利用地质统计学方法模拟岩石裂隙网络的三维空间分布——以云南个旧高松矿田为例

裂隙在地学的诸多领域中均具有重要意义,其空间分布可以使用地质统计学方法进行模拟,同时考虑裂隙的方向(走向和倾角)。利用序贯高斯模拟方法可以估计裂隙密度的空间分布,并根据裂隙密度数值随机产生裂隙位置的空间分布。裂隙方向被划分成若干(非)均等的方向组,将裂隙方向归属到其所属方向组,表示为由若干二值变量组成的指示形式,0和1分别代表该裂隙方向不属于和属于该组。为了便于计算,减少方向指示变量的成分数目,使用主成分分析法求出方向指示变量的主成分,用普通克里格法估计各主成分的空间分布。把估计结果反演为原始的指示形式,并找出其中数值最大的方向组且将其赋值为1。按照对应方向组内裂隙方向的累积密度函数,随机产生裂隙的方向。根据估计结果,将符合一定距离和角度标准的裂隙元连接为一个裂隙面,从而形成裂隙网络。根据在云南个旧锡矿高松矿田白云岩中进行裂隙网络模拟的应用,可见该方法由于组合了序贯高斯模拟法、普通克里格法和主成分分析法,可以较好地对岩石裂隙位置和方向进行合理的模拟。     

An Algorithm for Generating Rock Fracture Patterns: Mathematical Analysis

A statistical, rule-based algorithm for generating fracture patterns similar to those observed in Limestone is presented. For each fracture set, initial seed points are randomly positioned within the modelled domain with the same density as the fractures observed in the field. An orientation is associated with each point by sampling from the distribution of orientations for the corresponding fracture set. Fractures are then allowed to grow from the seed points in both directions with this orientation until they meet other fractures whereupon they continue or terminate according to a fixed probability. A mathematical analysis of this method is presented for the case in which fractures within a set are assumed to be parallel. Approximations to the distribution of semi-trace lengths are derived which are shown to be in good agreement with simulation results. Fracture spacing distributions are also derived for this case.     

地应力对破裂压力和水力裂缝影响的试验研究

为研究水力压裂时地应力对破裂压力和水力裂缝的影响规律,采用水力压裂试验系统,以相似材料作为研究对象,进行了水力压裂物理模拟试验,并借助煤岩断面三维扫描系统、位移计提取了水力裂缝信息。试验结果表明,随着主应力差的增大,破裂压力逐渐降低,破裂时间也逐渐缩短;随着主应力差的增大,破裂面的表面积逐渐增加,破裂面变得逐渐粗糙;围压相近时水力裂缝易出现转向、分叉,压裂液的动力效应越明显;水力裂缝张开度随着主应力差的增大而逐渐减小。研究结果可为水力压裂试验的进一步研究、裂缝网络系统的建立提供参考。     

The use of the fracture reopening pressure in hydraulic fracturing stress measurements

Summary Practitioners of the hydraulic fracture stress measurement technique commonly estimate the hydraulic fracture tensile strength as the difference between the initial formation breakdown pressure and the fracture reopening pressure. This method, first suggested by Bredehoeft et al. (1976), was developed with the assumption that the stress state in the cracked formation is identical to the stress state in the uncracked formation. In this paper, a relationship for the fracture reopening pressure based on Linear Elastic Fracture Mechanics is developed that takes the hydraulically induced fracture into account. Situations in which the Bredehoeft technique can be appropriately applied are presented.     

Double fracture method ofin situ stress measurement in brittle rock

Summary A new technique, the Double Fracture Method ofin situ stress measurement, is described with regard to its theoretical principles and field instrumentation. The method differs from the hydraulic fracture method in that the loading fluid is prevented from penetrating into the induced fractures. In the new method, the loading pressure is raised to create a set of two mutually perpendicular microfractures on the borehole boundary. The principal stresses and their orientation in the plane normal to the borehole can be deduced from the diametral deformation of the borehole. Laboratory and field measurements validating the method are discussed.     

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.     

