A New Method To Measure Directional Permeability

Abstract

Introduction and Theory The problem of measuring directional permeability by applying Darcy's law has been known for a long time, but so far it has been left unresolved. Here we show that for two-dimensional cases of anisotropy, three measurements must be made on a laboratory sample to calculate the maximum and minimum permeability from the data. These are (1) Angle B, which shows the direction of flow with respect to the direction of maximum permeability, (2) Angle A, which shows the direction of permeability, (2) Angle A, which shows the direction of flow with respect to the direction of the driving force gradient, and (3) the R11 element of the resistivity tensor that appears when Darcy's law is given the special form Rij qu=-grad p................... (1) Here Rij is the second-rank (symmetric) resistivity tensor defined by the transformation rule (2) In Eq. 2, lambda ii and lambda jj are the direction cosines between an i, j-axis frame and any other i, j- (rotated-) axis frame. Specifically, it is clear that an angle, - B, always can be found such that Rij will take on a diagonalized form. It and easy to prove that the inverses of R1 and R2, respectively, give the maximum and minimum Darcian permeabilities since the i, j-axis frame coincides with the permeabilities since the i, j-axis frame coincides with the principal directions of the permeability tensor. principal directions of the permeability tensor. JPT P. 1142