Directional Permeability Effects in Developed and Unconfined Five-Spots
Authors: Parsons R.W. 
Published: December 2007

This study considers the effect of directional permeability on the behavior of unit mobility ratio displacements in developed and unconfined five-spots. Computer-generated data included streamline and flood-front maps, sweep efficiencies, oil cuts, and pattern flow capacities. A conclusion is that anisotropy does influence the interpretation of pilot tests and the prediction of field projects.

Introduction
In all types of fluid injection programs for oil recovery, it is important to be able to analyze the behavior of pilot operations, and to predict the production performance of field-wide developments. performance of field-wide developments. A common pattern used for both pilot and field projects is the five-spot. We shall examine here some projects is the five-spot. We shall examine here some of the effects that anisotropy (lateral directional permeability) has on five-spot operations. This study is permeability) has on five-spot operations. This study is simplified to the extent that it considers only an ideal reservoir (homogeneous and infinite) and an ideal fluid displacement (perfect piston and unit mobility ratio).
The existence of directional permeability in naturally occurring porous media and the basic equations used to describe flow in these systems are accepted facts. Directional permeability trends in reservoirs can be detected by several methods. Both steady-state and transient pressure measurements can be analyzed to give the orientation and degree of anisotropy. The pulse-test techniques may be particularly suited to this type of determination. particularly suited to this type of determination. Although an extensive literature bas developed on pattern behavior in isotropic reservoirs (see Smith pattern behavior in isotropic reservoirs (see Smith for a comprehensive summary), there is a scarcity of material available on anisoptropic systems. The specific problem of this report a symmetrical five-spot in an anisotropic reservoir has been partially treated by Landrum and Crawford. Their five-spot data are for developed patterns only, and consist of flow capacity and of flood-front position and sweep efficiency at breakthrough.
The purpose of this report is to show how neglecting or not recognizing anisotropy might lead to erroneous interpretations of pilot projects or to bad predictions of field-wide projects. Admittedly, the predictions of field-wide projects. Admittedly, the assumptions used in this study are for an ideal reservoir; however the results can qualitatively indicate the effects for real reservoirs.
A streamline model was used to generate the results. Although similar types of models have already been described, ours will be discussed briefly.

Computer Model
Real Anisotropic --&gt;Equivalent Isotropic Transformation
The first computational step is a coordinate transformation that converts the real anisotropic reservoir to an equivalent isotropic system. This shrinking of coordinates in the maximum permeability direction and stretching of coordinates in the minimum permeability direction changes the single-phase (or unit mobility ratio) flow equations to the more familiar isotropic form. All of the reservoir engineering calculations are then done in this equivalent isotropic system, but the results apply equally to the real anisotropic reservoir. The only reason to make the reverse transformation (isotropic --&gt;anisotropic) is to generate streamline and flood-front maps.
JPT
P. 487