双层球壳结构准静态线性化学弹性问题的位移势函数解

本文研究了各向同性固体的化学-力学耦合问题,在传统化学弹性理论描述的扩散-变形耦合关系基础上,进一步考虑了化学反应与固体变形的相互作用关系,发展了等温状态下固体-扩散-反应-变形耦合的线性化学弹性理论,拓展了化学弹性力学的应用范围．该理论能够同时描述固体内介质扩散和固体与介质之间化学反应两个不同时间尺度的化学过程,并给出由此引起的弹性范围内的应变和应力．为应用该模型求解具体化学弹性问题,本文通过构造扩散-反应位移势函数来获得位移特解形式,再与齐次Lamé方程通解叠加获得完整解;针对反应控制问题,引入化学弹性准静态假设,将反应-扩散-变形全耦合的瞬态过程分解为两个可解耦的相继过程,从而获得相应位移解．基于此解法,本文获得了反应控制的双层球壳结构化学弹性问题的解析解,并分析了化学反应、几何结构和弹性模量对应力分布的影响．     

饱和黏弹性多孔介质中的平面波及能量耗散

研究了流体饱和不可压黏弹性多孔介质中的非均匀平面波及其能量流和能量耗散规律. 在流 相和固相物质微观不可压、固相骨架宏观服从积分型本构关系和小变形的假定下，利用 Helmholtz分解，得到了饱和黏弹性多孔介质中非均匀平面波的一般解以及纵波、横波相速 度和衰减率等的解析表达式，分析了平面波传播矢量和衰减矢量之间的关系. 数值结果表明 孔隙流体与固相骨架间的相互作用以及固相骨架的黏性对波的相速度、衰减率等有着显著的 影响. 同时，得到了饱和黏弹性多孔介质的能量方程，给出了能量流矢量和能量耗散率. 对 非均匀平面纵波和横波，推导了平均能量流矢量和平均能量耗散率的解析表达式.     

溶质输运问题的数值反演解

溶液在多孔介质中渗流,将发生溶质弥散、吸附、沉淀、离子交换等物理、化学作用。研究这种化学输运过程,对三次采油提高原油采收率以及地下污水处理,都有重要意义。Tang用Laplace变换法分别研究了单向和径向输运问题,经过解析反演,求得了精确解。但解是用复杂的旁义积分表的,不仅很难分析公式中各物理量的意义,而且求其数值结果也很繁琐,不易推广应...     

流固耦合地震波动问题的显式谱元模拟方法

流固耦合地震波动问题主要研究由流体和固体构成的复杂系统中地震波传播特性及其规律. 传统模拟方法中一般以声波方程、弹性波方程的数值解分别描述理想流体和弹性固体中的波动, 并实时地处理两种不同性质介质之间的相互耦合作用, 数值格式复杂且限制数值模拟精度与计算效率. 本文采用谱元法结合多次透射公式人工边界条件实现了一种流固耦合地震波动问题的高阶显式数值计算方法. 该方法利用了流固耦合问题统一计算框架,可将饱和多孔介质的Biot波动方程分别退化为理想流体的声波方程和弹性固体的弹性波方程. 通过P波垂直入射的水平成层理想流体-饱和多孔介质-弹性固体场地模型、P波斜入射的不规则层状界面以及任意形状界面的理想流体-饱和多孔介质-弹性固体场地模型等三个算例, 与传递函数法解析解以及集中质量有限元法计算结果进行对比分析, 证明了本文方法的正确性与有效性. 数值模拟结果表明, 本文方法相较传统有限元法可以少得多的节点数量获得更高的数值精度, 并且在较宽的频率范围内都能可靠地模拟出流固耦合系统的动力响应, 充分体现出本文方法兼顾高精度、计算效率和复杂场地建模灵活的特点.      

