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Transport in Porous Media

, Volume 118, Issue 2, pp 251–269 | Cite as

Coupled Effects of Ionic Strength, Particle Size, and Flow Velocity on Transport and Deposition of Suspended Particles in Saturated Porous Media

  • Lyacine Bennacer
  • Nasre-Dine AhfirEmail author
  • Abdellah Alem
  • HuaQing Wang
Article

Abstract

In this study, the coupled effect of ionic strength, particle size, and flow velocity on transport and deposition of suspended particles (SP) in saturated sand was undertaken. Three polydispersive SP populations (silt particles with the median of 3.5, 9.5 and 18.3 \(\upmu \)m) were investigated using a pulse injection technique. High ionic strengths were used and vary from 0 to 600 mM (NaCl). Two high velocities were tested: 0.15 and 0.30 cm/s. Suspended particles recovery and deposition kinetics were strongly dependent on the solution chemistry, the hydrodynamics, and the suspended particles size, with greater deposition occurring for increasing ionic strength, lower flow velocity, and larger ratios of the median diameter of the SP to the median sand grain diameter. A shift between the extended Derjaguin–Landau–Verwey–Overbeek theory prediction (the particles and sand grain surfaces are considered chemically and topographically homogeneous) and the experimental results for certain ionic strength was observed. So, as reported in recent literature, effects of surface heterogeneities should be considered. The residence time of the non-captured particles is dependent on ionic strength and hydrodynamic. A relationship between the deposition kinetics, particle and grain sizes, flow velocity, and ionic strength is proposed.

Keywords

Porous media Suspended particles size Physicochemical interaction Hydrodynamic Deposition 

List of symbols

A

Hamaker constant

a

A parameter which depends on the flow velocity (in \(a\sqrt{IS})\)

BTCs

Breakthrough curves

C

DT/SP concentration in solution

\(C_{0}\)

Initial concentration

\(C_\mathrm{R}\)

Relative concentration

\(d_{50}\)

Median diameter

DLVO

Derjaguin–Landau–Verwey–Overbeek

\(D_\mathrm{L}\)

Longitudinal dispersion coefficient

DT

Dissolved tracer

\(d_\mathrm{g}\)

Sand grain diameter

\(d_\mathrm{p}\)

Particles diameter

\(F_\mathrm{A}\)

Adhesion force

\(F_\mathrm{A1}\)

Adhesive force in the primary minimum

\(F_\mathrm{A2}\)

Adhesion force in the second minimum

\(F_\mathrm{D}\)

Hydrodynamic drag force

\(F_\mathrm{G}\)

Gravity force

\(F_\mathrm{R}\)

Repulsive force

g

Acceleration of gravity

IS

Ionic strength

K

Hydraulic conductivity

\(k_{0}\)

Initial permeability

\(k_\mathrm{B}\)

Boltzmann constant

\(K_\mathrm{dep}\)

Deposition kinetics coefficient

\(K_\mathrm{dep0}\)

Straining coefficient (value of \(K_\mathrm{dep}\) when \(\hbox {IS} = 0\) mM)

L

Column length

l

Pore diameter

m

Mass of DT/SP injected, equals \(V_\mathrm{inj}C_{0}\)

n

A constant (in \(K_\mathrm{dep0}=\alpha (dp/dg)^{n})\)

\(NV_\mathrm{p}\)

Number of pore volumes

Q

Volumetric flow rate

R

Recovery rate

Re

Reynolds number

S

Cross-sectional area

SP

Suspended particles

T

Temperature

t

Time

\(t_{c}\)

Residence time

\(t_\mathrm{DT}\)

Residence time of DT

\(t_\mathrm{SP}\)

Residence time of SP

\(t_\mathrm{r}\)

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

U

Darcy’s velocity

\(U_\mathrm{p}\)

Fluid velocity at the centre of the solid particle

u

Average pore velocity

\(V_\mathrm{inj}\)

Injected volume

\(V_\mathrm{p}\)

Pore volume of the porous medium

x

Travel distance (column length)

Greek symbols

\(\alpha \)

A constant (in \(K_\mathrm{dep0}=\alpha (dp/dg)^{n})\)

\(\delta \)

Separation distance between the particle and grain surface

\(\delta _\mathrm{max}\)

Separation distance between particle and grain surface of the energy barriers

\(\delta _\mathrm{min}\)

Separation distance between particle and grain surface of the primary/secondary minimum

\(\lambda \)

Filter coefficient

\(\varepsilon _{0}\)

Dielectric permittivity

\(\varepsilon _\mathrm{r}\)

Relative dielectric permittivity

\(\varPhi \)

Total interaction energy

\(\varPhi _\mathrm{BORN}\)

Born repulsion interaction energy

\(\varPhi _\mathrm{EDL}\)

Repulsive electrostatic double-layer interaction energy

\(\varPhi _\mathrm{VDW}\)

Van der Waals attractive interaction energy

\(\varPhi _\mathrm{min1}\)

Primary minimum

\(\varPhi _\mathrm{min2}\)

Secondary minimum

\(\varPhi _\mathrm{max}\)

Energy barrier

\(\gamma \)

A constant (in \(K_\mathrm{dep} = K_\mathrm{dep0} +\gamma U\sqrt{\hbox {IS}})\)

\(\kappa _\mathrm{d}\)

Debye length

\(\theta \)

Characteristic constant of the porous medium

\(\rho \)

Specific mass of water

\(\rho _\mathrm{p}\)

Specific mass of particles

\(\mu \)

Fluid viscosity

\(\omega \)

Porosity

\(\xi _\mathrm{g}\)

Zeta potentials of the sand grains

\(\xi _\mathrm{P}\)

Zeta potentials of the particles

\(\sigma _{p}\)

Collision diameter

Notes

Acknowledgements

This work was supported by Région Haute Normandie_R2015-CPER-0054A.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Lyacine Bennacer
    • 1
    • 2
  • Nasre-Dine Ahfir
    • 3
    Email author
  • Abdellah Alem
    • 3
  • HuaQing Wang
    • 3
  1. 1.Adrar UniversityAdrarAlgeria
  2. 2.Research Laboratory of Applied Hydraulics and EnvironmentBejaia UniversityBejaiaAlgeria
  3. 3.Normandie Univ, UNIHAVREUMR 6294 CNRS, LOMCLe HavreFrance

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