Model Reduction for Reservoir Simulation at the Crossroads: Is it Feasible to Construct an Input-Output Invariant Proxy Model?
High-fidelity reservoir simulation provides accurate characterizations of complex flow dynamics in the subsurface. Yet, it is not well suited for large scale optimization due to their prohibitive computational complexity. Reduced order models (ROM) endowed with accurate input-output tracking capabilities (and not only states) provides better alternatives to full scale simulations. ROM’s are with input-output capabilities are relatively easy to obtain for linear systems, but it becomes problem dependent (that is training dependent) for non-linear systems. In this talk, we show our recent developments towards develop a novel model reduction technique for reservoir simulation that mitigates the large dependencies on training data. We build upon the bilinear formulation of dynamical systems to construct accurate reduced-order model. A Combination of data-driven model reduction strategies and machine learning (deep-neural networks - ANN) is used to achieve state and the best correlated input-output matching simultaneously. I will show results from two-phase reservoir subject to a waterflooding plan with three wells (one injector and two producers). It is worthwhile noting that this method is a non-intrusive data-driven method since it does not need access to the reservoir simulation internal structure, and thus, it is easily applied to commercial reservoir simulators.