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Interplay Between Diffusion Anisotropy and Mesh Skewness in Hybrid High-Order Schemes Read chapter Read first chapter

2020 | OriginalPaper | Chapter

Global Implicit Solver for Multiphase Multicomponent Flow in Porous Media with Multiple Gas Phases and General Reactions

Authors : Markus M. Knodel, Serge Kräutle, Peter Knabner

Published in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Publisher: Springer International Publishing

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Abstract

Multiphase multicomponent flow processes in porous media have to be considered to study the efficiency of mineral trapping mechanisms for climate killing gas storage in deep layers. Robust predictions ask for the solution of large nonlinear coupled systems of diffusion-advection-reaction (partial differential) equations containing equilibrium reactions. In that we elaborate the fully globally implicit Kräutle-Knabner PDE reduction method (cf. a former paper Kräutle and Knabner in Water Resour Res 43(3):W03429 [8]) for the case of multiple gas phases, we solve the arising Finite Element discretized/Finite Volume stabilized equations by means of a semismooth nested Newton solver. We present preliminary simulation results for the case of mutual injection of CO\(_2\), CH\(_4\) and H\(_2\)S into deep layers and investigate the arising mineral trapping scenario. Our methods are applicable also to other fields such as nuclear waste storage or oil recovery.

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previous chapter A Comparison of Consistent Discretizations for Elliptic Problems on Polyhedral Grids
next chapter Partitioned Coupling Schemes for Free-Flow and Porous-Media Applications with Sharp Interfaces
Footnotes
1
Besides the relations for molar and mass densities and (also capillary) pressures in g and \(\ell \) phase.
 
2
Note that the terminus “gas injection” in our context always means that the gas is injected in purely dissolute form, but switches into equilibrium state within each time step.
 
Literature
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Ahusborde, E., Amaziane, B., El Ossmani, M.: Improvement of numerical approximation of coupled multiphase multicomponent flow with reactive geochemical transport in porous media. Oil Gas Sci. Technol. Revue d’IFP Energies nouvelles 73, 73 (2018)
2.
Becker, B., Guo, B., Bandilla, K., Celia, M.A., Flemisch, B., Helmig, R.: An adaptive multiphysics model coupling vertical equilibrium and full multidimensions for multiphase flow in porous media. Water Resour. Res. 54(7), 4347–4360 (2018)CrossRef
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Brunner, F., Frank, F., Knabner, P.: FV upwind stabilization of FE discretizations for advection–diffusion problems. In: J. Fuhrmann, M. Ohlberger, C. Rohde (eds.) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, pp. 177–185. Springer International Publishing (2014)
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Brunner, F., Knabner, P.: A global implicit solver for miscible reactive multiphase multicomponent flow in porous media. Comput. Geosci. 23(1), 127–148 (2019)MathSciNetCrossRef
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Hoffmann, J., Kräutle, S., Knabner, P.: A parallel global-implicit 2-D solver for reactive transport problems in porous media based on a reduction scheme and its application to the MoMaS benchmark problem. Comput. Geosci. 14(3), 421–433 (2010)CrossRef
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Hoffmann, J., Kräutle, S., Knabner, P.: A general reduction scheme for reactive transport in porous media. Comput. Geosci. 16(4), 1081–1099 (2012)MathSciNetCrossRef
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Kräutle, S.: The semismooth newton method for multicomponent reactive transport with minerals. Adv. Water Resour. 34(1), 137–151 (2011)CrossRef
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Kräutle, S., Knabner, P.: A reduction scheme for coupled multicomponent transport-reaction problems in porous media: generalization to problems with heterogeneous equilibrium reactions. Water Resour. Res. 43(3), W03429 (2007)CrossRef
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Sin, I., Lagneau, V., Windt, L.D., Corvisier, J.: 2D simulation of natural gas reservoir by two-phase multicomponent reactive flow and transport—description of a benchmarking exercise. Math. Comput. Simul. 137, 431–447 (2017)MathSciNetCrossRef
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Spycher, N., Pruess, K.: CO\(_{2}\)–H\(_{2}\)O mixtures in the geological sequestration of CO\(_{2}\). ii. partitioning in chloride brines at 12100 \(^{\circ }\)C and up to 600 bar. Geochimica et Cosmochimica Acta 69(13), 3309 – 3320 (2005)
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Wieners, C.: A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing. Comput. Visual. Sci. 13(4), 161–175 (2010)MathSciNetCrossRef
Metadata
Title
Global Implicit Solver for Multiphase Multicomponent Flow in Porous Media with Multiple Gas Phases and General Reactions
Authors
Markus M. Knodel
Serge Kräutle
Peter Knabner
Copyright Year
2020
Book
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Print ISBN: 978-3-030-43650-6

Electronic ISBN: 978-3-030-43651-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-43651-3_56

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