Analysis of a deformable fracture in permeable material

The response of deformable fractures to changes in fluid pressure controls phenomena ranging from the flow of fluids near wells to the propagation of hydraulic fractures. We developed an analysis designed to simulate fluid flows in the vicinity of asperity‐supported fractures at rest, or fully open fractures that might be propagating. Transitions between at‐rest and propagating fractures can also be simulated. This is accomplished by defining contact aperture as the aperture when asperities on a closing fracture first make contact. Locations on a fracture where the aperture is less than the contact aperture are loaded by both fluid pressure and effective stress, whereas locations where the aperture exceeds the contact aperture are loaded only by fluid pressure. Fluid pressure and effective stress on the fracture are determined as functions of time by solving equations of continuity in the fracture and matrix, and by matching the global displacements of the fracture walls to the local deformation of asperities. The resulting analysis is implemented in a numerical code that can simulate well tests or hydraulic fracturing operations. Aperture changes during hydraulic well tests can be measured in the field, and the results predicted using this analysis are similar to field observations. The hydraulic fracturing process can be simulated from the inflation of a pre‐existing crack, to the propagation of a fracture, and the closure of the fracture to rest on asperities or proppant. Two‐dimensional, multi‐phase fluid flow in the matrix is included to provide details that are obscured by simplifications of the leakoff process (Carter‐type assumptions) used in many hydraulic fracture models. Execution times are relatively short, so it is practical to implement this code with parameter estimation algorithms to facilitate interpretation of field data. Copyright © 2006 John Wiley & Sons, Ltd.     

Simulation of hydraulic fracture propagation near a natural fracture using virtual multidimensional internal bonds

A virtual multidimensional internal bond (VMIB) model developed to simulate the propagation of hydraulic fractures using the finite‐element method is formulated within the framework of the virtual internal bond theory (VIB) that considers a solid as randomized material particles in the micro scale, and derives the macro constitutive relation from the cohesive law between the material particles with an implicit fracture criterion. Hydraulic pressure is applied using a new scheme that enables simulation of hydraulically driven cracks. When the model is applied to study hydraulic fracture propagation in the presence of a natural fracture, the results show the method to be very effective. It shows that although the in situ stress ratio is the dominant factor governing the propagation direction, a natural fault can also strongly influence the hydraulic fracture behavior. This influence is conditioned by the shear stiffness of the fault and the distance to the original hydraulic fracture. The model results show that when the fault is strong in shear, its impact on hydraulic fracture trajectory is weak and the hydraulic fracture will likely penetrate the fault. For a weak fault, however, the fracture tends to be arrested at the natural fault. The distance between the fault and the hydraulic fracture is also important; the fault influence increases with decreasing distance. The VMIB does not require selection of a fracture criterion and remeshing when the fracture propagates. Therefore, it is advantageous for modeling fracture initiation and propagation in naturally fractured rock. Copyright © 2010 John Wiley & Sons, Ltd.     

等间距断裂控制机理探讨

断裂有时成组出现并且以规则等间距排列，这种现象有其必然性，并可以通过弹性力学的有限单元法对其生成时的应力状况予以模拟并解释。等间距断裂的形成受控于某些地质因素，如地质体物理力学特性及其边界地应力条件等。本文的讨论相信会有助于断层研究工作。     

Perturbed earth processes due to thermally induced deformation in a discontinuous granite mass

Summary The effect of thermally induced stress on fractured granite is considered, using mathematics to solve an engineering problem that includes: (1) physical information translated into a mathematical form; (2) a mathematical model proposing a solution of the problem and (3) interpretation of the solution in physical terms.This procedure, applied to an engineering problem demonstrates that theory and its physical applications are related.     

A model for crack connectivity in rocks, a discussion

We reanalyzed a model introduced by T. R. Madden for the evaluation of the state of connectivity among the microcrack population existing inside crystalline rocks. The model assumes that cracks are distributed randomly in a cubic lattice with a basic occupation probability, p.Depending on the value of p, the stale of connectivity can give rise to macroscopic paths, which allow electrical conduction of the sample, or to extended crack surfaces, which would be responsible for rock failure. The position of the phase boundaries, that is, the threshold values of pfor the onset of conductivity or macroscopic fracture, are estimated by a real-space renormalizalion-group (RG) technique. By identifying all the relevant configurations of the lattice model, we have been able to provide explicit analytic formulae for the critical lines. The criterion used by Madden to accept the existence of microscopic linear connectivity is modified and the new consequences discussed. We analyze the limitations of simple versions of the RG technique, in particular when concerned with anisotropic spatial distributions of cracks. Finally, we emphasize the interest of acquiring experimental data, especially to test the position of the conduction thresholds.     

