#
Prediction of Key Parameters in the Design of CO_{2} Miscible Injection via the Application of Machine Learning Algorithms

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## Abstract

**:**

_{2}-hydrocarbon solubility ratio (Rs), interfacial tension (IFT), and minimum miscibility pressure (MMP), is vital for the success of CO

_{2}-enhanced oil recovery (CO

_{2}-EOR) projects. This study presents a robust machine learning framework that leverages deep neural networks (MLP-Adam), support vector regression (SVR-RBF) and extreme gradient boosting (XGBoost) algorithms to obtained accurate predictions of these critical parameters. The models are developed and validated using a comprehensive database compiled from previously published studies. Additionally, an in-depth analysis of various factors influencing the Rs, IFT, and MMP is conducted to enhance our understanding of their impacts. Compared to existing correlations and alternative machine learning models, our proposed framework not only exhibits lower calculation errors but also provides enhanced insights into the relationships among the influencing factors. The performance evaluation of the models using statistical indicators revealed impressive coefficients of determination of unseen data (0.9807 for dead oil solubility, 0.9835 for live oil solubility, 0.9931 for CO

_{2}-n-Alkane interfacial tension, and 0.9648 for minimum miscibility pressure). One notable advantage of our models is their ability to predict values while accommodating a wide range of inputs swiftly and accurately beyond the limitations of common correlations. The dataset employed in our study encompasses diverse data, spanning from heptane (C

_{7}) to eicosane (C

_{20}) in the IFT dataset, and MMP values ranging from 870 psi to 5500 psi, covering the entire application range of CO

_{2}-EOR. This innovative and robust approach presents a powerful tool for predicting crucial parameters in CO

_{2}-EOR projects, delivering superior accuracy, speed, and data diversity compared to those of the existing methods.

## 1. Introduction

_{2}-EOR becomes even more crucial as part of carbon capture, utilization, and storage (CCUS) strategies [6]. This approach aligns with the industry’s goal to remain a leading energy system while addressing environmental concerns. By effectively managing and utilizing CO

_{2}emissions for oil recovery, the industry not only enhances its resource efficiency but also makes significant strides toward sustainability [7].

_{2}gas injection has emerged as the most widely implemented approach in numerous countries, particularly for light oil reservoirs [8]. With nearly 80% of global reservoirs suited for some form of CO

_{2}injection [9], this method’s growing prevalence can be attributed to the economic attractiveness of naturally sourced CO

_{2}, which provides a cost-effective supply [10].

_{2}-EOR project heavily relies on key parameters such as minimum miscibility pressure (MMP), interfacial tension (IFT), and solubility (Rs) [11]. When CO

_{2}is injected into oil reservoirs, it dissolves in the oil, causing the oil to swell and reducing its viscosity. This process also lowers the interfacial tension between fluid phases, aiding in the retrieval of trapped oil. Optimal conditions are achieved when the interfacial tension between fluid phases reaches zero, which signifies that CO

_{2}has become fully miscible with the oil, thereby facilitating the most efficient oil displacement [12].

_{2}injection, employing both experimental and numerical simulation techniques [16]. In recent times, machine learning methods have been increasingly used to gain valuable insights into EOR projects [15]. This study aims to further contribute to this burgeoning field by applying various supervised machine learning techniques to accurately predict key parameters including solubility (Rs), interfacial tension (IFT), and minimum miscibility pressure (MMP) required for effective CO

_{2}-EOR design.

## 2. Literature Review

_{2}miscible injection requires the prediction of key parameters such as the minimum miscibility pressure (MMP), CO

_{2}solubility, and phase behavior of the CO

_{2}–oil system.

_{2}miscible injection, as it indicates the pressure at which the injected CO

_{2}and the oil become completely miscible [17]. Accurate prediction of the MMP is necessary to optimize the design of the CO

_{2}injection process and increase oil recovery [18]. Several models and methods have been proposed to predict the MMP in CO

_{2}miscible injection. These models can be categorized into equation of state (EOS) models and empirical models [19]. EOS models are based on the principle of thermodynamics and can predict the phase behavior of the CO

_{2}–oil system as a function of pressure and temperature. Empirical models, on the other hand, use statistical methods to fit experimental data and predict the MMP [20].

_{2}and oil molecules and it can predict the phase behavior of the CO

_{2}–oil system [21]. Several modifications have been proposed to improve the accuracy of the PR model for predicting the MMP. For instance, Kiani et al. [22] developed a new PR model that accounts for the impact of asphaltene on MMP prediction. This model was validated using experimental data and demonstrated superior accuracy compared to that of existing models. Additionally, Tahsin Ahmed [23] utilized a modified version of the PR EOS, along with a newly introduced “Miscibility Function”, to estimate the injection pressure required for miscible gas injection. Meanwhile, Alshuaibi et al. [24] developed a novel formula for the Abu Dhabi reservoir, which incorporates parameters such as temperature, saturation pressure, and reservoir fluid composition to determine the MMP. Rajak and Ashutosh [25] used multiple EOS models, despite the limited laboratory data, to develop a novel approach for estimating the appropriate MMP value. These methods offer potential ways to optimize the design of CO

_{2}injection and enhance oil recovery.

_{2}miscible flooding. The results showed that the ANN prediction was overall better than the ANFIS technique. Li et al. [28] evaluated the reliability of four machine learning-based prediction models including neural network analysis (NNA), genetic function approximation (GFA), multiple linear regression (MLR), and partial least squares (PLS) using 136 sets of data. Other machine learning models have also been developed for MMP prediction, such as those developed by the authors of [18,29,30,31,32].

_{2}solubility in oil is another important parameter that affects the design of CO

_{2}miscible injection. Various models have been developed to accurately predict CO

_{2}solubility in crude oil. Zhang et al. [33] developed a novel method using artificial neural networks to predict CO

_{2}solubility in heavy oil, which was found to be accurate and more efficient than traditional simulation methods. Dadan et al. [34] provided a reliable model to predict CO

_{2}solubility in formation brines using ion-specific parameters and a binary interaction parameter between ions and CO

_{2}. The solubility of CO

_{2}in aqueous electrolyte solutions was also described using the electrolyte perturbed hard-sphere chain equation of state (e-PHSC) by Dadan et al. [34]. Zhen et al. [35] employed an artificial neural network (ANN) and support vector machine (SVM) to develop GC models based on 10,116 CO

_{2}solubility data measured in various ionic liquids (ILs) at different temperatures and pressures. These models can significantly aid in the design of a CO

_{2}miscible injection.

