Adjoint Multiscale Mixed Finite Elements (conf)
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We develop an adjoint model for a simulator consisting of a multiscale pressure solver and a saturation solver that works on flow adapted grids. The multiscale method solves the pressures on a coarse grid that is close to uniform in index space and incorporates fine-grid effects through numerically computed basis functions. The transport solver works on a coarse grid adapted by a fine-grid velocity field obtained by the multiscale solver. Both the multiscale solver for pressure and the flow-based coarsening approach for transport have earlier shown the ability to produce accurate results for high degree of coarsening. We present results for a complex realistic model to demonstrate that control settings based on optimization of our multiscale flow-based model closely matches or even outperforms th9ose found by using a fine-grid model. For additional speed-up, we develop mappings used for rapid system updates during the time-stepping procedure. As a result, no fine-grid quantities are required during simulations and all fine grid computations (multiscale basis functions, generation of coarse transport grid and coarse mappings) become a preprocessing step. The combined methodology enables optimization of water flooding on a complex model with 45,000 grid-cells in a few minutes.
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