基于XFEM-MBEM的嵌入式离散裂缝模型流固耦合数值模拟方法

离散缝网的表征与模拟是目前国内外研究的热点. 在非常规油气开发过程中, 由于地应力场的存在会对裂缝的流动属性产生显著影响, 若将裂缝视为静态对象, 与矿场数据会出现极大偏差, 因此要基于动态裂缝做更深入的研究. 本文针对致密油藏应力场?渗流场耦合力学问题, 提出了一种高效的混合数值离散化方法, 其中采用扩展有限元法 (XFEM) 求解岩石的弹性形变, 采用了混合边界元法 (MBEM) 精确计算基岩与裂缝间的非稳态窜流, 这两种数值格式是完全耦合的, 并对整体计算格式的时间项进行了全隐式求解, 可准确表征致密油藏开采过程中的裂缝变形及流体流动机理. 此外, 本文采用了嵌入式离散裂缝前处理算法显式表征大尺度水力压裂缝, 并考虑了支撑剂的作用; 采用了双孔有效应力原理和双重介质隐式裂缝表征方法, 可捕捉基质与小尺度天然裂缝的动态信息; 由此, 本文所提出的混合模型综合表征了基质?天然裂缝?水力压裂缝共同组成的致密油藏复杂渗流环境, 并通过几个实例论证了模型的准确性, 研究表明: 对致密油藏压裂水平井进行产能评价时, 应力场所引起渗流参数的改变及裂缝开度降低的影响不可忽略. 本文研究可为非常规油气资源的开发提供理论指导.      

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.     

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．     

Experimental Study of Fracture Permeability for Stimulated Reservoir Volume (SRV) in Shale Formation

“Stimulated reservoir volume”(SRV) makes shale gas production economic through new completion techniques including horizontal wells and multiple hydraulic fractures. However, the mechanism behind these treatments that provide sufficient permeability is not well understood. The effects of different stimulation treatments need to be further explored. To understand the effects of fracture surface roughness, fracture registration, confining pressure, proppant type and distribution mode, fiber and acidizing treatment on fracture permeability, a series of laboratory permeability experiments were performed on fractured cores from shale formation of Shengli Oilfield. The results of this study demonstrate that sedimentary bedding of shale has important influence on matrix permeability. At 35 MPa confining pressure, the permeability of aligned fracture (unpropped and without fracture offset) can increase about 1–3 orders of magnitude over shale matrix. The permeability of displaced fracture can increase about 1–2 orders of magnitude over the aligned fracture. The permeability of fracture propped with proppant can increase about 2–4 orders of magnitude over unpropped fracture. The greater the fracture surface roughness, the higher the permeability. The increasing degree of displaced fracture permeability is not proportional to the amount of fracture offset. In the microfracture of shale, the effect of ceramic proppant is still better than that of quartz sand, and the permeability of a centralized fairway distribution of proppant is about 1.2 times better than an even monolayer distribution of proppant. Under high pressure, proppant is easy to cause the break of fracture faces of brittle shale, and increase local fracture permeability to some extent. However, quartz sand are more easily broken to embed and block microcracks just made, which results in fracture permeability lower than that of ceramic proppant. At the same time, the argillation phenomenon is easy to happen on propped fracture faces of shale, which is one of the main factors that leads to a substantial decline in fracture permeability. The permeability of displaced fracture propped with proppant is greater than that of aligned fracture propped with proppant. Because of added fiber presence, the permeability of microfractures presented in SRV is greatly reduced. The pressure dependence of aligned fractures in shale obeys Walsh’s theory, but the pressure dependence of propped and displaced fractures in shale obeys Walsh’s law over a limited range of pressures. Deviations reflect proppant seating, proppant embedding and breaking. For shale formation with the high carbonate content, acidizing treatment should be carefully implemented. Experimental results may provide more valuable information for effective design of hydraulic fracturing in shale reservoir.     

Initialization of phase-field fracture propagation in porous media using probability maps of fracture networks.

