A deep learning model for contact angle prediction in carbonate reservoirs under smart water assisted foam injection (SWAF)

Abstract

Given the challenges in enhanced oil recovery (EOR) from carbonate reservoirs, this study investigates the application of machine learning models to predict contact angles under Smart Water Assisted Foam (SWAF) injection. SWAF, as an innovative and environmentally friendly approach, enhances sweep efficiency by altering reservoir rock wettability and controlling gas mobility. The primary objective is to develop accurate models for predicting contact angles based on input features such as ion concentrations (NaHCO₃, NaCl, CaCl₂, MgCl₂, KCl, Na₂SO₄), pressure, temperature, and contact time. The initial dataset comprised 1,615 samples from validated sources, which were expanded to 13,032 samples using data augmentation techniques including Gaussian noise, scaling transformations, and physically constrained Generative Adversarial Networks (GANs). The models examined include Convolutional Neural Networks (CNN), XGBoost, Support Vector Regression (SVR), Random Forest, and Multilayer Perceptron (MLP). Data were split into training, validation, and test sets in a 60:20:20 ratio, and hyperparameters were optimized using grid search combined with 5-fold cross-validation. Results indicate that XGBoost achieved the best performance (RMSE = 0.09°; R² = 0.99997), followed by Random Forest (RMSE = 0.13°; R² = 0.99994), SVR (RMSE = 0.32°; R² = 0.99963), MLP (RMSE = 0.39°; R² = 0.99944), and CNN (RMSE = 1.48°; R² = 0.997). While CNN serves as a novel deep learning benchmark for exploring complex pattern recognition in tabular data, tree-based models like XGBoost outperform it for this tabular SWAF dataset, highlighting the value of ensemble methods. Feature importance analysis revealed the dominant influence of MgCl₂ (28%) and Na₂SO₄ (22%), whereas pressure had the minimal effect (~ 3%). Temperature exhibited an inverse relationship with contact angle. These models provide powerful tools for optimizing SWAF processes and reducing the need for costly experimental work. Limitations include the exclusion of crude oil properties and field-scale data. Future work is recommended to extend these models with dynamic and field-scale datasets to enhance practical applicability in the oil industry.

Introduction

Enhanced oil recovery (EOR) encompasses advanced techniques to boost oil production from petroleum reservoirs after primary recovery declines. These methods often involve injecting water, gases (miscible or immiscible), chemicals, or thermal energy to stimulate reservoirs and improve oil displacement. For instance, miscible gas injection, such as carbon dioxide, reduces oil viscosity, enhancing flow in high-viscosity, low-API-gravity reservoirs by achieving gas-oil miscibility. Thermal methods, like steam injection, lower oil viscosity and raise reservoir temperature to facilitate extraction, particularly for heavy oils¹.

In recent years, attention to new and innovative methods for enhanced oil recovery has intensified. One such method involves the use of smart water in combination with foam. Smart water possesses specific chemical properties that can alter the wettability of reservoir rocks. This wettability alteration leads to improved oil displacement and enhanced reservoir productivity. Foam injection, on the other hand, acts as a blocking agent to control gas mobility within the reservoir, thereby improving the efficiency of gas injection processes. Recent advances in machine learning, such as Gaussian Process Regression (GPR), have demonstrated exceptional accuracy in predicting material properties, offering a promising avenue for optimizing EOR techniques^2,3. The combination of smart water and foam is particularly beneficial for carbonate reservoirs, which possess unique structural complexities and often present significant challenges for oil extraction. This combination assists in enhancing oil recovery by altering the wettability of carbonate rocks and improving the distribution of fluid phases within the reservoir³.

With growing concerns over climate change and depleting oil reserves, SWAF offers an environmentally friendly approach by improving recovery efficiency and reducing the need for new drilling. Given the concerns regarding climate change and the depletion of oil and gas reserves, the utilization of innovative and sustainable methods to enhance productivity and improve oil recovery has gained increasing importance. A bibliometric analysis reveals that applications of artificial intelligence and machine learning in the petroleum industry have grown exponentially in recent years, with over 62% of relevant publications appearing between 2018–2022⁴. New methods that leverage the combination of smart water and foam have emerged as one of the potential and efficient options in this regard. These techniques not only contribute to improving the performance of existing reservoirs but also help to reduce the need for new drilling activities and support environmental protection efforts. In the context of EOR, the synergistic effect of SWAF has shown considerable potential in modifying rock wettability. The alteration mechanism is mainly driven by ion exchange between divalent cations (e.g., Ca²⁺, Mg²⁺) and carbonate rock surfaces, which leads to expansion or compression of the electrical double layer. This interaction alters the surface free energy, facilitating a transition from oil-wet to more water-wet conditions. At the same time, foam acts as a mobility control agent by mitigating gas channeling and improving the sweep efficiency of the injected fluids. It should be noted, however, that wettability alteration is also affected by crude oil properties, including Total Acid Number (TAN), SARA fractions, and viscosity. Due to the unavailability of uniform crude oil property data across the dataset, these factors were excluded from the current model^1,3.

Artificial intelligence (AI), as an innovative and transformative field within computer science, focuses on the development of systems and machines capable of performing complex tasks that were previously thought to be exclusive to human capabilities. This technology has been developed with the aim of simulating human abilities such as thinking, learning and reasoning within machines and systems⁵.

In a comprehensive study, a group method of data handling (GMDH) model was developed to predict interfacial tension (IFT) in normal alkane-nitrogen systems over a wide range of pressures (0.1–69 MPa) and temperatures (295–442 K), using 60% of a dataset for training and 40% for testing. The model achieved an average absolute relative error (AARE) of 3.81% in training and 3.91% in testing, outperforming established models like Linear Gradient Theory (LGT), Density Gradient Theory (DGT), and Parachor approaches combined with Volume Translated Predictive Peng Robinson Equation of State (VT-PPR EOS) in both accuracy and computational efficiency. Additionally, a vanishing interfacial tension (VIT)-based algorithm was proposed for minimum miscibility pressure (MMP) estimation, demonstrating high precision in paraffin-nitrogen systems⁶.

An experimental study using axisymmetric drop shape analysis (ADSA) measured equilibrium interfacial tensions (IFTs) between crude oil and CO₂ at temperatures of 30–80 °C and pressures up to 20 MPa, revealing a decreasing IFT trend with temperature at low pressures and an increasing trend at high pressures. Minimum miscibility pressures (MMP) and first-contact miscibility pressures (P_max) were determined via the vanishing interfacial tension (VIT) technique, showing linear increases with temperature (MMP from ~ 10 MPa at 30 °C to ~ 18 MPa at 80 °C). The study also highlighted the critical role of paraffin content in IFT behavior and noted that lower resin-to-asphaltene ratios increase asphaltene precipitation risks, while higher molecular weights of heavy components elevate MMP values⁷.

One of the most significant advancements in this domain is deep learning, a subset of machine learning, which operates based on multilayer artificial neural networks and possesses the ability to identify complex patterns within large datasets^8,9. Deep learning, by employing complex and layered structures of neural networks, is capable of extracting key features from intricate data and providing highly accurate models¹⁰. This technique has had remarkable impacts particularly in the fields of image processing, speech recognition, and data analysis, leading to significant improvements in system performance and efficiency¹¹.

Rigorous modeling of natural gas viscosity was performed using radial basis function neural network (RBFNN), least-squares support vector machine (LSSVM), and multilayer perceptron neural network (MLPNN) on over 3800 data points, with inputs including pseudo-reduced properties and molecular weight. The MLP-Levenberg-Marquardt (MLP-LM) model excelled with a root mean square error (RMSE) of 0.001, surpassing MLP-Bayesian regularization (BR) (RMSE = 0.002) and existing literature models in accuracy, while requiring fewer inputs (no density data). Sensitivity analysis identified molecular weight as the most influential variable, underscoring the models’ utility in upstream and downstream gas processes¹². Advanced machine learning models, including multilayer perceptron (MLP) and radial basis function neural network (RBFNN), were applied to predict CO₂ solubility in brine based on NaCl molality, pressure, and temperature using 570 data points. Optimized by Levenberg-Marquardt (LM) for MLP and genetic algorithm (GA), particle swarm optimization (PSO), and artificial bee colony (ABC) for RBFNN, the RBFNN-ABC model achieved the highest accuracy with RMSE = 0.0289 and R²=0.9967, outperforming other models and literature correlations. The study confirmed model validity through outlier detection, identifying minimal doubtful data¹³.

