Investigation of the efficiency of post-processing methods in solving problems of multi-phase filtration

Methods for post-processing of finite element solutions in the simulation of multiphase flows are considered. To simulate filtration processes, a special method based on the implicit calculation of the pressure field and the explicit calculation of saturations is used. Post-processing of flows is performed using two technologies - the balancing method and the projection method. The method of balancing the numerical flows of the mixture ensures the fulfillment of local conservation laws by finding corrections to the flows of the mixture calculated using the FEM. For the closeness of the modified mixture flows to the original numerical ones, the regularization parameters in the balancing method are calculated using the averaged unbalance. In the projection method, the balanced values of fluxes through the faces of finite elements are corrected by adding constant corrections (constant per element). Computational experiments were carried out on a test problem, a model of a field with a simple structure, and a model of a real oil field in the Republic of Tatarstan. When modeling problems with the appropriate correction of the known mixture flows on the faces of the wells, the solutions obtained using the balancing method and the projection method have little difference. The results of research on problems have shown that both technologies provide conservative solutions for which conservation laws are satisfied. At the same time, the use of the method of balancing the numerical flows of the mixture provides a higher accuracy than the projection method, when the flows in the wells are corrected in the post-processing process (that is, in fact, production/injection is emulated while maintaining a fixed pressure). The projection method can be improved by using the weight functions proposed for the balancing method. However, even in this case, the balancing method allows obtaining more accurate solutions.