Two Phase Annular Flow Approximation Using 1-D Flow Equations Coupled With a Drift Flux Model for Concurrent Flow in Vertical or Near Vertical Channels

Abstract

Annular flow is a flow regime of two-phase gas-liquid flow dominated by high gas flowrate moving through the center of the pipe (gas core). In this paper we have developed and studied an innovative phenomenological model which combines the Zuber & Findlay’s Drift Flux Model’s weighted mean value approach [1] with the 1-D flow approximation equations. The flow is described in terms of a distribution parameter and an averaged local velocity difference between the phases across the pipe cross-section. The average void fraction is calculated as a function of the ratio of weighted mean gas velocity to the weighted mean liquid velocity (Slip ratio) and the drift flux velocity. The void fraction thus estimated is then applied to the 1-D continuity, momentum and energy equations. The equations are solved simultaneously to obtain the pressure gradient. Lastly, we obtain the liquid film thickness using the triangular hydrodynamic relationship between the liquid flow rate, pressure gradient and the liquid film thickness. The thickness of layer obtained, is then used to verify the original estimate of the void fraction. An iterative procedure is used to match the original estimate to the final value. The results from this study were validated against PipeSIM© software and two field measurements conducted on a wet-gas field in Brazil. As opposed to conventional drift flux models which are based on four simultaneous equations, this model relies on three, thereby significantly reducing the computational resources necessary and is more accurate as we account for variable velocities and void fractions across the pipe cross-section.