分形多孔介质传热传质过程的格子Boltzmann模拟

针对自然界中实际多孔介质具有的分形特性和随机性,利用中点替代算法和二值化处理构造统计上具有分形特性的随机多孔介质。分析了所构造的多孔介质盒维数与Hurst指数之间的关系。基于随机分形构造的原理,对二维实际多孔介质图像进行了重构。利用两点相关函数,分析了重构图像的结构相关性,并与实际目标多孔介质的结构特征进行比较。在与解析解对比验证的基础上,将基于二元混合理论的格子Boltzmann模型(LBM)用于模拟多孔介质内流体扩散过程。通过计算不同分形特性的二维多孔介质的有效扩散系数,研究了重构多孔介质的分形维数与有效扩散系数的关系。利用热耦合LBM模型计算多孔介质内传热过程,分析了不同的分形特性对多孔介质蓄热过程的影响。     

气体有效扩散系数的分形模型

多孔介质中杂乱无序的孔分布结构特性显示了多孔介质具有孔分形结构。气体扩散在孔道中的分形模型是建立在分形理论和气体扩散特点的基础上。在考虑孔的大小分布、连通性分布和2种气体扩散机理的影响下,推导出了气体有效扩散系数和结构参数的关系。从参数分析中,可以得出有效扩散系数与孔的面积分形维数、孔隙率、联通数、气体自由扩散路径、孔最大最小直径比值成正比,与孔道迂曲度、迂曲分形维数成反比。通过实验数据与模型预测值对比验证了分形模型的正确性。     

多孔介质内孔表面的分形表征

通过对多孔介质全吸附过程的分析.在脱附过程自由能平衡的基础上.结合分形几何理论,推导了利用脱附数据计算多孔介质内孔表面分形维数的脱附分维标度关系式.实验及计算结果表明该标度关系式可靠.数据处理也比较简便.     

分形多孔介质的孔隙特性对气体扩散的影响

采用随机行走方法建立了分形多孔介质生成模型,生成的颗粒在形貌上与真实多孔颗粒接近,且能够反映其固有分形特征。在此模型基础上,根据经典分子动理论建立扩散控制方程,对气体在多孔介质中的扩散进行数值模拟。分析了比表面积、平均孔径、孔隙率等孔隙特性参数对扩散的影响,获得了分形多孔介质中气体扩散系数与平均孔径的函数关系。结果表明,扩散系数随平均孔径的增大以幂函数形式增大,相应的指数表征扩散系数对平均孔径的敏感度,其值随孔隙率的增大呈线性减小。     

在多孔介质内气体扩散的分形表征

将多孔介质内孔抽象为分形曲线,并以该曲线的维数作为多孔介质的结构参数—谱维数d,藉此建立了气体在介质内的扩散通量计算式,并给出了测量分形结构码尺的计算方程和多孔介质谱维数的测定方法.由双组分气体在Ni/r- Al_2O_3催化剂上的扩散实验数据,计算出该催化剂的谱维数d=1.10.     

泡沫液在均质多孔介质内动态驱替过程的二维数值模拟研究

利用随机泡沫数目守恒模型,针对具有收缩进口及收缩出口的均质多孔介质二维模型,对泡沫流体驱替突破前的动态过程开展了数值模拟研究。采用IMPES方法对二维两相泡沫动态驱替过程的控制方程组进行求解,通过液相压力、液相饱和度、气泡数目等参数在多孔介质内的分布结果对泡沫动态驱替特性进行了分析研究。数值模拟结果表明,泡沫驱替过程显示出明显的入口效应,其压力分布、液相饱和度及泡沫数目分布随气体与活化剂溶液在缩小入口的注入呈现明显的发展过程。在泡沫液未完成驱替突破的情况下,缩小出口未显示出对泡沫液驱替特性的影响。数值计算结果与相应实验结果趋势一致,表明所采用的随机泡沫数目守恒模型能够正确表征多孔介质中泡沫的生成及湮灭机理,进而对泡沫液在均质多孔介质内的动态驱替特性进行准确模拟和预测。     

泡沫液在均质多孔介质内动态驱替过程的二维数值模拟研究

利用随机泡沫数目守恒模型,针对具有收缩进口及收缩出口的均质多孔介质二维模型,对泡沫流体驱替突破前的动态过程开展了数值模拟研究。采用IMPES方法对二维两相泡沫动态驱替过程的控制方程组进行求解,通过液相压力、液相饱和度、气泡数目等参数在多孔介质内的分布结果对泡沫动态驱替特性进行了分析研究。数值模拟结果表明,泡沫驱替过程显示出明显的入口效应,其压力分布、液相饱和度及泡沫数目分布随气体与活化剂溶液在缩小入口的注入呈现明显的发展过程。在泡沫液未完成驱替突破的情况下,缩小出口未显示出对泡沫液驱替特性的影响。数值计算结果与相应实验结果趋势一致,表明所采用的随机泡沫数目守恒模型能够正确表征多孔介质中泡沫的生成及湮灭机理,进而对泡沫液在均质多孔介质内的动态驱替特性进行准确模拟和预测。     

