The effect of particle shape and grain‐scale properties of shale: A micromechanics approach

Traditional approaches for modeling the anisotropic elasticity response of the highly heterogeneous clay fabric in shale have mainly resorted to geometric factors such as definitions of particles shapes and orientations. However, predictive models based on these approaches have been mostly validated using macroscopic elasticity data. The recent implementation of instrumented indentation aimed at probing nano‐scale mechanical behaviors has provided a new context for characterizing and modeling the anisotropy of the porous clay in shale. Nanoindentation experimental data revealed the significant contribution of the intrinsic anisotropy of the solid clay to the measured elastic response. In this investigation, we evaluate both the effects of geometric factors and of the intrinsic anisotropic elasticity of the solid clay phase on the observed anisotropy of shale at multiple length scales through the development of a comprehensive theoretical micromechanics approach. It was found that among various combinations of these sources of anisotropy, the elastic response of the clay fabric represented as a granular ensemble of aligned effective clay particles with spherical morphology and anisotropic elasticity compares satisfactorily to nanoindentation and ultrasonic pulse velocity measurements at nano‐ and macroscopic length scales, respectively. Other combinations of sources of anisotropy could yield comparable predictions, particularly at macroscopic scales, at the expense of requiring additional experimental data to characterize the morphology and orientations of particles. Copyright © 2009 John Wiley & Sons, Ltd.     

Nanochemomechanical assessment of shale: a coupled WDS-indentation analysis

Establishing the links between the composition, microstructure and mechanics of shale continues to be a formidable challenge for the geomechanics community. In this study, a robust methodology is implemented to access the in situ chemomechanics of this sedimentary rock at micrometer length scales. Massive grids of coupled wave dispersive spectroscopy (WDS) and instrumented indentation experiments were performed over representative material surfaces to accommodate the highly heterogeneous composition and microstructure of shale. The extensive datasets of compositional and mechanical properties were analyzed using multi-variate clustering statistics to determine the attributes of active phases present in shale at microscales. Our chemomechanical analysis confirmed that the porous clay (PC) mechanical phase inferred by statistical indentation corresponds to the clay mineral phase defined strictly on chemical grounds. The characteristic stiffness and hardness behaviors of the PC are realized spatially in regions removed from silt inclusions of quartz and feldspar. At the microscale shared by indentation and WDS experiments, a consistent chemomechanical signature for shale emerges in which the heterogeneities of the PC are captured by the standard deviations of indentation properties and concentrations of chemical elements. However, these local behaviors are of second order compared to the global trend observed for mean mechanical properties and the clay packing density, which synthesizes the relative volumes of clay and nanoporosity in the material. The coupled statistical indentation and WDS technique represents a viable approach to characterize the chemomechanics of shale and other natural porous composites at a consistent scale below the macroscopic level.     

The nanogranular origin of friction and cohesion in shale—A strength homogenization approach to interpretation of nanoindentation results

An inverse micromechanics approach allows interpretation of nanoindentation results to deliver cohesive‐frictional strength behavior of the porous clay binder phase in shale. A recently developed strength homogenization model, using the Linear Comparison Composite approach, considers porous clay as a granular material with a cohesive‐frictional solid phase. This strength homogenization model is employed in a Limit Analysis Solver to study indentation hardness responses and develop scaling relationships for indentation hardness with clay packing density. Using an inverse approach for nanoindentation on a variety of shale materials gives estimates of packing density distributions within each shale and demonstrates that there exists shale‐independent scaling relations of the cohesion and of the friction coefficient that vary with clay packing density. It is observed that the friction coefficient, which may be interpreted as a degree of pressure‐sensitivity in strength, tends to zero as clay packing density increases to one. In contrast, cohesion reaches its highest value as clay packing density increases to one. The physical origins of these phenomena are discussed, and related to fractal packing of these nanogranular materials. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical evaluation of mean-field homogenisation methods for predicting shale elastic response

