Flow Balancing in FEM Modelling of Multi-Phase Flow in Porous Media

The paper considers the method of balancing the flows, which are obtained by the finite element solution, for modeling the multi-phase flow in porous media. The method is based on the selection of the corrective components which satisfy the minimum of functional of the balance of mixture volumes with the use of regularization. The studies of this method application have been performed by the problem which emulates the performance of exploitation and a group of injection wells. The numerical results show that the application of the proposed method ensures the conservation of mass of substances of filtering mixture, makes it possible to use the finite element mesh with bigger cells, and, consequently, to provide the solution of the problem with the required accuracy and low computational cost.