Numerical investigation of hydraulic fracture network propagation in naturally fractured shale formations

Hydraulic fracture network (HFN) propagation in naturally fractured shale formations is investigated numerically using a 3D complex fracturing model based on the discrete element method. To account for the plastic deformation behavior of shales, the Drucker–Prager plasticity model is incorporated into the fracturing model. Parametric studies are then conducted for different Young's moduli, horizontal differential stresses, natural fracture (NF) properties, injection rates, and number and spacing of perforation clusters. Numerical results show that horizontal differential stress primarily determines the generation of a complex HFN. The plastic deformation of shale can reduce the stimulated reservoir volume; this is more obvious with Young's modulus of less than 20 GPa. In addition, a higher injection rate could largely increase the fracture complexity index (FCI). Moreover, increasing perforation cluster numbers per fracturing stage is beneficial for increasing the FCI, but it also increases the potential merging of neighboring fractures, which may lead to non-uniform development of HFN in far-wellbore regions. To achieve uniform development of HFN within a fracturing stage, the distribution of NFs should be fully considered. The results presented here may provide improved understanding of HFN generation and are favorable for optimizing fracturing treatment designs for shale formations.     

基于PFC2D数值模拟的交替压裂中应力阴影效应研究

为了探究应力阴影效应对交替压裂中压裂间距选取的影响,基于优化后的颗粒流离散元流固耦合计算模型,模拟并分析了双初始水力裂缝下因应力阴影效应产生的诱导应力的分布情况,并与理论解析解进行对比,证明了该数值方法的合理性。在此基础上,分析了应力阴影效应在不同各向异性地应力场及初始压裂间距条件下对新水力裂缝的起裂压力及扩展形态的影响,研究结果表明：初始各向异性应力场不改变裂缝周边的应力场,不影响新水力裂缝的起裂压力;随着初始压裂间距的减小,应力阴影效应增强,新水力裂缝的起裂压力逐渐增加。初始水力裂缝间距与初始各向异性应力场共同影响新水力裂缝的扩展形态,随着初始水力裂缝间距或初始水平地应力场差异系数的增大,应力阴影对新水力裂缝的扩展方向的影响逐步减弱;初始水力裂缝对新水力裂缝的扩展有一定的限制作用,在一定程度上不利于形成复杂的裂缝网络。根据以上分析结果,对交替压裂中压裂间距的优化进行了定性的探讨。     

龙马溪组页岩三维缝网重构及分形分析

传统上研究含气页岩宏观缝网特征的方法多是基于小样品开展,通过观察小样品的裂缝展布特征来了解页岩的裂缝发育的宏观特性。但是这类方法因尺度过小,缺乏代表性,不能获取连续面上的裂缝特征,难以分析裂缝发育和地应力方向之间的关系。为获取更详细的大尺度含气页岩的宏观裂缝特征,本文从重庆市涪陵地区石柱县采样获取2m×3m×0.7m完整大尺度岩块,并采用有序标号切割来获取30cm3规格岩样,在此基础上提取小岩样的表面裂缝并按照大尺度岩样切割的相对顺序构建三维裂缝网络。分析观测大尺度的三维裂缝网络可以发现,含气页岩的裂缝分布具有明显的规律性:水平主应力方向上的裂缝发育度普遍高于最小水平主应力方向;垂直方向上的裂缝与最小水平主应力的夹角为-62°。分维研究表明所有不同面上的裂缝均符合分维特性,说明小尺度裂缝特征和大尺度裂缝特征具有相似的规律性。此外,研究还表明最大水平主应力上的裂缝密度和分形维数最大,缝网结构最为复杂,最小水平主应力方向缝网结构次之,垂直主应力方向的裂缝结构最为简单;水平应力方向上主要以层理裂缝为主,垂直方向上以剪切缝为主,且与最小水平主应力的夹角为-62°。在掌握宏观裂缝分布特征基础上,研究可为页岩显微观测实验提供相应的理论依据。     