_{2}–oil system is another critical parameter that affects the design of a CO

_{2}miscible injection. Cheng et al. [36] investigated the effect of phase behavior on the design of a CO

_{2}miscible injection. The study showed that the CO

_{2}–oil system can exhibit different phase behaviors depending on the pressure and temperature conditions. Therefore, it is important to consider the phase behavior when designing CO

_{2}miscible injection. Zhao et al. [37] developed a new model to predict the CO

_{2}–oil phase behavior using the Grayson–Streed method. The model was validated using experimental data and was found to be more accurate than existing models.

## 3. Data Collection

#### 3.1. Solubility (Rs)

_{2}) in oil, taken with the experimental apparatus.

_{2}solubility. Furthermore, these properties are frequently utilized in artificial intelligence projects focusing on solubility.

_{2}solubility, ensuring that our dataset was relevant and precise. This selection also facilitated the effective development and execution of our machine learning models, allowing a meaningful analysis of the collected data. Table 1 shows a statistical description of the data.

_{2}(Rs) in both models. As the saturation pressure increases, the solubility also increases.

#### 3.2. Interfacial Tension (IFT)

_{2}–n-alkane interfacial tension (IFT, mN/m) were gathered from various research sources, including works by Zolghadr et al. [43], Philip T. Jaeger [44], and Georgiadis et al. [45]. It is important to note that the sessile drop technique at high pressures was the primary method used for experimentally determining the interfacial tension in most of these sources. The histogram displayed below (Figure 4) illustrates the data distribution for each component.

#### 3.3. Minimum Miscibility Pressure (MMP)

_{C5+}, g/mol), and the ratio of volatile to intermediate components (

_{xvol}/

_{xint}). This selection of inputs ensured that our model was guided by factors directly influencing the MMP, providing a reliable basis for accurate predictions.

## 4. Model Implementation

- Dead oil solubility model: the training and validation set comprised 85% of the dataset (90 samples), and a test set formed 15% of the dataset (15 samples).
- Live oil solubility model: the training set contained 80% of the dataset (60 samples), and a test set held 20% of the dataset (14 samples).
- Interfacial tension model: the training set included 80% of the dataset (856 samples), a cross-validation set made up 1/8 of the training set (107 samples), and a test set represented 20% of the dataset (215 samples).
- Minimum miscibility pressure model: the training set consisted of 84% of the dataset (162 samples), and a test set incorporated 16% of the dataset (31 samples).

#### 4.1. Dead Oil Solubility

^{2}) were computed (please refer to Appendix A for the definition and mathematical formulation of these metrics). The outcomes of these calculations are presented in Table 8. For visual validation, the predicted values versus the actual values for both the training and test data are depicted in Figure 14.

^{2}(check Table 9)and supplemented with an error histogram plot of the different correlations as depicted in Figure 15 below. Upon examination, the histogram of Chung et al. showcases a significant error in comparison to the other models. While the model by Emera and Sarma holds a considerable number of zero-error values, its distribution is skewed to the right with a somewhat wide error range. The model from Rostami et al. [52] presents a favorable error distribution with minimal values; nevertheless, the MLP-Adam model is still considered superior in comparison to those outlined in the literature.

#### 4.2. Live Oil Solubility

^{2}were computed, with the corresponding results presented in Table 11.

#### 4.3. Interfacial Tension

^{2}) were computed and the resulting performance are provided in Table 14.

^{2}(refer to Table 15), as well as through the construction of scatter plots that juxtapose the experimental IFT values with the respective predictions made by each model (see Figure 21).

#### 4.4. Minimum Miscibility Pressure

^{2})-were computed, and the results are presented in Table 17.

_{2}(100% CO

_{2}) and others for impure CO

_{2}(CO

_{2}containing percentages of C

_{1}, N

_{2}, H

_{2}S, etc.), the data was bifurcated into ‘pure’ and ‘impure’ based on the critical temperature. For pure CO

_{2}, the correlations of Alston et al. (pure) [48], Lee [56], and Emera-Sarma [57] were used, while for impure CO

_{2}, the correlations of Alston et al. (impure) [48] and Fathinasab-Ayatollahi [58] were utilized. Table 18 summarizes the results of the comparison.

_{2}case (Figure 25), it becomes apparent that while all correlations reasonably predict an acceptable quantity of values (roughly 20), they are subject to extensive error ranges and less satisfactory distributions when compared to the XGBoost model. The XGBoost model stands out with more than 50 values concentrated around 0, and an error range restricted to −1 to 0.5. This stark contrast emphasizes the superior performance and reliability of the XGBoost model when handling pure data.

_{2}(Figure 26), the Fathinasab-Ayatollahi [58] correlation delivered a relatively low error margin and a fairly decent distribution compared to that of Alston et al. [48]. However, it still could not rival the predictive efficiency of the XGBoost model, which exhibited a minimal error margin ranging from −2 to 2 and recorded over 60 values clustered around 0. This further emphasizes the robustness and precision of the XGBoost model in estimating impure CO

_{2}data.

## 5. Conclusions

_{2}-enhanced oil recovery (CO

_{2}-EOR) operations: the solubility of CO

_{2}in both dead and live oil, the interfacial tension, and the minimum miscibility pressure. These parameters are critical as they play a significant role in the planning and implementation of CO

_{2}-EOR projects. For instance, accurate estimation of the CO

_{2}solubility in oil can inform on oil displacement efficiency, while a precise calculation of interfacial tension aids in assessing the mobility of the injected CO

_{2}, and understanding the minimum miscibility pressure is essential for the economic feasibility of the operation.

_{2}-EOR projects remains an area for future exploration. Potential variability in the underlying data is another factor that could influence the models’ performance.

_{2}-EOR projects, contributing to the advancements in the field of petroleum reservoir studies.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Average Absolute Relative Deviation (AARD (%))

- n is the total number of observations;
- Actual refers to the actual value;
- Predicted refers to the predicted value.

#### Appendix A.2. Root Mean Square Error (RMSE)

- n is the total number of observations;
- Actual refers to the actual value;
- Predicted refers to the predicted value.

#### Appendix A.3. Coefficient of Determination (R_{2})

^{2}of a model is 0.50, then approximately half of the observed variation can be explained by the model’s inputs.

