Fast approximate adjoint and forward simulation for finding optimal rates and/or well placements for water flooding optimization.
Basic Ideas
couple MsMFEM for pressure and a flow-based coarsening for saturation for fast forward and adjoint simulation
for additional speed-up, compute coarse-grid communication mappings in a preprocessing step prior to the optimization loop
Features
Adjoint code developed for simulation of two-phase incompressible flow model on fine and coarse grids. Model speed-up through preprocessing applies both to forward and adjoint coarse models. For this simplified model, there is a natural relation between the adjoint variables on the fine and the coarse model through a dual coarse basis, which is similar, but not identical, to the forward coarse model basis. The methodology has been tested on rate-optimization for water flooding, and simple well-placement problems. Even coarse models with an upscaling factor of ~500 show good performance for optimization purposes.
Advantages
enables fast approximate simulations without initial full model run / snapshots
incorporates geological/geometrical features even for high degree of coarsening
only well-bases need to be updated in well-placement optimization
