Complexity of Horizontal Oil–Gas–Water Flows in Deepwater Simulation Well: Insights from Multiscale Phase Permutation Entropy Analysis

Deepwater oil–gas–water three-phase flow is widely regarded as a multiphase system. Intense interfacial interactions cause significant nonuniform fluid distributions in the wellbore, giving rise to complex nonlinear dynamics. In this study, a distributed conductance sensor (DCS) was developed to capture local flow information from a horizontal oil–gas–water simulation well. To quantify the complexity of nonlinear time series, phase permutation entropy (PPE) was first validated using artificial data, including the Tent map, Hénon map, and Lorenz system. PPE demonstrates superior capability in detecting abnormal dynamical changes compared with permutation entropy (PE). Subsequently, PPE is combined with the multiscale approach, i.e., multiscale phase permutation entropy (MPPE), to analyze the DCS signals and uncover the complexity of horizontal oil–gas–water flows. The results show that the MPPE analysis can reveal the spatial distribution characteristics of elongated gas bubbles, gas paths, dispersed bubbles and oil droplets.