Numerical modelling of the hydro‐chemo‐mechanical behaviour of geomaterials in the context of CO2 injection

Safety assessment of geosequestration of CO₂ into deep saline aquifers requires a precise understanding of the study of hydro‐chemo‐mechanical couplings occurring in the rocks and the cement well. To this aim, a coupled chemo‐poromechanical model has been developed and implemented into a research code well‐suited to the resolution of fully coupled problems. This code is based on the finite volume methods. In a 1D axisymmetrical configuration, this study aims to simulate the chemo‐poromechanical behaviour of a system composed by the cement well and the caprock during CO₂ injection. Major chemical reactions of carbonation occurring into cement paste and rocks are considered in order to evaluate the consequences of the presence of CO₂ on the amount of dissolved matrix and precipitated calcium carbonates. The dissolution of the solid matrix is taken into account through the use of a chemical porosity. Matrix leaching and carbonation lead, as expected, to important variations of porosity, permeability and to alterations of transport properties and mechanical stiffness. These results justify the importance of considering a coupled analysis accounting for the main chemical reactions. It is worth noting that the modelling framework proposed in the present study could be extended to model the chemo‐poromechanical behaviour of the reservoir rock and the caprock when subjected to the presence of an acidic pore fluid (CO₂‐rich brine). Copyright © 2013 John Wiley & Sons, Ltd.     

A numerical study of mechanical behavior of a cement paste under mechanical loading and chemical leaching

Based on relevant experimental data of a petroleum cement paste under mechanical loading and chemical leaching, an elastic‐plastic model is first proposed by taking into account plastic shearing and pore collapse. The degradation of mechanical properties induced by the chemical leaching is characterized by a chemical damage variable which is defined as the increase of porosity. Both elastic and plastic properties of the cement paste are affected by the chemical damage. The proposed model is calibrated from and applied to describe mechanical responses in triaxial compression tests respectively on sound and fully leached samples. In the second part, a phenomenological chemical model is defined to establish the relationship between porosity change and calcium dissolution process. The dissolution kinetics is governed by a diffusion law taking into account the variation of diffusion coefficient with calcium concentration. The chemical model is coupled with the mechanical model, and both are applied to describe mechanical response of cement paste samples subjected to progressive chemical leaching and compressive stresses. Comparisons between experimental data and numerical results are presented.     

From micron-sized needle-shaped hydrates to meter-sized shotcrete tunnel shells: micromechanical upscaling of stiffness and strength of hydrating shotcrete

Knowledge on the stresses in shotcrete tunnel shells is of great importance, as to assess their safety against severe cracking or failure. Estimation of these stresses from 3D optical displacement measurements requires shotcrete material models, which may preferentially consider variations in the water–cement and aggregate–cement ratios. Therefore, we employ two representative volume elements within a continuum micromechanics framework: the first one relates to cement paste (with a spherical material phase representing cement clinker grains, needle-shaped hydrate phases with isotropically distributed spatial orientations, a spherical water phase, and a spherical air phase; all being in mutual contact), and the second one relates to shotcrete (with phases representing cement paste and aggregates, whereby aggregate inclusions are embedded into a matrix made up by cement paste). Elasticity homogenization follows self-consistent schemes (at the cement paste level) and Mori–Tanaka estimates (at the shotcrete level), and stress peaks in the hydrates related to quasi-brittle material failure are estimated by second-order phase averages derived from the RVE-related elastic energy. The latter permits upscaling from the hydrate strength to the shotcrete strength. Experimental data from resonant frequency tests, ultrasonics tests, adiabatic tests, uniaxial compression tests, and nanoindentation tests suggest that shotcrete elasticity and strength can be reasonably predicted from mixture- and hydration-independent elastic properties of aggregates, clinker, hydrates, water, and air, and from strength properties of hydrates. At the structural level, the micromechanics model, when combined with 3D displacement measurements, predicts that a decrease of the water–cement ratio increases the safety of the shotcrete tunnel shell.     

