Automatic History Matching of Geologic Facies

Abstract

Summary The truncated pluri-Gaussian method for modeling geologic facies is appealing not only for the wide variety of textures and shapes that can be generated, but also because of the internal consistency of the stochastic model. This method has not, however, been widely applied in simulating distributions of reservoir facies or in automatic history matching. One reason seems to be that it is fairly difficult to estimate the parameters of the stochastic model that could be used to generate geological facies maps with the desired properties. The second is that because "facies type" is a discrete variable, it is not straightforward to apply the efficient gradient-based minimization method to generate reservoir facies models that honor production data. Nongradient methods, however, are too slow for large field-scale problems. In this paper, the nondifferentiable history-matching problem was replaced with a differentiable problem so that an automatic history-matching technique could be applied to the problem of conditional simulation of facies boundaries generated from the truncated pluri-Gaussian method. The resulting realizations are consistent with both the geostatistical model of the observed facies and the historic production. Application of the method requires efficient computation of the gradient of the objective function with respect to model variables. We present an example five-spot water-injection problem with more than 73,000 model variables conditioned to pressure data at wells. The gradient was computed using the adjoint method, and the minimization routine used a quasiNewton algorithm. The objective function decreased more than 98% in 13 iterations.