A Connectivity Index for Discrete Fracture Networks

Connectivity is an important measure for assessing flow transport in rock, especially through fractures. In this paper, rock fracture systems are modelled by a discrete fracture model simulated by a marked point process. A connectivity index is then introduced to quantify the connectivity between any two points in space. Monte Carlo simulation is used to evaluate the connectivity index for stationary cases and relationships between the connectivity index and the parameters of the discrete fracture model are analysed. The average number of intersections per fracture, X_f, and the fracture intensity, P12 (P32), are calculated and the relationships between these parameters and the connectivity index are investigated, concluding that X_f is the more suitable parameter for the classification of rock mass flow properties. The relationships between the connectivity index and the percolation state of the fractured medium are also discussed. An edge correction is briefly discussed and a practical example is used to demonstrate the method of computing the connectivity index.     

地下空间逾渗与裂缝属性的关系分析

裂缝连通性评价是地下空间研究的重要内容。逾渗分析是研究裂缝网络连通性的一种有效手段。裂缝网络逾渗临界值多使用裂缝间接表征参数(如分形维数)来确定,但存在裂缝网络连通性不同却有相同间接表征参数的情况,这降低了预测的可靠性。为避免此类问题并更加准确快速地表征裂缝网络的连通性,文章在构建逾渗临界值方程时,摒弃了间接参数简化的方式,使用裂缝直接表征参数(如裂缝数量、长度等)进行非线性拟合。通过二维数值模拟建立不同参数的离散裂缝网络模型,分析逾渗低、中、高概率临界条件与裂缝直接表征参数的关系,建立逾渗临界条件预测方程,并对方程在不同尺度研究区的应用进行了讨论和验证。结果表明：预测方程可有效地预测不同概率的逾渗临界值。同时文章在预测方程的基础上,建立了裂缝网络连通性评价标准,这对于裂缝发育地区的地下空间评价工作具有一定的指导和借鉴意义。     

Analysis of fracture network connectivity using percolation theory

Connectivity aspects of fracture networks are analyzed in terms of percolation theory. These aspects are of fundamental importance in characterization, exploitation, and management of fractured formations. General connectivity and power law relationships are determined that characterize the density of fractures and average number of intersections per fracture necessary to ensure network connectivity, the likelihood of a fractured formation being hydraulically connected, and the probability that any specific fracture is connected to the conducting portion of the network. Monte Carlo experiments with a two-dimensional fracture network model confirm the percolation theory predictions. These relationships may prove useful in formulating theoretically tractable approximations of fracture nerworks that capture the essential system properties.     

川西顺层斜坡破坏模式及层间弱面连通率对斜坡稳定性的影响

顺层岩质斜坡是沉积岩地区常见的一种斜坡类型,也是各种工程建设重点关注的一类斜坡。以川西雅安地区典型的顺层岩质斜坡为例,采用现场调查、无人机测绘、钻探、物探和稳定性计算等技术方法,归纳总结目前斜坡存在的变形破坏模式。分析计算斜坡在不同工况条件下,层间破碎带连通率与斜坡稳定性之间的关系。研究结果表明:层间破碎带对斜坡稳定性具有重要的影响或控制作用,当斜坡浅表部强风化岩体内层间破碎带连通率小于86%时,斜坡稳定性与现状调查结果吻合。研究结果对川西地区基础设施规划建设和防灾减灾具有重要的工程意义。     

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.     

塔里木盆地富满大型碳酸盐岩油气聚集区走滑断裂控储模式

塔里木盆地台盆区深层海相油气勘探目标由层间岩溶向断控岩溶转变,并在处于坳陷区的富满地区发现了以走滑断裂为主控因素的断控型油田。富满地区储层特征与盆地内古隆起区、斜坡区均有不同,因此需要建立适合研究区的走滑断裂控储模式。本次研究通过高密度三维地震资料刻画了研究区走滑断裂的分布,利用岩心、测井、试井资料以及缝洞体识别技术明确了不同类型的储层分布,分析了研究区走滑断裂样式与差异变形对储层发育的影响,建立了走滑断裂控储模式。研究结果表明:(1)富满大型碳酸盐岩油气聚集区储集空间主要由多期走滑构造破裂作用与岩溶作用形成的洞穴型、裂缝-孔洞型、裂缝型与孔洞型空间组成;(2)走滑断裂活动性越强,断裂带宽度越大,储层发育规模越大,张扭段与压扭段断层破碎带型储层较平移段平面分布范围更广,纵向发育深度更大;(3)张扭段为汇水区,断裂联通性好,有利于大气流体下渗以及热流体上涌从而对储层进行溶蚀改造;压扭段为分流区,岩溶储层多发育于断裂带两侧,断裂开启程度低,受流体改造程度低于张扭段。     

