History Matching by Spline Approximation and Regularization in Single-Phase Areal Reservoirs

An automatic history-matching algorithm is developed from bicubic spline approximations of permeability and porosity distributions and from the theory of regularization to estimate permeability or porosity in a single-phase, two-dimensional (2D) areal reservoir from well pressure data. The regularization feature of the algorithm, the theoretical details of which are described by Kravaris and Seinfeld, is used to convert the ill-posed history-matching problem into a well-posed problem. The algorithm uses Nazareth's conjugate gradient method as its core minimization method. A number of numerical experiments are carried out to evaluate the performance of the algorithm. Comparisons with conventional (nonregularized) automatic history-matching algorithms indicate the superiority of the new algorithm with respect to the parameter estimates obtained. A quasioptimal regularization parameter is determined without requiring a priori information on the statistical properties of the observations.