Deep-learning-based geological parameterizations for history matching complex geomodels

Geological parameterization enables the representation of geomodels in terms of a relatively small set of uncorrelated variables. Parameterization is therefore very useful in the context of history matching (data assimilation) and uncertainty quantification. Traditional geological parameterizations, however, may not be effective at preserving complex geological structures, such as fluvial channels, levees and deltaic fans. To address this issue, in this work we develop a deep-learning-based geological parameterization, referred to as CNN-PCA. The CNN-PCA procedure combines principal component analysis (PCA), a traditional parameterization technique, with deep learning. The main idea is to train a deep convolutional neural network (CNN), referred to as the model transform net, as a post-processor for models parameterized with PCA, to recover geological realism. The training loss for the model transform net involves a set of geomodel features (specifically Gram matrices) extracted from another pretrained CNN, referred to as the loss net. For more challenging 3D systems, a supervised-learning-based loss term is introduced. Hard data loss is included in both the 2D and 3D CNN-PCA formulations. The CNN-PCA procedure is first developed and applied for 2D geological systems. These include a binary fluvial channel system and a bimodal deltaic fan system. In both cases, CNN-PCA is shown to provide realizations that honor the geological features present in reference models generated using geomodelling software. Quantitative assessments are conducted for the binary channel system. For this case, connectivity measures and two-phase flow statistics obtained with random (test-set) CNN-PCA geomodels closely match results for reference models. A strategy for the formal selection of the various training weighting factors is developed based on the connectivity measures. History matching results for the binary channel system are presented. In this assessment CNN-PCA is applied with derivative-free optimization, and a subspace randomized maximum likelihood (RML) method is used to provide multiple posterior models. Data assimilation and significant uncertainty reduction are achieved for existing wells, and physically reasonable predictions are also obtained for new wells. We next describe a multilevel CNN-PCA-based history matching procedure, again using RML to generate posterior models. Mesh adaptive direct search (MADS), a pattern-search method that parallelizes naturally, is applied for optimization. Although the use of CNN-PCA parameterization reduces the number of variables that must be determined during history matching, the minimization problem can still be computationally demanding. The multilevel strategy addresses this issue by reducing the number of simulations that must be performed at each MADS iteration. Specifically, the PCA coefficients (which are the optimization variables after CNN-PCA parameterization) are determined in groups, at multiple levels, rather than all at once. History matching results are presented for a 2D binary channelized system and a 2D bimodal deltaic fan system. These computations demonstrate that substantial uncertainty reduction is achieved in both cases, that multilevel results are in essential agreement with reference single-level results, and that the multilevel strategy acts to substantially reduce the total number of flow simulations required. Finally, we extend the CNN-PCA procedure to handle complex 3D geological systems. The training loss for the 3D model transform net involves features of geomodels extracted from a pretrained 3D CNN, a new supervised-learning-based reconstruction loss, and a hard data loss. The 3D CNN-PCA algorithm is applied for the generation of conditional 3D realizations, defined on grids containing

Keywords: Energy Resources Engineering.
Advisor: Durlofsky Louis 
Horne Roland N. 
Tartakovsky Daniel