | |||

SVMs and their variations (e.g., LSSVM, SVRs) | [55,92,100,102,104,110,111,112,133,149,172,179,180,195,196,201,203,205,208,210,211] | |||

Deep Learning (ANN, encoder- decoder CNN, RNN, etc.) | [56,58,59,60,61,95,132,136,138,139,178,197,198,212] | |||

Theory guided networks | [63] | |||

MARS | [129] | |||

ANFIS | [204] | |||

GMDH | [142,143,144] | |||

Unsupervised | GAN | [62,137] | ||

Reinforcement Learning | Reinforcement algorithm | [167] | ||

Supervised | Dynamic predictions | RNNs (mostly LSTMs) | [20,44,54,66,71,72,73,75,106,108] | |

ANNs or ANNs with optimization techniques | [22,76,77,79,86,87,107,135,150,153,169,171,182,183] | |||

RBFNN | [153,170] | |||

SVMs and their variations (e.g., LSSVM, SVRs) | [152] | |||

MTS and VAR | [80] | |||

HONNs | [84,85] | |||

Gamma regression | [86,87] | |||

MLMVN | [89] | |||

Chaotic Neural Networks | [185] |

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**MDPI and ACS Style**

Samnioti, A.; Gaganis, V.
Applications of Machine Learning in Subsurface Reservoir Simulation—A Review—Part II. *Energies* **2023**, *16*, 6727.
https://doi.org/10.3390/en16186727

**AMA Style**

Samnioti A, Gaganis V.
Applications of Machine Learning in Subsurface Reservoir Simulation—A Review—Part II. *Energies*. 2023; 16(18):6727.
https://doi.org/10.3390/en16186727

**Chicago/Turabian Style**

Samnioti, Anna, and Vassilis Gaganis.
2023. "Applications of Machine Learning in Subsurface Reservoir Simulation—A Review—Part II" *Energies* 16, no. 18: 6727.
https://doi.org/10.3390/en16186727