Core Permeability Anisotropy
Authors: Lishman J.R. 
Published: March 2010

Abstract
Full-diameter core analysis measurements made on rocks from almost any reservoir suggest that permeability is an anisotropic property. Vertical permeability is almost always lower than permeability measured in any horizontal direction. There are usually sound petrographic reasons why this should be so. However, the practice of making measurements on plugs which are of length greater than their diameter magnifies true anisotropy.
Results from theoretical three-dimensional models built from completely random arrangements of isotropic permeability cells are given. They almost unerringly show vertical permeability lower than horizontal permeability where the vertical dimension is extended. The degree of false anisotropy increases with the vertical to horizontal cell ratio. As most reservoirs have thicknesses measured in feet, but areas measured in square miles, a core plug is a poor shape from which to determine the relative ease with which fluids can move vertically and horizontally within the reservoir. The reservoir engineer is given a misleading impression that vertical communication is more restricted than it really is. Conclusions from this study apply particularly to vuggy carbonate reservoirs, where true horizontal bedding is frequently lacking.

INTRODUCTION
THE TERM "PERMEABILITY ANISOTROPY", as used here, may be defined as the ratio of horizontal permeability (kmax or k90) to vertical permeability (kv). It is a quantity which affects, directly or indirectly, the solution of many problems arising in petroleum reservoirs. The actual ratio measured on a rock sample depends not only on lithology, but also on the geometric shape of the sample. Samples used in whole-core analysis vary widely in geometry. Some degree of simplification might be achieved if samples were always equidimensional. The measured ratio could then be called ‘true’ permeability anisotropy, and the component caused by irregular geometry could be referred to as ‘apparent’ or ‘false’ permeability anisotropy. Unfortunately, rigorous analysis of the problem is somewhat more complex. Also, in practice, in reservoir problems where the ratio of vertical to horizontal permeability is of importance, the ratio required is one which takes into account not only ‘true’ lithologic anisotropy, but also geometry – the geometry of the reservoir, or section of reservoir, under consideration.
Prediction of the exact permeability anisotropy factor to apply in a given reservoir situation, using measurements made in the laboratory, is probably difficult or impossible. The aim of this paper is to try only to convince the reader that it is not logical to transfer anisotropy measurements made on a core sample, which is usually higher than it is wide, to a reservoir which is almost always much wider than it is high.
A study was conducted with a simple computer model, simulating a three-dimensional matrix of cells. The permeability for each cell was chosen at random from a typical permeability distribution, and each cell was isotropic, i.e. vertical and horizontal permabilities were made the same. The computer calculated gross vertical and horizontal permeability. The model was run a large number of times, using many different matrix shapes, and using a different set of cell permeabilities each time.