页岩储层体积压裂裂缝扩展机制研究

页岩储层天然裂缝、水平层理发育,水力压裂过程中可能形成复杂的体积裂缝。针对页岩储层体积裂缝扩展问题,基于流-固耦合基本方程和损伤力学原理,建立了页岩储层水力压裂体积裂缝扩展的三维有限元模型。将数值模型的模拟结果与页岩储层裂缝扩展室内试验结果进行对比,二者吻合较好,从而证明了数值模型的可靠性。通过一系列数值模拟发现：（1）水力压裂过程中水平层理可能张开,形成水平缝,水平与垂直缝相互交错,形成复杂的体积裂缝网络;（2）水平主应力差增大,体积裂缝的分布长度（水平最大主应力方向压裂裂缝的展布距离）增加、分布宽度（水平最小主应力方向压裂裂缝的展布距离）减小,体积裂缝的长宽比增加;（3）压裂施工排量增大,体积裂缝的分布长度减小、宽度增加,压裂裂缝的长宽比降低;（4）天然裂缝的残余抗张强度增大,体积裂缝分布宽度减小、分布长度增加,体积裂缝的长宽比增加。研究成果可以为国内的页岩气的压裂设计和施工提供一定的参考和借鉴。     

基于3D-ILC含偏心内裂纹半圆弯拉断裂特性研究

断裂力学是各行业的基础学科之一。半圆弯拉(SCB)试验为该领域经典试验,目前含裂纹的SCB研究多为底部切口等表面裂纹或穿透型裂纹研究。内裂纹和内部类裂纹缺陷是材料的固有属性,但是对于SCB内裂纹扩展规律研究较少。基于3D-ILC（三维激光疲劳内裂纹）技术,分析了表面无任何影响的情况下凭空生成任意参数的纯内裂纹,在SCB试样中生成内裂纹,对含内裂纹试样进行SCB试验,分析了裂纹生长过程、应力双折射规律、I-II-III型裂纹扩展面、破坏形态、宏微观断口特征,开展数值模拟,得到裂纹尖端应力强度因子分布规律及扩展路径,与物理试验一致。结果表明：（1）基于3D-ILC的SCB内裂纹及I-II-III型扩展断裂规律明显,3D-ILC为断裂力学中的内裂纹问题研究提供了有力工具;（2）应力云纹在内裂纹处显示应力集中,SCB整体云纹在内裂纹处发生明显变异;（3）SCB试样从预制裂纹处发生压剪型起裂,发生I-II-III型裂纹扩展,分为光滑区和撕裂区,持续生长转变为动态断裂进而破坏,动态断口存在裂纹分叉出现雾化区、羽毛区特征;（4）根据M积分和最大周向应力准则,对试样进行了数值模拟,得到了试样内裂纹尖端应力强度因子分布规律及扩展路径,与试验结果一致。结论与成果对断裂力学领域的SCB试验、内裂纹、I-II-III型断裂问题、裂纹扩展路径模拟问题的研究,具有重要意义。     

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。     

大尺寸真三轴页岩水平井水力压裂物理模拟试验与裂缝延伸规律分析

采用真三轴物理模型试验机、水力压裂伺服系统、声发射定位系统以及压裂液中添加示踪剂等方式,在真三轴条件下对大尺寸页岩水平井进行了水力压裂物理模拟试验,通过裂缝的动态监测和压裂后剖切等分析了裂缝的扩展规律,并对页岩压裂缝网的形成机制进行了初步探讨。结果表明：（1）水力裂缝自割缝处起裂并扩展、压开或贯穿层理面,形成相对较复杂的裂缝形态;（2）裂缝中既有垂直于层理面的新生水力主裂缝,又有沿弱层理面扩展延伸的次级裂缝,形成了纵向和横向裂缝并存的裂缝网络;（3）水力裂缝在延伸过程中会发生转向而逐渐垂直最小主应力;（4）水力裂缝在扩展过程中遇到弱层理面时的止裂、分叉、穿过和转向现象是形成页岩储层复杂裂缝网络的主要原因,而弱结构面的大量存在是形成复杂裂缝的基础。其研究结果可为页岩气藏水平井分段压裂开采等提供有力技术支持。     

基于离散裂隙网络模型的裂隙水渗流计算

离散裂隙网络模型(Discrete Fracture Network（DFN）)是研究裂隙水渗流最为有效的手段之一。文章根据裂隙几何参数和水力参数的统计分布,利用Monte Carlo随机模拟技术生成二维裂隙网络,基于图论无向图的邻接矩阵判断裂隙网络的连通,利用递归算法提取出裂隙网络的主干网或优势流路径。基于立方定律和渗流连续性方程,利用数值解析法建立了二维裂隙网络渗流模型,分析不同边界条件下裂隙网络中的流体流动。结果表明,该方法可以模拟区域宏观水力梯度和边界条件下,裂隙网络水力梯度方向总的流量,以及节点的水位、节点间的流量和流动方向的变化特征,为区域岩溶裂隙水渗流计算提供了一种实用、可行的方法。      

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.