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。     

爆炸气体驱动下岩体破裂的有限元-离散元模拟

在原有有限元/离散元（FEM/DEM）耦合分析方法中,实现了一种新的爆破计算模型。该模型考虑了在爆生气体的作用下,随着裂隙的扩展,气体占据的体积不断增大,气体压力逐渐减小这一问题。同时考虑了气体嵌入与爆腔联通的裂隙对裂隙的作用力。克服了原有FEM/DEM方法中的爆破模型仅仅将压力施加于爆腔四周的岩壁上,无法考虑爆生气体嵌入生成的裂隙对裂隙的作用。提出了一种新颖的贯通裂隙网络形成的递归搜索算法,只需通过编写一个简单的递归函数,即可实现复杂裂隙网络的搜索,采用一种简洁的方法完成了对复杂问题的处理。最后通过一个爆破算例,结果表明FEM/DEM方法可以对爆炸过程中应力波的传播及岩体中裂纹的萌生、扩展进行全程捕捉,展现了该方法用于爆破模拟的潜力。     

煤层水力压裂应力与裂隙演化的细观规律

水力压裂作为煤层强化增透技术的一种,其应力演化特征及裂隙形态与扩展范围的判断尤为重要。采用离散元数值方法,以导向压裂为背景,建立水力压裂流固耦合模型;通过应力路径、裂纹热点图等手段,探究水力压裂过程中压裂排量、泊松比、天然裂隙密度对应力演化和裂隙演化的影响及其细观规律。结果表明:不同压裂排量下的应力演化方向及最终应力路径曲线形状有着明显的不同,低排量下裂隙附近的应力比值逐渐增大,而在高排量下先增大后减小;煤层泊松比越大,平均压裂半径越低,但对起裂时间及裂隙的扩展形态影响不明显;天然裂隙的发育情况对水力裂隙的扩展起着关键性作用,高裂隙发育煤层水力裂隙扩展的方向性无法预测,应力演化方向会出现反转现象;压裂过程中不同区域的应力演化特征能够反映出裂隙的扩展状态,现场可通过监测压裂区域附近应力变化,判断水力压裂缝网的扩展范围。      

Numerical Simulation of 3D Hydraulic Fracturing Based on an Improved Flow-Stress-Damage Model and a Parallel FEM Technique

The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress–axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures.     

多场耦合作用下岩体裂隙扩展演化关键问题研究

裂隙岩体热-水-应力（THM）耦合是目前研究的热点和难点。首先总结了裂隙岩体多场耦合的机制、模型、方法及研究内容,并通过分析裂隙对THM耦合的重要控制作用,提出了在THM耦合中考虑裂隙网络扩展演化及模拟的关键问题,同时指出了研究的3个关键点：（1）建立考虑裂隙网络演化的耦合模型;（2）裂隙扩展的数值模拟方法;（3）THM耦合及岩体变形、失稳全过程的数值模拟算法。随后通过对模拟多场耦合和裂隙扩展数值方法的归类比较,重点论述了目前适用于模拟多场耦合下裂隙扩展模拟的各种数值方法（包括有限单元法、无单元法、单位分解法、离散单元法、岩石破裂过程分析方法和数值流形方法）的优缺点,并通过对比研究,推荐采用数值流形方法（NMM）来实现对关键问题的模拟研究。最后,对研究思路和难点进行了初步探讨。     

不同尺度岩体结构面对页岩气储层水力压裂裂缝扩展的影响

储层岩体中的天然结构面对水力压裂缝网改造具有重要的影响。本文采用真实破裂过程分析软件RFPA2D-Flow,在考虑岩体非均质性和岩体渗流-应力-损伤破裂特性的基础上,对不同尺度天然结构面影响的水力压裂裂缝扩展与演化行为进行了模拟分析和讨论,研究结果表明:（1）当水力裂缝遇天然非闭合裂隙时,在水力裂缝靠近非闭合裂隙区间形成拉张应力区,水力裂缝与区间非闭合裂隙间微元体累进性张拉破坏是导致水力裂缝与非闭合裂隙贯通的主要机制;（2）层理等优势结构对水力压裂裂缝扩展及缝网形态影响十分显著,当最大主应力方向与层理面走向小角度相交时,层理结构面对水力裂隙的扩展起主要作用,当最大主应力方向与层理面走向大角度相交时,最大主压应力与层理面共同对缝网扩展起主导作用,随着优势结构面的增多和差应力的增大,水力压裂形成的缝网范围和复杂性程度随之增大;（3）储层水力压裂是一种局部范围内的短暂动力扰动过程,尽管断层的存在可以极大地影响水力裂缝的扩展模式,增大水力裂隙扩展高度,但相比于储层埋深,水力压裂对断层封闭性的破坏范围和断层活动性的扰动程度十分有限。     

