A novel approach for measuring plane anisotropic permeability through steady-state flow between two concentric cylinders

Abstract

Abstract Anisotropy is a common feature for most of fibrous and porous media. This article reports a new method for measuring the 2D anisotropic permeability of a porous rock utilizing the measurements obtained from the steady-state flow between two concentric cylinders. The mathematical analysis of the experimental data is based on the general solution of the pressure equation derived for the steady-state flow equation for an anisotropic porous medium between two concentric cylinders. The general solution, incorporating the degree of anisotropy and the ratio between inner and outer cylinder radii, is presented in a dimensionless form. The solution shows that pressure distribution between the two cylinders is composed of an isotropic part plus a series representing the contribution of the anisotropy. The solution is validated through the comparison against numerically derived results and the analytical solution of two extreme cases; when the clearance between the two cylinders vanishes, and when the material is isotropic. The validation shows a perfect performance of the proposed solution even in the vicinity of the inner cylinder not like the approximate solutions existing in the literature. The validation also shows that the truncation of the series part has an impact on the results specially in the case of extreme anisotropy. Two experimental procedures 1) basic approach and 2) modified approach, utilizing the “pear” and “tent” charts derived from the general solution, demonstrate how to obtain the principle permeabilities and their directions. The applicability of the proposed experimental techniques is attained through the application of the modified approach over real experimental data from a holed core experiment to estimate anisotropic permeability parameters. The application of the proposed technique and the required modifications for measuring the anisotropy in tight cores are discussed. Also, the relation between the three-dimension anisotropy and the presented plane anisotropy is presented.