Efficient Technique for Inversion of Reservoir Properties Using Iteration Method

Abstract

Summary In light of the inverse solution theory, an efficient solution procedure has been developed to generate reservoir descriptions conditioned to statistics for rock properties, hard data, and dynamic data. The technique yields realizations for wellbore skin factors at each active well and porosity and permeability which honor a priori information and dynamic production data. The technique invokes inverse solution theory to construct the objective function and uses the gradient method to generate the maximum a posteriori estimates. Differing from the previous works, we derived and implemented a two-loop iteration method to perform the minimization. By using Krylov space-based methods to solve the linear part involved in the minimization, the explicit construction of the sensitivity coefficient matrix is avoided. Complexity analysis and computational results indicate the new algorithm is more efficient than several available methods due to the decrease of the number of the nonlinear iterations demanded for convergence. We also developed a modified procedure for computing realizations using the Chebyshev approximation of the decomposed a posteriori covariance matrix. In this way, the expensive computational cost of the construction and decomposition of the a posteriori covariance matrix is substantially reduced. When estimating multiple categories of parameters, which is the case in this study, our new procedure produces much more accurate results than the conventional Chebyshev method.