University of Tabriz Computational Methods for Differential Equations 2345-3982 11 4 2023 07 01 Mathematical modeling of a nonlinear two-phase flow in a porous medium and the inflow of volatile oil to a well taking into account inertial effects 664 675 16068 10.22034/cmde.2023.48570.2032 EN Fikret Ahmadali Aliev Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan. Institute of Information Technologies of the National Academy of Sciences of Azerbaijan, Baku, Azerbaijan. Mahammad Jamalbayov Socar "Oil gas scientific research project" Institute, AZ1122, Hasan Bey Zardabi, Baku, Azerbaijan. Ilyas Hasanov Socar "Oil gas scientific research project" Institute, AZ1122, Hasan Bey Zardabi, Baku, Azerbaijan. Nazim Valiyev Socar Head Office Nazile Hajiyeva Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan. Journal Article 2021 10 26 This paper discusses a semi-analytic solution for the volatile oil influx into the well on the base of Forchheimer flow law. The solution is developed employing the concept of binary model for the two-phase petroleum hydrocarbon system in view of phase transformations and interphase mass transfer. Algorithms are developed for calculating the volatile oil reservoir key performance indicators by applying the material balance equations, which take into account the compaction behavior of rocks. A computer simulator for the volatile oil reservoir is modeled, proceeding from these algorithms. The inertial effects on the development process of a volatile oil reservoir, the rocks of which are exposed to elastic deformation, are studied by this simulator. In regard thereto, the reservoir development process is simulated in two variants in conformity with the constant depression: in the first case, it is assumed that the filtration occurs according to Darcy's law, while in the second one, the process is considered on the base of Forchheimer equation. A comparison of the results of these options made it possible to demonstrate the nature of the inertial effects on the volatile oil reservoir key performance indicators. https://cmde.tabrizu.ac.ir/article_16068_690fec16072c4d6c289b4948131598c4.pdf