煤层气在非饱和水流阶段的非定常渗流摄动解

煤层甲烷由煤层的割理裂隙系统流入生产井一般经历：单相水流、非饱和流和气、水两相饱和流三个阶段，在非饱和流阶段，储层压力降至临界解吸压力之后，储存在煤基质中的吸附气体少量被解吸出来形成互不连续的气泡并阻止水的流动，含气量尚未达到饱和程度。同时煤层甲烷运移包含渗流场、变形场和应力场的动态耦合过程。本文考虑渗流过程中水-气两相不溶混流体与固体耦合作用，建立了非饱和水流阶段非定常渗流问题的流固耦合数学模型，对该强非线性一维数学模型采用摄动法和积分变换法进行解析求解，并讨论了其压力动态特性，分析了压力随饱和度S及时间t变化的规律和气相及耦合作用的影响，这些研究对煤层气、石油和天然气的开采等地下工程领域具有一定的指导意义。     

The Constitute Law of Gas Seepage in Rock Fractures Undergoing Three-dimensional Stress

This paper is based on the research we have done in recent years of the constitute law of gas seepage in rock fractures. Both experiments and theoretical derivations will be discussed. The gases used in our experiments include methane and CO₂, both of which are highly adsorptive. The experiments were conducted mainly in coal fractures. The results reveal that the permeability coefficient of gas in rock fractures varies parabolically with respect to fracture pore pressure. When the pore pressure is below a certain value, the permeability coefficient decreases while the pore pressure increases. It is different from the water seepage law in fractures. Analysis shows that this abnormality is caused by adsorption. It is also concluded that the tangent deformation has the same effects as normal deformation on gas seepage law. The permeability of gas in fractures has a negative exponent relationship with both normal deformation and tangent deformation.     

煤层瓦斯流动的固－气耦合数学模型及数值解法的研究

本文根据煤层瓦斯流动时，固体变形与瓦斯流动的基本理论，提出了耦合数学模型，并证明该耦合数学模型解的存在性和光滑性，给出了这一非线性数学模型的数值解法。     

基于REV尺度格子Boltzmann方法的页岩气流动数值模拟

结合页岩扫描电镜图像,提出页岩气藏物理模型,采用表征单元体积(representative elementary volume,REV)尺度格子Boltzmann方法,考虑滑脱效应,模拟页岩气在页岩气藏中的流动.模拟结果表明,页岩气主要沿着天然裂缝窜进,但在有机质和无机质中也存在缓慢的流动,且有机质中的流速要略大于无机质中的流速.通过改变地层压力,研究地层压力对页岩气渗流特性的影响.研究结果表明,整个流场的速度和渗透率均随着地层压力的下降而增加.     

A mathematical model for solid-gas coupled problems on the methane flowing in coal seam

Based on the fundamental theories of the solid deformation and methane flowing, a mathematical model for solid-gas coupled problem on methane flowing is developed. The smoothness and existence of the solution of this model are proved, and the numerical method for solving the present problem is presented.This project was supported by the Shanxi Province Natural Science Foundation.     

Investigation of Stress Field and Fracture Development During Shale Maturation Using Analog Rock Systems

The emergence of hydrocarbons within shale as a major recoverable resource has sparked interest in fluid transport through these tight mudstones. Recent studies suggest the importance to recovery of microfracture networks that connect localized zones with large organic content to the inorganic matrix. This paper presents a joint modeling and experimental study to examine the onset, formation, and evolution of microfracture networks as shale matures. Both the stress field and fractures are simulated and imaged. A novel laboratory-scale, phase-field fracture propagation model was developed to characterize the material failure mechanisms that play a significant role during the shale maturation process. The numerical model developed consists of coupled solid deformation, pore pressure, and fracture propagation mechanisms. Benchmark tests were conducted to validate model accuracy. Laboratory-grade gelatins with varying Young’s modulus were used as scaled-rock analogs in a two-dimensional Hele-Shaw cell apparatus. Yeast within the gelatin generates gas in a fashion analogous to hydrocarbon formation as shale matures. These setups allow study and visualization of host rock elastic-brittle fracture and fracture network propagation mechanisms. The experimental setup was fitted to utilize photoelasticity principles coupled with birefringence properties of gelatin to explore visually the stress field of the gelatin as the fracture network developed. Stress optics image analysis and linear elastic fracture mechanics (LEFM) principles for crack propagation were used to monitor fracture growth for each gelatin type. Observed and simulated responses suggest gas diffusion within and deformation of the gelatin matrix as predominant mechanisms for energy dissipation depending on gelatin strength. LEFM, an experimental estimation of principal stress development with fracture growth, at different stages was determined for each gelatin rheology. The interplay of gas diffusion and material deformation determines the resulting frequency and pattern of fractures. Results correlate with Young’s modulus. Experimental and computed stress fields reveal that fractures resulting from internal gas generation are similar to, but not identical to, type 1 opening mode.