One of the advanced applications of deep learning is the development of predictive models and data analysis tools, which can assist in uncovering hidden patterns and relationships within large datasets. These applications have proven highly effective across various fields, including data science, medicine, and market analysis. In particular, deep learning algorithms can process and analyze complex and unstructured data such as images and texts, thereby becoming indispensable tools in scientific and industrial research¹⁰. An artificial neural network (ANN) was designed to estimate formation permeability from geophysical well logs, using data from five wells in a heterogeneous reservoir. The three-layer feed-forward backpropagation network with 15 hidden neurons achieved accurate predictions, overcoming limitations of traditional porosity-permeability correlations (e.g., scattered plots with no credible linear fit). The ANN’s pattern recognition capabilities enabled superior permeability estimation compared to regression-based methods, demonstrating its effectiveness in heterogeneous formations¹⁴.

In the contemporary world, deep learning techniques are widely employed across diverse industries to enhance prediction accuracy, data analysis, and process automation. These advancements not only contribute to achieving more accurate and faster results but also lead to overall improvements in efficiency and productivity across scientific and industrial sectors¹⁰.

A pattern recognition-based AI approach using surrogate reservoir models (SRM) was developed for assisted history matching in a synthetic heterogeneous oilfield with 24 wells and 30 years of production history. The SRM, built from geological realizations and running in fractions of a second, accurately replicated full-field simulation results by tuning permeability, achieving high precision and speed. This method reduced computational time compared to traditional history matching, demonstrating SRM’s potential as an efficient tool for reservoir parameter adjustment¹⁵.

Seven advanced machine learning models, including cascade forward neural network (CFNN), generalized regression neural network (GRNN), wavelet neural network (WNN), and support vector regression (SVR) optimized by particle swarm optimization (PSO), farmland fertility algorithm (FFA), and grasshopper optimization algorithm (GOA), were applied to predict equivalent circulating density (ECD) in drilling mud using 2367 field data points from Iranian wells with water-based fluids. The GOA-SVR model outperformed others with average absolute percent relative errors (AAPRE) of 0.0823% (training), 0.0975% (testing), and 0.0869% (overall), while a group method of data handling (GMDH) correlation surpassed existing empirical models. Sensitivity analysis showed surface mud weight as the most influential variable, with leverage techniques identifying minimal outliers (~ 1-2.5%)¹⁶.

Recent studies on optimizing EOR processes through the integration of molecular dynamics (MD) simulations and machine learning (ML) techniques highlight the potential of this approach for predicting interfacial properties between oil and brine, such as interfacial tension (IFT). In 2020, Alexsandro Kirch and colleagues applied MD simulations to represent oil–brine systems, followed by the implementation of four different ML algorithms, including a linear regression (LR) model, to predict IFT. The findings revealed that ML models significantly outperformed LR, providing higher predictive accuracy and demonstrating the effectiveness of combining MD with ML for interfacial property estimation.

In a 2020 study by Alexsandro Kirch et al., molecular dynamics (MD) simulations and four machine learning (ML) algorithms, including linear regression (LR), were used to predict interfacial tension (IFT). The results showed that ML models achieved higher accuracy than LR¹⁷.

In a 2020 study by Zhi Zhong et al., the cDC-GAN surrogate model, based on deep learning and zero-sum game theory, was applied to predict fluid distribution in reservoirs under water injection. The model accurately predicted water and oil compositions and production rates, demonstrating its effectiveness in accelerating reservoir simulations and optimizing water injection strategies¹⁸.

In a 2021 study by Rashida Salimova et al., it was shown that low salinity water (LSW) injection for enhancing oil recovery from carbonate reservoirs can be effectively evaluated using machine learning (ML) models. The study highlighted that ML models, particularly decision trees, can capture complex relationships among parameters such as salinity, ion concentration, and interfacial tension to assess LSW performance. Overall, integrating molecular dynamics (MD) with ML provides a powerful tool for more accurate prediction and optimization of oil recovery processes, supporting petroleum engineers in improving EOR and IOR strategies¹⁹.

In a study by Fiki Hidayat et al. (2021), the random forest regression algorithm was applied to assess the effectiveness of low salinity water injection (LSWI) in carbonate reservoirs. Using Computer Modelling Group Simulation Optimization Tool (CMOST) simulation software, they identified a few dominant parameters—particularly sulfate concentration and injection volume—as having significant influence on oil recovery, while other factors showed minimal impact. Their findings underline the importance of optimizing key ion concentrations and injection strategies in designing effective LSWI processes²⁰.

In 2021, Hamidreza Afifi et al. investigated the use of SiO₂ nanoparticles to enhance the properties of smart water-based foam for EOR applications. Using a carbonate-patterned glass micromodel, they examined the effects of combining smart water with synthesized SiO₂ nanoparticles on foam stability and oil displacement efficiency. The results showed that the nanoparticle-enhanced foam was more stable than foams prepared with deionized water or smart water alone, with maximum stability achieved at 3000 ppm nanoparticle concentration. Under these conditions, foam half-life (t₁/₂) reached 3812 s and the R5 parameter rose to 99.2, compared to 2813 s and 91.5 for foam without nanoparticles. Foam injection experiments in a micromodel showed that silica nanoparticles enhanced foam stability by forming thicker layers, delaying foam collapse, and improving the oil recovery factor. The nanoparticles facilitated a stable emulsion between foam and oil droplets, reducing density and increasing sweep efficiency. The study concluded that smart water is an innovative EOR method that improves recovery by altering reservoir rock wettability through ion modification. Furthermore, combining smart water-based foam with SiO₂ nanoparticles can significantly enhance oil recovery and foam stability²¹.

In 2021, Anas Mohamed Hassan and colleagues conducted an experimental investigation on a hybrid method for improving oil recovery through SWAF injection in carbonate rocks. The approach involved three stages: (1) evaluating rock wettability to determine the optimal smart water composition, (2) chemical screening to identify stable foam systems in the presence and absence of crude oil, and (3) core flooding experiments to select the most effective formulations. The results showed that the combination of smart water (MgCl₂ at 3500 ppm) with the surfactant CTAB exhibited the greatest potential for enhancing wettability and foam stability. This formulation, tested with type A and type B crude oils, significantly altered wettability and increased oil recovery. Moreover, the generated foams remained stable even in the presence of crude oil. Overall, the study demonstrated that SWAF represents an innovative and effective technique for IOR/EOR, offering both environmental and economic advantages by improving wettability and foam stability²².

In 2022, Anas Mohamed Hassan et al. investigated foamability and foam stability within the SWAF technique for EOR, which integrates smart water and foam to enhance rock wettability and stabilize foam structures. A range of surfactants (CTAB, DTAB, AOS, Alpha Foamers) were examined with different crude oils, and the influence of CO₂ and N₂ gases on foam generation was assessed. The findings revealed that CTAB and AOS, particularly in MgCl₂ solutions, achieved the highest stability—approximately 80% in the presence of oil and 90% in its absence. Foam stability improved further with higher surfactant concentrations and when N₂ was used instead of CO₂. Moreover, MgCl₂ solutions with CTAB and AOS exhibited the lowest surface and interfacial tensions. Overall, the study demonstrated that SWAF is a novel, efficient, cost-effective, and environmentally sustainable method for EOR³.

In 2022, Anas Mohamed Hassan and colleagues presented a method for predicting the contact angle in carbonate rocks by combining SWAF with ANNs. The model provided an efficient alternative to conventional measurements, demonstrating high accuracy in analyzing existing data and supporting analytical processes in the oil and gas industry. It also facilitated the identification of optimal conditions for SWAF application to improve recovery efficiency. The study further highlighted model limitations and suggested directions for improvement²³.

In 2022, Anas Mohammed Hassan and colleagues conducted a comprehensive study on the simultaneous injection of SWAF in carbonate reservoirs. This novel method was investigated as an EOR technology. The research, carried out through laboratory experiments and numerical simulations using CMG-STARS, demonstrated that SWAF can achieve up to 42% additional oil recovery (corresponding to a total of 92% of the original oil in place). Furthermore, surface complexation modeling (SCM) was employed to analyze the interactions among oil, brine, and rock. The findings revealed that, beyond its high recovery efficiency, this technology also offers economic and environmental advantages, thereby providing a solid basis for potential field pilot applications²⁴.

In 2023, Anas Mohammad Hassan et al. conducted a comprehensive study on smart water-assisted foam (SWAF) injection in carbonate reservoirs using numerical modeling with CMG simulation software. A core-scale model was used for parameter sensitivity analysis via tornado diagrams, SOBOL, and Morris methods. Polynomial regression and radial basis function (RBF) neural networks were tested for surrogate modeling, with the RBF model outperforming polynomial regression. Sensitivity analysis identified liquid production rate, foam concentration, and Mg²⁺ concentration as key factors affecting oil recovery. Furthermore, particle swarm optimization (PSO) outperformed the DECE method, achieving a recovery factor of 97.89%. This study represents one of the first numerical modeling efforts of SWAF, providing a foundation for reservoir-scale design and pilot projects²⁵.

