Dynamics of rock dehydration on multiple scales

Background

This project deals with the dynamic formation of dehydration-related fluid flow structures within rocks. As a consequence of pressure and temperature increase, chemical reactions are induced by which the rock releases water that subsequently leads to formation of pores,channels and cracks. Field observations of natural occurrences along with thermodynamic calculations reveal that rock dehydration is characterized by three stages:

i) The initial formation of porosity caused by fluid liberation during dehydration reactions.
ii) The intermediate stages of fluid pooling and vein network formation.
iii) The final stages of fluid release from dehydrating system.

While the initial stage is primarly induced by chemical processes, the later stages are dominated by mechanical interaction of solid and fluid. In particular, an increase of fluid pressure causes mechanical stresses that ultimately lead to 'fast' fracturing. On the other side dehydration-associated mineral reactions are mainly driven by slow conductive heat transfer and occur on grain boundaries scales, hence on μm-scales. In contrast, fracture-related fluid release may occur within the time scale of seismic events and up to km-scales.

Sequence of images showing the dehydration effects on different length scales. In particular, chemical reactions and sequent vein networks are dominant phenomena on small scales (on the left), whereas large fractures become the main fluid liberation process on larger scales (on the right).

Objectives

The goal of this project is to decipher the hierarchical structure of the interacting processes on multiple time and length scales. We set up a prototype model, based on [1], featuring the coupling fluid and heat transport with chemical reactions and with deformation and fracturing of the solid in a thermodynamically consistent way.

As an input to this model we gather comprehensive field data on multiple scales from natural observations on serpentinite, a hydrous rock that has not experienced dehydration. This dataset will cover domain sizes ranging from μm², m² up to tens of m².

In parallel, we study the well-posedness of the protoype model. Modifications of this model will be obtained by incorporating scaling paramtersor by restricting certain processes to spatial, scale-dependent subdomains. Via Γ-convergence and homogenization methods the scaled protoype model will be mathematically rigorously carried over different scales. This will ultimately lead from the (modified) prototype model (root model) to hierarchical multiscale model that encodes the aggregated dynamics.

We implement the prototype model and its extensions in a numerical code. We will apply the numerical model to stimulate the dehydration network pattern formation using natural data. To validate our model, simulation output will be compared to observed network patterns developed within the same rock type that has undergone dehydration.

Project-related events

• GAMM 2021, 91st Annual GAMM Meeting, Kassel, March 15-19, 2021.  Section S14 "Applied Analysis" organized by D. KNEES(University of Kassel) and M. THOMAS.
• CRC 1114 "Scaling Cascades in Complex Systems", March 1-3, 2021. Mini symposium MSDI4: Modeling and analysis of geological fluid flows, organized by M. THOMAS and T. JOHN.
• Thematic Einstein Semester on Energy-based Mathematical Methods for Reactive Multiphase Flows (Online), winter term 2020/21.
• PDE 2019: Partial Differential Equations in Fluids and Solids, WIAS, September 9-13, 2019.

