Analysis of fracture propagation and shale gas production by intensive volume fracturing

This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing. The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM) and the Picard iterative method. The shale gas flow considers multiple transport mechanisms, and the flow in the fracture network is hand...     

STOCHASTIC ELASTO-PLASTIC FRACTURE ANALYSIS OF ALUMINUM FOAMS

Model I quasi-static nonlinear fracture of aluminum foams is analyzed by considering the effect of microscopic heterogeneity. Firstly, a continuum constitutive model is adopted to account for the plastic compressibility of the metallic foams. The yield strain modeled by a two- parameter Weibull-type function is adopted in the constitutive model. Then, a modified cohesive zone model is established to characterize the fracture behavior of aluminum foams with a cohesive zone ahead of the initial crack. The tensile traction versus local crack opening displacement relation is employed to describe the softening characteristics of the material. And a Weibull statistical model for peak bridging stress within the fracture process zone is used for considering microscopic heterogeneity of aluminum foams. Lastly, the influence of stochastic parameters on the curve of stress-strain is given. Numerical examples are given to illustrate the numerical model presented in this paper and the effects of Weibull parameters and material properties on J-integral are discussed.     

Inverse analysis determining interfacial properties between metal film and ceramic substrate with an adhesive layer

In the present study, peel tests and inverse analysis were performed to determine the interracial mechanical parameters for the metal film/ceramic system with an epoxy interface layer between film and ceramic. Al films with a series of thicknesses between 20 and 250 μm and three peel angles of 90°, 135° and 180° were considered. A finite element model with the cohesive zone elements was used to simulate the peeling process. The finite element results were taken as the training data of a neural network in the inverse analysis. The interracial cohesive energy and the separation strength can be determined based on the inverse analysis and peel experimental result     

NUMERICAL PREDICTIONS AND EXPERIMENTAL VALIDATIONS OF DUCTILE DAMAGE EVOLUTION IN SHEET METAL FORMING PROCESSES

Prediction of forming limit in sheet metal forming is among the most important challenges confronting researchers. In this paper, a fully coupled elastic-plastic-damage model has been developed and implemented into an explicit code. Due to the adoption of the plane stress and finite strain theories, model can predict deformation and damage of parts quickly and accurately. Also, damage initiation, propagation, and fracture in some operations are predicted and validated with experiments. It is concluded that finite strain combined with continuum damage mechanics can be used as a quick tool to predict ductile damage, fracture, and forming limits in sheet metal forming processes.     

SHEAR BEAM MODEL FOR INTERFACE FAILURE UNDER ANTIPLANE SHEAR (Ⅰ)—FUNDAMENTAL BEHAVIOR

The propagation of interlayer cracks and the resulting failure of the interface is a typical mode occurring in rock engineering and masonry structure. On the basis of the theory of elasto~plasticity and fracture mechanics, the shear beam model for the solution of interface failure was presented. The concept of `cohesive crack’ was adopted to describe the constitutive behavior of the cohesive interfacial layer. Related fundamental equations such as equilibrium equation, constitutive equations were presented. The behavior of a double shear beam bonded through cohesive layer was analytically calculated. The stable propagation of interface crack and process zone was investigated.     

An energy-consistent fracture model for ferroelectrics

The fracture behavior of ferroelectrics has been intensively studied in recent decades, though currently a widely accepted fracture mechanism is still lacking. In this work, enlightened by previous experimental observations that crack propagation in ferroelectrics is always accompa-nied by domain switching, we propose a micromechanical model in which both crack propagation and domain switch-ing are controlled by energy-based criteria. Both electric energy and mechanical energy can induce domain switching, while only mechanical energy can drive crack propagation. Furthermore, constrained domain switching is considered in this model, leading to the gradient domain switching zone near the crack tip. Analysis results show that stress-induced ferroelastic switching always has a toughening effect as the mechanical energy release rate serves as the driving force for both fracture and domain switching. In compari-son, the electric-field-induced switching may have either a toughening or detoughening effect. The proposed model can qualitatively agree with the existing experimental results.     

