Speaker
Description
This seminar deals with two so far independent topics:
A nested Newton solver for multiphase multicomponent flow in porous media, and the generation of highly anisotropic grids for fracture representation.
In order to study the efficiency of the various forms of trapping including mineral
trapping scenarios for CO2 storage behavior in deep layers of porous media, highly
nonlinear coupled diffusion-advection-reaction partial differential equations (PDEs)
including kinetic and equilibrium reactions modeling the miscible multiphase
multicomponent flow have to be solved. We apply the globally fully implicit PDE
reduction method (PRM) developed by Kräutle and Knabner (Water Resour. Res.
43(3), 2007) which was extended to the case of one gas in the study of Brunner and
Knabner (Computational Geosciences 23:127-148, 2019). We extend the method to
the case of an arbitrary number of gases in gaseous phase, because CO2 is not the
only gas that threats the climate, and usually is accompanied by other climate killing gases. The application of the PRM leads to an equation system consisting of PDEs, ordinary differential equations, and algebraic equations. The Finite Element discretized / Finite Volume stabilized equations are separated into a local and a global system but nevertheless coupled by the resolution function and evaluated with the aid of a nested Newton solver, so our solver is fully global implicit. Published simulation results are presented.
Concerning the second topic:
Often, the fractures have a major role within the transport of components within porous media. However, due to their complex geometric structure requiring anisotropic meshes, numerical computations are quite demanding when it comes to the interplay of the rock matrix and the mostly comparably very thin fractures. Within former studies of some of ours, effective scenarios were considered where the aperture of the fracture was negligible compared to the surrounding matrix, for being averaged along the width within the PDE model of the transport equations. Still, this simplification cannot be applied in many cases, as there might be effects which cannot be resolved by means of a low dimensional approach. A major bottleneck to allow for full dimensional computations of the transport phenomena in the fractures is the expansion of the fractures into the fully 3D space, namely in the context of unstructured grids. This study presents the implementation of the ARTE algorithm to allow for highly unstructured grid generation with fractures. The application of the ARTE algorithm allows for an exact and valid expansion of the fractures into the 3D space. Work in progress is the computation of ground water flow upon such highly aniotropic fractured realistic networks of porous media.
Literature:
M. M. Knodel, S. Kräutle, and P. Knabner. “Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions.” Computational Geosciences 26.3 (2022), pp. 697–724. DOI: 10. 1007/s10596-022-10140-y.
M. M. Knodel, A. Nägel, D. Logashenko, H. Zhao, A. Gehrke, A. Schneider, and G. Wittum. “Expansion of finite sized fractures in grids for porous media with the ARTE algorithm.” In preparation (2026)
| Country | Germany |
|---|---|
| Green Housing & Porous Media Focused Abstracts | This abstract is related to Green Housing |
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