Publications

• A. ZAFFERI, M. THOMAS. Mathematical analysis of a porous-media model for rock-dehydration processes, Preprint, 2022.
• A. ZAFFERI, K. HUBER, D. PESCHKA, J. C. VRIJMOED, T. JOHN, M. THOMAS. A porous-media model for reactive fluid-rock interaction, FU Preprint, 2022. http://publications.imp.fu-berlin.de/2650/
• D. PESCHKA, A. ZAFFERI, L. HELTAI, M. THOMAS. Variational approach to fluid-structure interaction via GENERIC, in JNET, 2022. DOI 10.20347/WIAS.PREPRINT.2903
• K. HUBER, J. C. VRIJMOED, T. JOHN. Formation of olivine veins by reactive fluid flow in a dehydrating serpentinite, in: Geochemistry, Geophysics, Geosystems, 2022. DOI 10.1029/2021GC010267
• J. C. VRIJMOED, Y. Y. PODLADCHIKOV. Thermolab: a thermodynamics laboratory for non-linear transport processes in open systems, in: ESSOAr-Preprint, 2021. DOI 10.1002/essoar.10509513.1
• M. HEIDA, M. THOMAS. GENERIC for dissipative solids with bulk-interface interaction, accepted in Springer AWM Series, volume "Research in Mathematics of Material Science", 2021. DOI 10.20347/WIAS.PREPRINT.2872
• A. ZAFFERI, D. PESCHKA, M. THOMAS. GENERIC framework for reactive fluid flows, in: WIAS Preprint No. 2841, 2021. DOI 10.20347/WIAS.PREPRINT.2841
• M. THOMAS, S. TORNQUIST. Discrete approximation of dynamic phase-field fracture in visco-elastic materials, in: Discrete and Continuous Dynamical Systems - Series S14:1-60, 2021. DOI 10.3934/dcdss.2021067
• X. LIU, M. THOMAS, E. TITI. Well-posedness of Hilber's dynamical sea-ice model, in: WIAS Preprint No. 2833, 2021. DOI 10.20347/WIAS.PREPRINT.2833.
• E. IPOCOANA, A. ZAFFERI. Further regularity and uniqueness results for a non- isothermal Cahn-Hilliard equation, in: Communications on Pure and Applied Analysis, 20, Springer, 2021. DOI 10.3934/cpaa.2020289
• L. KAATZ, S. ZERTANI, E. MOULAS, T. JOHN, L. LABROUSSE, S, SCHMALHOLZ, T. ANDERSEN . Widening of hydrous shear zones during incipient eclogitization of metastable dry and rigid lower crust - Holsnoy, Western Norway, in: Tectonics,40(3):e2020TC006572, 2021. DOI 10.1029/2020TC006572
• A. BEINLICH, T. JOHN, J. C. VRIJMOED, M. TOMINAGA, T. MAGNA, Y. Y. PODLADCHIKOV .Instantaneous rock transformations in deep crust driven by reactive fluid flow, in: Nature Geoscience 13(4):307-311, 2020. DOI 10.1038/s41561-020-0554-9
• M. H. FARSHBAF SHAKER, M. THOMAS. Analysis of compressible Stokes-flow with degenerating and singular viscosity, in: WIAS Preprint No. 2786, 2020, DOI 10.20347/WIAS.PREPRINT.2786
• S. CHEN, R. C. HIN, T. JOHN, R. BROOKER, B. BRYAN, Y. NIU, T.ELLIOT. Molybdenum systematics of subducted crust record reactive fluid flow from underlying slab serpentine dehydration, in: Nature Communications, 10,4773, 2019. DOI 10.1038/s41467-019-12696-3
• D. PESCHKA, M. THOMAS, T. AHNERT A. MÜNCH, B. WAGNER. Gradient structures for flows of concentrated suspensions, in: Topics in Applied Analysis and Optimisation eds. Springer-CIM Series, pages 295-318, Springer, 2019. DOI 10.1007/978-3-030-33116-0_12

