Non-Intrusive Parametric Model Order Reduction with Error Correction Modeling for Changing Well Locations Using a Machine Learning Framework
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AbstractThe objective of this paper is to develop a non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations that can eventually be used for well placement optimization, to gain significant computational savings. In the past, model order reduction strategies developed for the case of changing infill well locations are limited to the scale of application, with majority of focus laid on development of MOR for changing controls of the wells for well control optimization. In this work, we propose a proper orthogonal decomposition (POD) based PMOR strategy that is non-intrusive to the simulator source code, as opposed to the convention of using POD as a simulator intrusive procedure, and hence extends its applicability to any commercial simulator. The non-intrusiveness of the proposed technique stems from formulating a novel Machine Learning (ML) based framework used with POD. The features of ML model (Random Forest used here) are designed such that they take into consideration the temporal evolution of the state solutions and thereby avoiding simulator access for time dependency of the solutions. The proposed PMOR method is global in the sense that a single reduced order model can be used for all the well locations of interest in the reservoir. We address a major challenge of explicit representation of the well location change as a parameter by introducing geometry-based features and flow diagnostics inspired physics-based features. An error correction model based on reduced model solutions is formulated later to correct for discrepancies in the state solutions at well gridblocks.The proposed methodology is applied to a heterogeneous channelized reservoir using a section of SPE10 model, to analyze and validate the proposed idea. It was observed that the global PMOR could predict the overall trend in the pressure and saturation solutions at the well blocks but some bias was observed that resulted in discrepancies in prediction of quantities of interest (QoI) like oil production rates and water cut. Thus, the error correction model proposed using Artificial Neural Networks (ANN) that considers the physics based reduced model solutions as features, proved to reduce the error in QoI significantly. Speed-ups of about 50x-100x were observed for different cases considered when running the test scenarios. The proposed workflow for reduced order modeling is "non-intrusive" and hence can increase its applicability to any simulator used. Also, the method is formulated such that all the simulation time steps are independent and hence can make use of parallel resources very efficiently and also avoid stability issues that can result from error accumulation over timesteps.
