页岩水力压裂中多簇裂缝扩展的全耦合模拟

水平井和水力压裂是页岩气开发中的关键技术。对水力压裂中多簇裂缝同时扩展的物理过程进行了数值模拟。采用扩展有限元法(XFEM)模拟岩石中裂缝沿着任意路径扩展,采用有限体积法(FVM)模拟裂缝中流体的流动,并且考虑井筒中流体流动以及在各簇裂缝间的流量动态分配。通过牛顿迭代对全耦合物理过程进行数值求解,重点研究了初始长度不同的两条裂缝的扩展过程,证明较大的射孔摩阻能促进两条裂缝的同时扩展。并通过算例证明了本方法的精度和有效性。     

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.      

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.     

Fluid flow in a porous medium containing partially closed fractures

The model of Snow, in which a fracture is represented by two parallel channel walls, has frequently been used to study the flow of fluid in fractured reservoirs. Although this model gives important insight into the flow in fractures, very few naturally occurring fractures have smooth parallel faces. In this paper, a simple model of partially contacting and en-echelon fractures frequently found in geological materials is presented. In this model, a fracture is viewed as a planar region where separation and contact zones both exist. To analyse the fluid flow in a porous medium containing fractures of this type, a planar array of periodically spaced fracture segments is analysed. The flow through a single fracture is deduced by taking the limit as the spacing between neighbouring fractures becomes large. The hydraulic conductivity parallel to the fractures is found to be the parallel combination of the conductivity of the porous matrix and the system of parallel fractures, the individual fracture conductance being a series combination of the hydraulic conductance of the separation and contact zones. This interpretation enables the conductance of the contact zones to be evaluated and the results to be generalised to the case in which the material in the contact regions has a hydraulic conductivity different to that of the matrix. This may arise, for example, from grain-size reduction during fracturing or may result from a partial mineralisation or cementation of the fracture.     

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。     

Asymptotic Analysis of an Elasticity Equation for a Finger-Like Hydraulic Fracture

We derive a novel integral equation relating the fluid pressure in a finger-like hydraulic fracture to the fracture width. By means of an asymptotic analysis in the small height to length ratio limit we are able to establish the action of the integral operator for receiving points that lie within three distinct regions: (1) an outer expansion region in which the dimensionless pressure is shown to be equal to the dimensionless width plus a small correction term that involves the second derivative of the width, which accounts for the nonlocal effects of the integral operator. The leading order term in this expansion is the classic local elasticity equation in the PKN model that is widely used in the oil and gas industry; (2) an inner expansion region close to the fracture tip within which the action of the elastic integral operator is shown to be the same as that of a finite Hilbert transform associated with a state of plane strain. This result will enable pressure singularities and stress intensity factors to be incorporated into analytic models of these finger-like fractures in order to model the effect of material toughness; (3) an intermediate region within which the action of the Fredholm integral operator of the first kind is reduced to a second kind operator in which the integral term appears as a small perturbation which is associated with a convergent Neumann series. These results are important for deriving analytic models of finger-like hydraulic fractures that are consistent with linear elastic fracture mechanics. Submitted to Journal of Elasticity on February 5, 2007. Re-submitted with revisions on May 30, 2007.     

A variational approach to analyze a natural fault with hydraulic fracture based on the strain energy density criterion

A simplified analytical model of the interaction between a hydraulic fracture and an existing natural fault is developed. The mechanical activation of the natural fault as a result of contact with a pressurized fracture is described for plane strain conditions and quasi-static fracture propagation approximation. Using a variational approach, the normal and shear stresses, as well as the boundaries of the open and sliding zones along the fault, are predicted for three stages of the fracturing process (fracture approaching, coalescence, and fluid penetration). An accumulated concentration of shear stress at the tip of the fault’s sliding zone is shown to create sufficient tensile stress to initiate a new tensile crack on the opposite side of the fault, provided either the differential in situ stress is low or the friction coefficient is sufficiently large. The results of direct numerical simulation of the fracture interaction fit the model predictions made from the strain energy density fracture criterion.     

Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: asymptotic solutions

This paper presents an analysis of the propagation of a penny-shaped hydraulic fracture in an impermeable elastic rock. The fracture is driven by an incompressible Newtonian fluid injected from a source at the center of the fracture. The fluid flow is modeled according to lubrication theory, while the elastic response is governed by a singular integral equation relating the crack opening and the fluid pressure. It is shown that the scaled equations contain only one parameter, a dimensionless toughness, which controls the regimes of fracture propagation. Asymptotic solutions for zero and large dimensionless toughness are constructed. Finally, the regimes of fracture propagation are analyzed by matching the asymptotic solutions with results of a numerical algorithm applicable to arbitrary toughness.     

