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.     

Effect of bedding structural diversity of coal on permeability evolution and gas disasters control with coal mining

Bedding structure has affected gas flow in coal seam greatly, which also controls gas permeation direction and gas extraction results, and finally it has tremendous influence on prevention and control of gas disaster accidents. Combined with engineering practice of gas disaster prevention and control in China, in this paper, permeability evolution of nature coal in different bedding directions in the condition of loading is studied, and the results showed that in three directions of bedding fractures, permeability of coal which is parallel to bedding planes is the highest; it would be much easier for gas percolation along the bedding planes than other directions. In the unloading process, tension–shear destruction appears in coal sample which is oblique to bedding along the bedding planes, with a sudden increase in permeability. It is difficult for the crack damage from loading process to recover in unloading process, that is, permeability of unloading isn’t just a simple reverse process of loading. Combined with the permeability evolution of the three coal samples in the whole process, three permeability evolution models which include elasticity, plasticity and fracture are proposed. Based on the experimental results, gas extraction using boreholes along coal seam and through coal seam is compared during depressurized mining. Due to the bedding structure of coal seam, a large area of fracture network of “boreholes–bedding fractures” is formed among boreholes through coal seam and bedding structure, which makes the good effect of gas extraction using boreholes through coal seam. Research results will be of important guiding significance for choosing the best gas extraction scheme, layout of setting parameters of drilling boreholes and gas disaster prevention in the underground coal mine.     

Anisotropic mechanical properties and brittleness evaluation of layered phylliteEI北大核心

为了研究层状千枚岩的力学特性与各向异性特征,开展了不同层理倾角与不同围压下的千枚岩力学试验。对比分析了千枚岩试样强度、变形、脆性与破坏模式等各向异性特征。结果表明:(1)随着层理倾角β增加,岩样的强度、变形特征曲线形状呈U型;随围压增加,岩样强度及塑性增强,各向异性度逐渐减弱稳定。(2)采用多种强度准则描述岩样强度各向异性,其中Saeidi准则和改进Ramamurthy准则能很好地预测岩样在不同层理倾角下的抗压强度。(3)基于岩样峰前应力-应变曲线与能量特征提出了综合脆性评价指标,在层理倾角β=45°左右时,岩样脆性指标较低,更易发生剪切滑移破坏,得出脆性下降顺序为:沿层理面拉伸劈裂>穿层理面拉伸劈裂>沿层理面剪切>穿层理面剪切。(4)千枚岩的破坏模式与层理倾角和围压有关,单轴条件下,岩样劈裂破坏后易形成复杂裂纹网络;高围压下,岩样破裂后多形成单一的沿层理面或贯穿多层理面的剪切破坏。     

Hydromechanical behavior during constant-rate pumping tests in fractured gneiss

Deformation and fluid pressure during constant-rate pumping tests were characterized by sensitivity analyses using a theoretical model of a deformable fracture, and by conducting and analyzing field tests at a site underlain by fractured biotite gneiss in western South Carolina, USA. The sensitivity analysis indicates that displacement is a hysteretic function of fluid pressure during constant-rate pumping tests, and the signals are affected by properties of the fracture (normal stiffness, aperture, and heterogeneities in the fracture plane) and enveloping rock (elastic modulus and permeability). The field tests used a removable borehole extensometer to measure axial displacements in the pumping well. The field results are generally similar to simulations, and the hydraulic and mechanical properties obtained by inversion of the pumping test results are essentially the same as results from hydromechanical slug tests. The observed displacements early in the pumping tests are less than, whereas late in the test they are greater than predicted values assuming a uniform fracture. This difference can be explained as a consequence of preferential flow within the fracture. These results indicate that displacements in a wellbore are sensitive to details of fracture connectivity and preferential flow that are difficult to detect through the pressure signal alone.     

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.     

Non-Darcian flow in low-permeability media: key issues related to geological disposal of high-level nuclear waste in shale formations

In clay or other low-permeability media, water flow becomes non-Darcian and characterized by the non-linear relationship between water flux and hydraulic gradient. This work is devoted to addressing a number of key issues related to geological disposal of high-level nuclear waste in clay/shale formations. It is demonstrated that water flow velocity in the damaged zone (often considered as a potential preferential advection paths in a repository) surrounding the tunnel is extremely small, as a result of non-Darcian flow behavior, such that solute transport is dominated by diffusion, rather than advection. The finding is also consistent with the often-observed existence of persistent abnormal pressures in shale formations. While relative permeability is the key parameter for modeling the unsaturated flow process, without incorporating non-Darcian flow behavior, significant errors can occur in the determination of relative permeability values from traditional measurement methods. An approach for dealing with temperature impact on non-Darcian flow and a formulation to calculate non-Darcian water flux in an anisotropic medium are presented, taking into consideration that a geological repository is subject to temperature evolution in the near field as a result of heat generated by nuclear waste, and that shale formations are generally anisotropic.     

