Heterogeneous Porous Media and Domain Decomposition Methods

The physics governing flow in porous media are character ized by localized phenomena taking place on scales that are small compared to the overall size of the reservoir. To obtain proper resolution, local refinement, both in space and time, seems to be promising. The approach is especially attractive within the framework of domain-decomposition, where the global solution is constructed from local computations on sub-domains where the resolution and even the entire solution strategy can be specially designed to match local properties of the model. The strategy is well suited for parallel computer architectures as well as integration into existing large scale simulators. In the present paper we will focus on heterogeneous rock properties. Core-samples, well-tests and production data provide information on widely different scales. To be useful in simulations, all the data have to be brought to the scale of the discrete blocks of the simulator. For this purpose, a stochastic approach based on assuming a multivariate lognormal distribution of permeability data will be investigated in the context of local grid refinement.