Fractured reservoir simulation is important and applicable to understand many processes related to subsurface geo-energy recovery and storage, such as shale gas/oil, enhanced geothermal systems, and CO2 sequestration in basaltic rocks. However, such simulations are often computationally expensive to capture the high contrast of permeability and pore volume between matrix and fracture. Therefore, a reduced order model (ROM) can be extremely beneficial for fractured reservoir simulation to reduce computational costs for iterative history-matching and reservoir optimization workflows.

In this study, we propose a novel ROM that flexibly honors fracture representations, namely DiagNet. In DiagNet, we generate the coarse matrix nodes based on the reservoir outlines, and add extra diagonal connections between non-neighboring matrix nodes if intersecting fractures traverse them, which avoids the inclusion of additional fracture nodes. Since dimensionality reduction methods, such as Principal Component Analysis (PCA) can facilitate the model parameterization, we adopt PCA to generate quality priors for sampling of the matrix transmissibility and pore volume arrays. Further, the DiagNet models are then calibrated to the well observation data (such as well flow rates and bottom-hole pressures), and a gradient-based optimization method is implemented in a general automatic-differentiable simulator framework to tune the model parameters (e.g., matrix/fracture transmissibilities, pore volumes, and well indices).

Our results show that we can perform robust calibration of DiagNet based on the synthetic well observation data from a fine-scale reference simulation model. We have found that it is necessary to incorporate the dominant flow physics (i.e., water breakthrough) from the observation data to improve the training convergence and the prediction accuracy for DiagNet. Further, PCA for parameterization improves the convergence rate of model calibration, as compared to random initialization. Interpretation of the calibrated transmissibility field from DiagNet aligns with high connectivity regions from the fine-scale reference model. As a result, the new DiagNet is interpretable in terms of reservoir connectivity or geology and thus can be used for reservoir history-matching using observation data from the field and the further optimization.

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