The Effects of Capillary Pressure on Displacements in Stratified Porous Media

The purpose of this study is to obtain a better understanding of capillary pressure effects on fluid dis-placement in stratified porous media. We do this by pre-senting and validating dimensionless scaling parameters which will assist in the evaluation of these effects. The interpretation of flow perpendicular to strati-fied layers is important because it is one of the greatest causes of mixing, thus, determining the longitudinal satura-tion profile. In stratified layers with large permeability contrast, the transverse flow (crossflow) due to capillary imbibition retards the fronts in higher permeability layers and advances the fronts in lower permeability layers. Conse-quently greater oil recovery results when compared to a no-crossflow case. In this study, emphasis was placed on the analysis of transverse capillary crossflow effects. First, a semi-implicit two-phase, two-dimensional, incompressible fluid simulation model is developed by a finite difference method. A three-point weighting scheme is incorporated to reduce numerical dispersion (truncation error) in a routine of inter-block transmissibility evaluation. Next five dimensionless parameters are introduced to correlate the porous medium's heterogeneity with mixing caused by capillary crossflow. Those are the dimensionless time (t0), the transverse capillary number (NCT), the longi-tudinal capillary number (NCL) , the heterogeneity function (R¢K) and the Leverett j-function. Finally the dimensional analysis is verified through computer simulation of two-layered porous media models, and several dimensionless correlation graphs are drawn. The study provides a basis for analyzing displace-ment behavior in stratified media and also suggests the same analysis can be extended to more complicated media.