Investigation of hydraulic fracturing operation and fracture propagation simulation in reservoir rock

For many decades most oil wells in Iran have produced using their natural flow potential and haven’t needed to be fractured. As time goes by, the reservoir pressure depletes and the need for hydraulic fracturing as a stimulation practice arises. Nonetheless there is no record of successful hydraulic fracturing in Iran.

The Bangestan reservoir with a suitable amount of oil in place and good rock reservoirs, has been selected for the present research work. In this work, the in situ stress profile was calculated by using the available petrophysical data. This is achieved by using poroelastic theory for the stresses, and the Mohr–Coulomb criterion to predict failure. The model leads to easily computed expressions for calculating the pressure required to maintain hydraulic fracturing. Then the appropriate depth for treatment was determined. The results indicate that Ilam and Sarvak formations could be good candidates for hydraulic fracturing. Then, for two layers, a hydraulic fracture was designed and the production was predicted and the Net Present Value (NPV) resulting from the fracture of both layers was investigated.     

水力压裂扩展特性的数值模拟研究

采用ABAQUS建立了水力压裂计算模型,模拟了地应力、岩石力学特性、压裂液流体特性等各种复杂因素对水力压裂扩展的影响。通过计算分析得到一些有益结论：（1）在注入压力一定的情况下起裂压力与最小水平地应力、临界应力、初始孔隙压力成正比,而与压裂液黏度、最大水平地应力、弹性模量无关;（2）裂缝扩展长度和最大缝宽与最小水平地应力、初始孔隙压力、弹性模量成反比,而与最大水平地应力无关;（3）水力压裂作业中,缝长的扩展过程可分为无扩展阶段、快速扩展阶段、稳定扩展阶段以及缓慢扩展阶段等4个阶段。研究结论对于水力压裂作业优化具有参考价值。     

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。     

煤岩水力压裂起裂压力和裂缝扩展机制实验研究

为了研究煤岩水力压裂的起裂压力和水力压裂裂缝扩展规律,采用型煤试样,利用自主研发的水力压裂实验系统,参照现场压裂施工制定了“施加三向应力-顶部注水”的煤岩水力压裂物理模拟实验方案并开展了水力压裂实验,分析了不同条件下泵注压力和水力压裂裂缝。实验结果表明：压裂液泵注排量越大,起裂压力越大。三向应力满足最大水平主应力σ_H > 垂向应力σ_v > 最小水平主应力σ_h,水力压裂裂缝沿着垂直于σ_h的方向扩展。σ_v和σ_h一定,随着σ_H的增大,煤岩起裂压力先增大后减小,水力压裂裂缝扩展路径越平直。当σ_H远大于σ_v和σ_h时,水力压裂裂缝扩展路径越复杂,分叉缝角度越大。研究结果可为煤岩水力压裂理论的完善提供一定的参考和借鉴。     

水力劈裂对岩体中自然裂纹的影响研究

建立了求解自然裂纹和水力裂纹扩展的扩展有限元法,对裂纹附近区域的节点采用广义形函数,并采用线增函数消除混合单元,以提高裂纹附近的精度。引入水力劈裂的非耦合模型,即假设裂纹中的水压力为均布力;用砂浆法（线段-线段接触法）结合增广型拉格朗日乘子法处理受压裂纹段的接触条件。并通过算例分析了以下内容：计算了受压裂纹和裂纹面分布均布水压力的水力裂纹的应力强度因子,并与解析解进行了比较,结果表明,提出的方法具有很高的精度;模拟了水力裂纹对自然裂纹面的影响,并分析了自然裂纹面上的接触力和接触状态。     

水力压裂扩展的流固耦合数值模拟研究

以临界应力作为裂纹扩展准则并采用流固耦合模型模拟了水力压裂扩展问题,推导出裂缝面内的压降方程表达式,并编写出用户子程序嵌入到ABAQUS中。建立的计算模型能够模拟地应力、岩石力学特性、压裂液流体特性等各种复杂因素对水力压裂扩展的影响。通过计算分析得到一些有益结论,采用有限元软件ABAQUS求解可渗透油藏水力压裂扩展过程问题是可行的;提出了临界宽度的概念,它可以作为判断裂缝是作为起渗透作用的孔隙通道还是作为起导流作用的裂缝的依据;其结论对于压裂作业优化具有参考价值。     

Anisotropic porothermoelastic solution and hydro‐thermal effects on fracture width in hydraulic fracturing

