Propagation Of Compaction Bands Research Articles

Development of Compaction Localization in Leitha Limestone: Finite Element Modeling Based on Synchrotron X‐Ray Imaging

AbstractThe mechanical behavior and failure mode of porous rocks vary with their microstructures. The formation of compaction bands (CBs) has been captured with high precision via in situ synchrotron CT and kinematic characteristics can be attained by image analysis. However, the stress characteristics cannot be directly evaluated from images, and how porosity heterogeneity triggers local instability and leads to the formation of CBs is not yet fully understood. To address this problem, we established a finite element (FE) model of the solid skeleton of a Leitha limestone sample based on X‐ray μCT data, considering the heterogeneity of pores and plastic hardening, and reproduced the evolution of strain localization and CBs. Our results revealed that the heterogeneity of porosity has a profound influence on the formation and propagation of CBs. Precursory stresses always appear very early around the pores where compaction bands develop, and the stress state of most points in CBs is quasi‐uniaxial compression, which has significantly high maximum principal stress σ1 in a direction subparallel to the sample axis, causing yield then compaction failure. Also, using a simplified FE mesh and ignoring the fracture of particles underestimate the extreme stress and porosity reduction—these can be improved by using fine mesh and involving grain‐scale fracture mechanics. Our study proves the feasibility and reliability of the CT‐FE simulation scheme, which can be extended to investigating the stress distribution and evolution of different rock types with a spectrum of failure modes if in situ CT data of rock deformation is available.

Modeling heterogeneity and permeability evolution in a compaction band using a phase-field approach

Compaction bands are tabular zones of localized compressive deformation associated with porosity and permeability reduction. Depending on their orientation, compaction bands can act as barriers to fluid flow, and can be detrimental to fluid production in oil and gas reservoirs, as well as in CO2 sequestration. The process of permeability reduction and the development of excess pore pressures during compaction band formation in a heterogeneous rock mass are not fully understood. Furthermore, few studies have modeled compaction band formation considering coupled hydromechanical processes. In this study, we propose a coupled hydromechanical, phase-field approach for capturing the formation and propagation of compaction bands in heterogeneous porous media. Breakage mechanics is adopted to characterize the free energy function in the intact and damaged material. The resulting phase-field variable provides a measure of the degree of grain crushing. Permeability reduction in the zone of compaction localization is modeled using the Kozeny–Carman equation accounting for microstructural evolution. Numerical simulations demonstrate the ability of the model to capture compaction band formation, porosity reduction, and permeability evolution under drained and undrained conditions. The results highlight the role of effective confining pressure, drainage conditions, and material parameters on the styles of compaction bands that form.

A phase‐field approach for compaction band formation due to grain crushing

AbstractCompaction bands are tabular regions of localized compressive deformation with little or no shear offset. Often observed in high‐porosity rocks, they can be classified into several subtypes based on their pattern and orientation with respect to the maximum principal stress. The combined effects of material properties and loading conditions on the type of compaction bands that develop are not fully understood, and realistic simulations of their formation are not always successful. In this study, a phase‐field approach for capturing the formation and propagation of compaction bands is proposed. The fracture energy utilized in classic phase‐field formulations is interpreted to be driven by grain crushing and is herein characterized by breakage mechanics theory. A new decomposition of the free energy function is introduced in which the energy stored by plastic compactive flow drives grain crushing. Depending on the value of the energy release rate, the model predicts different styles of compaction bands that are remarkably consistent with those observed in the field. Numerical simulations demonstrate the role of confining pressure, plasticity, and critical breakage energy on the styles of the predicted compaction bands.

Role of pore attribute in the localized deformation of granular rocks: A numerical study

Practical attempts are made for a better understanding of the deformation mechanisms among porous siliciclastic, carbonate and volcanic rocks, in which the localized compaction has commonly been detected, with emphasis on the effect of micro-pore and size difference between grains and macro-pores. Based on a distinct element model comprised of multiple identical elements, the variation in relative macro-pore size is obtained through a building-block approach to the grain or macro-pore element, while the micro-pores are randomly extracted from the grain interior. The micro-cracking activity, energy budget and associated grain crushing are recorded to reveal the localization process under contractional regimes across the brittle-ductile transition. Numerical results suggest that the formation of shear bands is a universal feature at low confining pressures, and the macro-pore is an essential prerequisite for the compaction localization at high confining pressures. The reduction in either macro-porosity or relative macro-pore size contributes to a distributed cataclasis, and the abundance of micro-pore promotes the inception and propagation of compaction bands. Generally, macro-pore structure dominates the rupture morphology, on which the micro-porosity exerts a limited effect unless it represents a high portion of total porosity. Within the tested relative macro-pore size range that corresponds to ~2.65 to 0.25 times the grain size, the grain-scale fracture always favors the periphery of macro-pores, and the localized compaction derives from the competition of tensile and shear failures on both interior and boundary of a grain, which is heavily dependent on pore attributes such as the relative size and abundance of macro-pores. Typically, the micro-cracking activity shows a gradual growth before peak stress during shear localization, whereas the compaction localization is characterized by intermittent stress drops that related to surges in the micro-cracking activity. In addition, the influences of pore attributes on strength and deformation parameters are also discussed.