Despite these advancements, prior research on SWAF in carbonate reservoirs has primarily focused on experimental evaluations of wettability alteration and foam stability, with limited integration of deep learning models for predictive purposes. While machine learning has been applied to related EOR parameters like IFT and solubility, there remains a gap in developing comprehensive deep learning frameworks specifically tailored for contact angle prediction under SWAF conditions, which is critical for optimizing wettability and recovery efficiency in heterogeneous carbonate systems. This study addresses this gap by proposing a deep learning model that accurately predicts contact angles in carbonate reservoirs during SWAF injection, leveraging key input parameters to enhance EOR decision-making and operational planning.

Modeling methodology

Data collection

In this study, a total of 1,615 datasets were compiled from peer-reviewed published sources for carbonate rocks from various countries in order to develop machine learning models — including convolutional neural networks (CNN), gradient boosting (XGBoost), support vector regression (SVR), random forests (RandomForest), and multilayer perceptron (MLP) — to predict contact angle^{22,23,26–29}. These data were extracted from articles focusing on contact-angle measurements under enhanced oil recovery (EOR) conditions and encompassed diverse scenarios, including smart-water injection alone (40%, 646 samples) and smart-water assisted foam (SWAF) injection (60%, 969 samples), thereby ensuring model generalizability across different EOR settings. The dataset was partitioned into three subsets: 60% for training (969 samples), 20% for validation (323 samples), and 20% for testing (323 samples). This split was chosen in accordance with common machine learning practice (e.g., Goodfellow et al., 2016) to balance pattern learning, hyperparameter tuning, and performance evaluation; the appropriateness of this partitioning is supported by the models’ outcomes (e.g., R² = 0.99997 for XGBoost). The dataset underwent quality control procedures, including cross-validation against original sources to verify data integrity and outlier removal using the interquartile range (IQR) method (excluding values outside 1.5×IQR), which led to the elimination of less than 2% of the data, thereby ensuring dataset reliability.

Input features used to predict contact angle comprised ionic and salt concentrations (in ppm) — specifically NaHCO₃, NaCl, CaCl₂, MgCl₂, KCl, and Na₂SO₄ — together with pressure (psia), temperature (°C), and time (hours). These features were selected based on surface-chemistry principles and prior EOR studies (e.g., Lashkarbolooki et al., 2014; Hassan et al., 2022), since they directly influence electrostatic interactions at the rock–fluid interface and play a key role in wettability alteration. Feature-importance analysis performed with XGBoost revealed that MgCl₂ (28%) and Na₂SO₄ (22%) exerted the largest influence on contact angle predictions, whereas pressure was of relatively low importance (~ 3%). Crude oil properties (e.g., TAN, SARA) and rock heterogeneity attributes (e.g., porosity) were excluded due to lack of uniformly available data, which may reduce model accuracy under heavy-oil conditions; future studies are recommended to incorporate these standardized features when available.

The variable “time” denotes the contact duration of the carbonate rock sample with the smart-water or SWAF solution, measured from initial contact until the contact-angle measurement. The temporal range was 1–48 h (mean 12.13 h), selected on the basis of experimental studies (e.g., Zhu et al., 2022) because it represents the time required to approach surface equilibrium in EOR experiments and aligns with field low-salinity injection timescales (from several hours to a few days). It should be noted that this “time” variable reflects static surface interaction rather than dynamic flow time. The associated data and their types are summarized in Table 1. Numerical and graphical data were extracted from the selected publications and the dataset was further expanded from 1,615 to 13,032 samples using data-augmentation techniques and generative adversarial networks (GANs); details are provided in the subsequent section. Augmentation procedures included the application of Gaussian noise (standard deviation = 0.01 × parameter value) and scaling transforms (factors between 0.95 and 1.05), and the GANs were constrained by physical priors (for example, the empirically supported inverse relationship between temperature and contact angle) to produce physically plausible synthetic samples. The augmented data distribution was validated against the original data using the Kolmogorov–Smirnov (KS) test (p-value > 0.05).

Table 1.

Presents the statistical summary of all the compiled data points.

Parameter	Contact Angle (Degrees)	NaHCO3 (ppm)	NaCl (ppm)	CaCl2 (ppm)	MgCl2 (ppm)	KCl (ppm)	Na2SO4 (ppm)	Pressure (psia)	Temperature (°C)	Time (Hours)
Minimum	37.71872	1.343699	389.1732	232.634	200.4575	0.077604	157.7388	36.37901	50.14587	0.112408
Maximum	108.5034	505.0249	144072.7	95491.61	81997.51	43.81005	76832.8	2931.674	120.3925	45.88932
Mean	70.08408	148.7364	39315.18	25183.1	20998.85	10.00552	18535.05	808.1986	67.40163	12.1348
Standard Deviation	17.62482	103.1398	26549.81	17444.68	14392.74	7.442265	13273.13	544.9286	12.52279	8.396788
Skewness	-0.87969	-0.08662	0.022471	0.114382	0.142239	0.524554	0.32703	0.101199	0.296763	0.108201
Kurtosis	0.127816	0.694042	0.68559	0.734207	0.725564	0.895275	0.813187	0.744234	0.814793	0.731716

Input data were extracted from validated experimental studies on carbonate rocks such as Indiana limestone, micritized wackestone, and dolomite, whose mineralogical compositions and petrophysical properties were confirmed by the cited references. These lithologies were selected because of their widespread use in EOR studies and their diversity in carbonate fabric, thereby enhancing the models’ generalizability.

In the expanded dataset, categorical group features—namely lithology, pore-type, and textural class—were incorporated via one-hot encoding to model their influence on wettability; this augmentation improved model performance (e.g., RMSE = 0.09° for XGBoost). All records contain both initial and final (post-reaction) contact-angle measurements; however, advancing and receding contact-angle data were generally unavailable. Consequently, the model employs the mean/equilibrium contact angle, a limitation explicitly acknowledged in the study. To address this constraint, future work should incorporate dynamic contact-angle measurements (advancing and receding) and field-scale datasets (e.g., CMG-STARS simulation outputs) to improve predictive accuracy under realistic reservoir conditions.

Model implementation process

Data enhancement and augmentation

This study employed three principal methods to augment and enhance data for the machine learning models: standard data augmentation, generative adversarial networks (GANs), and multi-task learning (MTL). These approaches were designed to expand the dataset from 1,615 to 13,032 samples, improve model accuracy (e.g., R² = 0.99997 for XGBoost), reduce overfitting, and increase generalizability in contact-angle prediction under SWAF conditions. Standard data augmentation for numerical features comprised adding Gaussian noise (standard deviation = 0.01 × parameter value, e.g., up to 50 ppm for MgCl₂) and applying scaling transforms (factors between 0.95 and 1.05) to emulate small experimental variations, while enforcing physical constraints (e.g., preventing negative concentrations). This procedure increased the dataset from 1,615 to approximately 5,000 samples. Image-based augmentations (such as rotations or added noise) were considered but not applied, since the study focused on tabular data (salt concentrations, temperature, pressure, time).

The GAN architecture consisted of two adversarial networks. The Generator comprised four Dense layers with 128, 256, 256, and 9 output neurons, using ReLU activations and Batch Normalization, and generated 9-dimensional synthetic feature vectors from Gaussian noise of dimension 100. The Discriminator comprised four Dense layers with 128, 256, 256, and 1 output neuron, using ReLU activations and Dropout (0.3) to distinguish real from synthetic samples. A physics-constrained GAN implementation was used, with constraints such as the inverse relationship between temperature and contact angle and the low influence of pressure, to prevent violations of physical laws. Training used a learning rate of 0.0002, batch_size = 64, and 1,000 epochs. Synthetic-data quality was validated using the Kolmogorov–Smirnov (KS) test (p-value > 0.05) and t-SNE visualizations of distributional similarity. The GAN step expanded the dataset from ~ 5,000 to 13,032 samples and—unlike naïve noise-based augmentation—produced synthetic data with distributions and correlations closely matching the real data, which improved model accuracy (e.g., RMSE = 0.09° for XGBoost). Multi-task learning (MTL) leveraged a shared model to learn multiple tasks simultaneously (see Fig. 1). In this study, MTL was applied to predict contact angle and to estimate feature importance (for example, MgCl₂ with 28% influence), thereby exploiting shared information across tasks (such as inter-salt correlations). The MTL architecture comprised shared layers with 128 neurons and task-specific output layers for each target, as depicted in Fig. 1.

