Abstract
This study experimentally investigates the effect of particle size, particle concentration and flow velocity on the migration of suspended particles of size 1.02–47 μm in porous media. The results show that at the same flow velocity, the peak values of the breakthrough curves decrease and corresponding pore volumes increase slightly with increasing particles size. The migration velocity of smaller suspended particles is even greater than water flow velocity, which is attributed to the size exclusion effect. With increase of the injected particle concentration, the deposition coefficients of small single particles increase at first and then tend to a steady state or even decrease slightly, explained by the maximum retention concentration. The dispersivity of small particles decreases with increasing velocity. However, at a high flow velocity, the hydrodynamic dispersivity becomes increasingly dominant with the increase of particle size. The deposition coefficients for large-sized particles are higher than those for small-sized particles, which is attributed to considerable mass removal due to straining. An analytical solution, considering the release effect of sorbed particles, is developed to account for the one-dimensional flow and dispersive effect using a source function method, and then three transport parameters—dispersivity, deposition coefficient and release coefficient—are fitted using the experimental results. Finally, suspended-particle migration is predicted by the proposed model for short-time constant-concentration injection and repeated three-pulse injection. Overall, particle size has a significant effect on the seepage migration parameters of suspended particles in porous media such as the particle velocity, dispersivity and deposition coefficient.
Résumé
Cette étude examine de manière expérimentale l’effet de la taille des particules, de la concentration des particules et de la vitesse d’écoulement sur la migration de particules en suspension de taille comprise entre 1.02 et 47 μm dans le milieu poreux. Les résultats montrent qu’à la même vitesse d’écoulement, les valeurs au pic des courbes de percée diminuent et que le volume des pores correspondant augmente légèrement avec l’augmentation de la taille des particules. La vitesse de migration des plus petites particules en suspension est même plus grande que la vitesse d’écoulement de l’eau, ce qui est attribué à l’effet d’exclusion par la taille. Avec l’augmentation de la concentration de particules injectées, les coefficients de dépôt de petites particules individuelles augmentent d’abord, puis tendent vers un état permanent ou même décroissent légèrement, ce qui est expliqué par la concentration maximale de rétention. La dispersivité de petites particules diminue avec l’augmentation de la vitesse. Cependant, à une vitesse d’écoulement élevée, la dispersivité hydrodynamique devient de plus en plus dominante avec l’augmentation de la taille des particules. Les coefficients de dépôt pour les particules de grande taille sont plus élevés que ceux des particules de petite taille, ce qui est attribué à l’élimination considérable de masse en raison de la tension. Une solution analytique, considérant l’effet de libération des particules absorbées, est développée afin de tenir compte de l’écoulement à une dimension et de l’effet dispersif en utilisant une méthode de la fonction de la source, puis trois paramètres de transport—dispersivité, coefficient de dépôt et coefficient de libération—sont calibrés à l’aide des résultats expérimentaux. Enfin, la migration des particules en suspension est prédite par le modèle proposé pour une injection à concentration constante et de courte durée et pour des injections répétées selon trois impulsions. En général, la taille des particules a un effet significatif sur les paramètres de migration d’infiltration de particules suspendus dans un milieu poreux, tels que la vitesse des particules, la dispersivité et le coefficient de dépôt.
Resumen
Este estudio investiga experimentalmente el efecto del tamaño de partícula, de la concentración de partículas y de la velocidad de flujo en la migración de las partículas en suspensión de un tamaño de 1.02−47 μm en medios porosos. Los resultados muestran que a la misma velocidad de flujo, los valores pico en las curvas de ruptura disminuyen y los volúmenes porales correspondientes aumentan ligeramente con el aumento de tamaño de las partículas. La velocidad de migración de las partículas en suspensión más pequeñas es incluso mayor que la velocidad del flujo de agua, lo cual se atribuye a un efecto de exclusión por tamaño. Con el aumento de la concentración de las partículas inyectadas, los coeficientes de la depositación de las partículas individuales pequeñas aumentan al principio y luego tienden a un estado estable o incluso a disminuir ligeramente, explicados por la concentración máxima de retención. La dispersividad de pequeñas partículas disminuye al aumentar la velocidad. Sin embargo, a una alta velocidad de flujo, la dispersividad hidrodinámica se convierte en cada vez más dominante con el aumento de tamaño de partícula. Los coeficientes de depositación de partículas de tamaño grande son superiores a las de partículas de tamaño pequeño, lo cual se atribuye a la eliminación de una masa considerable debido a la presión. Se desarrolló una solución analítica, teniendo en cuenta el efecto de liberación de partículas absorbidas, para tener en cuenta el flujo unidimensional y el efecto de dispersión utilizando un método de función de fuente, y luego tres parámetros de transporte—dispersividad, coeficiente de depositación y coeficiente de liberación—ajustados con los resultados experimentales. Por último, la migración de partículas en suspensión es predicha por el modelo propuesto para una inyección de concentración constante de corta duración y repetida por la inyección de tres impulsos. El tamaño global de partícula tiene un efecto significativo en los parámetros de la migración de la filtración de las partículas en suspensión en medios porosos, tales como la velocidad de partícula, la dispersividad y el coeficiente de depositación.
