Uniform investigation of hydraulic fracturing propagation regimes in the plane strain model

The hydraulic fracturing propagation regimes in the plane strain model are uniformly investigated using a numerical method based on the finite element method. The regimes range from toughness‐dominated cases to viscosity‐dominated cases, covering zero leak‐off situations and small leak‐off situations. Unlike the asymptotic solutions, the numerical method is independent of the energy dissipation regimes and fluid storage regimes. The numerical method pays no special attention to the fracture tip, and it simulates fracture tip behaviors by increasing the number of functions in a natural and uniform manner. The numerical method is verified by comparing its results with the asymptotic solutions. The effect of the model sizes on the numerical method is discussed along with the robustness of the numerical method. Copyright © 2014 John Wiley & Sons, Ltd.     

Shale experiment and numerical investigation of casing deformation during volume fracturing

The casing deformation issues have occurred widely in Changning-Weiyuan National Shale Gas Demonstration Area. During multi-stage volume fracturing process, a large amount of fracturing fluid is injected into the formation, leading to tremendous change of stratum property and formation stress field. To assess the influence of shale formation on casing deformation, the acoustic velocity is measured to obtain the shale rock elastic modulus after saturation with water for different times. Then, the three-dimensional physical and finite element models are established using the stage finite element method considering transient thermal-pressure coupling. Shale anisotropy, shale stiffness degradation, and formation slip are taken into account to investigate the influences on casing deformation. Experiment results indicate that shale stiffness degrades dramatically after saturation with water for 24 h. Numerical simulations indicate that the shale modulus degradation mainly leads to large casing stress. Formation slipping not only causes excessive casing stress, but also causes large casing displacement. When slipping distance is larger than 15 mm, casing stress can reach up to the yield stress for P110 grade casing. Meanwhile, the casing deformation will be 14.95 mm, blocking the fracturing tools into the well bottom. Shale anisotropy has a minor influence on casing deformation.     

Fluid pressure and hydraulic fracturing in hydrothermal ore formation at gold deposits

The active role of fluids in the formation of ore-localizing structures expressed in dilatancy and hydraulic fracturing is suggested from the results of detailed comprehensive study of the Tokur gold deposit in the Upper Amur region, Russia, and the surveying of the published data on fluid pressure that characterizes formation of other hydrothermal deposits different in depth, morphology of orebodies, and their localization with respect to rocks of various permeability. Development conditions and possible implications of hydraulic fracturing for ore formation are considered. Indications of involvement of this mechanism in the orebody formation at the Pokrovsky, Berezovsky, and Nezhdaninsky gold deposits in Russia and the Bendigo deposit in Australia are discussed.     

Major factors influencing proppant behaviour and proppant-associated damage mechanisms during hydraulic fracturing

The ultra-low permeability of shale reservoirs necessitates engineering applications such as hydraulic fracturing to enable the extraction of economically viable amounts of gas. In this process, a high-pressure fluid is injected into the reservoir to create a network of fractures. Proppants are solid, spherical, high-strength particles with size range between 8 and 140 mesh (105 μm–2.38 mm), which are injected into the reservoir simultaneously with fracturing fluid to prompt the opening of the fractures created, and they play a major role in the hydraulic fracturing process. As a result, appropriate management of proppants in shale reservoirs based on precise identification of their behaviour in shale reservoirs is necessary, because unexpected proppant performance or behaviour, commonly known as proppant damage mechanisms, can greatly reduce fracture conductivity. Therefore, it is essential to determine the major factors affecting proppant behaviour in order to maintain constant fracture conductivity. Numerous factors have been found in previous studies, and they can be summarized into three major groups: proppant properties, reservoir properties and hydraulic fracturing production, which affect proppant damage mechanisms. In the present paper, case studies have been provided on the determination of potential factors influencing proppant behaviour, followed by a discussion of their effects on fracture conductivity. The aim of this study is to present current opinions on potential factors influencing proppant behaviour based on a comprehensive literature review.     

A numerical and laboratory investigation into the behaviour of a dry underclay beam

A simple and inexpensive laboratory device has been developed and used to simulate the behaviour of a dry underclay beam as the floor of an underground roadway subjected to a uniformly distributed uplift pressure. The Airy stress function method proved to be a useful means of expressing and predicting of the uplift of such beams. This method has been related to both classical beam theory and laboratory investigations. It was found that the Airy stress function method, utilizing polynomial equations, provides a closer fit to the mechanism of beam deformation and stress developments under dry laboratory conditions.     

