| 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 algorithm 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 computational 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 formulations 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 between 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. |
