A Parallel Multi-Block/Multi-Physics Approach for Multi-Phase Flow in Porous Media

The main purpose of this dissertation is to investigate accurate and efficient numerical techniques for simulation of multi-phase/ multi-component flow and transport phenomena in porous media which are of major importance in the petroleum and environmental industries. We propose to emphasize a novel numerical methodology, which is called the multi-block algorithm. This algo-rithm is based on the decomposition of the simulation domain into multiple non-overlapping subdomains (blocks) according to the geological, geometric and physical / chemical properties. One then applies the most suitable grid, numerical scheme and physical model in each subdomain, so that the com-putational cost is reduced and accuracy is preserved. Across the interface of neighboring subdomains, the consistent primary variables and the continuity of the component mass fluxes are imposed in a weak sense. In this dissertation we first discuss the mathematical and numerical for-mulations of physical models, such as the implicit black-oil model, the implicit and IMPES two-phase hydrology models. We then formulate the multi-block black-oil model coupling different grids, which can be non-matching on the interface. In addition, we define the multi-model couplings; in particular, the coupling of the implicit and IMPES schemes for two-phase immiscible flow, and the coupling of the implicit three-phase black-oil model and the implicit two-phase hydrology model. Computational examples are presented to demonstrate the scalability of the multi-block / multi-model simulators over the traditional single-block / single-model simulators. Excellent agreements of the results be-tween these two approaches are shown. Parallel computation issues, especially the MPI (Message Passing Interface) multi-communicator implementation and model-based load balancing strategies for the parallelism of the multi-model problem are also considered. Summary of these results is presented in the last chapter.Petroleum and Geosystems Engineerin