Measuring fracture orientation at exposed rock faces by using a non-reflector total station

Measurements of fracture orientation are usually taken by using a compass-inclinometer device on exposed rock faces. The drawbacks when using this method is that it is time-consuming if many fractures are measured and that measurement might be impossible if the rock face cannot be safely reached physically. To improve field mapping of rock fractures, a method for applying a non-reflector total station to measuring fracture orientation is presented in this paper. A non-reflector total station is a geodetic device that captures three-dimensional co-ordinates of target points without using a reflector. Therefore, physical touching the rock surfaces is no longer required. To determine a fracture orientation, co-ordinates of a set of points on the exposed fracture surface are captured at a distance from the rock face. The best-fit plane of the exposed fracture surface is defined by the co-ordinates of the target points, and the orientation (e.g. dip angle and dip direction) of the fracture surface is determined as that of its best-fit plane. This paper presents the technical procedure and a portable system designed for the field mapping of fracture orientation. Results of a case study performed at an exposed rock face are also included.     

An enhanced stochastic optimization in fracture network modelling conditional on seismic events

This paper presents an approach to modelling fracture networks in hot dry rock geothermal reservoirs. A detailed understanding of the fracture network within a geothermal reservoir is critically important for assessments of reservoir potential and optimal production design. One important step in fracture network modelling is to estimate the fracture density and the fracture geometries, particularly the size and orientation of fractures. As fracture networks in these reservoirs can never be directly observed there is significant uncertainty about their true nature and the only feasible approach to modelling is a stochastic one. We propose a global optimization approach using simulated annealing which is an extension of our previous work. The fracture model consists of a number of individual fractures represented by ellipses passing through the micro-seismic points detected during the fracture stimulation process, i.e. the fracture model is conditioned on the seismic points. The distances of the seismic points from fitted fracture planes (ellipses) are, therefore, important in assessing the goodness-of-fit of the model. Our aims in the proposed approach are to formulate an appropriate objective function for the optimal fitting of a set of fracture planes to the micro-seismic data and to derive an efficient modification scheme to update the model parameters. The proposed objective function consists of three components: orthogonal projection distances of the seismic points from the nearest fitted fractures, the amount of fracturing (fitted fracture areas) and the volumes of the convex hull of the associated points of fitted fractures. The functions used in the model update scheme allow the model to achieve an acceptable fit to the points and to converge to acceptable fitted fracture sizes. These functions include two groups of proposals: one for updating fracture parameters and the other for determining the size of the fracture network. To increase the efficiency of the optimization, a spatial clustering approach, the Distance-Directional Transform, was developed to generate parameters for newly proposed fractures. A simulated dataset was used as an example to evaluate our approach and we compared the results to those derived using our previously published algorithm on a real dataset from the Habanero geothermal field in the Cooper Basin, South Australia. In a real application, such as the Habanero dataset, it is difficult to determine definitively which algorithm performs better due to the many uncertainties but the number of association points, the number of final fractures and the error are three important factors that quantify the effectiveness of our algorithm.     

Permeability Tensors of Anisotropic Fracture Networks

Analytical models are presented to provide enhanced capabilities for modeling fluid flow through natural fractures nested in parallel plate type configurations. The modeled fractures may be arbitrarily positioned, but subgrouped according to the consistent parallel sequences. The derived analytical expressions for fracture permeability can be considered as an extension to those in which flow within fractures is uniform and isotropic. This modification offers a correction for the traditional permeability calculations whenever fractures are oblique to the flow orientation. For the fracture flow scenarios, the graphical solutions show the permeability envelope normal to any arbitrary planes within the calculated domain. Consideration of rock anisotropy may significantly improve the accuracy in determining the formation permeability in cases where natural fractures exhibit a dominant control in regional fluid flow.     

Fracture and bedding plane control on groundwater flow in a chalk aquitard

Shallow groundwater in the northern Negev desert of Israel flows preferentially through a complex system of discontinuities. These discontinuities intersect what would otherwise be a massive, low-conductivity, high-porosity Eocene chalk. Vertical fractures and horizontal bedding planes were observed and mapped along approximately 1,200 m of scanline, 600 m of core and 30 two-dimensional trace planes. A bimodal distribution of size exists for the vertical fractures which occur as both single-layer fractures and multi-layer fractures. A bimodal distribution of log transmissivity was observed from slug tests conducted in packed-off, vertical intervals within the saturated zone. The different flow characteristics between the horizontal bedding planes and vertical-type fractures appear to be the cause of the bimodality. Two distinct conceptual models (discrete fracture network) were developed based on the fracture orientation, size, intensity and transmissivity statistics derived from field data. A correlation between fracture size and hydraulic aperture was established as the basis for calibrating the simulated model transmissivity to the field observations. This method of defining transmissivity statistically based on prior information is shown to be a reasonable and workable alternative to the usual conjecture approach towards defining transmissivity in a fractured-rock environment.     

