Organizers: Marita Thomas, Timm John

Abstract Part B: 

Large-scale geodynamic behavior emerges from the interplay between deformation, rheology, and multiphase flow. This session addresses the modeling and mathematical methods with a focus on mechanical aspects of fluid-bearing rocks, including viscous, plastic, and brittle regimes of large scale deformations. This includes two-phase flow systems with dynamically evolving porosity-permeability relationships and feedbacks between compaction, dilation, and fluid pressure.

Speakers:

Simon Boisserée

Abstract:

In models of porous media flows, the porosity of the solid matrix is often treated as a static quantity. However, under certain circumstances, such as in soft sedimentary rocks or in magma flows, the porosity of the solid material can evolve under the influence of fluid pressure which can lead to the formation of solitary porosity waves and of higher-porosity channels. We consider a system of nonlinear PDEs for porosity and effective pressure, based on a poroviscoelastic model, which describes such phenomena. We briefly recall well-posedness results for this PDE problem. Then we turn to results on an adaptive numerical method, which is based on a fixed-point scheme inspired by the analysis, combined with a space-time least-squares formulation. This yields an appropriate treatment of discontinuities and enables spatially varying time steps, which are required for efficient approximations of the strongly spatially and temporally localized features of solutions. We numerically also show its quasi optimality. Furthermore, we show first results on a preconditioner for the space-time least squares method to allow for efficient iterative solvers also in higher dimensions. Lastly, we indicate the potential of the space-time approach to solve related inverse problems since it allows to calculate the solution of (time-reversed) adjoint equations in a memory-efficient manner.

Fan Cheng

Liudmila Khakimova

Abstract:

Metamorphic (de)volatilization reactions, such as hydration and dehydration, play a fundamental role in the evolution of rocks. Coupled with fluid transport, these reactions may localize into narrow reaction zones that propagate as sharp fronts, separating reacted and unreacted assemblages. Predicting the propagation of such fronts remains challenging because their characteristic time scales are not necessarily governed by hydraulic or chemical diffusion alone, but also by mass balance across the moving reaction boundary.

This contribution presents a front-tracking analytical framework for both pressure-driven and chemically driven metamorphic (de)volatilization processes in reactive fluid-rock systems. The reaction zone is treated as a sharp moving boundary, enabling Stefan-like analytical solutions for front propagation. The formulation covers both single-front systems and systems with multiple coupled fronts, such as dehydration followed by vaporization of the liberated pore water or cascades of metamorphic reactions propagating through distinct mineral assemblages. The resulting solutions predict an effective diffusivities that control front positions and the characteristic time scale of fluid-rock transformations.

The derived analytical solutions are applied to several geodynamically relevant hydration and dehydration systems. To demonstrate its generality, the fundamentals of pressure-driven reaction-front propagation are first illustrated using a simple brucite-periclase system, in which reaction progress and the associated density change are controlled by variations in fluid pressure. The framework is then extended to chemically driven reactions, in which mineral transformation is controlled by gradients in the concentration of a mobile fluid component. A chemically driven hydration example considers an initially porous forsterite-brucite assemblage exposed to a fluid composition that stabilizes antigorite and talc. Diffusive transport of dissolved components drives mineral replacement and generates a sharp propagating hydration front separating the initial and altered assemblages. This example demonstrates that chemically induced metamorphic reactions can be described using the same front-tracking analytical approach as pressure-driven (de)volatilization fronts.

The framework is also applied to published gypsum dehydration experiments by Fusseis et al. (2012) and Leclère et al. (2018). The analytical solutions provide an alternative interpretation of the observed transformation patterns as a system of coupled sharp fronts, in which dehydration-driven fluid release is followed by vaporization of the liberated pore water. Overall, the presented front-tracking framework enables quantitative prediction of front velocities, effective diffusivities, and transformation time scales in metamorphic fluid-rock systems driven by pressure perturbations, compositional perturbations, or their combination.

Fusseis, F., Schrank, C., Liu, J., Karrech, A., Llana-Funez, S., Xiao, X. and Regenauer-Lieb, K., 2012. Pore formation during dehydration of a polycrystalline gypsum sample observed and quantified in a time-series synchrotron X-ray micro-tomography experiment. Solid Earth, 3(1), pp.71-86.

Leclère, H., Faulkner, D., Llana-Fúnez, S., Bedford, J. and Wheeler, J., 2018. Reaction fronts, permeability and fluid pressure development during dehydration reactions. Earth and Planetary Science Letters, 496, pp.227-237.