Support-operators method in the identification of permeability tensor orientation

The dependence of rock permeability on direction, or permeability anisotropy, is confirmed by numerous field examples. Therefore, the ability to carry out a numerical simulation of an anisotropic reservoir is very important. The support-operators method provides a conservative discretization scheme, allowing one to solve nonisotropic problems on a grid of practically arbitrary structure. Moreover, a discretization designed with the support-operators method provides a natural and convenient way of deriving and solving the adjoint system for evaluation of the gradient and second-order differential in inverse problems. After a theoretical introduction into the support-operators method, we consider an illustrative parameter-identification problem. More specifically, we evaluate the orientation angle of a nonisotropic permeability tensor in a horizontal reservoir. We assume that the principal permeabilities near a cored or otherwise logged well are already known. To accomplish this task, we need pressure measurements in monitoring wells. We consider both rectangular and curvilinear grids. In either case, the orientation angle has been recovered with a high accuracy.