A PRECISE SINGULAR FINITE ELEMENT FOR CRACK ANALYSIS

The multi-variable finite element algorithm based on the generalized Galerkin’smethod is more flexible to establish a finite element model in the continuum mechanies.Byusing this algorithm and numerical tests a new singular finite element for elasto-plasticfracture analysis has been formulated.The results of numerical tests show that the newelement possesses high accuracy and good performance.Some rules for formulating amulti-variable singular finite element are also discussed in this paper.     

Numerical analysis of ossicular chain lesion of human ear

Abstract Lesion of ossicular chain is a common ear disease impairing the sense of hearing. A comprehensive numerical model of human ear can provide better understanding of sound transmission. In this study, we propose a three-dimensional finite element model of human ear that incorporates the canal, tympanic membrane, ossicular bones, middle ear suspensory ligaments/muscles, middle ear cavity and inner ear fluid. Numerical analysis is conducted and employed to predict the effects of middle ear cavity, malleus handle defect, hypoplasia of the long process of incus, and stapedial crus defect on sound transmission. The present finite element model is shown to be reasonable in predicting the ossicular mechanics of human ear.     

SIMULATION OF PARTICLE COATING IN THE SUPERCRITICAL FLUIDIZED BED

Fluidized bed technology using supercritical carbon dioxide both as a fluidizing gas and as a solvent for the coating material makes possible the production of thin, uniform and solvent-free coatings. But operation at low fluidizing velocities, which is favorable to facilitate gas cleaning under the high pressure conditions, may lead to uneven distribution of the coating in the fluidized bed and to unstable operation due to agglomeration. Therefore a model has been developed which describes local fluid dynamics within the high pressure fluidized bed. Based on this model, the coating process is described and the distribution of the coating inside the fluidized bed is calculated. Furthermore a submodel for the calculation of local concentrations of liquid paraffin has been set up, which may be used as a basis for the prediction of agglomeration and thus stability of operation.     

Numerical well test for well with finite conductivity vertical fracture in coalbed

A new well test model is developed for the hydraulic fractured well in coalbed by considering the following aspects： methane desorption phenomena, finite conductivity vertical fractures, and asymmetry of the fracture about the well. A new parameter is introduced to describe the storage of the fracture, which is named as a combined fracture storage. Another new concept called the fracture asymmetry coefficient is used to define the asymmetry of the fracture about the well. Finite element method （FEM） is used to solve the new mathematical model. The well test type curves and pressure fields are obtained and analyzed. The effects of the combined fracture storage, desorption factor, fracture conductivity, and fracture asymmetry coefficient on the well test type curves are discussed in detail. In order to verify the new model, a set of field well test data is analyzed.     

水力压裂解析模型裂缝扩展参数敏感性分析

水力压裂形成复杂裂缝网络是致密储层油气开采的重要技术,掌握水压裂缝扩展机理是控制压裂行为和优化压裂效果的关键．水压裂缝动态扩展行为涉及储层岩体、注入压裂液、压裂实施工艺等方面,其中水力压裂扩展时间、压裂液流体动力粘度系数、压裂液流体注入流速、储层岩石剪切模量成为决定裂缝扩展长度和裂缝开度的重要因素．本研究采用KGD、PKN两类等高解析模型对主控因素的参数敏感性进行分析,直观、快速、可靠地获得水压裂缝扩展长度、张开度动态演化行为的量化数值．研究发现,压裂持续开展过程中水压裂缝扩展长度呈线性增长、开度逐渐趋于稳定,高流体动力粘度导致裂缝难扩展、形成较大裂缝开度,通过增加压裂液流体注入流速可同时增加裂缝扩展长度和开度,较高的岩石剪切模量将降低水压裂缝的开度．通过对比两类解析模型在不同参数下的水压裂缝扩展结果,分析压裂参数与裂缝扩展的相关性和敏感系数,讨论水力压裂解析模型的裂缝扩展参数敏感性．     