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.     

A statistically based numerical model for heat conduction in fractured rock masses

A computational procedure for simulating heat conduction in fractured rock masses is proposed and illustrated within the context of the finite element method. The procedure makes use of simple local models for conduction in the vicinity of a single open fracture. The local models allow effective thermal properties for fractured rock to be expressed in terms of fracture characteristics such as spacing, orientation and aperture. The distributions of fractures and fracture properties within the finiteelement model are derived from a statistical representation of geological field data. The procedure is demonstrated to satisfactorily reproduce heat transfer results across single fractures and provide an efficient means of representing conduction in formations with multiple fractures.     

Prediction of water inflow into underground excavations in fractured rocks using a 3D discrete fracture network (DFN) model

Groundwater flow is a major issue in underground opening in fractured rocks. Because of finding the fracture connectivity, contribution of each fracture in flow, and fracture connectivity to excavation boundary, the prediction of water flow to underground excavations is difficult. Simulation of fracture characteristics and spatial distribution is necessary to obtain realistic estimation of inflow quantity to tunnel and underground excavations. In this research, a computer code for three-dimensional discrete fracture network modeling of water inflow into underground excavations was developed. In this code, the fractures are simulated as ellipsoid while geometrical properties of the fractures are reproduced using a stochastic method. Properties such as the size, orientation, and density of the fractures are modeled by their respective probability distributions, which are obtained from field measurements. According to the fracture condition, the flow paths in rock mass are determined. The flow paths are considered as channels with rectangular sections in which channel width and fracture aperture determine geometry of channel section. Inflow into excavation is predicted ignoring matrix permeability and considering the hydrogeological conditions. To verify presented model, simulation results were compared to a part of the Cheshmeh-Roozieh water transfer tunnel in Iran. The results obtained from this research are in good agreement with the field data. Thus, the average of the predicted inflow has just an approximation error equal to 17.8%, and its standard deviation is 8.6 l/s, which is equal to 21% of the observed value that demonstrates low dispersion of the predicted values.     

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.

     

A methodology to constrain the parameters of a hydrogeological discrete fracture network model for sparsely fractured crystalline rock,exemplified by data from the proposed high-level nuclear waste repository site at Forsmark,Sweden

The large-scale geological structure of the crystalline rock at the proposed high-level nuclear waste repository site at Forsmark, Sweden, has been classified in terms of deformation zones of elevated fracture frequency. The rock between deformation zones was divided into fracture domains according to fracture frequency. A methodology to constrain the geometric and hydraulic parameters that define a discrete fracture network (DFN) model for each fracture domain is presented. The methodology is based on flow logging and down-hole imaging in cored boreholes in combination with DFN realizations, fracture connectivity analysis and pumping test simulations. The simulations suggest that a good match could be obtained for a power law size distribution where the value of the location parameter equals the borehole radius but with different values for the shape parameter, depending on fracture domain and fracture set. Fractures around 10–100 m in size are the ones that typically form the connected network, giving inflows in the simulations. The report also addresses the issue of up-scaling of DFN properties to equivalent continuous porous medium (ECPM) bulk flow properties. Comparisons with double-packer injection tests provide confidence that the derived DFN formulation of detailed flows within individual fractures is also suited to simulating mean bulk flow properties and their spatial variability.     

Rockfall Hazard Analysis From Discrete Fracture Network Modelling with Finite Persistence Discontinuities

Developing an accurate representation of the rock mass fabric is a key element in rock fall hazard analysis. The orientation, persistence and density of fractures control the volume and shape of unstable blocks or compartments. In this study, the discrete fracture modelling technique and digital photogrammetry were used to accurately depict the fabric. A volume distribution of unstable blocks was derived combining polyhedral modelling and kinematic analyses. For each block size, probabilities of failure and probabilities of propagation were calculated. A complete energy distribution was obtained by considering, for each block size, its occurrence in the rock mass, its probability of falling, its probability to reach a given location, and the resulting distribution of energies at each location. This distribution was then used with an energy–frequency diagram to assess the hazard.     

A Spatial Clustering Approach for Stochastic Fracture Network Modelling

Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for  fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach followed by a real 3D case study of the Habanero reservoir in the Cooper Basin, Australia.     

