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

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Abstract

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.

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Abbreviations

BTCs:

Breakthrough curves

\(C\) :

DT/SP concentration in solution

\(C_0 \) :

Initial concentration

\(C_\mathrm{R} \) :

Relative concentration

\(d_{50}\) :

Median diameter

\(D_0 \) :

Molecular diffusion coefficient

\(D_\mathrm{L} \) :

Longitudinal dispersion coefficient

DT:

Dissolved tracer

\(K\) :

Hydraulic conductivity

\(K_\mathrm{{dep}}\) :

Deposition kinetics coefficient

\(L\) :

Column length

\(M\) :

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

\(m\) :

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

NTU:

Nephelometric turbidity units

\(n\) :

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

\(P_\mathrm{{ed}}\) :

Diffusion Péclet number

\(P_\mathrm{e} \) :

Dynamic Péclet number

\(Q\) :

Flow rate

\(R\) :

Recovery rate

SP:

Suspended particles

\(t\) :

Time

\(t_\mathrm{c}\) :

Convection time

\(t_\mathrm{{DT}}\) :

Residence time of DT

\(t_\mathrm{r}\) :

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

\(t_\mathrm{{SP}}\) :

Residence time of SP

\(U\) :

Darcy’s velocity

\(u\) :

Average pore velocity

\(V_\mathrm{{inj}}\) :

Injected volume

\(V_\mathrm{P}\) :

Pore volume of the porous medium

\(x\) :

Travel distance (column length)

\(\alpha \) :

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

\(\tau \) :

Tortuosity

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Acknowledgments

This work was supported by Région Haute Normandie (CPER) and the Franco-Algerian program for higher education (PROFAS). The authors would like to thank the anonymous reviewers for their valuable comments and constructive criticism to improve the manuscript.

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Authors and Affiliations

  1. Université d’Adrar, Route National No. 6, 01000 , Adrar, Algeria

    Lyacine Bennacer

  2. LOMC, UMR 6294 CNRS, Université du Havre, 53 rue de Prony, BP 540, 76058 , Le Havre Cedex, France

    Lyacine Bennacer, Nasre-Dine Ahfir, Abdellah Alem & Huaqing Wang

  3. Université Abou Bekr Belkaid, BP 119, 13000 , Tlemcen, Algeria

    Lyacine Bennacer & Abderrazak Bouanani

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  1. Lyacine Bennacer
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  2. Nasre-Dine Ahfir
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  3. Abderrazak Bouanani
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  4. Abdellah Alem
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  5. Huaqing Wang
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Correspondence to Nasre-Dine Ahfir.

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Bennacer, L., Ahfir, ND., Bouanani, A. et al. Suspended Particles Transport and Deposition in Saturated Granular Porous Medium: Particle Size Effects. Transp Porous Med 100, 377–392 (2013). https://doi.org/10.1007/s11242-013-0220-4

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