考虑化学-力学耦合的稳态裂纹问题

含有化学过程的多场耦合问题广泛存在于天然多孔介质、生物组织和新型功能材料中，其中各物质组分在应力、化学势梯度、温度差和电势差等共同作用下，会发生质量、动量和能量的传递和转化．本文研究了稳态扩散下有限厚度平板中的I型裂纹问题．通过傅里叶变换和引入位错密度函数，将问题归结为求解一组奇异积分方程，采用Lobatto-Chebyshev方法对其进行数值求解，最后对化学势分布和应力强度因子进行了讨论．     

混凝土中化学-热-湿-力耦合过程的数值方法

提出了一个火灾下混凝土中化学-热-湿-力耦合过程分析的两级数学模型. 混凝 土模型化为充满两种非混溶孔隙流体的非饱和变形多孔多相介质. 数学模型基于控制干空 气、湿份及基质溶解物的质量守恒、混凝土介质混合体的动量守恒和焓(能量)守恒的耦合 偏微分方程组. 模型中特别考虑到了高温下的脱盐过程. 构造了一个用于数值模拟 化学-热-湿-力耦合行为的有限元求解过程的混合弱形式. 并且针对其中具有非自伴随算子特性的 双曲线控制方程的空间离散进行了特殊考虑. 数值结果例题显示所发展的数学模型和数值方 法在重现火灾条件下的混凝土中化学-热-湿-力耦合行为的有效性.     

二维拉氏辐射流体力学人为解构造方法

人为构造解方法是复杂多物理过程耦合程序正确性验证的重要方法之一，适用于二维拉氏大变形网格的流体、辐射耦合人为解模型较为少见。针对拉氏辐射流体力学程序正确性验证的需要，从二维拉氏辐射流体力学方程组出发，基于坐标变换技术，给出了拉氏空间到欧氏空间的物理变量导数关系式，开展了辐射流体耦合的人为解构造方法研究，构造了一类质量方程无源项的二维人为解模型，并应用于非结构拉氏程序LAD2D辐射流体力学计算的正确性考核，为流体运动网格上的辐射扩散计算提供了一种有效手段。数值结果显示观测到的数值模拟收敛阶与理论分析一致。     

压裂页岩气藏多尺度耦合流动数值模拟研究

在碳达峰的国策背景之下,页岩气成为传统能源向绿色清洁低碳能源转型的重要过渡和能源支点.压后页岩气藏流体流动力学成为高效开发页岩气的关键力学问题.文章将小尺度低导流天然裂缝等效升级为连续介质,建立有机质-无机质-天然裂缝三重连续介质模型,同时对大尺度高导流裂缝采用离散裂缝模型刻画,嵌入天然裂缝连续介质中,构建多重连续/离散裂缝模型.综合考虑吸附气的非平衡非线性解吸附和表面扩散,自由气的黏性流和克努森扩散,给出页岩气在多尺度复杂介质中的非线性耦合流动数学模型.提出多尺度扩展有限单元法对离散裂缝进行显式求解,创新性构建三类加强形函数捕捉离散裂缝的局部流场特征,解决了压后页岩海量裂缝及多尺度流动通道的流动模拟难题.文章提出的模型和方法既能准确刻画高导流裂缝对渗流的影响,又克服了海量多尺度离散裂缝导致计算量增大的问题.通过算例展示了压后页岩各连续介质的压力衰减规律,发现裂缝中自由气、有机质中自由气、无机质中吸附气依次滞后的压力(浓度)扩散现象,重点分析了吸附气表面扩散系数、自由气克努森扩散系数、天然裂缝连续介质渗透率和吸附气解吸附速率对页岩气产量的影响.文章重点解决压后页岩多尺度流动通道的表征和...     

水蚀性岩层中的渗流和无机污染物的迁移

介绍水蚀性岩层中的渗流及金属和无机污染物迁移问题．通过对含有污染物的某些蓄水系统中的物理和化学过程的分析得出一些结论，并对这些过程不仅作了详细的说明，而且采用恰当的数学和化学方程加以讨论．在水蚀性岩层中无机污染物的迁移用高渗透率多孔介质中流动的基本方程近似地描述，而对流、水动力学扩散、稀释等影响可作为物理过程来阐述．总的说来，控制裂隙岩体中地下水流动与污染物输运的物理和化学机理是建立水蚀性岩层中无机污染物输运近似方法的基础．     