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     

裂缝性储层裂缝的阵列侧向测井响应数值模拟

为了研究裂缝性储层裂缝的阵列侧向测井响应, 采用裂缝组平板裂缝模型, 利用三维有限元方法, 进行不同裂缝参数条件下的高分辨率阵列侧向测井响应数值模拟.表明阵列侧向视电导率和裂缝孔隙度与裂缝流体电导率成线性关系; 低角度裂缝的阵列侧向深浅视电阻率呈现负差异特征, 高角度缝呈现正差异; 相同裂缝孔隙度下, 裂缝密度增加可使得阵列侧向视电阻率增加, 当裂缝密度足够大时, 测井响应特征基本不随裂缝密度发生变化; 交叉缝的测井响应与具有相同角度的平行裂缝组差异明显, 且不同倾角组合的交叉缝的测井响应之间差异明显.阵列侧向测井对裂缝有较强的敏感性, 根据其测井视电阻率大小可以评价裂缝孔隙度, 根据深浅视电阻率的幅度差异可以研究裂缝的产状, 这些为将阵列侧向测井用于裂缝性储层裂缝评价有指导意义.      

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     

Fractal and geostatistical methods for modeling of a fracture network

The modeling of fracture networks is useful for fluid flow and rock mechanics studies. About 6600 fracture traces were recorded on drifts of a uranium mine in a granite massif. The traces have an extension of 0.20–20 m. The network was studied by fractal and by geostatistical methods but can be considered neither as a fractal with a constant dimension nor a set of purely randomly located fractures. Two kinds of generalization of conventional models can still provide more flexibility for the characterization of the network: (a) a nonscaling fractal model with variable similarity dimension (for a 2-D network of traces, the dimension varying from 2 for the 10-m scale to 1 for the centimeter scale, (b) a parent-daughter model with a regionalized density; the geostatistical study allows a 3-D model to be established where: fractures are assumed to be discs; fractures are grouped in clusters or swarms; and fracturation density is regionalized (with two ranges at about 30 and 300 m). The fractal model is easy to fit and to simulate along a line, but 2-D and 3-D simulations are more difficult. The geostatistical model is more complex, but easy to simulate, even in 3-D.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

The rock fracture experiment with a drive control: A spatial aspect

The statistical analysis of the space–time distributions of acoustical signals emitted from the compressed samples of Westerly granite is presented. The samples were uniaxially loaded in two regimes, one of which included a feedback loop controlled by the current acoustical emission (AE) activity. The distribution of distances between newly-appeared hypocenters follows the power law with the exponent that does not depend on the mode of loading. In both regimes, a transient period of the decorrelated accumulation of damaged sites was revealed between the initial and focal stages of the fracture process. The Hurst analysis indicates a more pronounced trend to planar organization of final damage structure in the case of AE-controlled loading.     

岩石压剪性断裂特性及Ⅰ—Ⅱ型复合断裂判据

本文系统阐述了岩石压剪性断裂的特性,认为金属断裂力学复合断裂判据基本上不适用于压剪状态下的岩石斯裂;在此基础上,提出了新的岩石压剪性断裂判据:2COSθ_0/2(cosθ_0-1)[(1+1/f~2)~(1/2)-1]K_Ⅰ+[(sin θ_0/2-3sin 3θ_0/2)(1+1/f~2)~1/2+4sin θ_0/2]K_Ⅱ=4K_(Ⅰc),推导了起始断裂角ψ_0,说明了实验验证结果,指出了该判据在工程地质领域中的应用途径。     

Modeling three‐dimensional hydraulic fracture propagation using virtual multidimensional internal bonds

Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.     

基于水压致裂法的岩石抗拉强度研究

为了揭示水压致裂法和巴西劈裂法测量岩石抗拉强度的关系,开展了理论和现场试验研究。基于经典的水压致裂法理论,推导了不同围压下钻孔破裂压力和抗拉强度。利用断裂力学理论建立了水压致裂法和巴西劈裂法测得抗拉强度的关系。利用预制切槽方法模拟天然裂纹,对水力裂缝的起裂压力进行了研究。结果表明：围压为最大主应力等于3倍最小主应力测得的抗拉强度大于围压为0测得的抗拉强度;水压致裂法和巴西劈裂法测量抗拉强度关系与应力场、裂纹长度、断裂韧度3个变量有关;通过在晋城矿区王台铺矿的预制切槽试验,运用断裂力学建立的抗拉强度计算式更为符合现场实际。研究结果可为坚硬难垮落顶板预制切槽的水力压裂设计提供参考。     

水压致裂煤层裂缝发育特点的研究

本文对煤岩基本力学性质、煤层水压致裂缝形成条件、裂缝形态以及裂缝开裂角方位等基本理论进行了研究与探讨，通过大量煤岩力学性质测试，证实了试验区目的层煤岩弹性模量低，泊松比较高，脆性大，易破碎，易压缩。文章还得出了目的层煤岩Ｍｏｈｒ断裂准则二次抛物线型包络线，煤层水压致裂裂缝形式判断，裂缝开裂角方位的计算公式以及有关结论。     

