Spatial statistics for predicting fluid flow through a single rock fracture

Steady-state laminar flow through single rock fractures is predicted in terms of spatial statistics computed from the arrangement of voids and contact areas within the fracture. Within the voids, aperture is assumed to be constant. One statistic measures how often pixels alternate from void to contact area in the rows parallel to the flow direction. Two others measure the dispersion of voids in the rows and columns of the pattern. Fractures with complexity typical of observed data are simulated. Flow through patterns with 80% voids is predicted in terms of a linear combination of the three statistics. Using an extended model involving one of the three statistics, flow through patterns with other void fractions is predicted.The author did this work at the Earth Sciences Division at Lawrence Berkeley Laboratory, Berkeley, California. It is part of a Ph.D. thesis which was submitted at Stanford University.     

Modelling fluid flow through a single fracture with different contacts using cellular automata

The representation of the surface of a rock fracture and a numerical method to simulate fluid flow in single fractures are the keys to understanding the hydraulic behaviour of rock fractures. In this paper, a cellular automaton (CA) approach is used to generate the single fracture structure, which is assumed to be composed of contacts and voids. We develop a CA evolution rule to produce a contact area, and randomly model a single rock fracture with different contact ratios to reflect natural fracture properties such as dead voids, islands and tortuous flow path. Then, based on the localisation theory of a CA, a numerical method to simulate fluid flow in single fractures with contacts is developed. In this method, the fracture is discretised into a system composed of cell elements. Different apertures, i.e., zero for contacts and non-zero for voids, are assigned to each cell element. Therefore, the contribution of the cell elements in a contact on a cell’s transmissivity can be ignored completely. The local transmissivity is assumed to conform to the cubic law. The fluid flow in a fracture with different contact situations is then modelled using the method established in this paper. The fluid flow path, flow velocity and fluid head distributions as well as the channel flow in the fracture are well-modelled. The flow behaviour of the fracture strongly depends on the effective fluid flow path.     

单裂隙曲折率对流体渗流过程的影响

从裂隙的细观结构出发，分析了裂隙曲折率对流体渗流过程的影响，得出了不规则裂隙的渗流规律，并把该结果应用于有限元分析，得出了裂隙突出坡度对渗流过程的影响。     

洪水水流压力及其影响因素模型试验研究

洪水对洪泛区建筑会造成较大的危害,洪水荷载研究是洪泛区建筑脆弱性研究的基础。通过模型试验,研究不同水深流速的洪水对建筑表面的水流压力及其分布规律。试验在波流水槽中设置可调整出水口来控制作用于模型迎流面水流的深度和流速,模型分为2层,1层有洞口,2层无洞口,固定于出水口下游。结果表明:模型迎流面水流流速分布不均匀,水流压力从下至上逐渐减小;基于试验数据发现动水压力随着流速的增加而增加,且呈非线性关系,并据此提出了动水压力修正系数,改进了水流压力计算公式;水流压力和水深近似呈线性关系;洞口和边界会在一定程度上减小迎流面水流流速与水流压力。研究结果为洪泛区建筑的抗洪设计和抗洪能力评价提供依据。     

An experimental study of single and two-phase fluid flow through fractured granite specimens

Triaxial tests on the two-phase flow of air and water through fractured granite specimens were performed to discover whether the two-phase fluid flow within rock fractures was laminar or turbulent. The two-phase flow characterization was carried out based on the macroscopic two-phase steady state flow model and the homogeneous steady state flow model. Rock specimens with a single natural fracture (joint roughness coefficient, JRC < 10) were tested using two-phase, high pressure triaxial rig. Experimental results show that the estimated Reynolds numbers for various inlet fluid pressures are well below 1000. The findings of this study reveal that both single and two-phase flow through rock fractures (JRC < 10) can be characterized as laminar flows at moderate inlet fluid pressures. However, for single-phase air flow, an increase in inlet air pressures may result in the formation of turbulent flow.     

Micro- and macro-behaviour of fluid flow through rock fractures: an experimental study

Microscopic and macroscopic behaviour of fluid flow through rough-walled rock fractures was experimentally investigated. Advanced microfluidic technology was introduced to examine the microscopic viscous and inertial effects of water flow through rock fractures in the vicinity of voids under different flow velocities, while the macroscopic behaviour of fracture flow was investigated by carrying out triaxial flow tests through fractured sandstone under confining stresses ranging from 0.5 to 3.0 MPa. The flow tests show that the microscopic inertial forces increase with the flow velocity with significant effects on the local flow pattern near the voids. With the increase in flow velocity, the deviation of the flow trajectories is reduced but small eddies appear inside the cavities. The results of the macroscopic flow tests show that the linear Darcy flow occurs for mated rock fractures due to small aperture, while a nonlinear deviation of the flow occurs at relatively high Reynolds numbers in non-mated rock fracture (Re?>?32). The microscopic experiments suggest that the pressure loss consumed by the eddies inside cavities could contribute to the nonlinear fluid flow behaviour through rock joints. It is found that such nonlinear flow behaviour is best matched with the quadratic-termed Forchheimer equation.     

