Nonlinear multi-scale dynamic stability of oil–gas–water three-phase flow in vertical upward pipe

• We design a rotating electric field conductance sensor to measure three-phase flow.
• We use recurrence plot and AOK TFR to recognize three-phase flow patterns.
• We propose a MS-WCECP to study the stability and nonlinearity of three-phase flow.
• Our analysis yields novel insights into fluid dynamics from the disequilibrium view.

Characterizing stability and nonlinearity underlying oil–water–gas three-phase flow is a challenging problem of significant importance. We carry out experiments and measure the fluctuation signals from a rotating electric field conductance sensor with eight electrodes. We use recurrence plot and adaptive optimal kernel time–frequency representation to recognize different oil–water–gas three-phase flow patterns from experimental measurements. Then we employ multi-scale weighted complexity entropy causality plane (MS-WCECP) to explore the nonlinear characteristics for five typical oil–water–gas three-phase flow structures. The results suggest that our method enables to indicate flow pattern transitions. In particular, with the increase of scales, more information will be lost. Slug flow ends up in chaotic region, representing high complexity; Churn flow falls down from the chaotic to the random noise area, indicating the decreasing stability; while the drop degree of bubble flow is the biggest, suggesting that bubble flow has the most randomness. These findings demonstrate that multi-scale weighted complexity entropy causality plane can effectively depict the transitions of three-phase flow structures and serve as a useful tool for probing the nonlinear dynamics of the three-phase flows.