A Simple Method to Account for Permeability Anisotropy in Reservoir Models and Multi-Well Pressure Interference Tests

Abstract

Permeability anisotropy, via full permeability tensor, has not been accurately accounted for in reservoir models because of the implementation complexity. Specifically, numerical implementation of the off-diagonal components of the permeability tensor is inconvenient and cumbersome. This paper shows how directional permeability, calculated from a full permeability tensor, can be used as a simple replacement both in coding numerical models and in day-to-day engineering analysis. For the former, we have implemented the directional permeability for single-phase flow in a 9-point finite-difference formulation, which is easy to code. This formulation, however, is easily applicable to any control-volume formulation including the perpendicular bisector (PEBI) grid. The implementation of this technique has produced excellent numerical results in numerical simulation of multi-phase flow displacement. For routine engineering applications, we have also applied this technique to generate pressure responses for a four-well interference test in a highly anisotropic system. The analysis of the test results by conventional type-curve matching produced the correct reservoir geometric-average permeability and a very good approximation for the direction of the maximum permeability, which is a testimony to the credibility of the formulation. The use of this formulation should be very useful in determining major natural fracture trends in reservoirs undergoing water or gas injection, and in modeling fracture trends in other fractured reservoir situations, such as tight sands.