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.     

Extension of Biot theory to the problem of saturated microporous elastic media with isolated cracks or/and vugs

The purpose of this paper is to develop the macroscopic model of hydro‐mechanical coupling for the case of a porous medium containing isolated cracks or/and vugs. In the development, we apply the asymptotic expansion homogenization method. It is shown that the general structure of Biot's model is the same as in the case of homogeneous medium, but the poro‐elastic parameters are modified. Two numerical examples are presented. They concern the computations of Biot's parameters in isotropic and anisotropic cases. It can also be seen how the presence of near‐zero‐volume cracks influences Biot's parameters of the porous matrix. It can significantly affect the coupled hydro‐mechanical behaviour of damaged porous medium. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic response to fluid extraction from a poroelastic half‐space

In this study, the dynamic response of a poroelastic half‐space to a point fluid sink is investigated using Biot's dynamic theory of poroelasticity. Based on Biot's theory, the governing field equations are re‐formulated in frequency domain with solid displacement and pore pressure. In a cylindrical coordinate system, a method of displacement potentials for axisymmetric displacement field is proposed to decouple the Biot's field equations to three scalar Helmholtz equations, and then the general solution to axisymmetric problems are obtained. The full‐space fundamental singular solution for a point sink is also derived using potential methods. The mirror‐image method is finally applied to construct the fundamental solution for a point sink buried in a poroelastic half‐space. Furthermore, a numerical study is conducted for a rock, that is, Berea sandstone, as a representative example. Copyright © 2013 John Wiley & Sons, Ltd.     

History matching of enhanced coal bed methane laboratory core flood tests

Enhanced coalbed methane (ECBM) involves the injection of a gas, such as nitrogen or carbon dioxide, into the coal reservoir to displace the methane present. Potentially this strategy can offer greater recovery of the coal seam methane and higher rates of recovery due to pressure maintenance of the reservoir. While reservoir simulation forms an important part of the planning and assessment of ECBM, a key question is the accuracy of existing approaches to characterising and representing the gas migration process. Laboratory core flooding allows the gas displacement process to be investigated on intact coal core samples under conditions analogous to those in the reservoir. In this paper a series of enhanced drainage core floods are presented and history matched using an established coal seam gas reservoir simulator, SIMED II. The core floods were performed at two pore pressures, 2 MPa and 10 MPa, and involve either nitrogen or flue gas (90% nitrogen and 10% CO₂) flooding of core samples initially saturated with methane. At the end of the nitrogen floods the core flood was reversed by flooding with methane to investigate the potential for hysteresis in the gas displacement process. Prior to the core flooding an independent characterisation programme was performed on the core sample where the adsorption isotherm, swelling with gas adsorption, cleat compressibility and geomechanical properties were measured. This information was used in the history matching of the core floods; the properties adjusted in the history matching were related to the affect of sorption strain on coal permeability and the transfer of gas between cleat and matrix. Excellent agreement was obtained between simulated and observed gas rates, breakthrough times and total mass balances for the nitrogen/methane floods. It was found that a triple porosity model improved the agreement with observed gas migration over the standard dual porosity Warren-Root model. The Connell, Lu and Pan hydrostatic permeability model was used in the simulations and improved history match results by representing the contrast between pore and bulk sorption strains for the 10 MPa cases but this effect was not apparent for the 2 MPa cases. There were significant differences between the simulations and observations for CO₂ flow rates and mass balances for the flue gas core floods. A possible explanation for these results could be that there may be inaccuracy in the representation of mixed gas adsorption using the extended Langmuir adsorption model.     