Compaction Banding in High‐Porosity Carbonate Rocks: 2. A Gradient‐Dependent Plasticity Model

AbstractBased on the experimental study on Saint‐Maximin limestone presented in a companion paper (Abdallah et al., 2020), a gradient‐dependent plasticity model is developed to account for the key role of porosity heterogeneity in the formation and propagation of compaction bands. The constitutive law, developed in the frame of a micromorphic continuum theory, contains two hardening variables: the porosity and its second gradient. A calibration method for the additional micromechanical parameters is proposed. Data from the companion paper are used in a four‐step calibration procedure. First, the standard Cauchy component is calibrated by means of the macroscopic stress‐strain curves. An Asymmetric Cam‐Clay (ACC) model is adopted for the yield surface. The dominant wavelength of the porosity heterogeneity of the material is evaluated by applying the fast Fourier transformation (FFT) on several porosity profiles obtained on samples before loading. This wavelength is interpreted as the material length that appears in the model. In addition to the deformation maps computed from digital volume correlation (DVC), a method that evaluates the second gradient of porosity is developed to calibrate the hardening laws. A linear stability analysis (LSA) is performed to calibrate the higher‐order elastic modulus. The constitutive model is implemented in a finite element code, and triaxial loading experiments are simulated. The numerical results are consistent with the experimental data in terms of the onset of compaction bands, their thickness, and plastic strain. The size effect of the sample is explored, and a regular band spacing, comparable to the band thickness, is obtained.

Constitutive modelling of compaction localisation in porous sandstones

Porous sandstones exhibit localised modes of failure in the form of shear or compaction bands. In particular, shear localisation is associated with brittle behaviour under low confining pressures, while under increasing confining pressures, their failure gradually becomes more ductile with the onset and propagation of compaction bands. The orientation and size of these localisation bands vary with the loading and material properties. As a consequence, a correct description of the behaviour of porous sandstones must take into account all these characteristics of localised failure. As a departure from existing approaches that take into account the orientation of localisation band, we present in this study a new approach to incorporate both size and orientation of localisation zone in constitutive models for geomaterials. Based on this approach, a breakage mechanics constitutive model is enhanced with localised mode of failure and used for the post-localisation analysis of porous sandstones. The concepts together with technical details, and numerical results are presented to show the potentials of the new approach.

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. [] 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.

Initiation and Propagation of Compaction Bands in Dry and Wet Bentheim Sandstone

We investigated initiation and propagation of compaction bands (CB) in six wet and four dry Bentheim sandstone samples deformed in axial compression tests with strain rates ranging from 3.2 9 10 -8 s -1 to 3.2 9 10 -4 s -1 . Circumferential notches with 0.8-mm width and 5-mm depth served to initiate CB at mid- sample length. Wet samples were saturated with distilled water and deformed at 195 MPa confining pressure and 10 MPa pore pressure. Dry samples were deformed at 185 MPa confining pressure. Twelve P-wave sensors, eight S-wave sensors and two pairs of orthogonally oriented strain-gages were glued to the sample surface to monitor acoustic emission (AE), velocities and local strain during the loading process. Nucleation of compaction bands is indicated by AE clusters close to the notch tips. With progressive loading, AE activity increased and AE hypocenters indicated propagation of a single CB normal to the sample axis. CB propagation from the sample periphery towards the centre was monitored. Microstructural analysis of deformed samples shows excellent agreement between location of AE clusters and CBs. In both dry and wet samples the lateral propagation of CBs was about 100 times faster than axial shortening rates. At the slowest displacement rate, AE activity during band propagation was reduced and CB nucleation in wet samples occurred at 20% lower stresses. This may indicate an increasing contribution of stress corrosion processes to the formation of the compaction bands. In dry and wet samples inelastic compaction energy per area ranged between 16 and 80 kJ m -2 . This is in good agreement with previous estimates from laboratory and field studies.

About this title - Rock Physics and Geomechanics in the Study of Reservoirs and Repositories

The study of reservoir and repository performance requires the integration of many different fields in Earth sciences, among them rock physics and geomechanics. The aim of this book is to emphasize how rock physics and geomechanics help to get a better insight into important issues linked to reservoir management for exploitation of natural resources, and to repository safety assessment for hazardous waste storage in geological environment. The studies presented here deal with the hydromechanical coupling in fractured rocks, the key experiments in safety assessment of repositories, the development of damaged zones during excavation in a shaley formation, the influence of temperature on the properties of shales, the poroelastic response of sandstones, the development and propagation of compaction bands in reservoir rocks, imaging techniques of geomaterials, the characterization and modelling of reservoirs using 4D seismic data, the mechanical behaviour of fractured rock masses, the petrophysical properties of fault zones, models for rock deformation by pressure solution and the elastic anisotropy in cracked rocks.

A numerical study on localized volume reduction in elastic media: Some insights on the mechanics of anticracks

Porous rocks, subjected to compressive stress, often undergo mechanical compaction via grain crushing and grain rearrangement, and chemical compaction by pressure solution. Such volume reduction processes are known to spontaneously localize under certain conditions, creating compaction and compacting shear bands, solution seams, and stylolites. However, the localization process is poorly understood. The formation and propagation of compaction bands have recently been studied using an elastoplastic spring network model (Katsman et al., 2005). In this paper, the same technique was employed to systematically analyze localized volume reduction (LVR) defects and their interactions with the surrounding elastic media, i.e., the stress distribution around an LVR region. Simulation results show that LVR regions experience stress concentrations at their tips, reminiscent of mode I cracks. However, aside from this similarity point, comparison of stress around LVR regions to stress around cracks reveals that the stress/strain distribution in such LVR defects is quite different than that surrounding mode I cracks. Implications for stylolites and compaction band are thoroughly discussed.