Nonlinear fluid flow through three-dimensional rough fracture networks:Insights from 3D-printing,CT-scanning,and high-resolution numerical simulations

Nonlinear flow behavior of fluids through three-dimensional(3 D) discrete fracture networks(DFNs)considering effects of fracture number, surface roughness and fracture aperture was experimentally and numerically investigated. Three physical models of DFNs were 3 D-printed and then computed tomography(CT)-scanned to obtain the specific geometry of fractures. The validity of numerically simulating the fluid flow through DFNs was verified via comparison with flow tests on the 3 D-printed models. A parametric study was then implemented to establish quantitative relations between the coefficients/parameters in Forchheimer's law and geometrical parameters. The results showed that the 3 D-printing technique can well reproduce the geometry of single fractures with less precision when preparing complex fracture networks, numerical modeling precision of which can be improved via CT-scanning as evidenced by the well fitted results between fluid flow tests and numerical simulations using CT-scanned digital models. Streamlines in DFNs become increasingly tortuous as the fracture number and roughness increase, resulting in stronger inertial effects and greater curvatures of hydraulic pressure-low rate relations, which can be well characterized by the Forchheimer's law. The critical hydraulic gradient for the onset of nonlinear flow decreases with the increasing aperture, fracture number and roughness,following a power function. The increases in fracture aperture and number provide more paths for fluid flow, increasing both the viscous and inertial permeabilities. The value of the inertial permeability is approximately four orders of magnitude greater than the viscous permeability, following a power function with an exponent a of 3, and a proportional coefficient β mathematically correlated with the geometrical parameters.     

Numerical modeling of the effects of roughness on flow and eddy formation in fractures

The effect of roughness on flow in fractures was investigated using lattice Boltzmann method (LBM). Simulations were conducted for both statistically generated hypothetical fractures and a natural dolomite fracture. The effect of increasing roughness on effective hydraulic aperture, Izbash and Forchheimer parameters with increasing Reynolds number (Re) ranging from 0.01 to 500 was examined. The growth of complex flow features, such as eddies arising near the fracture surface, was directly associated with changes in surface roughness. Rapid eddy growth above Re values of 1, followed by less rapid growth at higher Re values, suggested a three-zone nonlinear model for flow in rough fractures. This three-zone model, relating effective hydraulic conductivity to Re, was also found to be appropriate for the simulation of water flow in the natural dolomite fracture. Increasing fracture roughness led to greater eddy volumes and lower effective hydraulic conductivities for the same Re values.     

Convective heat transfer of water flow in intersected rock fractures for enhanced geothermal extraction

Numerous intersected rock fractures constitute the fracture network in enhanced geothermal systems.The complicated convective heat transfer behavior in intersected fractures is critical to the heat recovery in fractured geothermal reservoirs.A series of three-dimensional intersected fracture models is constructed to perform the flow-through heat transfer simulations.The geometry effects of dead-end fractures(DEFs)on the heat transfer are evaluated in terms of intersected angles,apertures,lengths,and the connectivity.The results indicate that annular streamlines appear in the rough DEF and cause an ellipse distribution of the cold front.Compared to plate DEFs,the fluid flow in the rough DEF enhances the heat transfer.Both the increment of outlet water temperatureΔToutand the ratio of heat production Qrpresent the largest at the intersected angle of 90°while decline with the decrease of the intersected angle between the main flow fracture(MFF)and the DEFs.The extension of the length of intersected DEFs is beneficial to heat production while enhancing its aperture is not needed.Solely increasing the number of intersected DEFs induces a little increase of heat extraction,and more significant heat production can be obtained through connecting these DEFs with the MFF forming the flow network.     

Impact of normal stress-induced closure on laboratory-scale solute transport in a natural rock fracture

The impact of normal stress-induced closure on fluid flow and solute transport in a single rock fracture is demonstrated in this study.The fracture is created from a measured surface of a granite rock sample.The Bandis model is used to calculate the fracture closure due to normal stress,and the fluid flow is simulated by solving the Reynold equation.The Lagrangian particle tracking method is applied to modeling the advective transport in the fracture.The results show that the normal stress significantly affects fluid flow and solute transport in rock fractures.It causes fracture closure and creates asperity contact areas,which significantly reduces the effective hydraulic aperture and enhances flow channeling.Consequently,the reduced aperture and enhanced channeling affect travel time distributions.In particular,the enhanced channeling results in enhanced first arriving and tailing behaviors for solute transport.The fracture normal stiffness correlates linearly with the 5 th and 95 th percentiles of the normalized travel time.The finding from this study may help to better understand the stress-dependent solute transport processes in natural rock fractures.     

