温度梯度水分扩散对双重孔隙岩体中THM耦合影响的有限元分析

建立了一种饱和-非饱和遍有节理岩体的双重孔隙-裂隙介质热-水-应力耦合模型,并研制出相应的二维有限元程序.通过一个假定的位于非饱和双重孔隙-裂隙岩体中的高放废物地质处置库算例,就温度梯度水分扩散系数不同的三种工况,考察了岩体中的温度、孔隙水压力、饱和度、地下水流速和主应力的变化、分布情况.结果显示:各工况计算域中温度场及应力场基本相同,当岩体温度梯度水分扩散系数较大时,近场的负孔隙水压力上升到很高的数值,负裂隙水压力有所下降,饱和度亦有相应的变化,当温度梯度水分扩散系数小到一定程度后,其影响也将逐渐消失.     

双重孔隙介质THMM耦合模型及其有限元分析

建立了一种饱和-非饱和遍有节理岩体的双重孔隙-裂隙介质热-水-应力-迁移耦合模型,其特点是应力场和温度场是单一的,但具有不同的孔隙渗流场、裂隙渗流场和孔隙浓度场、裂隙浓度场,以及可考虑裂隙的组数、间距、方向、连通率和刚度对本构关系的影响;并开发了相应的二维有限元程序.针对一个假定的高放废物地质处置库,就岩体为非饱和双重孔隙-裂隙介质和放射性核素泄漏的情况进行了数值分析,考察了岩体中的温度、负孔隙水压力、饱和度、地下水流速、核素浓度和主应力的状态.结果显示:孔隙和裂隙中的负水压力及核素浓度呈现不同的变化、分布;尽管裂隙水饱和度平均仅为孔隙水饱和度的1/10,但因裂隙的渗透系数比孔隙的渗透系数大4个数量级,故裂隙中地下水的流速约是孔隙中相应值的3倍;孔隙和裂隙中核素浓度的量值接近.     

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.     

基于孔与裂隙网络模型的平行微裂隙对驱油的影响规律研究

认识双重多孔介质中油水两相微观渗流机制是回答形成什么类型的裂隙网络可提高油藏采收率的关键. 微裂隙的分布可以提高多孔介质的绝对渗透率,但对于基质孔隙中的流体介质,微裂隙的存在会引起多孔介质中局部流体压力和流场的变化,导致局部流动以微裂隙流动为主,甚至出现窜流现象,降低驱油效率. 本文基于孔与裂隙双重网络模型,在网络进口设定两条平行等长且具有一定间隔的微裂隙,分析微裂隙的相对间隔(微裂隙之间距离/喉道长度)和微裂隙相对长度(微裂隙长度/喉道长度)对于微观渗流特征的影响. 结果表明:随微裂隙相对长度的增加,出现驱油效率逐渐降低,相对渗透率曲线中的油水共渗区水饱和度和等渗点增加,油水两相的共渗范围减小等现象;随着微裂隙之间相对间隔增大,周围越来越多的基质孔穴间的压力差减小,在毛管压力的限制下,驱替相绕过这些区域,而导致水窜现象.      

基于孔与裂隙网络模型的平行微裂隙对驱油的影响规律研究

认识双重多孔介质中油水两相微观渗流机制是回答形成什么类型的裂隙网络可提高油藏采收率的关键.微裂隙的分布可以提高多孔介质的绝对渗透率,但对于基质孔隙中的流体介质,微裂隙的存在会引起多孔介质中局部流体压力和流场的变化,导致局部流动以微裂隙流动为主,甚至出现窜流现象,降低驱油效率.本文基于孔与裂隙双重网络模型,在网络进口设定两条平行等长且具有一定间隔的微裂隙,分析微裂隙的相对间隔(微裂隙之间距离/喉道长度)和微裂隙相对长度(微裂隙长度/喉道长度)对于微观渗流特征的影响.结果表明:随微裂隙相对长度的增加,出现驱油效率逐渐降低,相对渗透率曲线中的油水共渗区水饱和度和等渗点增加,油水两相的共渗范围减小等现象;随着微裂隙之间相对间隔增大,周围越来越多的基质孔穴间的压力差减小,在毛管压力的限制下,驱替相绕过这些区域,而导致水窜现象.     

露天矿边坡饱和渗透系数随机场数值模型研究

为分析强降雨入渗及渗透系数空间变异性对闭坑露天矿边坡渗流场的影响程度,基于非饱和渗流理论和随机场理论,采用非侵入式随机方法,通过FISH语言编写非饱和区单元饱和度、渗透系数与基质吸力的修正函数,建立饱和-非饱和渗流随机场模型,开展强降雨作用的高大陡深岩质边坡渗流特征研究。研究结果表明,修正饱和-非饱和渗流随机场模型能够准确地描述露天矿边坡的降雨入渗过程。且降雨入渗主要影响到露天矿边坡浅层渗流场。随降雨持时变化,在坡面与地下水位线之间形成包围的且逐渐缩小的非饱和区。坡面最早出现暂态饱和区且厚度逐渐增加,但增幅逐渐放缓。同时坡面点孔隙水压力最早达到稳定值零,离坡面越远的点孔隙水压力达到稳定值零的用时会越长。该结论可为闭坑露天矿边坡的地质灾害风险预测提供参考意义。     

