A coupled compressible flow and geomechanics model for dynamic fracture aperture during carbon sequestration in coal

This paper presents the development of a discrete fracture model of fully coupled compressible fluid flow, adsorption and geomechanics to investigate the dynamic behaviour of fractures in coal. The model is applied in the study of geological carbon dioxide sequestration and differs from the dual porosity model developed in our previous work, with fractures now represented explicitly using lower-dimensional interface elements. The model consists of the fracture-matrix fluid transport model, the matrix deformation model and the stress-strain model for fracture deformation. A sequential implicit numerical method based on Galerkin finite element is employed to numerically solve the coupled governing equations, and verification is completed using published solutions as benchmarks. To explore the dynamic behaviour of fractures for understanding the process of carbon sequestration in coal, the model is used to investigate the effects of gas injection pressure and composition, adsorption and matrix permeability on the dynamic behaviour of fractures. The numerical results indicate that injecting nonadsorbing gas causes a monotonic increase in fracture aperture; however, the evolution of fracture aperture due to gas adsorption is complex due to the swelling-induced transition from local swelling to macro swelling. The change of fracture aperture is mainly controlled by the normal stress acting on the fracture surface. The fracture aperture initially increases for smaller matrix permeability and then declines after reaching a maximum value. When the local swelling becomes global, fracture aperture starts to rebound. However, when the matrix permeability is larger, the fracture aperture decreases before recovering to a higher value and remaining constant. Gas mixtures containing more carbon dioxide lead to larger closure of fracture aperture compared with those containing more nitrogen.     

Impact of Gas Adsorption Induced Coal Matrix Damage on the Evolution of Coal Permeability

It has been widely reported that coal permeability can change from reduction to enhancement due to gas adsorption even under the constant effective stress condition, which is apparently inconsistent with the classic theoretical solutions. This study addresses this inconsistency through explicit simulations of the dynamic interactions between coal matrix swelling/shrinking induced damage and fracture aperture alteration, and translations of these interactions to permeability evolution under the constant effective stress condition. We develop a coupled coal–gas interaction model that incorporates the material heterogeneity and damage evolution of coal, which allows us to couple the progressive development of damage zone with gas adsorption processes within the coal matrix. For the case of constant effective stress, coal permeability changes from reduction to enhancement while the damage zone within the coal matrix develops from the fracture wall to further inside the matrix. As the peak Langmuir strain is approached, the decrease of permeability halts and permeability increases with pressure. The transition of permeability reduction to permeability enhancement during gas adsorption, which may be closely related to the damage zone development in coal matrix, is controlled by coal heterogeneity, external boundary condition, and adsorption-induced swelling.     

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.     

Modelling of anisotropic coal swelling and its impact on permeability behaviour for primary and enhanced coalbed methane recovery

Coal swelling/shrinkage during gas adsorption/desorption is a well-known phenomenon. For some coals the swelling/shrinkage shows strong anisotropy, with more swelling in the direction perpendicular to the bedding than that parallel to the bedding. Experimental measurements performed in this work on an Australian coal found strong anisotropic swelling behaviour in gases including nitrogen, methane and carbon dioxide, with swelling in the direction perpendicular to the bedding almost double that parallel to the bedding. It is proposed here that this anisotropy is caused by anisotropy in the coal's mechanical properties and matrix structure. The Pan and Connell coal swelling model, which applies an energy balance approach where the surface energy change caused by adsorption is equal to the elastic energy change of the coal solid, is further developed to describe the anisotropic swelling behaviour incorporating coal property and structure anisotropy. The developed anisotropic swelling model is able to accurately describe the experimental data mentioned above, with one set of parameters to describe the coal's properties and matrix structure and three gas adsorption isotherms. This developed model is also applied to describe anisotropic swelling measurements from the literature where the model was found to provide excellent agreement with the measurement. The anisotropic coal swelling model is also applied to an anisotropic permeability model to describe permeability behaviour for primary and enhanced coalbed methane recovery. It was found that the permeability calculation applying anisotropic coal swelling differs significantly to the permeability calculated using isotropic volumetric coal swelling strain. This demonstrates that for coals with strong anisotropic swelling, anisotropic swelling and permeability models should be applied to more accurately describe coal permeability behaviour for both primary and enhanced coalbed methane recovery processes.     

