Automatic History Matching of Geologic Facies

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Abstract The truncated plurigaussian 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 properties 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 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. Non-gradient methods, however, are too slow for large field-scale problems. In this paper, the non-differentiable 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 plurigaussian method. The resulting realizations are consistent both with 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 simulator method, and the minimization routine used a quasi-Newton minimization. The data mismatch decreased more than 90% in the first two …