^{2}is as follows:

- SSres is the sum of squares of the residual errors.
- SStot is the total sum of squares.

## Appendix B

#### Appendix B.1. Feed Forward Equation of our MLP-Adam Model

- Initialize the input data. Let us denote the input vector as X.
- Calculate the activations of the neurons in the first hidden layer by applying the ReLU activation function (this function computes the maximum value between 0 and the input x. If x is positive, the output is equal to x, and if x is negative, the output is set to 0) to the resulting sum to introduce non-linearity. This is carried out using the following equation:$$a{1}_{j}=f\left(z{1}_{j}\right)=ReLU\left({\displaystyle \sum}_{i=1}^{n}{w}_{ji}\xb7{X}_{i}+{b}_{j}\right)$$

- 3.
- The same process is repeated for the second hidden layer. The output of the second hidden layer is denoted as $a2$.$$a{2}_{k}=f\left(z{2}_{k}\right)=ReLU\left({\displaystyle \sum}_{k=1}^{p}{w}_{jk}\xb7a{1}_{j}+{b}_{k}\right)$$

- 4.
- Finally, the output of our MLP-Adam model can be calculated by applying the purelin function to the output of the ReLU function as shown below:$${Y}_{P}={\displaystyle \sum}_{k=1}^{p}{w}_{kl}\xb7a{2}_{k}+{b}_{l}$$

#### Appendix B.2. Example Calculations using MLP-Adam Model

${\mathit{w}}_{\mathit{j},\mathit{M}\mathit{W}}$ | ${\mathit{w}}_{\mathit{j},\mathit{\gamma}}$ | ${\mathit{w}}_{\mathit{j},\mathit{T}}$ | ${\mathit{w}}_{\mathit{j},\mathit{P}\mathit{s}}$ | ${\mathit{b}}_{\mathit{j}}$ |
---|---|---|---|---|

0.423479229 | −0.518270671 | 0.088841140 | 0.164605036 | −0.182387754 |

−0.316850155 | 0.578180193 | −0.627018213 | −0.370452255 | −0.037461437 |

−0.260930061 | 0.121095933 | 0.302609562 | 0.177341118 | 0.035739433 |

0.153113961 | −0.273656278 | 0.023316100 | −0.014185284 | −0.152793422 |

0.326721847 | 0.163599714 | 0.017112899 | 0.437370806 | −0.370236605 |

0.467836350 | −0.183758318 | −0.116376496 | 0.173847764 | 0.190825283 |

0.207402825 | −0.402902960 | 0.277075022 | 0.077882327 | −0.256408870 |

0.430666834 | 0.488847017 | 0.382416307 | 0.316209614 | −0.437328159 |

−0.378489106 | −0.191637143 | −0.586777627 | 0.073175244 | −0.207403078 |

−0.280519455 | −0.169934719 | −0.038683220 | 0.464787781 | 0.129119664 |

−0.012112551 | −0.279909700 | 0.314301490 | −0.553606331 | 0.127572730 |

0.203990727 | 0.348036944 | 0.120888933 | −0.571946859 | −0.362548828 |

**Table A2.**Weights and biases of the second hidden layer and the output layer of the proposed MLP-Adam model.

${\mathit{w}}_{1,\mathit{k}}$ | ${\mathit{w}}_{2,\mathit{k}}$ | ${\mathit{w}}_{3,\mathit{k}}$ | ${\mathit{w}}_{4,\mathit{k}}$ | ${\mathit{w}}_{5,\mathit{k}}$ | ${\mathit{w}}_{6,\mathit{k}}$ | ${\mathit{w}}_{7,\mathit{k}}$ | ${\mathit{w}}_{8,\mathit{k}}$ |

0.144444540 | 0.227294683 | −0.281868785 | −0.386379957 | −0.244969561 | 0.250844776 | −0.042056944 | 0.090741582 |

−1.246394872 | −0.613879323 | −0.806254267 | 0.332979083 | 0.174128487 | −0.160888448 | −0.905039012 | 0.223389938 |

0.158317938 | 0.136602625 | 0.250266492 | −0.048559281 | −0.043032091 | −0.009495512 | 0.364784896 | −0.316569924 |

−0.292102873 | 0.049241617 | 0.113946393 | 0.185241475 | −0.189562544 | 0.473260581 | 0.171075671 | −0.035240747 |

−0.311310201 | −1.128083109 | −0.132358402 | −0.147601380 | 0.150322437 | −0.051223963 | −0.059710107 | 0.302232533 |

−0.527317762 | 0.004510418 | −0.090777598 | 0.033773034 | 0.003524607 | 0.325446367 | −0.200799241 | −1.144739747 |

0.641047120 | −0.064388409 | 0.391169577 | −0.684768438 | −0.434764891 | 0.371954649 | −0.063837923 | −0.090706437 |

−0.190623462 | 0.257651656 | 0.394092589 | 0.200460493 | −0.200868785 | 0.064583137 | 0.155178993 | 0.315470844 |

0.193483933 | −0.301786810 | 0.255001187 | −0.513664782 | −0.427212923 | −0.234824061 | −0.042243052 | 0.111917041 |

−1.080619454 | 0.096860095 | 0.129510939 | 0.049882758 | 0.238265812 | −1.272954463 | 0.236488863 | −0.735467910 |

−0.364739000 | −0.515439033 | −0.178362324 | −0.179078683 | −0.595661461 | −0.054487861 | −0.096768409 | −0.003158351 |

−0.499953687 | 0.379382699 | −0.177857115 | −0.423149019 | −0.938039004 | 0.343048214 | −0.956486344 | 0.245499372 |

${\mathit{w}}_{9,\mathit{k}}$ | ${\mathit{w}}_{10,\mathit{k}}$ | ${\mathit{w}}_{11,\mathit{k}}$ | ${\mathit{w}}_{12,\mathit{k}}$ | ${\mathit{b}}_{\mathit{k}}$ | ${\mathit{w}}_{\mathit{k},\mathit{l}}$ | ${\mathit{b}}_{\mathit{l}}$ | |

−0.792608916 | −0.343328714 | −0.205415770 | −0.539200484 | 0.158580690 | 0.079246789 | 0.300516456 | |

0.365020424 | −0.149115592 | −0.426100313 | 0.130489438 | 0.123922713 | 0.187488675 | ||

0.137588575 | 0.520926713 | −0.278029352 | −0.333180844 | −0.322128087 | −0.186551764 | ||