Homogenisation techniques have been successfully used to estimate the mechanical response of synthetic composite materials, due to their ability to relate the macroscopic mechanical response to the material microstructure. The adoption of these mean-field techniques in geo-composites such as shales is attractive, partly because of the practical difficulties associated with the experimental characterisation of these highly heterogeneous materials. In this paper, numerical modelling has been undertaken to investigate the applicability of homogenisation methods in predicting the macroscopic, elastic response of clayey rocks. The rocks are considered as two-level composites consisting of a porous clay matrix at the first level and a matrix-inclusion morphology at the second level. The simulated microstructures ranged from a simple system of one inclusion/void embedded in a matrix to complex, random microstructures. The effectiveness and limitations of the different homogenisation schemes were demonstrated through a comparative evaluation of the macroscopic elastic response, illustrating the appropriate schemes for upscaling the microstructure of shales. Based on the numerical simulations and existing experimental observations, a randomly distributed pore system for the micro-structure of porous clay matrix has been proposed which can be used for the subsequent development and validation of shale constitutive models. Finally, the homogenisation techniques were used to predict the experimental measurements of elastic response of shale core samples. The developed methodology is proved to be a valuable tool for verifying the accuracy and performance of the homogenisation techniques.     

Role of smectite-rich shales in frequent foundation failures in southeast Nigeria

This paper investigated the geotechnical properties of smectite-rich shale, and its implications as foundation material. Ten expansive shale samples were collected from foundation materials at Akpugo in Nkanu West L.G.A. of Enugu State, southeast Nigeria. Samples were subjected to grading, Atterberg limits-cum-compaction tests, slake durability, specific gravity, permeability, undrained triaxial tests and x-ray diffraction scan. Fines and sand contents of the soil samples range from 51–97% and 3–49% respectively. Liquid limit, plastic limit and plasticity index have average values of 60.7, 19.1 and 43.3% respectively. Linear shrinkage and free swell showed average of 16.3% and 76%. These results are indicative of predominant clay soil with high plasticity, compressibility and water holding capacity. XRD scan established presence of smectite and illite clay minerals, confirming soil high plasticity, capable of causing instability in foundation soil. The shale achieved maximum dry density range between 1.79 and 1.94 kg/m³ at optimum moisture content range of 6.9–12.8%, indicating poor to fair foundation materials. The shale cohesion ranges from 15 to 30 kPa while the angle of friction ranges between 10° and 18°, signifying an average strength soil material. Samples slake durability index and specific gravity fall within 24–55% and 2.50–2.58 respectively, suggesting non-durable and weak soil. Permeability of the samples ranges between 7.36 ×10^?6 and 4.77 ×10^?8 cm/s which suggested low drainage capable of causing water-log at sites. Therefore, the shale could be generally classified as poor to fair foundation material, which on moisture influx experience reduction in strength due to deterioration of its constituent minerals, especially clay and cement materials during the lifespan of engineering structures. Authors therefore recommend modification of foundation soil, appropriate foundation design and good drainage control as ways of improving stability of engineering structures underlain by expansive shale.     

The influence of anisotropy on compaction bands: The case of coaxiality between stress and fabric anisotropy tensors

Compaction bands are localized failure patterns that appear in highly porous rock material under the effect of relatively high confining pressure. Being affected mainly by volumetric compression, these bands appear to be almost perpendicular to the most compressive principal stress of a stress state at the so-called “cap” of the yield surface (YS). In this study, we focus on the mechanism that leads to the onset of compaction bands by using a viscoplasticity model able to describe the post-localization response of these materials. The proposed constitutive framework is based on the overstress theory of Perzyna (1966) and the anisotropic clay plasticity model of Dafalias (1986), which provides not only the necessary “cap” of the YS, but introduces a rotational hardening (RH) mechanism, thus, accounting for the effect of fabric anisotropy. Following the analysis of Veveakis and Regenauer-Lieb (2015), we identify the compaction bands as “static” cnoidal wave formations in the medium that occur at a post-yield regime, and we study the effect of rotational and isotropic hardening on their onset. Moreover, we determine a theoretical range of confining pressures in triaxial compression tests for the compaction bands to develop. Under the assumption of coaxiality between stress and anisotropy tensors, the results show that the isotropic hardening promotes compaction localization, whereas the RH has a slightly negative effect on the onset of compaction localization.     

Quantifying the heterogeneity of shale through statistical combination of imaging across scales

Shale is a highly heterogeneous material across multiple scales. A typical shale consists of nanometer-scale pores and minerals mixed with macroscale fractures and particles of varying size. High-resolution imaging is crucial for characterizing the composition and microstructure of this rock. However, it is generally not feasible to image a large sample of shale at a high resolution over a large field of view (FOV), thus limiting a full characterization of the microstructure of this material. We present a stochastic framework based on multiple-point statistics that uses high-resolution training images to enhance low-resolution images obtained over a large FOV. We demonstrate the approach using X-ray micro-tomography images of organic-rich Woodford shale obtained at two different resolutions and FOV. Results show that the proposed technique can generate realistic high-resolution images of the microstructure of shale over a large FOV.     

