History Matching with Generative Adversarial Networks

Abstract

Summary Conditioning reservoir models with complex non-Gaussian spatial patterns on nonlinear production data is complicated by the need to preserve the expected geological features to maintain solution plausibility. Generative adversarial networks (GANs) have recently been proposed as a promising approach for low-dimensional representation of complex high-dimensional images. It has also been adopted for low-rank parameterization of complex geologic models to facilitate data integration and uncertainty quantification workflows. A challenging aspect in adopting parametric methods for history matching is the ease of data conditioning. While conditional GAN (CGAN) has been developed for conditioning on image labels, reservoir engineering applications require conditioning on nonlinear flow data, which is a far more complex problem. We present two approaches for generating flow-conditioned models with complex spatial patterns using GAN. The first method is through CGAN, whereby a production response label is used as an auxiliary input when training CGAN. The label is derived from clustering the flow responses of the prior model realizations. The underlying assumption of this approach is that CGAN can learn the association between the spatial features corresponding to the production responses within each cluster. An alternative method that involves two steps is also presented, where in the first step a neighborhood selection algorithm identifies the subset of relevant flow responses around the observed data (using the training models). The second step employs GAN to generate conditional models based on the realizations selected in the first step. In this case, GAN is not required to learn the relation between production responses and spatial patterns. Instead, it is tasked to learn the patterns that are involved in the selected realizations. This approach allows for exploring the spatial variability in the conditional realizations, which can be critical for decision-making. We present several examples, including non-Gaussian prior models with linear and non-linear forward models, to evaluate the performance of the two methods in generating flow-conditioned models. The results show that the generated conditional models preserve geologic realism and can reproduce the field production data within a specified error. An important advantage of GAN for data conditioning is that it automatically honors the geological feasibility constraint, which is not trivial to accomplish using existing low-dimensional parameterization methods. Moreover, it achieves this performance even when very few latent variables (parameters) are used, which is desirable for uncertainty quantification. We present and discuss the important properties of GAN for data conditioning with several examples with increasing complexity.