开采扰动下考虑损伤破裂的深部煤体渗透率模型研究

为了研究深部煤体在开采扰动影响下的渗透率演化规律,以三向应力条件下的煤体渗透率模型为基础,从吸附解吸作用引起裂隙变形和损伤破裂造成煤基质弹性模量劣化的角度进行理论推导,引入内膨胀应变系数的概念,同时基于Drucker-Prager破坏准则的损伤本构关系建立了两种考虑煤体损伤破裂的渗透率演化模型——指数型和立方型,并且对常规三轴加载、开采扰动加卸载和改变气体压力下的瓦斯渗透试验结果进行了拟合分析。结果表明：所构建的两种模型可以较好地反映常规三轴加载和开采扰动加卸载下煤体渗透率的分区段变化特征,也可以描述有效围压恒定条件下煤体渗透率随气体压力升高而降低的规律。在开采扰动加卸载和改变气体压力的试验中,指数型的拟合效果略优于立方型。研究结果可为深部煤炭开采及瓦斯抽采的工作提供指导。     

CO2注入对煤储层应力应变与渗透率影响的实验研究

以沁水盆地成庄矿煤样为研究对象,利用实验室自主研发的CO₂注入与煤层气强化开采实验模拟装置进行不同有效应力和CO₂吸附压力下的煤岩渗透率测试。实验结果表明,煤岩的裂隙压缩系数受到CO₂吸附的影响,初始状态下、亚临界CO₂吸附和超临界CO₂吸附煤样裂隙压缩系数分别为0.066、0.086和0.089。引起裂隙压缩系数改变的原因主要有两方面:CO₂和煤中矿物反应提高了煤基质的不连续性;CO₂软化了煤基质同时降低了煤岩的力学性质。利用考虑吸附应变以及内部膨胀系数的渗透率模型对实测渗透率进行拟合,发现有效应力和内部膨胀系数成正比。CO₂吸附压力和有效应力的增大均提高了煤岩的内部膨胀系数,这影响了煤岩孔裂隙的开度,降低了煤储层的渗透率,并最终降低CO₂在煤储层中的可注性。      

山西沁水盆地中-南部煤储层渗透率物理模拟与数值模拟

通过对山西沁水盆地中南部上主煤层宏观裂隙观测,力学参数测量和应力渗透率实验,分别建立了裂隙面密度、裂隙产状、裂隙宽度与煤储层渗透率之间的预测数学模型;利用FLAC—3D软件,模拟了该区上主煤层内现代地应力状态,结合煤层气试井渗透率资料,构建了应力与渗透率之间关系预测的数学模型,并对该区上主煤层渗透率进行了全面预测。通过吸附膨胀实验,揭示了各煤类煤基质的收缩特征,构建了有效应力、煤基质收缩与渗透率之间的耦合数学模型,并对煤层气开发过程中渗透率动态变化进行了数值模拟。     

Evaluation of the reservoir permeability of anthracite coals by geophysical logging data

Permeability is one of the most significant reservoir parameters. It is commonly obtained by experiment, history simulation, injection/falloff well test and geophysical logging. Among these, geophysical logging remains as the most economic and efficient technique in evaluating coal permeability in the vicinity of an open-hole. In this paper, geophysical logging data are used to evaluate the coal reservoir permeability for the No. 3 coal seam in the southern Qinshui Basin (Fanzhuang and Zhengzhuang coal zones). Ideally coal reservoirs consist of coal matrix and fracture networks that can be represented by a model called a collection of sheets. Based on the model, coal reservoir permeability can be quantitatively calculated using the theoretical formula of k_f = 8.50 × 10^− 4 w²φ_f, in which fracture width (w) and fracture porosity (φ_f) were obtained by dual laterolog and density logging data, respectively. Calculative results show that coal reservoir permeability ranged from 0.017 mD to 0.617 mD for the Fanzhuang coal zone and from 0.047 mD to 1.337 mD for the Zhengzhuang coal zone. The permeability decreases with coal burial depth, reflecting variations in penetration capability of coal reservoirs at varying depths. Comparing results with those from injection/falloff well tests, however, shows that the model-calculated permeability is slightly higher. This is expected because the model did not include the influence from coal anisotropy.     

