Circular scanlines and circular windows: new tools for characterizing the geometry of fracture traces

We introduce new estimators for fracture trace intensity, trace density and mean trace length that exploit the use of circles as efficient sampling tools. A fracture trace is the commonly observed surface expression of a fracture, i.e. the intersection of a fracture with an exposed surface such as a rock pavement or a mine drive wall. Trace intensity, trace density and mean trace length estimators are derived and shown to form a self-consistent set of two-dimensional fracture abundance measures. The intensity estimator n/4r uses the number, n, of intersections between fracture traces and a circular scanline of radius r. The density estimator m/2πr² uses the number, m, of trace endpoints inside a circular window. The mean trace length estimator (n/m)πr/2 uses the ratio of the number of trace intersections on the circle to the number of endpoints in the circle.The circular sampling tools and estimators described here eliminate most sampling biases due to orientation and also correct many errors due to censoring and length bias that plague established scanline and areal measurement techniques. Performance of the estimators is demonstrated by comparison with areal samples of a synthetic fracture trace population with known intensity, density and mean trace length. The estimators are also applied successfully to a natural rock pavement with two orthogonal fracture sets, one of which is severely censored. Because the new circle-based estimators only require counts of trace–circle intersections and/or trace endpoints, they are more time-efficient than current methods for estimating geometric characteristics of fracture traces.     

Regional fracture network permeability using outcrop scale measurements

Estimating the hydraulic properties of fractured aquifers is challenging due to the complexity of structural discontinuities that can generally be measured at a small scale, either in core or in outcrop, but influence groundwater flow over a range of scales. This modeling study uses fracture scanline data obtained from surface bedrock exposures to derive estimates of permeability that can be used to represent the fractured rock matrix within regional scale flow models. The model is developed using PETREL, which traditionally benefits from high resolution data sets obtained during oil and gas exploration, including for example seismic data, and borehole logging data (both lithological and geophysical). The technique consists of interpreting scanline fracture data, and using these data to generate representative Discrete Fracture Network (DFN) models for each field set. The DFN models are then upscaled to provide an effective hydraulic conductivity tensor that represents the fractured rock matrix. For each field site, the upscaled hydraulic conductivities are compared with estimates derived from pumping tests to validate the model. A hydraulic conductivity field is generated for the study region that captures the spatial variability of fracture networks in pseudo-three dimensions from scanline data. Hydraulic conductivities estimated using this approach compare well with those estimated from pumping test data. The study results suggest that such an approach may be feasible for taking small scale fracture data and upscaling these to represent the aquifer matrix hydraulic properties needed for regional groundwater modeling.     

Geomechanical paleostress inversion using fracture data

We describe a fast geomechanically-based paleostress inversion technique that uses observed fracture data to constrain stress through multiple simulations. The method assumes that the local stress field around individual fractures is heterogeneous and derives the far field tectonic stress, that we also call the far field boundary conditions. We show how such far field tectonic stress can be recovered through a mechanical stress inversion technique using local observations of natural fractures (i.e. mechanical type, orientation and location). We test the paleostress inversion against outcrop analogues of fractured carbonates from both Nash Point, U.K., where there are well exposed faults and joints and the Matelles, France, where there are well exposed faults, veins and stylolites. We demonstrate through these case studies how the method can be efficiently applied to natural examples and we highlight its advantages and limitations. We discuss how such method could be applied to subsurface problems and how it can provide complementary constraints to drive discrete fracture models for better fractured reservoir characterization and modelling.     

Curved scanline theory

This work develops the theory of measuring fracture frequency with curved scanlines, as a direct development of work done by others on straight scanlines. Various possible shapes for curved scanlines range between triangular and rectangular, with circular as a reasonable preliminary selection. The discrepancy among different selections decreases with increasing roughness amplitude of the scanline. Analytic solutions for average fracture frequency are given for circular scanlines through single and multiple fracture sets. Results for single fracture sets are plotted. The analytic solution for the general situation of any shape scanline through multiple fracture sets is given. Analytic solutions are given and plotted for circular scanlines through a fracture fabric ellipsoid. A circular scanline spanning 180 degrees yields a global fracture frequency of statistical significance.     