瓦斯压力影响下煤岩力学性质与冲击能量指数演化规律及机制

深部煤层冲击地压诱发瓦斯涌出、突出事故频繁发生,对井下安全生产带来了巨大威胁,厘清瓦斯对煤岩力学性质、冲击倾向性演化规律是建立有效防治手段的基础。运用物理试验方法,基于自主研发的可视化煤岩流?固耦合试验系统,研究瓦斯压力影响的煤岩吸附、力学性质及碎块分布规律,分析瓦斯影响的煤岩冲击能指数演化特征与机制。结果表明:具有强冲击倾向性煤岩的瓦斯等温吸附曲线符合Langmuir模型,随瓦斯压力升高,煤岩软化特性越发明显,弹性模量、软化模量均呈阶段性降低,瓦斯对二者在煤岩峰值前后具有不同的影响效果且存在临界压力,试样破坏形式呈“脆性张拉→剪切→张拉+塑性流动”过渡,冲击能指数与试样碎块尺度均呈先减小后增大的“V”形变化特征,破碎后具有更多盈余能;含瓦斯煤岩小尺度碎块是灾害发生的客观条件,瓦斯膨胀能为煤体动态失稳提供了额外的能量,增大了冲击地压发生过程的强动力性和破坏性,这种煤岩基质骨架与瓦斯运移的固?流耦合降低了冲击地压发生的临界指标且具有更高的致灾潜能。研究成果与启示为进一步判定深部高瓦斯煤层灾变倾向并建立行之有效的防治手段提供了试验基础和研究思路。      

On the causes of pressure oscillations in low‐permeable and low‐compressible porous media

Nonphysical pressure oscillations are observed in finite element calculations of Biot's poroelastic equations in low‐permeable media. These pressure oscillations may be understood as a failure of compatibility between the finite element spaces, rather than elastic locking. We present evidence to support this view by comparing and contrasting the pressure oscillations in low‐permeable porous media with those in low‐compressible porous media. As a consequence, it is possible to use established families of stable mixed elements as candidates for choosing finite element spaces for Biot's equations. Copyright © 2011 John Wiley & Sons, Ltd.     

A theoretical model for gas adsorption-induced coal swelling

Swelling and shrinkage (volumetric change) of coal during adsorption and desorption of gas is a well-known phenomenon. For coalbed methane recovery and carbon sequestration in deep, unminable coal beds, adsorption-induced coal volumetric change may cause significant reservoir permeability change. In this work, a theoretical model is derived to describe adsorption-induced coal swelling at adsorption and strain equilibrium. This model applies an energy balance approach, which assumes that the surface energy change caused by adsorption is equal to the elastic energy change of the coal solid. The elastic modulus of the coal, gas adsorption isotherm, and other measurable parameters, including coal density and porosity, are required in this model. Results from the model agree well with experimental observations of swelling. It is shown that the model is able to describe the differences in swelling behaviour with respect to gas species and at very high gas pressures, where the coal swelling ratio reaches a maximum then decreases. Furthermore, this model can be used to describe mixed-gas adsorption induced-coal swelling, and can thus be applied to CO₂-enhanced coalbed methane recovery.     

A solution around a backfilled cavity in a low‐permeability poroelastic medium with application in in situ heating tests

Thermo‐hydro‐mechanical responses around a cylindrical cavity drilled or excavated in a low‐permeability formation are studied when the cavity is subjected to a time‐dependent thermal loading. The cavity is considered backfilled after it is supported by casing or lining. Solutions of temperature, pore water pressure, stress, and displacement responses are analytically formulated based on Biot's consolidation theory with the assumption that the backfilling material, supporting material, and surrounding low‐permeability formation are poroelastic media. The solution is expressed in Laplace space, and numerical inversion techniques are used to find field variables in the real‐time domain. After the solution is verified with the numerical results, it is applied in a large‐scale in situ heating test – PRACLAY heating test – for a predictive reference calculation and an extensive parametric study. Another medium‐scale in situ heating test – ATLAS III heating test – is also analyzed using the solution, which provides reasonable agreement with measurements. The new analytical solution proves to be a convenient tool for a good understanding of the resulting coupled thermo‐hydro‐mechanical behavior and is therefore valuable for the interpretation of measured data in engineering practices and for a rational design of potential radioactive waste repositories. Copyright © 2016 John Wiley & Sons, Ltd.     