页岩各向异性力学特性微观测试方法研究

页岩力学各向异性特征是地应力、 井壁稳定、 水力裂缝扩展相关研究的重要基础参数.针对页岩力学各向异性宏观测试中存在样品制取困难、制样成功率低的特点,采用来源丰富的钻井岩屑或破碎岩块,通过研究纳米压痕实验原理、实验方法和数据解释方法,采用连续刚度测试方法对平行层理和垂直层理的页岩试样进行纳米压痕测试;基于硬度的分类准则将...     

Radial Permeability Measurements for Shale Using Variable Pressure Gradients

Shale gas is becoming an important component of the global energy supply, with permeability a critical controlling factor for long-term gas production. Obvious deviation may exist between helium permeability determined using small pressure gradient(SPG) methods and methane permeability obtained under actual field production with variable pressure gradients(VPG). In order to more accurately evaluate the matrix permeability of shale, a VPG method using real gas(rather than He) is established to render permeability measurements that are more representative of reservoir conditions and hence response. Dynamic methane production experiments were performed to measure permeability using the annular space in the shale cores. For each production stage, boundary pressure is maintained at a constant and the gas production with time is measured on the basis of volume change history in the measuring pump. A mathematical model explicitly accommodating gas desorption uses pseudo-pressure and pseudo-time to accommodate the effects of variations in pressuredependent PVT parameters. Analytical and semi-analytical solutions to the model are obtained and discussed. These provide a convenient approach to estimate radial permeability in the core by nonlinear fitting to match the semi-analytical solution with the recorded gas production data. Results indicate that the radial permeability of the shale determined using methane is in the range of 1×10-6– 1×10-5 mD and decreases with a decrease in average pore pressure. This is contrary to the observed change in permeability estimated using helium. Bedding geometry has a significant influence on shale permeability with permeability in parallel bedding orientation larger than that in perpendicular bedding orientation. The superiority of the VPG method is confirmed by comparing permeability test results obtained from both VPG and SPG methods. Although several assumptions are used, the results obtained from the VPG method with reservoir gas are much closer to reality and may be directly used for actual gas production evaluation and prediction, through accommodating realistic pressure dependent impacts.     

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.     

3‐D mesoscale simulation of crack‐permeability coupling in the Brazilian splitting test

In this paper, mesoscale hydromechanical simulations are performed to study (1) fracture features and (2) crack‐gas permeability coupling evolution in the context of the tensile splitting test. The mesostructure is based on a 2‐phase 3‐D representation of heterogeneous materials, such as concrete, where stiff aggregates are embedded into a mortar matrix. To take into account these heterogeneities without any mesh adaptation, a weak discontinuity is introduced into the strain field. In addition, a strong discontinuity is also added to take into account microcracking. This mechanical model is cast into the framework of the enhanced finite element method. Concerning the coupling with gas permeability, a double‐porosity method is used to simulate the flow through the cracks and the porosity. The apparent gas permeability is afterwards evaluated by a homogenization method. On the basis of finite element simulations, influence of aggregate size on ultimate crack opening, macroscopic ultimate tensile stress, total dissipated energy, and gas permeability evolution is numerically investigated. Furthermore, gas permeability evolution is also compared with experimental results from the literature. In addition, in the spirit of a sequential multiscale approach, macroscale gas permeability equations are identified from the hydromechanical results coming from the mesoscale computations. These equations lead to a relation between macroscale gas permeability evolution and crack opening. Besides, we show how the aggregate size influences the percolation threshold and that after this threshold, a cubic relation between macroscale gas permeability and crack opening is obtained.     

考虑页岩层理剪切滑移的水力裂缝几何参数计算方法

针对现有页岩气体积压裂层理裂缝扩展模型及其计算方法研究的不足,基于三点弯曲试验,结合数字图像法获取了页岩层理关键力学参数;利用弹性力学理论和线弹簧模型建立了页岩气体积压裂层理裂缝扩展拟三维数学模型,并得到了试验验证;开发了裂缝几何参数计算程序,计算分析了层理参数与压裂施工参数对水力裂缝扩展的影响规律。结果表明：当层理刚度小于10 GPa/m及大于30 GPa/m时,剪切滑移量达到极大值及极小值,且基本保持不变,当层理刚度在10～30 GPa/m之间时,层理刚度与剪切滑移量呈线性负相关关系;当层理密度为5～7条时,主裂缝会沟通更多的层理;当层理强度为5～8 MPa时,水力裂缝易穿层扩展,且能使层理产生剪切滑移,从而生成复杂裂缝;当压裂液排量和压裂液黏度分别在9～12 m3/min和2.5～5m Pa·s范围内时,水力裂缝易穿层扩展,最终形成十字型裂缝,有助于复杂裂缝的形成。该研究对认识页岩层理力学性能及其对层理裂缝扩展规律的影响有一定的指导意义。     

