岩土介质非稳态热固结耦合问题的热源函数法

考虑耦合效应的饱和土体热固结问题控制方程,利用Fourier变换、Laplace变换给出其在变换域上的解,将初始温度场分布视为虚拟的热源或者将热源等价为特定的初始温度分布,利用热源函数法给出瞬时线热源非稳态温度场、应力场和位移场的解析求解方法,通过在时间域和空间域上进行积分,给出有初始温度场分布以及有分布内热源存在且热源强度随时间变化条件下的热固结问题计算方法。对一无限大物体内存在有平面矩形域热源情况下周围介质的温度、孔隙水压力以及位移等的变化特征进行分析。研究表明,热源函数法可有效地求解一系列复杂情况下的热固结问题。     

衰变热源作用下饱和多孔介质热固结问题的扩展精细积分法

热源作用下饱和多孔介质热固结效应是土木及能源工程领域的一个重要课题.由于问题的复杂性,已有的研究大多将介质假定为均匀各向同性,且将热源假定为恒定强度.实际工程中,天然饱和多孔介质常表现出明显的分层特性,热源强度也存在衰变性,为此本工作采用扩展精细积分法对衰变热源作用下层状饱和多孔介质的热固结问题进行研究.借助于积分变换,将饱和多孔介质热固结问题的偏微分方程转化为变换域内的常微分方程;然后对饱和多孔介质微层元进行合并消元,并结合边界条件,推导出衰变热源作用下层状饱和多孔介质热固结问题在积分变换域内的扩展精细积分解;对所得解答进行相应的数值积分逆变换,可获得所求温度、超静孔压及竖向位移在物理域内的解答.基于上述求解过程,编制相应的计算程序进行数值计算,通过与已有文献对比,验证本文扩展精细积分法在求解层状饱和多孔介质热固结问题中的适应性和正确性;最后通过几组算例,分析热源衰变周期、热源埋深及介质的成层性对热固结效应的影响.结果表明:热源衰变周期对温度和超静孔压的峰值、以及达到峰值的时间均有明显影响,衰变周期越长,二者峰值均越大,且达到峰值所需时间越长;热源埋深对超静孔压及竖向位移变化影响显著,深埋热源作用时热源两侧竖向位移呈对称分布,而浅埋热源两侧则无此现象;饱和多孔介质的分层特性对热固结效应影响明显.     

考虑热渗效应的有限热源固结近似解1）

通过建立考虑热渗效应和热流固耦合效应的饱和土体固结方程,研究了无限长圆柱热固结问题. 利用Fourier 和Laplace 变换及其逆变换,给出了热固结问题的解析解;然后对空间内无限长圆柱形热源问题进行研究,得到非等温条件下柱体周围饱和土体温度、孔隙水压力的近似解,并总结其规律,分析了热渗系数、固结系数对温度作用下土体固结的影响.     

Relaxation Effects of a Saturated Porous Media Using the Two-Dimensional Generalized Thermoelastic Theory

A model of the equations of a generalized thermoelasticity (GT) with relaxation times for a saturated porous medium is given in this article. The formulation can be applied to the GT theories: Lord–Shulman theory, Green–Lindsay theory, and Coupled theory for the porous medium. A two-dimensional thermoelastic problem that is subjected to a time-dependent thermal/mechanical source is investigated with the model of the generalized porous thermoelasticity. By using the Laplace transform and the Fourier transform technique, solutions for the displacement, temperature, pore pressure, and stresses are obtained with a semi-analytical approach in the transform domain. Numerical results are also performed for portraying the nature of variations of the field variables. In addition, comparisons are presented with the corresponding four theories.     

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffusivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases.     

热局部非平衡下一维半无限长饱和多孔柱体的温度场分析

对于端部受温度载荷的一维半无限长多孔介质柱体,给出了热局部非平衡下固相和流相温度场在Laplace变换域中的解析表达式.对于冲击温度载荷的情况,获得了温度场在短时间内的Laplace逆变换渐近解析解.数值分析了流、固两相热扩散系数之比以及热交换系数对固相和流相温度场的影响,比较了热局部非平衡下加权温度与热局部平衡下温度之间的差别.     

