Multifractal analysis of inclined oil-water countercurrent flow

Characterizing countercurrent flow structures in an inclined oil-water two-phase flow from one-dimensional measurement is of great importance for model building and sensor design. Firstly, we conducted oil-water two-phase flow experiments in an inclined pipe to measure the conductance signals of three typical water-dominated oil-water flow patterns in inclined flow, i.e., dispersion oil-in-water pseudo-slug flow (PS), dispersion oil-in-water countercurrent flow (CT), and transitional flow (TF). In pseudo-slug flow, countercurrent flow and transitional flow, oil is completely dispersed in water. Then we used magnitude and sign decomposition analysis and multifractal analysis to reveal levels of complexity in different flow patterns. We found that the PS and CT flow patterns both exhibited high complexity and obvious multifractal dynamic behavior, but the magnitude scaling exponent and singularity of the CT flow pattern were less than those of the PS flow pattern; and the TF flow pattern exhibited low complexity and almost monofractal behavior, and its magnitude scaling was close to random behavior. Meanwhile, at short time scales, all sign series of two-phase flow patterns exhibited very similar strong positive correlation; at high time scales, the scaling analysis of sign series showed different anti-correlated behavior. Furthermore, with an increase in oil flow rate, the flow structure became regular, which could be reflected by the decrease in the width of spectrum and the difference in dimensions. The results suggested that different oil-water flow patterns exhibited different nonlinear features, and the varying levels of complexity could well characterize the fluid dynamics underlying different oil-water flow patterns.