基于上限理论的孔隙水压力作用下隧道洞口段含裂缝仰坡稳定性分析

研究了孔隙水压力作用下隧道洞口段含裂缝仰坡的稳定性。采用极限分析上限法,构建了坡顶含竖向裂缝的对数螺旋转动破坏机制,推导了可反映边坡临界坡高的稳定系数计算公式,将计算结果与未考虑孔隙水压力作用下的含裂缝边坡稳定性极限分析结果进行对比,验证了所提研究方法的合理性。通过算例分析,研究了坡顶裂缝最不利位置分布及仰坡整体安全系数。结果表明:坡顶裂缝开裂深度、土体内摩擦角、坡角越大及水位分布越浅,裂缝位置越靠近坡顶边缘处;孔隙水压力系数、坡顶裂缝开裂深度越大,仰坡稳定性系数越小;坡顶裂缝越深、孔隙水压力系数越大、边坡越陡,越不利于仰坡稳定;而坡内水位分布越低,越有利于仰坡稳定。     

微通道中电渗流及微混合的离子浓度效应

电渗流广泛应用于微流控芯片中的流体输运与混合.该文提出了一种离子浓度梯度对电渗流及微混合产生影响的变量模型,采用有限元分析方法对微通道中电渗流及微混合的离子浓度效应进行了数值模拟,分别讨论了zeta电势、介电常数等对微通道内流场和浓度场的影响规律,定量分析了微混合效率.结果表明,当zeta电势和介电常数随浓度变化时,微通道中流场分布不均匀,离子分布不对称.当溶液浓度趋近1 mol/L时,溶液基本无法进入微通道.微混合效率随溶液间浓度差的增大而减小,而且浓度差越大越能在较短距离内到达充分混合.     

缝洞型低渗透碳酸盐岩油藏压裂井试井分析

缝洞型碳酸盐岩在我国油气资源储量中占有重要地位,因此,研究缝洞型碳酸盐岩压裂井井底压力变化具有重要意义.基于渗流力学基本原理,建立考虑应力敏感和启动压力梯度影响的碳酸盐岩渗流微分方程,利用点源函数理论、Laplace积分变换和Fourier余弦积分变换等方法求得Laplace空间顶底封闭、侧向无限大外边界点源解,通过对点源积分得到面源解;通过Stehfest数值反演得到实空间井底压力解并绘制试井曲线.通过模型对比分析验证了模型的正确性.结果表明:应力敏感系数越大,压力和压力导数曲线上翘越明显;启动压力梯度越大,压力和压力导数曲线上翘时间越早;压裂井打开程度越小,压力导数球形流特征越明显;窜流系数越大,“凹子”出现的时间越早;弹性储容比越大,“凹子”越宽越深.利用该模型可以有效地对缝洞型低渗透碳酸盐岩油藏压裂井的动态曲线进行分析.     

大挠度圆柱壳在温度场中的热弹耦合振动分析

对温度场与与应力场耦合时的圆柱壳的非线性热弹耦合的振动问题,推导得到了基本的振动方程,热传导方程和协调方程,对短圆柱壳运用伽辽金(Galerkin)法求解,得出振幅随时间变化的数值解,得到一些有价值的结论．即随着温度幅值和耦合系数的增大,振动衰减的速度变缓,热弹耦合效应减弱．随着长径比、长厚比的增大,振幅衰减的速度变快,同时热振动频率也随之增大,即热弹耦合效应增强．耦合系数越大,轴向应力、轴向力以及轴向弯矩越小．     

多孔介质一般非Darcy流问题的块中心有限差分算法

本文对描述多孔介质一般非Darcy流的非线性方程,提出一类数值求解的块中心有限差分算法.该格式保持局部质量守恒,并能够同时获得速度和压力近似解.在一般非均匀矩形网格上,本文证明了速度和压力近似在离散l~2模意义下的二阶误差估计.采用该格式进行的数值实验表明,收敛阶与理论分析一致.     