基于分形理论的油页岩有效扩散系数研究

以直径为1.6—2 mm柳树河油页岩为原料,采用扫描电镜法与氮吸附法得出油页岩吸附-脱附等温线,孔径分布曲线等;分析了油页岩内部孔隙结构,计算出孔道弯曲分形维数与孔隙面积分形维数,并研究油页岩内部的有效扩散系数。结果表明:油页岩吸附-脱附曲线属于Ⅲ型等温线,是一种典型的二端都开放的管状毛细孔型结构的多孔物质;其含有较发达孔隙,孔径分布为0.4—40 nm;油页岩孔道弯曲分形维数越小,孔道越平坦,孔隙面积分形维数为2.464;油页岩有效扩散系数与其内部结构和操作温度有关,温度越高,粒径越小,有效扩散系数越大。     

混凝土孔结构及其分形维数与氯离子扩散性能的关系

氯离子扩散系数是研究海洋环境下混凝土结构耐久性的重要参数之一。通过开展不同水胶比混凝土的压汞试验和盐雾扩散试验,研究了混凝土内部孔隙率、孔径分布及临界孔径对氯离子扩散系数的影响规律。结合Menger海绵体模型,建立孔体积分形维数与氯离子扩散系数的关系。结果表明:孔隙率和临界孔径与无量纲化氯离子扩散系数的相关性很高,可作为反映混凝土氯离子扩散性能的重要参数;通过数学分析计算得到的孔表面分形维数分布在2.56~3.86之间,孔体积分形维数分布在2.85~2.98之间;基于压汞法和分形理论计算得到的孔体积分形维数可以作为评价氯离子扩散系数的指标,在孔径小于10 nm、10～100 nm、100～1 000 nm以及大于1 000 nm四类区间,氯离子扩散系数随孔体积分形维数的增加而下降。     

基于完全并行细化算法的孔隙网络中轴提取方法

应用三维重构技术建立介尺度下的多孔介质孔隙网络模型是分析多孔介质内流体流动与传热传质过程的基础,其中孔隙网络中轴的提取是三维重构的关键环节。在提取中轴的细化算法中,简单点集合细化方法具有准确、可并行的特点,但较少应用于多孔介质的结构分析。基于简单点集合细化方法中的完全并行细化算法,建立了一种面向多孔介质的孔隙网络中轴提取方法,包含图像处理、重构矩阵生成、逐层标记、并行细化四个主要步骤。以计算机生成的230个典型的有序多孔介质模型及1个活性炭堆积试样重构模型为研究对象,应用本方法获得了与研究对象的孔隙空间具有拓扑等价性的孔隙网络中轴,快速准确地计算了孔隙半径,利用中轴形态与孔隙半径计算孔隙占据的空间大小与实际体积比较,发现研究对象的孔隙体积计算值相对误差最终稳定在6%以下。结果表明,由本方法获得的中轴反映了孔隙空间的几何形状、减小了孔隙与固体界面处不规则变化的干扰,可用于多孔介质孔隙结构的无损定量分析及孔隙网络建模。     

A diffusivity model for gas diffusion through fractal porous media

A fractal model for gas diffusivity in porous media is derived by using fractal theory and by considering rarefied gas effect in micro-/nano-channels/capillaries. The proposed gas diffusivity model is expressed as a function of micro-structural parameters (the fractal dimensions for pore area and for tortuosity of tortuous capillaries, porosity and pore sizes) of porous media. The effects of parameters such as porosity, microstructures of porous media and fractal dimensions on gas diffusivity are analyzed. The effective diffusivities predicted by the present fractal model are compared with the available experimental data, and a fair agreement between them is found when porosity is less than about 0.70.     

Strategy for predicting effective transport properties of complex porous structures

Measurements of effective transport properties of porous media, such as effective diffusivity and permeability, are well established by several experimental techniques. Effective transport properties can be also calculated from the spatially 3D reconstructed porous media, where the morphology characteristics required for the reconstruction are obtained from electron microscopy images. Here we demonstrate the reconstruction of porous alumina catalyst carrier with bimodal pore size distribution. Multi-scale concept is employed for the computation of effective diffusivity and permeability of reconstructed porous media and calculated effective transport properties are compared with transport parameters experimentally determined in Graham diffusion and simple permeation cell. The limitations of current state-of-the-art reconstruction techniques for porous media with broad pore size distribution are discussed. We show that the contribution of nano-pores towards the total diffusion flux is significant and cannot be neglected, but it is reasonable to neglect the contribution of nano-pores towards the sample permeability.     