The nanogranular nature of shale

Despite their ubiquitous presence as sealing formations in hydrocarbon bearing reservoirs affecting many fields of exploitation, the source of anisotropy of this earth material is still an enigma that has deceived many decoding attempts from experimental and theoretical sides. Sedimentary rocks, such as shales, are made of highly compacted clay particles of sub-micrometer size, nanometric porosity and different mineralogy. In this paper, we present, for the first time, results from a new experimental technique that allows one to rationally assess the elasticity content of the highly heterogeneous clay fabric of shales from nano- and microindentation. Based on the statistical analysis of massive nanoindentation tests, we find (1) that the in-situ elasticity content of the clayfabric at a scale of a few hundred to thousands nanometers is almost an order of magnitude smaller than reported clay stiffness values of clay minerals, and (2) that the elasticity and the anisotropy scale linearly with the clay packing density beyond a percolation threshold of roughly 50%. Furthermore, we show that the elasticity content sensed by nano- and microindentation tests is equal to the one that is sensed by (small strain) velocity measurements. From those observations, we conclude that shales are nanogranular composite materials, whose mechanical properties are governed by particle-to-particle contact and by characteristic packing densities, and that the much stiffer mineral properties play a secondary role.     

基于声波测试法对鹰滩页岩各向异性分析

页岩储层通常呈薄层状结构,一般认为其岩石力学参数具有横向各向同性,而其各向异性受围压（CP）、含水率和总有机质含量（TOC）等多种因素的影响。本文对不同围压下的鹰滩（Eagle Ford）页岩进行超声波波速进行测试实验,研究围压对鹰滩页岩波速及岩石力学各向异性的影响。实验结果表明,鹰滩页岩属于弱各向异性多孔介质,并具有横向各向同性、垂向各向异性的性质。纵波（P波）和横波（S波）波速随围压的增大而增大,特别是在低围压范围内增幅显著,同时围压增大会降低纵波和横波的各向异性,纵波各向异性比横波各向异性对围压更敏感。对鹰滩页岩各向异性分析为页岩储层压裂过程中裂缝的起裂和延伸规律研究提供了必要的力学参数。     

A parallel block preconditioner for large-scale poroelasticity with highly heterogeneous material parameters

Large-scale simulations of coupled flow in deformable porous media require iterative methods for solving the systems of linear algebraic equations. Construction of efficient iterative methods is particularly challenging in problems with large jumps in material properties, which is often the case in realistic geological applications, such as basin evolution at regional scales. The success of iterative methods for such problems depends strongly on finding effective preconditioners with good parallel scaling properties, which is the topic of the present paper. We present a parallel preconditioner for Biot’s equations of coupled elasticity and fluid flow in porous media. The preconditioner is based on an approximation of the exact inverse of the two-by-two block system arising from a finite element discretisation. The approximation relies on a highly scalable approximation of the global Schur complement of the coefficient matrix, combined with generally available state-of-the-art multilevel preconditioners for the individual blocks. This preconditioner is shown to be robust on problems with highly heterogeneous material parameters. We investigate the weak and strong parallel scaling of this preconditioner on up to 512 processors and demonstrate its ability on a realistic basin-scale problem in poroelasticity with over eight million tetrahedral elements.     

Generalized solution to the anisotropic Mandel's problem

Existing solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel-Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction.     

Nanomechanics of organic-rich shales: the role of thermal maturity and organic matter content on texture

Despite the importance of organic-rich shales, microstructural characterization and theoretical modeling of these rocks are limited due to their highly heterogeneous microstructure, complex chemistry, and multiscale mechanical properties. One of the sources of complexity in organic-rich shales is the intricate interplay between microtextural evolution and kerogen maturity. In this study, a suite of experimental and theoretical microporomechanics methods are developed to associate the mechanical properties of organic-rich shales both to their maturity level and to the organic content at micrometer and sub-micrometer length scales. Recent results from chemomechanical characterization experiments involving grid nanoindentation and energy-dispersive X-ray spectroscopy (EDX) are used in new micromechanical models to isolate the effects of maturity levels and organic content from the inorganic solids. These models enable attribution of the role of organic maturity to the texture of the indented material, with immature systems exhibiting a matrix-inclusion morphology, while mature systems exhibit a polycrystal morphology. Application of these models to the interpretation of nanoindentation results on organic-rich shales allows us to identify unique clay mechanical properties that are consistent with molecular simulation results for illite and independent of the maturity of shale formation and total organic content. The results of this investigation contribute to the design of a multiscale model of the fundamental building blocks of organic-rich shales, which can be used for the design and validation of multiscale predictive poromechanics models.     

