Analytical Approximate Expression for Cocurrent Imbibition during Immiscible Two-Phase Flow through Porous Media

Saroj R Yadav,Manoj N Mehta

doi:10.1155/2014/638409

Abstract

Cocurrent and countercurrent imbibitions are the crucial mechanism in many multiphase flow processes. In cocurrent imbibition wetting phase displaces nonwetting phase such that the nonwetting phase moves in the same direction to the wetting phase, whereas in countercurrent imbibitions wetting and non-wetting phase flow in opposite directions. However for cocurrent imbibitions, mathematical models need total flux condition as both phases flow in the same direction. Thus cocurrent imbibitions have been considered neglecting pressure gradient of nonwetting phase and only pressure gradient of displacing phase is considered which gives additional velocity to the displacing phase. An approximate analytical solution is derived by the method of small parameter; an approximate expression for the wetting phase saturation has been obtained. From analytical expression graphical presentation of saturation of wetting phase shows that cocurrent imbibition is faster than countercurrent imbibition. Also, the small parameter is chosen from initial wetting phase saturation and wetting phase saturation at imbibition phase, thus giving comparative behavior of imbibition at initial and later stage. It is shown that cocurrent imbibition proceeds faster with more amount of wetting phase present in porous matrix.

Highlights

Imbibition is one of the most important mechanisms, if wetting phase enters in porous matrix and displaces nonwetting phase (like air, oil, and nonaqueous phase liquids (NAPL))
Imbibition is defined as the displacement of nonwetting phase by wetting phase, where driving force is capillary pressure
Imbibition in water-wet porous media is commonly considered to be counter current, but studies have shown that when a porous matrix block is partially covered by wetting fluid, flow is dominated by cocurrent imbibition, not countercurrent [1]

Summary

Introduction

Imbibition is one of the most important mechanisms, if wetting phase (like water and brine) enters in porous matrix and displaces nonwetting phase (like air, oil, and nonaqueous phase liquids (NAPL)). Imbibition in water-wet porous media is commonly considered to be counter current, but studies have shown that when a porous matrix block is partially covered by wetting fluid, flow is dominated by cocurrent imbibition, not countercurrent [1]. Such situation may arise during water flowing in unsaturated soil or oil recovery from fractured porous matrix. In the present study cocurrent imbibition is formulated neglecting the nonwetting phase pressure gradient and considering that capillary pressure gradient and wetting fluid pressure gradient are equal [1, 3]). Governing differential equation is formulated and solved by method of small parameter; an approximate expression for saturation of wetting phase Sw(x, t) has been obtained

Governing Flow Equation for Imbibition

Solution of the Problem

Discussion and Conclusions