The Measurement Of Directional Permeability And The Application In Thermal Recovery Projects
Authors: Guppy K.H. , Marsden S.S. , Morris M. 
Published: December 2007

Abstract
An instrument has been designed, constructed and tested for measuring three-dimensional, directional permeability. Gas at known pressures flows radially permeability. Gas at known pressures flows radially from the center of 3-inch diameter sandstone samples to the surface at atmospheric pressure. The volumetric flow rate over small areas of the surface is measured by a special probe connected to a soap film flowmeter. Permeability at each point can be calculated by a modified version of the well known equation for spherical flow of a compressible fluid.
Graphs of the reciprocal of the square root of the permeability on polar coordinates give the expected ellipse in some, but not all cases. The results have also been plotted as stereographic projections, which can then be used to estimate permeability in directions other than those for which it was measured.

Introduction
Although it is well known that measured values of permeability for naturally occurring porous media depend on the orientation of the fluid flow relative to the sample itself, very little has appeared in the literature on this important subject. One hears of cases where (or of rules-of-thumb for) vertical permeability being one-half or one-tenth or some other permeability being one-half or one-tenth or some other small fraction of the horizontal permeability, but these are not well documented. Johnson and Hughes (1), as well as Johnson and Breston (2), reported measurements made on small plugs cut in known directions from larger cores and found that horizontal permeabilities also varied with the orientation of the plugs. Using theory developed by Ferrondon (3), Scheidegger (4) showed that with Johnson and Hughes' data, a plot of the reciprocal of the square root of the permeability on polar coordinates produced ellipses.
Because directional permeability* of porous media will govern fluid flow in the various fluid displacement processes used for enhanced oil recovery, it appears processes used for enhanced oil recovery, it appears to be a fundamental rock-fluid property which should be measured and the results used in designing such processes. Where differences in fluid densities and processes. Where differences in fluid densities and hence gravity effects are significant, it should be particularly important. Steam injection, especially particularly important. Steam injection, especially in thick reservoir sands, is a major example of this.
The method of Johnson and Hughes for getting directional permeability requires the cutting of a number of core plugs and then carring out measurements on each one. It will give horizontal permeabilities in different directions as well as a permeabilities in different directions as well as a vertical permeability, but without more and larger field cores than are usually available, it is not possible to get permeabilities at say 30 or 45 or 60 to possible to get permeabilities at say 30 or 45 or 60 to the horizontal. Hence, there appeared to be a need for a new method of measuring permeability which would give this property in all possible directions. The design, development and testing of such a method is described in this paper.

DESIGN OF THE INSTRUMENT
If we want to get directional permeability measurements on a single sample of rock, it becomes apparent that the sample must have a spherical shape. While the approach of Dykstra and Parsons and Duprey et al. using a "kissing probe" might have been used, we felt it desirable instead to take advantage of the well known radial flow in a sperical porous medium. For a compressible fluid of porous medium. For a compressible fluid of viscosity mu, the permeability, k, of an isotropic porous medium can be determined from measurements of porous medium can be determined from measurements of the internal and external pressures, pw and pw, the radii of a central hole and of the sphere, rw and re, and the external volumetric flow rate, Qe.
(1)
*By directional permeability we mean the flow in some specified direction from a point or origin and not back-and forth flow along one axis.