Numerical algorithms are developed to estimate petroleum reservoir properties such as absolute permeability, porosity, and relative permeabilities based on the noisy pressure and flow data. Regularization and spline approximation of spatially varying parameters are employed to convert the ill-posed nature of the problem to a well-posed one. A stabilizing functional with gradient operator is used to measure the non-smoothness of the parameter estimates. The number of spline coefficients along each spatial direction is chosen to be as much as the number of meshes for the reservoir PDE's. New history matching algorithms are developed that determine the regularization parameter during the computation without requiring a priori information and improve the parameter estimates stepwise. A partial conjugate gradient method is employed for the estimation of a single set of parameters, and the steepest descent algorithm is used for the simultaneous estimation of absolute and relative permeabilities. A rough parametric sensitivity analysis is carried out for the simultaneous estimation to improve the convergence. Numerical tests are carried out to estimate the parameters in single- and two-phase reservoirs for the different choices of the stabilizing functionals, the regularization parameters, and the degrees of spline approximation; and the effects of the observation error, the observation time, and the configuration of the observation points are investigated.The results show that the new algorithms generate better parameter estimates over the various possible choices of the estimation conditions.