Propagation of Rayleigh waves in fluid‐saturated non‐homogeneous soils with the graded solid skeleton distribution

The propagation characteristic of Rayleigh waves in a fluid‐saturated non‐homogeneous poroelastic half‐plane is addressed. Based on Biot's theory for fluid‐saturated media, which takes the inertia, fluid viscosity, mechanical coupling, compressibility of solid grains, and fluid into account, the dispersion equations of Rayleigh waves in fluid‐saturated non‐homogeneous soils/rocks are established. By considering the shear modulus of solid skeleton variation with depth exponentially, a small parameter, which reflects the relative change of shear modulus, is introduced. The asymptotic solution of the dispersion equation expressing the relationship between the phase velocity and wave number is obtained by using the perturbation method. In order to analyze the effects of non‐homogeneity on the propagation characteristic of Rayleigh waves, the variation of the phase velocity with the wave number is presented graphically and discussed through numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

An anisotropic damage–plasticity model for saturated quasi‐brittle materials

This article is devoted to numerical modeling of anisotropic damage and plasticity in saturated quasi‐brittle materials such as rocks and concrete. The damaged materials are represented by an isotropic poroelastic matrix containing a number of families of microcracks. Based on previous works, a discrete thermodynamic approach is proposed. Each family of microcracks exhibits frictional sliding along crack surfaces as well as crack propagation. The frictional sliding is described by a Coulomb–Mohr‐type plastic criterion by taking into account the effect of fluid pressure through a generalized effective stress concept. The damage evolution is entirely controlled by and coupled with the frictional sliding. The effective elastic properties as well as Biot's coefficients of cracked porous materials are determined as functions of induced damage. The inelastic deformation due to frictional sliding is also taken into account. The procedure for the identification of the model's parameters is presented. The proposed model is finally applied to study both mechanical and poromechanical responses of a typical porous brittle rock in drained and undrained compression tests as well as in interstitial pressure controlled tests. The main features of material behaviors are well reproduced by the model. Copyright © 2012 John Wiley & Sons, Ltd.     

A modified rock physics model for analysis of seismic signatures of low gas-saturated rocks

In seismic applications, the bulk modulus of porous media saturated with liquid and gas phases is often estimated using Gassmann's fluid substitution formula, in which the effective bulk modulus of the two-phase fluid is the Reuss average of the gas and liquid bulk moduli. This averaging procedure, referred to as Wood's approximation, holds if the liquid and gas phases are homogeneously distributed within the pore space down to sizes well below the seismic wavelength and if the phase transfer processes between liquid and gas domains induced by the pressure variations of the seismic wave are negligible over the timescale of the wave period. Using existing theoretical results and low-frequency acoustic measurements in bubbly liquids, we argue that the latter assumption of “frozen” phases, valid for large enough frequencies, is likely to fail in the seismic frequency range where lower effective bulk modulus and velocity, together with dispersion and attenuation effects, are expected. We provide a simple method, which extends to reservoir fluids a classical result by Landau and Lifshitz valid for pure fluids, to compute the effective bulk modulus of thermodynamically equilibrated liquid and gas phases. For low gas saturation, this modulus is significantly lower than its Wood's counterpart, especially at the crossing of bubble point conditions. A seismic reflector associated to a phase transition between a monophasic and a two-phase fluid thus will appear. We discuss the consequences of these results for various seismic applications including fizz water discrimination and hydrocarbon reservoir depletion and CO₂ geological storage monitoring.     