In this study, the effects of the temperature difference between hydraulic fracturing fluid and rock formation on the time‐dependent evolution of fracture width were investigated using a newly derived one‐dimensional anisotropic porothermoelastic analytical solution. The solution is shown to correctly reproduce existing solutions for special cases and corrections for an earlier publication are provided. An analysis of time‐dependent fracture width evolution using Woodford Shale data was also presented. It was found that when the fracturing fluid has the same temperature as the shale formation, the fracture gradually closes back after the initial opening due to the invasion of the fracturing fluid. Practically, in this scenario, proppants should be pumped into the fracture as soon as possible to obtain maximum fracture conductivity. On the other hand, with a fracturing fluid 60 °C colder than the formation, the thermal contraction of the rock dominates the fracture aperture evolution, resulting in a fracture aperture approximately 70% larger than that produced by the hotter fracturing fluid. Consequently, in this case, it is beneficial to delay proppant placement to take advantage of the widening fractures. Finally, it was found that the fracture aperture is directly controlled by the spacing of natural fractures. Therefore, the presence of natural fractures in the shale formation and their spacing influence not only the type of hydraulic fractures created but also what kind and size of proppants should be used to keep them open. Copyright © 2013 John Wiley & Sons, Ltd.     

煤岩水力压裂裂缝扩展形态试验研究

通过室内水力压裂物理模拟试验系统,对大尺寸原煤进行了水力压裂模拟试验,根据水力裂缝的空间展布形态分析了煤岩储层水力裂缝的延伸规律,揭示了网状裂缝的形成机制。结果表明：水力裂缝易在弱层理处分叉和转向,发育的层理和裂缝系统等结构面为压裂形成裂缝网络提供了前提条件。泵压曲线呈现出的频繁波动是煤岩内产生网状裂缝的一个显著特征。水力裂缝的起裂与延伸有4种基本模式,裂缝网络的形成多为这4种基本模式的组合。地应力差异系数和泵注排量对煤层水力裂缝形态有较大影响。较小的地应力差异系数更利于网状裂缝的形成;较高的压裂液排量易形成相对简单的裂缝形态,导致压裂改造效果较差。该试验方法和试验结果可为现场水力压裂参数设计和优化提供参考和依据。     

基于扩展有限元分析的页岩水力压裂裂缝扩展规律探究

水力压裂是开采地下页岩气资源的有效技术手段,探究页岩水力压裂裂缝的扩展规律,可为页岩气的高效开采提供科学的指导依据。通过运用大型有限元软件ABAQUS中的扩展有限元模块,针对不同地应力差工况条件下均质页岩中初始裂缝的位置、方位角、数量和含层理页岩中层理的构造方向、内部倾角、岩性对水力裂缝扩展的影响进行探究。结果表明：对于垂向扩展的水力裂缝,水平主应力增大使裂缝更不易扩展,裂缝扩展长度减小、起裂压力增大;在注液体积流量相同时,向初始裂缝两端同时起裂所形成的水力裂缝长度大于仅向一侧起裂;当初始裂缝处于页岩中部且呈45°方向时,裂缝会向最大水平主应力方向偏转,且偏转程度随最大水平主应力的增大而增大;分时多簇压裂时,裂缝间的扩展会相互干扰,且会较大地影响裂缝扩展的形态和起裂压力,但对裂缝注液点裂缝宽度的影响较小;对于含水平和竖直构造层理的页岩,改变层理内部倾角,水力裂缝会出现不同程度偏转,且其偏转程度随着层理内部倾角的增大而减小;对于含45°方向构造层理的页岩,水力裂缝在层理分别为砂岩、煤岩和泥岩中的偏转程度依次增大,且裂缝偏移比随着最大水平主应力的增大而增大。     

Semianalytical modeling on 3D stress redistribution during hydraulic fracturing stimulation and its effects on natural fracture reactivation

The hydraulic fracturing technique has been widely applied in many fields, such as the enhanced geothermal systems (EGS), the improvement of injection rates for geologic sequestration of CO₂, and for the stimulations of oil and gas reservoirs. The key points for the success of hydraulic fracturing operations in unconventional resources are to accurately estimate the redistribution of pore pressure and stresses around the induced fracture and predict the reactivations of preexisting natural fractures. The pore pressure and stress regime around hydraulic fracture are affected by poroelastic and thermoelastic phenomena as well as by fracture opening compression. In this work, a comprehensive semi-analytical model is used to estimate the stress and pore pressure distribution around an injection-induced fracture from a single well in an infinite reservoir. The model allows the leak-off distribution in the formation to be three-dimensional with the pressure transient moving ellipsoidically outward into the reservoir from the fracture surface. The pore pressure and the stress changes in three dimensions at any point around the fracture caused by poroelasticity, thermoelasticity, and fracture compression are investigated. With Mohr-Coulomb failure criterion, we calculate the natural fracture reactivations in the reservoir. Then, two case studies of constant water injection into a hydraulic fracture are presented. This work is of interest in the interpretation of microseismicity in hydraulic fracturing and in the estimation of the fracture spacing for hydraulic fracturing operations. In addition, the results from this study can be very helpful for the selection of stimulated wells and further design of the refracturing operations.     

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.     