     

Damage Evolution and Post-peak Gas Permeability of Raw Coal Under Loading and Unloading Conditions

Coalbed methane, a naturally occurring gas in coal, is regarded as a relatively clean-burning and eco-friendly resource. During mining, coalbed methane may be leaked to the environment, leading to potential coal mine catastrophes such as coal and gas outbursts, and gas explosions. In the interest of mine stability, and to enhance resource recovery and utilisation, it is fundamentally important to understand the permeability characteristics of coal, in particular its post-peak permeability behaviour. In this paper, an in-house developed tri-axial apparatus with the ability to investigate coupled thermal–hydrological–mechanical behaviour under servo-controlled seepage has been used to carry out a series of gas permeation experiments in coal samples. The coal samples were subjected to tri-axial tests, including the simulation of coal extraction by unloading the confining pressure applied on the test specimens. The deformation and permeability characteristics of raw coal during these tests were recorded. The volume changes of the coal samples during the tests were observed to occur in three stages: Stage 1: contraction, Stage 2: little or no volume change, and Stage 3: dilation. Corresponding to the volume changes, the gas seepage can also be divided into three stages: seepage decrease, steady seepage, and accelerated seepage. Based on the observed behaviour of coal samples during the tri-axial permeation tests, an analytical model to simulate damage evolution and its effect on the permeability of coal containing gas is proposed in this paper. It may be used to study the evolution of permeability with stress changes, and to provide insights into coal and gas outbursts in practice.     

Modeling Free-Surface Seepage Flow in Complicated Fractured Rock Mass Using a Coupled RPIM-FEM Method

The prediction of the free-surface seepage flow behavior in fractured rock mass is of significance in geotechnical engineering. There are two major issues in solving the seepage flow in complicated fractured rock mass based on the fractured porous medium (FPM) flow model, in which groundwater is assumed to flow simultaneously in both rock matrix and embedded fractures: One is the mesh generation of rock mass in the presence of the fracture network, especially when there exist a large number of stochastic fractures; the other is that a robust iteration algorithm is required since the free surface is unknown at the beginning of solution. Aiming at these two issues, this paper proposes a novel numerical method by coupling radial point interpolation method (RPIM) and finite element method (FEM), in which RPIM is utilized to model the rock matrix and FEM is utilized to model the fractures. On the basis of the variational inequality (VI) theory for free-surface seepage analysis, the computation formulations of the numerical method are derived and the corresponding computation program is developed. Three examples are solved with the present method. It is found that the VI theory can be extended to solve the free-surface seepage problem based on the FPM flow model. A crucial advantage of the present method is that the mesh generation can be greatly simplified. The present method has been verified to be a robust, efficient and reliable method for modeling the groundwater flow in complicated fractured rock mass.     

Numerical simulation of effect of convection-diffusion on oxygen transport in microcirculation

The entire process of oxygen transport in microcirculation by developing a 3D porous media model is calculated numerically with coupled solid deformation-fluid seepage-convection and diffusion . The principal novelty of the model is that it takes into account volumetric deformation of both capillary and tissues resulting from capillary fluctuation. How solid deformation, fluid seepage, and convection-diffusion combine to affect oxygen transport is examined quantitatively: (1) Solid deformation is more significant in the middle of capillary, where the maximum value of volumetric deformation reaches about 0.5%. (2) Solid deformation has positive influence on the tissue fluid so that it flows more uniformly and causes oxygen to be transported more uniformly, and eventually impacts oxygen concentration by 0.1%-0.5%. (3) Convection-diffusion coupled deformation and seepage has a maximum (16%) and average (3%) increase in oxygen concentration, compared with pure molecular diffusion. Its more significant role is to allow oxygen to be transported more evenly.     

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.      

裂隙岩体渗流模型研究现状与展望

裂隙岩体渗流对于边坡、地下工程及基础岩土体的承载能力有显著的制约作用。本文简要地介绍了多种裂隙岩体渗流模型研究现状,评述了几类比较有代表性的渗流模型特点以及存在的不足,为选取合理的数学模型用于求解具体的裂隙岩体渗流问题提供了参考依据,并在上述基础上提出了一些需要进一步研究的问题。指出就目前应用最为广泛的等效连续介质模型而言,裂隙岩体几何参数、有效孔隙度以及等效渗透张量的确定仍有待于更深入的研究,而从细观力学结构入手研究渗流耦合模型将具有重大的理论意义和实用价值。     

VISCOMETRIC FLOW OF ELASTOPLASTIC MATERIAL HEATED BY WALL FRICTION

Journal of Applied Mechanics and Technical Physics - A mathematical model of large deformations is used to solve a coupled boundary-value problem about the deformation of an elastoviscoplastic...     

