Modeling horizontal wells with the CVFA method in black oil reservoir simulations

This paper presents a new application of modeling horizontal wells in arbitrary directions (slanted wells) with the control volume function approximation (CVFA) method in reservoir simulation of the black oil model. The finite difference (FD) method is not flexible in representing horizontal wells whose directions are not along a Cartesian coordinate axis; furthermore, the rectangular grids used by the FD can cause the grid orientation effect. The standard finite element method does not conserve mass locally. In order to solve these problems, this paper uses a Voronoi gird as a basis grid to reduce the grid orientation effect and local grid refinement (LGR) and corner point deviation correction techniques to model accurately horizontal wells in arbitrary directions. To deal with the generated hybrid grids, the CVFA method is applied to discretizing the governing equations of the black oil model. The benchmark problem of the 7th comparative solution project and newly designed cases are used to verify the validity of our approach. The numerical experiment results show that the CVFA method can accurately model horizontal wells in arbitrary directions and is accurate and stable in modeling the horizontal wells where coning tendencies are strong. This method is also applied to designing development schemes of horizontal wells at field-scale to improve oil recovery.