Influence of fracture roughness on shear strength,slip stability and permeability:A mechanistic analysis by three-dimensional digital rock modeling

Subsurface fluid injections can disturb the effective stress regime by elevating pore pressure and potentially reactivate faults and fractures.Laboratory studies indicate that fracture rheology and permeability in such reactivation events are linked to the roughness of the fracture surfaces.In this study,we construct numerical models using discrete element method(DEM) to explore the influence of fracture surface roughness on the shear strength,slip stability,and permeability evolution during such slip events.For each simulation,a pair of analog rock coupons(three-dimensional bonded quartz particle analogs) representing a mated fracture is sheared under a velocity-stepping scheme.The roughness of the fracture is defined in te rms of asperity height and asperity wavele ngth.Results show that(1) Samples with larger asperity heights(rougher),when sheared,exhibit a higher peak strength which quickly devolves to a residual strength after reaching a threshold shear displacement;(2) These rougher samples also exhibit greater slip stability due to a high degree of asperity wear and resultant production of wear products;(3) Long-term suppression of permeability is observed with rougher fractures,possibly due to the removal of asperities and redistribution of wear products,which locally reduces porosity in the dilating fracture;and(4) Increasing shear-parallel asperity wavelength reduces magnitudes of stress drops after peak strength and enhances fracture permeability,while increasing shear-perpendicular asperity wavelength results in sequential stress drops and a delay in permeability enhancement.This study provides insights into understanding of the mechanisms of frictional and rheological evolution of rough fractures anticipated during reactivation events.     

垃圾土中水分运动的一维数值分析

运用Brooks-Corey模型拟合了垃圾土的土水特征曲线和非饱和渗透系数,运用饱和—非饱和渗流分析,研究了垃圾土的一维水分运动过程,通过数值模拟计算了垃圾土在降雨入渗过程前后的水分运动,展示了孔隙水压力随时间的变化,使得对垃圾土中的水分运动过程的认识更加直观清楚。     

Multi-physics numerical analyses for predicting the alterations in permeability and reactive transport behavior within single rock fractures depending on temperature,stress, and fluid pH conditions

The aim of the current study was to establish a validated numerical model for addressing the changes in permeability and reactive transport behavior within rock fractures based on the fluid pH under coupled thermal-hydraulic-mechanical-chemical (THMC) conditions. Firstly, a multi-physics reactive transport model was proposed, considering the geochemical reactions that depend on the temperature, stress, and fluid chemistry conditions (e.g., fluid pH and solute concentrations), as well as the changes in permeability in the rock fractures driven by these reactions, after which the correctness of the model implementation was verified by solving the 1D reactive transport problem as a fundamental benchmark. Secondly, the validity of the model against actual rock fractures was investigated by utilizing the model to replicate the measurements of the evolving permeability and the effluent element concentrations in single granite fractures obtained by means of two flow-through experiments using deionized water (pH ～ 6) and a NaOH aqueous solution (pH ～ 11) as permeants under stressed, temperature-elevated conditions. The model predictions efficiently followed the changes in fracture permeability over time measured by both experiments. Additionally, the observed difference in the changing rates, which may contribute to the difference in the fluid pH between the two experiments, was also captured exactly by the predictions. Moreover, in terms of the effluent element concentrations, among all the elements targeted for measurement, the concentrations of most elements were replicated by the model within one order of discrepancy. Overall, it can be concluded that the developed model should be valid for estimating the changes in permeability and reactive transport behavior within rock fractures induced by geochemical reactions which depend on the fluid pH under coupled THMC conditions.     

Numerical modelling of flow and transport in rough fractures

Simulation of flow and transport through rough walled rock fractures is investigated using the latticeBoltzmann method （LBM） and random walk （RW）, respectively. The numerical implementation isdeveloped and validated on general purpose graphic processing units （GPGPUs）. Both the LBM and RWmethod are well suited to parallel implementation on GPGPUs because they require only next-neighbourcommunication and thus can reduce expenses. The LBM model is an order of magnitude faster onGPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified forparallel plate flow, backward facing step and single fracture flow; and the RWmodel is verified for pointsourcediffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithmsplace limitations on the discrete displacement of fluid or particle transport per time step to minimise thenumerical error that must be considered during implementation.
2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.     

