Reservoir description using a binary level set model

We consider the inverse problem of permeability estimation for two-phase flow in porous media. In the parameter estimation process we utilize both data from the wells (production data) and spatially distributed data (from timelapse seismic data). The problem is solved by approximating the permeability field by a piecewise constant function, where we allow the discontinuity curves to have arbitrary shape with some forced regularity. To achieve this, we have utilized level set functions to represent the permeability field and applied an additional total variation regularization. The optimization problem is solved by a variational augmented Lagrangian approach. A binary level set formulation is used to determine both the curves of discontinuities and the constant values for each region. We do not need any initial guess for the geometries of the discontinuities, only a reasonable guess of the constant levels is required.