The Effect of an Immobile Liquid Saturation on the Non-Darcy Flow Coefficient in Porous Media

Abstract

Summary The results of an experimental research program to investigate the effects of immobile liquid saturations on the non-Darcy flow coefficient are presented. Sandstone cores of absolute permeabilities ranging from 50 to 800 md were used to investigate non-Darcy flow phenomena under multiphase conditions. Immobile liquid saturations were varied from 8 to 30% PV. The multiphase experiments were conducted with N2 gas as the flowing phase and glycerin as the immobile liquid phase. It was found that the non-Darcy flow coefficient for the multiphase case may be estimated with a dry-core non-Darcy-flow-coefficient/permeability relationship developed for the rock in question and the effective gas permeability at a given saturation. For the immobile multiphase cases, the non-Darcy flow coefficient consistently increased with increased saturation. The experimental data obtained from this research were compared with the limited multiphase data in the literature. Where comparisons could be made, the data reported in this paper agreed favorably with the existing published data. An analysis of the experimental data revealed that a unique relationship existed between the non-Darcy flow coefficient and the effective gas permeability, porosity, liquid saturation, and effective overburden pressure at a given temperature. Correlations were developed from this analysis to predict the non-Darcy flow coefficient as a function of rock and fluid properties. Where possible, the correlations were used to predict the non-Darcy coefficient measured by other researchers and were compared with the dry-core correlations developed by Janicek and Katz and with a theoretical equation developed by Geertsma.