煤体吸附膨胀变形模型理论研究

为了深入探讨煤体吸附瓦斯发生膨胀变形效应的力学行为,基于煤-气吸附界面的表面自由能变化等于煤体弹性能的变化基本假设,从理论上推导了煤体吸附膨胀模型中吸附膨胀变形表达式和吸附膨胀应力表达式,模型中各参数的物理意义明确。通过已有的试验数据分别从低气体压、中气体压和高气体压3个角度对吸附变形模型的适用性和正确性进行了验证。模拟结果表明,模型预测数据与已有的试验数据吻合度较高,能够很好地描述不同气体在不同压力条件下的煤体吸附膨胀差异性,拟合精度均较高;在综合考虑吸附膨胀应力和气体压力对煤体吸附膨胀变形影响前提下,忽略吸附气体体积Va对煤体吸附膨胀变形的影响。     

沿抽采井筒的煤储层渗透率模型研究

渗透率是表征瓦斯流动的重要参数,为保证煤矿瓦斯安全高效抽采,有必要探究距抽采井筒不同位置处煤层瓦斯渗流演化特征。然而,瓦斯抽采过程中伴随有效应力、煤基质对瓦斯的吸附/解吸能力以及煤储层温度的不断变化,甚至出现抽采损伤,使得煤层瓦斯运移行为异常复杂。为探究抽采过程的煤层瓦斯渗流特性,在圆柱坐标系下,考虑压力场与温度场变化对煤储层渗透率的影响,构建温度影响的孔隙压力时空演化函数,据此建立应力与温度作用下的煤储层渗透率模型。结果表明:建立的模型能合理描述沿抽采井筒孔隙压力的演化规律以及瓦斯的运移特性,即在恒定外应力的条件下,随抽采时间增加,不同位置处孔隙压力先降低后变化平缓,煤储层渗透率先降低后升高;此外,同一煤储层位置处,考虑温度比不考虑温度的渗透率计算值更低;通过讨论发现,随抽采时间增加,根据裂隙压缩与基质收缩对渗透率演化的不同效应,设置合理的负压抽采方式可提高瓦斯抽采量。      

单孔增透率算法的提出及其工程应用

低透煤层增透效果的定量描述和评价一直处于盲目状态,使得煤矿瓦斯治理中致裂措施、瓦斯抽采不能因地制宜。增透率可反映采动或人工增透措施对煤岩体渗透特性的改变,并可定量评价煤层增透效果,其分布和演化规律可精准圈定瓦斯富集区域,指导瓦斯抽采钻孔的合理布置。在简化钻孔和裂隙模型基础上,求解了采动条件下钻孔的体积应变,提出了针对单孔的增透率计算方法;依托同煤矿塔山矿8212采面,开展现场裂隙探测试验,研究了工作面前方采动裂隙网络发育演化及卸压增透变化规律,并分析了单孔增透率随回采面推进的演化特征。结果表明：裂隙网络呈现“从无到有、从短变长、从窄变宽、不断贯通”的趋势,煤岩体单孔增透率随回采面推进呈现先逐渐上升后保持平稳的趋势,该成果有望直接优化煤矿现场瓦斯抽采孔的布置设计。     

Influence of carbon dioxide on coal permeability determined by pressure transient methods

