An Algorithm for Determining Volume Fractions in Two-Phase Liquid Flows by Measuring Sound Speed

Abstract

This paper presents a method of determining the volume fractions of two liquid components in a two-phase flow by measuring the speed of sound through the composite fluid and the instantaneous temperature. Two separate algorithms are developed, based on earlier modeling work by Urick (Urick, 1947, “A Sound Velocity Method for Determining the Compressibility of Finely Divided Substances,” J. Appl. Phys., 18 (11), pp. 983–987) and Kuster and Toksöz (Kuster and Toksöz, 1974, “Velocity and Attenuation of Seismic Waves in Two-Phase Media: Part 1. Theoretical Formulations,” Geophysics, 39 (5), pp. 587–606). The main difference between these two models is the representation of the composite density as a function of the individual densities; the former uses a linear rule-of-mixtures approach, while the latter uses a nonlinear fractional formulation. Both approaches lead to a quadratic equation, the root of which yields the volume fraction (φ) of one component, subject to the condition 0≤φ≤1. We present results of a study with mixtures of crude oil and process water, and a comparison of our results with a Coriolis meter. The liquid densities and sound speeds are calibrated at various temperatures for each fluid component, and the coefficients are used in the final algorithm. Numerical studies of sensitivity of the calculated volume fraction to temperature changes are also presented.