Linear Elastic and Cohesive Fracture Analysis to Model Hydraulic Fracture in Brittle and Ductile Rocks

Hydraulic fracturing technology is being widely used within the oil and gas industry for both waste injection and unconventional gas production wells. It is essential to predict the behavior of hydraulic fractures accurately based on understanding the fundamental mechanism(s). The prevailing approach for hydraulic fracture modeling continues to rely on computational methods based on Linear Elastic Fracture Mechanics (LEFM). Generally, these methods give reasonable predictions for hard rock hydraulic fracture processes, but still have inherent limitations, especially when fluid injection is performed in soft rock/sand or other non-conventional formations. These methods typically give very conservative predictions on fracture geometry and inaccurate estimation of required fracture pressure. One of the reasons the LEFM-based methods fail to give accurate predictions for these materials is that the fracture process zone ahead of the crack tip and softening effect should not be neglected in ductile rock fracture analysis. A 3D pore pressure cohesive zone model has been developed and applied to predict hydraulic fracturing under fluid injection. The cohesive zone method is a numerical tool developed to model crack initiation and growth in quasi-brittle materials considering the material softening effect. The pore pressure cohesive zone model has been applied to investigate the hydraulic fracture with different rock properties. The hydraulic fracture predictions of a three-layer water injection case have been compared using the pore pressure cohesive zone model with revised parameters, LEFM-based pseudo 3D model, a Perkins-Kern–Nordgren (PKN) model, and an analytical solution. Based on the size of the fracture process zone and its effect on crack extension in ductile rock, the fundamental mechanical difference of LEFM and cohesive fracture mechanics-based methods is discussed. An effective fracture toughness method has been proposed to consider the fracture process zone effect on the ductile rock fracture.     

Experimental Calibration of ISRM Suggested Fracture Toughness Measurement Techniques in Selected Brittle Rocks

Summary A wide variety of specimen types and methods are employed in fracture toughness measurement of rocks, which result in scattered values for the same rock type. In order to provide some consistency to the values, the International Society for Rock Mechanics (ISRM) recommended three suggested methods using core based specimens, the Chevron Bend (CB) test, the Short Rod (SR) test and the Cracked Chevron Notch Brazilian Disc (CCNBD) test. This standardization helped obtain more consistent values but still a variation of 20–30% was observed in the values of fracture toughness obtained with the CB and SR methods. The values obtained with the CCNBD method were found to be consistently lower (30–50%) than those of the other two methods (CB and SR). Many reasons have been offered to explain this deviation. These include size of the specimen, anisotropy of rock, a dimensionless parameter in the fracture toughness calculation equation for the CCNBD test, etc. A comprehensive test program was initiated to identify the cause of these discrepancies between the CB and CCNBD methods. Three brittle rock types were selected for the study and more than 200 tests were conducted to measure the values of fracture toughness. A rigorous statistical analysis was carried out to determine the confidence level and find the significance of the test results. It was found that the CB and CCNBD methods were very comparable provided the correct equation for fracture toughness calculation was used for the CCNBD method and the size of the specimens was selected carefully. The error in the ISRM 1995 formula of fracture toughness for the CCNBD method could be the major factor responsible for the consistently lower values obtained with the method.     

Couple Effect of Joint Pore Pressure and Joint Orientations on Rock Strength Based on Numerical Modeling

Geotechnical and Geological Engineering - The joint pore pressure inside rock mass significantly affects groundwater bursting. To investigate the couple effect of joint pore pressure and joint...     

Influence of Weathering on Pore Size Distribution of Soft Rocks

Geotechnical and Geological Engineering - Soft rocks can weather and lose their structure within a short time due to drying out and rewetting. Thus they are very sensitive to weathering. Since...     