Characterizing Fracture Spatial Patterns by Using Semivariograms

Semivariogram is applied to fracture data obtained from detailed scanline surveys of nine field sites in western New York, USA in order to investigate the spatial patterns of natural fractures. The length of the scanline is up to 36 m. How both fracture spacing and fracture length vary with distance is determined through semivariogram calculations. In this study, the authors developed a FORTRAN program to resample the fracture data from the scanline survey. By calculating experimental semivariogram, the authors found five different types of spatial patterns that can be described by linear, spherical, reversed spherical, polynomial I (for a<0) and polynomial II (for a>0) models, of which the last three are newly proposed in this study. The well-structured semivariograms of fracture spacing and length indicate that both the location of the fractures and the length distribution within their structure domains are not random. The results of this study also suggest that semivariograms can provide useful infor     

Fracture sampling on a cylinder: From scanlines to boreholes and tunnels

Summary In this paper we develop correction factors for orientation bias when sampling rock fractures with a borehole. For a borehole with zero radius we obtain Terzaghi's result for scanline sampling: otherwise the appropriate correction factor may differ significantly from that obtained for the scanline model, depending on the relative size of the borehole and the rock fracture. Two separate cases are discussed: the sampling of fractures with a borehole and sampling with the surface of a borehole. Analytical expressions for the correction factors are graphed and tabulated.     

A method of estimating bulk potential permeability in fractured-rock aquifers using field-derived fracture data and type curves

A method is devised for estimating the potential permeability of fracture networks from attributes of fractures observed in outcrop. The technique, which is intended as a complement to traditional approaches, is based on type curves that represent various combinations of fracture lengths, fracture orientations and proportions (i.e., intensities) of fractures that participate in flow. Numerical models are used to derive the type curves. To account for variations in fracture aperture, a permeability ratio (R) defined as the permeability of a fracture network in a domain divided by the permeability of a single fracture with identical fracture apertures, is used as a dependent variable to derive the type curves. The technique works by determining the point on the type curve that represents the fracture characteristics collected in the field. To test the performance of the technique, permeabilities that were derived from fractured-rock aquifers of eastern Massachusetts (USA) are compared to permeabilities predicted by the technique. Results indicate that permeabilities estimated from type curves are within an order of magnitude of permeabilities derived from field tests. First-order estimates of fracture-network permeability can, therefore, be easily and quickly acquired with this technique before more robust and expensive methods are utilized in the field.     

Curved scanline theory

This work develops the theory of measuring fracture frequency with curved scanlines, as a direct development of work done by others on straight scanlines. Various possible shapes for curved scanlines range between triangular and rectangular, with circular as a reasonable preliminary selection. The discrepancy among different selections decreases with increasing roughness amplitude of the scanline. Analytic solutions for average fracture frequency are given for circular scanlines through single and multiple fracture sets. Results for single fracture sets are plotted. The analytic solution for the general situation of any shape scanline through multiple fracture sets is given. Analytic solutions are given and plotted for circular scanlines through a fracture fabric ellipsoid. A circular scanline spanning 180 degrees yields a global fracture frequency of statistical significance. This work was carried out under U.S. Department of Energy Contract No. DEAC03-76SF00098 for the Director, Office of Civilian Radioactive Waste Management, Office of External Relations, and was administered by the Nevada Operations Office, U.S. Department of Energy. This work also was supported partially by the Power Reactor and Nuclear Fuel Development Corporation of Japan.     

裂隙岩体岩石质量指标(RQD)的空间变化特征

岩石质量指标(RQD)是评价岩体破碎程度的一个重要参数,但在RQD的应用过程中往往忽略测线长度和测线方向的影响,给岩体质量的评价造成一定的误差。笔者通过从野外岩石露头这个二维平面上得到的RQD或节理参数,推导得到在三维空间中任意方向测线的RQD,进而研究RQD随测线方向的变化规律。结果表明,RQD不但在平面上具有各向异性,在空间也具有各向异性。笔者提出了假定测线起于节理的N-A RQD计算模型,使理论论证更加严密。此外,利用蒙特卡罗模拟产生随机值代表节理间距,随机值服从负指数分布的参数不同代表节理发育的密集程度不同,通过T-T、N-A、A-A和A-A-S 4种RQD计算模型来研究RQD均值及标准差随测线长度的变化规律,可以得出：测线越长,所得RQD值越精确;测线较短时,A-A-S模型所得的RQD值与其他3种模型相比更精确;布置较长的测线在节理较发育的地方可获得更可信的RQD值。     