     

页岩水平井多段分簇压裂起裂压力数值模拟

页岩储层孔隙度和渗透率极低,天然裂缝和水平层理发育,常规压裂增产措施无法满足页岩气的开发要求,水平井多段分簇压裂是页岩气开发的关键技术之一,该技术能够大幅度提升压裂改造的体积、产气量和最终采收率。为确定页岩储层水平井多段分簇射孔压裂的起裂点和起裂压力,采用有限元方法建立了水平井套管完井（考虑水泥环和套管的存在）多段分簇射孔的全三维起裂模型。数值模型的起裂压力与室内试验结果吻合较好,证明了数值模型的准确性和可靠性。利用数值模型研究了页岩水平井多段分簇射孔压裂的起裂点和起裂压力的影响因素,研究发现：射孔孔眼附近无天然裂缝或水平层理影响,起裂点发生在射孔簇孔眼的根部;射孔簇间距越小,中间射孔簇的干扰越大,可能造成中间的射孔簇无法起裂;射孔密度和孔眼长度增大,起裂压力降低;天然裂缝的存在,在某些情况能够降低起裂压力且改变起裂位置,主要与天然裂缝的分布方位及水平主应力差有关;水平层理可能会降低起裂压力,但与垂向主应力与水平最小主应力的差值有关。获得的起裂压力变化规律,可作为进一步研究水平井多段分簇射孔条件下的裂缝扩展规律的基础,可以为压裂设计和施工的射孔参数确定及优化给出具体建议。     

Semianalytical modeling on 3D stress redistribution during hydraulic fracturing stimulation and its effects on natural fracture reactivation

The hydraulic fracturing technique has been widely applied in many fields, such as the enhanced geothermal systems (EGS), the improvement of injection rates for geologic sequestration of CO₂, and for the stimulations of oil and gas reservoirs. The key points for the success of hydraulic fracturing operations in unconventional resources are to accurately estimate the redistribution of pore pressure and stresses around the induced fracture and predict the reactivations of preexisting natural fractures. The pore pressure and stress regime around hydraulic fracture are affected by poroelastic and thermoelastic phenomena as well as by fracture opening compression. In this work, a comprehensive semi-analytical model is used to estimate the stress and pore pressure distribution around an injection-induced fracture from a single well in an infinite reservoir. The model allows the leak-off distribution in the formation to be three-dimensional with the pressure transient moving ellipsoidically outward into the reservoir from the fracture surface. The pore pressure and the stress changes in three dimensions at any point around the fracture caused by poroelasticity, thermoelasticity, and fracture compression are investigated. With Mohr-Coulomb failure criterion, we calculate the natural fracture reactivations in the reservoir. Then, two case studies of constant water injection into a hydraulic fracture are presented. This work is of interest in the interpretation of microseismicity in hydraulic fracturing and in the estimation of the fracture spacing for hydraulic fracturing operations. In addition, the results from this study can be very helpful for the selection of stimulated wells and further design of the refracturing operations.     

Numerical Modeling of Natural Fracture Distributions in Shale

The production efficiency of shale gas is affected by the interaction between hydraulic and natural fractures. This study presents a simulation of natural fractures in shale reservoirs, based on a discrete fracture network (DFN) method for hydraulic fracturing engineering. Fracture properties of the model are calculated from core fracture data, according to statistical mathematical analysis. The calculation results make full use of the quantitative information of core fracture orientation, density, opening and length, which constitute the direct and extensive data of mining engineering. The reliability and applicability of the model are analyzed with regard to model size and density, a calculation method for dominant size and density being proposed. Then, finite element analysis is applied to a hydraulic fracturing numerical simulation of a shale fractured reservoir in southeastern Chongqing. The hydraulic pressure distribution, fracture propagation, acoustic emission information and in situ stress changes during fracturing are analyzed. The results show the application of fracture statistics in fracture modeling and the influence of fracture distribution on hydraulic fracturing engineering. The present analysis may provide a reference for shale gas exploitation.     

