A Multi-scale Framework for Modeling Instabilities in Fluid-Infiltrated Porous Solids (original) (raw)
Many natural and man-made materials, such as sand, rock, concrete and bone, are multi-constituent, fluid-infiltrated porous solids. The failure of such materials is important for various engineering applications, such as CO2 sequestration, energy storage and retrieval and aquifer management as well as many other geotechnical engineering problems aimed to prevent catastrophic failures due to pore pressure build-up. This dissertation investigates two mechanical aspects of fluid infiltrated porous media, i.e., the predictions of diffuse and localized failures of porous media and the heterogeneous microstructures developed after failures. We define failures as material conditions in which homogeneous deformation becomes unattainable. To detect instabilities, a critical state plasticity model for sand is implemented. By seeking bifurcation points of the incremental, linearized constitutive responses, we establish local criteria that detect onsets of drained soil collapse, static liquefaction and formation of deformation bands under locally drained and undrained conditions. Fully undrained and drained triaxial compression simulations are conducted and the stability of the numerical specimens are assessed via a perturbation method. To characterize deformation modes after failures, a multi-scale framework is designed to determine microstructural attributes from pore space extracted from X-ray tomographic images and improve the accuracy and speed of a multi-scale lattice Boltzmann/finite element hierarchical flow simulation algorithm. By comparing the microstructural attributes and macroscopic permeabilities inside and outside a compaction band formed in Aztec Sandstone, our numerical study reveals that elimination of connected pore space and increased tortuosity are the main causes that compaction bands are flow barriers.
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The propagation of compaction bands in porous rocks based on breakage mechanics
We analyze the propagation of compaction bands in high porosity sandstones using a constitutive model based on breakage mechanics theory. This analysis follows the work by Das et al. [2011] on the initiation of compaction bands employing the same theory. In both studies, the theory exploits the links between the stresses and strains, and the micromechanics of grain crushing and pore collapse, giving the derived constitutive models advantages over previous models. In the current post localization analysis, the bifurcation instability of the continuum model is suppressed by the use of a rate-dependent regularization. This allows us to perform a series of finite element analyses of drained triaxial tests on porous sandstone specimens. The obtained numerical results compare well with experimental counterparts, in terms of both the initiation and propagation of compaction bands, besides the macroscopic stress-strain responses. On this basis, a parametric study is carried out to explore the effects of loading rate, degree of structural imperfections, and confining pressure on the propagation of compaction bands.
A theoritical approach to the study of compaction bands in porous rocks
2011
The formation and propagation of compaction bands in high porosity sandstones is theoretically investigated in this paper using a new constitutive model based on the recently developed continuum breakage mechanics theory [1,2]. This model possesses a micromechanics-based link between the evolving grain size distribution (gsd) and the macroscopic stress strain relationship, through an internal variable called Breakage. This is an advanced feature over many existing plasticity based models in the literature, helping to faithfully track the evolving gsd and its related physics (e.g. permeability reduction). A localization analysis based on the acoustic tensor [3] is performed to determine both the onset and orientation of compaction bands due to grain crushing. It is shown that the model used is able to capture well both the material behaviour and formation of compaction band experimentally observed. An enhancement using rate-dependent regularization is applied to the model to deal with instability issues in the analysis of Boundary Value Problems. Based on the regularised model, the formation and propagation of compaction bands due to grain crushing is analysed through a numerical experiment on a porous rock specimen under triaxial loading condition. Good agreement between numerical predictions and experimental observations demonstrates the capability of the new model.
Tomographic images taken inside and outside a compaction band in a field specimen of Aztec sandstone are analyzed by using numerical methods such as graph theory, level sets, and hybrid lattice Boltzmann/finite element techniques. The results reveal approximately an order of magnitude permeability reduction within the compaction band. This is less than the several orders of magnitude reduction measured from hydraulic experiments on compaction bands formed in laboratory experiments and about one order of magnitude less than inferences from two-dimensional images of Aztec sandstone. Geometrical analysis concludes that the elimination of connected pore space and increased tortuosities due to the porosity decrease are the major factors contributing to the permeability reduction. In addition, the multiscale flow simulations also indicate that permeability is fairly isotropic inside and outside the compaction band.
Mechanical Compaction of Porous Sandstone
Oil & Gas Science and Technology
Compaction mécanique des grès poreux -Pour de nombreux problèmes de tectonique et d'ingénierie de réservoir, la capacité à prévoir à la fois la fréquence, l'ampleur de la déformation inélastique et les ruptures repose sur une compréhension fondamentale de la phénoménologie et de la micromécanique de compaction dans les roches-réservoirs. Cet article présente les résultats de recherches récentes sur la compaction mécanique des grès poreux. On insiste plus particulièrement sur la synthèse des données de laboratoire, la caractérisation microstructurale quantitative de l'endommagement, ainsi que sur les modèles théoriques basés sur un contact élastique et sur la mécanique de la rupture. Les attributs mécaniques de la compaction sur des échantillons initialement secs et saturés ont été étudiés sous des chargements hydrostatiques et non hydrostatiques dans une large gamme de pression. Les sujets spécifiques étudiés ici incluent : la comparaison des données d'émission acoustique et mécanique avec une théorie de la plasticité ; le contrôle microstructural du début et du développement de la compaction ; l'écrouissage et l'évolution spatiale de l'endommagement lors de la compaction ; enfin, l'effet affaiblissant de l'eau sur le seuil de compaction et l'évolution de la porosité.
