Compositional modeling of heterogeneous anisotropic naturally fractured oil reservoirs is a crucial issue when assessing the benefits of miscible and immiscible gas injection. This is especially true in large Middle East carbonate reservoirs. This paper presents an efficient methodology to model such reservoirs using a control-volume mixed finite-element technique (CVMFE). The formulation takes into account (1) the full permeability tensor without any compromise and (2) the local interaction of gravity, capillary and viscous forces between fracture and matrix. We give a clear account of the mathematical formulation so that the readers can utilize the method for writing their own computer code. The formulation pertains to a multi-component three-phase flow system using the dual-porosity model where capillary and gravity forces are accounted for, both on the local and global scales. The local scale is related to the fracture- matrix interaction, while the global scale represents the inter-well flow and flow migration across the field. The compositional formulation used (i.e. a volume-balance approach) is based on the fact that pore volume should be equal to the fluid volume in the control volume simulation grid. CVMFE method is used to discretize the flow equations for the pressure and velocity of each phase simultaneously. The CVMFE method provides a more accurate solution because the continuity of the velocity across the control volume boundaries is honored in spite of the fact that flow potential gradients are discontinuous in the heterogeneous anisotropic scenarios. After obtaining the pressure solution, we use a specific CVFE to calculate the molar compositions. Finally, a comparison of the mixed finite-element formulation with that of conventional finite-difference schemes is shown. Both methods emphasize the multi-scale issue of interaction of various reservoir forces and reservoir anisotropy which must be accounted for when planning a major gas injection project.
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