Use of deep learning and error correction for data-space inversion and model-based history matching
Keywords: Energy Resources Engineering.

In subsurface flow settings, data assimilation or history matching is challenging because of the computational cost associated with performing many high-fidelity simulations and due to the difficulty of maintaining geological realism in history-matched models. Two types of approaches for history matching are considered in this thesis -- data-space inversion and model-based calibration. In data-space inversion (DSI), posterior flow predictions for time series of interest are generated without calibrating model parameters. In model-based history matching, posterior (history matched) geomodels are constructed, and these can be used to provide flow predictions. We first develop and evaluate a new deep-learning-based approach for data parameterization in a data-space setting. Parameterization is useful in DSI as it reduces the number of variables to determine in the inversion, and it maintains the physical character of the data variables. The new parameterization uses a recurrent autoencoder (RAE) for dimension reduction, and a long-short-term memory (LSTM) recurrent neural network architecture to represent flow-rate time series. The RAE-based parameterization is combined with an ensemble smoother with multiple data assimilation (ESMDA) for posterior data sample generation. Results are presented for two- and three-phase flow in a 2D channelized system and a 3D multi-Gaussian model. The new DSI RAE procedure, along with several existing DSI treatments, including a parameterization based on principal component analysis (PCA) with histogram transformation, are assessed through detailed comparison to reference rejection sampling (RS) results. The new DSI methodology is shown to consistently outperform existing approaches, in terms of statistical (P10-P90 interval and Mahalanobis distance) agreement with RS results. The method is also shown to accurately capture derived quantities, which are quantities not treated directly within DSI. This requires correlations between variables to be properly captured, and accuracy in these relationships is demonstrated. We then apply the RAE-based DSI method to a realistic and much more complex 3D discrete fracture reservoir model involving three-phase flow, tracer injection and production, and complicated field and well management logic. Results for the reconstruction of new simulation data, not seen in training, using both the RAE-based parameterization and PCA with histogram transformation, are presented. The RAE-based procedure is shown to provide better accuracy for these data reconstructions. Detailed posterior DSI results for a particular true model (which is outside the prior ensemble), and summary results for five additional true models, demonstrate the advantages of DSI with RAE-based parameterization for this challenging fractured reservoir case. Subsurface flow models are inherently imperfect, though model error has not yet been treated in DSI settings. To address this limitation, we introduce model error treatments in DSI. The model error derives from the use of upscaled/coarsened models for the prior-model flow simulations required by DSI. Our error treatment entails the simulation of a set of corresponding pairs of fine and upscaled models. These results are used to construct a PCA representation of model error. A linear regression approach is introduced to capture the coupled nature of the coarse-scale simulation output and model error. To construct posterior DSI predictions, a joint inversion on coarse-scale simulation data and model error is performed using ESMDA. PCA and histogram transformation is applied to parameterize prior simulation data (the goal here is to construct the error model with as few high-fidelity simulations as possible). Results are presented for two-phase flow in 3D channelized geomodels. The corrected prior and DSI posterior results are compared to reference results generated from fine-scale simulations. Comparisons are presented for flow statistics, Mahalanobis distance, and relative error for multiple (synthetic) true models. The coupled model error treatment is shown to provide highly accurate prior results and posterior predictions that agree closely with reference results. Significant improvement relative to uncorrected coarse models is observed. Importantly, the treatments developed here can be used to represent error from many different sources. Finally, model-based history matching, where the goal is to construct posterior (calibrated) geomodels, is considered. We develop a transfer-learning-based surrogate model to reduce the computational costs associated with network training. In our framework, most of the training simulations are performed on coarsened (low-fidelity) geomodels. These models are constructed using the same flow-based upscaling method as was used for model error treatment in DSI. The framework involves the application of a transfer-learning procedure, incorporated within an existing recurrent residual U-Net architecture, in which network training is accomplished in three steps. In the first step, where the bulk of the training is performed, only low-fidelity simulation results are used. The second and third steps, in which the output layer is trained and the overall network is fine-tuned, require a relatively small number of high-fidelity simulations. Here we use 2500 low-fidelity runs and 200 high-fidelity runs, which leads to about a 90% reduction in training simulation costs. The method is applied for two-phase subsurface flow in 3D channelized systems, with flow driven by wells. The surrogate model trained with multifidelity data is shown to be nearly as accurate as a reference surrogate trained with only high-fidelity data in predicting dynamic pressure and saturation fields in new geomodels. The network is shown to provide results that are significantly more accurate than the low-fidelity simulations used for most of the training. The multifidelity surrogate is also applied for history matching using ESMDA, where accuracy relative to reference results is again demonstrated. The methods developed in this thesis, for both data-space and model-based history matching, should be applicable to a wide range of challenging subsurface flow problems