条形荷载下梯度非均匀非饱和土的动力响应分析

基于多孔介质混合物理论, 建立了梯度非均匀非饱和土地基模型, 研究了条形荷载作用下梯度非均匀非饱和土地基的动力响应问题. 通过傅里叶积分变换和Helmholtz矢量分解原理, 获得频域内非饱和土地基动力响应问题的通解, 结合回传射线矩阵法和边界条件, 求解获得了非均匀非饱和土层中位移、应力以及孔隙压力的计算列式. 假设沿深度方向梯度非均匀非饱和土的物理力学性质按幂函数连续变化, 通过数值傅里叶逆变换得到了非均匀非饱和土地基中的应力、位移以及孔隙压力等物理量的数值解, 分析讨论了土体非均匀性对非饱和土介质动力响应的影响规律. 结果表明: 土体非均匀性显著改变了非饱和土中竖向位移、正应力和孔隙压力在其深度方向上的振动模态, 其中孔隙气压在其深度方向的振动频率随着梯度因子的增加而不断增大, 波峰值不断靠近地表处附近; 竖向位移随着梯度因子的增大不断减小; 正应力和孔隙水压随着梯度因子的增大先增大后减小, 并且土体非均匀程度越高, 正应力与孔隙水压的幅值越大.      

非饱和土中的饱和度的求解方法

探讨非饱和土的饱和度测量几种测量方法。由于非饱和土试验方法的不同,造成饱和度的测量的偏差。本文根据GDS的试验结果,对几种测量饱和度的方法进行比较和分析,指出假设土样颗粒体积不变,土样体积改变是因为土样孔隙大小的改变的合理性,认为直接法是一种有效的方法。     

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。     

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。     

FEM ANALYSIS FOR INFLUENCES OF A FAULT ON COUPLED T-H-M-M PROCESS IN DUAL-POROSITY ROCK MASS

For the case in which a large geological structure like fault existing within the surrounding rock mass in the near field of a repository for high-level radioactive nuclear waste, one kind of coupled thermo-hydro-mechanical-migratory model of dual-porosity medium for saturatedunsaturated ubiquitous-joint rock mass was established. In the present model, the seepage field and the concentration field are double, but the stress field and the temperature field are single, and the influences of sets, spaces, angles, continuity ratios, stiffness of fractures on the constitutive relationship of the medium can be considered. At the same time, a two-dimensional program of finite element method was developed. Taking a hypothetical nuclear waste repository located at a rock mass being unsaturated dual-porosity medium as a calculation example, the FEM analysis for thermo-hydro-mechanical-migratory coupling were carried out under the condition of radioactive nuclide leaking for the cases with and without a fault, and the temperatures, pore pressures, flow velocities, nuclide concentrations and principal stresses in the rock mass were investigated. The results show that the fracture water in the fault flows is basically along the fault direction, and its flow velocity is almost three orders of magnitude higher than that of fracture water in rock mass; the nuclide concentration in the fault is also much higher than that without fault, and the nuclides move along the fault faster; moreover, the fault has obvious influences on the pore pressures and the principal stresses in the rock mass.     

Scalar turbulence model investigation with variable turbulent Prandtl number in heated jets and diffusion flames

Traditional turbulence models using constant turbulent Prandtl number fail to predict the experimentally observed anisotropies in the thermal eddy diffusivity and thermal turbulent intensity fields. Accurate predictions depend strongly on the turbulence model employed. Consequently, the objective of this paper is to assess the performance of turbulence model with variable turbulent Prandtl number in predicting of thermal and scalar fields quantities. The model is applied to axisymmetric turbulent round jet with variable density and in turbulent hydrogen diffusion flames using the flamelet concept. The k − ɛ turbulence model is used in conjunction with thermal field; the model involves solving supplemental scalar equations for the temperature variance and its dissipation rate. The model predictions are compared with available experimental data for the purpose of validating model. In reacting cases, velocity and scalar (including temperature and mass fractions) predictions agree relatively well in the near field of the investigated diluted hydrogen flames.     

Boiling-like phenomena in free-convection heat transfer at supercritical pressures

Four differently composed nickel-alloy wires and platinum wires were used as heaters to CO₂ in a wide range of pressures and temperatures. Visual observations exhibited three flow regimes: laminar flow, oscillatory flow and turbulent film flow. Boiling-like phenomena may only be attributed to the oscillatory and film regime with respect to the appearance of bubble-like structures and high heat transfer coefficients. The occurrence of these regimes depends on the thermal diffusivity of the wire material. Only laminar flow is observed for platinum wires with a high thermal diffusivity; all three regimes are observed with nichrome wires with low values of thermal diffusivity. The high heat transfer coefficients obtained with boiling-like action distinctly deviate from a correlation valid for platinum wire experiments.     

