A direct method for the identification of the permeability field of an anisotropic porous medium

In a recent publication [Zhan and Yortsos, 2000] we proposed a direct metho d for the inversion of the permeability field of an isotropic porous medium based on the analysis of the displacement of a passive tracer. By monitori ng the displacement front at successive time intervals (e.g., using a tomog raphic method), the permeability can be directly obtained from the solution of a nonlinear boundary value problem. In this paper we extend this approa ch to the case when the porous medium is anisotropic. When the principal ax es 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 two-dimensional (2-D) (or three-d imensional) problem). It is shown that the diagonal components can be obtai ned from the solution of two (or three) coupled boundary value problems inv olving the experimentally obtained fields of arrival times. Numerical examp les show that the method works well when the permeability variation is not very sharp (e.g., for correlated distributions). When the permeability tens er is full and the principal axes vary in space, a procedure involving the injection in three different directions (for the case of a 2-D problem) is also described.