A multiscale streamline method for inversion of production data

We propose two improvements to a recent streamline method by Wang and Kovscek for inversion of production data. The key idea of the Wang–Kovseck method is to associate increments in fractional flow curves (water-cut) with breakthrough of individual streamlines and match breakthrough times of each streamline by adjusting the effective streamline permeabilities. The perturbations in effective streamline permeabilities are given by a linear system, which can be solved in a decoupled fashion under additional simplifying assumptions. Finally, the permeability perturbations defined along streamlines are mapped onto the underlying simulation grid, typically using a geostatistical algorithm to constrain the corresponding corrections to the geological model to prior geological data.Our first improvement is to model the flow in each streamline independently using real time, instead of using Dykstra–Parsons' algorithm for all streamlines connected to a producer–injector pair. This way, there is no coupling between individual streamlines, and permeability modifications can be obtained directly. Our approach uses less approximations, enables extension of the formulation to include gravity, and enables history matching of porosity. Three synthetic test cases show that this approach gives a better match and faster convergence.Our second point is to use a multiscale inversion process, where the reservoir parameters are matched on a hierarchy of recursively coarsened grids. Two synthetic test cases demonstrate that this approach captures the large-scale trends of the reservoir parameters more accurately. The proposed approach has proven robust in the sense that it is able to capture structures of the permeability field on the basis of limited information.