Capillary Hysteresis in Neutrally Wettable Fibrous Media: A Pore Network Study of a Fuel Cell Electrode

Hysteresis in the saturation versus capillary pressure curves of neutrally wettable fibrous media was simulated with a random pore network model using a Voronoi diagram approach. The network was calibrated to fit experimental air-water capillary pressure data collected for carbon fibre paper commonly used as a gas diffusion layer in fuel cells. These materials exhibit unusually strong capillary hysteresis, to the extent that water injection and withdrawal occur at positive and negative capillary pressures, respectively. Without the need to invoke contact angle hysteresis, this capillary behaviour is re-produced when using a pore-scale model based on the curvature of a meniscus passing through the centre of a toroid. The classic Washburn relation was shown to produce erroneous results, and its use is not recommended when modelling fibrous media. The important effect of saturation distribution on the effective diffusivity of the medium was also investigated for both water injection and withdrawal cases. The findings have bearing on the understanding of both capillarity in fibrous media and fuel cell design.     

A semi-analytic solution of a wellbore in a non-isothermal low-permeability porous medium under non-hydrostatic stresses

The transient stress, displacement, pore pressure and temperature fields around a wellbore in a thermo-poro-elastic (THM) medium subject to non-hydrostatic remote stresses are analyzed under non-isothermal plane-strain conditions. The linear THM model proposed by Coussy (1989) is adopted in the analysis with a focus on thermal effects in low-permeability saturated rocks, characterized by a latent heat associated with local changes of fluid mass content. Non-dimensionalized parameters are identified by reformulating the fully-coupled governing equations and boundary conditions. The wellbore problem is simplified by decomposing it into axisymmetric and deviatoric loading cases. The corresponding analytical solutions are obtained in Laplace space. The inverse Laplace transforms are performed numerically to find the time-dependent distributions of field variables in the rock mass around the wellbore. These numerical results show that although the pore pressure diffusion has little influence on temperature and stress, temperature changes can strongly affect the pore pressure and stress around the wellbore. The temperature change can lead to changes in near-well stresses and the resulting significant change in wellbore breakdown pressure illustrates the importance of considering the THM coupling.     

Role of Thermal Diffusion on Heat and Mass Transfer in Porous Media

In this paper, thermal diffusion phenomena in a porous cavity are investigated. The Brinkman model, coupled with the energy and the mass balance equations was solved numerically using a finite element techniques. A two-component system was included in the model. Different models were investigated to demonstrate the importance of the Soret effect with the presence of gravity vector. We do not take into consideration the pressure effect in the thermal diffusion. Even with such simplification to the problem, results reveal that the thermal diffusion is important and drives a strong convection. A series of convection cells are observed and steady-state solutions are obtained. Asymmetric solutions are obtained for various cases of dual-porosity porous media. Variations in the gravity vector indicated that the convection patterns, as well as the role of Soret coefficient, are profoundly impacted. Finally, the importance of including thermal diffusion in petroleum reservoir simulation is discussed.     

Time-Dependent Shape Factors for Uniform and Non-Uniform Pressure Boundary Conditions

Matrix–fracture transfer functions are the backbone of any dual-porosity or dual-permeability formulation. The chief feature within them is the accurate definition of shape factors. To date, there is no completely accepted formulation of a matrix–fracture transfer function. Many formulations of shape factors for instantly-filled fractures with uniform pressure distribution have been presented and used; however, they differ by up to five times in magnitude. Based on a recently presented transfer function, time-dependent shape factors for water imbibing from fracture to matrix under pressure driven flow are proposed. Also new matrix–fracture transfer pressure-based shape factors for instantly-filled fractures with non-uniform pressure distribution are presented in this article. These are the boundary conditions for a case for porous media with clusters of parallel and disconnected fractures, for instance. These new pressure-based shape factors were obtained by solving the pressure diffusivity equation for a single phase using non-uniform boundary conditions. This leads to time-dependent shape factors because of the transient part of the solution for pressure. However, approximating the solution with an exponential function, one obtains constant shape factors that can be easily implemented in current dual-porosity reservoir simulators. The approximate shape factors provide good results for systems where the transient behavior of pressure is short (a case commonly encountered in fractured reservoirs).     

The double packer permeameter with long packers. An approximate analytical solution

The hydraulic diffusivity and permeability of a rock mass can be measured with a double packer permeameter, placed in a long bore hole. If the flow is steady, the relation between supply pressure and flux is a measure of the permeability whereas if the flow is transient, the relation is a measure of both the hydraulic diffusivity of the rock and the elasticity of the equipment. If the equipment is effectively rigid and the axial extent of the packers is much bigger than the radius of the hole the solution is characterized byone parameter viz. the ratio between the distance between the packers and the radius of the hole and by a dimensionless time. An approximate closed transient solution for engineering purpose can be derived for a given supply flux but not for a given supply pressure.