Development of a full 3D numerical model to investigate the hydraulic fracture propagation under the impact of orthogonal natural fractures

Although hydraulic fracturing has been massively studied and applied as a key technique to enhance the gas production from tight formations, some problems and uncertainties exist to accurately predict and analyze the fracture behavior in complex reservoirs, especially in the naturally fractured reservoirs like shale reservoirs. This paper presents a full 3D numerical model (FLAC3D) to study hydraulic fracturing behavior under the impact of preexisting orthogonal natural fractures. In this numerical model, the hydraulic fracture propagation direction is assumed perpendicular to the minimum principal stress and activated only by tensile failure, whereas the preexisting natural fractures can be activated by tensile or shear failure or a combination of them, and only tensile failure can open the natural fracture as well. The newly developed model was used to study the impact of preexisting orthogonal natural fractures on hydraulic fracturing behavior, based on a multistage hydraulic fracturing operation in a naturally fractured reservoir from the Barnett Shale formation, northwest of Texas in USA. In this multistage operation, two more representative stages, i.e., stage 1 with a relatively large horizontal stress anisotropy of 3.3 MPa and stage 4 with a comparatively small one of 1.3 MPa, were selected to conduct the simulation. Based on the numerical results, one can observe that the interaction between hydraulic and natural fracture is driven mainly by induced stress around fracture tip. Besides, the horizontal stress anisotropy plays a key role in opening the natural fracture. Thus, no significant opened fracture is activated on natural fracture in stage 1, while in stage 4 an opened fracture invades to about 90 m into the first natural fracture. Conversely, the hydraulic fracture length in stage 1 is much longer than in stage 4, as some fluid volume is stored in the opened natural fracture in stage 4. In this work, the shear failure on natural fractures is treated as the main factor for inducing the seismic events. And the simulated seismic events, i.e., shear failure on natural fractures, are very comparable with the measured seismic events.

     

考虑页岩层理剪切滑移的水力裂缝几何参数计算方法

针对现有页岩气体积压裂层理裂缝扩展模型及其计算方法研究的不足,基于三点弯曲试验,结合数字图像法获取了页岩层理关键力学参数;利用弹性力学理论和线弹簧模型建立了页岩气体积压裂层理裂缝扩展拟三维数学模型,并得到了试验验证;开发了裂缝几何参数计算程序,计算分析了层理参数与压裂施工参数对水力裂缝扩展的影响规律。结果表明：当层理刚度小于10 GPa/m及大于30 GPa/m时,剪切滑移量达到极大值及极小值,且基本保持不变,当层理刚度在10～30 GPa/m之间时,层理刚度与剪切滑移量呈线性负相关关系;当层理密度为5～7条时,主裂缝会沟通更多的层理;当层理强度为5～8 MPa时,水力裂缝易穿层扩展,且能使层理产生剪切滑移,从而生成复杂裂缝;当压裂液排量和压裂液黏度分别在9～12 m3/min和2.5～5m Pa·s范围内时,水力裂缝易穿层扩展,最终形成十字型裂缝,有助于复杂裂缝的形成。该研究对认识页岩层理力学性能及其对层理裂缝扩展规律的影响有一定的指导意义。     