Spectral-type simulation of spatially correlated fracture set properties

Fracture set properties such as orientation, spacing, trace length, and waviness tend to be spatially correlated. These properties can be efficiently simulated by spectral analysis procedures that take advantage of the computational speed of the fast Fourier transform. The covariance function of each property to be simulated is obtained from the variogram function estimated from mapped fracture set data and is typically referenced to the mean vector of the set. Simulation procedures for normally and exponentially distributed data involve generating uncorrelated Fourier coefficients that are assigned proper variance according to the spectral density, which is the Fourier transform of the covariance function. These coefficients are then reverse Fourier transformed to produce simulated set properties that have the desired variance and variogram function.     

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.     

裂隙宽度空间变异性和泄漏条件对网络裂隙中DNAPLs运移影响研究

DNAPLs本身的化学性质、裂隙的几何性质以及泄漏条件等影响重非水相流体（DNAPLs）在裂隙介质中的运移和分布。针对DNAPLs的运移规律研究多集中在孔隙介质和单裂隙中,在随机网络裂隙中的研究较少。本研究生成随机网络裂隙是基于蒙特卡罗方法,运用像素扫描识别并输出裂隙的坐标和宽度,然后采用PetraSim模拟四氯乙烯(PCE)在随机网络裂隙中的运移,探讨裂隙宽度空间变异性和泄漏条件（包括泄漏速率和泄漏位置）对DNAPLs运移的影响。数值模拟结果表明:DNAPLs的空间展布和运移路径受裂隙宽度空间变异性影响,随着网络裂隙中裂隙宽度空间变异性增大,出现优势通道,DNAPLs运移的速率加快,DNAPLs的质心位置和饱和度空间分布发生明显变化;DNAPLs的运移速率和空间展布受泄漏速率影响,泄漏速率越大,DNAPLs运移速率越快,模型底部蓄积的DNAPLs的饱和度越大,DNAPLs的空间展布也越大;同一网络裂隙中,泄漏位置不同,导致DNAPLs的运移路径及分布范围不同,不同的泄漏位置重力方向裂隙空间变异性不同,导致DNAPLs运移路径和空间展布各不相同。研究结果可以丰富裂隙介质中DNAPLs运移机理研究,为裂隙介质中DNAPLs污染修复提供模型参考。     

定面射孔新工艺对水力裂缝扩展影响研究

定面射孔技术是为了提高体积压裂改造效果而提出的一种新的射孔方案。根据岩石力学及流-固耦合理论,建立了定面射孔地层的三维弹塑性流固-耦合地应力模型,采用数值方法进行求解,结合最大拉应力准则,研究了定面射孔水力裂缝的起裂规律。经过大量计算发现：定面射孔条件下,裂缝首先在射孔面内的射孔眼起裂,然后射孔眼相互贯通而形成扇形裂缝面,增大了水力裂缝的波及体积及井筒的连通性;同一平面内两侧孔眼在中间孔眼上产生的附加应力降低了Y方向主应力而增大了X方向和Z方向主应力,导致正断层采用定面射孔时,起裂压力较大,起裂压力随射孔方位角的增大而降低,只有当射孔方位角大于60°时,定面射孔起裂压力低于螺旋射孔起裂压力;对于逆断层,射孔方位角越小,起裂压力越低,且均低于螺旋射孔起裂压力;减小射孔间夹角、增大射孔直径及深度均可降低起裂压力。     

改进的数值流形法在水力劈裂中的应用

数值流形法在非连续变形分析领域具有独特优势。结合裂纹尖端场函数的基本概念,分析了水力劈裂破坏问题,模拟了水力劈裂破坏过程,避免了扩展有限元中的阶跃函数和水平集概念。为了避免裂纹尖端在单元内部不同位置而产生误差,对裂纹尖端附近一定范围内的每一个物理覆盖附加奇异覆盖函数。选取一个算例比较分析了内水压力对应力强度因子的影响,当考虑裂纹面内压时,定量分析比较了各因素对应力强度因子的影响大小,并应用于分支裂纹水力劈裂破坏。计算结果表明,改进后的计算结果与解析解相吻合。未考虑裂纹面内压,误差往往较大。考虑裂纹面内压后,随着裂纹长度的增加,误差逐渐减小;随着网格密度的增加,误差也逐渐减小。分支裂纹的渐进破坏结果表明该改进方法的可行性,具有较大的实际应用价值。