0.191870614 | 0.492062687 | −0.308154106 | −0.205118045 | 0.259233176 | 0.440697550 | ||

−0.230481609 | −0.726262688 | 0.058385573 | −0.124779440 | −0.023145271 | 0.217374727 | ||

0.379300296 | 0.162133157 | 0.567164421 | 0.756009399 | −0.201348185 | −0.275265455 | ||

−0.633766531 | 0.062475737 | 0.018612951 | −0.710203170 | 0.197099491 | 0.088092155 | ||

0.158039510 | −0.123929366 | 0.011550034 | 0.471806019 | −0.221232160 | −0.171224877 | ||

0.196399033 | −0.388778716 | −0.568655312 | 0.230788096 | −0.103322580 | −0.453178435 | ||

0.274261921 | −0.640708744 | 0.155315384 | 0.250834226 | 0.017402615 | −0.166323795 | ||

0.512196242 | −0.019978577 | −0.330687165 | 0.177631750 | 0.079844228 | 0.371093213 | ||

−0.256439089 | 0.436899453 | −0.405297756 | 0.383212924 | −0.086818188 | 0.109248526 |

MW | γ | T | Ps | $\mathit{z}1$ | $\mathit{a}1$ | $\mathit{z}2$ | $\mathit{a}2$ | Rs-Pred | Rs-Exp |
---|---|---|---|---|---|---|---|---|---|

1.54606763 | 0.90499909 | 2.66878506 | 0.76176893 | 0.3657942 −1.9596565 0.68460845 −0.1123078 0.6618012 0.56967878 0.49840513 1.93238358 −2.4762450 −0.2075494 0.2726109 0.15474298 | 0.3657942 0 0.68460845 0 0.6618012 0.56967878 0.49840513 1.93238358 0 0 0.2726109 0.15474298 | 0.01417779 −0.9757543 −0.6840449 0.2759657 0.39354511 −2.3092059 0.31163391 0.64580446 −0.1985719 −2.0788913 −0.7179282 −0.8703367 | 0.01417779 0 0 0.2759657 0.39354511 0 0.31163391 0.64580446 0 0 0 0 | 0.4256788 | 0.42 |