Fig. 1.

Architecture of Multi-Task Learning.

The combination of the three methods—data augmentation, GANs, and MTL—enhanced model accuracy (e.g., R² = 0.99997 for XGBoost and R² = 0.997 for the CNN), mitigated overfitting (e.g., SD = 0.09° for XGBoost), and minimized the need for additional training data. However, limitations remain, such as the GAN’s reliance on pre-specified physics-based constraints and the lack of image-based data. For future work, we recommend incorporating dynamic measurements (e.g., advancing and receding contact angles) and crude-oil properties (e.g., TAN) into the GAN framework to increase data diversity. Table 2 summarizes the augmented dataset produced by the methods described above.

Table 2.

Summarizes the augmented dataset produced using multi-task learning methodologies.

ROW	Contact Angle	NaHCO3 (ppm)	NaCl (ppm)	CaCl2 (ppm)	MgCl2 (ppm)	KCl (ppm)	Na2SO4 (ppm)	Pressure (psia)	Temperature (°C)	Time
First few rows of augmented data:
1	63.3	99.4	26977.1	16909.0	14243.1	6.3	12092.4	547.2	61.3	8.2
2	100.1	342.9	88510.3	57767.3	47736.5	24.2	43538.3	1831.1	91.1	27.8
3	82.1	206.9	54356.5	34908.2	29058.7	13.9	25741.7	1110.6	74.2	16.8
4	74.7	161.7	42956.0	27358.5	22866.1	10.6	19959.6	873.5	68.7	13.2
5	50.9	42.8	11985.1	7346.3	6255.3	2.6	5117.7	252.1	54.8	3.5
Last few rows of augmented data:
13,028	53.8	54.5	15145.8	9334.8	7927.5	3.3	6543.9	313.1	56.1	4.5
13,029	52.8	50.7	14108.1	8680.0	7377.6	3.1	6072.7	293.0	55.6	4.2
13,030	56.9	68.4	18860.3	11692.7	9901.7	4.2	8253.0	385.7	57.7	5.6
13,031	59.7	81.3	22268.4	13873.2	11720.5	5.1	9849.0	453.1	59.2	6.7
13,032	62.6	95.6	25996.4	16274.7	13716.9	6.0	11621.8	527.5	60.9	7.8

Convolutional neural networks (CNNs)

CNNs originally designed for image analysis, were employed in this study to model non-image data, specifically for predicting the contact angle from time-series signals. The schematic representation of the developed CNN architecture is shown in Fig. 2.

Fig. 2.

Schematic architecture of the Convolutional Neural Network (CNN) model used for prediction.

In this work, a one-dimensional CNN model (Eq. 1) was constructed and trained using data imported from comma-separated value (CSV) files. The dataset was divided into features (X) and target variables (Y), and further split into training (60%), testing (20%), and validation (20%) subsets to ensure robust model evaluation and to prevent overfitting.

1

The CNN architecture consists of a one-dimensional convolutional layer (Conv1D), a max-pooling layer (MaxPooling1D), a flattening layer (Eq. 2), and fully connected dense layers (Eq. 3). The max-pooling operation is expressed in Eq. 4. These layers are integrated with activation functions optimized through the Adaptive Moment Estimation (Adam) optimizer and the mean squared error (MSE) loss function. The model was trained for 50 epochs using both the training and validation datasets.

2

3

4

To assess the performance of the CNN, several plots were generated, including the training and validation loss curves, as well as cross-plots comparing predicted and actual contact angles for the training, validation, and testing datasets.

To enhance the transparency and reproducibility of the model, the CNN architecture was structured with one-dimensional Conv1D layers (64 filters, kernel size = 3), followed by MaxPooling1D layers, ReLU activation, and dropout layers (dropout rate = 0.2) to prevent overfitting. The flattened output was connected to two dense layers (128 and 64 units), finalized with a single-node output layer for regression using linear activation. The model was compiled using the Adam optimizer (initial learning rate = 0.001) and trained with the mean squared error (MSE) loss function over 50 epochs. Performance metrics included Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and the coefficient of determination (R²).

To ensure robustness and prevent overfitting to specific data splits, 5-fold cross-validation was employed. Feature normalization was performed using standard scaling (zero mean and unit variance), and categorical variables such as lithology and texture were encoded via one-hot encoding. The pre- and post-augmentation data distributions were verified using boxplots and density plots to maintain statistical consistency (Fig. 3-A).

Fig. 3.

Boxplot comparison of prediction performance across different AI models. (A) Boxplot – CNN Model, (B) Boxplot – XGBoost Model, (C) Boxplot – SVR Model, (D) Boxplot – Random Forest, (RF) Model, (E) Boxplot – MLP Model.

Model training and generalization were further evaluated using the loss curves presented in Fig. 4-A. The downward trend in both Training and Validation Loss demonstrates that the CNN progressively learned the data patterns, achieving convergence without overfitting. Additionally, the predicted versus actual contact angle values for the training, test, and validation datasets (Fig. 5) reveal high correlation coefficients (R² = 0.996 for training, and R² = 0.997 for both test and validation sets), indicating strong predictive performance and generalization capability.

Fig. 4.

Learning Curve Comparison (R²) Among the CNN, XGBoost, Random Forest, and MLP. (A) Learning curve, (R²) for the CNN model, (B) Learning curve, (R²) for the XGBoost model, (C) Learning curve, (R²) for the Random Forest model, (D) Learning curve, (R²) for the MLP model.

Fig. 5.

Scatter Plots of Predicted vs. Actual Contact Angle for Training, Test, and Validation Datasets. (A) Training Data: Predicted vs. Actual Contact Angle, (B) Test Data: Predicted vs. Actual Contact Angle, (C) Validation Data: Predicted vs. Actual Contact Angle.

Overall, these results confirm that the CNN model reliably captures the underlying patterns in the data, generalizes well to unseen samples, and provides accurate contact angle predictions under the considered experimental conditions. The combination of cross-validation, normalization, and appropriate architectural design ensures robustness and practical applicability. Sensitivity analysis further indicated that bicarbonate concentration (NaHCO₃) is the most influential parameter, followed by contact time and temperature, while pressure and other salts have lower impact, highlighting the dominant role of chemical variables in controlling wettability under SWAF conditions.

XGBoost (eXtreme gradient Boosting)

The XGBoost (eXtreme Gradient Boosting) model is a powerful gradient-boosting machine-learning algorithm that builds strong predictive models by aggregating decision trees. Originally developed by Tianqi Chen, XGBoost is widely used for regression tasks due to its high computational speed, robust accuracy, and ability to handle large and complex datasets. In the present study, XGBoost was employed to predict contact angle. The algorithm is based on the ensemble of weak learners (individual trees) to form a strong learner, incorporating regularization terms in its formulation to mitigate overfitting and enhance generalizability. As illustrated in Fig. 6, the schematic architecture of the XGBoost model used for prediction demonstrates the aggregation of decision trees to produce the final output.

Fig. 6.

Schematic architecture of XGBoost model used for prediction.

The final prediction in XGBoost is given by the sum of the outputs of all trees:

5

where ​ is the prediction for sample , ​ denotes the prediction function implemented by tree , and is the total number of trees. The objective function combines a loss term and a regularization term:

6

where is the loss function (for regression we use the mean squared error, MSE), and the regularizer is commonly defined as

7

with the number of leaves in a tree, ​ the weight of leaf , and and are the regularization parameters. Also, at each stage, a new tree is constructed using the gradient and Hessian loss function:

8

For the MSE function, these are calculated as follows:

9

This construction allows XGBoost to systematically reduce errors and identify near-optimal splits. In this study, numerical features were standardized (zero mean, unit variance), and the dataset was divided into training (60%), validation (20%), and test (20%) sets. Hyperparameters were optimized using GridSearchCV, resulting in 500 trees (n_estimators), learning rate of 0.1, maximum depth of 6, minimum child weight of 2, and subsample ratio of 0.8. The model was trained with 5-fold cross-validation and evaluated using RMSE, R², AAPRE, and SD. The boxplot of prediction errors (Fig. 3-B) shows that errors are largely centered around zero with minimal bias, and the test set exhibits the smallest error dispersion, confirming the model’s stability and generalizability. The Williams plot for the XGBoost model illustrates the dispersion of standardized residuals against leverage (Fig. 7). The horizontal red lines represent the ± 3 threshold for residuals, while the vertical green lines indicate the critical leverage value. Most data points lie within the acceptable range (± 3), and the leverage of the majority of points is below the critical threshold. This indicates that the model is statistically reliable and that there are few influential or outlying data points, thereby confirming the robust performance of the model.

Fig. 7.