Relevance of SEM to Long-Term Mechanical Properties of Cemented Paste Backfill

This paper is an attempt to relate the microstructure to long-term mechanical properties of the cemented paste backfill produced from a hard rock mine tailing from North Queensland in Australia bound with flyash-based geopolymer (geopolymer), flyash-blended cement (FBC), and general purpose cement (GPC). A relatively high slump (260 mm) paste backfill mix with 74 wt% solids has been used to prepare cylindrical paste backfill samples with a diameter of 50 mm and a height of 100 mm. The uniaxial compressive strength tests were conducted on all samples after curing for 112 days to obtain their strength, failure strain and Young’s modulus. Fractured samples were examined under scanning electron microscope to understand the failure mechanisms at the microstructural scale. The results show that binders significantly affected the mechanical properties of paste backfills (ANOVA, p < 0.05). The paste backfill bound with geopolymer gave the lowest strength and Young’s modulus, while the paste backfills bounded with FBC and GPC showed comparable higher strength and modulus values. This was attributed to the relatively well-packed paste backfills with less cracks and smaller pore sizes in these paste backfills bound with FBC and GPC binders. In particular, needle-shaped particles, which were originally identified in GPC, highly influenced the mechanical property of paste backfills. These results indicate that fly ash can be used to partially replace the cement as a binder for paste backfills to achieve economic and environmental benefits.     

The influence of coupled physical swelling and chemical reactions on deformable geomaterials

Coupled thermo‐hydro‐mechanical‐chemical modelling has attracted attention in past decades due to many contemporary geotechnical engineering applications (e.g., waste disposal, carbon capture and storage). However, molecular‐scale interactions within geomaterials (e.g., swelling and dissolution/precipitation) have a significant influence on the mechanical behaviour, yet are rarely incorporated into existing Thermal‐Hydro‐Mechanical‐Chemical (THMC) frameworks. This paper presents a new coupled hydro‐mechanical‐chemical constitutive model to bridge molecular‐scale interactions with macro‐physical deformation by combining the swelling and dissolution/precipitation through an extension of the new mixture‐coupling theory. Entropy analysis of the geomaterial system provides dissipation energy, and Helmholtz free energy gives the relationship between solids and fluids. Numerical simulation is used to compare with the selected recognized models, which demonstrates that the swelling and dissolution/precipitation processes may have a significant influence on the mechanical deformation of the geomaterials.     

Chemo‐mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species

This paper studies the chemo‐mechanics of cemented granular solids in the context of continuum thermodynamics for fluid‐saturated porous media. For this purpose, an existing constitutive model formulated in the frame of the Breakage Mechanics theory is augmented to cope with reactive processes. Chemical state variables accounting for the reactions between the solid constituents and the solutes in the pore fluid are introduced to enrich the interactions among the microstructural units simulated by the model (i.e., grains and cement bonds). Two different reactive processes are studied (i.e., grain dissolution and cement precipitation), using the chemical variables to describe the progression of the reactions and track changes in the size of grains and bonds. Finally, a homogenization strategy is used to derive the energy potentials of the solid mixture, adopting probability density functions that depend on both mechanical and chemical indices. It is shown that the connection between the statistics of the micro‐scale attributes and the continuum properties of the solid enables the mathematical capture of numerous mechanical effects of lithification and chemical deterioration, such as changes in stiffness, expansion/contraction of the elastic domain, and development of inelastic strains during reaction. In particular, the model offers an interpretation of the plastic strains generated by aggressive environments, which are here interpreted as an outcome of chemically driven debonding and comminution. As a result, the model explains widely observed macroscopic signatures of geomaterial degradation by reconciling the energetics of the deformation/reaction processes with the evolving geometry of the microstructural attributes. Copyright © 2015 John Wiley & Sons, Ltd.     

碳酸盐岩储层原油裂解过程中的钙、硫分子地球化学研究—同步辐射XANES技术的应用

为了研究碳酸盐岩储层原油裂解过程中硫、钙元素赋存状态的变化,采集塔河油田TK772井奥陶系鹰山组产层的原油,通过半开放实验体系"地层孔隙热压生排烃模拟仪"开展仿真地层条件的成气模拟实验,利用同步辐射X射线吸收近边结物(XANES)技术对固体产物中的硫、钙元素的化学赋存状态进行精确检测。结果表明,原油直接裂解(原油+灰岩实验(系列1))固体产物中含硫化合物以噻吩类和硫酸钙为主,是原油裂解过程中部分噻吩类物质被氧化的结果;含钙化合物以碳酸钙为主。有溶解硫酸盐存在的原油裂解(原油+灰岩+硫酸镁实验(系列2))固体产物中含硫化合物以硫酸钙为主,噻吩类为辅,可能是溶解硫酸盐(硫酸镁)的加入、硫酸盐热化学还原反应(TSR)和溶蚀-沉淀作用共同作用的结果。系列2中伴随着温压的升高,H2S的生成和硫酸钙相对百分含量增加,指示原油裂解过程中发生了硫酸盐热化学还原反应(TSR);硫酸钙的生成和富集表明,TSR过程产生的酸性流体可以对碳酸盐岩储层产生明显的溶蚀作用,同时可能会生成次生膏盐。     

