Reparameterization Techniques for Generating Reservoir Descriptions Conditioned to Variograms and Well-Test Pressure Data

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Abstract
Recently, we have shown that reservoir descriptions conditioned to multiwell pressure data and univariate and bivariate statistics for permeability and porosity can be obtained by techniques developed from inverse problem theory. The techniques yield estimates of well skin factors and porosity and permeability fields which honor both the spatial statistics and the pressure data. Imbedded in the methodology is the application of the Gauss-Newton method to construct the maximum a posteriori estimate of the reservoir parameters. If one wishes to determine permeability and porosity values at thousands of gridblocks for use in a reservoir simulator, then inversion of the Hessian matrix at each iteration of the Gauss-Newton procedure becomes computationally expensive. In this work, we present two methods to reparameterize the reservoir model to improve the computational efficiency. The first method uses spectral (eigenvalue/eigenvector) decomposition of the prior covariance matrix. The second method uses a subspace method to reduce the' size of the matrix problem that must be solved at each iteration of the Gauss-Newton method. It is shown that proper implementation of the reparameterization techniques may significantly reduce the computational time required to generate realizations of the reservoir model, i.e., the porosity and permeability fields and well skin factors, conditioned to prior information on porosity and permeability and multiwell pressure data.

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