Resolving thermo-hydro-mechanical coupling: Spontaneous porous fluid and strain localisation

Localisation of deformation and flow is ubiquitously observed on Earth, spanning from sub-terraneous locations both in the deep interior and towards the shallow surface. Ductile strain localisation in tectonic processes or channelling and focusing of fluids in porous rocks are widely reported expressions of strain and flow localisation, governed by hydraulic, thermal and mechanical interactions. The intrinsic coupling of these different physical processes provides additional localisation mechanisms to well-established single-process physics. Models that address interactions between different physical processes must include non-linear feedbacks that may potentially trigger new and non-intuitive characteristic length and time scales. Accurately resolving this complex non-linear interplay resulting from coupled physics permits us to better understand the nature of multiphysics processes and to provide more accurate predictions on how, when and where to expect localisation. In many anthropogenic activities related to achieving a carbon-free energy transition, accurate predictions of mid-term to long-term behaviour for geosystems are vital. Engineered waste disposal solutions such as CO2 sequestration and nuclear waste deposits require coupled models in order to predict the complexities of the evolving system. However, there is a current lack in model capability to address the non-linear interactions resulting from multiphysics coupling. Available models often fail to reproduce major first-order field observations of localisation, mainly owing to poor coupling strategies and a lack of affordable resolution needed to resolve very local non-linear features, especially in three spatial dimensions. In this thesis, I address these issues using a supercomputing approach to resolve sufficiently high-resolution stain and flow localisation in non-linearly deforming porous media, relying on a thermodynamically consistent model formulation. The developed graphical processing unit-based parallel algorithms show close to linear weak scaling on the world’s third-largest supercomputer and are benchmarked against classical direct-iterative type solvers. The high-resolution computations are needed for the convergence of the calculations. The results confirm that a strong coupling between solid deformation, fluid flow and heat diffusion provides a viable mechanism for ‘chimney’ formation or strain localisation. Flow localisation in high-permeability chimneys provides efficient pathways for fast vertical fluid migration. By using model parameters relevant for sedimentary rocks, natural observations and their main characteristic features could be reproduced. In summary, this thesis provides an extensive study on hydro-mechanical interaction in fluid-saturated and non-linearly deforming porous rocks. Further, the predicted high-permeability pathways are vital to understand the formation of potential leakage pathways and are a prerequisite for reliable risk assessment in long-term waste storage. Finally, the developed solution strategy is successfully utilised to resolve strain localisation in thermo-mechanically coupled processes. -- La localisation de la déformation et des fluides est observée à l’échelle du Globe, allant des couches profondes jusqu’à la subsurface. Des phénomènes géologiques tels que la localisation de la déformation ductile ou la chenalisation des fluides dans les roches poreuses témoignent d’amplifications locales de la déformation et de la porosité et résultent d’interactions entre des processus hydrauliques, thermiques et mécaniques. Le couplage de ces divers processus physiques génère des rétroactions non-linéaires et aboutit à des nouvelles grandeurs caractéristiques non-triviales. Une résolution précise de ces interactions complexes permet de mieux comprendre la nature des processus multi-physiques et permet d’établir de meilleures prédictions quant à de possibles occurrences de localisation. Passablement d’activités anthropogéniques liées à la transition énergétique reposent sur des prédictions précises de l’évolution à long terme des géo-systèmes. La séquestration du CO2 ainsi que le stockage des déchets nucléaires requièrent l’utilisation de modèles couplés afin de prédire l’évolution des systèmes de confinement. Toutefois, les modèles actuels peinent à reproduire les observations de premier ordre, notamment les évidences de localisation des fluides et de la déformation. Les principales raisons sont le traitement des problèmes trop souvent effectué en deux dimensions, le manque de rigueur dans les stratégies de couplage entre les différents processus ainsi que l’utilisation de résolutions insuffisantes dans les modèles. Dans cette thèse, je propose une approche basée sur le calcul à haute performance permettant de résoudre avec des résolutions élevées les processus de localisation dans des milieux poreux déformables en utilisant des modèles thermodynamiquement consistants. Les algorithmes parallèles développés utilisent des processeurs graphiques disponibles entre autres sur le troisième plus performant superordinateur du monde et reportent un temps de calcul identique lorsque la taille du problème à résoudre grandi proportionnellement avec le nombre de ressources disponibles. Les résultats attestent de la convergence de la méthode et confirment le fait qu’un couplage important entre déformation, écoulement des fluides et diffusion de la chaleur permet la formation de chenaux à perméabilité élevée ainsi que la localisation de la déformation. Ces chenaux, ou drains, permettent l’écoulement focalisé ainsi qu’une migration verticale rapide des fluides. En prenant en compte les paramètres pétrophysiques caractéristiques des roches situées dans des bassins sédimentaires, ces écoulements préférentiels reproduisent les observations naturelles. La prédiction d’occurrence de chenaux à perméabilité élevée est vitale afin de mieux prévenir de potentiels risques de fuites et de fournir des solutions suˆres pour les générations futures en termes de stockage de déchets à risque. Pour conclure, cette thèse propose une étude extensive sur les interactions hydromécaniques dans des roches poreuses saturées avec des fluides. De manière analogue, la stratégie de solution développée a été appliquée pour étudier la localisation de la déformation ductile résultant d’un couplage thermomécanique