The permeability of coal samples from Pittsburgh Seam was determined using carbon dioxide as the flowing fluid. The confining pressure was varied to cover a wide range of depths. The permeability was determined as a function of exposure time of carbon dioxide while the confining stress was kept constant. The porosities of the coal samples were found to be very low and most of the samples had porosities less than 1%. The permeability of these coal samples was very low—less than 1 μD. Since the objective of this study was to investigate the influence of CO₂ exposure on coal permeability, it was necessary to increase the initial permeability of the coal samples by introducing a fracture. A longitudinal fracture was induced mechanically, and CT scans were taken to ensure that the fracture was present throughout the sample and that the sample was not damaged otherwise during the process. In this study, the permeability of coal was determined by using pressure transient methods. Two types of pressure pulses were used: A-spike and Sine-6 pressure transients. It was first established that the permeability of fractured coal samples did not change with exposure time when an inert gas (Argon) was used as the fluid medium in the experiments. However, the permeability of coal samples decreased significantly when carbon dioxide was used as the fluid medium. This reduction can be attributed to the coal swelling phenomenon. The results show that the permeability reduction in fractured coal samples can be over 90% of the original value, and the exposure time for such reductions can range from 1.5 days up to a week, typically about 2 days under laboratory conditions. The permeability decreased significantly with the increase in confining pressure. The higher confining pressure appears to close internal fractures causing a reduction in permeability.     

Permeability evolution in fractured coal: The roles of fracture geometry and water-content

We report laboratory experiments that investigate the permeability evolution of an anthracite coal as a function of applied stress and pore pressure at room temperature as an analog to other coal types. Experiments are conducted on 2.5 cm diameter, 2.5-5 cm long cylindrical samples at confining stresses of 6 to 12 MPa. Permeability and sorption characteristics are measured by pulse transient methods, together with axial and volumetric strains for both inert (helium (He)) and strongly adsorbing (methane (CH₄) and carbon dioxide (CO₂)) gases. To explore the interaction of swelling and fracture geometry we measure the evolution of mechanical and transport characteristics for three separate geometries — sample A containing multiple small embedded fractures, sample B containing a single longitudinal through-going fracture and sample C containing a single radial through-going fracture. Experiments are conducted at constant total stress and with varied pore pressure — increases in pore pressure represent concomitant (but not necessarily equivalent) decreases in effective stress. For the samples with embedded fractures (A and C) the permeability first decreases with an increase in pressure (due to swelling and fracture constraint) and then increases near-linearly (due to the over-riding influence of effective stresses). Conversely, this turnaround in permeability from decreasing to increasing with increasing pore pressure is absent in the discretely fractured sample (B) — the influence of the constraint of the connecting fracture bridges in limiting fracture deformation is importantly absent as supported by theoretical considerations. Under water saturated conditions, the initial permeabilities to all gases are nearly two orders of magnitude lower than for dry coal and permeabilities increase with increasing pore pressure for all samples and at all gas pressures. We also find that the sorption capacities and swelling strains are significantly reduced for water saturated samples — maybe identifying the lack of swelling as the primary reason for the lack of permeability decrease. Finally, we report the weakening effects of gas sorption on the strength of coal samples by loading the cores to failure. Results surprisingly show that the strength of the intact coal (sample A) is smaller than that of the axially fractured coal (sample B) due to the extended duration of exposure to CH₄ and CO₂. Average post-failure particle size for the weakest intact sample (A) is found to be three times larger than that of the sample B, based on the sieve analyses from the samples after failure. We observe that fracture network geometry and saturation state exert important influences on the permeability evolution and strength of coal under in situ conditions.     