Numerical simulation of crack propagation in layered formations

In the present study, a boundary element method based on the higher order displacement discontinuity formulation is presented to solve the general problem of hydraulic fracture propagation in layered formations. Displacement collocation technique is employed to model the higher order displacement variation along the crack and the special crack tip element near its ends. The hydraulic fracture propagation and its interaction with the layer interface in non-homogenous rock materials are studied by the proposed semi-analytical (hybridized boundary element-boundary collocation) method. The maximum tangential stress criterion (or σ-criterion) of fracture mechanics considering different elastic constants (Young modulus and Poisson’s ratio) is used to obtain the fracture path. The fracture propagation from stiff to soft and soft to stiff media for cracks having different inclination angles is modeled, and the effects of elastic constants on the hydraulic fracture propagation is studied. The results show that if the hydraulic fracture originates in the stiffer layer, its capability to cross the layer increases and is vice versa for the softer material. The comparison of the results gained from the numerical method with those in the literature show a good performance of the method in the case of propagation of hydraulic fracture in layered formations.     

Fracture Network Volume Fracturing Technology in High-temperature Hard Formation of Hot Dry Rock

It is more difficult for a hot dry rock to form a fracture network system than shale due to its special lithology, physical and mechanical properties under high temperature. The essential characteristics, rock mechanics and in-situ stress characteristics of a hot rock mass have been systematically studied by means of laboratory tests and true tri-axial physical simulation. The fracture initiation and propagation characteristics under different geological and engineering conditions are physically simulated, and the main controlling factors for the formation of a complex fracture network are revealed. The technology of low displacement for enhancing thermal cracking, gel fluid for expanding fracture and variable displacement cyclic injection for increasing a fracture network has been applied in the field, and good results have been achieved. Micro-seismic monitoring results demonstrate that complex fractures were formed in the field test, and the stimulation volume for heat exchanging reaches more than 3 million cubic meters. The research results play an important role in the stimulation technology of an enhanced geothermal system (EGS) and realize a breakthrough for power generation.     

Numerical simulation of fracture path and nonlinear closure for simultaneous and sequential fracturing in a horizontal well

Reservoir stimulation requires a model to evaluate the fracture path and closure for the simultaneous or sequential propagation of the hydraulic fracture (HF). This paper presents a fluid-solid coupled model to simulate multi-stage HF propagation. A non-linear joint model is proposed to evaluate the fracture closure when the created fractures are elastically propped. HF closure continues until the balance of external stress matches the proppant's resistance. The reservoir along the horizontal wellbore is not stimulated equally by the multi-stage fracturing. The HFs in the subsequent stage are ‘repelled’ and restrained by the HFs in the previous stage.     

Optimization and Evaluation of Multiple Hydraulically Fractured Parameters in Random Naturally Fractured Model Blocks: An Experimental Investigation

Researchers have recently realized that the non-tectonic natural fractures are developed in shale formations and significant for the exploitation of shale gas. Studies have shown that the tectonic fractures in naturally fractured reservoirs have influences on the maximization of stimulated reservoir volume (SRV) during hydraulic fracturing. However, the effect of the non-tectonic randomly natural fractures on the fracturing network propagation is not well understood. Laboratory experiments are proposed to study the evolution of fracturing network in naturally fractured formations with specimens that contain non-tectonic random fractures. The influences of the dominating factors were studied and analyzed, with an emphasis on natural fracture density, stress ratio, and injection rate. The response surface methodology was employed to perform the multiple-factor analysis and optimization in the maximization of the SRV. A sensitivity study reveals a number of interesting observations resulting from these parameters on the fracturing network evaluation. It is suggested from the geometry morphology of fracturing network that high natural fracture density and injection rate tend to maximize the fracturing network. The influence of stress contrast on fracturing network is nonlinear; an optimal value exists resulting in the best hydraulic fracturing effectiveness.     

