The oil and gas industry has increasingly prioritized the development of advanced technologies for the accurate monitoring and characterization of multiphase flows, which involve the simultaneous movement of two or more phases, such as liquid, gas, or solid. These flows may involve immiscible substances (e.g., oil and water) or different phases of the same component (e.g., steam and liquid water) transported through a pipeline (Díaz et al., 2021; Al-Naser et al., 2016). Accurate identification of flow patterns in horizontal pipes is essential across petrochemical and fluid transport operations, as it enables better system design, enhances operational efficiency, and reduces costs (Alhashem, 2020; Soot, 1970). Proper flow pattern recognition also aids in mitigating corrosion and erosion by optimizing chemical dosing strategies, ultimately extending the lifespan of pipeline infrastructure and minimizing maintenance (Al-Sarkhi et al., 2017). Furthermore, flow patterns strongly influence heat transfer, pressure drop, and phase distribution parameters critical for the safe and efficient operation of industrial processes (Osundare et al., 2020).

Flow patterns describe the spatial arrangement of immiscible phases within a conduit and are determined by variables such as superficial velocities, fluid properties, pipe geometry, and operating conditions (El and -Sebakhy, 2010). While traditional identification techniques such as high-speed imaging, wire-mesh sensors (WMS), and gamma-ray densitometry have provided valuable insights under controlled laboratory conditions (Hernández-Cely and Ruiz-Diaz, 2020; Lum et al., 2006; Wang et al., 2024; Abduvayt et al., 2004; Cai et al., 2012; Dasari et al., 2013), their practical application in real-time industrial environments remains limited. High instrumentation costs, complex calibration procedures, and the need for expert interpretation hinder scalability and automation (Figueiredo et al., 2016; Perera et al., 2017; Su et al., 2024).

In recent years, Artificial Neural Networks (ANNs) have emerged as a promising approach for multiphase flow analysis. Unlike empirical correlations and mechanistic models that require predefined physical assumptions, ANNs can learn complex, nonlinear relationships directly from data. This makes them particularly suitable for classifying flow patterns in highly dynamic and heterogeneous systems, such as oil-water mixtures in horizontal pipelines. ANNs offer multiple advantages: they are inherently scalable, require no predefined assumptions about flow regime transitions, and can be integrated into autonomous monitoring systems for continuous operation (Chimeno-Trinchet et al., 2020; Bahrami et al., 2019; Roshani et al., 2014). Their adaptability to new data enables rapid recalibration under changing conditions, a key asset in the context of real-world operations (Qin et al., 2021; Du et al., 2019).

Multiple studies have demonstrated the effectiveness of data-driven models in improving predictive accuracy in multiphase flow systems. For example, Huang et al. (2024) applied Support Vector Machine (SVM), Random Forest (RF), and an enhanced K-Nearest Neighbor model (KNN) for regime classification in small modular reactors, while Sun et al. (2025) employed a particle swarm-optimized ANN to predict core-annular oil-water flow, outperforming conventional models in terms of accuracy and generalization. Çolak (2025) reported a high-fidelity neural model for predicting waxy crude oil viscosity with a correlation coefficient of 0.9985. These works confirm the capacity of neural architectures to capture underlying physical dynamics even in complex, nonlinear environments. Despite these advances, limitations remain—especially the limited availability of large, well-labeled datasets and the interpretability of ANN models, which are often viewed as black-box systems (Shirley et al., 2012; Xu et al., 2021).

To address these issues, recent studies have explored hybrid techniques that combine ANNs with radiation-based sensing or advanced signal processing (Roshani et al., 2021; Salgado et al., 2010). Deep learning architectures, such as Transformer Neural Networks and Long Short-Term Memory (LSTM) models, have also been applied to multiphase systems, achieving improved performance in flow pattern recognition and volume fraction estimation (Ruiz-Díaz et al., 2024a; Hernández-Salazar et al., 2024). However, most of these approaches either target gas–liquid systems or rely on small or highly specific datasets, limiting their generalizability to oil-water flow conditions.

This study addresses a critical gap in the current literature related to the accurate predictive modeling of oil-water flow patterns in horizontal pipelines using machine learning. While previous studies have often relied on limited datasets or focused on specific flow regimes, this work integrates the most comprehensive and diverse experimental database reported to date for oil-water systems. A machine learning model based on ANNs was developed to classify six distinct flow patterns, providing a robust, scalable, and generalizable tool for flow pattern recognition. This approach aims to support more reliable flow assurance, pipeline design, and operational decision-making in the oil and gas industry, by addressing limitations associated with traditional empirical correlations and mechanistic models.

