Nonlinear Viscoelastic Compaction in Sedimentary Basins

In the mathematical modelling of sediment compaction and porous media flow, the rheological behaviour of sediments is typically modelled in terms of a nonlinear relationship between effective pressure $p_e$ and porosity $\phi$, that is $p_e=p_e(\phi)$. The compaction law is essentially a poroelastic one. However, viscous compaction due to pressure solution becomes important at larger depths and causes this relationship to become more akin to a viscous rheology. A generalised viscoelastic compaction model of Maxwell type is formulated, and different styles of nonlinear behaviour are asymptotically analysed and compared in this paper

3D FINITE ELEMENT MODEL FOR THERMO-POROMECHANICAL DEFORMATION IN SEDIMENTARY BASINS

Sedimentary basins form when an appreciable amount of sediments are deposited along geological time and transformed into rock through natural phenomena known as diagenesis. Compaction of sediments, fluid and thermal flows are fundamental coupled processes in sedimentary basin modelling. Purely mechanical phenomena prevail in the upper layers involving pore fluid expulsion and rearrangement of solid particles, while chemomechanical compaction resulting from Intergranular Pressure-Solution (IPS) dominates for deeper burial as stress and temperature increase. The thermal evolution of the basin may substantially affect both processes as heat modifies fluid viscosity and physicochemical properties of minerals, thus affecting fluid flow and mineral stability. The aim of the present contribution is to provide a comprehensive 3D framework for constitutive and numerical modelling of thermo-poro-mechanical deformation during diagenesis. Purely mechanical and chemo-mechanical deformations are respectively modelled by means of poroplastic and poroviscoplastic models. The numerical simulations are performed through the finite element method with a shared memory multiprocessing interface. The sedimentary basin is modelled as a fully saturated thermo-poro-elasto-visco-plastic material undergoing large strains. Special attention is given to temperature effects on the deformation history of the basin

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

Tensor compaction of porous rocks: theory and experimental verification

Compaction in sedimentary basins has been traditionally regarded as a one-dimensional process that ignores inelastic deformation in directions orthogonal to the active load. This study presents new experiments with sandstone demonstrating the role of three-dimensional inelastic compaction in cyclic true triaxial compression. The experiments were carried out on the basis of a triaxial independent loading test system in the Laboratory of Geomechanics of the Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Science. The elastic moduli of the material were estimated from the stress-strain curves and the elastic deformations of the sample in each of the three directions were determined. Subtracting the elastic component from the total deformation allowed to show that inelastic compaction of the sandstone is observed in the direction of active loading, whereas in the orthogonal directions there is a expansion of the material. To describe the three-dimensional nature of the compaction, a generalization of Athy law to the tensor case is proposed, taking into account the role of the stress deviator. The compaction tensor and the kinetic equation to describe the evolution of inelastic deformation, starting from the moment of the load application are introduced. On the basis of experiments on cyclic multiaxial compression of sandstone, the identification and verification of the constructed model of tensor compaction were carried out. The possibility of not only qualitative, but also quantitative description of changes in inelastic deformation under complex cyclic triaxial compression is shown

Stress and pore pressure histories in complex tectonic settings predicted with coupled geomechanical-fluid flow models

Most of the methods currently used for pore pressure prediction in sedimentary basins assume one dimensional compaction based on relationships between vertical effective stress and porosity. These methods may be inaccurate in complex tectonic regimes where stress tensors are variable. Modelling approaches for compaction adopted within the geotechnical field account for both the full three dimensional stress tensor and the stress history. In this paper a coupled geomechanical-fluid flow model is used, along with an advanced version of the Cam-Clay constitutive model, to investigate stress,pore pressure and porosity in a Gulf of Mexico style mini-basin bounded by salt subjected to lateral deformation. The modelled structure consists of two depocentres separated by a salt diapir. 20% of horizontal shortening synchronous to basin sedimentation is imposed. An additional model accounting solely for the overpressure generated due to 1D disequilibrium compaction is also defined. The predicted deformation regime in the two depocentres of the mini-basin is one of tectonic lateral compression, in which the horizontal effective stress is higher than the vertical effective stress. In contrast, sediments above the central salt diapir show lateral extension and tectonic vertical compaction due to the rise of the diapir. Compared to the 1D model, the horizontal shortening in the mini-basin increases the predicted present-day overpressure by 50%, from 20 MPa to 30 MPa. The porosities predicted by the mini-basin models are used to perform 1D, porosity-based pore pressure predictions. The 1D method underestimated overpressure by up to 6 MPa at 3400 m depth (26% of the total overpressure) in the well located at the basin depocentre and up to 3 MPa at 1900 m depth (34% of the total overpressure) in the well located above the salt diapir. The results show how 2D/3D methods are required to accurately predict overpressure in regions in which tectonic stresses are important

Flow-induced compaction of a deformable porous medium.

Fluid flowing through a deformable porous medium imparts viscous drag on the solid matrix, causing it to deform. This effect is investigated theoretically and experimentally in a one-dimensional configuration. The experiments consist of the downwards flow of water through a saturated pack of small, soft, hydrogel spheres, driven by a pressure head that can be increased or decreased. As the pressure head is increased, the effective permeability of the medium decreases and, in contrast to flow through a rigid medium, the flux of water is found to increase towards a finite upper bound such that it becomes insensitive to changes in the pressure head. Measurements of the internal deformation, extracted by particle tracking, show that the medium compacts differentially, with the porosity being lower at the base than at the upper free surface. A general theoretical model is derived, and the predictions of the model give good agreement with experimental measurements from a series of experiments in which the applied pressure head is sequentially increased. However, contrary to theory, all the experimental results display a distinct and repeatable hysteresis: the flux through the material for a particular applied pressure drop is appreciably lower when the pressure has been decreased to that value compared to when it has been increased to the same value.D.R.H. was supported by a Killam Postdoctoral Fellowship and a Research Fellowship at Gonville and Caius College, Cambridge. During the experimental part of this project, J.S.N. was supported by the division of Engineering Science, University of Toronto. J.A.N. is partly supported by a Royal Society University Research Fellowship.This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevE.93.02311

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