含裂隙饱和多孔介质流-固耦合的扩展有限元分析

基于应力平衡方程、渗流连续性方程以及改进的Biot有效应力原理,建立了含裂隙可变形饱和多孔介质流-固全耦合问题的控制方程。流体在介质和裂隙中的流动均满足达西定律,得到的非线性全耦合方程不仅反映多孔介质内部物理量的耦合效应,还考虑介质与裂隙之间的耦合作用。扩展有限元法在处理含裂隙问题时具有独特的优势,采用普通有限元和扩展有限元法构建了数值计算体系。在进行空间离散时,介质内部的位移和孔隙压力均采用普通的有限元进行离散;裂隙处的位移模式引入扩展有限元中的两类附加位移函数,以反映裂隙面的位移强不连续性和裂隙端部的应力奇异性;引入孔隙压力加强函数,以体现裂隙法向孔隙压力的弱不连续特征。使用向后差分格式进行时间离散。算例验证了该模型和算法的正确性和有效性,分析了裂隙的存在对流体流动的延迟作用、裂隙中张开位移及孔隙压力等物理量的分布情况,讨论了渗透率、外部流量的改变对计算结果的影响。     

流固耦合问题及研究进展

传统的渗流理论一般假设流体流动的多孔介质骨架是完全刚性的,即在孔隙流体压力变化过程中,固体骨架不产生任何弹性或塑性变形,这时可将渗流作为非耦合问题来研究。这种简化虽然可以得到问题的近似解,但存在许多缺陷,而且也不切合生产实际。比如:在油田开采过程中,孔隙流体压力会逐渐降低,将导致储层内有效应力的变化,使储层产生变形。近年来,流固耦合问题越来越受到人们的重视,这方面的研究涉及许多领域。该文介绍了有关工程涉及到的流固耦合问题,重点针对油、气开采问题,介绍了储层流固耦合渗流的特点及研究方法和理论进展,包括单相、多相流体渗流的流固耦合数学模型及有限元数值模型。      

孔隙气压对核废物地质处置热-流-固耦合影响的有限元分析

为考察孔隙气体压力对高放废物地质处置中的热-流-固耦合过程的影响,借用Leiws等建立的可变形孔隙介质中非等温空气流和水流模型,在其水连续性方程中加入了温度梯度引起的水分扩散项,研制出相应的热-水-气-应力耦合弹塑性二维有限元程序。针对一个假定的高放废物地质处置库模型,在相同的初始温度、孔隙水压力和岩体应力条件下,取3种缓冲层中的初始孔隙气体压力,通过数值模拟考察了处置库近场的主应力、饱和度、气和水的流速、温度和孔隙压力的分布与变化。结果显示,当缓冲层中的初始孔隙气压力较高时,其对围岩中应力影响较大。     

边坡大变形弹塑性有限元分析（I）：理论

本文采用以物理坐标变量的Ｕｐｄａｔｅｄ－Ｌａｇｒａｎｇｉａｎ描述方法,在考虑边坡非线性变形破坏的基础上,建立了边坡大变形破坏的弹塑性有限元模型,详细推导了有限元单元方程和数值分析公式,并考虑了边坡的初始应力和超孔隙不压力。     

不连续面在双重介质热-水-力三维耦合分析中的有限元数值实现

在建立双重介质热-水-力耦合微分控制方程的基础上,提出了裂隙岩体热-水-力耦合的三维力学模型,对不同介质分别建立以节点位移、水压力和温度为求解量的三维有限元格式,开发了双重介质热-水-力耦合分析的的三维有限元计算程序,在有限元数值分析中不连续面应力计算采用等厚度空间8节点节理单元进行离散,而不连续面渗流和热能计算时采用平面4节点等参单元进行离散,这样保证了不同介质之间的水量、热量交换和两类模型接触处节点水头、温度和位移相等。通过高温岩体地热开发算例,揭示了在热-水-力耦合作用下不连续面处于低应力区,其张开度随运行时间的延长呈非线性增加,非稳定渗流阶段不连续面显著地控制着渗流场的整体分布,它的水头远高于拟连续岩体介质的水头,而进入稳定渗流阶段不连续面的控渗作用不明显,由于高温岩体地热开发系统中存在大规模的热量补给,不连续面对岩体温度场分布的影响并不显著。     

边坡大变形弹塑性有限元分析[Ⅰ]: 理论

本文采用以物理坐标为变量的Ｕｐｄａｔｅｄ－Ｌａｇｒａｎｇｉａｎ描述方法,在考虑边坡非线性变形破坏的基础上,建立了边坡大变形破坏的弹塑性有限元模型,详细推导了有限单元方程和数值分析公式,并考虑了边坡的初始应力和超孔隙水压力。     

