A new kinematic wave model for interpreting cross correlation velocitymeasurements in vertically upward, bubbly oil-in-water flows

Abstract

A new model for the speed of propagation of kinematic waves invertical upward, bubbly oil-in-water flows has been proposed. The newkinematic wave model has been used in conjunction with (i) appropriate valuesfor the `distribution parameter' C0, the single-droplet terminal risevelocity vt0 and an exponent n, obtained from a drift velocity model;(ii) a statistical relationship for the quantity αUh(dC0/dα); and (iii) measurements of a cross correlation velocityUcc and the volume fraction of oil α to make predictions of thesuperficial velocities of the mixture, the oil and the water in verticalupward, bubbly oil-in-water flows. The systematic errors in these predictedvalues of the superficial velocities of the mixture, the oil and the waterwere 0.16, -0.04 and 0.04%, respectively. The kinematic wave model can thusbe used in conjunction with a cross correlation flow meter for accuratemeasurement of flow rates in vertical oil wells. It was inferred from thekinematic wave model and the experimental data that, for low values of thevolume fraction of oil α, the distribution parameter C0 decreasesrapidly with increasing α. At higher values of α the decrease inthe value of C0 with increasing α is less marked. This result isconsistent with the physical explanation that, at low values of α, theoil droplets tend to preferentially accumulate in the relatively fast movingregions of the flow. As α increases the oil droplets become moreuniformly distributed amongst the faster and slower moving regions of theflow.