Rapid simulation of multiple radially growing hydraulic fractures using an energy‐based approach

The goal of hydraulic fracturing stimulation of horizontal wells is typically to generate uniform, simultaneously growing hydraulic fractures from 3 to 6 initiation/entry sites that are spaced within a certain interval of the wellbore comprising a so‐called stage. Because of the stress interaction among growing hydraulic fractures, however, it is hard to attain simultaneous growth of all hydraulic fractures. While models have been proven useful for devising mitigation strategies of these so‐called stress‐shadow effects, the required simulations are so computationally expensive that optimization is possible only in the simplest cases. Here, we present an approximate (energy‐based) model capable of running an entire simulation in 1–2s, which is about one million times faster than the benchmark model. The approach is built on asymptotic solutions to approximate growth of radial hydraulic fractures, a far field approximation for the stress shadow interactions among growing hydraulic fractures, and coupling the effect of the stress shadow to fracture growth via a global energy balance equation. We show very close agreement in predictions of the lengths of each fracture in the array between the approximate model and the benchmark model, thus verifying that the new approximate model is useful for optimization of hydraulic fracture design. Copyright © 2015 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.     

基于零厚度内聚力单元的水力裂缝随机扩展方法研究

为有效模拟裂缝性页岩储层中水力裂缝随机扩展过程,基于单元节点的拓扑数据结构,利用网格节点分裂方式,建立了一种基于有限元网格嵌入零厚度内聚力单元的水力裂缝随机扩展新方法。利用KGD模型解析解和2种室内试验,验证了新方法的准确性和有效性。同时,通过数值算例研究了水平地应力差和储层非均质性对水力裂缝随机扩展过程的影响。研究表明:(1)该方法弥补了ABAQUS平台内置的内聚力单元无法有效模拟水力裂缝随机扩展的不足;(2)在较高水平地应力差下页岩储层非均质性越强,与水力裂缝相交的高角度天然裂缝越容易开启。所建方法能准确地描述复杂水力裂缝的随机扩展行为,可为裂缝性页岩储层的数值模拟提供新手段。     

岩石裂纹水力劈裂分析与临界水压计算

水力劈裂是深埋隧洞施工涌水或高压隧洞洞周岩体开裂渗漏的重要因素之一,对其破坏机理研究是岩土工程界的热点课题。根据裂纹面的应力状态,从断裂力学角度将岩体的裂纹扩展分为拉剪复合断裂及压剪复合断裂。应用工程近似裂纹失稳准则,分别推导出两种破坏模式的临界水压计算公式,并对其随裂纹方向及地应力侧压系数变化规律进行分析。结果表明,当侧压力系数等于1.0时,临界水压并不随裂纹的方向而变化;在拉剪复合断裂模式下,裂纹与主应力方向平行时最易发生水力劈裂;在压剪复合断裂模式下,当压剪断裂参数与裂纹面间摩擦系数之差大于零时,其规律性与拉剪复合断裂模式基本一致;但当其差值小于零时,裂纹与最大主应力夹角呈45°及135°时最易发生水力劈裂。     

基于ABAQUS平台的水力裂缝扩展有限元模拟研究

随着扩展有限元理论的深入研究,利用扩展有限元方法模拟水力压裂具有了一定的可操作性。相比于常规有限元方法,XFEM方法具有计算结果精度高和计算量小的优点。但是,如何模拟射孔孔眼、如何模拟流体与岩石相互作用以及分析水力裂缝的扩展规律仍然是难题。以研究水力压裂裂缝扩展规律为目的,建立了岩石多孔介质应力平衡方程、流体渗流连续性方程和边界条件。通过有限元离散化方法对耦合方程矩阵进行处理。通过富集函数定义初始裂缝（射孔孔眼）,选择最大主应力及损伤变量D分别作为裂缝起裂和扩展判定准则,利用水平集方法模拟水力裂缝扩展过程。数值模拟结果显示：增加射孔方位角、压裂液排量和减小水平地应力差,起裂压力上升;黏度对起裂压力无明显影响。增加射孔方位角、压裂液排量、黏度和减小水平地应力差值有助于裂缝宽度的增加。增加水平地应力差值、压裂液排量和减小射孔方位角以及压裂液黏度有助于裂缝长度增加,反之亦然。基于ABAQUS的水力裂缝扩展有限元法可对不同井型和诸多储层物性参数及压裂施工参数进行分析,且裂缝形态逼真,裂缝面凹凸程度清晰,结果准确。此研究可作为一种简便有效研究水力压裂裂缝扩展规律的方法为油田水力压裂设计与施工提供参考与依据。