频域内饱和多孔介质的参数反演分析

基于Biot理论,假定固体颗粒和孔隙内流体均不可压缩,建立了以固体骨架位移表示的的控制方程.考虑单层饱和多孔介质在竖向简谐荷载作用下一维动力响应,通过理论推导获得了骨架位移、应力以及孔隙流体压力等物理量的解析表达式.基于饱和土的简谐动力模型试验数据,与所得到的理论解答相结合,将饱和多孔介质材料参数反演问题归结为非线性多峰函数的最优化问题.全局最优解的求解采用了遗传算法和模拟退火算法,并通过试验和数值算例验证了所得材料参数的正确性.     

广义平面应力条件下径向渗流的液固耦合

考虑了多孔介质渗透率随孔隙变化的特点,建立了基本方程;对于广义平面应力条件下的径向渗流问题,提出了解耦方法,并求出了耦合条件下的孔隙压力及介质应力、应变、位移的解析解。实例计算表明,耦合效应不容忽略。      

变形介质流固耦合渗流的数值模型及其应用

在地下流体的开采过程中,随着地下流体的不断采出,必然造成孔隙流体压力的逐渐降低,由此导致储层岩石骨架的有效应力增大,地层产生变形或压实,甚至造成地表沉陷.针对饱和土固结问题,利用可变形多孔介质中流体渗流的流固耦合有限元数值模型,对该问题进行了数值模拟.同时,对油井开采过程进行了模拟.      

电场-渗流场-应力场耦合的电渗固结数值分析

在非饱和土多孔介质力学理论的基础上,根据电荷守恒原理、质量守恒原理、应力平衡方程、达西定律以及欧姆定律,推导了考虑电场、渗流场以及应力场相互耦合作用的电渗固结理论方程。采用Galerkin加权余量法对电渗固结理论方程进行空间离散,得到其有限元计算列式,编制了相应的计算程序,对室内电渗模型试验进行了数值模拟。结果表明,数值模拟与试验结果基本吻合,表明该电渗固结理论方程能够定量预测电渗固结过程中土体的孔隙水压力和位移发展规律。     

温庄尾矿库堆坝模型试验及坝体稳定性分析

以温庄尾矿库为工程背景,通过室内堆坝模型试验,获得到了在坝体堆积过程中尾矿颗粒在库内沉积分布特征、浸润线的变化规律等基础资料。在此基础上,以多孔介质有效应力理论为依据,建立了多孔介质流-固耦合数学模型,利用有限元软件ABAQUS对该库尾矿坝的应力场与渗流场进行了分析,获得了坝体内的应力场及孔隙压力的分布规律,研究成果可为尾矿库的设计、施工和安全生产提供技术支撑。     

填埋气体运移渗流场-应力场耦合模型及数值仿真

基于流固耦合机制和多孔介质流体动力学理论,根据Landgem产气方程、气体状态方程,结合达西定律、有效应力原理,建立了渗流场-应力场耦合填埋气体运移模型。利用伽辽金方法对模型进行了离散,通过有限元方法对耦合作用下填埋气体压力分布规律进行了数值仿真分析,同时对垃圾填埋变形介质参数以及垃圾降解系数对填埋气体产气量影响进行了定量评价,表明耦合作用下抽气时孔隙结构发生改变,阻滞气体的运移,导致耦合作用较未考虑耦合作用的气体压力低。垃圾填埋气体的产气量小,对变形介质参数和降解系数的定量评价结果表明,垃圾填埋气体的产气量随着渗透系数和降解系数的增大而增加,因此耦合作用不能忽略。这不仅为准确控制气体的挥发与扩散以及气体资源的再利用提供可靠的理论依据,而且对于生态环境的保护和垃圾资源化利用具有重要的理论意义和实际应用价值。     

A fully coupled numerical modeling to investigate the role of rock thermo-mechanical properties on reservoir uplifting in steam assisted gravity drainage

