A novel approach called Forward-Inverse Adaptive Techniques (FIAT) for reservoir characterization is developed and applied to three representative exploration cases. Inverse modeling refers to the determination of the entire reservoir permeability under steady state single-phase flow regime, given only field permeability, pressure and production well measurements. FIAT solves the forward and inverse partial differential equations (PDEs) simultaneously by adding a regularization term and filtering pressure gradients. An implicit adaptive-grid, Galerkin, numerical scheme is used to numerically solve the set of PDEs subject to pressure and permeability boundary conditions. Three examples are presented. Results from all three cases demonstrate attainable and reasonably accurate solutions and, more importantly, provide insights into the consequences of data undersampling.

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