It is well known in the geophysical community that surface deflection information/micro-seismic data are considered to be one of the best diagnostics for revealing the volume of rock fracture. However, the in-exactness of the data representing the deformation induced to calibrate and represent complex fracture networks created and connected during hydraulic fracturing presents a challenge. In this paper, we propose a technique that implements a phase-field approach to propagate fractures and their interaction with existing fracture networks using surface deflection data. The latter one provides a probability map of fractures in a heterogeneous reservoir. These data are used to initialize both the location of the fractures and the phase-field function. In addition, this approach has the potential for optimizing well placement/spacing for fluid-filled fracture propagation for oil and gas production and or carbon sequestration and utilization. Using prototype models based on realistic field data, we demonstrate the effects of interactions between existing and propagating fractures in terms of several numerical simulations with different probability thresholds, locations, and numbers of fractures. Our results indicate that propagating fractures interact in a complex manner with the existing fracture network. The modeled propagation of hydraulic fractures is sensitive to the threshold employed within the phase-field approach for delineating fractures.     

Simulation of proppant transport at intersection of hydraulic fracture and natural fracture of wellbores using CFD-DEM

Proppants transport is an advanced technique to improve the hydraulic fracture phenomenon, in order to promote the versatility of gas/oil reservoirs. A numerical simulation of proppants transport at both hydraulic fracture (HF) and natural fracture (NF) intersection is performed to provide a better understanding of key factors which cause, or contribute to proppants transport in HF–NF intersection. Computational fluid dynamics (CFD) in association with discrete element method (DEM) is used to model the complex interactions between proppant particles, host fluid medium and fractured walls. The effect of non-spherical geometry of particles is considered in this model, using the multi-sphere method. All interaction forces between fluid flow and particles are considered in the computational model. Moreover, the interactions of particle–particle and particle–wall are taken into account via Hertz–Mindlin model. The results of the CFD-DEM simulations are compared to the experimental data. It is found that the CFD-DEM simulation is capable of predicting proppant transport and deposition quality at intersections which are in agreement with experimental data. The results indicate that the HF–NF intersection type, fluid velocity and NF aperture affect the quality of blockage occurrence, presenting a new index, called the blockage coefficient which indicates the severity of the blockage.     

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基于射孔完井水平裂缝中支撑剂均匀充填，考虑充填层强度、油层和流体 物性以及裂缝的渗流条件，研究了地应力及渗流引起的附加应力联合作用的支撑剂充填层渗 流模型和力学模型，并进行现场应用. 研究表明，所建立的模型对压裂油井支撑剂回采出砂 状况分析具有较高的符合率，油井总体符合率、不出砂井符合率和出砂井符合率分 别为84.66\%, 84.18\%和88.10\%, 为大庆油田压裂油井防砂措施实施方案制定提 供了决策支持，有利于提高措施有效率.     

考虑多重运移机制耦合页岩气藏压裂水平井数值模拟

页岩作为典型的微纳尺度多孔介质,游离气与吸附气共存,传统的达西定律已无法准确描述气体在页岩微纳尺度的运移规律.基于双重介质模型和离散裂缝模型构建页岩气藏分段压裂水平井模型,其中基岩中考虑气体的黏性流、Knudsen 扩散以及气体在基岩孔隙表面的吸附解吸,吸附采用Langmuir等温吸附方程;裂缝中考虑黏性流和Knudsen扩散,在此基础上建立基岩-裂缝双重介质压裂水平井数学模型并采用有限元方法对模型进行求解.结果表明,基岩固有渗透率越小,表面扩散和Knudsen扩散的影响越大,反之则越小;人工裂缝的性质包括条数、开度、半长以及间距,主要影响压裂水平井生产早期,随着人工裂缝参数值的增加,压裂水平井产能增加,累产气量也越大.其次,页岩气藏压裂诱导缝和天然裂缝的发育程度对页岩气藏的产能有很大的影响,水平井周围只有人工裂缝,周围天然裂缝不开启或不发育时,页岩气藏的水平井的产能较低.      

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。     

Experimental Method to Simulate Coal Fines Migration and Coal Fines Aggregation Prevention in the Hydraulic Fracture

A simple and effective experimental method is proposed to simulate coal fines migration through the proppant pack; such migration inevitably occurs during the process of fracturing fluid flowback or dewatering and gas production in coalbed methane (CBM) reservoirs. The damage to conductivity caused by coal fines migration in the pack and the factors affecting such migration are analyzed. A dispersion agent of coal fines applicable to hydraulic fracturing in CBM is optimized, consequently solving the problem of coal fines aggregation and retention in the proppant pack. Discharging coal fines with water or water-based fracturing fluid from the proppant pack can be difficult because of the adsorption and hydrophobicity of coal fines. Thus, coal fines are likely to aggregate and be retained in the proppant pack, thereby resulting in pore throat plugging, which causes serious damage to fracture conductivity. Two percent coal fines can reduce propped fracture conductivity by 24.4 %. The mobility and retention of coal fines in the proppant pack are affected by proppant size, proppant type, flowback rate, and coal fines property. When flowback rate exceeds the critical value, coal fines can be discharged from the pack, consequently reducing damage to propped fracture conductivity. More importantly, the steady discharging of coal fines requires steady dewatering and gas production to avoid flow shock, which causes pressure disturbance to drive coal fines in a remote formation. The optimized dispersant FSJ-02 employed in this paper can effectively change the wettability and surface potential of coal fines to improve their suspension and dispersion in water-based fracturing fluid. The recovery rate of coal fines increased by 31.5 %, whereas conductivity increased by 13.3 %.     

