SINGULAR PERTURBATION SOLUTION OF THE PROBLEM VISCOUS FINGERING PHENOMENON IN MULTIFLUID IMMISCIBLE FLOW

Shailesh Patel

doi:10.29121/ijetmr.v5.i4.2018.208

Abstract

In this paper the phenomenon namely fingering which occurs in the flow problems of oil reservoir engineering has been discussed. The effects arises due to the fingering have been studied by using the Darcy’s law together with different kinds of suitable assumptions and conditions. The problem is then modeled into mathematical form which yields second order partial differential equation. The equation is then solved by using singular perturbation technique together with initial and boundary conditions. The solution is then interpreted in terms of fluid flow terms.

Highlights

It is well known that in oil reservoir field the phenomenon of fingering occurs which is caused due to the two immiscible flow in homogeneous porous media
When a fluid existing in the medium is displaced by another fluid of lesser viscosity, instead of regular displacement of the whole front, the fingers may occur which shoots through the porous medium at relatively great speed which is known as the phenomenon of fingering [1]
We considered here that a finite cylindrical piece of homogeneous porous medium of length L, fully saturated with an oil, which is displaced by injecting fluid water which give rise to fingers

Summary

Introduction

It is well known that in oil reservoir field the phenomenon of fingering occurs which is caused due to the two immiscible flow in homogeneous porous media. When a fluid existing in the medium is displaced by another fluid of lesser viscosity, instead of regular displacement of the whole front, the fingers may occur which shoots through the porous medium at relatively great speed which is known as the phenomenon of fingering [1]. These fingering depends in particular on the mobility ratio and more likely it is greater than 1. Sw (x,t) is the saturation of the water in porous medium represents the average cross-sectional area occupied by fingers [4], [5]

MATERIALS AND METHODS

Conclusions & Recommendations