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


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.


Porous media Suspended particles size Physicochemical interaction Hydrodynamic Deposition 

List of symbols


Hamaker constant


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


Breakthrough curves


DT/SP concentration in solution


Initial concentration


Relative concentration


Median diameter




Longitudinal dispersion coefficient


Dissolved tracer


Sand grain diameter


Particles diameter


Adhesion force


Adhesive force in the primary minimum


Adhesion force in the second minimum


Hydrodynamic drag force


Gravity force


Repulsive force


Acceleration of gravity


Ionic strength


Hydraulic conductivity


Initial permeability


Boltzmann constant


Deposition kinetics coefficient


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


Column length


Pore diameter


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


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


Number of pore volumes


Volumetric flow rate


Recovery rate


Reynolds number


Cross-sectional area


Suspended particles






Residence time


Residence time of DT


Residence time of SP


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


Darcy’s velocity


Fluid velocity at the centre of the solid particle


Average pore velocity


Injected volume


Pore volume of the porous medium


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

\(\omega \)


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

Zeta potentials of the sand grains

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

Zeta potentials of the particles

\(\sigma _{p}\)

Collision diameter



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


  1. Ahfir, N.-D., Wang, H.Q., Benamar, A., Alem, A., Masséi, N., Dupont, J.-P.: Transport and deposition of suspended particles in saturated porous media hydrodynamic effect. Hydrol. J. 15, 659–668 (2007)Google Scholar
  2. Ahfir, N.-D., Benamar, A., Alem, A., Wang, H.Q.: Influence of internal structure and medium length on transport and deposition of suspended particles: a laboratory study. Transp. Porous Media 76, 289–307 (2009)CrossRefGoogle Scholar
  3. Ahfir, N.-D., Hammadi, A., Alem, A., Wang, H.Q., Le Bras, G., Ouahbi, T.: Porous media grain size distribution and hydrodynamic forces effects on transport and deposition of suspended particles. J. Environ. Sci. (2016). doi: 10.1016/j.jes.2016.01.032 Google Scholar
  4. Alem, A., Elkawafi, A., Ahfir, N.-D., Wang, H.Q.: Filtration of kaolinite particles in a saturated porous medium: hydrodynamic effects. Hydrol. J. 21, 573–586 (2013)Google Scholar
  5. Al-Naeem, A.: Effect of excess pumping on groundwater salinity and water level in Hail region of Saudi Arabia. Res. J. Environ. Toxicol. 8(3), 124–135 (2014)CrossRefGoogle Scholar
  6. Benamar, A., Wang, H.-Q., Ahfir, N.-D., Alem, A., Masséi, N., Dupont, J.-P.: Flow velocity effects on the transport and the deposition rate of suspended particles in a saturated porous medium. C. R. Geosci. 337, 497–504 (2005)CrossRefGoogle Scholar
  7. Bennacer, L., Ahfir, N.-D., Bouanani, A., Alem, A., Wang, H.-Q.: Suspended particles transport and deposition in saturated granular porous medium: particle size effects. Transp. Porous Media 100, 377–392 (2013)CrossRefGoogle Scholar
  8. Bhattacharjee, S., Elimelech, M.: Surface element integration: a novel technique for evaluation of DLVO interaction between a particle and a flat plate. J. Colloid Interface Sci. 193, 273–285 (1997)CrossRefGoogle Scholar
  9. Bradford, S.A., Simunek, J., Bettahar, M., Van Genuchten, M.T.-H., Yates, S.R.: Modeling colloid attachment, straining, and exclusion in saturated porous media. Environ. Sci. Technol. 37, 2242–2250 (2003)CrossRefGoogle Scholar
  10. Bradford, S.A., Torkzaban, S., Walker, S.L.: Coupling of physical and chemical mechanisms of colloid straining in saturated porous media. Water Res. 41, 3012–3024 (2007)CrossRefGoogle Scholar