Hydraulic conductivity of rock fractures

The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the cubic law is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.     

Evaluation and Optimization of New Nanocomposite Fiber for Fracturing Technology Based on a New Equipment

The fiber has great advantages in hydraulic fracturing when considering fluid leak off and flow friction, proppant transportation and fracture damage, proppant or sand production, and fracture geometry. However, some drawbacks, such as poor chemical stability, mechanical properties, heat denaturation, and dispersivity, always emerge in oilfield cases. Accordingly, a new type of nanocomposite fiber is used to overcome these shortcomings in our research. Generally, fiber??s conventional performance, dispersivity and proppant suspension capability can be evaluated easily, but reliable evaluation and optimization of fiber applications could not be obtained by normal indoor experimental instruments. So we developed the ??fracture filling model??, a specially designed instrument to evaluate the performances of fracture conductivity, proppant backflow, and sand control. All the performances of the nanocomposite fiber were evaluated, and the length and concentration of the fiber were optimized. The results have great influences on both theoretical study and field treatments of the new nanocomposite fiber.     

页岩气和致密砂岩气藏微裂缝气体传输特性

页岩气和致密砂岩气藏发育微裂缝,其开度多在纳米级和微米级尺度且变化大,因此微裂缝气体传输机理异常复杂.本文基于滑脱流动和努森扩散模型,分别以分子之间碰撞频率和分子与壁面碰撞频率占总碰撞频率的比值作为滑脱流动和努森扩散的权重系数,耦合这两种传输机理,建立了微裂缝气体传输模型. 该模型考虑微裂缝形状和尺度对气体传输的影响. 模型可靠性用分子模拟数据验证.结果表明:(1)模型能够合理描述微裂缝中所有气体传输机理,包括连续流动,滑脱流动和过渡流动;(2)模型能够描述不同开发阶段,微裂缝中各气体传输机理对传输贡献的逐渐变化过程;(3)微裂缝形状和尺度影响气体传输,相同开度且宽度越大的微裂缝,气体传输能力越强,且在高压和微裂缝大开度的情况下表现更明显.      

New Correlative Models to Improve Prediction of Fracture Permeability and Inertial Resistance Coefficient

Presence of fracture roughness and occurrence of nonlinear flow complicate fluid flow through rock fractures. This paper presents a qualitative and quantitative study on the effects of fracture wall surface roughness on flow behavior using direct flow simulation on artificial fractures. Previous studies have highlighted the importance of roughness on linear and nonlinear flow through rock fractures. Therefore, considering fracture roughness to propose models for the linear and nonlinear flow parameters seems to be necessary. In the current report, lattice Boltzmann method is used to numerically simulate fluid flow through different fracture realizations. Flow simulations are conducted over a wide range of pressure gradients through each fracture. It is observed that creeping flow at lower pressure gradients can be described using Darcy’s law, while transition to inertial flow occurs at higher pressure gradients. By detecting the onset of inertial flow and regression analysis on the simulation results with Forchheimer equation, inertial resistance coefficients are determined for each fracture. Fracture permeability values are also determined from Darcy flow as well. According to simulation results through different fractures, two parametric expressions are proposed for permeability and inertial resistance coefficient. The proposed models are validated using 3D numerical simulations and experimental results. The results obtained from these two proposed models are further compared with those obtained from the conventional models. The calculated average absolute relative errors and correlation coefficients indicate that the proposed models, despite their simplicity, present acceptable outcomes; the models are also more accurate compared to the available methods in the literature.     

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.     