裂隙岩体水力特征数值模拟试验的初步结果

本文利用文献中的数据进行数值模拟试验,结果表明：流量等效和渗透作用力变形效果等效互不包容;不同级别结构面体系难以用连续介质方法处理,同级别结构面体系在工程作用力变化范围内,可由其静态水力特征推演动态特征;工程岩体结构面间充分连通的假设过于粗糙,常规试验手段获取的量值倾向于局部特征的反映。     

破碎岩石气体渗透性的试验测定方法

为了测试采矿工程中松散破碎岩体的气体渗透特性,设计了与MTS815.02岩石力学伺服机配套的气体渗透仪和测试系统。依靠MTS伺服机改变压力和位移条件,渗透仪用以稳定破碎岩石并连接气体测试系统,接入气源、组成回路和测试气透特性等由测试系统完成。通过对几组破碎砂岩岩样氮气渗透性能的测试,结合考虑状态方程的渗透率换算公式,得出破碎砂岩气体渗透率随压力和粒径条件的变化规律。该测试方法和测试结果在研究采动破碎岩体瓦斯等气体流动规律方面具有重要意义。     

裂隙岩体中非饱和渗流与运移的概念模型及数值模拟

探讨了裂隙岩体中非饱和地下水渗流与溶质运移的几种概念模型的构造及数值模拟问题 ,如裂隙网络模型、连续体模型、等效连续体模型、双孔隙度 (单渗透率 )模型、双渗透率模型、多组份连续体模型等。在裂隙岩体中 ,非饱和地下水的渗流可能只局限于岩体中的岩石组份、或裂隙网络 ,也可能在裂隙和岩石中同时发生 ;对前一种情形只需考虑单一连续体中的流动 ,而后一种情况则需要包括地下水在岩石和裂隙之间的交换。岩体中的裂隙网络往往是溶质运移的主要通道 ;但当溶质在裂隙与岩石之间的渗透和扩散是重要的运移机制时 ,就需要考虑岩石与裂隙界面处的溶质交换。为了模拟岩石与裂隙之间地下水和溶质的交换 ,就需要了解岩石与裂隙之间相互作用的模式和范围 ,使得这类问题的概念模型较单一连续体模型多了一层不确定性、其数值模拟也变得更为困难。因为在实际问题中不易、甚至根本不能判别非饱和渗流的实际形态 ,具体采用哪种模型主要取决于分析的目的和对现场数据的掌握程度。不论哪种模型都会受到模型及参数不确定性的影响 ,因此必须考虑与其他辅助模型的比较.     

低渗透煤层气藏中气-水两相不稳定渗流动态分析

针对低渗透煤层渗流问题,考虑启动压力梯度及其引起的动边界和动边界内吸附气解吸作用的渗流模型研究目前仅限于单相流,而更符合实际的气-水两相渗流动边界模型未见报道.本文综合考虑了煤层吸附气的解吸作用、气-水两相渗流、非达西渗流、地层应力敏感等影响因素,进行了低渗透煤层的气-水两相渗流模型研究.采用了试井技术中的"分相处理"方法,修正了两相渗流的综合压缩系数和流度,并基于含气饱和度呈线性递减分布的假设,建立了煤层气藏的气-水两相渗流耦合模型.该数学模型不仅可以描述由于低渗透煤层中渗流存在启动压力梯度而产生的可表征煤层有效动用范围随时间变化的移动边界,还可以描述煤层有效动用范围内吸附气的解吸现象以及吸附气解吸作用所引起的煤层含气饱和度的上升;为了提高模型精度,控制方程还保留了二次压力梯度项.采用了稳定的全隐式有限差分方法进行了模型的数值求解,并验证了数值计算方法的正确性,获得了模型关于瞬时井底压力与压力导数响应的双对数特征曲线,由此分析了各渗流参数的敏感性影响.本文研究结果可为低渗透煤层气藏开发的气-水两相流试井技术提供渗流力学的理论基础.     

考虑非线性变形的航天器柔性附件建模方法

针对航天器的柔性附件,将其简化为常见的大范围运动空间柔性梁结构。根据柔性体的非线性变形原理,考虑了弯曲和扭转的非线性因素的影响,在柔性梁的三个变形方向上均考虑了变形的二次耦合项。利用有限元方法进行离散并用Lagrange方程建立了非线性变形模式下的动力学方程,包含了较为完全的刚度矩阵和各种耦合项。对一大范围运动的空间梁进行了仿真计算,表明在运动速度较大并且基座具有大范围运动时,一次耦合模型与本文模型有一定差异,且初始变形对两种模型也会产生影响。     

岩体系统渗流场与应力场耦合的广义双重介质模型的应用研究

本文通过实验资料分析, 提出了裂隙岩体应力与渗流之间的分形几何关系式。以研究区岩体系统结构为基础, 提出了岩体系统应力场与渗流场耦合的广义双重介质模型, 并将该模型应用于某水利水电工程的渗流与控制中, 对坝区岩体进行了应力场和渗流场的耦合分析, 取得了比较满意的结果。     

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.      

Flow of Coal-Bed Methane to a Gallery

Coal-seam methane reservoirs have a number of unique feature compared to conventional porous or fractured gas reservoirs. We propose a simplified mathematical model of methane movement in a coal seam taking into account the following features: a relatively regular cleat system, adsorptive methane storage, an extremely slow mechanism of methane release from the coal matrix into cleats and a significant change of permeability due to desorption.Parameters of the model have been combined into a few dimensionless complexes which are estimated to an order of magnitude. The simplicity of the model allows us to fully investigate the influence of each parameter on the production characteristics of the coal seam. We show that the reference time of methane release from the coal matrix into cleats – the parameter which is most poorly investigated – may have a critical influence on the overall methane production.