Mechanical and flow behaviours and their interactions in coalbed geosequestration of CO2

Studying gas transport mechanisms in coal seams is crucial in determining the suitability of coal formations for geosequestration and/or CO₂-enhanced coal bed methane recovery (ECBM), estimating CO₂ storage capacity and recoverable volume of methane, and predicting the long-term integrity of CO₂ storage and possible leakages. Due to the dual porosity nature of coal, CO₂ transport is a combination of viscous flow and Fickian diffusion. Moreover, CO₂ is adsorbed by the coal which leads to coal swelling which can change the porous structure of coal and consequently affects the gas flow properties of coal, i.e. its permeability. In addition, during CO₂ permeation, the coal seam undergoes a change in effective stress due to the pore pressure alteration and this can also change the permeability of the coal seam. In addition, depending on the in situ conditions of the coal seam and the plan of the injection scheme, carbon dioxide can be in a supercritical condition which increases the complexity of the problem. We provide an overview of the recent studies on porous structure of coal, CO₂ adsorption onto coal, mechanisms of CO₂ transport in coalbeds and their measurement, and hydro-mechanical response of coal to CO₂ injection and identify opportunities for future research.     

Adsorption Mechanism and Kinetic Characterization of Bituminous Coal under High Temperatures and Pressures in the Linxing‐Shenfu Area

The majority of coalbed methane(CBM) in coal reservoirs is in adsorption states in coal matrix pores. To reveal the adsorption behavior of bituminous coal under high-temperature and high-pressure conditions and to discuss the microscopic control mechanism affecting the adsorption characteristics, isothermal adsorption experiments under hightemperature and high-pressure conditions, low-temperature liquid nitrogen adsorption-desorption experiments and CO2 adsorption experiments were performed on coal samples. Results show that the adsorption capacity of coal is comprehensively controlled by the maximum vitrinite reflectance(Ro, max), as well as temperature and pressure conditions. As the vitrinite reflectance increases, the adsorption capacity of coal increases. At low pressures, the pressure has a significant effect on the positive effect of adsorption, but the effect of temperature is relatively weak. As the pressure increases, the effect of temperature on the negative effect of adsorption gradually becomes apparent, and the influence of pressure gradually decreases. Considering pore volumes of pores with diameters of 1.7-100 nm, the peak volume of pores with diameters 10-100 nm is higher than that from pores with diameters 1.7-10 nm, especially for pores with diameters of 40-60 nm, indicating that pores with diameters of 10-100 nm are the main contributors to the pore volume. The pore specific surface area shows multiple peaks, and the peak value appears for pore diameters of 2-3 nm, indicating that this pore diameter is the main contributor to the specific surface area. For pore diameters of 0.489-1.083 nm, the pore size distribution is bimodal, with peak values at 0.56-0.62 nm and 0.82-0.88 nm. The adsorption capability of the coal reservoir depends on the development degree of the supermicroporous specific surface area, because the supermicroporous pores are the main contributors to the specific pore area. Additionally, the adsorption space increases as the adsorption equilibrium pressure increases. Under the same pressure, as the maximum vitrinite reflectance increases, the adsorption space increases. In addition, the cumulative reduction in the surface free energy increases as the maximum vitrinite reflectance increases. Furthermore, as the pressure increases, the surface free energy of each pressure point gradually decreases, indicating that as the pressure increases, it is increasingly difficult to adsorb methane molecules.     

On computation of strain‐dependent permeability of rocks and rock‐like porous media

