The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion

Flow in a single fracture (SF) is an important research subject in groundwater hydrology, hydraulic engineering, radioactive nuclear waste repository and geotechnical engineering. An abruptly changing aperture is a unique type of SF. This study discusses the relation between the values of the critical Reynolds number (Re_c) for the onset of symmetry breaking of flow and the expansion ratio (E) of SF, which is defined as the ratio between the outlet (D) and inlet (d) apertures. This study also investigates the effect of inlet aperture d on Re_c for flow in an SF with abruptly changing apertures (SF‐ACA) using the finite volume method. Earlier numerical and experimental results showed that flow is symmetric in respect to the central plane of the SF‐ACA at small Reynolds number (Re) but becomes asymmetric when Re is sufficiently large. Our simulations show that the value of Re_c decreases with the increasing E, and the relationship between the logarithm of Re_c and E can be described accurately using either a quadratic polynomial function or a logarithmic function. However, the relationship of Re_c and d for a given E value is vague, and Re_c becomes even less sensitive to d when E increases. This study also reveals that the hydraulic gradient (J) and flow velocity (v) follow a super‐linear relationship that can be fitted almost perfectly by the Forchheimer equation. The inertial component (J_i) of J increases monotonically with Re, whereas the viscous component (J_v) of J decreases monotonically with Re. The Re value corresponding to equal inertial and viscous components of J (named as the transitional point Re) decreases when E increases, and such a transitional point Re should be closely related to the critical Reynolds number Re_c, although a rigorous theoretical proof is not yet available. Copyright © 2015 John Wiley & Sons, Ltd.     

Large‐scale poroelastic fractured reservoirs modeling using the fast multipole displacement discontinuity method

An effective approach to modeling the geomechanical behavior of the network and its permeability variation is to use a poroelastic displacement discontinuity method (DDM). However, the approach becomes rather computationally intensive for an extensive system of cracks, particularly when considering coupled diffusion/deformation processes. This is because of additional unknowns and the need for time‐marching schemes for the numerical integration. The Fast Multipole Method (FMM) is a technique that can accelerate the solution of large fracture problems with linear complexity with the number of unknowns both in memory and CPU time. Previous works combining DDM and FMM for large‐scale problems have accounted only for elastic rocks, neglecting the fluid leak‐off from the fractures into the matrix and its influence on pore pressure and stress field. In this work we develop an efficient geomechanical model for large‐scale natural fracture networks in poroelastic reservoirs with fracture flow in response to injection and production operations. Accuracy and computational performance of the proposed method with those of conventional poroelastic DDM are compared through several case studies involving up to several tens of thousands of boundary elements. The results show the effectiveness of the FMM approach to successfully evaluate field‐scale problems for the design of exploitation strategies in unconventional geothermal and petroleum reservoirs. An example considering faults reveals the impact of reservoir compartmentalization because of sealing faults for both geomechanical and flow variables under elastic and poroelastic rocks. Copyright © 2015 John Wiley & Sons, Ltd.     

Reaction softening by dissolution–precipitation creep in a retrograde greenschist facies ductile shear zone,New Hampshire,USA

We describe strain localization by a mixed process of reaction and microstructural softening in a lower greenschist facies ductile fault zone that transposes and replaces middle to upper amphibolite facies fabrics and mineral assemblages in the host schist of the Littleton Formation near Claremont, New Hampshire. Here, Na‐poor muscovite and chlorite progressively replace first staurolite, then garnet, and finally biotite porphyroblasts as the core of the fault zone is approached. Across the transect, higher grade fabric‐forming Na‐rich muscovite is also progressively replaced by fabric‐forming Na‐poor muscovite. The mineralogy of the new phyllonitic fault‐rock produced is dominated by Na‐poor muscovite and chlorite together with late albite porphyroblasts. The replacement of the amphibolite facies porphyroblasts by muscovite and chlorite is pseudomorphic in some samples and shows that the chemical metastability of the porphyroblasts is sufficient to drive replacement. In contrast, element mapping shows that fabric‐forming Na‐rich muscovite is selectively replaced at high‐strain microstructural sites, indicating that strain energy played an important role in activating the dissolution of the compositionally metastable muscovite. The replacement of strong, high‐grade porphyroblasts by weaker Na‐poor muscovite and chlorite constitutes reaction softening. The crystallization of parallel and contiguous mica in the retrograde foliation at the expense of the earlier and locally crenulated Na‐rich muscovite‐defined foliation destroys not only the metastable high‐grade mineralogy, but also its stronger geometry. This process constitutes both reaction and microstructural softening. The deformation mechanism here was thus one of dissolution–precipitation creep, activated at considerably lower stresses than might be predicted in quartzofeldspathic rocks at the same lower greenschist facies conditions.     