Weak 2D Convective Plumes in a Sloping Permeable Layer

This is a study of thermal plumes in a permeable fluid-saturated slab of a porous medium (of finite uniform thickness but otherwise infinite extent) that is heated by either an instantaneous or a steady line source embedded in the medium. The slab, which may be horizontal or sloping, is initially at ambient conditions; the impervious upper surface remains at the ambient temperature, while the impervious base is thermally insulated. The transient temperature distribution, the surface heat flux and the convective flow velocity are calculated for small instantaneous line heat energy sources. They show how the flow develops, spreads and slows as time progresses, and an estimate of the time to decay is given. Steady-state temperature and velocity profiles are calculated for embedded line sources that provide heat energy at a small constant rate, and the surface heat flux distribution is calculated.     

THERMAL CONSOLIDATION OF LAYERED POROUS HALF-SPACE TO VARIABLE THERMAL LOADING

An analytical method was derived for the thermal consolidation of layered, saturated porous half-space to variable thermal loading with time. In the coupled governing equations of linear thermoelastic media, the influences of thermo-osmosis effect and thermal filtration effect were introduced. Solutions in Laplace transform space were first obtained and then numerically inverted. The responses of a double-layered porous space subjected to exponential decaying thermal loading were studied. The influences of the differences between the properties of the two layers (e.g., the coefficient of thermal consolidation, elastic modulus) on thermal consolidation were discussed. The studies show that the coupling effects of displacement and stress fields on temperature field can be completely neglected, however, the thermo-osmosis effect has an obvious influence on thermal responses.     

Lamb's integral formulas of two-phase saturated medium for soil dynamic with drainage

When dynamic force is applied to a saturated porous soil,drainage is common.In this paper,the saturated porous soil with a two-phase saturated medium is simulated,and Lamb's integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot's equation and Betti's theorem(the reciprocal theorem).According to the basic solution to Biot's equation,Green's function Gij and three terms of Green's function G4i,Gi4,and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented.The displacement field with drainage,the magnitude of drainage,and the pore pressure of the center explosion source are obtained in computation.The results of the classical Sharpe's solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared.Good agreement is observed.     

Thermo-Osmosis Effect in Saturated Porous Medium

In this paper, the thermo-poroelasticity theory is used to investigate the quasi-static response of temperatures, pore pressure, stress, displacement, and fluid flux around a cylindrical borehole subjected to impact thermal and mechanical loadings in an infinite saturated poroelastic medium. It has been reported in literatures that coupled flow known as thermo-osmosis by which flux is driven by temperature gradient, can significantly change the fluid flux in clay, argillaceous and many other porous materials whose permeability coefficients are very small. This study presents a mathematical model to investigate the coupled effect of thermo-osmosis in saturated porous medium. The energy balance equations presented here fulfill local thermal non-equilibrium condition (LTNE) which is different from the local thermal equilibrium transfer theory, accounting for that temperatures of solid and fluid phases are not the same and governed by different heat transfer equations. Analytical solutions of temperatures, pore pressure, stress, displacement, and fluid flux are obtained in Laplace transform space. Numerical results for a typical clay are used to investigate the effect of thermo-osmosis. The effects of LTNE on temperatures, pore pressure, and stress are also studied in this paper.     

The Onset of Convection in an Anisotropic Porous Layer Using a Thermal Non-Equilibrium Model

The stability of a horizontal fluid saturated anisotropic porous layer heated from below and cooled from above is examined analytically when the solid and fluid phases are not in local thermal equilibrium. Darcy model with anisotropic permeability is employed to describe the flow and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is implemented to compute the critical Rayleigh number and the corresponding wavenumber for the onset of convective motion. The effect of thermal non-equilibrium and anisotropy in both mechanical and thermal properties of the porous medium on the onset of convection is discussed. Besides, asymptotic analysis for both very small and large values of the interphase heat transfer coefficient is also presented. An excellent agreement is found between the exact and asymptotic solutions. Some known results, which correspond to thermal equilibrium and isotropic porous medium, are recovered in limiting cases.     

