A level-set corrector to an adaptive multiscale permeability prediction

摘要

We consider the inverse problem of permeability estimation for two-phase porous-media flow. The novel approach is based on regularization by zona-tion, where the geometry and size of the regions are chosen adaptively during the optimization procedure. To achieve this, we have utilized level-set functions to represent the permeability. The available data are sparsely distributed in space; hence, it is reasonable to confine the estimation to coarse-scale structures. The level-set approach is able to alter the boundaries between regions of different permeability without strict restrictions on their shape; however, when the data are sparse, a reasonable initial guess for the permeability is required. For this task, we use adaptive multiscale permeability estimation, which has the potential of identifying main permeability variations. These are described by a piecewise constant function, where the constant values are attained on rectangular zones. In the current work, we develop a level-set corrector strategy, assuming adaptive multiscale permeability estimation as a predictor.