This section presents the numerical values obtained from the iterative and organized process of testing and selecting the ANN structure. These results were derived from all the simulations carried out under different topological configurations, in which all the data from the simulation process were recorded. Subsequently, an analysis and model selection were performed to identify the one that presented the best performance results in predicting flow patterns. Various configurations were structured by adjusting parameters such as the training algorithm, the number of hidden layers, and the number of neurons in each hidden layer.

For each of the structured models, the following parameters were kept constant: the data distribution was set at 70% for the training stage, 15% for the validation stage, and 15% for the testing stage. The activation function for all hidden layers was the sigmoid function, and the Softmax activation function was used for the output layer. The error function to be optimized was cross-entropy, and two retrainings were performed for each configuration. Modifying the script lines generated by MATLAB’s Neural Network Pattern Recognition tool made all adjustments to the parameters. All experimental tests were conducted on an MSI Raider GE76 computer with a 12th Gen Intel(R) Core (TM) i7-12700H 2.70 GHz processor, 16 GB of installed RAM, and a 64-bit operating system, X64 processor.

Table 6 presents the configurations generated with different combinations of parameters to be applied to the ANN models. They were evaluated according to the training functions shown in Table 7. In this manner, 200 ANN tests were initially performed based on 100 different parameter configurations, from which the models that yielded the best performance values were identified, focusing on cross-entropy and those achieving over 90% accuracy in flow pattern predictions. Once these configurations were identified, the ANN model tests were repeated to obtain a second verification of the results and to filter the evaluated topologies to those that demonstrated the highest prediction accuracy across both retraining for flow patterns.

Table 8 presents the best results obtained from testing the different configurations in the topology for each training function. Additionally, it.

Table 8 presents a comparative summary of five ANN models trained with different algorithms, showing the accuracy values from the confusion matrices for the training, validation, and testing stages, as well as from the overall confusion matrix. All models use the same activation and loss functions but vary in topology and training method. Model 1 (TRAINRP) achieved the best overall performance, with the highest total accuracy (94.6%), strong validation and test accuracy, and a short training time (3 s), making it the most balanced and efficient configuration. Model 2 (TRAINSCG) also performed well, offering good accuracy (92.3%) with the shortest training time (1 s), indicating its suitability for fast iterative training. Model 3 (TRAINBFG) achieved competitive accuracy (91.2%) and low cross-entropy loss, but required 133 s to train. This extended time is due to the computational complexity of the BFGS algorithm and the use of a deeper network (5 hidden layers). Models 4 and 5 (TRAINCGP and TRAINCGB) yielded acceptable but slightly lower accuracies and higher loss values, despite fast training times. Overall, the results highlight TRAINRP as the most effective training function in terms of performance and computational efficiency. Once the learning algorithm was defined, a final experiment was conducted, maintaining the established parameters from Model 1, except for the number of neurons per hidden layer. This was further evaluated with 40, 50, 60, and 70 neurons to observe the performance and accuracy of the ANN model.

Table 9 presents the results of training the ANN model with 40, 50, 60, and 70 neurons in the hidden layers. The minimum cross-entropy error values were identified from the information collected, being 0.0342 and 0.024 for 40 and 50 neurons in the hidden layers, respectively, and total accuracy values of 92.7% and 95.4%. By analyzing the information presented in Table 9, it was determined that the optimal ANN for developing the predictive flow pattern model for two-phase (oil-water) flow in a horizontal pipe is the one that integrates the Resilient Backpropagation learning algorithm with three hidden layers, each with 50 neurons. The configuration of the selected model’s parameters is presented in Table 10.

With the selected ANN configuration, the model achieved a cross-entropy loss of 0.024, with a training accuracy of 97.1%, validation accuracy of 92.8%, and test accuracy of 90.3%. The overall classification accuracy, calculated from the complete confusion matrix across all data partitions, reached 95.4%, making this configuration the most effective among the 104 models evaluated. Figure 6 illustrates the evolution of cross-entropy loss throughout the training process for the training, validation, and testing stages. The best validation performance was observed at epoch 103, with a cross-entropy value of 0.03213. The training process was terminated at epoch 109 using early stopping criteria, which halts training when the validation error does not improve over six consecutive epochs (patience = 6). The final model thus corresponds to the point of minimum validation error, ensuring both high accuracy and generalization.

