DIMENSIONAL ANALYSIS OF PORE SCALE AND FIELD-SCALE IMMISCIBLE DISPLACEMENT

A basic re-examination of the traditional dimensional analysis of micr oscopic and macroscopic multiphase flow equations in porous media is p resented. We introduce a 'macroscopic capillary number' <(Ca)over bar> which differs from the usual microscopic capillary number Ca in that it depends on length scale, type of porous medium and saturation histo ry. The macroscopic capillary number <(Ca)over bar> is defined as the ratio between the macroscopic viscous pressure drop and the macroscopi c capillary pressure. <(Ca)over bar> can be related to the microscopic capillary number Ca and the Leverett J-function. Previous dimensional analyses contain a tacit assumption which amounts to setting <(Ca)ove r bar> = 1. This fact has impeded quantitative upscaling in the past. Our definition for <(Ca)over bar>, however, allows for the first time a consistent comparison between macroscopic flow experiments on differ ent length scales. Illustrative sample calculations are presented whic h show that the breakpoint in capillary desaturation curves for differ ent porous media appears to occur at <(Ca)over bar> approximate to 1. The length scale related difference between the macroscopic capillary number <(Ca)over bar> for core floods and reservoir floods provides a possible explanation for the systematic difference between residual oi l saturations measured in field floods as compared to laboratory exper iment.