One of the crucial consequences of steam assisted gravity drainage (SAGD) process is abnormal reservoir uplifting under thermal steam injection, which can significantly influence the reservoir rock deformation, specifically thin bed reservoirs and causes intensive failures and fractures into the cap rock formations. A thorough understanding of the influences of rock thermo-mechanical properties on reservoir uplifting plays an important role in preventing those aforementioned failures within design and optimization process in SAGD. In addition, coupling of reservoir porous medium and flowing of specific fluid with temperature as an additional degree of freedom with initial pore pressure and in-situ stress condition, are also very challenging parts of geomechanical coupled simulation which would be clearly explained. Thus, a fully coupled thermo-poro-elastic geomechanical model with finite element codes was performed in ABAQUS to investigate the role of rock thermo-mechanical parameters on reservoir vertical uplift during steam injection. It is clearly observed that, any increase in rock thermo-mechanical properties specifically rock’s thermal properties such as specific heat, thermal expansion, and formation’s thermal conductivity, have significant influences on reservoir uplift. So by coupling the temperature as an additional degree of freedom with the coupled pore-fluid stress and diffusion finite element model of SAGD process, the more realistic simulation will be conducted; hence, the errors related to not having heat as an additional degree of freedom will be diminished. In addition, Young’s modulus and specific heat are the rock thermo-mechanical parameters which have the maximum and minimum effects on the reservoir uplift, respectively.     

用流固耦合方法研究油藏压裂后应力应变和孔渗特性变化

油藏压裂后将引起地应力场发生变化，使岩石变形，导致孔隙度和渗透率变化，进而影响产量，为研究这一问题，作者建立了油藏压裂后流－固耦合渗流模型，考虑了以下因素：油藏岩石变形，地应力，孔隙度和渗透率变化，人工裂缝，流体渗流与岩石应变耦合，储藏渗流与裂缝渗流耦合，非达西效应等。较详细地给出了耦合方程及推导过程，控制方程包括的未知变量有压力，饱和度及位移，11个变量，和11个方程，用有限差分方法将流体渗流和岩石应变方程离散成主对角占优的七对角矩阵，可在修改已有三维二相渗流和三维固体力学程序的基础上，采用隐式迭代方法求解，示例分析表明，用此模型可以研究储层应力变变，孔隙度和渗透率随时间和空间变化规律，为开发方案制定，整体压裂设计，压后生产管理等方面提供定量分析技术。     

基于ABAQUS平台的水力裂缝扩展有限元模拟研究

随着扩展有限元理论的深入研究,利用扩展有限元方法模拟水力压裂具有了一定的可操作性。相比于常规有限元方法,XFEM方法具有计算结果精度高和计算量小的优点。但是,如何模拟射孔孔眼、如何模拟流体与岩石相互作用以及分析水力裂缝的扩展规律仍然是难题。以研究水力压裂裂缝扩展规律为目的,建立了岩石多孔介质应力平衡方程、流体渗流连续性方程和边界条件。通过有限元离散化方法对耦合方程矩阵进行处理。通过富集函数定义初始裂缝（射孔孔眼）,选择最大主应力及损伤变量D分别作为裂缝起裂和扩展判定准则,利用水平集方法模拟水力裂缝扩展过程。数值模拟结果显示：增加射孔方位角、压裂液排量和减小水平地应力差,起裂压力上升;黏度对起裂压力无明显影响。增加射孔方位角、压裂液排量、黏度和减小水平地应力差值有助于裂缝宽度的增加。增加水平地应力差值、压裂液排量和减小射孔方位角以及压裂液黏度有助于裂缝长度增加,反之亦然。基于ABAQUS的水力裂缝扩展有限元法可对不同井型和诸多储层物性参数及压裂施工参数进行分析,且裂缝形态逼真,裂缝面凹凸程度清晰,结果准确。此研究可作为一种简便有效研究水力压裂裂缝扩展规律的方法为油田水力压裂设计与施工提供参考与依据。     

Prediction and analysis of the stimulated reservoir volume for shale gas reservoirs based on rock failure mechanism

The ultra-low-permeability shale gas reservoir has a lot of well-developed natural fractures. It has been proven that hydraulic fracture growth pattern is usually a complex network fracture rather than conventional single planar fractures by micro-seismic monitoring, which can be explained as the shear and tensile failure of natural fractures or creation of new cracks due to the increase in reservoir pore pressure caused by fluid injection during the process of hydraulic fracturing. In order to simulate the network fracture growth, a mathematical model was established based on full tensor permeability, continuum method and fluid mass conservation equation. Firstly, the governing equation of fluid diffusivity based on permeability tensor was solved to obtain the reservoir pressure distribution. Then Mohr–Coulomb shear failure criterion and tensile failure criterion were used to decide whether the rock failed or not in any block on the basis of the calculated reservoir pressure. The grid-block permeability was modified according to the change of fracture aperture once any type of rock failure criterion was met within a grid block. Finally, the stimulated reservoir volume (SRV) zone was represented by an enhancement permeability zone. After calibrating the numerical solution of the model with the field micro-seismic information, a sensitivity study was performed to analyze the effects of some factors including initial reservoir pressure, injection fluid volume, natural fracture azimuth angle and horizontal stress difference on the SRV (shape, size, bandwidth and length). The results show that the SRV size increases with the increasing initial pore reservoir and injection fluid volume, but decreases with the increase in the horizontal principal stress difference and natural fracture azimuth angle. The SRV shape is always similar for different initial pore reservoir and injection fluid volume. The SRV is observed to become shorter in length and wider in bandwidth with the decrease in natural fracture azimuth angle and horizontal principal stress difference.     