Estimation of 2-D and 3-D Fracture Densities from 1-D Data - Experimental and Field Results

2-D and 3-D densities of fractures are commonly used in mining safety design, natural gas and oil production in fractured reservoirs, and the characterization of subsurface flow and transportation systems in fractured rocks. However, many field data sets are collected in 1-D frequency (f) (e.g., scanlines and borehole data). We have developed an ARC/ INFO-based technology to calculate fracture frequency and densities for a given fracture network. A series of numerical simulations are performed in order to determine the optimal orientation of a scanline, along which the maximum fracture frequency of a fracture network can be obtained. We calculated the frequency (f) and densities (both D1 and D2) of 36 natural fracture trace maps, and investigated the statistical relationship between fracture frequency and fracture density D1, i.e. D1=1.340f+ 0.034. We derived analytical solutions for converting dimensional density (D1) to non-dimensional densities (D2 and D3) assuming that fracture length distribution f     

柴达木盆地东部石炭系页岩三维裂缝网络模型研究

裂缝既是页岩气的聚集空间,同时也是页岩气的运移通道, 对页岩气成藏起着重要控制作用。裂缝的产状、密度、组合特征等很大程度上决定了页岩气是否具有开发价值。该研究对柴达木盆地东部的13个露头的岩石裂缝进行了野外观测统计,实测裂缝1 000多条,选取了三个具有代表性的页岩露头进行统计分析建模。通过野外观测和室内统计分析发现,工作区页岩裂缝发育有三组(某些地段一组不发育),各组裂缝的方向满足Fisher分布,迹线长度满足对数正态分布。确定了各组裂缝方向、长度的均值和方差,以及各组裂缝的密度,建立了三维裂缝网络模型,绘出了模拟的三维裂缝网络图。裂缝三维模型为圆盘模型,即假设单个裂缝三维空间上具有圆盘形状。建模过程采用了逆建模方法,其基本原则是通过拟合实测的二维露头观测数据,优化裂缝三维大小和密度参数,使模型能够准确再现野外所观测到的实际现象,包括露头面上不同裂缝的数量、密度和长度。该研究对柴达木盆地东部石炭系页岩裂缝描述达到了定量化,为研究页岩中油气运移提供了很好的基础数据。     

The correlation of fracture directions with sediment anisotropy in folded rocks of the Delamerian fold belt at Port Germein gorge, South Australia

Fracture patterns have been analysed across an anticline within the Delamerian fold belt. All fractures have orientations normal to bedding and have been separated into sets geometrically related and unrelated to the fold. The preferred orientation of quartz grain long axes in thin sections is statistically normal to the crests of small-scale ripple marks and these two directions correspond to the orientation of two sets of orthogonal joints unrelated to the fold geometry. It is therefore suggested that the sedimentary structures may have had a controlling influence on the fracture orientations.The presence of quartz fibres within fractures and consistent offsets between fracture sets allow time relations of fracture dilation to be determined. Dilation apparently occurred during or after folding. One set of fractures whose orientation correlates with the sedimentary anisotropy was dilated first and it is possible that these fractures were initiated before folding, possibly during diagenesis.     

Analytical solution of the problem for a set of shear fractures with Coulomb friction

A simplified solution of a two-dimensional problem on a set of interaction shear fractures with Coulomb friction along their wings is proposed. In the classical statement of this problem, the equality between shear stresses and friction stresses must necessarily hold in a new equilibrium state at each point along the fracture plane. The solution of the problem is reduced to the solution of a set of singular integral equations with respect to unknown functions of a shear jump on fractures. In reality, our knowledge of fracture conditions is rather approximate. In addition, in the problems of seismology and tectonophysics it is sufficient to approximately estimate dynamic (taking into account the inertia forces) and static perturbations from a fracture in the form of the first terms of a true solution series. With this aim in view, point models of an earthquake source or continual representation of discontinuous deformations are used. Within the framework of the requirements of such approaches, it is assumed that the condition of equality between the sum of shear stresses and friction stresses on the shear fractures in a new equilibrium state is met. In addition, the complex potential function is calculated for each fracture based on the function of the jump of its wings obtained in the problem for a solitary fracture. Such statement of the problem of a set of neighboring and even intersecting fractures makes it possible to reduce its solution to a set of linear algebraic equations with respect to shear stresses relieved at each fracture and the average along its length, they being the unknown values.     

