Bing Bai

Experimental investigation and modeling of particulate transportation and deposition in vertical and horizontal flows

Saturated soil column experiments were conducted to determine the influences of flow direction, flow rate, and particle-size distribution characteristics on the transport and deposition of particles in saturated porous media. Two bimodal-distribution particles and one unimodal-distribution particle were employed in these studies, and soil column experiments were performed using a variety of particle-size distributions and flow conditions. In addition, a modified convection–dispersion model for particle transport and deposition was developed, considering dispersive flux on the deposition kinetics. The experimental breakthrough curves fit well with the analytical solution of the modified convection–dispersion model. Regardless of particle-size distribution, the particles’ mean velocity increases linearly with the mean interstitial fluid velocity. The particles’ mean velocity in horizontal flow is lower than that in vertical flow. Furthermore, dispersivity decreases with increasing flow rate in vertical flow. The range of the particles’ dispersivity in vertical flow is larger than that in horizontal flow. Finally, the rate of particle deposition increases with particle size. Overall, this study highlights the complicated interdependence of the effects of flow rate, flow direction, and particle-size distribution on particulate transportation and deposition.RésuméDes expérimentations sur colonne de sol saturé ont été menées pour déterminer les influences de la direction et de la vitesse de l’écoulement et des caractéristiques de la distribution de la taille des particules sur le transport et le dépôt des particules dans un milieu poreux saturé. Deux distributions bimodales de particules et une distribution unimodale de particules ont été employées dans ces études, et les expérimentations sur colonne de sol ont été mises en œuvre en utilisant une variété de distribution de granulométrie et de conditions d’écoulements. De plus, un modèle de convection–dispersion modifié pour le transport de particules et pour le dépôt a été développé, en considérant l’influence d’un flux dispersif sur les cinétiques de dépôt. Les courbes de percée expérimentales correspondent bien à la solution analytique du modèle de convection–dispersion modifié. Quelle que soit la distribution des tailles de particules, la vitesse moyenne des particules augmente de manière linéaire avec la vitesse du fluide interstitiel. La vitesse moyenne des particules en écoulement horizontal est inférieure à celle en écoulement vertical. De plus, la dispersivité décroit avec l’augmentation de la vitesse d’écoulement en écoulement vertical. La gamme de valeurs de dispersivité des particules en écoulement vertical est plus grande qu’en écoulement horizontal. Enfin, le taux de dépôt des particules augmente avec la taille des particules. Dans l’ensemble, cette étude met en évidence l’interdépendance complexe des effets de la vitesse d’écoulement, de la direction d’écoulement, et de la distribution des tailles des particules sur le transport et le dépôt des particules.ResumenSe realizaron experimentos en columnas de suelos saturados para determinar la influencia de la dirección de flujo, velocidad de flujo y las características de la distribución del tamaño de partículas en el transporte y depositación de partículas en un medio poroso saturado. Se emplearon dos distribuciones bimodales y una unimodal de partículas en estos estudios, y los experimentos de columnas de suelo se llevaron a cabo usando una variedad de distribuciones de tamaño de partículas y condiciones de flujo. Además, se desarrolló un modelo modificado de convección – dispersión para el transporte y depositación de partículas, considerando un flujo dispersivo en la cinética de la depositación. Las curvas experimentales de ruptura ajustan bien con la solución analítica del modelo modificado de dispersión – convección. Independientemente de la distribución del tamaño de partículas, las velocidad media de las partículas se incrementa linealmente con la velocidad media del fluido intersticial. La velocidad media de las partículas en el flujo horizontal es más baja que en el flujo vertical. Además, la dispersividad disminuye con el incremento de la velocidad de flujo en la vertical. El rango de la dispersividad de las partículas en el flujo vertical es mayor que en el flujo horizontal. Finalmente, el ritmo de depositación de las partículas se incrementa con el tamaño de la partícula. En general, este estudio resalta la complicada interdependencia de los efectos sobre la velocidad de flujo, la dirección y el sentido de flujo y la distribución del tamaño de las partículas en el transporte y depositación.摘要进行了饱和土柱试验以确定水流方向、水流速度及粒径分布特征对饱和孔隙介质中微粒传输和沉积的影响。在这些研究中采用了两个双模分布微粒和一个单模分布微粒,土柱实验进行了使用各种不同的粒径分布和流动条件。此外,提出了一种改进的对流扩散模型–颗粒传输和沉积,考虑色散通量对沉积动力学。实验突破曲线与修改后的对流–色散模型解析解吻合良好。不论粒度分布,颗粒的平均速度呈线性增加的平均间质流体速度。粒子的平均速度水平流动是低于垂直流。此外,随着垂直流流量分散性降低。在垂直流粒子的分散性的范围是大于在水平流动。最后,颗粒沉积和颗粒尺寸的增加率。总体而言,本研究综合对复杂的相互依存的流量影响、流动方向和颗粒尺寸分布的颗粒传输和沉积。ResumoForam realizadas experiências de solos saturados em colunas para determinar as influências da direção de fluxo, do caudal e das caraterísticas de distribuição de tamanho de partículas no seu transporte e deposição em meios porosos saturados. Nestes estudos foram utlizadas distribuições bi- e uni-modais de partículas e realizadas experiências de colunas de solo utilizando uma variedade de distribuições granulométricas e de condições de fluxo. Além disso, foi desenvolvido um modelo de convecção-dispersão modificado para o transporte e a deposição de partículas, considerando-se o fluxo dispersivo na cinética de deposição. As curvas experimentais adequam-se bem com a solução analítica do modelo de convecção-dispersão modificado. Independentemente da distribuição de tamanho das partículas, a velocidade média das partículas aumenta linearmente com a velocidade média do fluido intersticial. A velocidade média das partículas no fluxo horizontal é menor do que a do fluxo vertical. Além disso, a dispersividade diminui com o aumento do caudal do fluxo vertical. A gama de dispersividade das partículas no fluxo vertical é maior do que a do fluxo horizontal. Finalmente, a taxa de deposição das partículas aumenta com o tamanho da partícula. Em síntese, este estudo destaca a interdependência complexa dos efeitos do caudal, da direção dos fluxos e da distribuição de tamanho das partículas no seu transporte e deposição.

