To main content

Adjoint Multiscale Mixed Finite Elements


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 pressure 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 those 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.  


Academic chapter/article/Conference paper





  • SINTEF Digital / Mathematics and Cybernetics




Society of Petroleum Engineers


SPE Reservoir Simulation Symposium, 2-4 February 2009, The Woodlands, Texas



View this publication at Cristin