An automated approach for conditioning discrete fracture network modelling to in situ measurements

Creation of a geological fracture network model conditioned to in situ geometric measurements is of great importance to geoprofessionals, as fractures dominate pathways for fluid flow, a major concern for many engineering applications. This paper introduces and applies the Stochastic Nelder Mead simplex method to automatically calibrate stochastic parameters of geometric characterisations of a discrete fracture network model. This method can overcome the non-convergence of a previous exploratory approach on the classic Nelder Mead method by others, and is an effective substitution to the manual trial-and-error method and is complementary to existing conditional simulation approaches. The procedure to integrate the Stochastic Nelder Mead with a discrete fracture network is presented in detail, and a case study was conducted. Results show that the improved model can better handle the stochastic nature of the underlying system and effectively simulates the observed number and mean trace length of these fractures, although the model results underestimate its standard deviation. Simulated distributions of trace lengths and spacings are within acceptable ranges except for some small offsets, which can be adjusted during model runs.     

裂隙网络管道模型弥散试验

为了探求不同裂隙几何参数对裂隙网络溶质运移的影响,基于离散裂隙网络思想和优势流、沟槽流理论,建立裂隙管道网络概念模型,搭建不同管径、不同连通方式的管道网络试验装置,进行渗流和溶质运移实验。运用应用广泛的模拟软件CHEMFLO-2000建立等效多孔介质模型,拟合不同几何参数下等效弥散度,定量刻画不同管道网络几何参数对溶质运移的影响,讨论了不同管径、连通方式等与等效弥散度之间的关系。通过进一步分析得出:在连通方式相同的情况下,不同管径的管道网络等效弥散度存在差异,但是差异不大;溶质在小管径中的穿透时间短于大管径,穿透曲线缓和程度相差不大;管道网络连通方式越复杂,其等效弥散度越大、对溶质运移的影响越大、穿透曲线越缓和、路径越长,等效弥散度越大;用这种等效弥散度的方法表征管道网络对溶质运移的影响,与多孔介质弥散度具有相似性;管道数目、管道面数目与等效弥散度成正相关关系,且等效弥散度随尺度的增大而增加。     

深切河谷附近岩溶地区打井找水模式

深切河谷附近岩溶地区地表水快速下渗,岩溶地下水深埋且集中径流,导致水资源匮乏,易成为较干旱缺水地区。同时在该类地区,受地表水构成的地下水排泄基准面控制,地下水水位埋深大,且以快速的管道流和裂隙流为主,储存空间分布和相互间连通性高度不均匀给打井找水带来了极大困难。发现下伏碎屑岩、逆断层和上覆碎屑岩均能将岩溶地下水和深切河谷地表水之间水力联系切断,导致局部富水,成为打井找水有利靶区。基于此3种类型,结合打井找水成功实例,将其归纳为3种打井找水模式：下伏碎屑岩隔水模式、逆断层阻水模式和上覆碎屑岩阻水模式,这些模式将对在深切河谷附近岩溶地区打井找水提供帮助。     

Permeability tensor and representative elementary volume of fractured rock masses

Based on a simulation of three-dimensional fracture networks and a superposition principle of liquid dissipation energy for fractured rock masses, a model of the fracture permeability tensor is proposed. An elastic constitutive model of rock fractures, considering fracture closure and dilation during shearing, is also proposed, based on the dilation angle of the fracture. Algorithms of flow-path searching and calculation of the effective flow coefficients for fracture networks are presented, together with a discussion on the influence of geometric parameters of the fractures (trace length, spacing, aperture, orientation and the number of fracture sets) on magnitude, anisotropy of hydraulic permeability and the size of a representative elementary volume (REV). The anisotropy of hydraulic permeability of fractured rock masses is mainly affected by orientation and the number of fracture sets, and the REV size is mainly influenced by trace length, spacing and the number of fracture sets. The results of studies on REV size and the influence of in-situ stress on hydraulic conductivity of the rock mass on the slope of Jinping-I hydropower station, China, are presented using the developed models and methods. The simulation results agreed well with the results obtained from field water-pressure measurements, with an error of less than 10 %.     