  11. Bradford, S.A., Torkzaban, S.: Determining parameters and mechanisms of colloid retention and release in porous media. Langmuir 31, 12096–12105 (2015)CrossRefGoogle Scholar
  12. Chen, X., Bai, B.: Experimental investigation and modeling of particulate transportation and deposition in vertical and horizontal flows. Hydrol. J. 23, 365–375 (2015)Google Scholar
  13. Chen, J.C., Elimelech, M., Kim, A.S.: Monte Carlo simulation of colloidal membrane filtration model development with application to characterization of colloid phase transition. J. Membr. Sci. 255, 291–305 (2005)CrossRefGoogle Scholar
  14. Chrysikopoulos, C.V., Katzoyrakis, V.E.: Colloid particle size-dependent dispersivity. Water Resour. Res. 51, 4668–4683 (2015). doi: 10.1002/2014WR016094 CrossRefGoogle Scholar
  15. Cissokho, M., Boussour, S., Cordier, Ph., Bertin, H., Hamon, G.: Low salinity oil recovery on clayey sandstone: experimental study. Paper SCA 2009-05 presented at the 23rd International Symposium of the Society of Core Analysts, Noordwijk, 27–30 September (2009)Google Scholar
  16. Corapcioglu, M.Y., Jiang, S.: Colloid-facilitated groundwater contaminant transport. Water Resour. Res. 29(7), 2215–2226 (1993)CrossRefGoogle Scholar
  17. Derjaguin, B.V., Landau, L.D.: Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochim. USSR 14, 733–762 (1941)Google Scholar
  18. Elimelech, M., Gregory, J., Jia, X., Williams, R.A.: Particle Deposition and Aggregation Measurement, Modeling, and Simulation. Butterworth-Heinemann, Oxford (1995)Google Scholar
  19. Foppen, J.W.A., Mporokoso, A., Schijven, J.F.: Determining straining of Escherichia coli from breakthrough curves. J. Contam. Hydrol. 76, 191–210 (2005)CrossRefGoogle Scholar
  20. Foppen, J.W.A., Schijven, J.F.: Evaluation of data from the literature on the transport and survival of Escherichia coli and thermotolerant coliforms in aquifers under saturated conditions. Water Res. 40, 401–426 (2006)CrossRefGoogle Scholar
  21. Frey, J.M., Schmitz, P., Dufreche, J., Gohr Pinheiro, I.: Particle deposition in porous media: analysis of hydrodynamic and weak inertial effects. Transp. Porous Media 37, 25–54 (1999)CrossRefGoogle Scholar
  22. Gao, B., Cao, X., Dong, Y., Luo, Y., Ma, L.Q.: Colloid deposition and release in soils and their association with heavy metals. Crit. Rev. Environ. Sci. Technol. 41(4), 336–372 (2011)CrossRefGoogle Scholar
  23. Gohr Pinheiro, I., Schmitz, P., Houi, D.: Particle capture in porous media when physico-chemical effects dominate. Chem. Eng. Sci. 54, 3801–3813 (1999)CrossRefGoogle Scholar
  24. Goldman, A.J., Cox, R.G., Brenner, H.: Slow viscous motion of a sphere parallel to a plane wall—II Couette flow. Chem. Eng. Sci. 22(4), 653–660 (1967)CrossRefGoogle Scholar
  25. Grolimund, D., Borkovec, M., Barmettler, K., Sticher, H.: Colloid-facilitated transport of strongly sorbing contaminants in natural porous media: a laboratory column study. Environ. Sci. Technol. 30, 3118–3123 (1996)CrossRefGoogle Scholar
  26. Grolimund, D., Barmettler, K., Borkovec, M.: Release and transport of colloidal particles in natural porous media: 2. Experimental results and effects of ligands. Water Resour. Res. 37(3), 571–582 (2001)CrossRefGoogle Scholar
  27. Herzig, J.P., Leclerc, D.M., Le Goff, P.: Flow of suspension through porous media—application to deep bed filtration. Ind. Eng. Chem. 62, 8–35 (1970)CrossRefGoogle Scholar
  28. Jadhunandan, P.P., Morrow, N.R.: Effect of wettability on waterflooding recovery for crude oil/brine/rock systems. SPE Reserv. Eng. 10(1), 40–46 (1995)CrossRefGoogle Scholar
  29. Johnson, W.P., Li, X., Assemi, S.: Deposition and re-entrainment dynamics of microbes and non-biological colloids during non-perturbed transport in porous media in the presence of an energy barrier to deposition. Adv. Water Resour. 30, 1432–1454 (2007)CrossRefGoogle Scholar
  30. Kaplan, D.A., Muñoz-Carpena, R.: Groundwater salinity in a floodplain forest impacted by saltwater intrusion. J. Contam. Hydrol. 169, 19–36 (2014)CrossRefGoogle Scholar
  31. Khilar, K.C., Fogler, H.S.: The existence of a critical salt concentration for particle release. J. Colloid Interface Sci. 101(1), 214–224 (1984)CrossRefGoogle Scholar
