A hybrid model to predict the pressure gradient for the liquid-liquid flow in both horizontal and inclined pipes for unknown flow patterns

Accurate prediction of the pressure gradient (PG) for the oil-water flow requires identification of the flow pattern (FP), which is usually achieved by using either an expensive measurement system or time-consuming manual observations. This study proposes a hybrid scheme where two machine-learning (ML) models are coupled in a series to predict the PG value without any conclusive FP information. The first model (M1) determines the oil-water FP, whereas the second model (M2) predicts the oil-water PG. 1637 experimental data points for the oil-water flow in both horizontal and inclined pipes are used to develop the models. The important feature subset is identified using the modified Binary Grey Wolf Optimization Particle Swarm Optimization (BGWOPSO) algorithm. The MLs' performance is evaluated using metrics including accuracy, sensitivity, specificity, and F1-score for the M1, and coefficient of variation of root mean squared error, mean absolute percentage error (MAPE), and median absolute percentage error for the M2. The evaluation metrics are cross-validated using a repeated train-test split strategy. The results showed that the overall FP classification accuracy is greater than 91%, with 90.61% sensitivity and 98.53% specificity using the weighted majority voting for M1. With the Gaussian Process regression for M2, the evaluation metrics for the PG prediction were found to be 10.65%, 86.26 Pa/m, and 0.96 for MAPE, root mean square error, and adjusted coefficient of determination, respectively. Statistical analysis showed that the selected features for liquids' and pipe's properties using the BGWOPSO algorithm were adequate to attain superior performance for both models. The achieved MAPE using the proposed hybrid model is superior to existing mechanistic or correlation-based models reported in the literature (between 26 and 69%). The proposed hybrid scheme can significantly reduce the costs associated with identifying the oil-water flow profile and be critical in designing energy-efficient transportation of liquid-liquid flow.