• Navigation überspringen
  • Zur Navigation
  • Zum Seitenende
Organisationsmenü öffnen Organisationsmenü schließen
Department Mathematik
  • FAUZur zentralen FAU Website
  • de
  • en
  • UnivIS
  • StudOn
  • meincampus
  • CRIS
  • Hilfe im Notfall

Department Mathematik

Menu Menu schließen
  • Department
    • Lehrstühle und Professuren
    • Verwaltung
    • Förderverein
    • Rechnerbetreuung
    • Kontakt und Anreise
    • Aktuelles
    Portal Department Mathematik
  • Forschung
    • Forschungsprojekte
    • Publikationen
    • Preprint-Reihe Angewandte Mathematik
    Portal Forschung
  • Studium
    • Beratung
    • Vor dem Studium
    • Im Studium
    • International
    Portal Studium
  • Veranstaltungen
  1. Startseite
  2. Angewandte Mathematik 1
  3. Forschung
  4. Poröse Medien Gruppe
  5. Multicomponent reactive transport

Multicomponent reactive transport

Bereichsnavigation: Angewandte Mathematik 1
  • Lehre
    • Skripte
    • Lehrveranstaltungen
  • Mitarbeitende A – Z
    • Dr. Marco Bresciani
    • Prof. Dr. Günther Grün
    • Dr. Rufat Badal
    • Apratim Bhattacharya
    • Astrid Bigott
    • Prof. Dr. Martin Burger
    • Sebastian Czop
    • Lea Föcke
    • Prof. Dr. Manuel Friedrich
      • Lehrveranstaltungen
      • Publikationen
      • Forschung
    • Dr. Stephan Gärttner
    • Samira Kabri
    • Lorenz Klein (AG Grün)
    • Jonas Knoch
    • Prof. Dr. Serge Kräutle
      • Lehrveranstaltungen (aktuelles Semester)
      • Lehre, frühere Semester
      • Vorlesungsskripte u. Klausuren
      • Publications
      • Research Interests, Awards, etc.
      • CV + Trekking in Greenland
    • Prof. Dr. Wilhelm Merz
      • Forschung
      • Lehrbücher
    • Dr. Stefan Metzger (AG Grün)
    • PD Dr. Maria Neuss-Radu
      • Forschung PD Dr. Maria Neuss-Radu
      • Anne Petzold
    • Dr. Alexander Prechtel
      • Forschung
      • Lehre
    • Dr. Nadja Ray
    • Tim Roith
    • Dr. habil. Raphael Schulz
      • Forschung
    • Joscha Seutter
    • Dr. Daniel Tenbrinck
    • Cornelia Weber
    • Lukas Weigand
    • Simon Zech
  • Forschung
    • Übersicht von Habilitationen und Dissertationen
    • Poröse Medien Gruppe
      • Multicomponent reactive transport
      • Multiscale problems in life sciences
      • Geophysical flows
      • Multiphase flow in porous media
      • Emergence in porous media
      • Stochastic modelling of porous media
    • Projekte
    • Software
      • SiMRX
      • flexBox
    • Gruppe Prof. Dr. Grün
      • Forschungsinteressen
      • Prof. Dr. Günther Grün
      • Projekte
  • Veranstaltungen
    • 50 Jahre Angewandte Mathematik
    • Math meets reality
    • Mathematical Modeling of Biomedical Problems
    • PDEs meet uncertainty
    • Short Course: Stochastic Compactness and SPDEs
    • Workshop on Modelling, Analysis and Simulation of Processes in Porous Media
  • Ehemalige Mitarbeitende
    • Prof. Dr. Vadym Aizinger
      • Forschung
        • Software
    • Dr. Leon Bungert
    • Dr. Antonio Esposito
    • Dr. Tobias Elbinger
    • Dr. Hubertus Grillmeier (AG Grün)
      • Forschung
    • Dr. Alicja Kerschbaum
    • Prof. Dr. Peter Knabner
      • CV
      • Forschung
      • Für jedermann
        • Festkolloquium
        • Karpfenrede
        • Laudatio zur Ehrenpromotion an Herrn Prof. Dr. Rolf Rannacher
      • Lehre
        • Frühere Lehrveranstaltungen
        • Skripte zu Lehrveranstaltungen
        • Bücher
          • Lineare Algebra
          • Lineare Algebra (Auflage 2013)
          • Lineare Algebra: Aufgaben und Lösungen
          • Mathematik für Ingenieure und Naturwissenschaftler
          • Mathematik für Ingenieure und Naturwissenschaftler: Band 2
          • Endlich gelöst! Aufgaben zur Mathematik für Ingenieure und Naturwissenschaftler
          • Endlich gelöst! Aufgaben zur Mathematik für Ingenieure und Naturwissenschaftler (Band 2)
          • Numerik partieller Differentialgleichungen
          • Mathematische Modelle für Transport und Sorption gelöster Stoffe in porösen Medien
          • Mathematische Modellierung
          • Mit Mathe richtig anfangen
    • Dr. Markus Knodel
      • Forschung
    • Alice Lieu, PhD
    • Dr. Balthasar Reuter
      • Forschung
      • LateX-Vorlagen
      • Lehre
    • Dr. Andreas Rupp
      • Forschung
    • Dr. Doris Schneider
      • Conference Preview
      • Forschung
    • Dr. Oliver Sieber (AG Grün)
    • Dr. habil. Nicolae Suciu
    • Dr. Philipp Wacker
    • Dr. Patrick Weiß (AG Grün)
    • Dr. Philipp Werner

