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Data-Driven Model Reduction, Scientific Frontiers, and Applications

Hardikkumar Zalavadia, Harold Vance Department of Petroleum Engineering
Parametric Model Order Reduction for Adaptive Basis Selection Using Machine Learning Techniques During Well Location Optimization


Model Order Reduction (MOR) aims at accelerating the numerical simulations for solving large-scale dynamical systems that inherently are computationally expensive while preserving the accuracy of the underlying solution. The objective of our work is to develop a Parametric Model Order Reduction technique for well location optimization problem that requires a large number of high fidelity simulation runs. Reduced order modeling methodologies for well control optimization have reached a good level of maturity, however, MOR for well placement optimization, required during the closed loop field development plan, is unexplored. MOR for well control optimization requires excitation of inputs to train the model, not drastically different from the test schedule, with fixed well configuration (locations). This reduced model is generally not robust to change in the well location, which we consider here as the system parameter.

This calls for Parametric Model Order Reduction (PMOR) where the goal is to generate reduced order models that characterize the system for different parameters, i.e., well locations. We propose local parametric reduced order models for new parameters using a machine Learning framework that prove to be more efficient than the global methods using snapshots/basis concatenation. Projection based PMOR using Proper Orthogonal Decomposition is implemented here. In this work, we use multi-layer Artificial Neural Network to predict the surrogate model error at a new well location with previously computed reduced models that help us choose appropriate basis. To train the neural network, input features are efficiently selected to represent the change in well location which also includes basis dimensions to account for optimal basis dimension at new parameters. The information from snapshots concatenation is added while training the neural network considering the fact that it is a better choice for some parameters.

This methodology applied to a synthetic channelized reservoir demonstrate the method to be accurate to obtain a good reduced model for new well locations. We show that the entire system can be represented by already existing ROMs from very few well locations. Machine Learning provide promising results to approximate the characteristics of the parametric reduced order models.