Numerical estimation of effective diffusion coefficients for charged porous materials based on micro-scale analyses

In order to describe diffusive transport of solutes through a porous material, estimation of effective diffusion coefficients is required. It has been shown theoretically that in the case of uncharged porous materials the effective diffusion coefficient of solutes is a function of the pore morphology of the material and can be described by the tortuosity (tensor) (Bear, 1988 [1]). Given detailed information of the pore geometry at the micro-scale the tortuosity of different materials can be accurately estimated using homogenization procedures. However, many engineering materials (e.g., clays and shales) are characterized by electrical surface charges on particles of the porous material which strongly affect the (diffusive) transport properties of ions. For these type of materials, estimation of effective diffusion coefficients have been mostly based on phenomenological equations with no link to underlying micro-scale properties of these charged materials although a few recent studies have used alternative methods to obtain the diffusion parameters (Jougnot et al., 2009; Pivonka et al., 2009; Revil and Linde, 2006 2, 3 and 4). In this paper we employ a recently proposed up-scaled Poisson–Nernst–Planck type of equation (PNP) and its micro-scale counterpart to estimate effective ion diffusion coefficients in thin charged membranes. We investigate a variety of different pore geometries together with different surface charges on particles. Here, we show that independent of the charges on particles, a (generalized) tortuosity factor can be identified as function of the pore morphology only using the new PNP model. On the other hand, all electro-static interactions of ions and charges on particles can consistently be captured by the ratio of average concentration to effective intrinsic concentration in the macroscopic PNP equations. Using this formulation allows to consistently take into account electrochemical interactions of ions and charges on particles and so excludes any ambiguity generally encountered in phenomenological equations.     

Influence of magnetic effect,anisotropy, irregularity,initial stress and heterogeneity on propagation of SH-wave in an irregular pre-stressed magnetoelastic monoclinic sandwiched layer

Monoclinic materials viz. quartz, lithium niobate and lithium tantalate are among the most abundant materials, finding numerous applications throughout the technological world. Moreover, the presence of irregularity, initial stresses, anisotropy and heterogeneity in a material medium is obvious. These facts motivate the study of magnetoelastic SH-wave propagation in an irregular monoclinic sandwiched layer between a heterogeneous isotropic layer and an isotropic half space, all under initial stress. The heterogeneity in the uppermost layer is caused due to exponential variation in rigidity, density and initial stress in terms of space variable pointing vertically downward. The dispersion relation has been obtained using first-order perturbation technique. The substantial effect of wave number, anisotropy, irregularity, width ratio of the layers, horizontal compressive/tensile initial stresses, heterogeneity and monoclinic-magnetoelastic coupling parameter associated with sandwiched layer on phase velocity of SH-wave has been studied and depicted by means of graph. Comparative study made for the case when pre-stressed irregular sandwiched layer is monoclinic-magnetoelastic to the case when it is isotropic magnetoelastic layer is one of the major highlights of the current study.     

Rate-independent fracture toughness of gray and black kerogen-rich shales

The objective of this investigation is to characterize the influence of the loading rate, scratch speed, mineralogy, morphology, anisotropy, and total organic content on the scratch toughness of organic-rich shale. We focus our study on a gray shale, Toarcian shale (Paris basin, France) and a black shale, Niobrara shale (northeastern Colorado, USA). Microscopic scratch tests are performed for varying scratch speeds and loading rates. We consider several orientations for scratch testing. For all gas shale specimens, the scratch toughness is found to increase with increasing scratch speed. In the asymptotic regime of high speeds, there is a convergence toward a single constant value irrespective of the loading rate. To understand this evolution of the scratch toughness, a nonlinear fracture mechanics model is built that integrates fracture dissipation with the various forms of viscous processes. In particular, a coupling is shown between the fracture energy and the viscoelastic characteristics. An inverse approach which combines scratch and indentation testing makes it possible to represent all tests in a single curve and retrieve the rate-independent fracture toughness of kerogen-rich shale materials. The presence of organic matter drastically alters the creep and fracture properties at the microscopic length-scale. The fracture behavior is anisotropic with the divider orientation yielding the highest fracture toughness value and the short transverse orientation yielding the lowest fracture toughness. Elucidating the fracture-composition-morphology relationships in organic-rich shale will promote advances in science and engineering for energy-related applications such as hydraulic fracturing in unconventional reservoirs or \(\hbox {CO}_2\) sequestration in depleted reservoirs.     