多孔介质的孔隙特性对气体扩散过程影响的直接数值模拟

引言多孔介质内的扩散过程广泛存在于化工、能源、环境和生物等领域,例如石油天然气开采、污水处理、填充床化学反应、催化剂和生物组织内的质量传递等,使得多孔介质内传质现象的研究尤为重要[1-2]。多孔介质由于结构和形状各异,难以有准确、有效且简单的描述方法,因而研究变得极为     

Modeling of ionic diffusivity in non-saturated cement-based materials using lattice Boltzmann method

The ionic diffusivity in non-saturated cement-based materials is quantitatively studied using lattice Boltzmann method. The Shan–Chen multi-phase lattice Boltzmann model modified by incorporating the Carnahan–Starling equation of state into the model is used to simulate the equilibrium distribution of water and gas phases with density ratio as high as 775 in the three-dimensional microstructure of cement paste at various degrees of water saturation. The lattice Boltzmann diffusion model is subsequently applied to simulate the diffusion process of the ionic species through the partially saturated cement paste. Before the application of the modified Shan–Chen model, the benchmark tests including bubble test and contact angle test are carried out to validate it. It is shown that the ionic diffusivity is greatly influenced by the degree of water saturation. The simulated relative ionic diffusivity as a function degree of water saturation is in good agreement with the experimental data obtained from literature. In addition, the effect of w/c ratio on the ionic diffusivity through cement paste under non-saturated conditions is investigated. It indicates that there is a significant difference between the relative diffusivity for cement paste with w/c ratios of 0.4 and 0.5 over the whole range of water saturation degree. However, the difference of relative diffusivity for cement paste with w/c ratios of 0.5 and 0.6 is not obvious.     

REV尺度多孔介质格子Boltzmann方法的数学模型及应用的研究进展

综述了多孔介质表征体元尺度(REV)格子Boltzmann模型的研究进展,根据对多孔介质处理方式主要分为部分反弹模型和阻力模型两类,分析归纳了各类模型的优缺点。由于阻力模型中渗流的广义格子Boltzmann方程(GLBE)的作用力是基于GUO等的作用力模型,可以准确得到宏观方程,不存在离散误差,且模型的平衡分布函数和作用力项中都包含反应介质特性的孔隙率,因而应用最为广泛。本文还重点介绍了REV尺度多孔介质LBE模型在流动、传热、传质、化学反应及相变等过程中的具体应用,认为REV尺度多孔介质内的三传一反数学模型中需要加入孔隙尺度因素,在更大工程尺度上应该考虑过程参数的各向异性,展望了REV尺度多孔介质LBE模型的发展和应用前景。     

分形多孔介质中气体的非稳态扩散

通过引入平均修正系数修正Fick第二扩散定律得到了描述分形多孔介质气体非稳态扩散的理论方程。基于“塞状流”扩散实验法建立了分形多孔介质非稳态扩散实验系统,对3个孔隙结构不同的分形多孔介质样品进行了非稳态扩散实验,通过实验对理论方程进行验证和修正。结果表明,Fick第二扩散定律不适用于分形多孔介质中气体非稳态扩散,分形多孔介质中气体非稳态扩散存在一定规律,且多孔介质孔隙结构不同其扩散规律不同。     

逾渗多孔介质对固体颗粒吸附过程的影响

研究了悬浮液中的颗粒在通过逾渗多孔介质时的被吸附特性。采用数值计算的方法;通过求解描述低速流体流动的Stokes方程以及简化的颗粒运动方程;初步得到颗粒在逾渗多孔介质中的运动轨迹;并在此基础上;求得颗粒与多孔介质内表面的碰撞概率;进而研究颗粒的被吸附特性。数值结果表明均匀多孔介质和分形多孔介质对颗粒的吸附存在本质差异。颗粒流出概率（实际中常表示为出口悬浮液中的颗粒浓度）与多孔床深度间的指数关系仅对均匀多孔介质成立;而对分形多孔介质并不成立。     

Particle flow behavior in three-phase fluidized beds

Non-uniform flow behavior of fluidized solid particles in three-phase fluidized beds has been analyzed by adopting the stochastic method. More specifically, pressure fluctuation signals from three-phase fluidized beds (0.152 m ID x 2.5 m in height) have been analyzed by resorting to fractal and spectral analysis. Effects of gas flow rate (0.01-0.07 m/s), liquid flow rate (0.06-0.18 m/s) and particle size (0.001-0.006 m) on the characteristics of the Hurst exponent, spectral exponent and Shannon entropy of pressure fluctuations have been investigated. The Hurst exponent and spectral exponent of pressure fluctuations attained their local maxima with the variation of liquid flow rate. The Shannon entropy of pressure fluctuation data, however, attained its local minima with the variation of liquid flow rate. The flow transition of fluidized solid particles was detected conveniently by means of the variations of the Hurst exponent, spectral exponent and Shannon entropy of pressure fluctuations in the beds. The flow behavior resulting from multiphase contact in three-phase fluidized beds appeared to be persistent and can be characterized as a higher order deterministic chaos.     

Determination of the effects of the pore size distribution and pore connectivity distribution on the pore tortuosity and diffusive transport in model porous networks

An efficient computation method to study flow and transport process of small molecules in porous media using a dual site-bond lattice model, DBSM, is described. The microscopic properties of the porous network take into account the influence of local heterogeneities during the simulations. The numerical experiments demonstrated the combined effect of pore size distribution and connectivity distribution on the mass transport properties and the structural tortuosity. The results indicate that the pore size distribution and percolation phenomena related with pore shielding effects, influence significantly the tortuosity and the effective diffusivity of the porous network. Also, the simulations raise the important role of the connectivity distribution among the various pores in the gas diffusive properties of the poorly connected networks.