Application of Stochastic Fracture Network with Numerical Fluid Flow Simulations to Groundwater Flow Modeling in Fractured Rocks

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脆性岩石单轴压缩变形强度的试验

主要讨论在单轴压缩条件下脆性岩石破坏的全过程,分析与破裂机制有关的问题及试验中主要影响因素,使试验结果为工程评价提供准确、可靠的保证。     

非均质含水层中地下水年龄数值模拟

地下水年龄数值模拟是近年来国际地下水领域的一个全新研究方向。在简单介绍地下水年龄数值模拟相关理论和方法基础上,通过一个简单算例模拟对比了稳定流条件下不同非均质含水层中的水流运动和年龄分布,探讨了夹层透水性的强弱对地下水年龄分布的影响。结果表明,在地下水系统保持补径排通量不变的前提下,弱透水夹层的存在对于特定区域地下水的深部循环和更新具有积极作用。同时,在模拟区域深部含水层的年龄分布时,不能忽略其弥散作用。地下水年龄模拟为研究区域尺度上的地下水循环和地下水资源可持续利用提供了一种新的途径。     

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.     

A Study on the Peak Strength of Brittle Rocks

Summary A study on the peak strength of brittle rock materials having random strength distributions was carried out using the re-normalization group theory approach. A major advantage of the approach is that it is scale invariant, and therefore, one can relate the micro-fractures with macro-fractures of rocks at the critical state. The stress transfer from the broken sub-sections to the unbroken sub-sections is defined by a conditional probability. The critical probability P ^* and the relation between the peak strength and the mean strength of the elements have been obtained theoretically. On the other hand, the whole process of rock brittle fracture has also been simulated numerically from micro-fracture to macro-fracture by using the Rock Failure Process Analysis (RFPA) code. The peak strengths obtained by the numerical model agree fairly well with those obtained by the re-normalisation group theory. Due to the stress transfer from the broken subsections to the unbroken subsections, the peak strength is considerably less than the mean strength of the elements. Received October 24, 2000; accepted February 26, 2002 Published online September 2, 2002     

Dynamic Study on Fracture Problems in Viscoelastic Sedimentary Rocks Using the Numerical Manifold Method

The viscoelastic deformation behavior of a sedimentary rock under different loading rates is numerically modeled and investigated by the numerical manifold method (NMM). By incorporating a modified 3-element viscoelastic constitutive mode in the NMM, crack initiation and propagation criteria, and crack identification and evolution techniques, the effects of the loading rates on the cracking behavior of a sedimentary rock, such as crack open displacement, crack sliding displacement, crack initiation, crack propagation and final failure mode, are successfully modeled. The numerical results reveal that under a high loading rate (>1,000 MPa/s), due to the viscoelastic property of the sedimentary rock, not only the structural behavior deviates from that of elastic model, but also different cracking processes and final failure modes are obtained.     

Role of Crystal Interlocking on the Strength of Brittle Rocks

Results of an experimental programme on heterogeneous rock-like specimens of dental plaster confirm the pronounced role of tensile microcracks on brittle failure. Microbuckling of very small rock-columns formed amid closely located tensile cracks was observed as the key incident connecting stable phenomenon of tensile cracking to unstable phenomenon of shearing and subsequent macroscopic failure. Using the classical beam and buckling theories and considering geometry of the problem a new failure criterion is proposed. As a novel attempt, this new failure criterion relates the compressive strength of rock to three basic microstructural properties, i.e. degree of crystal interlocking, average Young modulus and average tensile strength of rock forming minerals.     

岩石破裂行为的实验研究

岩样的破裂行为、破坏过程和参数测试是裂隙断裂构造研究的基础和依据。实验岩石样品采自四川东部和新疆北部地区,为测试准确起见,对岩样进行了应力等值线的有限元法计算。通过单轴和三轴实验的岩样破坏观察和应力应变曲线对比,将岩石的破裂行为、应力应变划分为四个阶段,即裂隙压密阶段、弹性变形阶段、微观劈裂阶段和宏观破裂阶段。基于单轴抗压实验岩石劈裂—破裂—碎裂发展过程的微观分析,可以看出宏观破裂主要是沿岩样原有的隐裂隙、临界裂隙发育的,许多新裂隙则主要是在宏观破裂阶段产生的。     

Numerical Modelling of the Heterogeneous Rock Fracture Process Using Various Test Techniques

Summary A series of numerical tests including both rock mechanics and fracture mechanics tests are conducted by the rock and tool (R–T^2D) interaction code coupled with a heterogeneous masterial model to obtain the physical–mechanical properties and fracture toughness, as well as to simulate the crack initiation and propagation, and the fracture progressive process. The simulated results not only predict relatively accurate physical–mechanical parameters and fracture toughness, but also visually reproduce the fracture progressive process compared with the experimental and theoretical results. The detailed stress distribution and redistribution, crack nucleation and initiation, stable and unstable crack propagation, interaction and coalescence, and corresponding load–displacement curves can be proposed as benchmarks for experimental study and theoretical research on crack propagation. It is concluded that the heterogeneous material model is reasonable and the R–T^2D code is stable, repeatable and a valuable numerical tool for research on the rock fracture process.     