## References

- Holdren, J.P. Population and the energy problem. Popul. Env.
**1991**, 12, 231–255. [Google Scholar] [CrossRef] - Laherrere, J.; Hall, C.B.; Bentley, R. How much oil remains for the world to produce? Comparing assessment methods, and separating fact from fiction. Curr. Res. Environ. Sustain.
**2022**, 4, 100174. [Google Scholar] [CrossRef] - Ozotta, O.; Ostadhassan, M.; Lee, H.; Pu, H.; Kolawole, O.; Malki, M.L. Time-dependent Impact of CO
_{2}-shale Interaction on CO_{2}Storage Potential. In Proceedings of the 15th Greenhouse Gas Control Technologies Conference, Abu Dhabi, United Arab Emirates, 18 March 2021; pp. 15–18. [Google Scholar] - Clonts, M.; Mazighi, M.; Touami, M. Reservoir simulation of the planned miscible gas injection project at Rhourde El Baguel, Algeria. In Proceedings of the European Petroleum Conference, Milan, Italy, 22–24 October 1996; OnePetro: Richardson, TX, USA, 1996. [Google Scholar]
- Malki, M.L.; Rasouli, V.; Saberi, M.R.; Sennaoui, B.; Ozotta, O.; Chellal, H.A. Effect of CO
_{2}on Mineralogy, Fluid, and Elastic Properties in Middle Bakken Formation Using Rock Physics Modeling. In Proceedings of the ARMA US Rock Mechanics/Geomechanics Symposium, Santa Fe, NM, USA, 26–29 June 2022. [Google Scholar] [CrossRef] - Hasan, M.M.F.; First, E.L.; Boukouvala, F.; Floudas, C.A. A multi-scale framework for CO
_{2}capture, utilization, and sequestration: CCUS and CCU. Comput. Chem. Eng.**2015**, 81, 2–21. [Google Scholar] [CrossRef] [Green Version] - Merzoug, A.; Mouedden, N.; Rasouli, V.; Damjanac, B. Simulation of Proppant Placement Efficiency at the Intersection of Induced and Natural Fractures. In Proceedings of the ARMA US Rock Mechanics/Geomechanics Symposium, Santa Fe, NM, USA, 26–29 June 2022. [Google Scholar] [CrossRef]
- Afari, S.; Ling, K.; Sennaoui, B.; Maxey, D.; Oguntade, T.; Porlles, J. Optimization of CO
_{2}huff-n-puff EOR in the Bakken Formation using numerical simulation and response surface methodology. J. Pet. Sci. Eng.**2022**, 215 Pt A, 110552. [Google Scholar] [CrossRef] - Taber, J.J.; Martin, F.D.; Seright, R.S. EOR screening criteria revisited -Part 1: Introduction to screening criteria and enhanced recovery field projects. SPE Reserv. Eng.
**1997**, 12, 189–198. [Google Scholar] [CrossRef] [Green Version] - Sennaoui, B.; Pu, H.; Afari, S.; Malki, M.L.; Kolawole, O. Pore- and Core-Scale Mechanisms Controlling Supercritical Cyclic Gas Utilization for Enhanced Recovery under Immiscible and Miscible Conditions in the Three Forks Formation. Energy Fuels
**2023**, 37, 459–476. [Google Scholar] [CrossRef] - Almobarak, M.; Wu, Z.; Daiyu, Z.; Fan, K.; Liu, Y.; Xie, Q. A review of chemical-assisted minimum miscibility pressure reduction in CO
_{2}injection for enhanced oil recovery. Petroleum**2021**, 7, 245–253. [Google Scholar] [CrossRef] - El-Hoshoudy, A.; Desouky, S. CO
_{2}Miscible Flooding for Enhanced Oil Recovery. In Carbon Capture, Utilization and Sequestration; InTech eBooks: London, UK, 2018. [Google Scholar] [CrossRef] [Green Version] - Mouedden, N.; Laalam, A.; Mahmoud, M.; Rabiei, M.; Merzoug, A.; Ouadi, H.; Boualam, A.; Djezzar, S. A Screening Methodology Using Fuzzy Logic to Improve the Well Stimulation Candidate Selection. In All Days; OnePetro: Richardson, TX, USA, 2022. [Google Scholar] [CrossRef]
- Boualam, A.; Rasouli, V.; Dalkhaa, C.; Djezzar, S. Stress-Dependent Permeability and Porosity in Three Forks Carbonate Reservoir, Williston Basin. In Proceedings of the 54th U.S. Rock Mechanics/Geomechanics Symposium, Physical Event Cancelled, Golden, CO, USA, 28 June–1 July 2020. [Google Scholar]
- Boualam, A.; Rasouli, V.; Dalkhaa, C.; Djezzar, S. Advanced Petrophysical Analysis and Water Saturation Prediction in Three Forks, Williston Basin. In Proceedings of the SPWLA Annual Logging Symposium, Online, 24 June–29 July 2020. [Google Scholar] [CrossRef]
- Koroteev, D.; Tekic, Z. Artificial intelligence in oil and gas upstream: Trends, challenges, and scenarios for the future. Energy AI
**2021**, 3, 100041. [Google Scholar] [CrossRef] - Dargahi-Zarandi, A.; Hemmati-Sarapardeh, A.; Shateri, M.; Menad, N.A.; Ahmadi, M. Modeling minimum miscibility pressure of pure/impure CO
_{2}-crude oil systems using adaptive boosting support vector regression: Application to gas injection processes. J. Pet. Sci. Eng.**2020**, 184, 106499. [Google Scholar] [CrossRef] - Sambo, C.; Liu, N.; Shaibu, R.; Ahmed, A.A.; Hashish, R.G. A Technical Review of CO
_{2}for Enhanced Oil Recovery in Unconventional Oil Reservoirs. Geoenergy Sci. Eng.**2022**, 221, 111185. [Google Scholar] [CrossRef] - Fath, A.H.; Pouranfard, A.-R. Evaluation of miscible and immiscible CO
_{2}injection in one of the Iranian oil fields. Egypt. J. Pet.**2014**, 23, 255–270. [Google Scholar] [CrossRef] [Green Version] - Lv, Q.; Zheng, R.; Guo, X.; Larestani, A.; Hadavimoghaddam, F.; Riazi, M.; Hemmati-Sarapardeh, A.; Wang, K.; Li, J. Modelling minimum miscibility pressure of CO
_{2}-crude oil systems using deep learning, tree-based, and thermodynamic models: Application to CO_{2}sequestration and enhanced oil recovery. Sep. Purif. Technol.**2023**, 310, 123086. [Google Scholar] [CrossRef] - Yang, G.; Li, X. Modified Peng-Robinson equation of state for CO
_{2}/hydrocarbon systems within nanopores. J. Nat. Gas Sci. Eng.**2020**, 84, 103700. [Google Scholar] [CrossRef] - Kiani, S.; Saeedi, M.; Nikoo, M.R.; Mohammadi, A.H. New model for prediction of minimum miscibility pressure and CO
_{2}solubility in crude oil. J. Nat. Gas Sci. Eng.**2020**, 80, 103431. [Google Scholar] [CrossRef] - Ahmed, T. Minimum Miscibility Pressure from EOS. In Proceedings of the Canadian International Petroleum Conference, Calgary, AB, Canada, 4–8 June 2000. [Google Scholar] [CrossRef]
- Alshuaibi, M.; Farzaneh, S.A.; Sohrabi, M.; Mogensen, K. An Accurate and Reliable Correlation to Determine CO
_{2}/Crude Oil MMP for High-Temperature Reservoirs in Abu Dhabi. In Proceedings of the Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, United Arab Emirates, 11–14 November 2019. [Google Scholar] [CrossRef] - Jhalendra, R.K.; Kumar, A. Reliable estimate of minimum miscibility pressure from multiple possible EOS models for a reservoir oil under data constraint. Pet. Sci. Technol.
**2022**, 40, 1898–1913. [Google Scholar] [CrossRef] - Sinha, U.; Dindoruk, B.; Soliman, M. Prediction of CO
_{2}Minimum Miscibility Pressure MMP Using Machine Learning Techniques. In Proceedings of the SPE Improved Oil Recovery Conference, Virtual, 31 August–4 September 2020. [Google Scholar] [CrossRef] - Shakeel, M.; Khan, M.R.; Kalam, S.; Khan, R.A.; Patil, S.; Dar, U.A. Machine Learning for Prediction of CO
_{2}Minimum Miscibility Pressure. In Proceedings of the Society of Petroleum Engineers—Middle East Oil, Gas and Geosciences Show, MEOS, Manama, Bahrain, 19–21 February 2023; SPE Middle East Oil and Gas Show and Conference, MEOS, Proceedings; Society of Petroleum Engineers (SPE): Richardson, TX, USA, 2023. [Google Scholar] [CrossRef] - Li, D.; Li, X.; Zhang, Y.; Sun, L.; Yuan, S. Four Methods to Estimate Minimum Miscibility Pressure of CO