摘要
通过室内试验研究多孔介质内粒径为1.02–47 μm的悬浮颗粒渗透迁移过程的尺度效应、颗粒浓度和渗透速度的影响。结果表明,在同一渗透速度下穿透曲线的浓度峰值随颗粒粒径的增大而减小,相应的孔隙体积数则略有增大。对于较小粒径的悬浮颗粒,其颗粒迁移速度甚至大于渗透水流的速度,其原因可归结为所谓尺寸排除效应。随注入颗粒浓度的增大,小颗粒的沉积系数先有所增大而后趋于稳定值甚至略有减小,其原因可由最大阻滞浓度函数的概念来解释。小颗粒的弥散性随渗透速度的增大而增大。 然而,在渗透速度较大时,水动力弥散效应随颗粒的增大而更加明显。大尺度颗粒的沉积系数要大于小尺度颗粒的沉积系数,其原因归结为多孔介质孔隙对颗粒的约束效应。根据源函数法,给出一维渗流情形下考虑吸附颗粒释放效应的解析解,并利用试验结果对弥散性、沉积系数和释放系数三个迁移参数进行拟合。最后,利用所建立的理论模型对短期恒定浓度注入和三个脉冲重复注入的情形进行预测。总体来看,颗粒尺度效应对多孔介质内悬浮颗粒渗透迁移的诸如颗粒迁移速度、弥散性和沉积系数有重要的影响。
Resumo
Esse estudo investiga experimentalmente o efeito do tamanho, da concentração e da velocidade do fluxo de migração de partículas suspensas de 1.02–47 μm no meio poroso. Os resultados demonstram que sob a mesma velocidade, os valores máximos da curva de identificação diminuem e os volumes de poros correspondentes levemente aumentam com o aumento no tamanho da partícula. A velocidade de migração de partículas suspensas menores é até maior que a velocidade de fluxo da água, que é atribuído ao efeito de exclusão do tamanho. Com o aumento da concentração de partículas injetadas, os coeficientes de deposição de pequenas partículas aumentam em principio e então tendem a um estado estável ou diminuir levemente, explicada pela concentração máxima de retenção. A dispersividade de pequenas partículas diminui com o aumento da velocidade. Entretanto, com velocidade de fluxo alta, a dispersividade hidrodinâmica se torna amplamente dominante com o aumento do tamanho da partícula. Os coeficientes de deposição para partículas maiores são maiores que para partículas menores, o que é atribuído a considerável remoção de massa pelo esforço. Uma solução analítica, considerando o efeito de liberação das partículas sorvidas, é desenvolvida para calcular o fluxo unidimensional e efeito dispersivo utilizando um método de função de fonte, e então três parâmetros de transporte—dispersividade, coeficiente de deposição, e coeficiente de liberação—foram ajustados utilizando resultados empíricos. Finalmente, a migração de partículas suspensas é predita pelo modelo proposto para uma injeção de concentração constante de período curto e injeção de repetição de três pulsos. No geral, tamanho de partícula tem efeito significativo nos parâmetros migração na percolação para partículas suspensas no meio poroso, assim como a velocidade, dispersividade e coeficiente de deposição da partícula.
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Acknowledgements
This work is financially supported by National Key Basic Research Program of China (2015CB057800) and the National Natural Science Foundation of China (51478034; 51279002), to which the authors are very grateful.
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Appendix: nomenclature
Appendix: nomenclature
- a, b, c :
-
Fitting parameters
- A :
-
Cross-sectional area of column
- C :
-
Particle concentration
- C 0 :
-
Particle concentration applied on the top surface of the column
- C c :
-
Coefficient of curvature
- C inj :
-
Concentration of injected particles
- C out :
-
Particle concentration at the outlet
- C R :
-
Relative concentration
- C u :
-
Uniformity index
- D :
-
Hydrodynamic dispersion coefficient
- D 50 :
-
Median diameter
- I :
-
Strength of the plane source
- I 0, I 1 :
-
Modified Bessel function of the first kind of order, zero and one
- k d :
-
Deposition coefficient
- k r :
-
Release coefficient
- L −1 :
-
Laplace inverse operator
- m :
-
Mass of particles injected
- n :
-
Porosity of porous medium
- N :
-
Turbidity level
- PV:
-
Pore volume
- Q :
-
Water flow rate
- R 2 :
-
Determination coefficient
- a, r :
-
Laplace transform variables of t and z
- t :
-
Time
- t 0 :
-
Duration of application on the top surface of the column
- t inj :
-
Sustained time of particle injection
- t p :
-
Interval of repeated injection
- t′:
-
Particle injection moment
- u :
-
Average interstitial particle velocity
- u 0 :
-
Average interstitial fluid velocity
- u r :
-
Relative interstitial particle velocity to water velocity
- v :
-
Darcy velocity
- V inj :
-
Volume of suspended particle liquid in each injection
- V P :
-
Pore volume of the entire soil column
- z:
-
Coordinate
- α :
-
Arbitrary constant
- α 1, α 2 :
-
Arbitrary constants
- α d :
-
Dispersivity
- δ(⋅):
-
Dirac delta function
- ρ s :
-
Bulk density of the solid matrix
- σ :
-
Concentration of particles deposited onto the solid matrix
- τ :
-
Dummy integration variable
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Bai, B., Xu, T. & Guo, Z. An experimental and theoretical study of the seepage migration of suspended particles with different sizes. Hydrogeol J 24, 2063–2078 (2016). https://doi.org/10.1007/s10040-016-1450-7
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DOI: https://doi.org/10.1007/s10040-016-1450-7