弹塑性地层水力压裂起裂模式及起裂压力研究

针对弹塑性储层,基于线弹性理论假设的传统起裂模型已不再适用,需要研究基于非线性本构方程的起裂模型。基于岩石非线性本构方程,运用塑性全量理论,建立了弹塑性地层井周应力场模型;结合"井壁"应力场模型和弹塑性岩石破坏准则,建立了弹塑性地层的起裂压力预测模型。结果表明:岩石产生塑性屈服,"井眼"应力集中效应会减弱,"周向张应力会减小",甚至无法产生。屈服后的起裂压力比线弹性理论预测值大,起裂模式存在拉张和剪切两种方式,剪切起裂存在破坏角。屈服后,幂硬化指数小于等于0.5的岩石只可能产生剪切起裂;幂硬化指数大于0.5的岩石,屈服应力、幂硬化指数、内摩擦角和凝聚力越小,越容易产生剪切起裂,反之越容易产生拉张起裂。     

A numerical representation of fracturing granular materials

This paper describes the computer algorithms used in a numerical simulation of the compression of an aggregate of crushable grains. It has been used in a model for the evolution of a granular medium under one-dimensional compression, in which the probability of fracture for individual particles is a function of applied stress, particle-size and co-ordination number. The information relating to the particles is represented in a compact way on the computer which allows the number of particles produced to become sufficiently large for satisfactory comparisons to be made with experimental data and which allows information, such as the positions and sizes of the particles, to be easily extracted. An algorithm based on the representation is used to locate neighbouring particles in a way which does not deteriorate unacceptably in terms of speed as the number of particles increases. © 1997 by John Wiley & Sons, Ltd.     

裂隙岩体水力劈裂研究综述

作为裂隙岩体渗流-应力耦合研究的一个子课题,岩体水力劈裂问题的研究尚处于初始阶段,许多基本的理论问题尚待深入研究。当今许多大型工程的建设已经在向地下发展,建设在地下的各种建筑结构离不开水压的作用。工程建设的需要正在推动岩体水力劈裂理论的研究。水力劈裂作为一种技术最初在石油工业用来增加油井产量,后来逐渐用于初始地应力测量等其他工程项目。随着水电工程建设、地下核废料储存、地热开发、井工矿产采掘等岩体工程越来越多的处于高水头、大埋深等恶劣水文地质条件下,水力劈裂作用正在受到越来越多工程岩体稳定性研究者的关注。通过对水力劈裂研究的现状作较为详细地综述,列举了当今研究的理论、方法和成果,以及目前水力劈裂研究的热点问题,并作了简单评述。最后,指出了目前需要重点研究的几个关键问题。     

Effects of mechanical layering on hydraulic fracturing in shale gas reservoirs based on numerical models

Generally, induced hydraulic fractures are generated by fluid overpressure and are used to increase reservoir permeability through forming interconnected fracture systems. However, in heterogeneous and anisotropic rocks, many hydraulic fractures may become arrested or offset at layer contacts under certain conditions and do not form vertically connected fracture networks. Mechanical layering is an important factor causing anisotropy in sedimentary layers. Hence, in this study, with a shale gas reservoir case study in the Longmaxi Formation in the southeastern Chongqing region, Sichuan Basin, we present results from several numerical models to gain quantitative insights into the effects of mechanical layering on hydraulic fracturing. Results showed that the fractured area caused by hydraulic fracturing indicated a linear relationship with the neighboring layer’s Young’s modulus. An increase of the neighboring layer’s Young’s modulus resulted in better hydraulic fracturing effects. In addition, the contact between two neighboring layers is regarded as a zone with thickness and mechanical properties, which also influences the effects of hydraulic fracturing in reservoirs. The initial hydraulic fracture was unable to propagate into neighboring layers under a relatively low contact’s Young’s modulus. When associated local tensile stresses exceeded the rock strength, hydraulic fractures propagated into neighboring layers. Moreover, with the contact’s Young’s modulus becoming higher, the fractured area increased rapidly first, then slowly and finally became stable.     

A numerical investigation to illustrate the consequences of hydraulic connections between granular and fractured-rock aquifers

Natural or artificial hydraulic connections between a granular aquifer in contact with a fractured-rock aquifer can have significant physical and chemical impacts at both a local and a regional scale. In this study, numerical simulations are conducted in order to illustrate the hydrogeological consequences of such hydraulic relationships. The numerical investigation, based on a conceptual model, focuses on the effects of the hydraulic connections when conducting a pumping test in a well that is set into a granular confined aquifer overlying a fractured-rock aquifer which presents a few fractures directly connected to the granular aquifer. It is illustrated that when interpreting the pumping test with the conventional methods consisting of plotting the drawdown versus time, a bias is introduced on the estimation of the transmissivity of the granular aquifer due to groundwater flowing from the fractured-rock aquifer via connecting fractures. However, it is underlined that plotting drawdown log-derivative versus time helps to diagnose the existence of these hydraulic relationships and therefore avoids committing a bias on the transmissivity estimation of the granular aquifer. Numerical simulation results also illustrate that hydraulic connections between the two aquifers can have significant impacts on the hydrogeochemical signature of the granular aquifer under investigation.     

Rheological behaviour effects of non-Newtonian fracturing fluids on propagation of a vertical hydraulic fracture

This communication investigates the effects fo the non-Newtonian behaviour of the fracturing fluids in the hydraulic fracturing mechanism. These effects are illustrated on the propagation of a vertical hydraulic fracture into an oil reservoir, in which the fracturing fluid is of power law and of pseudo-plastic type. The analytical solutions for evaluating the fracture lengrhs are presented for the cdases of large fluid loss and for no fiuid loss. The results obtained should be useful in the design of fracture treatments, permitting the finding of the rheological properties of the injected fluid for obtaining the desired fracture length and width.     