The influence of stress history on the grain size and microstructure of experimentally deformed quartzite

Deformation of middle crustal shear zones likely varies with time as a result of the stress build-up and release associated with earthquakes and post-seismic deformation, but the processes involved and their microstructural signature in the rock record are poorly understood. We conducted a series of experiments on quartzite at 900 °C to characterize microstructures associated with changes in stress and strain rate, and to investigate the feasibility of carrying out grain size piezometry in natural rocks that experienced analogous changes. Differential stress (referred to simply as “stress”) was varied in two-stage experiments by changing strain rate and by stopping the motor and allowing stress to relax. The two-stage samples preserve a microstructural record that can be interpreted quantitatively in terms of stress history. The microstructure associated with a stress increase is a bimodal distribution of recrystallized grain sizes. The smaller grains associated with the second deformation stage accurately record the stress of the second stage, and the surviving coarse grains remain similar in size to those formed during the earlier stage. The transient microstructure associated with stress decrease is a “partial foam” texture containing a larger concentration of stable 120° triple junctions than occur in samples deformed at a relatively constant strain rate. Our results indicate that microstructures preserved in rocks that experienced relatively simple, two-stage deformation histories can be used to quantitatively assess stress histories.Grain growth rates during deformation are similar to rates observed in previous isostatic growth experiments, supporting theoretical approaches to recrystallized grain size, such as the wattmeter theory (Austin and Evans, 2007), that incorporate static growth rates. From an analysis of the experimental data for quartz recrystallized grain size, we find: 1) Recrystallized grain size quickly reaches a value consistent with ambient deformation conditions. We argue that this explains a good match between average grain sizes predicted by the wattmeter after complete recrystallization and the recrystallized grain sizes of the experiments. 2) The present formulation of the wattmeter overestimates the rates at which porphyroclasts recrystallize by as much as an order of magnitude, and 3) owing to problems with extrapolation of grain growth data for quartz, the wattmeter is not presently applicable to natural samples deformed at low temperatures. We present a simplified flow law for quartz, and suggest that the change in slope of the quartz piezometer at high stress (regime 1) is related to a switch to a linear viscous rheology.     

Strain partitioning into dry and wet zones and the formation of Ca-rich myrmekite in syntectonic syenites: A case for melt-assisted dissolution-replacement creep under granulite facies conditions

The formation of Ca-rich myrmekites is described in syntectonic syenites crystallized and progressively deformed under granulite facies conditions. The syenites are found in high- and low-strain zones where microstructure and mineral composition are compared. Heterogeneously distributed water-rich, late-magmatic liquids were responsible for strain partitioning into dry and wet high-strain zones at outcrop scale, where contrasting deformation mechanisms are reported. In dry high-strain zones K-feldspar and clinopyroxene are recrystallized under high-T conditions. In wet high-strain zones, the de-stabilization of clinopyroxene and pervasive replacement of relatively undeformed K-feldspar porphyroclasts by myrmekite and subordinate micrographic intergrowths indicate dissolution-replacement creep as the main deformation mechanism. The reworking of these intergrowths is observed and is considered to contribute significantly to the development of the mylonitic foliation and banding. A model is proposed for strain partitioning relating a positive feedback between myrmekite-forming reaction, continuous inflow of late-magmatic liquids and dissolution-replacement creep in the wet zone at the expenses of original mineralogy preserved in the dry zones. Melt-assisted dissolution-replacement creep in syntectonic environments under granulite-facies conditions may extend the field of operation of dissolution-replacement creep, changing significantly the rheology of the lower continental crust.     

