Experimental and Numerical Simulation of Two-Phase Flow with Interphase Mass Transfer in One and Two Dimensions
Authors: Culham W.E. , Ali S.M. Farouq , Stahl C.D. 
Published: December 2007

Abstract
One- and two-dimensional mathematical models have been developed that simulate transient, two-phase flow of hydrocarbon mixtures in porous media in a manner that accounts for interphase mass transfer. Numerical simulations of one-dimensional depletion-drive experiments using a two-component hydrocarbon fluid were used to establish the validity of the mathematical models. In addition, the experimental and numerical data were used to demonstrate that production rate had a relatively insignificant effect on the recovery of individual hydrocarbon components from the experimental system, and that attainment of equilibrium between phases is possible for a wide range of liquid and vapor velocities in reservoirs containing light hydrocarbon fluids. Results of some two-dimensional numerical simulations are also presented.

Introduction
This study was undertaken to develop a mathematical model that would simulate transient, two-phase flow of hydrocarbon mixtures in porous media under conditions that result in interphase mass transfer and to test the validity of the assumptions used to set up the model. In addition, the study was designed to determine if production rate influences the recovery of individual hydrocarbon components from reservoirs producing by depletion drive.
Two-phase flow in porous media, with interchange of components between the two phases, is important in many petroleum recovery processes. Studies conducted within the last 3 years have outlined methods of solving multiphase flow problems incorporating mass transfer. Some of these studies have also indicated the importance of accounting for mass transfer under various producing conditions. An earlier works first demonstrated the importance of combining relative permeability data with equilibrium ratios in compositional balance methods.
The mathematical model presented in this paper is formulated so that a phase behavior package, as described in previous papers, is not required as an integral part of the routine employed to solve for the primary dependent variables. The finite difference formulation is designed so that all these variables can be solved for simultaneously. This is accomplished by utilizing one basic set of equations. These innovations, which are in contrast to other models but are similar in some respects to the approach used by Taylor, render the total problem computationally simpler than any of the previously referenced formulations.
The mathematical model was developed by combining Darcy's law with a continuity equation for each hydrocarbon component. The principal assumptions invoked in the formulation were that capillary forces and diffusional effects are negligible, and that thermodynamic equilibrium exists in the reservoir at all times. No assumption as to the type of vaporization process was made in formulating this model.
Experimental data were required to complete this study. These were generated by conducting several depletion drive experiments. The experimental apparatus consisted of a sandstone core enclosed in a pressurized casing. The apparatus was designed in such a manner that the core could be charged with a liquid hydrocarbon mixture and depleted at different production rates.
The experimental tests were designed to determine the effect of production rate on component recovery.