Multicomponent reactive transport

Multicomponent reactive transport in natural porous media
Participants: Serge Kräutle, Nadja Ray, Alexander Prechtel, Raphael Schulz, formerly Tobias Elbinger, Markus Knodel Fabian Brunner, Matthias Herz, Hari Mahato

The modeling of reactive transport problems in porous media leads to large systems consisting of partial and ordinary differential equations, coupled through source terms (e.g., arising from kinetic reactions) and through algebraic equations (coming from very fast, i.e., equilibrium reactions). If mineral precipitation-dissolution reactions are involved, then the system is additionally coupled to a complementarity problem.
Our work has the following main foci:

  1. The modelling of the processes (including mineral precipitation-dissolution, electrostatic forces, the influence of microbia),
  2. the development of efficient and robust numerical techniques for such systems, and
  3. the analysis of such systems, in particular the question of existence of global solutions, which is tackled with fixed point techniques in function spaces.

 

ad 2.:

2.1.: The efficient handling of variable non-Lipschitz size of mineral surface area in numerical simulations

The assumption, that on micro-scale, the mineral forms small hemispheres or cubes leads to the classical assumption that on macro-scale, the surface A of a mineral should depend like A=A(c)=c^(2/3) on the mineral amount c. This introduces a term in the model, which is not locally Lipschitz at c=0. This leads to non-uniquenss of solutions and to non-convergence of Newton’s method within numerical simulations. The classical way to deal with this difficulty is to force c>=epsilon for a prescribed epsilon>0, which is a modification of the original model. However, we propose to use a substitution c_neq := c^(1/3) instead which eliminates the non-Lipschitz term and leads to better convergence of Newton’s method.

For details see:

  • Kräutle, S., Hodai, J., Knabner, P.: Robust simulation of mineral precipitation-dissolution problems with variable mineral surface area, submitted 2019.  download preprint here

2.2.: Application of our cpu-time saving ‚Reduction Scheme‚ (within our software Richy2D/3D)

to the MoMaS Benchmark on Reactive Transport
See the following publications (among others):

  • Carrayrou, J., Hoffmann, J., Knabner, P., Kräutle, S., de Dieuleveult, C., Erhel, J., Van der Lee, J., Lagneau, V., Mayer, U., MacQuarrie, K.T.B.: Comparison of numerical methods for simulating strongly non-linear and heterogeneous reactive transport problems – the MoMaS benchmark case, Comput. Geosci. 14, p.483-502, 2010.
  • 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, p.421-433, 2010.

See here  for the description of the benchmark.
Figure: Chemistry: MoMaS Benchmark on multicomponent reactive transport. Geometry: our extension of the 2-D setting to 3-D: visualization of the tracer species; flow field computed with mixed finite elements.

Another Application: Carbon dioxide storage by mineral trapping

We consider a generic (simplified) set of chemical reactions that contains a principal mechanism which may take place in subsurface CO_2 storage sites. It consists of 3 mineral species, 3 sorption sites, 7 aqueous species, and 6 reactions, 3 of them at equilibrium.

Details see:

  • Kräutle, S.: The semismooth Newton method for multicomponent reactive transport with minerals, Advances Water Res. 34, p.137-151, 2011.

ad 3:

See the following publications (among others):

  • Kräutle, S.: Existence of global solutions of systems of reactive transport equations with mass action kinetics and species-dependent diffusion, submitted 2019.  download preprint here
  • Hoffmann J., Kräutle S., Knabner P.:
    Existence and uniqueness of a global solution for reactive transport with mineral precipitation-dissolution and aquatic reactions in porous media
    In: SIAM Journal on Mathematical Analysis 49 (2017), S. 4812-4837
    DOI: 10.1137/16M1109266
    URL: https://epubs.siam.org/doi/abs/10.1137/16M1109266
Friedrich-Alexander-Universität
Erlangen-Nürnberg

Schlossplatz 4
91054 Erlangen
  • Kontakt und Anreise
  • Interner Bereich
  • Mitarbeitende A-Z
  • Impressum
  • Datenschutz
  • DE/EN
Nach oben