Permeability evolution during progressive development of deformation bands in porous sandstones
2003
Triaxial deformation experiments were carried out on large (0.1 m) diameter cores of a porous sandstone in order to investigate the evolution of bulk sample permeability as a function of axial strain and effective confining pressure. The log permeability of each sample evolved via three stages: (1) a linear decrease prior to sample failure associated with poroelastic compaction, (2) a transient increase associated with dynamic stress drop, and (3) a systematic quasi-static decrease associated with progressive formation of new deformation bands with increasing inelastic axial strain. A quantitative model for permeability evolution with increasing inelastic axial strain is used to analyze the permeability data in the postfailure stage. The model explicitly accounts for the observed fault zone geometry, allowing the permeability of individual deformation bands to be estimated from measured bulk parameters. In a test of the model for Clashach sandstone, the parameters vary systematically with confining pressure and define a simple constitutive rule for bulk permeability of the sample as a function of inelastic axial strain and effective confining pressure. The parameters may thus be useful in predicting fault permeability and sealing potential as a function of burial depth and fault displacement.
Tectonophysics, 2011
The study of localized deformation in porous sandstones at the laboratory scale can yield valuable insights into the internal structures and mechanisms of shear zones and compaction bands that might impact on flow at a reservoir scale. Herein, we report results of a laboratory study of shear and compaction band formation in a porous sandstone using a range of full-field experimental techniques: acoustic emissions, ultrasonic tomography, X-ray tomography, and 3D volumetric digital image correlation, plus thin section and Scanning Electron Microscope observations. The two main mechanisms involved in shear and compaction band formation, grain breakage (damage) and porosity reduction (compaction), are both well captured by the combination of all these laboratory techniques. The combined use of these techniques demonstrated the processes of shear and compaction band generation and the associated strain components that developed in the laboratory, and potentially also increased understanding of the naturally developed equivalents. The physical mechanisms of shear and compaction involved seem to be similar, but at the laboratory scale they show differences in the proportions and the order of occurrence in time.
Porous rock deformation and fluid flow — numerical FE-simulation of the coupled system
1989
Das PMnomen der elastischen Kompaktion ist durch die Wechselwirkung zwischen deformierender Gesteinsmatrix und Fliissigkeitsbewegung bei entsprechenden mechanischen Bedingungen charakterisiert. Die grundlegende Theorie hierzu wurde yon Biot entwickelt. Um dem druck-abh~ingigen, tensorMlen Charakter der Permeabilifiit fiir eine geeignete Beschreibung der Wechselwirkung gerecht zu werden, ist eine Erweiterung der Biot'schen Theorie notwendig.
Grain crushing and pore collapse are the principal micromechanisms controlling the physics of compaction bands in porous rocks. Several constitutive models have been previously used to predict the formation and propagation of these bands. However, they do not account directly for the physical processes of grain crushing and pore collapse. The parameters of these previous models were mostly tuned to match the predictions of compaction localization; this was usually done without validating whether the assigned parameters agree with the full constitutive behavior of the material. In this study a micromechanics-based constitutive model capable of tracking the evolving grain size distribution due to grain crushing is formulated and used for a theoretical analysis of compaction band formation in porous rocks. Linkage of the internal variables to grain crushing enables us to capture both the material behavior and the evolving grain size distribution. On this basis, we show that the model correctly predicts the formation and orientation of compaction bands experimentally observed in typical high-porosity sandstones. Furthermore, the connections between the internal variables and their underlying micromechanisms allow us to illustrate the significance of the grain size distribution and pore collapse on the formation of compaction bands.
Thai Rock Conference, 2009
The mechanical and hydraulic behavior of a fractured porous media is described using the dual-porosity concept. A parameter for compressibility couples the response between the stress and fluid pressure. Fluid exchange between the matrix or the porous blocks and the fractures is governed by a coupling parameter which is a function of the fracture geometry. The derived equations are presented as a finite element statement which is then used to simulate the mechanical and fluid flow behavior of the Phu Thok Formation as a case study. Parametric studies show that the fracture spacing is a sensitive parameter for the Phu Thok sandstone. A simulation of excessive groundwater extraction above the safe yield shows closing of fractures in the y direction. 1 INTRODUCTION Fractured porous rock mass is one of many complex geological attributes that is of high interest. Due to its high permeability mostly contributed from the fractures, these rock masses serve as excellent reservoirs for groundwater and fossil fuel extraction. However, in many cases, the fluid flow within the intact rock is relatively significant in addition to the flow within the fracture. Therefore, it is important to understand the coupled mechanical and hydraulic behavior of the system including the fluid interaction between the fracture and matrix in order to gain insights to the behavior of the rock mass as a whole. Early mathematical models describe the behavior of a fractured porous rock by treating the fractures and the matrix as a continuous medium (Gray et al., 1976) and representing the fractured rock mass by an equivalent porous medium (Pritchett et al., 1976). However, general interaction theories are required to describe the effect of the motion of fluid on the motion of matrix and vice versa. Much of this has been satisfied through introduction of the general theory of consolidation (Biot, 1941) which relates the influence of pore pressure due to the existence of fluid in a porous rock. Nevertheless, this does not truly reflect the influences of fluid pressures and rock stresses on the fracture and the matrix owing to the porosity within the fracture being more sensitive than that of the matrix (Wittke, 1973).
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