Dynamic response of saturated layered half-space with different hydraulic interface conditions

Summary An analytic study of the response of saturated layered half-space under surface point loading is presented, with particular attention paid to the effect of hydraulic interface condition. A simplified formulation is adopted to describe the motion of the saturated porous medium, and a simple and direct approach is presented which does not involve the conventional Helmholtz decomposition in poroelasticity. Integral solutions for surface displacements are derived for different hydraulic interface conditions, and verified by reducing to well-known results of the Lamb's problem for a conventional one-phase medium. Numerical results for surface displacements in the near field are given, and the influence of the interface hydraulic condition on the displacements is shown. The present formulation possesses potential applications in practical engineering in solving various related source problems associated with uniform or layered saturated soil deposits. Received 30 September 1997; accepted for publication 14 July 1998     

Convective cooling/heating induced thermal stresses in a fluid saturated porous medium undergoing local thermal non-equilibrium

Local thermal non-equilibrium (LTNE) may have profound effects on the pore pressure and thermal stresses in fluid saturated porous media under transient thermal loads. This work investigates the temperature, pore pressure, and thermal stress distributions in a porous medium subjected to convective cooling/heating on its boundary. The LTNE thermo-poroelasticity equations are solved by means of Laplace transform for two fundamental problems in petroleum engineering and nuclear waste storage applications, i.e., an infinite porous medium containing a cylindrical hole or a spherical cavity subjected to symmetrical thermo-mechanical loads on the cavity boundary. Numerical examples are presented to examine the effects of LTNE under convective cooling/heating conditions on the temperature, pore pressure and thermal stresses around the cavities. The results show that the LTNE effects become more pronounced when the convective heat transfer boundary conditions are employed. For the cylindrical hole problem of a sandstone formation, the thermally induced pore pressure and the magnitude of thermal stresses are significantly higher than the corresponding values in the classical poroelasticity, which is particularly true under convective cooling with moderate Biot numbers. For the spherical cavity problem of a clay medium, the LTNE effect may become significant depending on the boundary conditions employed in the classical theory.     

考虑热渗效应的有限长圆柱热固结解

在作者已建立的饱和多孔介质耦合非线性热弹性理论基础上,考虑热渗效应,建立了饱和多孔介质耦合热弹性固结方程,并推导了有限长圆柱热固结问题的解析解,进而以温控三轴试验的试样为例进行了算例分析,同时利用COMSOL软件进行了数值模拟,并将解析结果和数值结果进行对比．结果表明：在不排水条件下,影响试样最终孔压大小的参数是：土的泊松比>弹性模量>水的体膨胀系数,渗透系数对孔压变化影响不大,考虑与不考虑水土压缩性不影响孔压的计算;相对线弹性情况,考虑非线弹性膨胀系数随温度变化时的孔压有所下降,轴向应变变化很小．     

Fundamental solution for transversely isotropic thermoelastic materials

We use the compact harmonic general solutions of transversely isotropic thermoelastic materials to construct the three-dimensional fundamental solutions for a steady point heat source in an infinite transversely isotropic thermoelastic material and a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material by three newly introduced harmonic functions, respectively. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results for hexagonal zinc are given graphically by contours.     

STUDY ON ANALYSIS METHOD OF “THREE BOX” IN HEAT AND MASS TRANSFER PROCESS OF RESERVOIR MEDIA

油藏多孔介质孔隙组成及结构变化多样,一些特性参数很难全部获得,精确描述和分析困难;另外,多孔介质内渗流过程水力条件和作用机理复杂,存在热流固耦合作用,目前的一些分析方法和研究模型具有一定的局限性.提出了油藏多孔介质的表征单元体（representative elementary volume,REV）描述表征方法;基于表征单元体建立了多孔介质的黑箱模型、灰箱模型和白箱模型,据此提出了多孔介质的“黑箱→灰箱→白箱”分析过程.基于黑箱模型和灰箱模型推导了REV导热系数计算公式、给出了REV热质传递过程的热平衡方程.结合中国油藏热采情况,对多孔介质导热系数变化规律和蒸汽驱热质传递特性进行了分析,得到了一些有意义的结果.该工作为多孔介质热质传递过程分析提供了新思路和新方法.     

