Heterogeneous geological features, such as fractures, faults, shale laminae, and cross-stratified beds, can exert significant effects on the flow performance. Accurate simulation of these complexities requires two model functions, i.e. abilities to accurately compute both pressure and velocity and to efficiently handle permeability tensor. In this paper, a flux continuous model incorporating full tensor permeability was developed for two -phase flow of immiscible and incompressible fluids. Flow systems were split into two subsystems of configurations, one for elliptic equation of global pressure and the other for parabolic equation of saturation, and solve both sequentially by means of the mixed finite volume element (MFVE) method.
Numerical examples of simulating flow in sand-shale system and fractured reservoirs are presented to prove the effectiveness and robustness of the model demonstrating particular suitability for handling high heterogeneities and accurately resolving steep pressure gradients. The MFVE method can accurately calculate the flow variables, and generate more realistic streamlines than the standard finite difference method for a discontinuous permeability field. Applications to naturally fractured reservoirs validate the use of full-tensor effective permeability for accurate and effective simulation.