Invited Talks, Talks, Posters

• Talk: A. ZAFFERI, Analysis of a reactive-diffusive porous media model for rock dehydration processes, GAMM Annual meeting, University of Aachen, Germany, August 15-19, 2022.
• Talk: A. ZAFFERI, Thermodynamics of reaction-diffusion-induced rock dehydration processes, 16th Joint European Thermodynamics Conference (Hybrid event), Charles University Prague, Czech Republic, June 14-18, 2021.
• Talk: M. THOMAS, GENERIC structures with bulk-interface interaction, 16th Joint European Thermodynamics Conference (Hybrid event), Charles University Prague, Czech Republic, June 14-18, 2021.
• Talk: K. HUBER, Olivine enrichment in dehydration veins in serpentinites by reactive fluid flow. European Geosciences Union General Assembly, Online, April 19-30, 2021.
• Poster: A. ZAFFERI, Dynamics of rock dehydration on multiple scales. CRC 1114 Conference (Online), March 1-3, 2021.
• Invited Talk: A. ZAFFERI , Coupling of thermoviscoelastic solids and reactive flows via GENERIC, CRC 1114 Conference 2021 (Online), WIAS, Berlin, March 1-3, 2021.
• Poster: A. ZAFFERI, K. HUBER, Dynamics of rock dehydration. CRC 1114: Scaling Cascades in Complex Systems (SCCS Days, Online), December 2-4, 2020.
• Series of Talks: M. THOMAS, Thermodynamical modelling via energy and entropy functionals, Thematic Einstein Semester on Energy-based Mathematical Methods for Reactive Multiphase Flows: Student Compact Course "Variational Methods for Fluids and Solids" (Online), WIAS, Berlin, October 12-23, 2020.
• Invited Talk: A. ZAFFERI, Lagrangian-Eulerian reduction of GENERIC systems, Thematic Einstein Semester on Energy-based Mathematical Methods for Reactive Multiphase Flows: Student Compact Course "Variational Methods for Fluids and Solids" (Online), WIAS, Berlin, October 12-23, 2020.
• Invited Talk: M. THOMAS, Modeling and analysis of flows of concentrated suspensions Colloquium of the RTG 2339 "Interfaces, Complex Structures, and Singular limits" (Online), University of Regensburg, July 10, 2020.
• Invited Talk: M. THOMAS, GENERIC structures with bulk-interface interaction SFB910 Symposium "Energy based modeling, simulation and control", Technical Univesity of Berlin, October 25, 2019.
• Poster: K. HUBER, Dynamics of rock dehydration on multiple scales. 5th EGU Summer School, University of Padova, August 24-30, 2019.
• Invited Talk: M. THOMAS, Gradient stractures for flows of concentrated suspensionsThematic Minisymposium "Recent advances in understandig suspensions and granular media flow, 9th International Congress o Industrial and Applied Mathematics (ICIAM), University of Valencia, July 15-19, 2019.
• Poster: A. ZAFFERI, An approach to multi-phase flows in geosciences. Summer School "MURPHYS-HSFS 2019", Politecnico di Torino, June 19, 2019.
• Poster: K. HUBER, Serpentinite dehydration on multiple scales. Deutsche Mineralogiesche Gesellschaft (DMG) Sektionstreffen Petrologie und Geochemie, University of Heidelberg, May 24-25, 2019.
• Talk: M. THOMAS, Dynamics of rock dehydration on multiple scales, SCCS Days 2019 of the Collaborative Research Center - CRC1114, Free University of Berlin, May 21, 2019.
• Talk: A. ZAFFERI, Some regularity results for a non-isothermal Cahn-Hilliard model. 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 "Applied Analysis'', University of Wien, February 20, 2019.
• Poster: A. ZAFFERI, Flows of concentrated suspensions in geosciences. Berlin Dresden Prague Würzburg Workshop "Mathematics of Continuum Mechanics'', November 29 - 30, 2018.
• Talk: A. ZAFFERI, Regularity results for a thermodynamically consistent non-isothermal Cahn-Hilliard model. Summer School "Dissipative Dynamical Systems and Applications'', University of Modena, September 6, 2018.
• Invited Talk: M. THOMAS, Gradient structures for flow of concentrated suspensions. The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 18 "Emergence and Dynamics of Patterns in Nonlinear Partial Differential Equations and Related Fields", National Taiwan University, July 7, 2018.

Highlights

• L. KAATZ was awarded the Beate Mocek Prize for her achievements in her PhD project.

Guests

• M. PAVELKA (Charles University of Prague), in Material Modeling seminar. December 3, 2019.
• R. FALKENBERG (BAM), in Material Modeling seminar. May 7, 2019.

Preliminary work