Prediction of pressure gradient for oil-water flow: A comprehensive analysis on the performance of machine learning algorithms

Abstract

Pressure gradient (PG) in liquid-liquid flow is one of the key components to design an energy-efficient transportation system for wellbores. This study aims to develop five robust machine learning (ML) algorithms and their fusions for a wide range of flow patterns (FP) regimes. The MLs include Support Vector Machine (SVM), Gaussian Process (GP), Random Forest (RF), Artificial Neural Network (ANN), k-Nearest Neighbor (kNN), and fusions of these five MLs. A total of eleven hundred experimental data points for nine FPs (two stratified and seven dispersed patterns) in horizontal wellbores are used to develop the MLs. The MLs' performance is evaluated using the metrics including mean absolute percentage error (MAPE), median absolute percentage error (MdAPE), coefficient of variation of root mean squared error (CV-RMSE), and adjusted coefficient of determination. The evaluation metrics are cross-validated using a repeated train-test split strategy. Seven important predictor variables are identified using a supervised feature selection approach: oil and water velocities, FP, input diameter, oil and water density, and oil viscosity. The results show that the high PG prediction accuracy can be achieved using GP compared to other MLs except for the ML-fusions (p < 0.05). A Friedman's test and Wilcoxon Sign-Rank post hoc analysis with Bonferroni correction show that PG prediction errors using GP are significantly lower than using the ANN model (p < 0.05). The values are 18.44 % and 23.9 % for CV-RMSE, 11.6 % and 10.06 % for MAPE, and 7.5 % and 6.75 % for MdAPE, using ANN and GP, respectively. While the previous studies mostly used ANN to demonstrate the capability of MLs to predict PG over the mechanistic or correlation-based models, the present research has shown that GP is even better than ANN using a wide range of FPs and a large data set. • Machine-learning algorithms are developed to predict the pressure gradient. • The Gaussian Process model produces significantly lower prediction error. • The median absolute percentage error using Gaussian Process is 6.75 %. • More than 95 % variation of pressure gradient can be explained using seven variables.