Interaction between hydraulic and natural fractures

The results of a numerical simulation of the interaction between a hydraulic fracture propagating under plane-strain conditions in an infinite impermeable elastic medium and an already existing natural fault are presented. The fracture is created by an incompressible Newtonian fluid injected at a constant flow rate from a source located at its center; the behavior of the fault is described by a dry friction model of the Mohr-Coulomb type. The results obtained are in agreement with the available studies in this field of research.     

ADVANCES IN RESEARCH OF HYDRAULIC FRACTURES IN UNCONSOLIDATED SANDS

疏松砂岩水力压裂裂缝的典型特征是大量分支缝、微裂缝和一定钝度的裂缝尖端及剪切带的形成等. 主要通过对相关文献的调研,分析了剪切作用、拉伸作用等对裂缝形态特征（起裂、转向、延伸）等力学行为所产生的影响,通过针对一些疏松砂岩的压裂实验研究发现,其滤失过程主要受到缝尖区域的影响,而且滤失一般发生在裂缝扩展之前. 裂缝缝尖周围的局部应力往往是影响裂缝起裂和裂缝开度的主导参数,裂缝的形态特征则是应力、渗透率、流态等综合作用的结果,对疏松砂岩裂缝形态特征的形成做了进一步的解释.     

页岩储层体积压裂的地应力变化研究

页岩储层属于致密超低渗透储层,需改造形成复杂缝网才有经济产能.体积压裂是页岩储层增产改造的主要措施,而地应力场特别是水平主应力差值是体积压裂的关键控制因素. 理论研究表明:(1)当初始两向水平主应力差较小时,容易形成缝网,反之不易产生缝网;(2)人工裂缝的形成能够改变地层初始应力场. 因此应在前人研究的基础上优化设计压裂方式,以克服和翻转初始水平主应力差值,产生体积缝网.基于此,建立了页岩气藏水平井体积压裂数值模型,模型中采用多孔介质流固耦合单元模拟页岩基质的行为,采用带有孔压的"cohesive"单元描述水力裂缝的性质,模型对"Texas Two-Step" 压裂方法进行了数值模拟,模拟结果得到了压裂过程中地层应力场的分布及其变化,模拟结果和解析公式计算结果吻合良好.模拟结果表明:(1)裂缝的产生减弱了地层应力场的各向异性;(2 对于低水平应力差页岩储层,采用"Texas Two-Step"压裂方法可以产生缝网. 对于采用"Texas Two-Step"压裂方法无法产生缝网的高应力差页岩储层,提出了三次应力"共振" 和四次应力"共振" 压裂方法并进行了数值模拟,模拟结果得到了压裂过程中页岩储层应力场的分布及其变化,得到了缝网形成的区域,模拟结果表明:(1)对于高应力差页岩储层,采用"Texas Two-Step" 压裂方法无法产生缝网;(2)对于高应力差页岩储层,三次应力"共振" 和四次应力"共振"压裂方法是有效的体积压裂缝网形成的方法.      

3-D Fracture Propagation Simulation and Production Prediction in Coalbed

NｏｍｅｎｃｌａｔｕｒｅＡ(ｘ,ｔ)—Ｃｒｏｓｓ＿ｓｅｃｔｉｏｎａｒｅａｏｆｆｒａｃｔｕｒｅａｔｔｉｍｅｔａｎｄｓｉｔｅｘ,ｍ2 ;Ｂｇ,Ｂｗ —Ｃｏａｌｂｅｄｇａｓａｎｄｗａｔｅｒｖｏｌｕｍｅｆａｃｔｏｒ,ｄｉ ｍｅｎｓｉｏｎｌｅｓｓ;ｂ—Ｌａｎｇｍｕｉｒｆａｃｔｏｒ,(ＭＰａ) - 1 ;Ｃｇ,ＣＲ,Ｃｗ —Ｃｏａｌｂｅｄｇａｓ,ｒｏｃｋａｎｄｗａｔｅｒｃｏｍ ｐｒｅｓｓｉｂｉｌｉｔｙｃｏｅｆｆｉｃｉｅｎｔ,(ＭＰａ) - 1 ;Ｃｐ —Ｓａｎｄｒａｔｉｏ ,ｄｉｍｅｎｓｉｏｎｌｅｓｓ;Ｃｔ(ｘ ,ｔ)—Ｔｏｔａｌｆｒａｃｔｕｒｉｎ…     

页岩气高效开采的可压裂度和射孔簇间距预测

页岩储层的可压裂性是影响页岩气产量的关键因素. 本文基于断裂力学理论, 以高围压下岩石层理弱面的剪切破坏为主要研究对象, 依据岩石抗拉强度和层理弱面抗剪强度的比值关系, 首先提出了可压裂度的概念, 给出了无量纲的定性曲线图, 涵盖了岩石脆性矿物质含量, 粘性主导和韧性主导裂缝尖端流体压强、射孔簇分布间距的综合地质与工程因素. 接着提出了一种新的表征高围压下页岩可压裂度的无量纲参数, 在保证达到充分解吸附的最小压裂间距前提下, 依据该参数可计算水平井压裂中的射孔簇间距, 可作为工程参考指标. 本文将断裂力学理论结合水力压裂高效开采页岩气工程, 具有力学理论意义和工程应用前景.      