Three-dimensional analysis of hydraulic fracturing

The formulation, development, implementation and application of a complete three-dimensional hydraulic fracturing simulator, 3DHFRAC, is described. The simulator consists of two principal components: the first represents the solid deformation, crack opening and propagation, using a surface integral scheme, hybridised with finite-elements as needed, and a condition of critical stress-intensity-factor or energy-release-rate to track the motion of the fracture perimeter; the second captures the fluid flow along the open fracture, and into the reservoir. The simulator has been tested extensively by comparison to analytical results, simpler models and laboratory experiments for which good agreement is obtained. It is finally used to study the general growth of 3-D fracture propagation under different fluid and reservoir conditions.     

Microscopic modelling of the hydraulic fracturing process

A microscopic perspective is introduced in this study which offers a detailed insight at the inter-particle level to the geo-mechanical responses caused by fluid injection and the resulting pressure build-up. This was achieved by employing the Discrete Element Method (DEM) to model the pressure development and the subsequent fracturing and/or cavity propagation. This technique represents the formation material as an assembly of discrete particles linked to each other through contacts. Numerical experiments were carried out on two sample materials. For the first instance, tests were carried out on a bulk material, representative of a generic intact rock, with the breakage of inter-particle bonds indicating the formation of cracks. The second series of tests was carried out on granular type materials such as sand, where particle separation signified cavity initiation and separation. It was observed from the DEM modelling results that the intact rock material showed a predominance of mode II fracturing at high fluid velocities. However, when the fluid velocity is reduced considerably the fracturing behaviour tended towards more of mode I. Also, records of the pressure development were taken from the numerical results and were used to monitor the fracturing events. The outcome of this study highlights important aspects of the hydraulic fracturing process especially at the particle–particle scale, and thus provides a strong basis for more exhaustive studies involving larger scale reservoir modelling and more complex fracturing scenarios.     

压裂液黏度对循环水力压裂影响的试验研究

中国石油大学（北京）石油天然气工程学院,北京 102249     

模拟水压致裂的另一种二维FDEM-flow方法

可考虑岩石本身渗透性的FDEM-flow方法充分利用原FEMDEM中节理单元和三角形单元独特的拓扑连接关系,将节理单元作为流体流动的天然通道,基于立方定律来表征流体在岩石本身及裂隙中的流动,而岩石本身渗透性则通过标定合适节理单元张开度来表征。用一个含解析解自由面稳态渗流算例初步验证了本文渗流算法及标定岩石本身渗透率方法的正确性。最后计算了一个水力压裂算例,验证了该FDEM-flow方法可同时考虑岩石本身的渗透性和裂隙的渗透性,用简单的纯裂隙渗流完成了对复杂问题的处理。研究结果表明:修改后的FDEM-flow方法能够很好地再现压裂过程中流体压力的分布及裂隙的扩展,可简洁地求解水力压裂这一复杂力学的问题,适用范围更广。为模拟页岩气开采、干热岩地热获取中的水力压裂问题提供新的求解工具。     

水力劈裂楔劈效应试验研究

心墙是否会发生水力劈裂关系土石坝的安全,该问题的难点和关键之一是水力劈裂的发生机制和条件。利用自制模型,在2种不同加压速率条件下,对有无初始裂缝和5种不同初始裂缝深度的试样进行了水力劈裂试验;结合数值模拟和CT观测试验,验证了水力劈裂的楔劈效应机制-当水压力作用在初始裂缝形成的劈背上,引起劈刃上的力超过临界值时就可能导致发生水力劈裂。研究结果表明：初始裂缝深度越大、加压速率越高,越容易发生水力劈裂。为避免土石坝发生水力劈裂破坏,应注意心墙迎水面的施工质量和平整性,宜采用较慢的蓄水方案。     

A stabilized extended finite element framework for hydraulic fracturing simulations

We present a stabilized extended finite element formulation to simulate the hydraulic fracturing process in an elasto‐plastic medium. The fracture propagation process is governed by a cohesive fracture model, where a trilinear traction‐separation law is used to describe normal contact, cohesion and strength softening on the fracture face. Fluid flow inside the fracture channel is governed by the lubrication equation, and the flow rate is related to the fluid pressure gradient by the ‘cubic’ law. Fluid leak off happens only in the normal direction and is assumed to be governed by the Carter's leak‐off model. We propose a ‘local’ U‐P (displacement‐pressure) formulation to discretize the fluid‐solid coupled system, where volume shape functions are used to interpolate the fluid pressure field on the fracture face. The ‘local’ U‐P approach is compatible with the extended finite element framework, and a separate mesh is not required to describe the fluid flow. The coupled system of equations is solved iteratively by the standard Newton‐Raphson method. We identify instability issues associated with the fluid flow inside the fracture channel, and use the polynomial pressure projection method to reduce the pressure oscillations resulting from the instability. Numerical examples demonstrate that the proposed framework is effective in modeling 3D hydraulic fracture propagation. Copyright © 2016 John Wiley & Sons, Ltd.