鄂尔多斯盆地延长组页岩裂缝特征与地应力研究

鄂尔多斯盆地延长组是我国近些年陆相页岩气的重点勘探区之一。本文从页岩的露头观测、岩石学特征、成像测井分析、地应力特征及可压裂性等方面,研究了鄂尔多斯盆地延长组泥页岩层段的裂缝发育特征,以及地应力对人工压裂诱导缝的影响。基于岩石学分析,延长组长7和长9段的泥页岩脆性矿物平均含量较高,分别为57.2%和44%。根据泥页岩露头观测和成像测井分析,长7段泥页岩发育有北东东向为主的垂直裂缝组,同时可见北北东向和南北向的垂直裂缝组。此外,压裂诱导缝的优势方位和成像测井分析结果表明,现今最大水平主应力方向为70°左右（即北东东向）。裂缝开启性分析表明,北东东向至近东西向裂缝组与现今最大水平地应力方向一致,开启性较好;而北北东裂缝组与现今最大水平地应力交角相对较大,开启性相对较差。因为现今地应力的水平应力比值（σH/σh = 1.54）相对较小,在后期人工压裂中延长组泥页岩中的诱导裂缝更倾向形成复杂的裂缝网格系统,这样会使裂缝与储层之间获得最大的接触,从而更有利于提高产能。     

赫兹破裂：一种被忽视的构造

赫兹破裂在工程和材料领域一直备受关注,但其在地质学领域的应用还很少,远未像里德尔破裂那样熟知。从微观尺度到露头尺度,从板块尺度到行星尺度,赫兹破裂在自然界都广泛存在。赫兹破裂作为一种点接触破裂区别于常见的里德尔剪切破裂。它们均是自然界中特殊而又普遍发育的破裂形式,代表了不同的边界和应力条件。典型的赫兹破裂属于弹性变形范畴,由于点接触而在三维空间中形成特征的锥形破裂,在平面上则表现为放射状及环状破裂。在剖面上锥形破裂一般会出现一定角度的拐折,下段破裂与接触面的角度变大,是锥形破裂的典型特征之一。在地质学领域,赫兹破裂有着重要的指示意义,可以表征物质的韧性（toughness）、解释环状和放射状构造、解释锥状以及弧形破裂成因与样式、判断冰川以及断层的运动学特征、区分不同破裂机制形成的新月形构造等,也可以应用于恢复沉积环境以及判断成岩过程中或者构造变形过程中的古应力及其方向。板块碰撞过程中,在特定环境下也可形成赫兹破裂,因此该类型破裂将会有助于我们理解一些断层的成因、发展以及大陆的变形,同时为类地行星（卫星）表层的构造提供解释方案。     

Structural controls on Witwatersrand gold mineralisation

Structural controls on the distribution of gold in the Witwatersrand Basin can be seen at scales ranging from that of thin sections up to regional seismic data sets. At the thin section scale, gold occurs largely in fractures with hydrocarbons. These fractures are associated with pulses of thrusting deformation that occurred in the latter stages of the basin's development. The distribution of thrust–fracture networks (and therefore gold) is controlled by the mechanical attributes of the host stratigraphy. Thrust displacements are generally very low, with structures exploiting depositional contacts and mesoscale sedimentary bedforms. Many of the small faults are isolated from each other with bimodal vergence between larger-scale thrusts of the same age. Early-formed faults and fractures become folded and faulted by subsequent propagation of larger-scale thrusts. These characteristics are consistent with formation of the mineralised thrust–fracture networks in the frontal, low-displacement parts of a thrust system. In the Carletonville goldfield, the prospectivity of the Ventersdorp Contact Reef (VCR) has been evaluated by using underground observations to pinpoint the structural habitat of gold, and therefore characterise the size of prospective zones around structures intersecting the VCR, mapped within 3D seismic data. In the Welkom goldfield, the controls on gold distribution at the Tshepong mine have been characterised from 3D seismic data, drilling and underground observations, and used to develop an ore-body model that aids reserve estimation and production planning.     