Quantifying Diapir Ascent Velocities in Power‐Law Viscous Rock Under Far‐Field Stress: Integrating Analytical Estimates, 3D Numerical Calculations and Geodynamic Applications

Diapirism is crucial for heat and mass transfer in many geodynamic processes. Understanding diapir ascent velocity is vital for assessing its significance in various geodynamic settings. Although analytical estimates exist for ascent velocities of diapirs in power-law viscous, stress weakening fluids, they lack validation through 3D numerical calculations. Here, we improve these estimates by incorporating combined linear and power-law viscous flow and validate them using 3D numerical calculations. We focus on a weak, buoyant sphere in a stress weakening fluid subjected to far-field horizontal simple shear. The ascent velocity depends on two stress ratios: (a) the ratio of buoyancy stress to characteristic stress, controlling the transition from linear to power-law viscous flow, and (b) the ratio of regional stress associated with far-field shearing to characteristic stress. Comparing analytical estimates with numerical calculations, we find analytical estimates are accurate within a factor of two. However, discrepancies arise due to the analytical assumption that deviatoric stresses around the diapir are comparable to buoyancy stresses. Numerical results reveal significantly smaller deviatoric stresses. As deviatoric stresses govern stress-dependent, power-law viscosity, analytical estimates tend to overestimate stress weakening. We introduce a shape factor to improve accuracy. Additionally, we determine characteristic stresses for representative mantle and lower crustal flow laws and discuss practical implications in natural diapirism, such as sediment diapirs in subduction zones, magmatic plutons or exhumation of ultra-high-pressure rocks. Our study enhances understanding of diapir ascent velocities and associated stress conditions, contributing to a thorough comprehension of diapiric processes in geology.ISSN:1525-202

Resolving Wave Propagation in Anisotropic Poroelastic Media Using Graphical Processing Units (GPUs)

Biot's equations describe the physics of hydromechanically coupled systems establishing the widely recognized theory of poroelasticity. This theory has a broad range of applications in Earth and biological sciences as well as in engineering. The numerical solution of Biot's equations is challenging because wave propagation and fluid pressure diffusion processes occur simultaneously but feature very different characteristic time scales. Analogous to geophysical data acquisition, high resolution and three dimensional numerical experiments lately redefined state of the art. Tackling high spatial and temporal resolution requires a high-performance computing approach. We developed a multi- graphical processing units (GPU) numerical application to resolve the anisotropic elastodynamic Biot's equations that relies on a conservative numerical scheme to simulate, in a few seconds, wave fields for spatial domains involving more than 1.5 billion grid cells. We present a comprehensive dimensional analysis reducing the number of material parameters needed for the numerical experiments from ten to four. Furthermore, the dimensional analysis emphasizes the key material parameters governing the physics of wave propagation in poroelastic media. We perform a dispersion analysis as function of dimensionless parameters leading to simple and transparent dispersion relations. We then benchmark our numerical solution against an analytical plane wave solution. Finally, we present several numerical modeling experiments, including a three-dimensional simulation of fluid injection into a poroelastic medium. We provide the Matlab, symbolic Maple, and GPU CUDA C routines to reproduce the main presented results. The high efficiency of our numerical implementation makes it readily usable to investigate three-dimensional and high-resolution scenarios of practical applications.ISSN:2169-9313ISSN:0148-0227ISSN:2169-935

Spontaneous formation of fluid escape pipes from subsurface reservoirs

Ubiquitous observations of channelised fluid flow in the form of pipes or chimney-like features in sedimentary sequences provide strong evidence for significant transient permeability-generation in the subsurface. Understanding the mechanisms and dynamics for spontaneous flow localisation into fluid conductive chimneys is vital for natural fluid migration and anthropogenic fluid and gas operations, and in waste sequestration. Yet no model exists that can predict how, when, or where these conduits form. Here we propose a physical mechanism and show that pipes and chimneys can form spontaneously through hydro-mechanical coupling between fluid flow and solid deformation. By resolving both fluid flow and shear deformation of the matrix in three dimensions, we predict fluid flux and matrix stress distribution over time. The pipes constitute efficient fluid pathways with permeability enhancement exceeding three orders of magnitude. We find that in essentially impermeable shale, vertical fluid migration rates in the high-permeability pipes or chimneys approach rates expected in permeable sandstones. This previously unidentified fluid focusing mechanism bridges the gap between observations and established conceptual models for overcoming and destroying assumed impermeable barriers. This mechanism therefore has a profound impact on assessing the evolution of leakage pathways in natural gas emissions, for reliable risk assessment for long-term subsurface waste storage, or CO2 sequestration

Ground penetrating radar in temperate ice: englacial water inclusions as limiting factor for data interpretation

