Two-phase bubbly-droplet flow through a contraction: Experiments and a unified model

Abstract

We have derived a consistent and general set of equations to describe the motion of two phases (or components) in flow through a contraction. One phase is continuous, the other dispersed and the range of density ratios ρ is wide. Given the density and flowrate of each component of the flow, the pressure, velocities and void fractions can be computed at any location along the pipe. The single-phase limit as well as the homogeneous-flow limit are both contained within our set of equations. The full mathematical model, based on the so-called interstitial velocity, requires only one fluid-dependent empirical input—the terminal rise (or fall) velocity U t of a single bubble (or droplet). In the text, the word “bubbles” is to be thought of as the dispersed or discontinuous component of the flow and may refer to air bubbles in water flow, oil drops in oil or water flow or water drops in air or oil flow. Extensive comparisons between results from the model and experimental data obtained in the Schlumberger Cambridge Research multiphase flow loop are presented and show very good agreement in predicting pressure from input flowrates. Our results demonstrate that, although the model is one-dimensional and neglects local bubble-bubble interactions, it is nevertheless robust in dealing with vertical flow and a wide range of density ratios with only one parameter ( U t ) necessary for calibration. For two density ratios ρ of 1000 and 1.26, the agreement between the mathematical predictions and the experiments was good in vertical flow. The implication of this conclusion is that the model should perform well at any intermediate values of the density ratio.