Numerical simulation of unsteady fluid flow and propagation of a circular hydraulic fracture

A computational procedure is developed for solving the problem of a circular hydraulic fracture propagating under the action of frac-0fluid being pumped in at a central wellbore. The crack is modelled as continuous distributions of ring dislocations and the resulting elasticity singular integral equation is solved numerically. The fluid flow equations are approximated by local and global interpolation finite difference schemes. The coupling between elasticity and fluid flow is handled numerically, by, two different algorithms: one iterates on crack tip velocity whereas the other varies the time step size until it agrees with the chosen increment in crack length. Sample results are given; it is found that the velocity algorithm is computationally more, efficient and more stable. The model allows detailed tracing of pressure distribution and fluid flow in the fracture, even under complex conditions of cyclic injection and fluid rheology. It may serve as a stand-alone model of (horizontal) hydrafracs–especially at shallow depths–or it may be used as a reference frame to test the various numerical formulation/algorithms required for the ongoing development of a fully 3-D hydrafrac simulator.     

Effect of roughness on water flow through a synthetic single rough fracture

A single fracture is usually idealized theoretically as smooth parallel plates, but the real fractures are rough-walled with points of contact. Though relative roughness is considered in quantifying the flow through a single rough fracture (SRF) previously, additional factors such as the distribution of rough elements and bending degree of streamlines should be considered in order to obtain more accurate results. Semiempirical friction factor (f) and discharge per unit width (q) equations are first deduced taking relative roughness, roughness elements distribution and streamline reattachment length into consideration. A horizontal SRF model was then set up and a series of experiments and simulations were performed. Main conclusions are drawn: Recirculation of streamlines arises in the rough element and the intensity of the recirculation increases with the angle from which the streamlines enter into the rough elements and Reynolds number (Re); streamlines are discontinuously distributed when asperity height is large and nonlinear flow occurs; the nonlinearity of the flow increases with the increasing the asperity height and Re; the critical value of related roughness used to judge whether the influence of roughness on water flow through a SRF can be ignored or not should be much lower than 0.033; the revised f and q equations under laminar flow through a SRF are proved to be better when calculating the f and q values.     

Chemical reactions accompanying fluid flow through granite held in a temperature gradient

Distilled water was passed at a low rate down a temperature gradient through cylinders of Barre and Westerly Granite. Temperatures ranged from 80–100°C at the outer edges of the cylinders to 250–300°C in central, drilled holes which housed the heating coils. The measured permeabilities of the granite cylinders decreased by as much as two orders of magnitude in experiments of 1–3 weeks' duration. The amount of permeability decrease varied directly with temperature and inversely with the rate of fluid flow. The compositions of the fluids discharged from the granites were functions of temperature and flow rate as well as mineral composition, with dissolved silica concentrations showing trends different from those of the other analyzed species. Fluids from experiments run at higher temperatures but at much lower initial rates of fluid flow had higher concentrations of most ions but substantially lower dissolved silica contents. In contrast, an increase in temperature at similar rates of fluid flow resulted in higher silica concentrations. In the experiments, the distilled water acquired enough dissolved materials at high temperatures to become supersaturated with respect to several minerals at the low-temperature edges of the cylinders. Some of this material, particularly silica, was deposited along grain boundaries and microfractures, causing the observed permeability decreases. The very low rates of fluid flow in some high-temperature experiments significantly increased the rates of SiO₂ precipitation and reduced dissolved silica concentrations relative to other species in the discharged fluids.     

考虑接触面积影响的粗糙节理渗流分析

节理中接触面积的存在使得渗流曲折效应更加明显,将对渗流产生显著影响。为了研究节理接触面积对节理渗流的影响,建立节理渗流概念模型,推导得到了节理渗流的接触面积影响系数;然后在节理渗流计算公式中引入该影响系数,得到了考虑接触面积影响的渗流计算公式。同时,由于接触面积的存在使得渗流曲折因子的计算更为复杂,在获得节理隙宽分布的基础上提出了计算节理渗流曲折因子的五点比较法。然后以人工大理岩节理试件为研究对象,在获得其三维表面形貌的基础上,一方面对其进行不同接触状态下5级法向应力作用下的渗流试验;另一方面,在根据节理试件的三维表面形貌数据计算节理的渗流平均曲折因子和接触面积比的基础上,分别采用考虑接触面积影响的渗流计算公式和Zimmerman计算公式对节理试件在不同法向应力作用下的渗流体积流量进行计算,并将计算结果与实测值进行比较。结果表明：考虑接触面积影响的渗流计算公式计算结果与实测值吻合较好,从而验证了考虑接触面积影响的渗流计算公式的正确性,而Zimmerman计算公式高估了节理的渗流流量。     

