History Matching Complex 3D Systems Using Deep-Learning-Based Surrogate Flow Modeling and CNN-PCA Geological Parameterization

The use of deep-learning-based procedures for geological parameterization and fast surrogate flow modeling may enable the application of rigorous history matching algorithms that were previously considered impractical. In this study we incorporate such methods – specifically a geological parameterization that entails principal component analysis combined with a convolutional neural network (CNN-PCA) and a flow surrogate that uses a recurrent residual-U-Net procedure – into three different history matching procedures. The history matching algorithms considered are rejection sampling (RS), randomized maximum likelihood with mesh adaptive direct search optimization (MADS-RML), and ensemble smoother with multiple data assimilation (ES-MDA). RS is a rigorous sampler used here to provide reference results (though it can become intractable in cases with large amounts of observed data). History matching is performed for a channelized geomodel defined on a grid containing 128,000 cells. The CNN-PCA representation of geological realizations involves 400 parameters, and these are the variables determined through history matching. All flow evaluations (after training) are performed using the recurrent residual-U-Net surrogate model. Two cases, involving different amounts of historical data, are considered. We show that both MADS-RML and ES-MDA provide history matching results in general agreement with those from RS. MADS-RML is more accurate, however, and ES-MDA can display significant error in some quantities. ES-MDA requires many fewer function evaluations than MADS-RML, however, so there is a tradeoff between computational demand and accuracy. The framework developed here could be used to evaluate and tune a range of history matching procedures beyond those considered in this work.