水力压裂中裂纹扩展的数值模拟

水力压裂是在高压粘滞流体或清水作用下地层内裂缝起裂与扩展的过程。由于包含岩石断裂和流-固耦合等复杂问题,对该过程的数值模拟具有相当大的挑战性。本文建立基于有限元与离散元混合方法的裂纹模型,模拟岩石裂纹扩展,实现了连续向非连续的转化;建立双重介质流动模型,裂隙流作为孔隙渗流的压力边界,孔隙渗流反作用裂隙的压力求解,处理了流体在基岩与人工裂缝中的协调流动;将裂纹模型与流体流动模式进行结合,建立断裂-应力-渗流耦合形式的力学模型,进一步分析了水力压裂的基本过程,综合多种数值计算方法,编写程序,在验证岩体裂纹模型与双重介质流动模型有效性的基础上,对压裂过程进行复现,将模拟结果与文献结果进行了对比,并讨论了所构建模型的优缺点。     

页岩水力压裂的关键力学问题

页岩气是指以吸附和游离时而还有流体相的形态状态赋存于泥页岩中的非常规天然气。页岩气开采成为我国绿色能源开发的新领域。尽管北美页岩气革命取得了成功,但目前仍仅有预期产量5~15%的油气采收率,问题出在什么地方？水力压裂被认为是提高采收率的关键一环,但水力压裂过程中复杂缝网的形成和力学控制机理尚不清楚,这给力学家提出了巨大的挑战和机遇。结合本课题组近期研究成果,本文从理论、计算和实验三个方面对页岩水力压裂中的关键基础力学问题进行介绍和总结。主要内容包括发展页岩人工裂缝扩展的大型物理模型实验,建立页岩本构模型和断裂力学理论,发展耦合断裂力学和流体力学的裂缝网扩展数值模拟方法。页岩水力压裂研究对发展断裂力学的实验技术、理论模型和数值模拟方法起到推动作用,对提高我国页岩气高效开采技术具有重要意义。     

基于混合方法的二维水力压裂数值模拟

水力压裂在页岩气开采中被广泛使用,采用数值方法研究压裂机理具有重要意义.基于连续-非连续单元法(CDEM) 和中心型有限体积法(FVM),提出解决水力压裂流固耦合问题的二维混合数值计算模型.该混合模型中,使用CDEM 求解应力场和裂缝扩展过程,使用FVM 求解裂隙渗流场.应力场裂缝扩展和渗流场均使用显式迭代求解, 并通过相互之间数据交换实现流固耦合.通过与KGD 理论模型进行对比, 验证数值模型的正确性.通过与颗粒离散元数值结果进行对比,验证数值模型的有效性.通过计算复杂缝网压裂模型,研究水力压裂机理,并说明该数值模型在水力压裂模拟中具有很好的前景.      

Model of stepwise propagation of the tip of a hydraulic fracture in the absence of filtration

Quasi-static stepwise propagation of a hydraulic fracture in rock with a regular structure in the absence of filtration is considered. It is proposed to use a brittle fracture diagram taking into account the hydraulic fracturing fluid pressure and the confining pressure. Fracture curves describing the brittle rock fracture where the hydraulic fracturing fluid partially fills the fracture are constructed and used to predicted the possibility of stepwise propagation of hydraulic fracturing in the case where the fluid gradually flows into the fracturing crack. The regularity of the structure of the brittle rocks fracture is estimated from the results of two full-scale experiments: the critical stress intensity factor and the tensile strength limit of the rock. Experiments on pulsed loading of polymethylmethacrylate samples with stepwise crack propagation along concentric circular arcs were performed. The results of the experiments are consistent with theoretical predictions.     

含水合物粉质黏土压裂成缝特征实验研究

水力压裂技术是一种重要的油气井增产、增注措施,已经广泛应用于页岩油气等非常规资源的商业开采中.目前对于粉质黏土水合物沉积物的水力压裂成缝能力尚不清楚.本文采用南海水合物沉积层的粉质黏土制备沉积物试样,并与实验室配制的粉细砂土沉积物对比,分析粉质黏土沉积物的水力成缝能力及主控因素.实验结果表明含水合物和冰的沉积物破裂压力较高,这与粉质黏土沉积物特殊的应力-应变特征和渗透性有关.当沉积物应变高于6%时, 试样强度迅速上升, 呈现应变强化的特征,对水力拉伸裂缝的扩展具有一定的阻碍作用. 粉质黏土沉积物粒径细小, 渗透性差,难以通过渗透作用传递压力, 提高了沉积层的破裂压力. 此外,粉质黏土水合物沉积层裂缝扩展存在明显延迟效应,说明裂缝扩展受到流体压力和热应力的共同影响. 适当延长注入时间,保持流体与沉积层充分接触, 会起到分解水合物、降低破裂压力的作用.该研究成果有利于深入理解水力裂缝在水合物沉积层中的扩展规律,对探索压裂技术在水合物沉积层开发中的应用具有重要意义.      

