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Mathematical modeling and numerical simulation of multiphase multicomponent flow in porous media

Two-phase flow in porous media appears in many petroleum and environment engineering problems, like secondary and tertiary oil recovery, the disposal of radioactive waste, sequestration of CO2 etc. This thesis covers both mathematical and numerical analysis of this type of flows. Significant part of this thesis is devoted to the mathematical modeling and analysis of multiphase flows, precisely to a formulation of a two-phase, two-component model with exchange of the mass between the phases and to study the existence of weak solutions to this model. Specifically, flow of the fluid composed of water and gas with possible dissolution of the gas in water is considered. The model is completed with the assumption of the low solubility of the gas. Numerical simulation often represents the only viable approach to the mathematical modeling of multiphase flows due to the nonlinearity of equations governing these flows, as well as heterogeneity of the domains where these flows occur. Therefore, an important part of this the- sis is devoted to numerical analysis of the model describing immiscible compressible two-phase flow in porous media by the concept of the global pressure. More precisely, the convergence of a fully coupled fully implicit petroleum engineering finite volume method based on the cell-centered discretization is studied and the result is proved under standard assumptions. A similar proof was given in [76] with different techniques. As a groundwork for future research regarding compositional flow in this thesis we also consider the fractional flow formulation with the global pressure as a primary variable in the case of immiscible compressible flow. An efficient numerical method is obtained once again through a cell-centered finite volume discretization. The proposed method is verified on important 1D, 2D and 3D benchmark test cases modeling different scenarios of water-gas (hydrogen) flow in porous media. For the code development we have used the DuMux , programming framework for implementation of the models describing the flow and transport processes in porous media.

Porous media flow, two-phase immiscible compressible flow, compositional flow, persistent variables, low solubility, finite volume method, global pressure, discontinuous capillary pressure

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