The Effects of Capillary Pressure on Immiscible Displacements in Stratified Porous Media

Abstract

ABSTRACT Reservoir mixing that occurs during a fluid displacement in a heterogeneous permeable medium could be an important factor in many secondary oil recovery processes. In a stratified medium, mixing may occur longitudinally or in the transverse direction from adjacent layers. One of the greatest causes of mixing in immiscible displacements, capillary imbibition, is described in this paper. To aid in interpretation and scaling of capillary imbibition effects, three dimensionless numbers and two dimensionless functions are introduced. These are a dimensionless time, a transverse capillary number, a longitudinal capillary number, a heterogeneity function and the Leverett j-function. Through computer simulation these quantities were verified to be accurate measures of capillary mixing in a stratified medium. A pseudo-function approach is also presented by which the vertical mixing phenomenon in a stratified medium may be described in a lower dimension simulation. Although a stratified model is the simplest form of reservoir heterogeneity, the approach used and results obtained in this study should provide a basis for analyzing fluid displacement in more complicated reservoirs.