History Matching under Uncertain Geologic Scenarios with Variational Autoencoders

Summary Inference of high-resolution reservoir models from limited production data leads to ill-posed inverse problems. Parameterization methods are used to reduce the number of unknowns while maintaining the salient connectivity features of the reservoir model. Existing parameterization methods, such as principle component analysis (PCA), are not suitable for capturing complex non-Gaussian connectivity patterns that are exhibited in certain geological formation such as fluvial systems. Recent advances in machine learning have given rise to new approaches for dimensionality reduction that can be applied for parameterization of reservoir models in history matching. Many conventional parameterization techniques exhibit strong sensitivity to diversity in the geologic features (e.g., when multiple scenarios are used to account for prior uncertainty). One potential advantage of the new techniques is their ability to learn complex and diverse patterns, which leads to robustness against geologic uncertainty. We present variational autoencoders (VAEs) as a special form of convolutional neural networks for parametrization of history matching problems under multiple geologic scenarios. Autoencoders have achieved great performance in data compression by taking advantage of the power of convolutional neural networks for detecting local spatial patterns. We present VAEs as an effective parameterization approach for complex spatial models with non-Gaussian statistics. These methods project complex spatial models to a low-dimensional latent space, where a small number of latent variables with simple probability density functions (e.g., Gaussian) approximate the original models. The latent space variables are used to update the reservoir model during history matching. We evaluate the dimensionality reduction power of VAEs and use them with stochastic gradient-based inversion methods to perform history matching. We present history matching results when the training data is based on a single geologic scenario and when multiple geologic scenarios lead to very diverse features in the training data. Comparison between the performance of VAE and PCA shows that the former offers important advantages over PCA. The performance difference between the two methods become more significant when multiple geologic scenarios are present. We present several examples to demonstrate the implementation of VAE and its important properties in comparison to PCA.