Permeability Anisotropy in Low Permeability Formations
Authors: Rose Walter 
Published: December 2007

The paper was presented at the SPE/DOE Unconventional Gas Recovery Symposium of the Society of Petroleum Engineers held in Pittsburgh, PA, May 16–18, 1982. The material is subject to correction by the author. Permission to copy is restricted to an abstract of not more than 300 words. Write: 6200 N. Central Expwy., Dallas, TX 75206.

Introduction
This paper describes a novel technique for measuring the directional permeability trends exhibitor by samples of sedimentary rock cores like permeability trends exhibitor by samples of sedimentary rock cores like those obtained from Western tight gas sands provinces. The technique is thought to be ingeneous, but in any case it finally does address an important laboratory measurement problem in a way that is free from some of the ambiguities associated with the several other methodologies previously referred to in the literature.
The book by Bear and the earlier definitive monograph by Scheidegger contain sufficiently extensive review of the subject so that in what follows only the theory of the measurement method under discussion needs to be developed.
PROCEDURE PROCEDURE It is assumed that core sample material is available that can be cut into plugs of uniform (say cylindrical) cross section, and therefore can be fit into a permeability core holder of the sort shown in Figure 1. As will be seen, the methodology to be described for measuring the permeability of anisotropic media is the same, in principle, both for single-phase and multiphase saturation and flow conditions. Similarly, the methodology is the same, in principle, regardless of what conditions of confining stress, pore fluid pressure and temperature are imposed. Even so, the data pore fluid pressure and temperature are imposed. Even so, the data presented below apply to single-phase gas flow conditions under ambient presented below apply to single-phase gas flow conditions under ambient laboratory conditions.
By definition, in an isotropic medium, permeability is a simple scalar, and in consequence the effluent stream that egresses from a right-cylindrical core sample will be uniformly distributed over the outflow face as shown in Figure 2a. In contrast, the effluent streams for anisotropic media will not be uniformly distributed (see Figures 2b and 2d) unless the end-faces are shaped to make a very special angle with the core axis (see Figure 2c).
Figure 1 shows how the effluent stream can be partitioned into upper and lower parts, respectively having flow rates Q UP and Q DOWN. If the sample is isotropic and has he shape of a right cylinder, Q UP = Q DOWN regardless of how the sample is placed along its axis in the core holder. On the other hand, reflection shows that for an arbitrary shaping of the end faces, an anisotropic core will display a Q UP/Q DOWN, ratio that is maximum (or minimum) only when the reference line, Z1 - Z2, shown in Figure 3 is uppermost in the core-holder as shown by Figure 4. Note that in these schematic presentations, it is implied that only a two-dimensional degree of anisotropy is involved - for example, as would be observed in bedded and cross-bedded sediments.
In the theoretical discussion given below it is shown that there is always a particular way to shape the end faces of anisotropic cores such that the Q UP /Q DOWN ratio is unity (see Figure 2c), but that or a other arbitrary shapings the ratio is either greater (see Figure 2b) or less (see Figure 2d) than unity. The object of the laboratory method in fact is to discover what the shaping angle, , must be so that Q UP /Q DOWN is unity (i.e. = where A is the angle made by the driving force vector with the axis of the core sample).
In order to choose under laboratory conditions the shaping of the end faces such that = (i.e. where Q UP / Q DOWN equals unity), a series of experiments are performed as suggested by Figure 5. For each shaping a permeability experiment is undertaken are measured. The and values for Q permeability experiment is undertaken are measured. The and values for Q UP and Q DOWN are measured. The ratios then are plotted versus the end-face angle in order to determine by trial-and-error the value of the angle A associated with the condition of uniform distribution of effluent fluid egressing from the end face of the core sample. Figure 6 shows that a semilog plot appears to be linear, meaning that a graphical interpolation can be trusted (at least for the cases so-far studied in the laboratory) in order to ascertain when the Q UP/Q DOWN ratio is unity (hence its logarithm is zero).
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