径向低渗非Darcy渗流动边界半解析模型

低渗油藏渗流过程中普遍存在启动压力梯度(TPG).考虑低渗渗流特征,建立了平面径向低渗非Darcy渗流动边界数学模型,给出了计算动边界移动速度的公式,通过Laplace变换结合无穷级数方法求得了模型的半解析解,并进行了Stehfest数值反演.详细讨论与分析了动边界问题特性、动边界变化和传播情况,解释了启动压力梯度导致动边界不断向外扩展的现象.计算了启动压力梯度对井底压力、压力导数的影响,并给出不同条件下的地层压力分布曲线和Gringarten-Bourdet图版,同时给出了实例分析.研究发现:低渗渗流模型与常规渗流模型有着显著不同,低渗非Darcy渗流压力降是随时间扩展的,在动边界外的地层压力降为零,压力分布曲线呈现紧支性.针对具有动边界的低渗透问题,需充分考虑启动压力梯度与动边界的影响,该模型为低渗油藏渗流机理和开采动态、解释与数值模拟提供了一定的理论基础.     

多孔介质中单相气体局部流动的均质化建模

该文研究了渐近均质法在单相气体渗流理论中的应用,开发了气体在孔隙尺度下流动的数学模型和数值方法.基于渐近均质法,建立了周期单元上描述周期性多孔结构孔隙尺度下单相气体流动的局部问题.讨论了局部问题的特殊数学性质和物理意义.利用一种基于对称性和反对称性扩展的简化方法,提出了求解局部问题的最小二乘有限元方法,克服了由于平均算子和周期性边界条件引起的数值困难.局部问题的求解能够获得单孔内速度和压力的精确分布,并且在仅知道孔隙几何形状的情况下评估多孔介质的渗透性.在局部问题的基础上,通过理论分析获得了微管中Poiseuille流动的解析解,验证了所提出的数学模型和数值算法.最后,考虑了一种三维周期性多孔结构,获得了单孔中气体局部流动的数值结果和多孔介质的渗透系数.     

超音速尖锥边界层中扰动演化特征的数值研究

采用高精度紧致格式, 对超音速尖锥边界层中二维扰动的空间演化, 进行了直接数值模拟．结果表明,虽然尖锥边界层流动存在一定的锥面法向速度,但小扰动的幅值及相位的演化都与由平行流假设得到的线性理论结果吻合．还研究了有限幅值扰动的演化,给出了其演化规律．并在扰动幅值增长到一定值时,发现了小激波．     

基于复杂网络演化博弈的企业低碳创新合作行为网络演化机理研究

针对企业低碳创新合作所面临的复杂问题,基于现实复杂网络结构特征,运用演化博弈理论研究有限理性下企业低碳创新合作行为网络演化机理,利用Matlab仿真技术探究无标度网络载体上微观因素对低碳创新合作行为的影响。研究结果表明:低碳创新利益分配、协同效益和违约惩罚对低碳创新合作行为网络演化结果的影响最为显著,网络规模越大网络演化速度越慢,网络规模越小对协同系数和利益分配系数的敏感性越强,网络规模越大对技术溢出系数和违约惩罚的敏感性越强。研究结论可以为企业低碳创新合作策略制定提供解决依据。     

异质材料有限长微通道电渗流热效应

采用数值方法,分析有限长PDMS/玻璃微通道电渗流热效应．数值求解双电层的Poisson-Boltzmann方程,液体流动的Navier-Stokes方程和流-固耦合的热输运方程,分析二维微通道电渗流的温度特性．考虑温度变化对流体特性（介电系数、粘度、热和电传导率）的反馈效应．数值结果表明,在通道进口附近有一段热发展长度,这里的流动速度、温度、压强和电场快速变化,然后趋向到一个稳定状态．在高电场和厚芯片的情况下,热发展长度可以占据相当一部分的微通道．电渗流稳定态温度随外加电场和芯片厚度的增加而升高．由于壁面材料的热特性差异,在稳定态时的PDMS壁面温度比玻璃壁面温度高．研究还发现在微通道的纵向和横向截面有温度变化．壁面温升降低双电层电荷密度．微通道纵向温度变化诱发流体压强梯度和改变微通道电场特性．微通道进流温度不改变热稳定态的温度和热发展长度．     