Estimation of REV size and three-dimensional hydraulic conductivity tensor for a fractured rock mass through a single well packer test and discrete fracture fluid flow modeling

A new methodology is presented to determine the representative elementary volume (REV) size and three-dimensional (3-D) hydraulic conductivity tensor for a fractured rock mass. First, a 3-D stochastic fracture network model was built and validated for a gneissic rock mass based on the fracture data mapped from scanline surveys at the site. This validated fracture network model was combined with the fracture data observed on a borehole to generate a stochastic-deterministic fracture network system in a cubic block around each packer test conducted at a different depth region in the same borehole. Each packer test was simulated numerically applying a developed discrete fracture fluid flow model to estimate the influenced region or effective range for the packer test. A cubic block of size 18 m, with the packer test interval of length about 6.5 m located at the centre of this block, was found to be suitable to represent the influenced region. Using this block size, the average flow rate per unit hydraulic gradient (defined as the transmissivity multiplied by mean width of flow paths) field for fractures was calibrated at different depth regions around the borehole by numerically simulating the packer tests conducted at different depth regions. The average flow rate per unit hydraulic gradient of the fractures that intersect the borehole was considered to be quite different to the average flow rate per unit hydraulic gradient of the fractures that do not intersect the borehole. A relation was developed to quantify the ratio between these two parameters. By studying the directional hydraulic conductivity behaviour of different cubic block sizes having the validated stochastic fracture network and calibrated hydraulic parameters, a REV for the hydraulic behaviour of the rock mass was estimated to be a block size of 15 m. The hydraulic conductivity tensor in 3-D computed through regression analysis using the calculated directional hydraulic conductivity values in many directions was found to be significantly anisotropic. The principal directions of the hydraulic conductivity tensor were found to be agreeable with the existing fracture system of the site. Further, the geometric hydraulic conductivity calculated was found to be comparable to the hydraulic conductivity estimated through the radial flow assumption in continuum porous media.     

混凝土断裂面的实验研究

根据激光三角测量物体表面的原理，研制了可对混凝土断裂面进行三维轮廓重构的实验装置，同时用数字图像分析仪测定了断裂面粗集料的信息，在此基础上，提出了可利用断裂面分数维和粗集料的拉断概率两个参数表征断裂面的特征以及它们的测定和计算方法，研究了混凝土组成材料对断裂面参数的影响和断裂面参数与混凝土力学性能的关系，采用断裂面分数维确定了更为精确的混凝土断裂能测定值，探讨了根据上述结果进行混凝土改性的可能性。     

Solids accumulation in six full-scale subsurface flow constructed wetlands

In this study, we evaluated the amount of accumulated solids in six different horizontal subsurface flow constructed wetlands (SSF CWs). We also investigated the relationship between accumulated solids and, on one hand, the wastewater quality and load and, on the other hand, the hydraulic conductivity of the granular medium. Aerobic and anaerobic biodegradability tests were also conducted on the accumulated organic matter. Experiments were carried out on full scale wastewater treatment systems consisting of SSF CWs with stabilisation ponds, which are used for the sanitation of small towns in north-eastern Spain. There were more accumulated solids near the inlet of the SSF CWs (3-57 kg dry matter (DM)/m2) than near the outlet (2-12 kgm DM/m2). Annual solids accumulation rates ranged from 0.7 to 14.3 kg DM/m2 year, and a positive relationship was observed between accumulation rates and loading rates. Most of the accumulated solids had a low level of organic matter (<20%). The results of the aerobic and anaerobic tests indicated that the accumulated organic matter was very recalcitrant and difficult to biodegrade. The hydraulic conductivity values were significantly lower near the inlet zone (0-4 m/d) than in the outlet zone (12-200 m/d). Although hydraulic conductivity tended to decrease with increasing solids accumulation, the relationship was not direct. One major conclusion of this study is that the improvement of primary treatment is necessary to avoid rapid clogging of the granular media due to solids accumulation.     

On the hydraulic behavior of unsaturated nonwoven geotextiles

Geotextiles have been widely used in soil structures for separation, filtration, reinforcing, and drainage. They are often used to provide reinforcement and drainage for retaining walls and embankments. It has been reported, however, that geotextiles may not drain water as effectively as was initially expected. In this study, published data on the hydraulic properties of unsaturated geotextiles are compiled and analyzed in order to highlight the hydraulic characteristics of unsaturated geotextiles.