Spatial sampling considerations and their applications to characterizing fractured rock and karst systems

Assessing the existence, location, and mapping of geologic anomalies, such as fractures and cavities within soil and rock, are common to both engineering and hydrologic project needs. There are numerous measurement techniques available to detect, map, and characterize fractures and cavities. A summary of the common methods available for fracture and cavity detection and mapping are presented along with their spatial sampling capabilities. The remote sensing and geophysical methods are but a small part of this list but provide a wide range of tools to attack the problem. They include some of the most effective methods for locating and mapping fractures and cavities and cover the complete range of spatial sampling, from regional to no more than the surface of a borehole wall. An understanding of all of the tools available and their spatial sampling limitations is a necessary part of planning and carrying out an effective fracture/cavity investigation.     

Quantifying a critical marl thickness for vertical fracture extension using field data and numerical experiments

In fractured reservoirs characterized by low matrix permeability,fracture networks control the main fluid flow paths.However,in layered reservoirs,the vertical extension of fractures is often restricted to single layers.In this study,we explored the effect of changing marl/shale thickness on fracture extension using comprehensive field data and numerical modeling.The field data were sampled from coastal exposures of Liassic limestone-marl/shale alternations in Wales and Somerset(Bristol Channel Basin,UK).The vertical fracture traces of more than 4000 fractures were mapped in detail.Six sections were selected to represent a variety of layer thicknesses.Besides the field data also thin sections were analyzed.Numerical models of fracture extension in a two-layer limestone-marl system were based on field data and laboratory measurements of Young's moduli.The modeled principal stress magnitude σ_3 along the lithological contact was used as an indication for fracture extension through marls.Field data exhibit good correlation(R~2=0.76) between fracture extension and marl thickness,the thicker the marl layer the fewer fractures propagate through.The model results show that almost no tensile stress reaches the top of the marl layer when the marls are thicker than 30 cm.For marls that are less than 20 cm,the propagation of stress is more dependent on the stiffness of the marls.The higher the contrast between limestone and marl stiffness the lower the stress that is transmitted into the marl layer.In both model experiments and field data the critical marl thickness for fracture extension is ca.15-20 cm.This quantification of critical marl thicknesses can be used to improve predictions of fracture networks and permeability in layered rocks.Up-or downsampling methods often ignore spatially continuous impermeable layers with thicknesses that are under the detection limit of seismic data.However,ignoring these layers can lead to overestimates of the overall permeability.Therefore,the understanding of how fractures propagate and terminate through impermeable layers will help to improve the characterization of conventional reservoirs.     

岩心中的天然缝与诱导缝的识别与分析——以鄂尔多斯盆地延长组岩心裂缝为例

由于取心成本昂贵, 从岩心中获得天然缝、诱导缝和其他构造特征的准确信息显得尤为重要。岩心裂缝识别中的一项重要任务是判识天然缝和诱导缝。文中综合论述了天然缝和诱导缝的物理特征, 重点分析了天然缝形态及发育过程和诱导缝的多种成因模式, 并以鄂尔多斯盆地延长组岩心中裂缝为例进行分析。文中引用了国外对裂缝研究常用的专业术语, 指出裂缝面形态结构是追踪模式Ⅰ裂缝(节理)从扩展初始点到终止处的运动学的关键, 这在岩心裂缝和露头裂缝分析中是非常有用的。     

陕甘宁盆地川口油田低渗透油藏长6油层裂缝特征

通过对野外野头观测，岩心观察，薄片鉴定、地层倾角测井解释等方法，对川口油田长6油层裂缝进行了研究，川口油田长6油层主层裂缝方向为近EW向，天然显裂缝规模小且不发育，裂缝在原始地层条件下多为闭合状态，只有在人工激发后才会表现出明显的裂缝特征，川口油田储层类型为孔隙型储集层，该区油层埋深500－700m，垂向应力为最小主应力，压裂后理论上应产生水平缝，但受到天然垂直（闭合）缝的影响，在裂缝发育区可能会形成垂直压裂缝，在目前注水条件下，注水实验区储层裂缝的作用还未表现出来。     

