  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.