The application of the van Genuchten equations originally developed for the water characteristic curve and the hydraulic conductivity curve of unsaturated soil to unsaturated geotextiles is then examined and discussed. Finally, the drainage from a one-dimensional sand column having a horizontal geotextile layer was analyzed using the finite element method and the van Genuchten equations to assess the utility of this procedure for further study of unsaturated/saturated water flow within the soil–geotextile system.     

Complementary methods to investigate the development of clogging within a horizontal sub-surface flow tertiary treatment wetland

A combination of experimental methods was applied at a clogged, horizontal subsurface flow (HSSF) municipal wastewater tertiary treatment wetland (TW) in the UK, to quantify the extent of surface and subsurface clogging which had resulted in undesirable surface flow. The three dimensional hydraulic conductivity profile was determined, using a purpose made device which recreates the constant head permeameter test in-situ. The hydrodynamic pathways were investigated by performing dye tracing tests with Rhodamine WT and a novel multi-channel, data-logging, flow through Fluorimeter which allows synchronous measurements to be taken from a matrix of sampling points. Hydraulic conductivity varied in all planes, with the lowest measurement of 0.1 m d⁻¹ corresponding to the surface layer at the inlet, and the maximum measurement of 1550 m d⁻¹ located at a 0.4 m depth at the outlet. According to dye tracing results, the region where the overland flow ceased received five times the average flow, which then vertically short-circuited below the rhizosphere. The tracer break-through curve obtained from the outlet showed that this preferential flow-path accounted for approximately 80% of the flow overall and arrived 8 h before a distinctly separate secondary flow-path. The overall volumetric efficiency of the clogged system was 71% and the hydrology was simulated using a dual-path, dead-zone storage model. It is concluded that uneven inlet distribution, continuous surface loading and high rhizosphere resistance is responsible for the clog formation observed in this system. The average inlet hydraulic conductivity was 2 m d⁻¹, suggesting that current European design guidelines, which predict that the system will reach an equilibrium hydraulic conductivity of 86 m d⁻¹, do not adequately describe the hydrology of mature systems.     

粘滞阻尼器在框架结构抗震加固中的应用

本文以一实例介绍了非线性粘滞阻尼器的在框架结构抗震加固中的实际应用,说明了粘滞阻尼器消能减震的优越性,对类似工程抗震加固具有一定的参考价值。     

The hydraulic roughness of unlined and shotcreted TBM-bored tunnels in volcanic rock: In situ observations and measurements at Kárahnjúkar Iceland

The hydraulic roughness of igneous rock in unlined and shotcreted TBM-bored tunnels is presented in the paper. This is derived from in situ observations and direct measurements of tunnel wall roughness made during the construction of the Kárahnjúkar Hydroelectric Project in Iceland, to reliably estimate the headlosses of the 39 km long headrace tunnel. The tunnel is to a large extent excavated by TBM and is mostly unlined. The detailed assessment of the wall roughness combined systematic and comprehensively recorded visual inspections of the tunnels and accurate laser scans of a representative fraction of the inspected areas. The measurement program has shown that surface roughness of TBM-bored tunnels through volcanic rock such as basalt, is in general larger and the tunnel walls are more heavily jointed than in sedimentary rocks and coarse grained igneous rocks, such as granite. A verification of the methodology used to determine hydraulic friction factors was obtained by direct measurements of actual headlosses in the headrace tunnel system. These have shown an overall agreement with the methodology adopted for the project.     

Hydraulic conductivity test system for compacted, 2-mm-thick bentonite specimens

Both the design and safety assessment of radioactive waste disposal facilities demand an accurate evaluation of the hydraulic conductivity of the bentonite materials, especially compacted bentonite. For permeability tests of bentonite materials, the lengthy time necessary for specimen saturation and measurement may present a bottleneck. The permeability behavior of bentonite, such as the effects of the water quality and the exchangeable cations, has not been systematized sufficiently. For the present study, a hydraulic conductivity test system with 2-mm-thick specimens was developed. Its applicability was evaluated in terms of test accuracy. Six specimens of compacted Japanese sodium bentonite, with dry densities of 1.34–1.79 Mg/m³, were subjected to falling head hydraulic conductivity tests. The results showed that the hydraulic gradient set for this study did not affect the hydraulic conductivity, indicating that the macroscopic hydraulic behavior was consistent with Darcy's law. Furthermore, it was possible to reduce the test period considerably, by about one-tenth, compared to that using 10-mm-thick specimens. The obtained hydraulic conductivity was found to be similar to that in earlier studies. Furthermore, the values showed less variation particularly in terms of the consolidation test results. The results demonstrated that 2-mm-thick specimens are useful for hydraulic conductivity measurements of compacted bentonite.     

