Computer Simulations of Immiscible Displacement In a Porous Medium Containing a Region of Different Wettability
Authors: Kiriakidis Dennis G. , Mitsoulis Evan , Neale Graham E. 
Published: March 2010

Abstract
Two-fluid immiscible displacement flow through a zone of different wettability in a porous medium has been studied. A deterministic model based on a microscopic approach has been used to determine the flow pattern of the invading fluid, The porous medium is represented by a two-dimensional square network of interconnected channels. Computer simulations for three distinct wettability cases and for four different values of the capillary number show that the effects of heterogeneity of the wettability on the behaviour of the invading fluid are very strong when capillary forces are significant and even stronger when there is a wettability contrast from an oil-wet to water-wet zone in the porous medium.

Introduction
An understanding of how heterogeneities m wettability affect displacement flow in porous media is fundamental to the study of water/oil displacement processes in underground petroleum reservoirs. As noted by Morro(1), the reservoir wettability is not a simply defined property and the classification of reservoirs as being either oil-wet or water-wet constitutes a great oversimplification (measurements show that reservoir wettability can cover a broad spectrum of wetting conditions that range from water-wet to oil-wet). As further noted by Morrow(1), there has been a notable revival during the last decade ill the mathematical analysis of pore networks for modelling displacement processes in porous media, and the choice of the assumptions and rules to account for wettability effects in network models is a problem that has only recently begun to receive the attention that it deserves.
The present study investigates two-fluid displacement flow through a porous medium containing a zone of different wettability. The porous medium is represented by a two-dimensional square network of interconnected channels. The wettability is characterized by cos θ where θ is the contact angle between the solid surface and the fluid interface measured through the displaced phase. Thus, for cos θ = 1, we have drainage displacement of a strongly wetting fluid (W) by a non-wetting fluid (NW). For cos θ = -1, we have imbibition displacement of a non-wetting fluid by a strongly wetting fluid. Finally, for cos θ = 0. we have neutralwettability.
In the present work three cases are examined (Figure 1), namely (a) drainage displacement in a macroscopically homogeneous porous medium, (b) drainage displacement in the presence of a central zone of neutral wettability, and (c) drainage displacement in the presence of a central zone where imbibition takes place (cos θ = -1). Computer simulations have been performed in order to examine these three cases in terms of the interplay between viscous and capillary forces as expressed by the capillary number. NCi = V μi/ γcos θ, defined at injection conditions where V is the injection velocity of the invading fluid, i the viscosity of the invading fluid and γ the interfacial tension. The viscosity ratio, M = μi/ μd, is defined as the ratio of the viscosity of the invading fluid, μi, to that of the displaced fluid, μd.
The viscosity ratio is maintained constant at M = 0.1 for the entire series of simulations undertaken in the present work.