The objective of this thesis is to develop a multiscale finite volume method on unstructured grids for simulation of incompressible two phase flow in two-dimensional porous media. In this research, methods are presented to overcome challenges posed by the extension of multiscale finite volume method to unstructured grids. The main approach of this thesis is to generate primal and dual coarse grids as the main challenge in extension of multiscale finite volume method to unstructured grids. New and efficient algorithms for generating multiscale unstructured grids compatible with multiscale finite volume method are designed and presented. For partitioning unstructured grids and generating primal coarse grid, a new algorithm based on multilevel paradigm is presented. To improve the partition quality at each level, a robust algorithm based on tabu search is developed. To generate a dual coarse grid on the primal coarse grid, an algorithm based on geometrical information of the fine scale grid is designed. The presented algorithms for generating primal and dual coarse grids are employed for simulation of incompressible two phase flow in porous media. To improve the multiscale results of unstructured grids, the multiscale finite volume operator is employed as a preconditioner for the Richardson iterative scheme. To reduce the error of multiscale finite volume method and remove non-physical pressure peaks in highly heterogeneous permeability field, algorithms for generating adaptive unstructured coarse grids based on local changes in permeability are presented. The adaptive primal coarse grid is generated based on local movement of fine scale cells. In this algorithm, fine scale cells located on the boundaries of primal coarse cells are moved such that the placement of cells with very low and very high permeability values is avoided. The adaptive dual coarse grid algorithm is generated based on Dijkstra algorithm. In this algorithm, dual coarse cells are generated such that strong variation of permeability along their boundaries is prevented. Numerical simulation results for highly heterogeneous permeability fields show that the unstructured coarse grids have considerable effects on the accuracy of the multiscale finite volume method.

Three dimensional grid generation and flow simulation in hydrocarbon resercoirs contained discrete fractures have been presented in this thesis. A novel algorithm for discretization of hydrocarbon reservoirs with complex geometries is presented that considers the effect of geological and geometrical factors within grid refinement procedure. Grid refinement procedure is based on point insertion and cell subdivision methods that has been applied for first time on hydrocarbon reservoir grid refinement. This grid refinement is able to adapte grid based on geological features and geometrical parameters. Distribution of grid vertices has automatically been controlled around well locations and fracture geometries. Geometry adaptation of three dimensional unstructured grids based on underground contours map is one more abilities of the presented algorithm. Different algorithms of grid quality improvement included topologic and non-topologic techniques have been used in grid generation algorithm. Topological algorithms are 2→2, 2→3, 3→2 and 4→4 flips. The performance of the presented grid generation algorithm has been studied with the geometry discretization of the Rag-e-Sefid hydrocarbon reservoir and the Masjid-e-Soleiman fractured reservoir. Finally, the computationality of the generated grids has been tested using water and oil two-phase flow solution based on discrete-fracture simulation model and implicite-pressure-explicite-saturation method. Flow simulation in five-spot reservoir problems, effect of flow fingering near production well, flow simulation in fractured reservoirs, effect of fracture on flow transport, effect of fracture on production well performance and effect of capillary pressure on oil production are among flow simulation results. The obtained numerical results were identical with Eclips simulation results and published data.