Leverage Plot for the Best-Performing Model.

The XGBoost model demonstrated outstanding predictive performance for contact angle, achieving a test-set R² of 0.99997, RMSE and SD below 0.1°, and an AAPRE of approximately 0.11%, indicating both high absolute and relative accuracy. In comparison, other models, such as CNNs, exhibited higher RMSE values (1.48°), reflecting lower predictive capability. The learning curves (Fig. 4-B) show stable R² values near 0.99997 for both training and validation sets as the number of samples increased, confirming robust generalization and effective hyperparameter optimization. Evaluation metrics summarized in Table 3 further corroborate the model’s accuracy and stability across all datasets.

Table 3.

XGBoost model results across datasets.

Dataset (Avg/Best)	RMSE	R²	AAPRE (%)	SD
Train (Avg)	0.0911	0.9999724	0.1069	0.0911
Train (Best)	0.0905	0.9999729	0.1065	0.0904
Validation (Avg)	0.0923	0.9999723	0.1088	0.0923
Validation (Best)	0.0912	0.9999729	0.1066	0.0912
Test (Avg)	0.0901	0.9999720	0.1079	0.0900
Test (Best)	0.0875	0.9999735	0.1055	0.0875

The XGBoost model exhibited exceptionally high predictive performance, with a test-set R² of 0.99997, RMSE and SD below 0.1°, and an AAPRE of approximately 0.11%, indicating precise agreement between predictions and observations and high stability across the dataset. Compared to alternative models, such as CNN (RMSE = 1.48°), XGBoost achieved markedly superior accuracy, demonstrating its suitability for tabular datasets with highly correlated features, such as ionic concentrations.

Sensitivity analysis (Fig. 8) revealed that NaHCO₃ concentration (NaHCO₃_ppm) is the most influential parameter, followed by contact time and temperature, whereas pressure and other salts have minimal effect. Higher temperatures and longer contact times reduced the contact angle, promoting more water-wet surfaces. These results are consistent with previous studies and highlight the dominant chemical factors in controlling wettability under SWAF conditions.

Fig. 8.

Sensitivity analysis of input parameters on contact angle.

The scatter plots of predicted versus actual contact angles for training, test, and validation datasets (Fig. 9) further confirm the model’s performance, showing predictions closely aligned with experimental values and indicating robust generalization across all data subsets.

Fig. 9.

Scatter Plots of Predicted vs. Actual Contact Angle for Training, Test, and Validation Datasets. (A) Training Data: Predicted vs. Actual Contact Angle, (B) Test Data: Predicted vs. Actual Contact Angle, (C) Validation Data: Predicted vs. Actual Contact Angle.

Support vector regression (SVR)

Support Vector Regression (SVR) is a well-established margin-based machine-learning approach that is particularly effective for regression tasks on moderate-dimensional, noisy datasets. The core idea of SVR is to find a regression function that keeps predictions within an ε-tube around the true values, such that only samples outside this margin are managed via slack variables. In this study, the radial basis function (RBF) kernel was used to map the data into a higher-dimensional feature space, enabling proper modeling of the complex nonlinear relationships among ionic compositions, pressure and temperature conditions, and contact angle. As shown in Fig. 10, which illustrates the schematic architecture of the XGBoost model employed for prediction, a similar approach of nonlinear mapping is leveraged in SVR. The RBF kernel was chosen because of its robustness to noise and its ability to represent complex multivariate nonlinear interactions.

Fig. 10.

Schematic architecture of SVR model used for prediction.

The SVR regression function can be expressed in kernel form as:

10

where is the RBF kernel, ​ and ​ are Lagrange multipliers, and is the model bias the objective of SVR optimization is to minimize the following function:

11

With restrictions:

12

The RBF kernel function is also expressed as follows:

13

where controls the width of the Gaussian distribution and scales the Euclidean distance.

The dataset was split into training (60%), validation (20%), and test (20%) subsets. Hyperparameters were tuned via grid search combined with 5-fold cross-validation. The optimal hyperparameter values found were: =100 (controlling the trade-off between margin width and training error), =0.01 (RBF kernel scale), and =0.1 ( -tube width).

The Support Vector Regression (SVR) model was evaluated for predicting contact angles under SWAF conditions, with results summarized in Table 4. The model demonstrated exceptionally high accuracy, achieving a mean coefficient of determination (R²) of approximately 0.99963 across training, validation, and test sets, indicating its ability to capture the variations in contact-angle measurements with high fidelity. Figure 3-C presents the boxplot of prediction performance for the SVR model in comparison with other AI models, illustrating its relative precision. While the SVR outperforms the CNN model (RMSE ≈ 0.32° vs. 1.48° for CNN), it shows slightly lower performance compared with ensemble tree-based models such as XGBoost (RMSE ≈ 0.09°) and Random Forest (RMSE ≈ 0.13°), highlighting its comparative limitation against boosted and bagging algorithms.

Table 4.

SVR model results across datasets.

Dataset	RMSE	R²	AAPRE (%)	SD
Train (Avg)	0.379911	0.999516	0.424705	0.369270
Train (Best)	0.347840	0.999599	0.345630	0.339308
Validation (Avg)	0.402909	0.999468	0.435991	0.392252
Validation (Best)	0.380759	0.999528	0.364683	0.372473
Test (Avg)	0.322274	0.999632	0.424216	0.311176
Test (Best)	0.275716	0.999738	0.347914	0.265471

Figure 11 displays scatter plots of predicted versus actual contact-angle values for the training, test, and validation datasets. The data points for SVR are tightly clustered around the diagonal line, particularly within the 40°–110° range, confirming the model’s reliability and low prediction error. Prediction errors, as visualized in Fig. 3-C, are mostly confined within ± 2°, with occasional deviations in the training set down to − 8°, suggesting minor noise effects but overall model stability.

Fig. 11.

Scatter Plots of Predicted vs. Actual Contact Angle for Training, Test, and Validation Datasets. (A) Training Data: Predicted vs. Actual Contact Angle, (B) Test Data: Predicted vs. Actual Contact Angle, (C) Validation Data: Predicted vs. Actual Contact Angle.

Permutation feature-importance analysis revealed that MgCl₂ and Na₂SO₄ were the most influential factors, contributing approximately 28% and 22%, respectively, reflecting their roles in surface electrostatics and chemical equilibrium. Temperature and contact time contributed 18% and 15%, respectively, while pressure had a minimal effect (~ 3%), consistent with physical expectations for the experimental conditions. The SVR model’s robustness is further enhanced by the use of GAN-augmented data and optimized hyperparameters via Grid Search, which collectively improve generalization and predictive accuracy. In summary, the SVR model provides accurate, stable, and interpretable predictions of contact-angle behavior under SWAF conditions. However, its sensitivity to feature scaling requires careful preprocessing, and scalability may be a concern for substantially larger datasets, suggesting directions for future research in large-scale reservoir applications. This analysis was conducted using the Permutation Importance method within the framework of the SVR model and clearly demonstrates that the model exhibits greater sensitivity to chemical parameters (e.g., bicarbonates) than to physical parameters (e.g., pressure). These findings are consistent with previous experimental studies, particularly Hassan et al. (2022), thereby reinforcing the validity of the obtained results. Furthermore, the present results highlight the novelty of this research, as they demonstrate that the employed model is capable of focusing on the key factors in the SWAF process and can serve as a practical tool for optimizing smart water compositions in EOR operations.

Random forest (RF)

The Random Forest (RF) algorithm is an ensemble learning method that constructs a prediction model by aggregating multiple decision trees. Using bootstrap aggregating (bagging) and random feature selection at each split, RF produces stable and accurate predictions. The ensemble of many trees reduces variance and enhances generalizability while providing strong resistance to overfitting. As illustrated in Fig. 12, which shows the schematic architecture of the XGBoost model used for prediction, the ensemble concept in RF similarly relies on combining multiple base learners to improve model performance. An additional advantage of RF is its ability to compute feature importance, enabling quantification of each variable’s relative contribution to model predictions—an especially valuable property for complex, multidimensional datasets such as those encountered in Smart Water Assisted Foam (SWAF) studies.

Fig. 12.

Schematic architecture of RF model used for prediction.

For an input sample the RF prediction is the average of the individual tree outputs:

14

where is the output of tree and is the total number of trees. The choice of splitting at nodes is defined based on the least squares method, which is written as:

15

The importance of features was also calculated through the average reduction in gross error, which shows the percentage contribution of each feature to improving the model’s prediction. The Random Forest model was tuned via grid search with 5-fold cross-validation. Model hyperparameters were set as follows: number of trees K = 500, maximum tree depth = 10, the square root of the number of features used as the maximum features per split, minimum samples for a split = 2, and minimum samples per leaf = 1. Model performance was evaluated on training, validation, and test sets; a summary of results is provided in Table 5.

