Numerical Simulation of Emulsion Flow Through Porous Media
Authors: Islam M.R. , Ali S.M. Farouq 
Published: March 2010

Abstract
Flow of emulsion in porous media is of great interest to the oil industry because emulsions play an important role in various enhanced oil recovery processes. Even though many laboratory studies have been conducted to understand the rheology of emulsions and mechanisms of emulsion flow through porous media, relatively few efforts have been made towards the mathematical simulation of emulsion rheology and propagation in a porous medium. Only a few researchers have attempted to simulate emulsion flow through porous media, and most of them have considered the case for which emulsion is the only phase present in the system. Besides, mechanisms involved in selectively blocking high-permeability channels have not been incorporated. Also, phenomena of emulsion breaking and formation have been poorly defined by existing flow models.
The formulation developed in the present work explains the blocking mechanism of emulsion, incorporates emulsion breaking and formation, and relates emulsion stability and permeability reduction to emulsion throughput and absolute permeability. The mathematical model is tested against experimental results available in the literature, showing excellent agreement.

Introduction
Emulsion flow in porous media is of interest in almost all enhanced oil recovery (EOR) processes, Emulsions have been used as selectively plugging agents to improve oil recovery in waterflooding as well as chemical and steam-flooding operations. Also, it is believed that emulsion flow occurs by accident in thermal processes (such as in-situ combustion, steam flooding, etc.), chemical flooding, waterflooding or even in primary depletion(1). Natural porous media often provide enough shear to generate emulsions in-situ.
McAuliffe(2,3) is one of the first researchers to report the use of oil-in-water emulsions in improving oil recovery during water floods. Broz et al.(4) reported laboratory results in the development of emulsion blocking technique for the correction and control of stem override and channeling.
While emulsions have been well accepted as effective blocking Agents, very little has been reported on mathematical modeling of emulsion flow through porous media in 1979, Alvarado and Marsden(5) introduced their bulk viscosity model in which an emulsion was considered to be a continuous, single-phase fluid. No permeability reduction was introduced and emulsion flow was different from that described by Darcy's law only when the bulk emulsion viscosity was shear-rate dependent. The so-called ‘droplet retardation model’ was introduced by McAuliffe(2) and was used by Devereux(6) who modified the Buckley-Leverett theory for two-phase flow by including a retardation factor in the pressure driving force of the dispersed oil phase. This model implies that the permeability of the porous medium decreases as emulsion is injected, until steady state is reached. The model also implies that the permeability reduction increases with decreasing flow rate and increasing drop-size to pore-size ratio. One of the problems of this model is that the permeability of the porous media rises back to the initial value when emulsion is followed by water. Soo and Radke(7) presented another mechanism for reducing permeability by emulsion. They argued that, when emulsions are injected into a porous medium, droplets not only block pores of throat sizes smaller than their own but they are captured on pore walls and in crevices forming an ensemble of smaller droplets.