Capacitive Phase Shift Detection for Measuring Water Holdup in Horizontal Oil–Water Two-Phase Flow

In this paper, a phase shift detection system of flow impedance is designed based on a concave capacitance sensor (CCS). The flow impedance of oil–water stratified flow is investigated by establishing an equivalent circuit model and a finite element model. The influence of exciting frequency and sensor geometric parameters on the phase shift output of the CCS is studied to access an optimal phase shift measurement system. An experiment of horizontal oil–water two-phase flows was conducted during which four flow patterns are observed, i.e., stratified flow (ST), stratified wavy flow (SW), dual continuous flow (DC), and dispersed oil-in-water and water flow (DO/W&W). The phase shift responses of the CCS to the water holdup variation are collected. The results indicate that the phase shift response of the CCS presents satisfied sensitivity for ST and SW flow patterns, which is consistent with the predictions of the equivalent circuit model and the finite element model. Although the flow structures of DC and DO/W&W flows are extremely nonuniform, the phase shift response of the CCS still shows better linearity and sensitivity to the water holdup variation. In general, the capacitive phase shift detection technology exhibits advantages for water holdup measurement in horizontal oil–water two-phase flow with nonuniform phase distributions and conductive water