Insight into flow pattern evolution of vertical oil–water flows with large-diameter pipe

A profound revelation about the nonlinearity of the oil–water flow structure evolution is crucial for the prediction of well production profile parameters. In this paper, we propose a nonlinear analysis method which is refined composite multivariate multiscale fractional weighted permutation entropy (RCmvMFWPE) to analyze the flow pattern evolution of vertical oil–water flows with large-diameter pipe. We begin by describing the algorithm's calculating procedure, and the RCmvMFWPE is employed to analyze the multivariate time series of vertical multielectrode array conductance sensor which contains the local and global flow pattern information of oil–water flows in a vertical upward 125 mm inner-diameter pipe. The results demonstrate that the entropy of each flow pattern behaves with different characteristics. It indicates that the RCmvMFWPE is sensitive to the evolution of flow pattern, thus allowing the detection of the instability of flow pattern transition.