Shrinkage and swelling of coal induced by desorption and sorption of fluids: Theoretical model and interpretation of a field project

Geologic sequestration in deep unmineable coal seams and enhanced coalbed methane production is a promising choice, economically and environmentally, to reduce anthropogenic gases such as carbon dioxide in the atmosphere. Unmineable coal seams are typically known to adsorb large amounts of carbon dioxide in comparison to the sizeable amounts of sorbed methane, which raises the potential for large scale sequestration projects. During the process of sequestration, carbon dioxide is injected into the coalbed and desorbed methane is produced. The coal matrix is believed to shrink when a gas is desorbed and swell when a gas is sorbed, sometimes causing profound changes in the cleat porosity and permeability of the coal seam. These changes may have significant impact on the reservoir performance. Therefore, it is necessary to understand the combined influence of swelling and shrinkage, and geomechanical properties including elastic modulus, cleat porosity, and permeability of the reservoir.The present paper deals with the influence of swelling and shrinkage on the reservoir performance, and the geomechanical response of the reservoir system during the process of geologic sequestration of carbon dioxide and enhanced coalbed methane production in an actual field project located in northern New Mexico. A three-dimensional swelling and shrinkage model was developed and implemented into an existing reservoir model to understand the influence of geomechanical parameters, as well as swelling and shrinkage properties, on the reservoir performance. Numerical results obtained from the modified simulator were compared to available measured values from that site and previous studies. Results show that swelling and shrinkage, and the combination of geomechanical and operational parameters, have a significant influence on the performance of the reservoir system.     

混合型缓冲回填材料膨胀力试验研究

与纯膨润土相比,混合型缓冲回填材料（膨润土与石英砂混合物）能够实现防渗阻隔能力、热传导性能、力学强度和可施工性能的最佳组合。选用高庙子钠基膨润土（GMZ001）为缓冲回填材料的主料,添加不同比例的石英砂,对掺砂比分别为0、10%、20%、30%、40%和50%的膨润土-砂混合物压实试样进行室内试验。结果表明,混合物的液限、塑限随掺砂率的增大而线性降低;膨胀力随时间呈指数增长。初始含水率较大时,最大膨胀力随初始含水率的增大略有降低。掺砂率一定时,最大膨胀力随初始干密度指数增长。提出了有效黏土密度的概念,建立了一定初始含水率条件下,任意掺砂率和初始干密度的高庙子膨润土-砂混合物最大膨胀力归一化模型,为混合型缓冲回填材料膨胀力的预测与控制提供了依据。     

损伤和剪胀效应对裂隙煤体渗透率演化规律的影响研究

煤层瓦斯渗透率是影响瓦斯抽采和动力灾害防治的重要参数。为了研究煤体损伤和剪胀变形对渗透率的影响,首先引入损伤变量反映煤体损伤破坏状态,建立了基于体应变增量的煤体损伤本构模型。并采用Hurst指数表征裂隙表面粗糙度,基于裂隙表面的分形特征,建立了裂隙渗透率在压缩和剪切作用下的演化模型。通过对TOUGH2和FLAC3D软件进行二次开发,建立了基于双重孔隙模型的TOUGH2(CH4)-FLAC气-固耦合数值分析工具。采用本软件对煤样单轴压缩过程进行模拟分析,结果表明：煤体的破坏是损伤单元累积和贯通的结果,最终形成贯通煤体的损伤带是造成煤体失稳破坏的主因;围岩内的渗透率增加区域与损伤区位置基本一致,其中裂隙系统的渗透率增加幅度最大可达2个数量级;剪切破坏区的裂隙发生剪胀变形,引起裂隙渗透率大幅增加。建立的理论模型与数值计算工具为制定瓦斯治理措施提供了理论指导。     

A numerical model simulating reactive transport and evolution of fracture permeability

A numerical model is presented to describe the evolution of fracture aperture (and related permeability) mediated by the competing chemical processes of pressure solution and free‐face dissolution/precipitation; pressure (dis)solution and precipitation effect net‐reduction in aperture and free‐face dissolution effects net‐increase. These processes are incorporated to examine coupled thermo‐hydro‐mechano‐chemo responses during a flow‐through experiment, and applied to reckon the effect of forced fluid injection within rock fractures at geothermal and petroleum sites. The model accommodates advection‐dominant transport systems by employing the Lagrangian–Eulerian method. This enables changes in aperture and solute concentration within a fracture to be followed with time for arbitrary driving effective stresses, fluid and rock temperatures, and fluid flow rates. This allows a systematic evaluation of evolving linked mechanical and chemical processes. Changes in fracture aperture and solute concentration tracked within a well‐constrained flow‐through test completed on a natural fracture in novaculite (Earth Planet. Sci. Lett. 2006, in press) are compared with the distributed parameter model. These results show relatively good agreement, excepting an enigmatic abrupt reduction in fracture aperture in the early experimental period, suggesting that other mechanisms such as mechanical creep and clogging induced by unanticipated local precipitation need to be quantified and incorporated. The model is applied to examine the evolution in fracture permeability for different inlet conditions, including localized (rather than distributed) injection. Predictions show the evolution of preferential flow paths driven by dissolution, and also define the sense of permeability evolution at field scale. Copyright © 2006 John Wiley & Sons, Ltd.     