Thermal Responses of Saturated Silty Clay During Repeated Heating–Cooling Processes

The thermal responses of the saturated silty clay to repeated heating–cooling are studied in laboratory. Results show that the pore pressure induced by undrained heating increases with increasing temperature, but the peak pore pressure appears a degradation trend with increasing temperature cycles. During the consolidation process at an elevated temperature, the specimen contracts due to the dissipation of the pore pressure; however, the thermally induced pore pressure is under no conditions fully dissipated to zero, therefore, there always exists a residual pore pressure in the specimens once a thermal loading higher than the ambient temperature is applied. During the undrained cooling, pore pressure continues to decline and eventually falls below zero. During the isothermal consolidation at the original temperature, the specimen begins to expand due to water absorption caused by the negative pore pressure, and eventually reaches a steady value. In addition, the consolidation volumetric strain generated during the drainage process at 50°C is greater than that during the water absorption process at 25°C, the difference seems to be most obvious for the first three cycles, and begins to diminish gradually thereafter.

Solutions for cylindrical cavity in saturated thermoporoelastic medium

Based on the thermodynamics of irreversible processes, the mass conservation equation and heat energy balance equation are established. The governing equations of thermal consolidation for homogeneous isotropic materials are presented, accounting for the coupling effects of the temperature, stress and displacement fields. The case of a saturated medium with a long cylindrical cavity subjected to a variable thermal loading and a variable hydrostatic pressure (or a variable radial water flux) with time is considered. The analytical solutions are derived in the Laplace transform space. Then, the time domain solutions are obtained by a numerical inversion scheme. The results of a typical example indicate that thermodynamically coupled effects have considerable influences on thermal responses.

Thermal Response of Saturated Porous Spherical Body Containing a Cavity under Several Boundary Conditions

A semi-analytical solution for the saturated porous spherical body containing a hollow space is discussed under several boundary conditions, including pervious surface versus impervious surface, boundary surface subjected to a variable temperature loading versus adiabatic surface, boundary surface subjected to a variable mechanical loading versus fixed displacement surface, and combined boundary conditions. Methods for determining the integration constants of the analytical expressions are derived. Numerical analyses are compared to demonstrate the thermal effects on the evolution of temperature, pore pressure, radial displacement, radial and tangential stresses in and around the geometry of the hollow spherical body subjected to thermal or mechanical perturbations.

The effect of temperature on the seepage transport of suspended particles in a porous medium

The main purpose of this study is to experimentally investigate the effect of temperature on the seepage transport of suspended particles (SP) with a median diameter of 10 − 47 µm in a porous medium for various seepage velocities. The results show that the rise of temperature accelerates the irregular movements of SPs in the porous medium and reduces their migration velocity. As a result, the pore volume corresponding to the peak value of the breakthrough curves is apparently delayed, and the peak value in the effluent is decreased. The migration velocity of SPs decreases with increasing particle size, regardless of the Darcy velocity and temperature. The longitudinal dispersivity of SPs decreases slightly with increasing temperature and then remains almost unchanged. Larger particles experience more irregular movements induced by the limit of pore size, which leads to a larger dispersivity. The deposition coefficient increases with increasing temperature, especially in the case of a high seepage velocity, and then tends to be stable. The deposition coefficient for large-sized particles is higher than that for small-sized particles, which can be attributed to the restriction of large-sized particles by the narrow pores in the porous medium. The recovery rate decreases slightly with the increase of temperature until a critical value is reached, beyond which it remains almost unchanged. In summary, temperature is a significant factor affecting the transport and deposition of SPs in the porous medium, and the transport parameters such as particle velocity, dispersivity and deposition coefficient.

SPH-FDM Boundary Method for the Heat Conduction of Geotechnical Materials Considering Phase Transition

A coupled SPH-FDM boundary is proposed for the analysis of thermal process in geotechnical materials, in which the smoothed particle hydrodynamics (SPH) method is used in the inner computational domain; and the finite difference method (FDM) is used as the function approximation near the boundary. The proposed coupled SPH-FDM boundary is applicable to the analysis of heat conduction in geotechnical materials, including the problems with discontinuous interface in the computational domain and the solidification of porous materials with a moving phase transition boundary. The effect of latent heat released in the phase transition is considered in the SPH method, and a weighted mean is used to determine the thermal parameters at the phase transition interface, which can be easily used to analyze the evolution of the moving phase transition interface over time. In general, there is a good agreement between the SPH results obtained using the three boundary treatments (coupled SPH-FDM boundary, no virtual particles, and virtual particles) and the analytical solution. The maximum error decreases gradually over time. Besides, it shows that as the thermal diffusion coefficient increases after the phase transition, the velocity of the moving phase transition interface increases, and the reduction rate in temperature in the non-solidified region decreases.

The Penetration Processes of Red Mud Filtrate in a Porous Medium by Seepage

This study investigated the effect of flow velocity, the concentration of red mud particles, and the concentration of

Fluctuation responses of saturated porous media subjected to cyclic thermal loading

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