横观各向同性油气藏水力压裂裂纹扩展规律研究

针对横观各向同性与各向同性油气藏水力压裂裂纹扩展的差异性,基于扩展有限元法建立水力压裂力学模型,通过ABAQUS子程序开发了各向同性和横观各向同性岩体的起裂判据。在各向同性岩体数值模拟结果与解析解以及现场压裂典型曲线对比吻合的基础上,得到了包含层理构造的横观各向同性岩体水力压裂过程中裂纹扩展规律。层理类岩体水力压裂的裂缝扩展方向由地应力状态、层理方向以及岩体与层理界面抗拉强度共同决定;水力压裂过程中,注水压力在裂纹尖端产生应力集中,层理面法向分量先达到界面抗拉强度时,裂纹沿层理方向开裂,反之裂纹沿垂直最小地应力的方向扩展;裂纹扩展速度随层理抗拉强度的增加而降低;由于地层的滤失,随压裂液的注入,裂纹长宽尺度增长速率降低。     

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．     

含层理页岩气藏水力压裂裂纹扩展规律解析分析

页岩气蕴藏在页岩层中,页岩层的层理性构造使其水力压裂裂纹扩展与常规均质储层不同.为研究页岩储层水力压裂的裂纹扩展规律,基于复变函数保角变换,得出裂纹尖端应力集中解,考虑页岩非均质、强度各向异性特点,通过比较裂纹沿各方向扩展所需的裂缝尖端水压力,推导出水力压裂裂纹垂直于最小地应力方向稳定扩展过程中在斜交层理后的扩展判据.分别定义了水力压裂裂纹在层理处起裂和沿层理扩展的弱层和岩石基体临界强度比,根据两个临界强度比确定水力压裂裂纹遇层理时在层理处起裂和沿层理扩展的层理弱面强度范围,以此表示水力压裂裂纹转向层理扩展的难易程度.通过对裂纹扩展判据的分析得出:层理起裂弱层和岩石基体临界强度比随层理走向线与第一主应力夹角和层理倾角的减小以及第三主应力和岩石基体强度的增大而增大;层理走向角小于35.26°时,层理起裂弱层和岩石基体临界强度比随第一主应力的减小以及第二主应力的增大而增大;反之,层理起裂弱层和岩石基体临界强度比随第一主应力的减小以及第二主应力的增大而减小;层理扩展弱层和岩石基体临界强度比随层理走向线与第一主应力夹角、层理倾角和地应力差的减小以及岩石基体抗拉强度的增大而增大.层理起裂条件与层理扩展条件同时满足时,水力压裂裂纹转向层理方向扩展.      

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.     

不同围压作用下非均匀岩石水压致裂过程的数值模拟

从岩石细观非均匀性的特点出发，提出一个描述非均匀材料渗流和破裂相互作用的数值模型。在这个数值模型中，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。算例表明，该模型能较好地模拟出岩石类材料在水力压裂作用下，微结构非均匀分布和不同围压比对破裂模式、失稳压力的影响，非均匀性导致试件的开裂压力、失稳压力明显不同，裂纹扩展路径不规则发展，模拟结果和实验结果较为一致。     

动载荷作用下裂隙岩体的止裂机理分析

为深层次了解裂隙岩体在动载荷作用下的动态断裂特性及止裂机理,采用TWSRC（tunnel with single radial crack）构型进行中低速冲击实验,选择砂岩作为原材料制作裂隙岩体试样,以落锤冲击试验装置与裂纹扩展计实验系统对裂纹的动态起裂、扩展及止裂过程进行全过程监测,重点研究动态破裂过程的破裂行为及止裂现象。使用有限差分法程序进行数值模拟,验证冲击实验结果的科学性与准确性。研究发现:裂隙岩体的动态断裂过程是由起裂加速-高速扩展-缓慢减速-止裂-再次起裂加速-再次高速扩展等多次循环的过程构成,且止裂区间尺寸为微秒量级;裂隙岩体止裂位置的穿晶断裂比例远小于初始起裂点,青砂岩动态断裂过程的穿晶断裂比例稍大于黑砂岩;裂隙岩体中止裂点再次起裂所需的能量,远小于预制裂纹初始起裂所需要的能量。     

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.      

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。     

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.     

Analysis of power-law self-similar solutions to the problem of hydraulic fracture crack formation

The problem of hydraulic fracture crack propagation in a porous medium is studied in the approximation of small crack opening and the inertialess flow of an incompressible Newtonian hydraulic fracturing fluid inside the crack. A one-parameter family of power-law self-similar solutions is considered in order to determine the crack width evolution, the fluid velocity in the crack, and the seepage depth in the case of high and low seepage rates through the soil when a fluid flow rate is given at the crack inlet.     

Interaction between crack tip advancement and fluid flow in fracturing saturated porous media

We address stepwise crack tip advancement and pressure fluctuations, which have been observed in the field and experimentally in fracturing saturated porous media. Both fracturing due to mechanical loading and pressure driven fracture are considered. After presenting the experimental evidence and the different explanations for the phenomena put forward and mentioning briefly what has been obtained so far by published numerical and analytical methods we propose our explanation based on Biot’s theory. A short presentation of three methods able to simulate the observed phenomena namely the Central Force Model, the Standard Galerkin Finite Element Method SGFEM and extended finite element method XFEM follows. With the Central Force Model it is evidenced that already dry geomaterials break in an intermittent fashion and that the presence of a fluid affects the behavior more or less depending on the loading and boundary conditions. Examples dealing both with hydraulic fracturing and mechanical loading are shown. The conditions needed to reproduce the observed phenomena with FE models at macroscopic level are evidenced. They appear to be the adoption of a crack tip advancement/time step algorithm which interferes the least possible with the three interacting velocities, namely the crack tip advancement velocity on one side, the seepage velocity of the fluid in the domain and from the crack (leak-off), and the fluid velocity within the crack on the other side. Further the crack tip advancement algorithm must allow for reproducing jumps observed in the experiments.     

