Geodesic
Finite element modeling of multiphase flows with their balancing while setting the working pressure on wells during oil production
Numerical methods and programming, Tome 23 (2022) no. 1, pp. 60-74.

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Approaches to modeling multiphase flow in oil reservoir while setting the working pressure for the perforation zones of active wells are considered. The proposed numerical method is based on an implicit calculation of the pressure and an explicit recalculation of the phase saturations in the mesh cells at each time step. Description of the mathematical model, general computational scheme, finite element approximation of the pressure field are presented. To ensure conservation of the mixture flows, special method of balancing is used, and its algorithm is presented. The studies were carried out on the problem of the comparative project SPE-10, for which the calculation of flows for the perforated zones of wells with a set pressure was carried out using two approaches.
Keywords: multiphase flow in porous media, numerical 3D modeling of hydrocarbon reservoirs, finite element method, local flows conservation. 
@article{VMP_2022_23_1_a3,
     author = {A. S. Ovchinnikova and I. I. Patrushev and A. M. Grif and M. G. Persova and Yu. G. Soloveichik},
     title = {Finite element modeling of multiphase flows with their balancing while setting the working pressure on wells during oil production},
     journal = {Numerical methods and programming},
     pages = {60--74},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2022_23_1_a3/}
}
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A. S. Ovchinnikova; I. I. Patrushev; A. M. Grif; M. G. Persova; Yu. G. Soloveichik. Finite element modeling of multiphase flows with their balancing while setting the working pressure on wells during oil production. Numerical methods and programming, Tome 23 (2022) no. 1, pp. 60-74. http://geodesic.mathdoc.fr/item/VMP_2022_23_1_a3/