Parameter estimation in quasilinear parabolic equations oil reservoir applications

A method to determine parameters appearing in systems of nonlinear parabolic partial differential equations and associated boundary conditions is described from the point of view of obtaining numerical solutions for the inverse problem. The method utilizes a generalized Newton-Raphson method, finite differences and least squares fitting criteria to estimate the parameters. The unknown parameters are allowed to have a nonuniform distribution over the domain of the space variables. Numerical results are presented for a number of problems related to the estimation of certain parameters (porosity and permeability) appearing in oil reservoir problems. The results indicate that the generalized Newton-Raphson method yield accurate estimates for the parameters within a reasonable number of iterations. The effects of the initial estimates, number of unknown parameters, false zonation and noise on the data are considered. It is found that the generalized Newton-Raphson method is an efficient method to estimate distributed parameters in partial differential equations.