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.      

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…     

Growth of a main crack under the influence of gas moving inside it

The motion of a gas or liquid in a growing main crack is examined in connection with the problem of the hydraulic fracture of an oil-bearing bed [1, 2] and evaluation of the quantity of gaseous products escaping from the cavity formed by the underground explosion into the atmosphere by way of the crack [3]. The studies [1, 2] formulated and solved a problem on the quasisteady propagation of an axisymmetric crack in rock under the influence of an incompressible fluid pumped into the crack. An exact solution was obtained in [4] to the problem of the hydraulic fracture of an oil-bearing bed with a constant pressure along the crack. The Biot consolidation theory was used as the basis in [5] for an examination of the growth of a disk-shaped crack associated with hydraulic fracture of a porous bed saturated with fluid. A numerical solution to a similarity problem on the motion of a compressible gas ina plane crack was obtained in [6]. Here we examine the problem of the propagation of a main crack (plane and axisymmetric) under the influence of a gasmoving away from an underground cavity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 116–122, July–August, 1986.We thank V. M. Entova for his remarks, which helped to improve the investigation.     

RESEARCH OF STEPPING PRESSURE AND CONTROL OF NEAR FIELD ROOF OF TASHAN COAL MINE BASED ON NUMERICAL SIMULATION1)

煤层坚硬顶板采用水力压裂技术进行定向弱化可有效控制来压步距,降低事故风险。基于黏聚力模型,利用有限元二次开发建立了压裂前后煤层开采数值计算模型,模拟分析了顶板垮落规律及影响因素,优化裂缝间距设计。结果表明：来压跨距与顶板厚度、强度呈正相关性,与埋深呈负相关性。预制裂缝在拉应力集中区可促进起裂扩展,应全面勘测各岩层位地质参数,利用计算出的应力集中区位置设计裂缝间距,实现经济有效地控制来压步距。     

围压下泥岩断裂韧性测试与解释方法

根据围压条件下的断裂力学理论 ,采用双翼裂纹厚壁圆筒 ,对泥岩进行了不同围压和不同泥质含量条件下的人工岩样断裂韧性测试。建立了有限元方法解释断裂韧性的数值模型。在进行大量实验测试的基础上 ,通过回归分析表明 ,断裂韧性与围压、泥质含量有较好的线性统计关系。解决了水力压裂设计中断裂韧性参数的准确获取问题 ,有利于提高压裂设计、预测的精度     

Self-similar solution for deep-penetrating hydraulic fracture propagation

The propagation of a vertical hydraulic fracture of a constant height driven by a viscous fluid injected into a crack under constant pressure, is considered. The fracture is assumed to be rectangular, symmetric with respect to the well, and highly elongated in the horizontal direction (the Perkins and Kern model). The fracturing fluid viscosity is assumed to be different from the stratum saturating fluid viscosity, and the stratum fluid displacement by a fracturing fluid in a porous medium is assumed to be piston-like. The compressibility of the fracturing fluid is neglected. The stratum fluid motion is governed by the equation of transient seepage flow through a porous medium.A self-similar solution to the problem is constructed under the assumption of the quasi-steady character of the fracturing fluid flow in a crack and in a stratum and of a locally one-dimensional character of fluid-loss through the crack surfaces. Crack propagation under a constant injection pressure is characterized by a variation of the crack sizel in timet according to the lawl(t)=l _o (1+At)^1/4, where the constantA is the eigenvalue of the problem. In this case, the crack volume isVl, the seepage volume of fracturing fluidV _f l ³, and the flow rate of a fluid injected into a crack isQ ₀l ^–1.     

水力劈裂问题的态型近场动力学建模

将态型近场动力学理论引入水力劈裂问题的模拟。构建了能反映岩土类材料准脆性断裂特征的态型近场动力学本构模型,并在物质点间相互作用力模型中加入等效水压力项,以实现在新生裂纹面上跟踪施加水压力。同时,考虑裂纹面间的接触,引入物质点间的短程排斥力作用,并设计了相应的接触算法。通过自编程序将模型和算法应用于含初始裂纹、不含初始裂纹以及含坝基软弱结构面的混凝土重力坝在高水头作用下的水力劈裂过程模拟,并与扩展有限元等模拟结果对比,验证了本文模型和算法的可行性和准确性。     

Hydraulic fracture crack propagation driven by a non-Newtonian fluid

The problem of hydraulic fracture crack propagation in a porous medium is considered. The fracture is driven by an incompressible viscous fluid with a power-law rheology of the pseudoplastic type. The fluid seepage is described by an equation generalizing the Darcy law in the hydraulic approximation. It is shown that the system of governing equations has a power-law self-similar solution, whereas, in the limiting cases of low and high fluid saturation in the porous medium, there are some families of power-law or exponential self-similar solutions. The complete self-similar solution is constructed. The effect of the nonlinear rheology of the fracturing fluid on the behavior of the solution is studied. The problem is solved analytically for an arbitrary boundary condition at the crack inlet when the viscous stresses in the non-Newtonian fluid are close to a constant.     

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.