Effect of thermal dispersion on free convection in a fluid saturated porous medium

The present article considers a numerical study of thermal dispersion effect on the non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. Forchheimer extension is considered in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. The non-dimensional governing equations are solved by the finite element method (FEM) with a Newton–Raphson solver. Numerical results for the details of the stream function, velocity and temperature contours and profiles as well as heat transfer rates in terms of Nusselt number are obtained. The study shows that the increase in thermal dispersion coefficient of the porous medium results in more heat energy to disperse away in the normal direction to the wall. This induces more fluid to flow along the wall, enhancing the heat transfer coefficient particularly near the wall.     

A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function

Based on Biot’s theory, the dynamic 2.5-D Green’s function for a saturated porous medium is obtained using the Fourier transform and the potential decomposition methods. The 2.5-D Green’s function corresponds to the solutions for the following two problems: the point force applied to the solid skeleton, and the dilatation source applied within the pore fluid. By performing the Fourier transform on the governing equations for the 3-D Green’s function, the governing differential equations for the two parts of the 2.5-D Green’s function are established and then solved to obtain the dynamic 2.5-D Green’s function. The derived 2.5-D Green’s function for saturated porous media is verified through comparison with the existing solution for 2.5-D Green’s function for the elastodynamic case and the closed-form 3-D Green’s function for saturated porous media. It is further demonstrated that a simple form 2-D Green’s function for saturated porous media can be been obtained using the potential decomposition method.     

Thermoelastostatic equilibrium of a spatial quadrant: Green’s function and solution in integrals

In this study, a new Green??s function and a new Green-type integral formula for a 3D boundary value problem (BVP) in thermoelastostatics for a quarter-space are derived in closed form. On the boundary half-planes, twice mixed homogeneous mechanical boundary conditions are given. One boundary half-plane is free of loadings and the normal displacements and the tangential stresses are zero on the other one. The thermoelastic displacements are subjected by a heat source applied in the inner points of the quarter-space and by mixed non-homogeneous boundary heat conditions. On one of the boundary half-plane, the temperature is prescribed and the heat flux is given on the other one. When the thermoelastic Green??s function is derived, the thermoelastic displacements are generated by an inner unit point heat source, described by ??-Dirac??s function. All results are obtained in elementary functions that are formulated in a special theorem. As a particular case, when one of the boundary half-plane of the quarter-space is placed at infinity, we obtain the respective results for half-space. Exact solutions in elementary functions for two particular BVPs for a thermoelastic quarter-space and their graphical presentations are included. They demonstrate how to apply the obtained Green-type integral formula as well as the derived influence functions of an inner unit point body force on volume dilatation to solve particular BVPs of thermoelasticity. In addition, advantages of the obtained results and possibilities of the proposed method to derive new Green??s functions and new Green-type integral formulae not for quarter-space only, but also for any canonical Cartesian domain are also discussed.     

Three-dimensional steady-state closed form solution for multilayered fluid-saturated anisotropic finite media due to surface/internal point source

A three-dimensional(3 D)steady-state solution of fluid saturated anisotropic finite media is presented.The eigenequation method and the pseudo-Stroh formalism are used to obtain the exact solution for homogeneous saturated finite media.The propagator matrix method is introduced to deal with the corresponding multilayered poroelastic media.The poroelastic solutions due to surface or internal point fluid source are obtained.The comparison of the results of the saturated isotropic media in a half space and those obtained by the finite element method is given to illustrate the accuracy of the solution in a finite domain.Numerical solutions of a sandwich poroelastic medium are presented to analyze its hydromechanical behaviors.Two ratios of the horizontal permeability to vertical permeability and different source positions are investigated.The results show that the fluid parameters and source positions have great influence on the hydromechanical behaviors of the layered media.