The Determination of Transverse Permeabilities In Anisotropic Porous Media

Abstract The method used to interpret laboratory transverse permeability observations is based on a theory which assumes horizontal permeability to be isotropic. This paper presents an alternative theory which does not require that assumption. Comparison of the two methods on ten laboratory data sets indicates that the current method yields biased results. For data taken with a screen half angle of45 degrees, the current method yields Kmax values which are too large and K L900 values which are too small. For screen half angles less than 45 degrees, the current method further biases Kmax values due to what appears as a misapplication of the geometric factor. INTRODUCTION In full-diameter core analysis, it is common practice to determine a vertical or axial permeability and two horizontal or transverse permeabilities at right angles to each other. The lat- ter are obtained by placing the cylindrical core in a holder so that the axis is vertical and permitting horizontal gas flow through a sector of the radial surface, and then rotating the core through an angle π/2 and repeating the test. The larger permeability is then termed kmax and the smaller k L90◦. This practice was developed over the past thirty years on the basis of a method proposed by Kelton(1) and another proposed by Collins(2), which he subsequently extended and elucidated(3). Although Kelton devised the method in order to measure transverse permeabilities in fractured and vugular limestones and employed it to measure a transverse permeability in the direction of the fractures and another at right angles to it, the interpretation technique he used was based on observations made on nearly uniform synthetic cores and checked by means of electrolyte model studies(4). Collins, on the other hand, proposed a method for determining permeability parallel to the bedding in a core by conducting transverse flow tests. The interpretation technique he proposed was based on the assumption that the transverse permeability, though different from the axial, was independent of direction(5). That is, his method was intended for use in those cases where the porous medium is isotropic in the transverse sense. Since current practice with regard to the measurement of transverse permeabilities consists of conducting transverse flow tests in two directions at right angles to each other and interpreting the data by means of the application of geometric factors, either obtained on uniform cores or derived theoretically, but intended for use in cores where kmax equals kL90◦ the results obtained are open to question in those cases where kmax is not equal to k L90◦ As it has recently been shown that Collins" theory can be modified to apply to anisotropic media(6}, it is the object of this paper to describe the modified method and to discuss the influence of its application on the results obtained. Theory In the original method, Collins considers steady transverse plane horizontal gas flow through an arc of a circle. That is, the fluid enters the circular region through an are subtended by the angle 2α and exits through an are of equal length directly opposite, the remainder of the circular boundary being sealed.