The model’s performance and accuracy data are complemented by an error histogram, presented in Figure 7, showing the error values obtained in each stage of the ANN’s development. The histogram exhibits a centered normal distribution, with a clear central and narrow tendency towards error values close to zero, indicating that the model is well-trained and highly accurate. The high frequency observed in the central column, where most data comes from the training, validation, and testing stages, suggests that the model generalizes well and does not overfit the training data.

Figure 8 illustrates the ROC (Receiver Operating Characteristic) curves corresponding to the (a) training, (b) validation, (c) testing, and (d) overall stages of the ANN model. These plots provide a visual assessment of the classifier’s ability to distinguish between the six flow pattern classes across different stages of model development.

In each subplot, the ROC curve compares the model’s true positive rate (TPR) against the false positive rate (FPR) across various classification thresholds. The area under each ROC curve (AUC) serves as a scalar metric for the model’s discriminative power, with values closer to 1 indicating near-perfect classification. The diagonal line in each plot represents the performance of a random classifier (AUC = 0.5), which serves as a baseline for comparison.

In the training stage (Figure 8a), the ROC curves demonstrate excellent separation between classes, with all curves approaching the top-left corner, reflecting high sensitivity and low false positive rates. This indicates that the model has learned the patterns in the training data effectively. A similar trend is observed during the validation stage (Figure 8b), suggesting that the model maintains generalization capability and avoids overfitting. The testing stage (Figure 8c) also shows strong ROC curves, further validating the model’s robustness and confirming that the classification performance remains stable on previously unseen data.

The overall ROC plot (Figure 8d), which aggregates performance across all stages, shows that the classifier consistently performs well across the six flow pattern categories. The concentration of the curves toward the upper-left corner signifies high true positive rates with minimal false classifications. These results reinforce the ANN model’s capacity to reliably differentiate among complex flow regimes under varying operating conditions.

Together, these ROC analyses underscore the high sensitivity and specificity of the selected ANN configuration. The network’s performance across all evaluation stages aligns with the confusion matrix results and statistical metrics, providing strong evidence of the model’s effectiveness for real-time multiphase flow pattern recognition in horizontal oil-water pipeline systems.

Figure 9 presents the confusion matrices obtained during the (a) training, (b) validation, (c) testing, and (d) overall evaluation phases for the selected ANN model. These matrices provide a detailed breakdown of the model’s prediction performance for each of the six flow pattern categories: stratified, stratified with mixture, oil-in-water dispersion, water-in-oil dispersion, annular, and slug.

In each matrix, the diagonal elements represent the TP—that is, the number of instances correctly classified as a specific flow pattern. Off-diagonal entries reflect misclassifications, further categorized as FP and FN. A false positive occurs when the model incorrectly predicts a sample as belonging to a given class, while a false negative arises when the model fails to recognize an instance of that class. The TN, although not explicitly visible in the matrix, can be inferred as all other correctly classified instances not associated with the current class under evaluation.

The confusion matrices show a high concentration of values along the diagonal, indicating that the majority of predictions across all evaluation stages were correct. In the training stage (Figure 9a), the model achieved an accuracy of 97.1%, confirming its strong capacity to learn from the dataset. During the validation phase (Figure 9b), accuracy slightly decreased to 92.8%, suggesting that the model generalizes well to unseen data while maintaining high predictive consistency. The testing stage (Figure 9c) resulted in an accuracy of 90.3%, demonstrating reliable performance even on completely new data. Finally, the overall confusion matrix (Figure 9d), which aggregates predictions from all stages, reports a high total classification accuracy of 95.4%, underscoring the robustness and generalization capability of the selected ANN configuration.

Beyond overall accuracy, the confusion matrices also reveal class-specific performance trends. Certain patterns such as Do/w and Dw/o exhibit nearly perfect classification with minimal off-diagonal values, suggesting that the model captures their distinguishing features with high fidelity. Meanwhile, flow patterns such as S and ST & MI, which are often characterized by overlapping or transitional behaviors, show slightly higher misclassification rates, pointing to the physical complexity and subtlety involved in accurately separating these regimes.

In Table 11, the respective precision, recall, and F1 values for each flow pattern are presented, along with the accuracy values for both the confusion matrix in the testing stage and the overall confusion matrix, calculated according to Equations 14–17. Accuracy refers to the proportion of all correctly classified samples across all classes, calculated as (sum of diagonal entries)/(total number of samples). Precision, recall, and F1-score are computed per class, and their values reflect the model’s behavior in distinguishing each individual flow pattern. The averages refer to the mean of these class-specific values. For example, for the testing stage, referencing the ST pattern, the true positives value is TP = 55, from the diagonal entry corresponding to the ST class in the test stage confusion matrix, see Figure 9c. By summing the other values on the main diagonal, the TN total is 195. Summing the other values in the ST row gives the FP as 6, and summing the other values in the ST column gives the FN as 8. Notice that for a multiclass confusion matrix, accuracy is computed as the sum of all correct predictions (250) over the total number of predictions (277). The values shown for precision, recall, and F1 are class-specific, but accuracy is aggregate.