Table 5.

Random forest model results across datasets.

Dataset (Avg/Best)	RMSE (°)	R²	AAPRE (%)	SD (°)
Train (Avg)	0.1285	0.99994	0.1603	0.1285
Train (Best)	0.1279	0.99994	0.1597	0.1279
Validation (Avg)	0.1298	0.99994	0.1621	0.1298
Validation (Best)	0.1281	0.99994	0.1599	0.1281
Test (Avg)	0.1292	0.99994	0.1615	0.1291
Test (Best)	0.1266	0.99994	0.1586	0.1266

For the Support Vector Regression (SVR) model, the predictive performance demonstrates strong agreement between predicted and observed contact angles across all datasets. As shown in Table 5, the R² values approach unity, indicating that the model captures the underlying trends with high fidelity. The RMSE and SD values, approximately 0.32° and similar, reflect moderate predictive precision, while the AAPRE around 0.35% confirms reliable performance on a relative scale.

Figure 3-D presents the boxplot for SVR, illustrating that the distribution of prediction errors is tightly clustered, with minimal outliers, suggesting consistent model performance. Figure 4-C shows the learning curves (R²) for both training and validation sets; the curves demonstrate stable convergence, with training R² slightly higher than validation R², indicative of good model fit without evident overfitting.

Scatter plots in Fig. 13-B (test dataset) confirm the accuracy of SVR predictions, with most data points closely aligned along the diagonal line, and minimal dispersion observed across the contact-angle range. Similar trends are observed in Figs. < link rid="fig13”>13</link>-A and 13-C for training and validation datasets, further supporting the model’s generalizability and stability.

Fig. 13.

Scatter Plots of Predicted vs. Actual Contact Angle for Training, Test, and Validation Datasets. (A) Training Data: Predicted vs. Actual Contact Angle, (B) Test Data: Predicted vs. Actual Contact Angle, (C) Validation Data: Predicted vs. Actual Contact Angle.

Although the SVR model achieves satisfactory performance, comparison with other models in Fig. 3 reveals that XGBoost (Fig. 3-B) outperforms SVR in terms of RMSE, while Random Forest (Fig. 3-D) shows comparable precision. Feature-importance assessment is less straightforward for SVR due to its kernel-based formulation, yet the model demonstrates sensitivity primarily to MgCl₂ and Na₂SO₄ concentrations, in line with chemical control over wettability in SWAF systems. These results are consistent with prior studies and highlight the SVR model as a reliable alternative for predictive modeling of contact-angle behavior.

Multi-Layer perceptron (MLP)

The Multi-Layer Perceptron (MLP), one of the simplest yet most widely used feedforward neural network architectures, was employed in this study to predict contact angles under Smart Water Assisted Foam (SWAF) conditions. This model was selected due to its standardized structure and its ability to capture nonlinear relationships between variables, while also serving as a benchmark for comparison with other methods, including CNN, XGBoost, SVR, and Random Forest. As illustrated in Fig. 14, which presents the schematic architecture of the XGBoost model used for prediction, similar principles of feature mapping and nonlinear relationship representation are leveraged in the MLP approach. In the employed architecture, the input data consisted of nine primary features related to salt concentrations, pressure, temperature, and time, which were normalized before being fed into the model. Hidden layers utilized ReLU activation functions to capture complex patterns, while the output layer, containing a single neuron, predicted the contact angle.

Fig. 14.

Schematic architecture of MLP model used for prediction.

The output of the model for each input sample can be expressed as:

16

where W₁​ and W₂​ are weight matrices, b₁​ and b₂​ are bias vectors, and is the ReLU activation function. The model was trained using the Mean Squared Error (MSE) loss function:

17

Optimization was performed using the Adam algorithm with an initial learning rate of 0.001. To prevent overfitting, dropout with a rate of 0.2 was applied to the hidden layers, and early stopping was employed to halt training when validation error ceased to improve. The network architecture included two hidden layers with 50 and 25 neurons, respectively. The dataset was divided into training (60%), validation (20%), and test (20%) subsets. Additionally, 5-fold cross-validation was employed to enhance model generalization.

Model performance was evaluated using RMSE, coefficient of determination (R²), average absolute percentage relative error (AAPRE), and standard deviation of errors (SD). The results are summarized in Table 6. These results indicate that the MLP model successfully captured the nonlinear relationships between the input features and contact angle. The R² value of approximately 0.9994 demonstrates a very high correlation between predicted and observed values. However, the average RMSE of around 0.39° indicates lower accuracy compared to tree-based methods such as XGBoost (RMSE = 0.09°) and Random Forest (RMSE = 0.13°). Nevertheless, MLP outperformed the CNN model, which had an RMSE of 1.48°, indicating that a simple feedforward network can provide satisfactory and even superior performance compared to CNN for tabular SWAF data.

Table 6.

Multi-Layer perceptron (MLP) model results across datasets.

Dataset (Avg/Best)	RMSE (°)	R²	AAPRE (%)	SD (°)
Train (Average)	0.3932	0.9994	0.4329	0.3932
Train (Best)	0.3912	0.9995	0.4310	0.3912
Validation (Average)	0.3957	0.9994	0.4357	0.3957
Validation (Best)	0.3923	0.9995	0.4323	0.3923
Test (Average)	0.3946	0.9994	0.4346	0.3946
Test (Best)	0.3912	0.9995	0.4312	0.3912

Figure 3-E presents the boxplot comparison of the prediction performance for the MLP model in relation to other AI models. The MLP exhibits consistent prediction behavior, with slightly wider error dispersion compared to tree-based methods, reflecting the model’s flexibility in capturing nonlinear relationships in complex datasets. Figure 4-D illustrates the learning curve (R²) for the MLP model across increasing sample sizes. The curve demonstrates rapid convergence, stabilizing around 0.9994 for both training and validation sets, indicating robust model generalization and minimal overfitting. Scatter plots in Fig. 15 show the alignment of predicted versus actual contact angle values for the validation dataset. Most data points are closely clustered along the diagonal line, confirming high predictive accuracy and model stability. Comparable scatter plots for training and test datasets similarly indicate that the MLP predictions remain largely within ± 0.5° error, with occasional deviations up to 1° in the training set, highlighting overall reliability with minor noise.

Fig. 15.

Scatter Plots of Predicted vs. Actual Contact Angle for Training, Test, and Validation Datasets. (A) Training Data: Predicted vs. Actual Contact Angle, (B) Test Data: Predicted vs. Actual Contact Angle, (C) Validation Data: Predicted vs. Actual Contact Angle.

Feature importance analysis, performed via the Permutation Importance method, reveals that MgCl₂ ions (~ 28%) and Na₂SO₄ ions (~ 22%) are the most influential predictors for contact angle, while pressure contributes minimally (~ 3%). These results are chemically and physically consistent and align with previous Enhanced Oil Recovery (EOR) studies. Overall, while the MLP model shows slightly lower accuracy compared to tree-based models, it provides an effective and flexible framework for modeling nonlinear phenomena and serves as a valuable benchmark for assessing predictive performance of other AI models in petroleum applications. This analysis was performed using the Permutation Importance method within the MLP (Multilayer Perceptron) model and indicates that the model is more sensitive to chemical variables than to physical variables. These findings are consistent with previous experimental studies (e.g., Hassan et al., 2022) and underscore the importance of focusing on key chemical compositions in the SWAF process. Consequently, the novelty of the present study lies in providing a new approach for optimizing smart water compositions in EOR operations and offering a practical tool for designing enhanced oil recovery strategies.

The trend plots presented in Fig. 16 illustrate the performance of five different models in predicting the contact angle, providing a comparison between actual and predicted values. In Fig. 16-A, the CNN model generally exhibits good alignment with the experimental data, and the gentle slope of the curves indicates an appropriate fit with the samples, although noticeable deviations are observed at certain points, likely due to the model’s sensitivity to data noise. While CNN serves as a novel deep learning benchmark for tabular SWAF data, it is outperformed by tree-based models, highlighting the advantage of ensemble methods in this context. The XGBoost model, as shown in Fig. 16-B, demonstrates very high accuracy, with predictions closely matching the actual values; the strong agreement between the actual and predicted lines, particularly at higher ranges, highlights the model’s superior capability in estimating the contact angle. The SVR model, depicted in Fig. 16-C, also shows reasonable agreement between actual and predicted values, although minor deviations occur at certain points, which may result from the use of the RBF kernel and the handling of data noise through slack variables, reflecting a balance between accuracy and model flexibility. Figure 16-D, representing the Random Forest model, shows strong correspondence between actual and predicted values with low dispersion, and the uniformity of the curves confirms the model’s high generalizability to new data. Finally, the MLP model in Fig. 16-E exhibits overall satisfactory alignment with the experimental data; however, deviations are more pronounced at the extremes of the spectrum compared to other models, potentially due to the higher complexity of the neural network and the need for more precise parameter tuning. Overall, the examination of these trend plots indicates that each model possesses specific strengths and limitations, and model selection depends on the required level of accuracy and sensitivity to data variability.

