Dimensional Analysis of Pore Scale and Field Scale Immiscible Displacement

R. Hilfer, P.E. Øren

Transport in Porous Media 22, 53 (1996)

submitted on
Wednesday, July 27, 1994

A basic re-examination of the traditional dimensional analysis of microscopic and macroscopic multiphase flow equations in porous media is presented. We introduce a ‘macroscopic capillary number’ which differs from the usual microscopic capillary number in that it depends on length scale, type of porous medium and saturation history. The macroscopic capillary number is defined as the ratio between the macroscopic viscous pressure drop and the macroscopic capillary pressure. It can be related to the microscopic capillary number and the Leverett-J-function. Previous dimensional analyses contain a tacit assumption which amounts to setting the macroscopic capillary number equal to unity. This fact has impeded quantitative upscaling in the past. Our definition, however, allows for the first time a consistent comparison between macroscopic flow experiments on different length scales. Illustrative sample calculations are presented which show that the breakpoint in capillary desaturation curves for different porous media appears to occur at values around unity. The length scale related difference between the macroscopic capillary number for core floods and reservoir floods provides a possible explanation for the systematic difference between residual oil saturations measured in field floods as compared to laboratory experiment.

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