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IAMCS Workshop in Large-Scale Inverse Problems and Uncertainty Quantification

Eduardo Gildin, Texas A&M University
Model Order Reduction in Porous Media Flow


The development of efficient numerical reservoir simulation is an essential step in devising advanced production optimization strategies and uncertainty quantification methods applied to porous media flow. In this case, a highly accurate and detailed description of the underlying models leads to a solution of a set of partial differential equations which, after discretization, induce dynamical systems of very large dimensions. In order to overcome the computational costs associated with these large-scale models, several forms of model-order reduction have been proposed in the literature. In porous media flow, two different approaches are used: (1) a "coarsening" of the discretization grid in a process called upscaling and multiscale methods; and (2) a reduction in the number of state variables (i.e., pressure and saturations) directly in a process called approximation of dynamical systems. Recently, the idea of combining both approaches has been proposed using the multiscale formulation combined with balanced truncation.

In this talk, I will describe the model reduction methods in a systems framework and will show their applicability to mitigate the computational cost in optimization and uncertainty quantification. Several methods will be discussed in the linear and nonlinear settings and the connections to multiscale methods will be proposed.