Based on the information shown in Table 11, the following average values were determined for the different flow patterns within the testing stage of the model: an average precision of 89.8%, an average recall of 90.3%, an average F1 score of 89.9%, and an accuracy of 90.3%. From the overall confusion matrix, an average precision of 95.5%, an average recall of 95.8%, an average F1 score of 95.6%, and an accuracy of 95.4% were obtained.

To ensure the credibility of the proposed ANN model, the dataset was randomly partitioned into 70% for training, 15% for validation, and 15% for testing. The model’s performance was evaluated through multiple statistical metrics, including accuracy, precision, recall, F1-score, and cross-entropy error, across all three data partitions. Confusion matrices and ROC curves were used to provide a comprehensive visualization of the classifier’s behavior. Additionally, retraining was conducted for each configuration to verify repeatability and robustness, with consistent outcomes observed between runs.

The credibility of the model is reinforced by the use of a large and diverse dataset compiled from 11 independent experimental studies, representing a wide range of fluid properties, pipe diameters, and flow regimes. This diversity enhances the model’s generalization capabilities and supports its applicability across varied operating conditions.

A two-phase oil-water flow database in horizontal pipes was structured based on information reported in the literature by various authors, yielding 1,846 experimental data points. The dataset included parameters related to oil-water multiphase flows, such as the superficial velocities of the oil and water fluids, water volumetric fraction, pipe diameter, oil viscosity, and oil density. Six representative flow pattern categories were defined and standardized: stratified, stratified with mixture, slug, annular, oil-in-water dispersion, and water-in-oil dispersion.

An ANN model using feedforward backpropagation was developed in MATLAB^® and its Neural Network Pattern Recognition tool. Through an iterative and systematic experimental process, 339 training sessions were performed based on 104 different ANN topological configurations to select the optimal model. The final model consisted of an input layer with six neurons corresponding to each input variable, three hidden layers with 50 neurons each, and an output layer with six neurons. The resilient backpropagation training algorithm was employed, with sigmoid activation functions in the hidden layers and softmax in the output layer, using cross-entropy as the loss function.

The developed ANN model demonstrated outstanding performance, achieving a training accuracy of 97.1%, a validation accuracy of 92.8%, a testing accuracy of 90.3%, and an overall accuracy of 95.4%. These results suggest that the trained model is highly effective at predicting the six flow patterns. Notably, the training process required only 2 s, indicating high computational efficiency. The precision of the ANN model in recognizing flow patterns suggests opportunities to optimize pipeline design and maintenance processes by estimating critical process parameters, such as pressure gradients and volumetric fractions in the flow system.

Beyond its strong predictive performance, the proposed model demonstrates substantial potential for practical deployment in industrial settings. Its ability to classify flow patterns with high reliability and low latency makes it suitable for integration into real-time monitoring systems, such as SCADA platforms or embedded diagnostic tools for pipeline infrastructure. This opens opportunities for automated decision-making in flow assurance, chemical dosing optimization, corrosion control, and maintenance scheduling, all of which are critical for operational safety and efficiency in the oil and gas industry.

Additionally, because the model was trained on a diverse and comprehensive experimental database, it offers high scalability and adaptability across a broad range of pipeline geometries, fluid properties, and operating conditions. These features enable its use in varied field applications, including offshore platforms, onshore transport systems, and laboratory-scale experimental setups, without significant retraining or hardware constraints.

Nevertheless, several limitations should be acknowledged. First, the model was trained on laboratory-generated data, which may not fully capture the complexities encountered in field-scale operations, such as temperature fluctuations, scale deposition, or transient behaviors. Second, an imbalance in the number of data points per flow pattern category may lead to classification bias toward the majority classes. Third, as with most neural network architectures, the model functions as a “black box”, offering limited interpretability regarding the physical mechanisms underlying its predictions.

To address these limitations, future work will focus on external validation using new experimental data from controlled laboratory test rigs and real pipeline operations. The integration of explainable AI techniques and comparisons with alternative machine learning models will also be explored to enhance interpretability and benchmarking. Moreover, the construction of a more balanced and expanded database, particularly in underrepresented flow pattern classes, is recommended to enhance robustness and reduce bias in predictive performance.