考虑渗透率变化的煤层气储层数值模拟及参数敏感性研究

煤层气开采过程中储层渗透率的变化对产气量影响较大,通过引入S＆D渗透率变化模型,建立了考虑渗透率变化的煤储层三维气水两相渗流数学模型,完成模型检验后应用所编制软件研究了煤储层参数、吸附参数及渗透率模型特征参数对开发效果的影响。结果表明,煤层气产量随着初始含气量、煤层有效厚度、裂缝渗透率和Langmuir压力的增大而增大,随储层原始压力、裂缝孔隙度和Langmuir体积的增大而减小,而解吸时间对产气量影响不大;裂缝渗透率随着杨氏模量和基质收缩/膨胀系数的增大而增大,随泊松比和裂缝压缩系数的增大而减小。引入S＆D模型后计算的累积产气量要比常规模型低1.3%,因此不可忽视煤层气产出过程中渗透率的变化。     

盐溶液对膨润土膨胀性的影响

膨润土因其优良的膨胀性和低渗透性常被用作深层地质处置库的缓冲和回填材料,但其膨胀性会受到地下流体溶液浓度的影响。针对这种现象,利用单轴固结仪研究了压实商用膨润土在不同上覆荷载和不同浓度NaCl溶液作用下的膨胀变形特性。结果表明：随着NaCl溶液浓度升高,该膨润土的膨胀性显著降低,且最大膨胀应变与上覆荷载之间在双对数坐标系下存在良好的线性关系。利用有效压力的概念和计算方法,实现了用唯一一条曲线来描述不同盐溶液浓度作用下膨润土的膨胀变形行为,同时证明了有效压力理论的合理性。     

Determination of in-situ stress direction from cleat orientation mapping for coal bed methane exploration in south-eastern part of Jharia coalfield, India

Accurate prediction of in-situ stress directions plays a key role in any Coal Bed Methane (CBM) exploration and exploitation project in order to estimate the production potential of the CBM reservoirs. Permeability is one of the most important factors for determination of CBM productivity. The coal seams in Jharia coalfield generally show low permeability in the range of 0.5 md to 3 md. To estimate the in-situ stress direction in the study area, an attempt has been made to undertake the cleat orientation mapping of four regional coal seams of two underground coal mines located at south-eastern part of Jharia coalfield, India. Cleat orientation mapping is critical to determine the maximum principal compressive horizontal stress (S_H) direction for CBM exploration and exploitation, which in turn controls the direction of maximum gas or water flow though coal beds. From the field study it is found that the average face and butt cleat azimuths are towards N15°W and N75°E respectively. Average permeability of the four above-mentioned major coal seams has been calculated from well logs of nine CBM wells distributing over an area of 7.5 km², adjacent to the underground mines. The cleat orientations are congruous with the regional lineament pattern and fits well with the average permeability contour map of the study area to infer the orientation of in-situ maximum horizontal stress. Goodness of fit for the exponential regressions between vertical stress and permeability for individual coal seams varies between 0.6 and 0.84. The cleat orientation is further validated from the previous fracture analysis using FMI well log in Parbatpur area located southern part of the Jharia coalfield. The major coal seams under the study area exhibit directional permeability, with the maximum permeability, oriented parallel to the direction of face cleat orientation.