New Observations on the Brittle Failure Process of Simulated Crystalline Rocks

A biaxial testing program has been performed to study the process of brittle failure in crystalline rocks. Dental plaster has been selected as a model material, and mixing with different ratios of distilled water, different types of common minerals of crystalline rocks have been simulated in the form of brick-like small elements. These elements have been interlocked together according to four systematic patterns and final specimens with 180 × 180 × 76 mm dimensions have been obtained. Details of different types of cracks observed during loading process, effects of mechanical, geometrical and confining pressure on the cracking intensity, the influence of different types of heterogeneity on the macroscopic properties of a system of interlocked elements, and the sequence of events during the failure process are presented in this paper. Based on these observations, a revised mechanism for brittle failure is proposed.     

Fracture Toughness and Fracture Roughness in Anisotropic Granitic Rocks

In this paper we present an experimental approach aimed at assessing the correlation between fracture toughness (K _IC) and fracture roughness of two granitic rocks (Barre and Stanstead granites) exhibiting significant fracture toughness anisotropy. Roughness values have been estimated for fractured surfaces obtained from Chevron Cracked Notch Brazilian Disc samples failed under mode I along three orthogonal planes with respect to their microstructural fabrics. There exists a clear correlation between roughness and toughness within each rock examined along the three planes. Specific orientation of micro-crack alignment could result in preferred out-of-plane propagation of the test-crack irrespective of grain-size distribution. These experimental observations reinforce the hypothesis of the existence of a link among pre-existing petrofabric anisotropy, fracture toughness, fracture roughness, and the evolution and extent of the associated induced fractures within the process zone of granitic rocks along specific directions. This study also highlights the need for employment of pre-failure and advanced post-failure diagnostic techniques in quantifying these inter-relationships.     

A Numerical Investigation of Fracture Infilling and Spacing in Layered Rocks Subjected to Hydro-Mechanical Loading

In order to better understand opening-mode fracture initiation and propagation perpendicular to the bedding plane at depth in sedimentary rocks, a series of two-dimensional (2D) numerical simulations is conducted. First, the stress states between two adjacent fractures for a typical three-layer model with pre-assigned fractures are simulated. Second, the same three-layer model without pre-assigned fractures is adopted to study the initiation and propagation of fractures in layered rocks. Numerical results show that infilling fractures grow more easily from flaws located near the interface than from those in the middle of the fractured layer. Flaws can begin to propagate to form a complete infilling fracture when the size of the flaws exceeds half of the thickness of the central layer. Under different overburden stress conditions and internal fluid pressure, the numerically obtained ratio of the critical fracture spacing to layer thickness varies between 0.465 and 0.833. This range encompasses the often-cited ratios of spacing to layer thickness in the literature for well-developed fracture sets. In addition, both the fracture pattern and the critical value of the fracture spacing to layer thickness ratio are strongly dependent on the heterogeneous characteristics of the central layer. In cases with a relatively homogeneous central layer, more interface fractures occur, and the interface delamination evidently influences the fracture saturation.     