微通道周期流动电位势及电粘性效应

求解了双电层的Poisson-Boltzmann方程和流体运动的Navier-Stokes方程,得到在周期压差作用下,二维微通道的周期流动电位势,流动诱导电场和液体流动速度的解析解．量纲分析表明,流体电粘性力与以下3个参数有关:1) 电粘性数,它表示定常流动时,通道最大电粘性力与压力梯度的比;2) 形状函数,它表示电粘性力在通道横截面的分布形态; 3) 耦合系数,它表示电粘性力的振幅衰减特征和相位差．分析结果表明,微通道周期流动诱导电场、流动速度与频率Reynolds数有关．在频率Reynolds数小于1时,流动诱导电场随频率Reynolds数变化很慢．在频率Reynolds数大于1时,流动诱导电场随频率Reynolds数的增加快速衰减．在通道宽度与双电层厚度比值较小情况下,电粘性效应对周期流动速度和流动诱导电场有重要影响．     

Derivation of the Double Porosity Model of a Compressible Miscible Displacement in Naturally Fractured Reservoirs

We derive a double porosity model for a displacement of one compressible miscible fluid by another in a naturally fractured reservoir. The microscopic model consists of the usual equations describing Darcy flow in a reservoir except that the porosity and the permeability coefficients are highly discontinuous. The viscosity is assumed to be constant. Over the matrix domain, the coefficients are scaled by a parameter ? representing the size of the matrix blocks. This scaling preserves the physics of the flow in the matrix as ? tends to zero. Using homogenization theory, we derive rigorously the corresponding double porosity model. To this purpose, we mainly use the concept of two-scale convergence. The less permeable part of the rock then contributes as nonlinear memory terms. To specify them in spite of the strong nonlinearities and of the coupling, we then use some appropriate dilation operator.     

Numerical modeling of the influence of heat exchange of reservoir beds with enclosing rocks on gas production from a single well

In the computational experiment, the influence of heat exchange through the top and bottom of the gas-bearing reservoir on the dynamics of temperature and pressure fields in the process of real gas production from a single well is investigated. The experiment is carried out with a modified mathematical model of nonisothermal gas filtration, obtained from the energy and mass conservation laws and the Darcy law. The physical and caloric equations of state together with the Newton-Richman law of heat exchange of a gas reservoir with surrounding enclosing rocks are used as closing relations. It is shown that the influence of the heat exchange with environment on the temperature field of a gas-bearing reservoir is localized in a narrow zone near its top and bottom, although the size of this zone increases with time.     

双重介质分形油藏渗流问题

将油井有效半径引入双重介质分形油藏渗流问题的内边界之中,从而建立了双重介质分形油藏的一种渗流模型,并在考虑了井筒储集和表皮效应的情况求得了外边界为无限大、有界封闭和有界定压三种情况下双重介质分形油藏压力分布的精确解析表达式,利用拉氏数值反演Stehfest方法分析了双重介质分形油藏压力动态特征,讨论了各种参数对压力动态的影响。     

Block‐centered upwind multistep difference method and convergence analysis for numerical simulation of oil reservoir

The three‐dimensional displacement of two‐phase flow in porous media is a preliminary problem of numerical simulation of energy science and mathematics. The mathematical model is formulated by a nonlinear system of partial differential equations to describe incompressible miscible case. The pressure is defined by an elliptic equation, and the concentration is defined by a convection‐dominated diffusion equation. The pressure generates Darcy velocity and controls the dynamic change of concentration. We adopt a conservative block‐centered scheme to approximate the pressure and Darcy velocity, and the accuracy of Darcy velocity is improved one order. We use a block‐centered upwind multistep method to solve the concentration, where the time derivative is approximated by multistep method, and the diffusion term and convection term are treated by a block‐centered scheme and an upwind scheme, respectively. The composite algorithm is effective to solve such a convection‐dominated problem, since numerical oscillation and dispersion are avoided and computational accuracy is improved. Block‐centered method is conservative, and the concentration and the adjoint function are computed simultaneously. This physical nature is important in numerical simulation of seepage fluid. Using the convergence theory and techniques of priori estimates, we derive optimal estimate error. Numerical experiments and data show the support and consistency of theoretical result. The argument in the present paper shows a powerful tool to solve the well‐known model problem.     

On generalized Stokes’ and Brinkman’s equations with a pressure- and shear-dependent viscosity and drag coefficient

We study generalizations of the Darcy, Forchheimer, Brinkman and Stokes problem in which the viscosity and the drag coefficient depend on the shear rate and the pressure. We focus on existence of weak solutions to the problem, with the chief aim to capture as wide a group of viscosities and drag coefficients as mathematically feasible and to provide a theory that holds under minimal, not very restrictive conditions. Even in the case of generalized Stokes system, the established result answers a question on existence of weak solutions that has been open so far.     

