A multicomponent flow model in deformable porous media

0503792 - MÚ 2020 GB eng J - Journal Article
Detmann, B. - Krejčí, Pavel
A multicomponent flow model in deformable porous media.
Mathematical Methods in the Applied Sciences. Roč. 42, č. 6 (2019), s. 1894-1906. ISSN 0170-4214. E-ISSN 1099-1476
Keywords : flows in porous media * hysteresisn * onlinear evolution equations
OECD category: Pure mathematics
Impact factor: 1.626, year: 2019
https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5482

We propose a model for multicomponent flow of immiscible fluids in a deformable porous medium accounting for capillary hysteresis. Oil, water, and air in the soil pores offer a typical example of a real situation occurring in practice. We state the problem within the formalism of continuum mechanics as a slow diffusion process in Lagrange coordinates. The balance laws for volumes, masses, and momentum lead to a degenerate parabolic PDE system. In the special case of a rigid solid matrix material and three fluid components, we prove under further technical assumptions that the system is mathematically well posed in a small neighborhood of an equilibrium.
Permanent Link: http://hdl.handle.net/11104/0295585