|Project head:||Marita Thomas (WIAS), Timm John (FU)|
|Staff:||Andrea Zafferi (WIAS), Konstantin Huber (FU)|
|Funding period:||July 2018 - June 2022|
|Collaborators:||Dirk Peschka (WIAS), Johannes C. Vrijmoed (FU), Lisa Kaatz (FU)|
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.
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 , 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.
- D.PESCHKA, M. THOMAS, T. AHNERT A. MÜNCH, B. WAGNER. Gradient structures for flows of concentrated suspensions. WIAS Preprint No. 2543, (2018), in: Topics in Applied Analysis and Optimisation eds. Springer-CIM Series, Springer, 2019. DOI 10.2034/WIAS.PREPRINT.2543.
Invited Talks, Talks, Posters
- Invited Talk:M. THOMAS, GENERIC structures with bulk-interface interaction SFB910 Symposium "Energy based modeling, simulation and control", Technische Universität Berlin, October 25, 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), Universidad de Valencia, July 15-19, 2019.
- Talk:M. THOMAS, Dynamics of rock dehydration on multiple scales, SCCS Days 2019 of the Collaborative Research Center - CRC1114, Freie Universität Berlin, May 21, 2019.
- Poster: A. ZAFFERI, An approach to multi-phase flows in geosciences. Summer School "MURPHYS-HSFS 2019", Politecnico di Torino, June 19, 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, Department of Physics, Informatics and Mathematics, 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.
- M. PAVELKA (Charles University of Prague), in Material Modeling seminar. December 3, 2019.
- R. FALKENBERG (BAM), in Material Modeling seminar. May 7, 2019.