基于统一相场理论的锂电池电极颗粒断裂模拟研究

锂电池充放电过程中, 锂离子的脱出和嵌入会引发电极颗粒的不均匀体积变化和机械应力. 上述锂离子扩散过程诱发的应力与电极颗粒的尺寸大小、截面形状和冲放电速率有关, 可能会导致电极颗粒出现裂缝起裂、扩展甚至断裂等力学失效, 对锂离子电池的容量和循环寿命等性能产生不利影响. 为准确模拟并预测电极颗粒的力学失效过程, 在笔者前期提出的统一相场理论框架内进一步考虑化学扩散、力学变形和裂缝演化等耦合过程, 建立化学–力学耦合相场内聚裂缝模型, 发展相应的多场有限元数值实现算法, 并应用于二维柱状和三维球体锂电池电极颗粒的力学失效分析. 由于同时涵括了基于强度的起裂准则、基于能量的扩展准则以及基于变分原理的裂缝路径判据, 这一模型不仅适用于带初始缺陷电极颗粒的开裂行为模拟, 而且适用于无初始缺陷电极颗粒的损伤破坏全过程分析. 数值计算结果表明, 相场内聚裂缝模型能够模拟锂离子扩散引发的电极颗粒裂缝起裂、扩展、汇聚等复杂演化过程, 可为锂离子电池电极颗粒的力学失效预测和优化设计提供有益的参考.      

A sequential numerical chemical compositional simulator

Chemical flooding in the petroleum industry has a larger scale of oil recovery efficiency than water flooding. On the other hand, it is far more technical, costly, and risky. Numerical reservoir simulation can be employed to conduct mechanism study, feasibility evaluation, pilot plan optimization, and performance prediction for chemical flooding to improve recovery efficiency and reduce operational costs. In this article, we study numerical simulation of chemical flooding such as alkaline, surfactant, polymer, and foam (ASP+foam) flooding. The main displacement mechanisms in this type of flooding are interfacial tension lowering, capillary desaturation, chemical synergetic effects, and mobility control. The model of chemical flooding involves such physicochemical phenomena as dispersion, diffusion, adsorption, chemical reactions, and in situ generation of surfactant from acidic crude oil. The numerical simulator is based on a sequential solution approach that solves both pressure and compositions implicitly, and is applied to three experiments, a chemical flow without mass transfer between phases, a laboratory sandstone core, and an ASP+foam displacement problem with mass transfer, and to a real oilfield. A comparison with UTCHEM is also performed. These applications and comparison indicate that this numerical simulator is practical, efficient, and accurate for simulating complex chemical flooding processes.      

Microscopic Roles of “Viscoelasticity” in HPMA polymer flooding for EOR

A polymer solution with a transient network structure due to the entanglement of long chain molecules exhibits a viscoelastic behavior when it flows through a tortuous and diverging/converging channel in porous media. A constitutive equation is first developed to represent the viscoelastic behavior of polymer solutions in this article. Then a 3D viscoelastic polymer flooding model is established to examine the effect of elasticity of polymers on EOR (enhanced oil recovery). The model is validated in comparison with laboratorial coring data. The simulated results show that the oil recovery of viscoelastic polymer flooding can be enhanced by larger displacement efficiency due to its microscopic roles. In the meanwhile, the injection pressure required increases correspondingly if the elastic effect is significant. Relaxation time as a major characteristic parameter of viscoelastic polymer plays a decisive role, and therefore the HPAM (partially hydrolyzed polyacrylamide) with evident elastic property is recommended in chemical flooding.     

考虑介质微观非均质特征的乳状液渗流模型

油水乳化渗流是三元复合驱和热力采油过程中常见的现象,地层介质的微观孔隙结构特征对乳状液流动有着重要影响.现有描述乳状液渗流的理论模型都属于确定性方法,只能反映出介质孔隙结构的体积平均效果.当介质内部微观非均质性相比其尺寸不能被忽略时,采用确定性方法描述会与实验结果存在偏差.基于连续时间随机游走理论建立了描述乳状液渗流的随机理论模型.该模型引入反映液滴微观运动特征的跃迁时间和跃迁位移两个概率分布函数来反映多孔介质微观非均质特征.研究结果表明该模型能很好地刻画实验曲线中出现的与介质尺度相关的拖尾现象,可作为更一般的过滤模型.     