One‐dimensional analysis of a poroelastic medium during freezing

A solution to the problem of freezing of a poroelastic material is derived and analysed in the case of one‐dimensional deformation. The solution is sought within the framework of thermo‐poroelasticity, with specific account of the behaviour of freezing materials. The governing equations of the problem can be combined into a pair of coupled partial differential equations for the temperature and the fluid pressure, with particular forms in the freezing and the unfrozen regions. In the freezing region, the equations are highly non‐linear, partly due to the dependence of thermal and hydraulic properties on water saturation, which varies with temperature. Consequently, the solution is obtained through numerical methods, with special attention to the propagation of the freezing front boundary. The response to one‐dimensional freezing is illustrated for the case of cement paste. Finally, the influence on the solution of varying selected parameters is analysed, such as the temperature boundary conditions, the parameters characterizing the geometry of the porous system, the ratio of fluid and thermal diffusivities, and the rate of cooling applied at the freezing end. Copyright © 2008 John Wiley & Sons, Ltd.     

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.     

Physical and numerical investigation of a cemented granular assembly of steel spheres

In this paper, steel spheres embedded in a cement matrix were studied using numerical and physical ISRM testing procedures. A challenge in discrete element simulations is to select appropriate micro‐mechanical models and parameters, to recover the observed macro‐mechanical behavior. An ideal experiment on cohesive granular assemblies constructed identical to numerical ones would validate these micro models for a set of measured micro‐parameters. The first part of the paper summarizes the previous studies in this area, outlines such experimental methodology and depicts the steps followed for the preparation and the testing of cemented granular assemblies together with the derivation of micro‐parameters. The second part discusses the results of numerical and physical ISRM standard tests including uniaxial and triaxial compression, Brazilian tensile and shear box tests. Physical samples were prepared using steel balls bonded with Portland cement, cured under controlled laboratory conditions and tested in compression, tension and shearing. Acoustic emissions were monitored in uniaxial tests to characterize the damage thresholds relative to volumetric strains. Numerical simulations were conducted with PFC 3D using micro‐mechanical parameters derived from physical testing. Parametric sensitivity studies were carried out to look into the dependency of macroscopic responses on the parameters. The results from both numerical and physical tests showed good correspondence in macroscopic behavior i.e. peak strength, stages of damage, mode of failures. However, the numerical simulations reflected a stiffer mechanical response than physical assemblies. Copyright © 2010 John Wiley & Sons, Ltd.     

Characterization of clastic rock using a biconcave bond model of DEM

This paper presents a biconcave bond model to investigate the effect of the cementation between grains on the mechanical behavior of rock. The proposed model considers the shape of the bonds among particles that have a biconcave cement form, based on observations of microscopic rock images. The general equations of the proposed model are based on Dvorkin theory. The accuracy and efficiency of the bond model is improved in three ways. After the biconcave bond model is implemented in the discrete element method software Particle Flow Code in 2 Dimensions, a series of numerical uniaxial compression tests were performed to investigate the relationships between the micro‐ to macro‐parameters. The simulations revealed that the biconcave bond model reflects the effect of micro‐parameters, such as the elastic modulus and Poisson's ratio of the cement, on the macroscopic deformation of cemented granular material. Variations in the bond geometry caused extremely diverse macro‐mechanical behaviors. Experimental results concerning rock demonstrate that the biconcave bond model accurately captures the mechanical behavior of intact rock and supports an innovative method for investigating the relationships between the micro‐ and macro‐parameters of cemented granular material. Copyright © 2016 John Wiley & Sons, Ltd.     

On incremental non‐linearity in granular media: phenomenological and multi‐scale views (Part I)

On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto‐viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro‐mechanical models based on multi‐scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro‐mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non‐linear character of their behaviour. It is shown that both phenomenological and micro‐mechanical models exhibit an incremental non‐linearity. In addition, the multi‐scale approach reveals that the macroscopic incremental non‐linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright © 2005 John Wiley & Sons, Ltd.     