_{2}-Oil Based on Machine Learning. Chin. J. Chem.**2019**, 37, 1271–1278. [Google Scholar] [CrossRef] - Ekechukwu, G.K.; Falode, O.; Orodu, O.D. Improved Method for the Estimation of Minimum Miscibility Pressure for Pure and Impure CO
_{2}–Crude Oil Systems Using Gaussian Process Machine Learning Approach. ASME J. Energy Resour. Technol.**2020**, 142, 123003. [Google Scholar] [CrossRef] - Dong, P.; Liao, X.; Chen, Z.; Chu, H. An improved method for predicting CO
_{2}minimum miscibility pressure based on artificial neural network. Adv. Geo-Energy Res.**2019**, 3, 355–364. [Google Scholar] [CrossRef] [Green Version] - Huang, C.; Tian, L.; Zhang, T.; Chen, J.; Wu, J.; Wang, H.; Wang, J.; Jiang, L.; Zhang, K. Globally optimized machine-learning framework for CO
_{2}hydrocarbon minimum miscibility pressure calculations. Fuel**2022**, 329, 125312. [Google Scholar] [CrossRef] - Ge, D.; Cheng, H.; Cai, M.; Zhang, Y.; Dong, P. A New Predictive Method for CO
_{2}-Oil Minimum Miscibility Pressure. Geofluids**2021**, 2021, 8868592. [Google Scholar] [CrossRef] - Chemmakh, A.; Merzoug, A.; Ouadi, H.; Ladmia, A.; Rasouli, V. Machine Learning Predictive Models to Estimate the Minimum Miscibility Pressure of CO
_{2}-Oil System. In Proceedings of the Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, United Arab Emirates, 15–18 November 2021. [Google Scholar] [CrossRef] - Ramdan, D.; Najmi, M.; Rajabzadeh, H.; Elveny, M.; Alizadeh, S.M.S.; Shahriari, R. Prediction of CO
_{2}solubility in electrolyte solutions using the e-PHSC equation of state. J. Supercrit. Fluids**2022**, 180, 105454. [Google Scholar] [CrossRef] - Song, Z.; Shi, H.; Zhang, X.; Zhou, T. Prediction of CO
_{2}solubility in ionic liquids using machine learning methods. Chem. Eng. Sci.**2020**, 223, 115752. [Google Scholar] [CrossRef] - Cheng, Y.; Zhang, X.; Lu, Z.; Pan, Z.J.; Zeng, M.; Du, X.; Xiao, S. The effect of subcritical and supercritical CO
_{2}on the pore structure of bituminous coals. J. Nat. Gas Sci. Eng.**2021**, 94, 104132. [Google Scholar] [CrossRef] - Zhao, W.; Zhang, T.; Jia, C.; Li, X.; Wu, K.; He, M. Numerical simulation on natural gas migration and accumulation in sweet spots of tight reservoir. J. Nat. Gas Sci. Eng.
**2020**, 81, 103454. [Google Scholar] [CrossRef] - Srivastava, R.K.; Huang, S.S.; Dyer, S.B. Measurement and Prediction of PVT Properties of Heavy and Medium Oils with Carbon Dioxide; No. CONF-9502114-Vol. 1; UNITAR: New York, NY, USA, 1995. [Google Scholar]
- Kokal, S.L.; Sayegh, S.G. Phase behavior and physical properties of CO-saturated heavy oil and its constitutive fractions. In Proceedings of the Annual Technical Meeting, Calgary, AB, Canada, 9–12 June 1990; OnePetro: Richardson, TX, USA, 1990. [Google Scholar]
- Simon, R.; Graue, D.J. Generalized correlations for predicting solubility, swelling and viscosity behavior of CO
_{2}-crude oil systems. J. Pet. Technol.**1965**, 17, 102–106. [Google Scholar] [CrossRef] - Simon, R.; Rosman, A.; Zana, E. Phase-behavior properties of CO
_{2}-reservoir oil systems. Soc. Pet. Eng. J.**1978**, 18, 20–26. [Google Scholar] [CrossRef] - Sim, S.S.K.; Udegbuanam, E.; Haggerty, D.J.; Baroni, J.; Baroni, M. Laboratory experiments and reservoir simulation studies in support of CO
_{2}injection project in Mattoon field, Illinois, USA. In Proceedings of the Annual Technical Meeting, New Orleans, LA, USA, 25–28 September 1994; OnePetro: Richardson, TX, USA, 1994. [Google Scholar] - Zolghadr, A.; Escrochi, M.; Ayatollahi, S. Temperature and Composition Effect on CO
_{2}Miscibility by Interfacial Tension Measurement. J. Chem. Eng. Data**2013**, 58, 1168–1175. [Google Scholar] [CrossRef] - Jaeger, P.T.; Alotaibi, M.B.; Nasr-El-Din, H.A. Influence of Compressed Carbon Dioxide on the Capillarity of the Gas−Crude Oil−Reservoir Water System. J. Chem. Eng. Data
**2010**, 55, 5246–5251. [Google Scholar] [CrossRef] - Georgiadis, A.; Llovell, F.; Bismarck, A.; Blas, F.J.; Galindo, A.; Maitland, G.C.; Trusler, J.P.M.; Jackson, G. Interfacial tension measurements and modelling of (carbon dioxide + n-alkane) and (carbon dioxide + water) binary mixtures at elevated pressures and temperatures. J. Supercrit. Fluids
**2010**, 55, 743–754. [Google Scholar] [CrossRef] - Cronquist, C. Carbon dioxide dynamic miscibility with light reservoir oils. In Proceedings of the Fourth Annual US DOE Symposium, Tulsa, OK, USA; 1978. [Google Scholar]
- Yellig, W.; Metcalfe, R. Determination and Prediction of CO
_{2}Minimum Miscibility Pressures (includes associated paper 8876). J. Pet. Technol.**1980**, 32, 160–168. [Google Scholar] [CrossRef] - Alston, R.; Kokolis, G.; James, C. CO
_{2}minimum miscibility pressure: A correlation for impure CO_{2}streams and live oil systems. Soc. Pet. Eng. J.**1985**, 25, 268–274. [Google Scholar] [CrossRef] - Yuan, H.; Johns, R.T.; Egwuenu, A.M.; Dindoruk, B. Improved MMP correlations for CO
_{2}floods using analytical gas flooding theory. In Proceedings of the Society of Petroleum Engineers—SPE/DOE Symposium on Improved Oil Recovery, IOR, Tulsa, OK, USA, 17–21 April 2004; (Proceedings—SPE Symposium on Improved Oil Recovery; Vol. 2004-April); Society of Petroleum Engineers (SPE): Richardson, TX, USA, 2004. [Google Scholar] - Chen, B.L.; Huang, H.D.; Zhang, Y. An Improved Predicting Model for Minimum Miscibility Pressure (MMP) of CO
_{2}and Crude Oil. J. Oil Gas Technol.**2013**, 35, 126–130. [Google Scholar] - Chung, F.T.H.; Jones, R.A.; Burchfield, T.E. Recovery of Viscous Oil Under High Pressure by CO
_{2}Displacement: A Laboratory Study. In Proceedings of the International Meeting on Petroleum Engineering, Tianjin, China, 1–4 November 1988. [Google Scholar] [CrossRef] - Rostami, A.; Arabloo, M.; Kamari, A.; Mohammadi, A.H. Modeling of CO
_{2}solubility in crude oil during carbon dioxide enhanced oil recovery using gene expression programming. Fuel**2017**, 210, 768–782. [Google Scholar] [CrossRef] - Emera, M.K.; Sarma, H.K. Prediction of CO
_{2}Solubility in Oil and the Effects on the Oil Physical Properties. Energy Sources Part A Recovery Util. Environ. Eff.**2007**, 29, 1233–1242. [Google Scholar] [CrossRef] - Yu, H.; Xie, T.; Paszczynski, S.; Wilamowski, B.M. Advantages of Radial Basis Function Networks for Dynamic System Design. IEEE Trans. Ind. Electron.
**2011**, 58, 5438–5450. [Google Scholar] [CrossRef] - Mirzaie, M.; Tatar, A. Modeling of interfacial tension in binary mixtures of CH
_{4}, CO_{2}, and N_{2}-alkanes using gene expression programming and equation of state. J. Mol. Liq.**2020**, 320 Pt B, 114454. [Google Scholar] [CrossRef] - Lee, I. Effectiveness of Carbon Dioxide Displacement under Miscible and Immiscible Conditions; U.S. Department of Energy Office of Scientific and Technical Information: Oak Ridge, TN, USA, 1979. [Google Scholar]
- Emera, M.K.; Javadpour, F.; Sarma, H.K. Genetic algorithm (GA)-based correlations offer more reliable prediction of minimum miscibility pressures (MMP) between reservoir oil and CO
_{2}or flue gas. J. Can. Pet. Technol.**2007**, 46, 19–25. [Google Scholar] [CrossRef] - Fathinasab, M.; Ayatollahi, S. On the determination of CO
_{2}–crude oil minimum miscibility pressure using genetic programming combined with constrained multivariable search methods. Fuel**2016**, 173, 180–188. [Google Scholar] [CrossRef]