Determination of transport properties of geomaterials is an important issue in many fields of engineering analysis and design. For example, in petroleum engineering, in situ permeability of an oil reservoir may be crucial in establishing its viability for exploitation, whilst prevention of leakage from underground storage facilities for oil and gas, nuclear waste as well as viability of CO₂ sequestration projects crucially depends on its long‐term values. Permeability is indirectly related to the porosity, pore‐size distribution and pore architecture of the porous media. These parameters evolve when a strain field is imposed. Physical measurement of permeability under a strain field in laboratory conditions is difficult, expensive and prone to a number of uncertainties. In the past, pore network models have been used to compute permeability of materials under stress/strain‐free conditions. In this paper, we propose an enhanced pore network model to compute permeability of rocks and rock‐like porous media under a stress/strain field. Data of pore‐size distribution obtained from mercury intrusion porosimetry are used to compute permeability of rock samples from various unspecified oilfields in the world. It is shown that the two permeabilities can be predicted from the model with sufficient accuracy. A hypothesis for change in porosity, pore‐size distribution and pore architecture as a result of imposed mechanical strains is then proposed. Based on this, permeability is computed again for one of the rock samples under uniaxial and triaxial compressive and tensile strain fields. It is shown that depending on the state of strain field imposed, permeability evolves in an anisotropic manner. Permeability under tensile strain field increases dramatically compared with the reduction that takes place under compressive strain field of the same magnitude. Copyright © 2014 John Wiley & Sons, Ltd.     

Key factors controlling the gas adsorption capacity of shale: A study based on parallel experiments

This article performed a series of parallel experiments with numerical modeling to reveal key factors affecting the gas adsorption capacity of shale, including shale quality, gas composition and geological conditions. Adsorption experiments for shales with similar OM types and maturities indicate that the OM is the core carrier for natural gas in shale, while the clay mineral has limited effect. The N₂ and CO₂ adsorption results indicate pores less than 3 nm in diameter are the major contributors to the specific surface area for shale, accounting for 80% of the total. In addition, micropores less than 2 nm in diameter are generated in large numbers during the thermal evolution of organic matter, which substantially increases the specific surface area and adsorption capacity. Competitive adsorption experiments prove that shale absorbs more CO₂ than CH₄, which implies that injection CO₂ could enhance the CH₄ recovery, and further research into N₂ adsorption competitiveness is needed. The Langmuir model simulations indicate the shale gas adsorption occurs via monolayers. Geologically applying the adsorption potential model indicates that the adsorption capacity of shale initially increases before decreasing with increasing depth due to the combined temperature and pressure, which differs from the changing storage capacity pattern for free gases that gradually increase with increasing depth at a constant porosity. These two tendencies cause a mutual conversion between absorbed and free gas that favors shale gas preservation. During the thermal evolution of organic matter, hydrophilic NSO functional groups gradually degrade, reduce the shale humidity and increase the gas adsorption capacity. The shale quality, gas composition and geological conditions all affect the adsorption capacity. Of these factors, the clay minerals and humidity are less important and easily overshadowed by the other factors, such as organic matter abundance.     

Experiments on Methane Displacement by Carbon Dioxide in Large Coal Specimens

Carbon dioxide (CO₂) is considered to be the most important greenhouse gas in terms of overall effect. CO₂ geological storage in coal beds is of academic and industrial interest because of economic synergies between greenhouse gas sequestration and coal bed methane (CH₄) recovery by displacement/adsorption. Previously, most work focused on either theoretical analyses and mathematical simulations or gas adsorption?Cdesorption experiments using coal particles of millimeter size or smaller. Those studies provided basic understanding of CH₄ recovery by CO₂ displacement in coal fragments, but more relevant and realistic investigations are still rare. To study the processes more realistically, we conducted experimental CH₄ displacement by CO₂ and CO₂ sequestration with intact 100?×?100?×?200?mm coal specimens. The coal specimen permeability was measured first, and results show that the permeability of the specimen is different for CH₄ and CO₂; the CO₂ permeability was found to be at least two orders of magnitude greater than that for CH₄. Simultaneously, a negative exponential relationship between the permeability and the applied mean stress on the specimen was found. Under the experimental stress conditions, 17.5?C28.0 volumes CO₂ can be stored in one volume of coal, and the displacement ratio CO₂?CCH₄ is as much as 7.0?C13.9. The process of injection, adsorption and desorption, displacement, and output of gases proceeds smoothly under an applied constant pressure differential, and the CH₄ content in the output gas amounted to 20?C50% at early stages, persisting to 10?C16% during the last stage of the experiments. Production rate and CH₄ fraction are governed by complex factors including initial CH₄ content, the pore and fissure fabric of the coal, the changes in this fabric as the result of differential adsorption of CO₂, the applied stress, and so on. During CO₂ injection and CH₄ displacement, the coal can swell from effects of gas adsorption and desorption, leading to changes in the microstructure of the coal itself. Artificial stimulation (e.g. hydraulic fracturing) to improve coalbed transport properties for either CO₂ sequestration or enhanced coal bed methane recovery will be necessary. The interactions of large-scale induced fractures with the fabric at the scale of observable fissures and fractures in the laboratory specimens, as well as to the pore scale processes associated with adsorption and desorption, remain of profound interest and a great challenge.     

