Two-Step Predict and Correct Non-Intrusive Parametric Model Order Reduction for Changing Well Locations Using a Machine Learning Framework

Abstract

The objective of this paper is to develop a two-step predict and correct 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 two-step PMOR procedure, where, in the first step, a Proper Orthogonal Decomposition (POD)-based strategy that is non-intrusive to the simulator source code is introduced, as opposed to the convention of using POD as a simulator intrusive procedure. The non-intrusiveness of the proposed technique stems from formulating a novel Machine Learning (ML)-based framework used with POD. The features of the ML model (Random Forest was used here) are designed such that they take into consideration the temporal evolution of the state solutions and thereby avoid simulator access for the time dependency of the solutions. The proposed PMOR method is global, since a single reduced-order model can be used for all the well locations of interest in the reservoir. We address the major challenge of the explicit representation of the well location change as a parameter by introducing geometry-based features and flow diagnostics-inspired physics-based features. In the second step, an error correction model based on reduced model solutions is formulated to correct for discrepancies in the state solutions at well grid blocks expected from POD basis for new well locations. The error correction model proposed uses Artificial Neural Networks (ANNs) that consider the physics-based reduced model solutions as features, and is proved to reduce the error in QoI (Quantities of Interest), such as oil production rates and water cut, significantly. This workflow is applied to a simple homogeneous reservoir and a heterogeneous channelized reservoir using a section of SPE10 model that showed promising results in terms of model accuracy. Speed-ups of about 50×–100× 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. Additionally, 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 time steps.

Use of low-fidelity models with machine-learning error correction for well placement optimization

“…More recent work in this area is discussed in the review by Jansen and Durlofsky [11]. POD-based methods have received limited attention for WPO problems, though they were applied in this setting by Zalavadia and Gildin [12,13]. Other simplified modeling procedures, such as capacitanceresistance methods, have also been used for well control optimization [14].…”