各向异性软岩的变形与渗流耦合特性试验研究

根据泥质粉砂岩和泥岩在垂直和平行于层理面的条件下进行的三轴压缩和渗流试验,得到了不同围压及岩石成层条件下泥质粉砂岩和泥岩的弹性模量,建立了基于层理面夹角和围压的软岩弹性模量控制方程。渗透张量与应力的耦合关系是各向异性渗流耦合分析的关键问题,通过引入应力主轴与渗透主轴非一致时渗透张量与应力的响应关系,建立了各向异性渗透张量与应力耦合的控制方程,并对比了试验数据与计算结果,为各向异性软岩渗流应力耦合分析模型的建立奠定了理论基础。     

层理面特性对砂岩断裂力学行为的影响研究

层理弱面对层状岩石的力学特性影响较显著，为了研究层理面特性对岩石断裂力学特性的影响，开展了具有不同层理方向的砂岩试样三点弯试验，探讨了砂岩断裂韧度及断裂模式的各向异性。之后基于有限元中的黏聚单元建立了数值模型，采用数值模拟方法研究了层理面强度对各层理角度试样断裂力学行为的影响规律。结果表明：层理方向影响下砂岩的断裂韧度及模式存在各向异性；同一层理方向试样的断裂韧度随层理面强度的增大而增大，且试样的层理面与加载方向夹角越小，断裂韧度受层理面强度变化影响越明显；试样的断裂模式不仅与层理面强度有关，还受层理倾角的控制，层理面与加载方向夹角θ = 0o试样断裂模式基本不受层理面强度影响，θ = 30o试样主要沿层理面张拉或剪切破坏，且沿层理面的破裂长度随层理面强度的降低逐渐增大；层理面强度较大时，θ = 45o试样主要沿层理面张拉破坏，θ = 60o～90o试样主要以贯穿层理的张拉破坏为主；层理面强度较小时，θ = 45o～90o试样均以沿层理面的剪切破坏为主，其中θ = 45o试样沿层理剪切长度最大。另外，通过数值模拟结果分析了层理面强度及方向对试样的起裂角及裂纹扩展路径产生的影响。该研究成果可作为层状岩石断裂力学理论的有益补充。     

Anisotropy of gas permeability associated with cleat pattern in a coal seam of the Kushiro coalfield in Japan

An underground investigation has been performed in a subbituminous coal seam exhibiting a particular cleat pattern in the Kushiro coalfield, Japan. The coal cleat pattern shows some analogy to isolated straight joints, and is believed to have been formed during the late Tertiary period by a compressive tectonic stress, roughly in the east–west direction. Three cylindrical coal specimens representing the three orthogonal axes of the coal seam with respect to the bedding plane and its associated cleat were cored from a large block of coal. Gas permeabilities of the three coal specimens were measured under the same hydrostatic pressure conditions. Results clearly revealed anisotropy in permeability of the coal seam under relatively low confining pressures of less than about 12 MPa. The specimen cored parallel to both the bedding plane and cleat strike showed the highest permeability, even though the cleats were partly filled with calcite and clay minerals. The permeability in this direction was 2.5 times higher than perpendicular to the bedding plane, and 3 times higher than in the direction parallel to the bedding plane but perpendicular to the cleat strike. This suggests that the cleats play a greater role than bedding planes in controlling fluid flow in the coal seam. The permeability in the three orientations, however, converged to the same value at confining pressures above about 16 MPa. This may suggest that both cleats and bedding planes in a coal seam can close due to earth pressure if the coal seam is located below a certain depth. It further indicates that the traditional view that gas permeability is always greater parallel to the coal bedding than perpendicular to it should be reconsidered.     

页岩各向异性特征的试验研究

为研究彭水页岩气区块储层的各向异性特征,开展了石柱县龙马溪组页岩的单轴和三轴压缩试验,分析了其力学特性、强度特征和破裂模式的各向异性,并揭示了其破坏机制的各向异性。结果表明：(1) 龙马溪组页岩具有明显的各向异性特征,弹性模量在平行层理方向最大,垂直层理方向最小,且围压的增加使其增加速率不断减小;0°、30°和60°、90°页岩的泊松比随围压的增加呈现出了相反的变化规律,这可能与页岩层理间孔隙和微裂缝的良好发育有关。(2) 相同围压下,0°试样强度最高,90°次之,30°最低,总体上呈现出两边高、中间低的U型变化规律,而不同角度的Hoek-Brown强度准则能较好地反映其强度的各向异性特征。(3) 页岩破裂模式的各向异性是由破坏机制的各向异性引起的,而强度的各向异性是由破坏机制的各向异性控制的。单轴压缩时,0°页岩为沿层理的张拉劈裂破坏,30°为沿层理的剪切滑移破坏,60°为贯穿层理和沿层理的复合剪切破坏,90°为贯穿层理的张拉破坏。三轴压缩时,0°为贯穿层理的共轭剪切破坏,30°为沿层理的剪切滑移破坏,60°和90°为贯穿层理的剪切破坏;页岩地层的层状沉积结构和层理间的弱胶结作用是破坏机制各向异性的根源。研究结果为水平井井壁的稳定性分析和水力压裂施工设计等提供了技术参考。     