Displacement velocity effects on rock fracture shear strengths

Triaxial shear tests are performed to assess the effects of displacement velocity and confining pressure on shear strengths and dilations of tension-induced fractures and smooth saw-cut surfaces prepared in granite, sandstone and marl specimens. A polyaxial load frame is used to apply confining pressures between 1 and 18 MPa with displacement velocities ranging from 1.15 × 10⁻⁵ to 1.15 × 10⁻² mm/s. The results indicate that the shearing resistances of smooth saw-cut surfaces tend to be independent of the displacement velocity and confining pressure. Under each confinement the peak and residual shear strengths and dilation rates of rough fractures increase with displacement velocities. The sheared-off areas increase when the confining pressure increases, and the displacement rate decreases. The velocity-dependent shear strengths tend to act more under high confining pressures for the rough fractures in strong rock (granite) than for the smoother fractures in weaker rocks (sandstone and marl). An empirical criterion that explicitly incorporates the effects of shear velocity is proposed to describe the peak and residual shear strengths. The criterion fits well to the test results for the three tested rocks.     

Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

A universal particle velocity based algorithm for simulating hydraulic fractures, previously proposed for Newtonian fluids, is extended to the class of shear-thinning fluids. The scheme is not limited to any particular elasticity operator or crack propagation regime. The computations are based on two dependent variables: the crack opening and the reduced particle velocity. The application of the latter facilitates utilization of the local condition of Stefan type (speed equation) to trace the fracture front. The condition is given in a general explicit form which relates the crack propagation speed (and the crack length) to the solution tip asymptotics. The utilization of a modular structure, and the adaptive character of its basic blocks, result in a flexible numerical scheme. The computational accuracy of the proposed algorithm is validated against a number of analytical benchmark solutions.     

渝东南下古生界页岩构造裂缝形成及分布控制因素

天然裂缝对页岩气储集和渗流有重要影响,但目前对页岩构造裂缝研究不够深入。本文通过露头、岩心裂缝观察和分析,探讨了渝东南下古生界页岩构造裂缝类型、形成机理及分布控制因素。基于裂缝特征及力学成因,将剪切裂缝分为高角度剪切裂缝、倾斜滑脱裂缝和水平滑脱裂缝。倾斜滑脱裂缝是在上覆岩层重力和水平构造应力共同作用下沿应力集中的软弱面发生剪切滑动形成,水平滑脱裂缝是在构造挤压应力作用条件下主要沿页理面方向的剪切或层间滑动形成;页理发育程度及岩层曲率是控制水平滑脱裂缝形成的关键因素,岩石矿物组成、构造作用及岩层厚度是控制其它类型构造裂缝形成和分布的主要因素,页岩岩石力学层的划分需要根据裂缝特征、岩性变化特征、岩石力学参数及沉积界面等综合确定,岩层厚度与层间构造裂缝密度呈负相关关系。     

北大巴山闹阳坪锌萤石矿区断裂特征与找矿预测

闹阳坪锌萤石矿床位于北大巴山逆冲推覆褶皱带平利隆起东侧,为该区首次发现的受构造裂隙控制的气水–热液型锌萤石矿床。本文从矿区断裂入手,通过对该区矿床地质、断裂特征、矿体特征的研究,总结了该区断裂的演化序列及其对成矿的控制机制与规律。认为NW-SE向断裂组是矿区的主要控矿构造,矿区断裂变形发育演化序列为晚印支–早燕山期形成近EW向断裂F1,早燕山期形成NW-SE向断裂F7和NE-SW向断裂F4,随后的右行走滑作用叠加有张扭性应力,形成有利于成矿热液运移充填成矿的张扭性右行走滑断裂。并明确了成矿期应变椭球体,恢复了成矿期主压应力方向为NNW向(340°~350°)。在此基础上,预测平面上闹阳坪矿区F7与F8断裂之间为下一步找矿重点地段,剖面上K3萤石矿体下伏北东方向可能存在隐伏矿体。     

三维高密度电阻率法在堤坝工程中的模拟试验

为检测堤坝中裂隙、洞穴及渗漏层等隐患的存在,利用三维高密度电阻率法对数字模型和物理模型建立的裂隙隐患进行探测,结果表明室内建立的物理模型在立体图和分层切片图中裂隙的形态有些变化,但其分布范围、位置与相对各自模型中实际的比例尺寸相差不大,说明数值模拟得出的结论可以为实际工程进行理论指导,具有一定的参考价值。