A relationship between tensile strength and loading stress governing the onset of mode I crack propagation obtained via numerical investigations using a bonded particle model

Numerical models based on the discrete element method are used to study the fracturing process in brittle rock‐like materials under direct and indirect tension. The results demonstrate the capacity of the model to capture the essential characteristics of fracture including the onset of crack propagation, stable and unstable crack growth, arrest and reinitiation of fracturing, and crack branching. Simulations of Brazilian indirect tension tests serve to calibrate the numerical model, relating macroscopic tensile strength of specimens to their micromechanical breakage parameters. A second suite of simulations reveals a linear relationship between the tensile strength of specimens and the loading stress for which mode I tensile crack propagation ensues. Based on these results, a crack initiation criterion for brittle materials is proposed, prescribing the stressing conditions required to induce tensile failure. Such a criterion, if broadly applicable, provides a practical means to rapidly assess the failure potential of brittle materials under tensile loads.     

砂岩断裂及其亚临界断裂的力学行为和细观机制

通过三点弯曲的SEM试验,详细研究了砂岩断裂的力学特征和细观机制。结果表明：砂岩断裂是一个复杂的过程,它不但与砂岩的物理成分、微缺陷等有关,还与砂岩中碎屑颗粒的分布密切相关,存在明显的亚临界断裂。亚临界断裂裂纹和断裂主裂纹形态相似。亚临界断裂裂纹较多的样品呈现延性断裂破坏的特征,而亚临界断裂裂纹较少的样品则呈现脆性断裂破坏的现象。     

油气盆地低渗透储层裂缝预测研究现状及进展

我国拥有相当数量裂缝型低渗储层的地质储量,在我国油气生产中起举足轻重的作用。系统开展低渗储层中裂缝特征和分布规律研究预测,无疑对我国的低渗透储层油气勘探开发具有指导作用。目前,国内外在油气盆地低渗透储层中对裂缝预测及评价已经形成了很多富有特色的方法,但是由于裂缝成因的复杂性、发育的多阶段性,对低渗储层裂缝的预测及评价研究还处于探索阶段。本文较为系统地综述了油气盆地低渗透储层裂缝预测研究现状与进展、不同成因的裂缝预测方法、裂缝研究存在问题和解决方法。     

Electromagnetic emissions during dilating fracture of a rock

A lot of experiments on electromagnetic emissions (EMEs) have been reported under axial compressive fracture, shear fracture, indentation fracture and stick–slip (friction) in lab and blasting in situ, but there are rare reports on the in-lab experimental work on EMEs during dilating fracture of a rock which is helpful in studying and understanding EMEs related to slow earthquakes and the earthquakes due to volcanic activities and water level changes of reservoirs. Therefore, in the present paper in order to check whether there are detectable EMEs during dilating fracture of a rock in lab, dilating fracture experiments were conducted. The dry cuboid specimens of initially intact granodiorite and limestone were tested inside magnetic field free space (MFFS) at room temperature. We arranged evenly 20 EME antennas whose resonance frequencies range from 2.5 kHz to 540 kHz close to rock specimens. Our experimental results strongly indicate that detectable EMEs could generate during dilating fracture of a rock. They were recorded only associated with some but not all phases of fracture. Their waveforms often took on the trend that a peak arrived at first and then attenuated sharply and followed by a series of low-amplitude oscillations. The electromagnetic (EM) signals after eliminating the effects of EME antennae via deconvolution had the maximum peak-to-peak amplitudes of about 80.0 mV and 40.5 mV for granodiorite and limestone, respectively. Their main spectral components often concentrated in the band of several kHz to ∼60 kHz and of several kHz to ∼280 kHz. The emission of electrons and charged particles from fracture surfaces and/or micro-fracture electrification could be possible mechanisms for our experimental results.     

断层相关裂缝定性识别：原理与应用

介绍一种定性识别和预测断层相关裂缝的新方法-断面脱空法。该方法以断面脱空理论为基础,通过建立断面脱空空间与断层相关裂缝之间的置换模型,从而实现通过观察断层形迹开展地下断层相关裂缝的定性识别。以塔中Ⅰ号断裂带西侧中古3、塔中72两个井区下奥陶统良里塔格组（O₃l）为例,基于地震资料分别开展剖面和平面上的断层相关裂缝识别,并将预测结果与钻井、测井及地震属性分析获得的裂缝发育特征进行对比研究。结果表明:利用断面脱空原理预测结果与钻测井揭示结果基本一致,与根据均方根检测的裂缝平面分布对比,细节上有差异,但总体特征基本一致,表明利用断面脱空原理可以定性地对断层相关裂缝做出预测。断面脱空理论的提出不仅为定性评价地表、地下断层相关裂缝发育分布规律提供一种新思路,更为定量表征断层相关裂缝提供重要的理论依据。