Numerical simulation of two-phase flow in conceptualized fractures

Two-phase flow in fractured rock is an important phenomenon related to a range of practical problems, including non-aqueous phase liquid contamination of groundwater. Although fractured rocks consist of fracture networks, the study of two-phase flow in a single fracture is a pre-requisite. This paper presents a conceptual and numerical model of two-phase flow in a variable fracture. The void space of the fracture is conceptualized as a system of independent channels with position-dependent apertures. Fundamental equations, governing two-phase displacement in each channel, are derived to represent the interface positions and fractional flows in the fracture. For lognormal aperture distributions, simple approximations to fractional flows are obtained in analytical form by assuming void occupancy based on a local capillary allowability criterion. The model is verified by analytical solutions including two-phase flow in a parallel-plate fracture, and used to study the impacts of aperture variation, mobility ratio and fracture orientation on properties of two-phase flow. Illustrative examples indicate that aperture variation may control the distribution of wetting and non-wetting fluids within the fracture plane and hence the ability of the fracture to transmit these fluids. The presence of wetting fluid does little to hinder non-wetting fluid flow in fractures with large aperture variations, whereas a small volume of non-wetting fluid present in the fracture can significantly reduce wetting fluid flow. Large mobility ratios and high fracture slope angles facilitates the migration of non-wetting fluid through fractures.     

断层相关褶皱概念模型中的裂缝域

断层相关褶皱对裂缝的控制作用主要体现在岩层的几何形态对裂缝方位的影响和变形对岩石破裂的控制程度。本文在断层相关褶皱概念模型的基础上提出了裂缝域,并以Suppe的平行膝折概念模型为对象,利用几何学方法对模型中区域性裂缝的裂缝域进行分区描述,并提出了断层相关褶皱的曲线概念模型中区域性裂缝的分布规律。以新疆卡普沙良河一处断层转折褶皱剖面上裂缝的实测数据为依据,对模型进行验证,发现测量结果同模型基本一致。该方法为前陆冲断带地区断层相关褶皱对裂缝控制作用的定量预测提供了一种全新的思路。     

利用FMI资料分析塔河油田南部中—下奥陶统储层构造应力场

钻探结果表明,塔河油田南部地区上奥陶统覆盖区中—下奥陶统碳酸盐岩储层发育与分布明显地受断裂和裂缝控制。裂缝主要为构造开启缝,其次为钻井诱导缝,裂缝走向具有明显方向性,其形成与古构造应力场关系密切。利用大量中—下奥陶统钻井FMI资料进行裂缝识别、成因分类和走向统计分析,认为钻井诱导缝受现今构造应力场控制,构造开启缝主要受古构造应力场控制,裂缝走向与最大主应力方向一致。塔河油田南部地区诱导缝优势走向为北东向,现今最大主应力方向为北东向;构造开启缝优势走向主要有北北东向和北东东向两组,北北东向裂缝中可见充填缝,反映北北东向裂缝形成时间早于北东东向,其分别与加里东中期和海西早期的古构造应力场最大主应力方向相一致。     

湘中锑矿带断裂构造信息维特征及其意义

运用信息维的原理与方法对湘中锑矿带断裂构造体系的二维平面分布特征进行了研究。结果表明,信息维较之容量维更能反映断裂体系的结构特征,各矿带信息维值的差异定量地刻画了断裂的相对发育程度及分布特点。结合各矿带内锑矿床的分布特征,可发现信息维值的大小对成矿流体的运移和矿床定位有一定的指示作用,锑矿（点）产出较多、矿床储量较大的地区,其信息维值较大。     

Analogue modeling of overlapping spreading centers: insights into their propagation and coalescence

The propagation and segmentation of mid-ocean ridges is studied using centrifuged analogue models built with non-linear materials. The deformation of the brittle-ductile model is controlled by diapiric uprise of buoyant analogous asthenospheric material induced by a centrifugal body force. This linear upwelling laterally stretches the model mantle that, in turn, induces failure in the upper layer simulating the brittle crust. Arrays of fractures initiate within zones of high stress concentration above the diapir. Fractures propagate laterally in a direction perpendicular to the maximum tensile (the minimum principal) stress. Secondary tension cracks initiate in the vicinity of parent fracture tips. Through-going fractures that crosscut the model surface develop by short fractures propagating toward each other and coalescing in different types of patterns. The overlap, overstep and inclination of fractures developed at the initial stage of extension control their subsequent growth and coalescence. Non-overlapping sub-parallel fractures propagate along nearly straight paths and coalesce to produce a single planar fracture. If overlapping fractures are parallel, they propagate towards each other along curved paths that enclose an intervening elliptical core of intact material. Fracture curvature in this case results from crack–crack interaction and is similar to that of overlapping spreading centers (OSCs) observed along mid-ocean ridges. Overlapping non-parallel fractures tend to coalesce by one of their tips propagating sub-parallel to the spreading direction toward the other fracture. Such offsets can serve as models for the development of the orthogonal ridge-transform fault patterns common along mid-ocean ridges.