成像测井缝洞解释评价研究进展

综合露头刻度井、数值模拟和物理模拟的实验结果对微电阻率扫描成像测井缝洞解释评价的研究进展进行了总结和探讨,分别包括岩芯归位、缝洞刻度率、岩芯和成像裂缝参数的差异性,以及裂缝宽度和地层孔隙度的计算。岩芯归位确定了缝洞体在地层中的深度和方位。电成像测井对过井眼未充填缝和孔洞发育段的刻度率为100%,而单个孔洞在岩芯和电成像测井中通常无法一一对应。单条裂缝的倾角或井周长度在岩芯和成像测井中具有较高的相关性,而裂缝宽度的相关性一般。数模和物模的结果表明电成像测井裂缝宽度的计算受多种因素影响,当裂缝的视宽度大于0.1 mm时,电成像测井计算的裂缝宽度和裂缝视宽度基本一致,当小于0.1 mm时,电成像测井计算的宽度值误差较大。目前电成像测井通过孔隙度谱法和图像分割法计算地层的孔隙度,但都受限于除孔洞的其他低阻地质体的影响,因此需要加强岩芯刻度的功能。     

成像测井缝洞解释评价研究进展

综合露头刻度井、数值模拟和物理模拟的实验结果对微电阻率扫描成像测井缝洞解释评价的研究进展进行了总结和探讨,分别包括岩芯归位、缝洞刻度率、岩芯和成像裂缝参数的差异性,以及裂缝宽度和地层孔隙度的计算.岩芯归位确定了缝洞体在地层中的深度和方位.电成像测井对过井眼未充填缝和孔洞发育段的刻度率为100％,而单个孔洞在岩芯和电成像...     

Fracture step structure: geometrical characterization and effects on fluid flow and breakthrough curve

Groundwater flow and solute transport through fractured rock is highly responsive to the hydraulic anisotropy and heterogeneity that are specific to every major fracture. A major fracture is modeled as the combination of some primal master fractures and several splay fractures that branch out from primal master fractures: step structures (or jog parts). Step structures are commonly observed along a major fracture on various scales. Master fractures were formed and developed by shear movement while some splay fractures were formed by extension normal to their wall. This difference in fracturing process may lead to a permeability difference between master fractures and splay fractures which seems to be one of the major factors controlling flow and solute transport through the fracture networks due to its hydraulic anisotropic and heterogeneous features. This study is composed of two major components: (1) identification and characterization of a step structure from borehole data; (2) evaluation of effect of some idealized step structures on breakthrough curve by numerical simulations. The fracture data of four 1000-m boreholes were used to make clear fracture patterns in the Tono area of Japan. Some major fractures were identified using stereographic projection technique. On the basis of these results, several idealized models of a major fracture having a step was constructed for the numerical study. The obtained results from numerical simulations clearly imply that geometry of step structure plays an important role in flow and transport through the fracture networks.     

Identification of fracture development period and stress field analysis based on fracture fabrics in tectonic superposition areas

As a direct consequence of multiple periods of stress applied on areas with tectonic superposition, the multiple-periods fractures have complex abutting relationships, and the field study of fractures is usually restricted by outcrop conditions, such as section direction. Therefore, previous studies of superposed stress fields based on fractures have been generally performed in areas with proper observation conditions and clear abutting relationships. In contrast, in many other areas, the identification of fracture development period based on field observation is often infeasible. Compared to abutting relationships, fracture fabrics obtained from field measurement are not affected by the restriction of outcrops and consequently are more representative of the fractures. According to the analysis of fracture fabrics and fracture features, this paper has separated and extracted the superposed fracture sets and identified the fracture development period in the area without available abutting relationships. Taking the southern segment of the Longmen Mountain thrust belt as an example, fractures of two development periods are identified and timed in the tectonic superposition area between two adjacent fold belts. The analysis of stress direction in each period suggests that the structural boundaries, consisting of such pre-existing structures as faults and anticlines, could have induced directional rotation in the subsequent stress. An equivalent result was achieved using a finite element simulation of the stress field. Based on the stress analysis of the field sites and the stress field simulation, the stress variation in the tectonic superposition area is well modeled.