海陆过渡相页岩气藏不稳定渗流数学模型

海陆过渡相页岩常与煤层和砂岩呈互层状产出, 储层连续性较差、横向变化快、非均质性强, 水力压裂技术是其获得经济产量的关键手段. 然而, 目前缺乏有效的海陆过渡相页岩气藏不稳定渗流数学模型, 对其渗流特征分析及储层参数评价不利. 针对这一问题, 首先建立海陆过渡相页岩气藏压裂直井渗流数学模型, 其次采用径向复合模型来反映强非均质性, 采用Langmuir等温吸附方程来描述气体的解吸和吸附, 分别采用双重孔隙模型和边界元模型模拟天然裂缝和水力裂缝, 建立并求解径向非均质的页岩气藏压裂直井不稳定渗流数学模型, 分析海陆过渡相页岩气藏不稳定渗流特征, 并进行数值模拟验证和模型分析应用. 分析结果表明, 海陆过渡相页岩气藏不稳定渗流特征包括流动早期阶段、双线性流、线性流、内区径向流、页岩气解吸、内外过渡段、外区径向流及边界控制阶段. 将本模型应用在海陆过渡相页岩气试井过程中, 实际资料拟合效果较好, 其研究成果可为同类页岩气藏的压裂评价提供一些理论支撑, 具有较好应用前景.      

单裂缝中携砂液流动规律研究

裂缝中携砂液流动是一种固液两相流,携砂液的运移与支撑剂的铺置是水力压裂裂缝保持导流能力的关键.本文基于FLUENT流体计算软件,采用双流体模型,将颗粒看作拟流体,携砂液按照牛顿流体处理,分析了支撑剂体积分数α_s、阿基米德数Ar、颗粒雷诺数Re以及裂缝入口边界对流动规律的影响.研究结果表明:携砂液在裂缝中的流动过程中,发展成为支撑剂体积分数不同的四个区域,包括砂堤区、颗粒悬浮区、颗粒滚流区和无砂区;支撑剂的沉降程度随着支撑剂体积分数和阿基米德数的增加而增加,而随着雷诺数增加而降低;入口为网眼型时,进入裂缝后过流面积的增加导致流速突降,使得支撑剂更容易在入口处产生堆积,在同一入口流速下,较均匀入口的工况铺砂高度大.     

Non-Fickian Transport in Transparent Replicas of Rough-Walled Rock Fractures

We present an experimental investigation and modeling analysis of tracer transport in two transparent fracture replicas. The original fractures used in this work are a Vosges sandstone sample with nominal dimensions approximately 26 cm long and 15 cm wide, and a granite sample with nominal dimensions approximately 33 cm long and 15.5 cm wide. The aperture map and physical characteristics of the fractures reveal that the aperture map of the granite fracture has a higher spatial variability than the Vosges sandstone one. A conservative methylene blue aqueous solution was injected uniformly along the fracture inlets, and exited through free outlet boundaries. A series of images was recorded at known time intervals during each experiment. Breakthrough curves were subsequently determined at the fracture outlets and at different distances, using an image processing based on the attenuation law of Beer–Lambert. These curves were then interpreted using a stratified medium model that incorporates a permeability distribution to account for the fracture heterogeneity, and a continuous time random walk (CTRW) model, as well as the classical advection–dispersion equation (ADE). The stratified model provides generally satisfactory matches to the data, while the CTRW model captures the full evolution of the long tailing displayed by the breakthrough curves. The transport behavior is found to be non-Fickian, so that the ADE is not applicable. In both stratified and CTRW models, parameter values related to the aperture field spatial variability indicate that the granite fracture is more heterogeneous than the Vosges sandstone fracture.     

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。     

Effects of the Correlation Length on the Hydraulic Parameters of a Fracture Network

We consider the influences of correlation length and aperture variability on the REV, the equivalent permeability of a fracture network, and the uncertainty in the equivalent permeability using a two-dimensional orthogonal bond percolation model. The percolation threshold, correlation length, effective conductivity, and coefficient of variation of the effective conductivity are investigated over statistically representative multiple realizations with Monte Carlo simulations in 2D fracture networks that have log-normally distributed individual fracture permeabilities. We show that although the aperture variability is large, the REV and the correlation length are similar near the percolation threshold. In contrast, when the fracture density is much larger than the percolation threshold they diverge as the aperture variability increases. We characterize the effects of correlation length and aperture variability on effective conductivity with a simple function. From the coefficient of variation analysis, the correlation length can be a criterion for evaluating which conceptual model is appropriate for describing the flow system for a given fracture network when aperture variability is sufficiently small. However, discrete fracture network models are recommended for flow simulation models because of the difficulty of REV estimation and the uncertainty in equivalent hydraulic parameters when aperture variability is large.