Discussing the definition of the second‐order work for unsaturated soils

The volumetric compaction due to wetting processes is a phenomenon observed quite often in unsaturated soils. Under certain circumstances, saturation events can result into a sudden and unexpected collapse of the system. These phenomena are usually referred to as wetting‐induced collapses, without providing any detailed theoretical justification for this terminology. In order to predict in a general fashion the occurrence of coupled instabilities induced by saturation processes, a generalization of the theoretical approaches usually employed for saturated geomaterials is here provided. More specifically, this paper addresses the problem of hydro‐mechanical instability in unsaturated soils from an energy standpoint. For this purpose, an extension of the definition of the second‐order work is here suggested for the case of unsaturated porous media. On the basis of some examples of numerical simulations of laboratory tests, coupled hydro‐mechanical instabilities are then interpreted in the light of this second‐order energy measure. Finally, the implications of the theoretical results here presented are commented from a constitutive modelling perspective. Two possible alternative approaches to formulate incremental coupled constitutive relations are indeed discussed, showing how the onset of hydro‐mechanical instabilities can be predicted using an extended form of Hill's stability criterion. Copyright © 2010 John Wiley & Sons, Ltd.     

渗透压-应力耦合作用下煤体常规三轴试验的颗粒流模拟

为了研究在渗透压-应力耦合作用下围压和瓦斯压力对煤体变形破坏规律的影响,借助PFC2D软件进行了340组抗压及抗拉试验模拟,建立了煤体宏观力学参数与细观参数之间的关系。利用平行黏结模型和推导得出的细观参数,对煤体进行了不同围压和瓦斯压力条件下常规三轴试验的颗粒流模拟,并将模拟结果与物理试验结果进行对比及误差分析,对煤体宏观力学参数的变化规律进行了总结。分析结果表明,经过推导得到的宏细观参数关系,可以控制模拟结果的误差在10%之内,能较好地模拟煤体的力学特征;围压增大时,煤体的抗压强度、残余强度及弹性模量呈增大趋势,泊松比以及煤体的破裂角度变小,与物理试验所得围压对煤体的刚度和强度起增强作用的结论一致;瓦斯压力的升高会导致煤体抗压强度,残余强度及弹性模量减小,泊松比以及煤体破裂角度变大,验证了物理试验中瓦斯压力对煤体强度具有劣化作用的结论。     

含瓦斯煤孔隙率和有效应力影响因素试验研究

以孔隙率基本定义和力学平衡原理为出发点,充分考虑由煤层瓦斯的吸附膨胀和解吸收缩、温度效应的热胀冷缩和煤体骨架受孔隙瓦斯压力的压缩共同引起的本体变形,建立了在压缩条件下(扩容前)的含瓦斯煤孔隙率动态演化模型和以吸附热力学参数及瓦斯压力表达的有效应力方程,并分别根据现场实测孔隙率数据和含瓦斯煤三轴应力试验数据,对所建立的理论模型进行了验证。结果表明,理论计算值与实测资料和试验结论一致性较好,理论模型拟合精度较好,误差不大,所得结论对煤层气开采和矿井瓦斯灾害防治具有一定的指导意义。