A Fully Coupled Chemo-Poroelastic Analysis of Pore Pressure and Stress Distribution around a Wellbore in Water Active Rocks

Water active rocks consist of minerals that hold water in their crystalline structure and in pore spaces. Free water from drilling fluid can be attracted by the formation depending on the potential differences between pore space and drilling fluid. The fluid movement into the formation or out of the formation can lead to a change in effective stress, thus causing wellbore failures. In all previous studies it is found that the solute transport from or to the formation is primarily controlled by diffusion process and the effect of advection on solute transfer is negligible for a range of very low permeable shale formations (>10⁻⁵ mD). In this study a range of permeable shale formations (10⁻⁵ to 10⁻³ mD) commonly encountered in drilling oil and gas wells are considered to investigate the solute transfer between drilling fluid and formation due to advection. For this purpose a finite element model of fully coupled chemo-hydro-mechanical processes was developed. Results of this study revealed that the solute transfer between the drilling fluid and the shale formation is controlled primarily by permeability of the shale formations. For the range of shale formations studied here, there exists a threshold permeability below which the solute transfer is dominated by diffusion process and above which by fluid in motion (fluid flow). Results from the numerical experiments have shown that when the permeability of shales is greater than this threshold permeability, the chemical potential gradient between the pore fluid and drilling fluid reaches equilibrium faster than that when the permeability of shales is below this threshold value. Also it has been found that when advection is taken into account, effective radial and tangential stresses decrease around the wellbore, particularly near the wellbore wall where the solute concentration has reached near equilibrium.     

Numerical Analyses of the Influence of Blast-Induced Damaged Rock Around Shallow Tunnels in Brittle Rock

Most of the railway tunnels in Sweden are shallow-seated (<20 m of rock cover) and are located in hard brittle rock masses. The majority of these tunnels are excavated by drilling and blasting, which, consequently, result in the development of a blast-induced damaged zone around the tunnel boundary. Theoretically, the presence of this zone, with its reduced strength and stiffness, will affect the overall performance of the tunnel, as well as its construction and maintenance. The Swedish Railroad Administration, therefore, uses a set of guidelines based on peak particle velocity models and perimeter blasting to regulate the extent of damage due to blasting. However, the real effects of the damage caused by blasting around a shallow tunnel and their criticality to the overall performance of the tunnel are yet to be quantified and, therefore, remain the subject of research and investigation. This paper presents a numerical parametric study of blast-induced damage in rock. By varying the strength and stiffness of the blast-induced damaged zone and other relevant parameters, the near-field rock mass response was evaluated in terms of the effects on induced boundary stresses and ground deformation. The continuum method of numerical analysis was used. The input parameters, particularly those relating to strength and stiffness, were estimated using a systematic approach related to the fact that, at shallow depths, the stress and geologic conditions may be highly anisotropic. Due to the lack of data on the post-failure characteristics of the rock mass, the traditional Mohr–Coulomb yield criterion was assumed and used. The results clearly indicate that, as expected, the presence of the blast-induced damage zone does affect the behaviour of the boundary stresses and ground deformation. Potential failure types occurring around the tunnel boundary and their mechanisms have also been identified.     

离散裂隙渗流方法与裂隙化渗透介质建模

流体渗流模拟的连续介质方法通常适用于多孔地质体，并不一定适用于裂隙岩体，由于裂隙分布及其特征与孔隙差异较大。若流体渗流主要受裂隙的控制，对于一定尺寸的裂隙岩体，多孔介质假设则较难刻划裂隙岩体的渗流特征。离散裂隙渗流方法不但可直接用于模拟裂隙岩体非均质性和各向异性等渗流特征，而且可用其确定所研究的裂隙岩体典型单元体及其水力传导（渗透）张量大小。主要讨论了以下问题：（1）饱和裂隙介质中一般的离散流体渗流模拟；（2）裂隙岩体中的REV（典型单元体）及其水力传导（渗透）张量的确定；（3）利用离散裂隙网络流体渗流模型研究裂隙方向几何参数对水力传导系数和REV的影响；（4）在二维和三维离散裂隙流体渗流模型中对区域大裂隙和局部小裂隙的处理方法。调查结果显示离散裂隙流体渗流数学模型可用来评价不同尺度上的裂隙岩体的水力特征，以及裂隙方向对裂隙化岩体的水力特征有着不可忽视的影响。同时，局部小裂隙、区域大裂隙应当区别对待，以便据其所起的作用及水力特征，建立裂隙化岩体相应的流体渗流模型。     

A Review of the Influence of Microscopic Characteristics on the Progressively Brittle Failure of Foliated Rocks Subjected to Compression Loading

Geotechnical and Geological Engineering - The progressively brittle failure of foliated rocks involving the initiation, propagation, and aggregation modes is closely related to the microscopic...