**Figure 7.**The heatmap of correlation coefficients between interfacial tension and the other parameters.

**Figure 9.**Boxplot of MMP data. The presence of six outliers (indicated by the six black diamonds) exceeds the right threshold (30 MPa).

**Figure 13.**Flowchart of the multilayer perceptron using the Adam optimization algorithm for the proposed model.

**Figure 14.**Comparative plot of predicted and experimental dead solubility values: an analysis of training data, test data, and the complete dataset.

**Table 1.**A brief description of the experimental data used for the two solubility models (dead oil and live oil).

Oil State | Experimental Data | No. of Samples | Mean | Std | Min | 25% | 50% | 75% | Max |
---|---|---|---|---|---|---|---|---|---|

Dead Oil | MW (gr/mole) | 105 | 350.6415 | 92.0752 | 196 | 246 | 358 | 424 | 490 |

γ | 105 | 0.9257 | 0.0481 | 0.8382 | 0.8654 | 0.9452 | 0.9677 | 0.9867 | |

T (°C) | 105 | 53.8450 | 35.75 | 18.33 | 26.17 | 48.89 | 69.0275 | 140 | |

Ps (MPa) | 105 | 6.9716 | 4.5963 | 0.5 | 3.5475 | 6.02 | 9.5725 | 27.38 | |

Rs (Mole fraction) | 105 | 0.4575 | 0.1725 | 0.1 | 0.313 | 0.4789 | 0.6048 | 0.847 | |

Live Oil | MW (gr/mole) | 74 | 152.8364 | 61.9598 | 80.7 | 115.7 | 133.2 | 173.575 | 391.6 |

γ | 74 | 0.8371 | 0.0617 | 0.6748 | 0.8348 | 0.8498 | 0.8789 | 0.9663 | |

T (°C) | 74 | 65.9297 | 19.122 | 28 | 59 | 64.7 | 67 | 123.9 | |

Pb (MPa) | 74 | 8.5052 | 5.8059 | 2.15 | 3.05 | 6.2 | 11.91 | 18.52 | |

Ps (MPa) | 74 | 13.6241 | 7.1675 | 3.23 | 8.3075 | 12.33 | 17.24 | 32.76 | |

Rs (Mole fraction) | 74 | 0.4103 | 0.1677 | 0.1083 | 0.2716 | 0.4182 | 0.5381 | 0.7201 |

Oil State | Experimental Data | MW (gr/mole) | γ | T (°C) | Pb (MPa) | Ps (MPa) |
---|---|---|---|---|---|---|

Dead Oil | Rs (Mole fraction) | −0.0713 | −0.0934 | −0.1696 | - | 0.7813 |

Live Oil | Rs (Mole fraction) | 0.0231 | 0.0181 | 0.0774 | −0.0132 | 0.3844 |

Experimental Data | No. Of Samples | Mean | Std | Min | 25% | 50% | 75% | Max |
---|---|---|---|---|---|---|---|---|

MW (g/mol) | 1071 | 175.6069 | 64.6520 | 96 | 134 | 175 | 222 | 275 |

P (MPa) | 1071 | 6.3848 | 4.1064 | 0.097 | 3.025 | 6 | 9.085 | 17.1 |

T (K) | 1071 | 350.6999 | 31.6949 | 297.85 | 323.175 | 344.3 | 373.1 | 443.05 |

IFT (mN/m) | 1071 | 9.8366 | 5.8556 | 0.001 | 5.225 | 9.37 | 14.15 | 27.05 |

Experimental Data | MW (gr/mole) | P (MPa) | T (K) |
---|---|---|---|

IFT (mN/m) | 0.2918 | −0.8577 | −0.2042 |

Experimental Data | No. of Samples | Mean | Std | Min | 25% | 50% | 75% | Max |
---|---|---|---|---|---|---|---|---|

TR (K) | 201 | 345.4395 | 24.3101 | 307.55 | 327.59 | 338.71 | 362.040 | 410.37 |

Tc (K) | 201 | 302.7178 | 8.3058 | 281.45 | 295.29 | 304.19 | 304.190 | 338.77 |

MW_{C5+} (g/mol) | 201 | 194.6348 | 40.1033 | 136.26 | 171.1 | 187.80 | 211.213 | 391 |

_{xvol}/_{xint} | 201 | 1.5955 | 2.0928 | 0 | 0.51 | 0.74 | 1.5 | 13.6067 |

MMP (MPa) | 201 | 16.0235 | 6.1184 | 6.50 | 11.138 | 14.80 | 19.12 | 38.52 |

Experimental Data | T_{R} (K) | Tc (K) | MW_{C5+} (g/mol) | x_{vol}/x_{int} |
---|---|---|---|---|

MMP (MPa) | 0.6845 | −0.1829 | 0.4657 | 0.3133 |

Number of hidden layers | 2 |

Number of neurons in the hidden layers | 12 |

Number of epochs | 1000 |

Optimization algorithm | Adam |

Activation function | Relu |

Performance Indicator | MSE, MAE |

Validation dataset | 16 Samples |

Model | Training Data | Test Data | All Data | ||||||
---|---|---|---|---|---|---|---|---|---|

AARD (%) | RMSE | R^{2} | AARD (%) | RMSE | R^{2} | AARD (%) | RMSE | R^{2} | |

MLP-Adam | 2.0161 | 0.0123 | 0.9948 | 3.9629 | 0.0234 | 0.9807 | 2.3099 | 0.0145 | 0.9928 |

**Table 9.**The comparison between the statistical parameters of MLP-Adam and the different correlations found in the literature.

