Transport in Porous Media

, Volume 100, Issue 3, pp 377–392 | Cite as

Suspended Particles Transport and Deposition in Saturated Granular Porous Medium: Particle Size Effects

  • Lyacine Bennacer
  • Nasre-Dine Ahfir
  • Abderrazak Bouanani
  • Abdellah Alem
  • Huaqing Wang


An experimental study on the transport and deposition of suspended particles (SP) in a saturated porous medium (calibrated sand) was undertaken. The influence of the size distribution of the SP under different flow rates is explored. To achieve this objective, three populations with different particles size distributions were selected. The median diameter \(d_{50}\) of these populations was 3.5, 9.5, and \(18.3~\upmu \hbox {m}\). To study the effect of polydispersivity, a fourth population noted “Mixture” (\(d_{50} = 17.4\; \upmu \hbox {m}\)) obtained by mixing in equal proportion (volume) the populations 3.5 and \(18.3\;\upmu \hbox {m}\) was also used. The SP transfer was compared to the dissolved tracer (DT) one. Short pulse was the technique used to perform the SP and the DT injection in a column filled with the porous medium. The breakthrough curves were competently described with the analytical solution of a convection–dispersion equation with first-order deposition kinetics. The results showed that the transport of the SP was less rapid than the transport of the DT whatever the flow velocity and the size distribution of the injected SP. The mean diameter of the recovered particles increases with flow rate. The longitudinal dispersion increases, respectively, with the increasing of the flow rates and the SP size distribution. The SP were more dispersive in the porous medium than the DT. The results further showed that the deposition kinetics depends strongly on the size of the particle transported and their distribution.


Porous medium Transport Suspended particles Size distribution Deposition kinetics 

List of Symbols

Latin Symbols


Breakthrough curves


DT/SP concentration in solution

\(C_0 \)

Initial concentration

\(C_\mathrm{R} \)

Relative concentration


Median diameter

\(D_0 \)

Molecular diffusion coefficient

\(D_\mathrm{L} \)

Longitudinal dispersion coefficient


Dissolved tracer


Hydraulic conductivity


Deposition kinetics coefficient


Column length


Mass of DT/SP injected, equals \(V_\mathrm{{inj}} C_0 \)


A power coefficient (in \(D_\mathrm{L} =D_0 \tau ^{2}+\alpha _\mathrm{L} u^{m})\)


Nephelometric turbidity units


A power coefficient (in \(K_\mathrm{{dep}} =\alpha U^{n})\)


Diffusion Péclet number

\(P_\mathrm{e} \)

Dynamic Péclet number


Flow rate


Recovery rate


Suspended particles




Convection time


Residence time of DT


Retardation factor, equals t\(_\mathrm{{SP}}/t_\mathrm{{DT}}\)


Residence time of SP


Darcy’s velocity


Average pore velocity


Injected volume


Pore volume of the porous medium


Travel distance (column length)

Greek Symbols

\(\alpha \)

A constant (in \(K_\mathrm{{dep}} =\alpha U^{n})\)

\(\alpha _\mathrm{L}\)

Longitudinal dispersivity

\(\delta (t)\)

Dirac function

\(\beta \)

A power coefficient (in \(\alpha _\mathrm{L} =\kappa d_{50}^\beta )\)

\(\kappa \)

A constant (in \(\alpha _\mathrm{L} =\kappa d_{50}^\beta )\)

\(\tau \)



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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Lyacine Bennacer
    • 1
    • 2
    • 3
  • Nasre-Dine Ahfir
    • 2
  • Abderrazak Bouanani
    • 3
  • Abdellah Alem
    • 2
  • Huaqing Wang
    • 2
  1. 1.Université d’AdrarAdrarAlgeria
  2. 2.LOMC, UMR 6294 CNRSUniversité du HavreLe Havre CedexFrance
  3. 3.Université Abou Bekr BelkaidTlemcenAlgeria

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