重复压裂转向机制流-固耦合分析

重复压裂已成为油田老井挖潜、稳产增产的重要技术手段,而地应力转向机制与压裂时机选择一直是制约该技术增产效果的关键问题。对ABAQUS有限元软件平台进行了二次开发,考虑储层孔隙度和渗透性随岩石体积应变的动态演化,实现了流体压力变化与岩石物性参数的全面耦合,并分析了重复压裂转向机制。结果表明,地应力转向现象普遍存在,人工裂缝对地应力的影响范围有限,而孔隙压力变化是造成地应力转向的主要因素;随着生产的持续进行,地层压力下降变缓,岩石体积应变变化趋缓,导致渗透率下降趋于平稳,应力转向距离逐渐增大并最终趋稳;应力差越大、应力转向距离越小,越难形成重复压裂转向裂缝。其研究结果实现了流-固耦合作用下地应力转向的可视化描述,直观地模拟结果有利于指导重复压裂的应用实施。     

含天然气水合物沉积物分解过程的有限元模拟

温度和压力的变化会引起含天然气水合物沉积物的分解,其过程伴随着相态转换、孔隙水压力和气压力耗散、热传导、骨架变形等过程的相互耦合作用。基于多孔介质理论建立了描述含天然气水合物沉积物分解过程的数学模型,考虑了水合物分解产生的水、气流动、水合物相变和分解动力学过程、热传导、骨架变形等过程的耦合作用。基于有限元法,建立了模拟水合物分解过程的数值模型,并编制了计算机分析程序。通过对降压法和升温法开采过程的数值模拟,揭示了在水合物分解过程中沉积物储层的变形、压力、温度等因素的变化规律。结果表明：降压法和升温法都会导致储层变形以及产生超孔隙压力,但两种方法作用效果不同;同时,水合物分解过程包含渗流及热传导作用。     

Numerical simulation of carbon dioxide migration in a sandstone aquifer considering the fluid–solid coupling

Very limited investigations have been done on the numerical simulation of carbon dioxide (CO₂) migration in sandstone aquifers taking consideration of the interactions between fluid flow and rock stress. Based on the poroelasticity theory and multiphase flow theory, this study establishes a mathematical model to describe CO₂ migration, coupling the flow and stress fields. Both finite difference method (FDM) and finite element method (FEM) were used to discretize the mathematical model and generate a numerical model. A case study was carried out using the numerical model on the Jiangling sandstone aquifer in the Jianghan basin, China. The rock mechanics parameters of reservoir and overlying strata of Jiangling depression were obtained by triaxial tests. A two-dimensional model was then built to simulate carbon dioxide migration in the sandstone aquifer. The numerical simulation analyzes the carbon dioxide migration distribution rule with and without considering capillary pressure. Time-dependent migration of CO₂ in the sandstone aquifer was analyzed, and the result from the coupled model was compared with that from a traditional non-coupled model. The calculation result indicates a good consistency between the coupled model and the non-coupled model. At the injection point, the CO₂ saturation given by the coupled model is 15.39 % higher than that given by the non-coupled model; while the pore pressure given by the coupled model is 4.8 % lower than that given by the non-coupled model. Therefore, it is necessary to consider the coupling of flow and stress fields while simulating CO₂ migration for CO₂ disposal in sandstone aquifers. The result from the coupled model was also sensitized to several parameters including reservoir permeability, porosity, and CO₂ injection rate. Sensitivity analyses show that CO₂ saturation is increased non-linearly with CO₂ injection rate and decreased non-linearly with reservoir porosity. Pore pressure is decreased non-linearly with reservoir porosity and permeability, and increased non-linearly with CO₂ injection rate. When the capillary pressure was considered, the computed gas saturation of carbon dioxide was increased by 10.75 % and the pore pressure was reduced by 0.615 %.