Model | AARD (%) | RMSE | R^{2} |
---|---|---|---|

MLP-Adam | 2.3099 | 0.0145 | 0.9928 |

Chung et al., 1988 [51] | 99.4213 | 0.5138 | 0.0083 |

GA—Emera and Sarma, 2011 [53] | 6.1521 | 0.0546 | 0.8987 |

Rostami et al., 2017 [52] | 3.8709 | 0.02045 | 0.9858 |

Hyperparameter | C | Epsilon | Gamma |
---|---|---|---|

Range | 0.1–50,000 | 0.0001–0.1 | 0.001–10 |

Optimal value | 950 | 0.039 | 0.01035 |

Model | Training Data | Test Data | All Data | ||||||
---|---|---|---|---|---|---|---|---|---|

AARD (%) | RMSE | R^{2} | AARD (%) | RMSE | R^{2} | AARD (%) | RMSE | R^{2} | |

SVR-RBF | 2.4618 | 0.0088 | 0.9972 | 4.2742 | 0.0209 | 0.9835 | 2.8047 | 0.0120 | 0.9948 |

**Table 12.**The comparison between the statistical parameters of SVR-RBF and the different correlations found in the literature.

Model | AARD (%) | RMSE | R^{2} |
---|---|---|---|

SVR-RBF | 2.8047 | 0.0120 | 0.9948 |

Chung et al. [51] | 99.9250 | 0.4425 | 0.0097 |

GA—Emera and Sarma [53] | 4.9734 | 0.0295 | 0.9686 |

Rostami et al. [52] | 3.7642 | 0.0203 | 0.9851 |

Model | Hyperparameter | Range | Optimal Value |
---|---|---|---|

XGBoost | Number of trees | 100, 200, 400, 800, 1000, 2000 | 1000 |

Regularization parameter λ | 0.0001, 0.001, 0.1, 0.3, 10, 100 | 0.001 | |

Regularization parameter α | 0.01, 0.04, 0.09, 0.1 | 0.09 | |

Gamma γ | 0, 0,1, 1, 10 | 0 | |

Max. depth | 2, 4, 6, 8 | 4 | |

Learning rate | 0.001, 0.01, 0.1 | 0.1 |

Model | Training Data | Test Data | All Data | ||||||
---|---|---|---|---|---|---|---|---|---|

AARD (%) | RMSE | R^{2} | AARD (%) | RMSE | R^{2} | AARD (%) | RMSE | R^{2} | |

XGBoost | 1.9386 | 0.0952 | 0.9997 | 8.6422 | 0.4698 | 0.9931 | 3.2844 | 0.2271 | 0.9985 |

Model | AARD (%) | RMSE | R^{2} |
---|---|---|---|

XGBoost | 3.2844 | 0.2271 | 0.9984 |

PR EOS | 60.5471 | 2.6261 | 0.7949 |

GEP | 219.1053 | 1.4437 | 0.9391 |

Model | Hyperparameters | Range | Optimal Value |
---|---|---|---|

XGBoost | Number of trees | 100, 1000, 4000, 5000, 8000 | 8000 |

Regularization parameter λ | 0.0001, 0.001, 0.1, 0.3, 15, 100 | 15 | |

Regularization parameter α | 0.01, 0.02, 0.09, 0.1 | 0.02 | |

Gamma γ | 0, 0,1, 01, 10 | 0 | |

Maximum depth | 2, 4, 6, 8 | 2 | |

Learning rate | 0.001, 0.01, 0.1 | 0.1 |

Model | Training Data | Test Data | All Data | ||||||
---|---|---|---|---|---|---|---|---|---|

AARD (%) | RMSE | R^{2} | AARD (%) | RMSE | R^{2} | AARD (%) | RMSE | R^{2} | |

XGBoost | 0.9326 | 0.1893 | 0.9986 | 4.0043 | 0.941 | 0.9648 | 1.4262 | 0.4151 | 0.9934 |

Model | AARD (%) | RMSE | R^{2} | |
---|---|---|---|---|

Pure CO_{2} | XGBoost (Pure) | 0.9161 | 0.1936 | 0.9988 |

Lee [56] | 18.781 | 5.1538 | 0.5146 | |

Alston et al. (Pure) [48] | 18.177 | 5.5472 | 0.7063 | |

Emera-Sarma [57] | 13.2203 | 3.7385 | 0.6161 | |

Impure CO_{2} | XGBoost (Impure) | 1.9525 | 0.558 | 0.9856 |

Alston et al. (Impure) [48] | 34.5324 | 6.4668 | 0.5967 | |

Fathinasab-Ayatollahi [58] | 15.0134 | 2.702 | 0.7019 |

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**MDPI and ACS Style**

Hamadi, M.; El Mehadji, T.; Laalam, A.; Zeraibi, N.; Tomomewo, O.S.; Ouadi, H.; Dehdouh, A.
Prediction of Key Parameters in the Design of CO_{2} Miscible Injection via the Application of Machine Learning Algorithms. *Eng* **2023**, *4*, 1905-1932.
https://doi.org/10.3390/eng4030108

**AMA Style**

Hamadi M, El Mehadji T, Laalam A, Zeraibi N, Tomomewo OS, Ouadi H, Dehdouh A.
Prediction of Key Parameters in the Design of CO_{2} Miscible Injection via the Application of Machine Learning Algorithms. *Eng*. 2023; 4(3):1905-1932.
https://doi.org/10.3390/eng4030108

**Chicago/Turabian Style**

Hamadi, Mohamed, Tayeb El Mehadji, Aimen Laalam, Noureddine Zeraibi, Olusegun Stanley Tomomewo, Habib Ouadi, and Abdesselem Dehdouh.
2023. "Prediction of Key Parameters in the Design of CO_{2} Miscible Injection via the Application of Machine Learning Algorithms" *Eng* 4, no. 3: 1905-1932.
https://doi.org/10.3390/eng4030108