Engineering properties of unfired clay masonry bricks

The shortage of low cost and affordable housing in the UK has led to many investigations into new building masonry materials. Fired clay masonry bricks are conventionally used for mainstream masonry wall construction but suffer from the rising price of energy plus other related environmental problems such as high energy usage and carbon dioxide emission. The use of stabilised unfired clay bricks for masonry construction may solve these problems.This paper reports on the engineering properties of unfired clay bricks produced during the first industrial trial of unfired clay material development carried out at Hanson Brick Company, in Stewartby, Bedfordshire, under the Knowledge Exploitation Fund (KEF) Collaborative Industrial Research Project (CIRP) programme. The mixes were formulated using a locally available industrial by-product (Ground Granulated Blastfurnace Slag — GGBS) which is activated with an alkaline (lime or Portland cement) combined with clay soil. Portland cement was not used in the formulation of the unfired stabilised masonry bricks, except as a control, which is a significant scientific breakthrough for the building industry. Another breakthrough is the fact that only about 1.5% lime was used for GGBS activation. This level of lime is not sufficient for most road construction applications where less strength values are needed and where 3–8% lime is required for effective soil stabilisation. Hence, the final pricing of the unfired clay bricks is expected to be relatively low.The laboratory results demonstrate that the compressive strength, moisture content, rate of water absorption, percentage of void, density and durability assessment (repeated 24-hour freezing/thawing cycles) were all within the acceptable engineering standards for clay masonry units. The paper also discusses on the environmental performance of the unfired clay in comparison to the bricks, used in mainstream construction of today. The bricks produced using this technology can be used for low-medium cost housing and energy efficient masonry wall construction.     

Micromechanical approach to unsaturated water flow in structured geomaterials by two-scale computations

This article presents a micromechanical approach to the problem of unsaturated water flow in heterogeneous porous media in transient conditions. The numerical formulation is based on the two-scale model obtained previously by periodic homogenization. It allows for a coupled solution of the non-linear flow equations at macroscopic and microscopic scales and takes into account the macroscopic anisotropy of the medium and the local non-equilibrium of the capillary pressure. The model was applied to simulate two-dimensional water infiltration at constant flux into an initially dry medium containing inclusions of square and rectangular shapes. The numerical results showed the influence of the inclusion–matrix conductivity ratio and the local geometry on the macroscopic behavior. The influence of the conductivity ratio manifested itself by the acceleration or retardation of the onset of the macroscopic water flux at the outlet, while the local geometry (anisotropy) significantly affected the macroscopic spatial distribution of the water flux. Such type of approach can be extended to simulate coupled phenomena (for example hydro-mechanical problems) with evolving local geometry.     

Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

We describe a new approach for simulation of multiphase flows through heterogeneous porous media, such as oil reservoirs. The method, which is based on the wavelet transformation of the spatial distribution of the single-phase permeabilities, incorporates in the upscaled computational grid all the relevant data on the permeability, porosity, and other important properties of a porous medium at all the length scales. The upscaling method generates a nonuniform computational grid which preserves the resolved structure of the geological model in the near-well zones as well as in the high-permeability sectors and upscales the rest of the geological model. As such, the method is a multiscale one that preserves all the important information across all the relevant length scales. Using a robust front-detection method which eliminates the numerical dispersion by a high-order total variation diminishing method (suitable for the type of nonuniform upscaled grid that we generate), we obtain highly accurate results with a greatly reduced computational cost. The speed-up in the computations is up to over three orders of magnitude, depending on the degree of heterogeneity of the model. To demonstrate the accuracy and efficiency of our methods, five distinct models (including one with fractures) of heterogeneous porous media are considered, and two-phase flows in the models are studied, with and without the capillary pressure.