Modeling of Emulsion Flow In Porous Media
Authors: Abou-Kassem J.H. , Ali S.M. Farouq 
Published: March 2010

Abstract
A mathematical description of non-Newtonian fluids, in particular, emulsions, is of special importance now that most of the enhanced oil recovery methods are being modelled in increasing detail. Only recently a few characteristics of emulsion flow have been incorporated in some of the simulators. Nearly all enhanced oil recovery processes involve emulsion formation and flow in some form or other. Representation of such flow in mathematical models is still inadequate.
This paper investigates the rheology of emulsions, their formation in porous media, and subsequent flow, from a mathematical standpoint A critical evaluation of several models describing the flow of pseudoplastic fluids in porous media is presented. The models are expressed in a unified form that makes it possible to detect differences between the various models. The assumptions underlying the various models are discussed in detail. Furthermore, the paper gives a summary of the rheology and in situ formation of emulsions, the role of a variety of other factors responsible for emulsification in porous media, and it introduces a flow model for both Newtonian and non-Newtonian emulsions that is practical, and especially suitable for use in numerical simulation of EOR processes.

Introduction
Two-thirds or the world's crude oil and three-quarters of the U.S. crude oil is produced in an emulsion form(1,3). Emulsified oil is produced from oil/tar sands undergoing thermal recovery. New methods of secondary recovery that use high viscosity emulsions have been developed(2.4). Filtration of water using porous material also involves dilute concentrations of dispersed oil in water(4,5). These factors and others(6,7) have promoted interest in research related to the now behaviour of non-Newtonian fluids in porous media fur a quarter of a century.
The fact that nearly all enhanced oil recovery methods involve emulsion formation and flow coupled with the wide-spread acceptance of reservoir simulation as a valuable tool in the development and optimization of oil recovery from petroleum reservoirs, have contributed to incorporating a few characteristics of emulsion flow in a number of simulators. Mathematical modelling of emulsion flow in porous media calls for the understanding of the rheology of emulsions and the formation of emulsion in oil reservoirs. Emulsion flow in porous media can be modelled through non-Newtonian rheology. as discussed in this paper. A more comprehensive approach would require phase behaviour of the emulsion system and drop size distribution to account for mobility changes in response to drop entrapment.

Nature and Rheology of Emulsions
An emulsion is a dispersion of one liquid (internal or dispensed phase) with another (external or continuous phase) in the presence of surface -active agents (emulsifiers) (8). The volume fraction of the dispersed phase is called emulsion quality, θ. The emulsion consists of an oil-soluble portion and water-soluble portion. By virtue of its special structure the emulsifier aids in reducing the interfacial tension between the two liquids involved enabling an easier formation of an extended interface and in preventing the coalescence of the dispersed particles once emulsion is formed.
There are two types of emulsion water-in-oil (W/O) and oil-in-water (O/W) emulsions.