The objective of this paper is to develop a global non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations in an oil field, that can eventually be used for well placement optimization to gain significant computational savings. In this work, we propose a proper orthogonal decomposition (POD) based PMOR strategy that is non-intrusive to the simulator source code 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 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. We represent well location changes 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. It was observed that the global PMOR could predict the overall trend in pressure and saturation solutions at the well blocks but some bias was observed that resulted in discrepancies in prediction of quantities of interest (QoI). Thus, the error correction model that considers the physics based reduced model solutions as features, proved to reduce the error in QoI significantly. This workflow is applied to a heterogeneous channelized reservoir that showed good solution accuracies and speed-ups of 50x-100x were observed for different cases considered. 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.

中文翻译：

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使用机器学习框架更改井位的非侵入式参数模型降阶与误差校正建模

本文的目标是开发一种全局非侵入式参数模型降阶 (PMOR) 方法来解决油田中井位变化的问题，最终可用于优化井位，从而显着节省计算量。在这项工作中，我们提出了一种基于适当正交分解 (POD) 的 PMOR 策略，该策略不干扰模拟器源代码，因此将其适用性扩展到任何商业模拟器。所提出技术的非侵入性源于制定与 POD 一起使用的新型基于机器学习 (ML) 的框架。ML 模型的特征被设计为考虑到状态解决方案的时间演变，从而避免模拟器访问解决方案的时间依赖性。我们通过引入基于几何的特征和基于物理的特征的流动诊断来将井位变化表示为参数。基于简化模型解的误差修正模型随后被公式化，以修正井格块的状态解的差异。据观察，全局 PMOR 可以预测井块压力和饱和度解决方案的总体趋势，但观察到一些偏差，导致感兴趣量 (QoI) 的预测存在差异。因此，将基于物理的简化模型解作为特征的纠错模型被证明可以显着降低 QoI 的误差。此工作流程应用于非均质通道化储层，该储层显示出良好的解算精度，并且在所考虑的不同情况下观察到 50x-100x 的加速。