Fundamental solutions in the linear theory of consolidation for elastic solids with double porosity

This paper concerns the theory of consolidation for elastic solids with double porosity, and the governing fully coupled linear quasi-static equations are considered. The system of these equations is based on the equilibrium equations for a solid, conservation of fluid mass, the effective stress concept, and Darcy’s law for material with double porosity. Two levels of spatial cases of consolidation theory for a solid with double porosity are considered: equations of steady vibrations and equations of equilibrium. The fundamental solutions of these equations are constructed by means of elementary functions. Finally, the basic properties of these solutions are established.     

Fluid flow in an inhomogeneous granular medium

The seepage of a compressible fluid in an inhomogeneous undeformable granular medium is investigated. It is assumed that the fluid flow in a porous space is described by the Navier–Stokes equations. It is shown that, in the case of an inhomogeneous velocity field, a tensor of additional effective stresses occurs in connection with the transfer of fluid particles in a transverse direction when flow occurs around the granules of the medium in a longitudinal direction. Using the fundamental propositions of Reynolds’ averaging theory and Prandtl's mixing path, the structure of the effective viscosity coefficient is determined and hypotheses are formulated which enable it to be assumed to be independent of the flow velocity. It is established by comparison with experimental data that the effective viscosity coefficient can exceed the viscosity coefficient of the flowing fluid by an order of magnitude. The equations of average motion are obtained, which in the case of an incompressible fluid have the form of the Navier–Stokes equations with body forces proportional to the velocity. It is established that, in addition to the well-known dimensionless flow numbers, there is a new number which characterizes the ratio of the Darcy porous drag forces to the effective viscosity forces. The proposed equations are extended to the case of the flow of an aerated fluid. The components of the angular momentum vector are used as the required functions instead of the components of the velocity vector. This enables a solving system of equations to be obtained, which, apart from the notation, is identical with the similar equations for the case of an incompressible fluid. The solution of a new problem of the fluid flow in a plane channel with permeable walls is presented using three models: Darcy's law for an incompressible and aerated fluid, and also of an aerated fluid taking the effective viscosity into account. It is established that, for the same pressure drop, the maximum flow rate corresponds to Darcy's law. Compressibility leads to its reduction, but by simultaneously taking into account the compressibility and the effective viscosity one obtains minimum values of the flow rate. The effective viscosity and aeration of the fluid has a considerable effect on the flow parameters.     

多孔介质驱动问题的混合元最小二乘特征有限元方法及其收敛分析

１．引言多孔介质二相驱动问题的数学模型是偶合的非线性偏微分方程组的初边值问题．该问题可转化为压力方程和浓度方程［１－４］．浓度方程一般是对流占优的对流扩散方程,它的对流速度依赖于比浓度方程的扩散系数大得多的Ｆａｒｃｙ速度．因此Ｄａｒｃｙ速度的求解精度直接影响着浓度的求解精度．为了提高速度的求解精度,７０年代Ｐ．Ａ．Ｒａｖｉａｔ和Ｊ．Ｍ．Ｔｈｏｍａｓ提出混合有限元方法［５］．Ｊ．ＤｏｕｇｌａｓＪｒ,Ｔ．Ｆ．Ｒｕｓｓｅｌｌ,Ｒ．Ｅ．Ｅｗｉｎｇ,Ｍ．Ｆ．Ｗｈｅｅｌｅｒ［１］－［４］,［９］,［１２］袁…     

On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium

Homotopy analysis method (HAM) is employed to investigate the momentum, heat and mass transfer characteristics of MHD natural convection flow and heat generation fluid driven by a continuously moving permeable surface immersed in a fluid saturated porous medium. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Prandtl number, Darcy number, the dimensionless inertia coefficient, the dimensionless heat generation/absorption coefficient and the dimensionless suction/blowing coefficient. A parametric study of all governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for velocity and temperature distributions as well as the local friction coefficient and local Nusselt number. Finally, a proper discussion is derived on the obtained results and some remarkable conclusions are mentioned.