Deep-Learning-Based 3D Geological Parameterization and Flow Prediction for History Matching

Abstract

In recent work we have developed deep-learning-based procedures for parameterizing complex 2D geomodels (Liu et al., 2019) and for predicting the detailed flow responses of such systems (Tang et al., 2019). The parameterization method, referred to as CNN-PCA, entails the use of principal component analysis in combination with convolutional neural networks, while the flow surrogate model involves the application of a recurrent residual U-Net procedure. The combination of these two capabilities enables efficient history matching to be performed. This is because the variables that must be determined during data assimilation correspond to the relatively small set of parameters associated with the CNN-PCA description, and the requisite flow simulations can all be accomplished using the deep-learning-based surrogate model. The overall methodology has been successfully applied to 2D channelized systems (as shown in Tang et al., 2019).

In this work, we extend these capabilities to 3D systems. The 3D CNN-PCA procedure differs from the 2D method in that we no longer use a style loss term (as we did in 2D), but instead apply a supervised learning approach. With this method we train the network using PCA realizations along with their corresponding (desired) channelized representations. This treatment, in common with our 2D procedure, leads to faster training than some other approaches since the underlying PCA representation already captures aspects of the spatial statistics (covariance). The 3D recurrent R-U-Net consists of 3D convolutional and recurrent (convLSTM) neural networks, which are designed to capture the spatial and temporal information associated with dynamic systems. This approach shows advantages over autoregressive procedures. The recurrent R-U-Net is trained on O(3000) randomly generated 3D geomodels and their corresponding (simulated) dynamic 3D state maps; e.g., saturation and pressure at a set of time steps.

Results are first presented for each method individually. Specifically, we validate the geological parameterization procedure by demonstrating that the prior flow statistics, for a 3D channelized system, generated using CNN-PCA agree closely with those from (reference) geostatistical models. The recurrent R-U-Net surrogate flow model is validated through detailed comparisons of oil-water flow results for particular (new) realizations and through error statistics for an ensemble of new models. Finally, a 3D history matching example, in which the two procedures are used in combination, will be presented.