A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation

A three-phase hydro-mechanical model for hydraulic fracturing is proposed. Three phases include: porous solid, fracturing fluid and host fluid. Discontinuity is handled using extended finite element method (XFEM) while cohesive crack model is used as fracturing criterion. Flow through fracture is defined as one-dimensional laminar flow, and flow through porous medium (host reservoir) is defined as two-dimensional Darcy flow. Coupling between two fluids in each space, fracture and pore, is captured through capillary pressure–saturation relationship, while the identical fluids in fracture and pore are coupled through a so-called leak-off mass transfer term. Coupling between fluids and deformation is captured through compatibility of volumetric strain of fluids within fracture and pore, and volumetric strain of the matrix. Spatial and temporal discretisation is achieved using the standard Galerkin method and the finite difference technique, respectively. The model is verified against analytical solutions available from literature. The leaking of fracturing fluid into the medium and suction of porous fluid into the fracture around the tip, are investigated. Sensitivity analyses are carried out for cases with slow and fast injection rates. It is shown that the results by single-phase flow may underestimate the leak-off.     

Rheological behaviour effect of non-newtonian fluids on steady and unsteady flow through a porous medium

This paper describes the flow behaviour of certain non-Newtonian fluids through a porous medium. A generalized Bingham rheological model of power-law in the presence of a yield stress has been considered. Several problems of fluid mechanics, which appear currently in oil reservoir engineering, have been investigated and the rheological behaviour effect has been emphasized. The short time solutions have been formulated in terms of a moving boundary problem. The approximate solutions in a closed formwere obtained by means of the integral method. Several dimensionless groups have been found to be relevant in evaluating the rheological effect on the steady and unsteady and unsteady flow behaviour. The deviation from Newtonian flow behaviour has been illustrated using several numerical examples.     

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.     

Geometric nature of hydraulic fracture propagation in naturally-fractured reservoirs

The geometry of hydraulic fracture propagation in the absence and presence of natural fractures in reservoirs was studied. The results revealed a marked influence of natural fractures on the symmetry of fracture propagation observed for rock free of natural fractures. Natural fracture properties such as stiffness and approaching angle, and the distance from wellbore to the natural fracture were found to influence the hydraulic fracture geometry. Furthermore, the location of the wellbore with respect to the natural fractures in a reservoir having a system of natural fractures displayed a significant influence on the resulting geometry of hydraulic fracture propagation.     

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。      

The use of the fracture reopening pressure in hydraulic fracturing stress measurements

Summary Practitioners of the hydraulic fracture stress measurement technique commonly estimate the hydraulic fracture tensile strength as the difference between the initial formation breakdown pressure and the fracture reopening pressure. This method, first suggested by Bredehoeft et al. (1976), was developed with the assumption that the stress state in the cracked formation is identical to the stress state in the uncracked formation. In this paper, a relationship for the fracture reopening pressure based on Linear Elastic Fracture Mechanics is developed that takes the hydraulically induced fracture into account. Situations in which the Bredehoeft technique can be appropriately applied are presented.     

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     

薄互层水力裂缝垂向扩展控制因素试验研究

新疆油田某地区油藏的储隔层岩性组合复杂,呈现突出的薄互层产状特征,研究合、分压判断条件有利于提高压裂效率,增强储层动用程度与压后改造效果。水力裂缝在薄互层中的穿层与裂缝扩展行为受薄互层地质特征与压裂施工参数的影响。基于此,开展了薄互层物理模型压裂试验,研究界面胶结、岩层分布、岩层厚度、压裂液黏度与注液排量对薄互层中水力裂缝垂向扩展的影响分析。试验结果表明：薄互层的地层特征界面胶结与岩层分布是水力裂缝垂向扩展的主要控制因素,界面胶结强度对裂缝垂向扩展行为的影响强于岩层分布;由于弱胶结界面的存在,水力裂缝垂向扩展穿层时可发生方向偏转,抑制裂缝垂向扩展;提高压裂液黏度与注液排量有利于薄互层中水力裂缝的穿层垂向扩展。     

Numerical simulation of unsteady fluid flow and propagation of a circular hydraulic fracture

A computational procedure is developed for solving the problem of a circular hydraulic fracture propagating under the action of frac-0fluid being pumped in at a central wellbore. The crack is modelled as continuous distributions of ring dislocations and the resulting elasticity singular integral equation is solved numerically. The fluid flow equations are approximated by local and global interpolation finite difference schemes. The coupling between elasticity and fluid flow is handled numerically, by, two different algorithms: one iterates on crack tip velocity whereas the other varies the time step size until it agrees with the chosen increment in crack length. Sample results are given; it is found that the velocity algorithm is computationally more, efficient and more stable. The model allows detailed tracing of pressure distribution and fluid flow in the fracture, even under complex conditions of cyclic injection and fluid rheology. It may serve as a stand-alone model of (horizontal) hydrafracs–especially at shallow depths–or it may be used as a reference frame to test the various numerical formulation/algorithms required for the ongoing development of a fully 3-D hydrafrac simulator.