Numerical modelling of fluid flow tests in a rock fracture with a special algorithm for contact areas

The fluid flow in rock fractures during shear processes has been an important issue in rock mechanics and is investigated in this paper using finite element method (FEM), considering evolutions of aperture and transmissivity with shear displacement histories under different normal stress and normal stiffness conditions as measured during laboratory coupled shear-flow tests. The distributions of fracture aperture and its evolution during shearing were calculated from the initial aperture, based on the laser-scanned sample surface roughness results, and shear dilations measured in the laboratory tests. Three normal loading conditions were adopted in the tests: simple normal stress and mixed normal stress and normal stiffness to reflect more realistic in situ conditions. A special algorithm for treatment of the contact areas as zero-aperture elements was used to produce more accurate flow field simulations, which is important for continued simulations of particle transport but often not properly treated in literature. The simulation results agree well with the measured hydraulic apertures and flow rate data obtained from the laboratory tests, showing that complex histories of fracture aperture and tortuous flow fields with changing normal loading conditions and increasing shear displacements. With the new algorithm for contact areas, the tortuous flow fields and channeling effects under normal stress/stiffness conditions during shearing were more realistically captured, which is not possible if traditional techniques by assuming very small aperture values for the contact areas were used. These findings have an important impact on the interpretation of the results of coupled hydro-mechanical experiments of rock fractures, and on more realistic simulations of particle transport processes in fractured rocks.     

Size effect on the hydraulic behavior of fluid flow through rough-walled fractures: a case of radial flow

Hydrogeology Journal - This study provides a numerical approach to investigate radial flow through a single rough-walled fracture. To facilitate the size-dependency investigation, rough-walled...     

构造应力对裂缝形成与流体流动的影响

裂缝是低渗透储层流体流动的主要通道,控制了低渗透油气藏的渗流系统。低渗透储层裂缝的形成与流体密切相关,高流体压力引起岩石内部的有效正应力下降,导致岩石剪切破裂强度下降,使岩石容易产生裂缝。高孔隙流体压力还造成某一点的应力摩尔圆向左移动,可以使其最小主应力(σ3)由压应力状态变成拉张应力状态,从而在岩石中形成拉张裂缝。裂缝的渗透性受现今应力场的影响,通常与现今应力场最大主压应力近平行分布的裂缝呈拉张状态,连通性好,开度大,渗透率高,是主渗透裂缝方向。构造应力对沉积盆地流体流动的影响主要表现在三个方面:(1)构造应力导致的岩石变形,不仅提供了流体流动的通道,而且还改变了岩石的渗透性能;(2)在构造强烈活动时期,构造应力的快速变化是流体流动的重要驱动力;(3)岩石中应力状态影响多孔介质的有效应力,从而影响介质中的渗流场。当作用在含流体介质上的构造应力发生改变时,岩石孔隙体积变小,构造应力首先由岩石的骨架来承担;当岩石孔隙体积减小到一定程度时,构造应力由孔隙流体来承担,从而影响岩层渗流场的变化。     

单裂隙面渗流特性及等效水力隙宽

首先讨论了描述单裂隙面几何特性的两个最基本参数——隙宽和粗糙性的确定方法,系统地总结和分析了现有有关单裂隙面渗流特性方面的研究成果,并对不同粗糙性描述下的裂隙等效水力隙宽的确定问题进行了探讨,提出了自已的看法,并指出进一步要解决的问题。     

加筋土强度影响因素的试验研究

通过室内大三轴试验方法,对加筋土强度影响因素进行了研究,探讨了在不同加筋情况下试样强度的变化规律。试验结果表明：加筋作用的效果随着轴向应变增大而作用越明显;对于强度较低的试样,加筋后强度提高明显;对于同一试样,加筋材料本身强度越高,加筋效果越明显;对于同一种加筋材料,加筋层数越多,筋层间距越小,加筋效果越明显;试样自身的密实度越高,加筋效果越明显。     

Laboratory study of the clogging process and factors affecting clogging in a tailings dam

Laboratory simulation of clogging in the Lixi tailings dam (Shaanxi Province, China) is urgently required because clogging is an important factor affecting the dam stability. This work firstly presents the results of ferrous iron oxidation experiments using buffer solution. The results indicate that the ferrous iron oxidation follows first order kinetics, and the oxidation process is strongly dependent on pH, a higher pH resulting in a higher oxidation rate. Furthermore, when the pH exceeds 7.0, the oxidation rate constant increases significantly. Secondly, a column experiment was carried out under the conditions of the pH ranging from 6.8 to 7.5 and the natural oxygen supply. Ferrous iron oxidation and precipitation were found to reach equilibrium under these conditions. After 23 days, the column experiment was stopped when the clogging materials blocked the column outlet. The clogging materials were found to be a mixture of ferric hydroxide and its converted products, and these existed in amorphous form with a loose cluster microstructure according to the results of XRD and SEM.     

A pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures

This paper aims at developing a pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures. A simple general relationship between the local hydraulic conductivity and the flow velocity is proposed. A new governing equation for non-Darcy fluid flow through rough-walled fractures is then derived by introducing this relationship into the Reynolds equation. Based on the non-linear finite element method, a self-developed code is used to simulate the non-Darcy fluid flow through fractures. It is found that the macroscopic results obtained by the numerical simulation agree well with the experimental results. Furthermore, some interesting experimental observations can be reproduced.     

碳酸盐岩单裂隙渗流-溶蚀耦合模型及其参数敏感性分析

岩溶地下水系统是由碳酸盐岩裂隙含水介质演化形成的,系统初始的裂隙网络介质特征及边界条件决定了其演化过程。为揭示岩溶系统演化过程中裂隙介质特征和边界条件的影响程度,建立了裂隙溶蚀扩展的渗流-溶蚀耦合模型,并对不同边界条件下不同隙宽的单裂隙溶蚀扩展特征进行了模拟分析。结果表明:裂隙溶蚀扩展受水的侵蚀性(CO2分压)、水动力条件(水力梯度)、裂隙介质特征(裂隙初始隙宽)等综合作用影响,Ca2+的平衡浓度、水力梯度以及裂隙初始隙宽等参数的增加均能促进裂隙的快速扩展。在这些参数中,初始隙宽B0对岩溶发育的影响最为敏感,水力梯度J和Ca2+平衡浓度Ceq对岩溶发育具有相同的敏感性;此外,随着各参数值的不断增大,参数变化对岩溶发育的敏感程度越来越低。     

不同侧压力系数下裂隙网络岩体非线性渗流特性

基于人工裂隙网络模型,展开一系列不同边界荷载作用下含不同交叉点个数的裂隙网络渗流试验。针对所有试验工况,模型进水口水压力范围均为0～0.6 MPa,侧压力系数均由1.0增加至5.0。试验结果表明：裂隙网络体积流速和水力梯度之间的相关性可以通过Forchheimer函数进行拟合,拟合方程中线性和非线性项系数均随着侧压力系数的增加逐渐增大,而随着裂隙网络交叉点个数的增加逐渐减小;渗流试验过程中,非线性效应系数E和水力梯度J之间的相关性可采用一个幂指数函数进行描述,随着水力梯度的增加,非线性效应系数逐渐增大;随着侧压力系数的增加,裂隙网络临界水力梯度呈现逐渐增大的趋势,对于所有裂隙网络交叉点个数（1～12）,当侧压力系数由1.0增加至5.0,临界水力梯度由0.63～12.13增加至6.01～81.55;提出数学模型 对归一化导水系数 随水力梯度的增大而减小的特征进行分析,随着侧压力系数的增加,两者之间的拟合曲线逐渐上移,拟合系数 整体呈现逐渐增大的趋势。裂隙网络的等效渗透系数随侧压力系数的增加逐渐降低。     

Erratum: Properties of a pair of fracture networks produced by triaxial deformation experiments: insights on fluid flow using discrete fracture network models

Results of a series of deformation experiments conducted on gabbro samples and numerical models for computation of flow are presented. Rocks were subjected to triaxial tests (σ1 > σ2 = σ3) under σ3 = 150 MPa confining pressure at room temperature, to generate fracture network patterns. These patterns were either produced by keeping a constant confining pressure and loading the sample up to failure (conventional test: CT), or by building up a high differential stress and suddenly releasing the confining pressure (confining pressure release test: CPR). The networks are similar in overall density but differ primarily in the orientation of smaller fractures. In the case of CT tests, a conjugate fracture set is observed with one dominant fracture zone running at about 20° from σ1. CPR tests do not show such a conjugate pattern and the mean fracture orientation is at around 35° from σ1. Discrete fracture network (DFN) methodology was used to determine the distribution of flow and hydraulic head for both fracture sets under simple boundary conditions and uniform transmissivity values. The fracture network generated by CT and CPR tests exhibit different patterns of flow field and hydraulic head configurations, but convey approximately the same amount of flow at all scales for which DFN models were simulated. The numerical modelling results help to develop understanding of qualitative differences in flow distribution that may arise in rocks of the same mineralogical composition and mechanical properties, but under the influence of different stress conditions, albeit at similar overall stress magnitude.