Error Analysis in History Matching: The Optimum Level of Parameterization

Abstract

The accuracy of the porosity and permeability estimates obtained in reservoir history matching is investigated using covariance analysis. The estimate covariance matrix is obtained for the following cases: (1) estimation of all individual grid properties, (2) parametrization using sensitivity vectors, (3) parametrization by zonation, and (4) Bayesian estimation. The trace of the covariance matrix used as a measure of the over-all accuracy is studied as a function of the number of unknown parameters, and a procedure for selecting the parameters, and a procedure for selecting the optimum parametrization is developed. Numerical calculations with a one-dimensional reservoir are used to illustrate the theory.

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