雷家地区沙四段致密油储层特征研究

雷家地区沙四段致密油的开采和研究刚刚起步,在地质认识方面尚不够深刻。本文通过对雷家地区沙四段岩芯观察、XRD衍射、铸体薄片、场发射扫描电镜、氩离子抛光扫描电镜、CT扫描及氮气吸附等方法对沙四段储层地质特征展开系统分析,结果发现:该区主要发育白云岩,根据组成矿物含量的不同可分为白云岩类、方沸石岩类和泥岩类3大类15种岩;孔隙度分布范围1.68%～11.65%,渗透率介于0.01～6.35mD,属于特低孔特低渗型储层;储集空间类型多样,主要发育溶蚀孔、晶间孔、有机质孔裂缝,该区孔隙结构较复杂,存在少量大孔,但主要由纳米孔组成,孔隙分布较为分散,喉道数量少,连通性差;根据该段储层孔隙结构及储集空间分布特征,将该段储层分为孔隙型、裂缝型和裂缝-孔隙型3类,其中孔隙型储层孔隙分布较为分散、连通性较差,裂缝型储层岩性主要为泥岩类,裂缝-孔隙型储层物性相对较好且主要发育在杜家台段。     

西秦岭夏河-合作地区断裂构造分形结构特征及成矿预测

西秦岭夏河-合作地区是中国重要的金矿及多金属矿床开发地带,区内断裂构造复杂,构造控矿作用显著。文章利用分形理论方法对夏河-合作地区不同方向断裂构造作定量分析,统计计算断裂构造容量维和信息维,结合矿床空间分布分形特征和矿床Fry分析,探讨研究区构造分形特征及断裂与矿床的空间展布关系。研究结果表明,研究区全部断裂容量维1.2374,北东向断裂容量维0.8229,北西向断裂容量维1.2296,近东西向断裂容量维1.0312,全部断裂容量和北西向断裂容量维处于断裂分形临界值（1.22~1.38）区域,显示研究区断裂构造连通性较好。研究区全部断裂信息维1.1118,北东向断裂信息维1.018,北西向断裂信息维1.2296,近东西向断裂信息维1.0217,北西向断裂信息维处于断裂分形临界值区域,反映北西向对矿床的控制最强。断裂构造分形维数可以表征矿床的沉积部位,以容量维、信息维等值线图以及Fry图划分出3个有利成矿区。     

高放废物深地质处置地下水流数值模拟方法研究进展

地下水流数值模型不仅是认识深部水动力场形成演化机制的有效工具,也是建立核素迁移数值模型的基础,因而是高放废物处置场选址和安全评价中重要的技术手段。高放废物深地质处置地下水流数值模拟方法较多,如何选择适当的方法也是值得关注的问题。针对高放废物深地质处置地下水流数值模拟技术展开研究,通过阅读大量国内外文献,文章系统阐述了目前常用的4 类地下水流数值模拟方法的研究进展、适用条件和实例应用;综述了深地质处置中常用的模型不确定性分析方法及研究成果,列表给出了适用于放射性废物地质处置的地下水流数值模拟软件及其在废物处置选择和安全评价中的应用。研究结果表明:等效连续介质模型适用于大区域、长序列、裂隙发育程度较高或较均匀的地区,该类模型方法成熟、所需的数据和参数易于获得,但是不能精确刻画裂隙介质中地下水的流动特征。离散裂隙网络模型适合解决处置场地、储罐尺度等需要精细刻画的地下水流问题,但由于需要大量裂隙及其连通性数据、相关参数等,该方法存在着工作量大、耗时多的缺点。双重介质模型主要用于解决区域尺度裂隙水流问题,但并不能表现出裂隙介质的各向异性、不连续性等特征,因而适用范围存在一定的限制。等效-离散耦合模型可以通过区域分解法对裂隙密度大的区域采用等效连续介质模型,对于裂隙密度较小的地区采用离散裂隙网络模型,从而更符合一般地质条件下裂隙渗流的特征,但也存在交换量难以确定、模型耦合技术问题。通过灵敏度分析,将不同敏感因子对模型敏感指标的影响程度进行排序,提高模型精度、减少参数不确定性分析的工作量。蒙特卡罗法是目前常用的一种模型不确定性方法,原理简单、易于实现。文章展望了数值模型在仿真性、不确定性分析、预测和多介质耦合等方面的研究前景。     