A micro‐mechanical study of peak strength and critical state

We present a micro‐mechanical analysis of macroscopic peak strength, critical state, and residual strength in two‐dimensional non‐cohesive granular media. Typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain‐scale counterparts (e.g., inter‐particle contact forces, fabric, particle displacements, and velocities), providing an across‐the‐scale basis for a better understanding and modeling of granular materials. These multi‐scale relations are derived in three steps. First, explicit relations between macroscopic stress and strain rate with the corresponding grain‐scale mechanics are established. Second, these relations are used in conjunction with the non‐associative Mohr–Coulomb criterion to explicitly connect internal friction and dilation angles to the micro‐mechanics. Third, the mentioned explicit connections are applied to investigate, understand, and derive micro‐mechanical conditions for peak strength, critical state, and residual strength. Copyright © 2015 John Wiley & Sons, Ltd.     

Wellbore cement fracture evolution at the cement–basalt caprock interface during geologic carbon sequestration

Composite Portland cement–basalt caprock cores with fractures, as well as neat Portland cement columns, were prepared to understand the geochemical and geomechanical effects on the integrity of wellbores with defects during geologic carbon sequestration. The samples were reacted with CO₂–saturated groundwater at 50 °C and 10 MPa for 3 months under static conditions, while one cement–basalt core was subjected to mechanical stress at 2.7 MPa before the CO₂ reaction. Micro-XRD and SEM–EDS data collected along the cement–basalt interface after 3-month reaction with CO₂–saturated groundwater indicate that carbonation of cement matrix was extensive with the precipitation of calcite, aragonite, and vaterite, whereas the alteration of basalt caprock was minor. X-ray microtomography (XMT) provided three-dimensional (3-D) visualization of the opening and interconnection of cement fractures due to mechanical stress. Computational fluid dynamics (CFD) modeling further revealed that this stress led to the increase in fluid flow and hence permeability. After the CO₂-reaction, XMT images displayed that calcium carbonate precipitation occurred extensively within the fractures in the cement matrix, but only partially along the fracture located at the cement–basalt interface. The 3-D visualization and CFD modeling also showed that the precipitation of calcium carbonate within the cement fractures after the CO₂-reaction resulted in the disconnection of cement fractures and permeability decrease. The permeability calculated based on CFD modeling was in agreement with the experimentally determined permeability. This study demonstrates that XMT imaging coupled with CFD modeling represent a powerful tool to visualize and quantify fracture evolution and permeability change in geologic materials and to predict their behavior during geologic carbon sequestration or hydraulic fracturing for shale gas production and enhanced geothermal systems.     

丹霞地貌砂岩的微观化学风化作用电子探针研究

利用偏光显微镜观察、电子探针分析等手段对江西龙虎山丹霞地貌崖壁砂岩的微观化学风化作用的发展过程进行了研究,重点观测黑云母蛭石化以及长石黏土化过程中矿物组分的变化,进而探讨丹霞地貌砂岩的微观化学风化作用机理。在微观化学风化下,强风化层胶结物中的方解石迅速分解流失,从而导致黑云母大量发生蛭石化和铁的氧化物在矿物边部富集;长石则大量发生黏土化而使高岭石、石英等矿物富集。研究表明丹霞地貌砂岩在微观化学风化作用下矿物分解以及新矿物的形成都破坏原来岩石中的力学平衡,因而风化作用在宏观上表现为岩面片状剥离和重力崩塌,据此推断更大尺度的风化作用可能与岩石中矿物的微观化学风化作用存在着密切联系,是微观化学风化作用长期累积后在宏观上的综合表现。      

Numerical Modelling of Dissolving and Driving Exploitation of Potash Salt in the Qarhan Playa ? A Coupled Model of Reactive Solute Transport and Chemical Equilibrium in a Multi-component Underground Brine System

Firstly, the macroscopic chemical equilibrium state of a series of chemical reactions between intercrystal brine and its media salt layer （salt deposit） in Qarhan Salt Lake was studied by using the Pitzer theory. The concept of macroscopic solubility product and its relation with accumulated ore dissolving ratio were presented, which are used in the numerical model of dissolving and driving exploitation of potassium salt in Qarhan Salt Lake. And secondly, with a model forming idea of transport model for reacting solutes in the multi-component fresh groundwater system in porous media being a reference, a two-dimensional transport model coupled with a series of chemical reactions in a multi-component brine porous system （salt deposits） was developed by using the Pitzer theory. Meanwhile, the model was applied to model potassium/magnesium transport in Qarhan Salt Lake in order to study the transfer law of solid and liquid phases in the dissolving and driving process and to design the optimal injection/abstraction strategy for dissolving and capturing maximum Potassium/ Magnesium in the mining of salt deposits in Qarhan Salt Lake.