Free Flow at the Interface of Porous Surfaces: A Generalization of the Taylor Brush Configuration

A solution to the problem of shallow laminar water flow above a porous surface is essential when modeling phenomena such as erosion, resuspension, and mass transfer between the porous media and the flow above it. Previous studies proposed theoretical, experimental, and numerical insight with no single general solution to the problem. Many studies have used the Brinkman equation, while others showed that it does not represent the actual interface flow conditions. In this paper we show that the interface macroscopic velocity can be accurately modeled by introducing a modification to the Brinkman equation. A moving average approach was proved to be successful when choosing the correct representative elementary volume and comparing the macroscopic solution with the average microscopic flow. As the size of the representative elementary volume was found to be equal to the product of the square root of the permeability and an exponential function of the porosity, a general solution is now available for any brush configuration. Given the properties of the porous media (porosity and permeability), the flow height and its driving force, a complete macroscopic solution of the interface flow is obtained.     

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.     

Boundary domain integral method for transport phenomena in porous media

A boundary domain integral method (BDIM) for the solution of transport phenomena in porous media is presented. The complete, so‐called modified Navier–Stokes equations (Brinkman‐extended Darcy formulation with inertial term included) have been used to describe the fluid motion in porous media. Velocity–vorticity formulation (VVF) of the conservative equations is employed. In this paper, the proposed numerical scheme is tested on a particular case of natural convection and the results of flow and heat transfer characteristics of a fluid in a vertical porous cavity heated from the side and saturated with Newtonian fluid are presented in detail. Copyright © 2001 John Wiley & Sons, Ltd.     

A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs

The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.     

Fully-developed conjugate heat transfer in porous media with uniform heating

We propose a computational method for approximating the heat transfer coefficient of fully-developed flow in porous media. For a representative elementary volume of the porous medium we develop a transport model subject to periodic boundary conditions that describes incompressible fluid flow through a uniformly heated porous solid. The transport model uses a pair of pore-scale energy equations to describe conjugate heat transfer. With this approach, the effect of solid and fluid material properties, such as volumetric heat capacity and thermal conductivity, on the overall heat transfer coefficient can be investigated. To cope with geometrically complex domains we develop a numerical method for solving the transport equations on a Cartesian grid. The computational method provides a means for approximating the heat transfer coefficient of porous media where the heat generated in the solid varies “slowly” with respect to the space and time scales of the developing fluid. We validate the proposed method by computing the Nusselt number for fully developed laminar flow in tubes of rectangular cross section with uniform wall heat flux. Detailed results on the variation of the Nusselt number with system parameters are presented for two structured models of porous media: an inline and a staggered arrangement of square rods. For these configurations a comparison is made with literature on fully-developed flows with isothermal walls.     

Development and Validation of a New Model for In Situ Foam Generation Using Foamer Droplets Injection

Transport in Porous Media - Foam generation and transport in porous media are a proven method to improve the sweep efficiency of a flooding fluid in enhanced oil recovery process and increase the...     

A numerical study of fluids with pressure‐dependent viscosity flowing through a rigid porous medium

Much of the work on flow through porous media, especially with regard to studies on the flow of oil, are based on ‘Darcy's law’ or modifications to it, such as Darcy–Forchheimer or Brinkman models. While many theoretical and numerical studies concerning flow through porous media have taken into account the inhomogeneity and anisotropy of the porous solid, they have not taken into account the fact that the viscosity of the fluid and drag coefficient could depend on the pressure in applications, such as enhanced oil recovery (EOR). Experiments clearly indicate that the viscosity varies exponentially with respect to the pressure and the viscosity can change, in some applications, by several orders of magnitude. The fact that the viscosity depends on pressure immediately implies that the ‘drag coefficient’ would also depend on the pressure. In this paper we consider modifications to Darcy's equation wherein the drag coefficient is a function of pressure, which is a realistic model for technological applications, such as EOR and geological carbon sequestration. We first outline the approximations behind Darcy's equation and the modifications that we propose to Darcy's equation, and derive the governing equations through a systematic approach using mixture theory. We then propose a stabilized mixed finite element formulation for the modified Darcy's equation. To solve the resulting nonlinear equations we present a solution procedure based on the consistent Newton–Raphson method. We solve representative test problems to illustrate the performance of the proposed stabilized formulation. One of the objectives of this paper is to show that the dependence of viscosity on the pressure can have a significant effect both on the qualitative and quantitative nature of the solution. Copyright © 2010 John Wiley & Sons, Ltd.