储层非均质性对水力压裂的影响

从岩石细观非均质性的特点出发,采用RFPA2D-Flow软件对单孔和双孔数值模型进行压裂计算,研究岩石非均质性对水力压裂的响应,重点探讨双孔模型孔间吸引效应对裂纹演化形态的影响。岩石细观单元的力学、水力学特性由统计分布生成以体现岩石的随机不均质性,水力压裂过程中流体压力传递通过单元渗流-损伤耦合迭代来实现。数值计算结果表明:(1)岩石非均质性影响裂缝的扩展形态,导致水力裂纹尖端微裂纹的分支。随着均质度的增加,水力裂纹的扩展形态变得更加平直光滑,单孔模型两侧裂纹更加对称,双孔间裂纹的连通性变差。(2)岩石的非均匀性对于岩石的起裂压力和地层破裂压力影响较大。随着均质度的增大,起裂应力和地层破裂应力增大,并且两者间的差值逐渐变小,在储层为均质的条件下,两者几乎相等。(3)相同的边界条件下,均质模型的应力分布曲线光滑连续,非均质模型的应力分布曲线呈现出明显波动,井眼对称剖面上的应力分布不尽相同,反映了细观单元强度非均匀性及裂缝扩展形态对应力分布的影响。(4)双孔模型孔间存在孔隙水压力增加带,孔间产生吸引效应,双孔方位影响临界压力。研究结果对水压裂试验设计和现场压裂施工具有一定的参考意义。     

Fracture analysis in Tabnak hydrocarbon field of Iran by using fractal geometry and multi-fractal analysis

High gas production from the Dashtak formation of Tabnak hydrocarbon field in Fars province, Iran, indicates the presence of natural fractured reservoir whose production potential is dominated by the structural fracture. The connectivity of fractured media depends upon the power?Claw exponent and the fracture density. Fracture pattern traces obtained from the outcrops of producing formations of six different stations in Tabnak hydrocarbon field. 2D fracture network maps of Tabnak hydrocarbon field have been analyzed from their scaling properties. The fractal analysis of fracture intensity showed heterogeneous multi-fractal structure characterized by generalized dimensions. Distribution of fracture lengths exhibits power?Claw behavior with specific exponent. Scaling laws serve to make extrapolations and to study the fracture connectivity related to scale. Fracture distribution model and reservoir productivity can be estimated, which are of great interest in decision making to optimize gas production.     

塔里木盆地塔中北斜坡奥陶系鹰山组深部优质岩溶储层的形成与分布

塔中地区是塔里木盆地的重点勘探区域,奥陶系鹰山组蕴藏了丰富的油气资源。鹰山组发育大套台地相碳酸盐岩,以高能相的台内滩沉积为主。鹰山组埋藏较深,但岩溶储层呈大面积厚层状分布。早奥陶世塔中I号断裂使得塔中隆起隆升并遭受强烈剥蚀形成下奥陶统鹰山组顶部风化壳,以孔洞型和裂缝-孔洞型储层为主。通过古地貌恢复、地震属性分析和地震测井联合波阻抗反演技术和方法识别溶洞发育带和断层裂缝发育带,确定出有利储层的分布范围。研究认为,岩性岩相是岩溶型储层发育的重要基础,层间岩溶控制了储层的成层性和横向展布规模,断裂和裂缝网络是岩溶水的主要渗滤通道,埋藏岩溶形成大量有效的缝洞空间,极大地提高了储集性能。研究发现,优质储层主要分布在鹰山组顶面以下120m地层厚度范围内,横向有一定连通性,在断层、构造裂缝和溶蚀作用下形成统一的储集体,呈准层状展布。     

大倾角煤层水力裂缝扩展物理模拟实验

为研究大倾角煤层水力压裂裂缝扩展形态，采用大尺寸真三轴压裂模拟系统，分别开展最大水平主应力沿地层走向和沿地层倾向的60°倾角煤层水力裂缝扩展物理模拟实验。结果表明:最大主应力方向沿地层走向时，裂缝起裂容易，缝高受限，裂缝连通性好，裂缝的开启主要沿层理和天然裂缝，形成垂直缝形态，地层倾角对压裂施工影响相对较小，建议进行大规模压裂以充分改造煤储层；最大主应力方向沿地层倾向时，裂缝起裂困难，前期缝高受限，后期缝高失控，裂缝连通性差，受节理影响，不易形成主缝，所以裂缝扩展困难，转向及多级破裂较多，此类煤层建议进行多级小规模压裂改造。实验结果对新疆等地区大倾角煤层的改造模式和改造规模具有指导作用。      

裂隙岩体渗流-应力耦合等效渗流阻模型

针对含区域主干裂隙岩体在应力作用下的渗透特性进行了研究。运用单裂隙平行板渗流理论、弹性力学方法,结合模拟电路知识,提出等效渗流阻的概念。在分析裂隙岩体区域中主干裂隙系统几何构造的基础上,建立了基于等效渗流阻的- 渗流-应力耦合模型,得到了裂隙岩体等效渗流阻、渗透率与应力之间的关系,从而为研究含区域主干裂隙岩体的应力-渗流耦合规律提供了方便。结合一个基于等效渗流阻模型的算例,考察了含“人”字形组合裂隙试样的渗透特性。经进一步细化后,该模型可用于分析地应力作用下的含区域主干裂隙岩体渗流演化规律。     

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.