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.     

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。     

Finite Element study of fracture initiation in flaws subject to internal fluid pressure and vertical stress

Hydraulic fracturing is a method used routinely in oil and gas exploitation and in engineered geothermal systems. While used frequently, there are many aspects of hydraulic fracturing, such as the direction of propagation of the newly-created fractures, which are not very well understood. Even though it is known that the local stress field plays a fundamental role in the orientation of the new fractures, there may be other factors, such as the geometry of the existing fractures and the magnitude of the hydraulic pressure applied, that may play a major role in the path that a new fracture follows when pressurized.The main goal of this study is to numerically analyze the effect of the ratio between a vertical load, or stress, and the hydraulic pressure applied in existing flaws on the stress field in the vicinity of the flaw tips. For that purpose, a double flaw geometry 2a-30-30 was modeled in the Finite Element code ABAQUS, and different vertical loads and internal flaw pressures were applied to the model. The variation of the maximum principal stresses and maximum shear stresses around the flaw tips were analyzed and related to fracture initiation.The study showed that the ratio between the water pressure applied in the flaws and the vertical load/stress (WP/VL) plays a crucial role in the magnitude and shape of the stress field around a flaw tip, and therefore in the location of tensile and shear fracture initiation. As WP/VL increases, the location of initiation of new tensile fractures shifts from the upper face of the studied flaw towards the region right ahead of the flaw tip; simultaneously, the location of initiation of new shear fractures shifts from the region ahead of the flaw tip to the upper face of the analyzed tip.     

Experiment and simulation of slurry flow in irregular channels to understand proppant transport in complex fractures

Slurry flow and proppant placement in irregular fractures are crucial to evaluate hydraulic fracturing stimulation but need to be better understood. This study aims to investigate how irregular fracture affects proppant transport and distribution using laboratory experiments and micro-scale numerical models. The unresolved method of the computational fluid dynamics (CFD) and the discrete element method (DEM) considers Saffman lift force, Magnus force, and virtual mass force to accurately capture the frequent interaction between proppant and slickwater. Experimental results validated the reliability of the optimized CFD-DEM model and calibrated primary parameters. The effects of crack height and width, bending angle, and distance between the crack and inlet on particle distribution were studied. The results indicated that the improved numerical method could rationally simulate proppant transport in fractures at a scale factor. The small crack height causes downward and upward flows, which wash proppant to the fracture rear and form isolated proppant dunes. A wider region in the fracture is beneficial to build up a large dune, and the high dune can hinder particle transport into the fracture rear. When the crack is close to the inlet, the primary fracture without proppants will close to hinder gas production. The smaller the bending angle, the smaller the proppant dune. A regression model can precisely predict the dune coverage ratio. The results fundamentally understand how complex fractures and natural cracks affect slurry flow and proppant distribution.     

脆性岩石破裂过程损伤与渗流耦合数值模型研究

大量的实验结果表明，脆性岩石的渗透性不是一个常量，而是应力和应力诱发损伤破裂的函数．建立了一个描述非均匀岩石渗流-应力-损伤耦合数学模型(FSD Model)，开发出岩石破裂过程渗流-应力-损伤耦合分析计算系统(F-RFPA^2D)．在该系统中，单元的力学、水力学性质根据统计分布而变化，以体现材料的随机不均质性，材料在开裂破坏过程中流体压力传递通过单元渗流-损伤耦合迭代来实现．该系统能够对岩石试件在孔隙水压力和双轴荷载作用下裂纹的萌生、扩展过程中渗透率演化规律及其渗流-应力耦合机制进行模拟分析．最后，给出两个算例：算例1模拟载荷作用下岩石应力应变-渗透率全过程．模拟结果表明，非均匀性对岩石的应力峰值强度、峰值前后其渗透性演化规律及其破裂机制影响十分明显，模拟结果和实验结果较为一致；算例2模拟孔隙水压力作用下岩石拉伸断裂过程，通过和物理实验对比验证，验证了模型计算结果的可靠性。     

基于孔隙弹性的水力压裂耦合方法与压裂状态参数数值研究

本文系统地阐述基于多孔介质渗流-损伤耦合原理,进行水力压裂FEM的数值实现方法。基本架构为：(1)引入孔隙流体压力膨胀系数将孔隙流体压力与应力场进行耦合;(2)基于损伤局部化模型,提出裂缝张开度表达式; (3)提出水力压裂引起的多孔介质水-力学属性的各向异性表达式; (4)提出全流量加载的耦合分析方案。最后作为实例,模拟三维地层水压裂缝扩展形态,通过比较模型的数值解和经典理论解,验证该方法的正确性。