A scaling exponent for indicating the non-homogenous distribution of oil droplet in vertical oil–water two-phase flows

• We measure the flow structure of vertical upward oil–water two-phase flow with low velocity.
• We provide a novel multi-scale morphological analysis approach based on first-order difference scatter plot.
• The extracted scaling exponents can effectively characterize the non-homogeneous distribution of oil droplets in dispersion phase.
• The approach can roundly describe the coalescence and breakup process of dispersed droplets in oil–water two-phase flow

The multi-scale analysis is one of the most effective tools in detecting nonlinear system. In this study, we provide a novel multi-scale morphological analysis aiming at nonlinear time series. We firstly investigate typical chaotic and fractal systems by extracting a scaling exponent from the multi-scale second-order moment in the first-order difference scatter plot, it is proved that the proposed method has a good anti-noise and signal resolution ability. In this regard, we apply it to analyze the conductance sensor signals measured from vertical oil slug flow, oil dispersed flow and very fine oil dispersed flow. We find that the invariant of scaling exponent is sensitive to the change of oil droplet size, and the trend of scaling exponent with flow conditions is helpful to understand the process of coalescence and breakup of the dispersed droplets. The research results show that the multi-scale nonlinear analysis is a useful diagnostic tool for indicating the non-homogenous distribution of the dispersed droplets in oil–water two-phase flows.