Ground penetrating radar (GPR) has been extensively used in glaciology to infer glacier's ice thickness, liquid water content, water drainage pathways, and other properties. The interpretation of such GPR data is not always straightforward and for temperate glaciers, the signal is often affected by strong scattering and attenuation. It has often been suggested that such effects originate from englacial water inclusions, since water and ice have a large contrast in their di-electric permittivity. To investigate such effects quantitatively, we perform an extensive numerical modeling study of GPR signals. By exploring how different liquid water contents (LWC) and water-inclusions size affect the GPR signal, we show that their effects are much larger than the potential presence of a wet snowpack or a heterogeneous distribution of ice permittivity. In particularly, we show that the presence of such water inclusions is a necessary and sufficient condition for reproducing the typical characteristics of GPR data acquired in the field. Further, we find that for 25 MHz GPR antennas, a bulk LWC $\gtrsim$ 0.2%, associated with decimeters-scale water inclusions already limits bedrock detectability for ice thicknesses $\gtrsim 100$ m. Since these values are typical for Alpine glaciers, they clarify why the quality of GPR data is often poor in such environments

11th EGU Galileo Conference: Solid Earth and Geohazards in the Exascale Era Consensual Document

The 11th Galileo Conference in Barcelona (May 23-26, 2023) addressed Exascale computing challenges in geosciences. With 78 participants from 15 countries, it focused on European-based research but welcomed contributions from worldwide institutions. The conference had four sessions covering HPC applications, data workflows, computational geosciences, and EuroHPC infrastructures. It featured keynote presentations, poster sessions, and breakout sessions, including Master Classes for 22 Early Career Scientists supported by EGU. This document represents the consensus among participants, capturing outcomes from breakout sessions and acknowledging diverse opinions and approaches.The 11th Galileo Conference of the European Geosciences Union (EGU) focused on "Solid Earth and Geohazards in the Exascale Era." This abstract presents the main outcomes and conclusions from the conference breakout sessions, which aimed to provide recommendations for the future of solid earth research. The discussions highlighted the challenges and opportunities associated with high-performance computing (HPC) in solid earth sciences. The key findings include the need for collaboration between computer scientists and solid earth domain-specific scientists, the importance of portability software layers for different hardware architectures, the adoption of programming models for easier development and deployment of applications, the necessity of HPC training at all career stages, the improvement of accessibility and authentication mechanisms for European machines, and the readiness of urgent computing services for natural catastrophes. The conference also emphasized the significance of sustainable funding, software engineering best practices, and the development of modular and interoperable codes and workflows. Overall, the conference provided insights into the current status of computational solid earth research and offered recommendations for future advancements in the field.European Geosciences Union (EGU), the EuroHPC Center of Excellence for Exascale in Solid Earth (ChEESE) under Grant Agreement No 101093038 (https://cheese2.eu), and the European Union's Next Generation/PRTR Program through grant PCI2022-134973-2.Peer reviewe

PTsolvers/SphericalStokes: SphericalStokes.jl 1.0.0

<h1>Release notes</h1> <ul> <li>Add codes for diaper paper (@LilouMa)</li> <li>Add code for plateau paper draft (@LilouMa)</li> <li>Refactor repo structure (@luraess)</li> </ul&gt

PTsolvers/PseudoTransientHMC.jl: PseudoTransientHMC.jl 0.3.0

Release notes Include latest codes Refactor repo for 2023 publication Update tests include make-based visualisatio

Resolving hydro-mechanical coupling in two and three dimensions

International audienceEvidences of localised flow patterns are ubiquitous on Earth and drive a range of geo-processes across all scales.Classical Dacian models predict a diffusive behaviour leading to spreading and delocalisation, observations rathersuggest focusing of porous fluids within fingers, veins or channels.We aim to investigate numerically a physical mechanism, the de-compaction weakening, which leads to theformation and propagation of localised flow pathways in fluid saturated porous media. We use high-resolutiontwo- and three-dimensional numerical modelling to solve nonlinear Darcian porous flow in a viscously deformingmatrix using a nonlinear Stokes flow. In order to accurately capture strong localisation in space and time, westreamline matrix-free Pseudo-Transient approaches on graphical processing units. The Pseudo-Transient routinesconverge towards identical solutions compared to Direct-Iterative solving strategies.We discuss performance benefits of the matrix-free method on modern parallel hardware. We show thathigh porosity channels may be a dynamic and natural outcome of sufficiently resolved hydro-mechanical couplingand de-compaction weakening. In addition, we systematically study the channel propagation velocity as a functionof bulk and shear viscosity ratios.We conclude on the viability of buoyancy driven fluid migration at rates up to the three orders of magnitudehigher than expected by pure Darcian flow regimes. We provide both the two-dimensional MATLABbased Direct-Iterative and Pseudo-Transient routines for full reproducibility and suggest our model setup as akey benchmark case to validate implementation of hydro-mechanical coupling in two- and three-dimensionalnumerical code