In this thesis I develop and test new numerical methods for the numerical modelling of flow in highly heterogeneous and fractured reservoirs. We present the governing equations for immiscible two-phase fluid flow in a slightly compressible porous medium with capillary pressure. We discretize these equations using the node control volume finite element (NCVFE) method. The NCVFE method solves the pressure at the vertices of elements, and the control volumes are constructed around them. We present a numerical study of the method to test its accuracy in modelling multi-phase fluid flow in heterogeneous systems. Particularly, we study the performance of the method in domains with large contrasts in their material properties such as fractures, sealing or conductive faults, and highly heterogeneous reservoirs. We also present a study on the effects of petro-physical properties on the oil recovery for fractured reservoirs such as the permeability contrast between the fractured and matrix regions and the presence of capillary pressure in the matrix.
We then present a new numerical method to overcome the limitations of the current NCVFE approach. The new method is called the interface control volume finite element (ICVFE) method. The method drastically decreases the smearing effects observed in the NCVFE method, while being mass conservative and numerically consistent. The pressure is computed at the interfaces of elements, and the control volumes are constructed around them. Its accuracy and convergence are benchmarked using three-dimensional tetrahedron elements for various complex cases. We show ICVFE is more accurate for modelling multi-phase flow in highly heterogeneous and fractured reservoirs than NCVFE.
Furthermore, we present a new upstream mobility calculation method for NCVFE that improves the modelling for multi-phase fluid flow problems.