A Direct Method for the Identification of the Permeability Field of an Anisotropic Porous Medium

Abstract

Abstract In a recent publication1 we proposed a direct method for the inversion of the permeability field of an isotropic porous medium based on the analysis of the displacement of a passive tracer. By monitoring the displacement front at successive time intervals (for example, using a tomographic method), the permeability can be directly obtained from the solution of a non-linear boundary-value problem. In this paper we extend this approach to the case when the porous medium is anisotropic. When the principal axes of anisotropy are known and fixed, a procedure is proposed, in which the tracer is injected two (or three) consecutive times along the two (or three) principal directions (for the case of a 2-D (or 3-D) problem, respectively). It is shown that the diagonal components can be obtained from the solution of two (or three) coupled boundary-value problems involving the experimentally obtained fields of arrival times. Numerical examples show that the method works well when the permeability variation is not very sharp (for example, for correlated distributions). When the permeability tensor is full and the principal axes vary in space, we propose a procedure involving the injection in three different directions (for the case of a 2-D problem). In principle, the components of the permeability tensor can be determined from the solution of three coupled boundary-value problems. However, the inversion method encounters significant numerical problems. For the case of small off-diagonal components, a practical procedure is proposed to decouple the problems in the inversion method for both 2-D and 3-D.