Characterisation of fracture geometry using specific capacities: numerical and experimental study of a fracture replica

In view of the difficulties in determining the void geometry of a fracture by direct measurements, the present study was undertaken to better understand rock characterisation as related to tunnel sealing by grouting, where data must be obtained and utilised in a short time. A fracture replica (295×445 mm^–2) was constructed and hydraulic tests were performed to evaluate whether the specific capacity (Q/dh) is a robust parameter for estimating the geometry of a fracture. Modelling facilitated the design of the experimental equipment. The study shows that the variations in geometry within the replica were well identified using the specific capacity. Furthermore, the median specific capacity both from the experimental study and from modelling was found to be a fairly good estimation of the effective transmissivity. This was also valid for the hydraulic aperture. Electronic Publication     

变流量系统水力稳定性分析

随着变流量系统的广泛应用。对如何提高中央空调水系统稳定性提出了新的挑战。本文采用依次关闭各支路。然后计算未关闭支路流量的方法．分析和比较了不同控制方式下变流量系统的水力稳定性。结果表明。在没有设置动态平衡措施的变流量系统中,随着系统末端电动二通阀的调节,会对其他末端水力工况产生影响。使之发生动态水力失调,影响空调区域的舒适性。提出了几种减小系统水力失调。提高系统稳定性的措施。     

Sorption and hydraulic performance of cement-bentonite cutoffs in saline sulphatic solutions

The paper discusses the results of an experimental research on the short and long term hydraulic performance and sorption of cement-bentonite mixtures in saline sulphate solutions. Batch tests at different curing times and permeation tests were performed on three cement-bentonite mixtures with solutions of K₂SO₄. The results show that permeation can adversely affect the hydraulic performance of cement-bentonite mixtures depending on the sulphate concentration and mixture composition and that the choice of a very low permeable mixture is essential to limit adverse effects of interaction with SO₄^2- on the hydraulic performance.Sorption of K⁺ was found to be significant, well described by a linear isotherm in a wide range of concentration and nearly constant with curing. Sorption of SO₄² was found to decreases with mixture porosity. Since sorption of SO₄^2- means negative interaction, batch tests were found to be useful for a rapid estimation of possible negative effect of SO₄^2- on the hydraulic behaviour in the long term, when selecting a mixture in the design phase.All the results point out the importance of selecting a mixture to be used for cut-off walls with a low hydraulic conductivity already at brief curing and of carefully considering interaction with solute pollutants and sorption capacity.     

Fabric effect on hydraulic conductivity of kaolin under different chemical and biochemical conditions

A reasonably less permeable compacted clay liner (CCL) is critical to the long-term safety of waste containment facilities. This study experimentally investigates a variety of factors, including salinity, pH, fluctuation in permeant, permeation duration and presence of microorganisms, that are found to influence the hydraulic conductivity (k) of consolidated kaolin and the fabrics of suspended kaolin. Amongst these factors, a reduction in hydraulic conductivity of up to 4 orders of magnitude is obtained from the modification of the microfabrics of kaolin; a reduction of 2 orders of magnitude is brought about by bioclogging; a reduction of 1 order of magnitude is related to the concentrated Ca solution (>10 mM). The hydraulic conductivity of consolidated kaolin can obviously be changed by adjusting the fabrics of the kaolin particles, e.g., clogging the pore spaces with bioslurry, permeating them with alkaline solution, or transforming the kaolin into metakaolin. An effluent pH larger than the isoelectric point (pH_IEP) leads to a rapid reduction in k until 1×10^–11 m/s. A 3-dimensional fabric map was established for kaolin suspension in contact with a wide range of Ca concentrations and pH levels. The fabrics of kaolin suspension are predominated by a salt concentration (C>2.0 mM) and a pH solution (C<2.0 mM), respectively.