Fig. 16.

Trend Plots of Predicted vs. Actual Values for Various Machine Learning Models. (A) Trend plot– CNN Model, (B) Trend plot– XGBoost Model, (C) Trend plot– SVR Model, (D) Trend plot– Random Forest, (RF) Model, (E) Trend plot– MLP Model.

According to Table 7, which presents a statistical comparison of the performance of different artificial intelligence models on the test dataset, the performance of each model can be analyzed in detail. The evaluation metrics include RMSE (Root Mean Square Error), R² (coefficient of determination), AAPRE (Average Absolute Percentage Relative Error), and SD (standard deviation). The XGBoost model, with an RMSE of 0.08 and an AAPRE of 0.07, exhibits the best performance in terms of prediction accuracy and stability against noise, confirming its high capability in accurately estimating the contact angle. The SVR model, with an RMSE of 0.27 and an AAPRE of 0.34, provides acceptable performance but is less accurate than XGBoost and Random Forest (RMSE = 0.12). The MLP model demonstrates the lowest accuracy, with the highest RMSE (0.39) and AAPRE (0.43), likely due to the network’s higher complexity or the need for more training data for parameter optimization. Despite differences in prediction accuracy, all models exhibit high coefficients of determination (R² ≈ 0.99), indicating their overall ability to capture the trends of the actual data. It should be noted that while these exceptionally high R² values demonstrate strong fit, potential overfitting or data leakage due to GAN-based augmentation cannot be fully excluded; real-world validation with independent field data is recommended to confirm generalization. Notably, the CNN model, with an RMSE of 0.06 and an SD of 0.06, emerges as a prominent model within this dataset, reflecting a well-balanced trade-off between predictive accuracy and flexibility in handling data variations and demonstrating strong generalization capability to new samples. Moreover, experimental validation refers to consistency with previously reported EOR studies (e.g., Hassan et al., 2022) rather than new laboratory replication, and supplementary figures provide visual confirmation that GAN-generated data trends align with physical and chemical expectations. This statistical analysis, in addition to corroborating the observations from the trend plots in Fig. 16, provides a comprehensive overview of the relative performance of each model and facilitates informed model selection based on accuracy, robustness, and generalizability.

Table 7.

Statistical comparison of different AI models on the test dataset (Best performance).

RMSE	R²	AAPRE (%)	SD	Model
0.08	0.99	0.10	0.08	XGBoost
0.27	0.99	0.34	0.26	SVR
0.12	0.99	0.15	0.12	Random Forest
0.39	0.99	0.43	0.39	MLP
0.06	0.99	0.07	0.06	CNN

Histogram of contact angle error

The histogram of contact angle errors (relative error percentage) for the training, validation, and test datasets is presented in the following figures, illustrating the distribution of prediction errors between the measured and machine learning model–predicted contact angles. For each model, the histograms are presented collectively (a: training, b: validation, c: test) to allow a comparative assessment of the error distributions. These histograms are accompanied by KDE (Kernel Density Estimation) curves to represent the approximate normal distribution of errors.

Across all models, errors are centered around zero, indicating high accuracy and minimal overfitting. Analysis of these histograms reveals that tree-based models (XGBoost and Random Forest) exhibit tighter error distributions, whereas neural network models (MLP and CNN) show greater dispersion, likely due to increased sensitivity to noise in the data. SVR demonstrates a moderate distribution, falling between the tree-based and neural models. This comparison indicates that XGBoost achieves the best performance with errors concentrated within a smaller range (± 0.1°), while CNN exhibits a wider error range (± 0.6°), which may reduce accuracy under noisy conditions. This analysis is based on 5-fold cross-validation and demonstrates the robustness of the models in predicting contact angles.

Figure 17 shows that the error distribution for the XGBoost model is highly concentrated around zero, with the highest frequency in the range of -0.1° to 0.1°, accompanied by a smooth and symmetric KDE. This nearly normal distribution, with SD = 0.09° and AAPRE = 0.11%, indicates very high accuracy and no systematic error. Compared to other models, XGBoost exhibits lower dispersion than MLP (SD = 0.39°) and CNN (SD = 1.47°), attributable to the gradient boosting structure and its inherent regularization.

Fig. 17.

Histogram of contact angle errors for the XGBoost model. (a) Training dataset, (b) Validation dataset, (c) Test dataset.

Figure 18 indicates that the SVR model errors are also centered around zero, but with slightly greater dispersion (SD = 0.31°) than XGBoost. The highest frequency occurs in the − 0.2° to 0.2° range, with a sharp KDE peak, confirming good accuracy (AAPRE = 0.42%). Compared to Random Forest (AAPRE = 0.16%), SVR shows higher relative error, yet performs better than MLP (0.43%), demonstrating its balanced capability in handling nonlinear relationships using the RBF kernel.

Fig. 18.

Histogram of contact angle errors for the SVR model. (a) Training dataset, (b) Validation dataset, (c) Test dataset.

The histogram in Fig. 19 illustrates that the Random Forest errors are tightly distributed around zero, with the highest frequency in the − 0.1° to 0.1° range and SD = 0.13°. The symmetric KDE suggests no overfitting, and AAPRE = 0.16%. Compared to XGBoost (AAPRE = 0.11%), Random Forest is slightly more dispersed but outperforms SVR (0.42%) and neural network models (MLP and CNN), due to the ensemble of decision trees and variance reduction via bagging.

Fig. 19.

Histogram of contact angle errors for the Random Forest model. (a) Training dataset, (b) Validation dataset, (c) Test dataset.

Figure 20 shows that MLP errors are centered around zero but exhibit greater dispersion (SD = 0.39°) compared to tree-based models. The highest frequency occurs in the − 0.4° to 0.4° range, with a slightly wider KDE, indicating acceptable accuracy (AAPRE = 0.43%). Compared to CNN (AAPRE = 0.43%), MLP performs similarly but is less accurate than XGBoost (0.11%) and Random Forest (0.16%) due to neural networks’ higher sensitivity to noise and the need for finer hyperparameter tuning.

Fig. 20.

Histogram of contact angle errors for the MLP model. (a) Training dataset, (b) Validation dataset, (c) Test dataset.

In the Convolutional Neural Network (CNN) model, Fig. 21 shows that contact angle errors are mainly centered around zero but exhibit significant dispersion (SD ≈ 1.47°). The highest frequency occurs in the − 1° to 1° range, with KDE confirming a sharp peak, indicating high prediction accuracy (AAPRE ≈ 0.43%). However, comparing error dispersion reveals that MLP (SD ≈ 0.39°) achieves higher accuracy than CNN. This difference arises from the nature of the data: SWAF data are tabular and lack spatial structure, limiting CNN’s ability to extract local patterns effectively. In contrast, MLP and tree-based models like XGBoost and Random Forest provide superior numerical accuracy. Feature importance analysis using permutation-based methods yielded results similar to MLP, where MgCl₂ and Na₂SO₄ concentrations exerted the highest influence on contact angle predictions, followed by temperature and exposure time, which directly affect electrostatic interactions at the rock–fluid interface. Pressure had the least influence, consistent with physical expectations.

Fig. 21.

Histogram of contact angle errors for the CNN model. (a) Training dataset, (b) Validation dataset, (c) Test dataset.

Furthermore, a comparison of CNN with reference models, including a feedforward artificial neural network (ANN) and Random Forest Regression (RFR), indicated that CNN outperforms both (RMSE: CNN = 1.48°, ANN = 2.36°, RFR = 3.01°; R²: CNN = 0.997, ANN = 0.984, RFR = 0.974) but underperforms compared to advanced tree-based models such as XGBoost and Random Forest (XGBoost: RMSE = 0.09°, R² = 0.99997; Random Forest: RMSE = 0.13°, R² = 0.99994). These findings demonstrate that while CNN generalizes well and exhibits no systematic error, simpler tree-based models are more effective for tabular, non-spatial datasets. Overall, the error distributions centered around zero and feature importance analysis confirm the reliability of CNN predictions across datasets while highlighting the limitations of convolutional architectures for non-image data.

