Pipeline Two-Phase Flow Pressure Drop Algorithm for Multiple Inclinations

Abstract

A Generalized Additive Model (GAM) is proposed to predict the pressure drop in a gas–liquid two-phase flow at horizontal, vertical, and inclined pipes based on 21 different dimensionless numbers. It is fitted from 4605 points, considering a fluid pattern classification as Annular, Bubbly, Intermittent, and Segregated. The GAM non-parametric method reached high prediction capacity and allowed a great degree of interpretability (i.e., it helped to visualize and test statistical inference), considering that each predictor’s marginal effects could be described, unlike in other Machine Learning (ML) methods. The prediction capacity of the GAM model for the pressure gradient obtained an adjusted R2 and a mean relative error of 99.1% and 12.93%, respectively. This capacity is maintained even when ignoring Bubbly flow in the training sample. A regularization technique to filter some variables was used, but most of the predictors must maintain the model’s high predictive ability. For example, dimensionless numbers such as the Reynolds, Froude, and Weber numbers show p-values of less than 0.01% to explain the pressure gradient in the different flow patterns. The model performs adequately on 500 randomly sampled data points not used to fit the model with an error lower than 15%. The variable importance for the model and the relationship with the pressure gradient is evaluated based on the obtained splines and p-values.