Multivariate multiscale entropy analysis of horizontal oil–water two-phase flow

• We use distributed conductance sensor to obtain experimental signals.
• We use multivariate multiscale entropy (MMSE) to uncover the dynamic flow behavior.
• Our analysis yields deep insights into the flow behavior of oil–water flows.
• Broader applicability of the MMSE method is demonstrated and articulated.

Characterizing flow behavior underlying horizontal oil–water flows from experimental measurements is a challenging problem in the fields of time series analysis and fluid mechanics. We systematically conduct a horizontal oil–water two-phase flow experiment and use our designed distributed conductance sensor to measure multivariate signals from five different flow patterns. Taking two coupled Lorenz systems as examples, we first demonstrate that the multivariate multiscale entropy (MMSE) enables to uncover the one-way/both-way coupling structure of dynamic systems. Then we use MMSE method to analyze the experimental measurements and extract the slopes and mean values from low scales of MMSE to quantitatively characterize the flow behavior. The results suggest that the MMSE enables to quantitatively distinguish different horizontal oil–water flow patterns and further allows deeply uncovering dynamic flow behavior in the transitions of different flow patterns.