不同应变率单轴加载条件下页岩的各向异性力学行为

基于静载条件下的常规力学试验可以证明,页岩层理面的存在是导致其力学行为各向异性的主要原因,而应变率的变化势必也影响着页岩各向异性特征的变化。为探究应变率对页岩各向异性力学行为的影响,分别在10-4 s-1、5×10-4 s-1、10-3 s-1和10-2 s-1 4种应变率条件下对不同层理角度的页岩进行单轴压缩力学试验。研究表明:（1）页岩弹性模量的各向异性程度随应变率升高而减弱,泊松比的各向异性程度受应变率的影响不明显;（2）页岩峰值强度随应变率升高而增加,其中45°~60°试样应变率敏感性最强,页岩的强度各向异性度随应变率升高而降低;（3）随着应变率升高,层理面对页岩破坏模式的控制作用得到削弱,破坏模式的各向异性程度减弱。总体而言,页岩的各向异性力学特征随应变率升高而减弱,研究结论有助于页岩力学行为的深入理解。     

Characterization of preferential flow paths between boreholes in fractured rock using a nanoscale zero-valent iron tracer test

Recent advances in borehole geophysical techniques have improved characterization of cross-hole fracture flow. The direct detection of preferential flow paths in fractured rock, however, remains to be resolved. In this study, a novel approach using nanoscale zero-valent iron (nZVI or ‘nano-iron’) as a tracer was developed for detecting fracture flow paths directly. Generally, only a few rock fractures are permeable while most are much less permeable. A heat-pulse flowmeter can be used to detect changes in flow velocity for delineating permeable fracture zones in the borehole and providing the design basis for the tracer test. When nano-iron particles are released in an injection well, they can migrate through the connecting permeable fracture and be attracted to a magnet array when arriving in an observation well. Such an attraction of incoming iron nanoparticles by the magnet can provide quantitative information for locating the position of the tracer inlet. A series of field experiments were conducted in two wells in fractured rock at a hydrogeological research station in Taiwan, to test the cross-hole migration of the nano-iron tracer through permeable connected fractures. The fluid conductivity recorded in the observation well confirmed the arrival of the injected nano-iron slurry. All of the iron nanoparticles attracted to the magnet array in the observation well were found at the depth of a permeable fracture zone delineated by the flowmeter. This study has demonstrated that integrating the nano-iron tracer test with flowmeter measurement has the potential to characterize preferential flow paths in fractured rock.     

Flow–stress coupled permeability tensor for fractured rock masses

In this paper a new analytical model is proposed to determine the permeability tensor for fractured rock masses based on the superposition principle of liquid dissipation energy. This model relies on the geometrical characteristics of rock fractures and the corresponding fracture network, and demonstrates the coupling effect between fluid flow and stress/deformation. This model empirically considers the effect of pre‐peak shear dilation and shear contraction on the hydraulic behavior of rock fractures and can be used to determine the applicability of the continuum approach to hydro‐mechanical coupling analysis. Results of numerical analysis presented in this paper show that the new model can effectively describe the permeability of fractured rock masses, and can be applied to the coupling analysis of seepage and stress fields. Copyright © 2008 John Wiley & Sons, Ltd.     

基于嵌入离散裂缝的页岩气藏视渗透率模型

页岩储层具有不同类型的储集空间,但综合考虑不同储集空间,对页岩储层渗透率进行评价的模型未见报道.基于嵌入离散裂缝模型,建立的页岩气藏视渗透率模型包括4个步骤:（1）构建天然裂缝、有机质和无机质的空间分布模型;（2）筛选不同类型储集空间的渗透率计算方法;（3）基于嵌入离散裂缝模型,结合空间分布模型和渗透率计算方法,建立数值模拟模型;（4）在模型的入口和出口端施加压差,求得一定压差下通过该岩心的气体流量,采用达西定律得到该页岩气藏的视渗透率.其计算结果与文献报道的渗透率实验值吻合较好.通过对不同因素的探讨,结果表明,天然裂缝对页岩气藏视渗透率的贡献大于无机质和有机质孔隙.因此,计算页岩视渗透率时有必要对天然裂缝、有机质和无机质孔隙进行综合考虑.      

川西新场须二段致密砂岩储层甜点类型及成因机制

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