Identification of the permeability field of a porous medium from the injection of a passive tracer

We propose a method for the direct inversion of the permeability field of a porous medium from 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 nonlinear boundary-value problem. Well posedness requires knowledge of the pressure profile or the permeability at no-flow boundaries. The method is tested using synthetic data in two dimensions (2D) (and some 3D) geometries for a variety of heterogeneous fields and found to work well when the permeability contrast is not too large. However, it is sensitive to sharp variations in permeability. In the latter case, a modified approach based on the successive injection in both directions and the use of an optimization technique leads to improved estimates. The sensitivity to measurement errors is analyzed. An important feature of the direct method is that it also applies to anisotropic porous media. When the principal axes of anisotropy are known, a suitable procedure is proposed and demonstrated using synthetic data.