Model error rate

The model inputs included salt concentrations (NaHCO₃, NaCl, CaCl₂, MgCl₂, KCl, Na₂SO₄), pressure, temperature, and contact time. Trend analysis indicated that increasing salt concentrations raised the contact angle, whereas pressure had minimal effect, and temperature exhibited an inverse relationship with contact angle—higher temperatures reduced the contact angle, making the surface more water-wet. All models (XGBoost, SVR, RandomForest, MLP, CNN) were able to capture these trends.

XGBoost achieved the best performance with RMSE = 0.09° and R² = 0.99997, accurately predicting surface behavior in the presence of salts. SVR and tree-based models also performed well, while CNN showed lower accuracy due to its design for image data. The use of GAN-augmented data and hyperparameter optimization via Grid Search further improved model performance. The residual error distributions for these models, as visualized in Fig. 22, highlight XGBoost’s exceptional precision with a narrow error spread (residuals within ± 0.3°), reinforcing its leading RMSE and R². RandomForest and SVR follow with moderate spreads (up to ± 0.6°), while MLP shows a wider distribution (up to ± 1°), and CNN exhibits the largest range (up to ± 2.5°), underscoring its misfit for the dataset’s tabular nature.

Fig. 22.

Residual Error Distribution for the Developed Models.

Study limitations include neglecting crude oil properties, rock heterogeneity at the pore scale, dynamic flow conditions, and the absence of field validation. Additionally, the models predict only static contact angles and do not account for advancing, receding, or dynamic angles. To enhance generalizability, incorporating field data and dynamic flow characteristics is recommended, particularly for CNN, which could achieve better performance with structured data.

Development of the empirical model

An empirical model based on multiple linear regression (MLR) was developed to complement the analyses presented in this study and to enhance predictive capability. This model is intended as a simple and interpretable tool for predicting the contact angle (θ) in carbonate reservoirs under smart water–assisted foam (SWAF) injection. The model was constructed using input features comprising ionic concentrations (ppm), pressure (psia), temperature (°C), and contact time (hours), with the target variable being the contact angle (degrees). To ensure dimensional consistency and to improve generalizability, the input variables were normalized based on the statistical means reported in Table 1. In this procedure, each variable was normalized as where denotes the mean of that feature in the collected dataset. The empirical equation is presented as follows:

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The constant 142.49 represents the baseline contact angle (in degrees) and serves as the initial offset of the equation; this value was determined from the mean of the contact angle measurements in the dataset. The term indicates a negative effect of contact time on the contact angle, where the mean time is 12.13 h; this term implies that, on average, a one-unit increase in the normalized contact time corresponds to a 5° decrease in contact angle, consistent with interfacial balance considerations in rock–fluid interactions. The term denotes a negative temperature effect, with a mean temperature of 67.40 °C, indicating that the contact angle decreases with increasing normalized temperature, in agreement with the inverse relationship observed between temperature and contact angle in the data. The term is a small positive pressure coefficient, where the mean pressure is 808.20 psia, implying a minor increasing effect of pressure on the contact angle (contributing approximately 3% according to the feature-importance analysis).

The ionic concentration terms show predominantly negative contributions to the contact angle: reflects the negative influence of Na₂SO₄ concentration, with a mean of 18535.05 ppm and an importance of 22% as indicated by XGBoost; indicates a negative effect of KCl (mean 10.01 ppm); is the largest negative coefficient among the ionic terms, corresponding to MgCl₂ with mean 20998.85 ppm and an importance of 28% (XGBoost); denotes the negative impact of CaCl₂ (mean 25183.1 ppm); shows the negative contribution of NaCl (mean 39315.18 ppm); and represents the negative effect of NaHCO₃ (mean 148.74 ppm). These coefficients capture the linear relationships observed in the dataset, and the negative signs for temperature and most ionic concentrations indicate their roles in reducing the contact angle (promoting more water-wet conditions), whereas the small positive pressure coefficient indicates a minimal opposite effect. The model was calibrated using the dataset’s statistical properties (e.g., the means and standard deviations reported in Table 1) and incorporates insights from feature-importance analysis using XGBoost.

For empirical evaluation, key metrics were calculated on a synthesized dataset aligned with the summary statistics of Table 1: the root-mean-square error (RMSE) is approximately 1 (reflecting an approximate fit with added noise; results may differ with real data), the coefficient of determination is 0.996 (indicating a strong linear fit; more complex machine-learning models capture nonlinear effects at higher accuracy), and the standard deviation of residuals is approximately 1 (with minor added noise; real-world applications may differ). This empirical model assumes linear relationships and the specified units (ppm for ionic concentrations, psia for pressure, °C for temperature, and hours for time); normalization ensures dimensional consistency because the calibrated coefficients balance contributions from variables with different scales. Extrapolation outside the data ranges reported in Table 1 (minimum and maximum) should be performed with caution. The empirical model serves as a simple and interpretable alternative to more complex machine-learning models (e.g., XGBoost with ), which capture nonlinearities and interactions for improved accuracy.

Conclusion

In enhanced oil recovery (EOR) from carbonate reservoirs, contact angle prediction is essential for assessing wettability alteration and optimizing sweep efficiency under Smart Water Assisted Foam (SWAF) injection. SWAF combines ion-modified smart water with foam to alter rock surfaces from oil-wet to water-wet, facilitating better oil displacement and reducing gas mobility. The novelty of this work lies in the integration of physically constrained Generative Adversarial Networks (GANs) for data augmentation, expanding the dataset from 1,615 to 13,032 samples while preserving physical realism (e.g., inverse temperature-contact angle relationship), and the use of Convolutional Neural Networks (CNN) as a benchmark for deep learning on tabular data. Furthermore, several advanced machine learning models, including CNN, XGBoost, Support Vector Regression (SVR), Random Forest, and Multilayer Perceptron (MLP), have been utilized to predict contact angle. While CNN serves as a novel deep learning benchmark, tree-based models like XGBoost outperform it for this tabular SWAF dataset, highlighting the value of ensemble methods. The models utilized in this study demonstrated a high degree of adaptability to complex data and varying conditions, resulting in superior performance in predicting contact angle compared to other models. Additionally, these models exhibited robustness to noisy and inconsistent data, enabling accurate predictions even in the presence of discontinuous and irregular data sets. Moreover, the feature importance analysis developed in this work outperforms existing approaches in terms of accuracy, providing a more reliable and trustworthy predictive framework for contact angle estimation. The models were trained and evaluated using nine input parameters including ion concentrations (NaHCO₃, NaCl, CaCl₂, MgCl₂, KCl, Na₂SO₄), pressure, temperature, and contact time on a dataset consisting of 13,032 data points, and their performance was evaluated through statistical analysis and graphical representations. The key outcomes of this study can be outlined as follows:

1. Among the suggested models, the XGBoost model indicated exceptional accuracy, achieving an overall RMSE of 0.09° and R² of 0.99997. The Random Forest and SVR models, following the XGBoost model, showed the next highest levels of accuracy, with RMSE values of 0.13° and 0.32°, respectively. These findings underscore the superior performance of the XGBoost model in predicting contact angle.

2. The outcomes of the feature importance analysis indicated that MgCl₂ (28%) and Na₂SO₄ (22%) exert the dominant influence, with temperature exhibiting an inverse relationship with contact angle, while pressure had the minimal effect (~ 3%).

3. The sensitivity analysis indicated that NaHCO₃ has the strongest influence on the model (~ 1.0), with time and temperature following at moderate levels, both affecting the output inversely for temperature. On the other hand, pressure shows a minimal effect with a value of ~ 0.03.

4. The outcomes of the histogram and error distribution analysis validate the precision of the contact angle data set and highlight the strong reliability of the XGBoost and Random Forest models in contact angle estimation. Additionally, tree-based models exhibited tighter error distributions (± 0.1°), while neural models (MLP and CNN) showed greater dispersion (± 0.6°).

Finally, it is recommended that future research extend the models by incorporating diverse field data and applying them to specific EOR conditions, such as heavy oils and dynamic flow. Additionally, integrating physical modeling approaches with data-driven methods could substantially improve the accuracy and generalizability of contact angle predictions.

Author contributions

Siavash Partonia: Conceptualization, Methodology, Software, Formal analysis, Data curation, Investigation, Model development, Validation, Visualization, Writing – original draft, Writing – review & editing. Seyyed Alireza Tabatabaei-Nezhad: Supervision, Conceptual guidance, Project administration, Writing – review & editing.

Data availability

The dataset used in this study was collected and compiled from several published research articles, including experimental data. The dataset was further developed and expanded by the authors through data augmentation and model-based generation techniques. However, due to licensing and integration restrictions, the dataset is not publicly available.

Declarations

Competing interests

The authors declare no competing interests.