页岩气藏压裂缝网扩展数值模拟

为探究页岩气藏水力压裂复杂裂缝网络的形成机理,开展了缝网扩展的数值模拟研究.考虑应力阴影和天然裂缝作用,建立了井筒和裂缝中流体流动模型,利用位移不连续方法求解应力与位移不连续量,然后构建了压力与裂缝宽度的迭代方程,并采用牛顿迭代法求解.通过比较数值解经典模型解析解,验证了模型和迭代解法的正确性.多簇裂缝同步扩展时裂缝间距越小,压裂液分配到各条裂缝越不均匀,靠近井筒跟部的裂缝的分流量越大,从而裂缝宽度越大;考虑天然裂缝作用时,逼近角越小或者应力各向异性越弱,水力裂缝越容易发生转向扩展,裂缝网络越复杂.      

On the problem of fluid leakoff during hydraulic fracturing

While a hydraulic fracture is propagating, fluid flow and associated pressure drops must be accounted for both along the fracture path and perpendicularly, into the formation that is fractured, because of fluid leakoff. The accounting for the leakoff shows that it is the main factor that determines the crack length. The solved problem is useful for the technology of hydraulic fracturing and a good example of mass transport in a porous medium. To find an effective approach for the solution, the thin crack is represented here as the boundary condition for pore pressure spreading in the formation. Earlier such model was used for heat conduction into a rock massif from a seam under injection of hot water. Of course, the equations have other physical sense and mathematically they are somewhat different. The new plane solution is developed for a linearized form that permits the application of the integral transform. The linearization itself is analogous to the linearization of the natural gas equation using the real gas pseudo-pressure function and where the flux rates are held constant and approximations are introduced only into the time derivatives. The resulting analytical solution includes some integrals that can be calculated numerically. This provides rigorous tracking of the created fracture volume, leakoff volume and increasing fracture width. The solutions are an advance over existing discreet formulations and allow ready calculations of the resulting fracture dimensions during the injection of the fracturing fluid.     

考虑单元劈裂的流-固耦合连续-非连续方法及定向水力压裂模拟

为了更真实地模拟水力压裂过程中的岩石变形、裂缝扩展及流体流动,在自主开发的拉格朗日元与离散元耦合的连续-非连续方法的基础上,发展了一种流-固耦合方法。在该方法中,裂缝可沿四边形单元对角线和单元边界扩展,流体流动满足立方定律。通过与单一裂缝非稳态渗流模型及KGD模型的理论解进行对比,验证了该方法的正确性。由定向射孔水力压裂的模拟结果可以发现,(1)距离射孔越远,流体压力越小;随着时间的增加,裂缝中流体压力降低。(2)随着射孔角度的增加,裂缝起裂和扩展过程中的流体压力及转向距离增加;随着x方向水平应力的增加,裂缝起裂和扩展过程中的流体压力增加;两个方向水平应力之差越大,裂缝转向距离越小。(3)随着时间的增加,裂缝区段数目的增速变慢,这与裂缝体积增加变快有关。     

Exact quasi-steady solution of the problem of hydraulic fracturing of a permeable formation

An exact solution of the problem of hydraulic fracturing in a permeable medium with continuous fluid injection in a partially penetrated formation is constructed using the Perkins-Kern fracture model. The amount of fluid leakage from the fracture is determined using the pressure field of the fluid filtrate defined by the Shchelkachev equation (of the piezoconductivity type). Universal profiles of the fluid pressure in the fracture and the rate of fluid flow from it are obtained. It is shown that at the Perkins-Kern fracture tip, there is a dramatic increase in the leakage from the fracture.