  32. Khilar, K.C., Vaidya, R.N., Fogler, H.S.: Colloidally-induced fines release in porous media. J. Pet. Sci. Eng. 4, 213–221 (1990)CrossRefGoogle Scholar
  33. Kim, H.N., Bradford, S.A., Walker, S.L.: Escherichia coli O157 H7 transport in saturated porous media: role of solution chemistry and surface macromolecules. Environ. Sci. Technol. 43, 4340–4347 (2009)CrossRefGoogle Scholar
  34. Kretzschmar, R., Barmettler, K., Grolimund, D., Yan, Y.D., Borkovec, M., Sticher, H.: Experimental determination of colloid deposition rates and collision efficiencies in natural porous media. Water Resour. Res. 33(5), 1129–1137 (1997)CrossRefGoogle Scholar
  35. Li, Y.: Oil recovery by low salinity water injection into a reservoir: a new study of tertiary oil recovery mechanism. Transp. Porous Med. 90, 333–362 (2011)CrossRefGoogle Scholar
  36. Magal, E., Weisbrod, N., Yakirevich, A., Yechieli, Y.: The use of fluorescent dyes as tracers in highly saline groundwater. J. Hydrol. 358, 124–133 (2008)CrossRefGoogle Scholar
  37. Magal, E., Weisbrod, N., Yechieli, Y., Walker, S.L., Yakirevich, A.: Colloid transport in porous media: impact of hyper-saline solutions. Water Res. 45, 3521–3532 (2011)CrossRefGoogle Scholar
  38. McCarthy, J.F., Zachara, J.M.: Subsurface transport of contaminants. Environ. Sci. Technol. 23, 496–502 (1989)Google Scholar
  39. McDowell-Boyer, L.M., Hunt, J.R., Sitar, N.: Particle transport through porous media. Water Resour. Res. 22(13), 1901–1921 (1986)CrossRefGoogle Scholar
  40. Mesticou, Z., Kacem, M., Dubujet, P.: Coupling effects of flow velocity and ionic strength on the clogging of a saturated porous medium. Transp. Porous Media 112, 265–282 (2016)CrossRefGoogle Scholar
  41. Minssieux, L., Nabzar, L., Chauveteau, G., Longeron, D., Bensalem, R.: Permeability damage due to asphaltene deposition: experimental and modeling aspects. Revue Française de l’institut du Pétrole. 53(3), 313–327 (1998)CrossRefGoogle Scholar
  42. O’Neill, M.E.: A sphere in contact with a plane wall in slow linear shear flow. Chem. Eng. Sci. 23, 1293–1298 (1968)CrossRefGoogle Scholar
  43. Porubcan, A.A., Xu, S.: Colloid straining within saturated heterogeneous porous media. Water Res. 45, 1796–1806 (2011)CrossRefGoogle Scholar
  44. Raychoudhury, T., Tufenkji, N., Ghoshal, S.: Straining of polyelectrolyte-stabilized nanoscale zero valent iron particles during transport through granular porous media. Water Res. 50, 80–89 (2014)CrossRefGoogle Scholar
  45. Ryan, J.N., Gschwend, P.M.: Effects of ionic strength and flow rate on colloid release: relating kinetics to intersurface potential energy. J. Colloid Interface Sci. 164, 21–34 (1994)CrossRefGoogle Scholar
  46. Ryan, J.N., Elimelech, M.: Colloid mobilisation and transport in groundwater. Colloids Surf. A 107, 1–56 (1996)CrossRefGoogle Scholar
  47. Redman, R.A., Walker, S.L., Elimelech, M.: Bacterial adhesion and transport in porous media role of the secondary energy minimum. Environ. Sci. Technol. 38, 1777–1785 (2004)CrossRefGoogle Scholar
  48. Ruckenstein, E., Prieve, D.C.: Adsorption and desorption of particles and their chromatographic separation. AIChE J. 22, 276–285 (1976)CrossRefGoogle Scholar
  49. Saiers, J.E., Hornberger, G.M., Liang, L.: First- and second-order kinetics approaches for modeling the transport of colloidal particles in porous media. Water Resour. Res. 30(9), 2499–2506 (1994)CrossRefGoogle Scholar
  50. Sefrioui, N., Ahmadi, A., Omari, A., Bertin, H.: Numerical simulation of retention and release of colloids in porous media at the pore scale. Colloids Surf. A 427, 33–40 (2013)CrossRefGoogle Scholar
  51. Sen, T.K., Khilar, K.C.: Review on subsurface colloids and colloid-associated contaminant transport in saturated porous media. Adv. Colloid Interface Sci. 119, 71–96 (2006)CrossRefGoogle Scholar
  52. Sharma, M.M., Chamoun, H., Sarma, D.S.H.S.R., Schechter, R.S.: Factors controlling the hydrodynamic detachment of particles from surfaces. J. Colloid Interface Sci. 149(1), 121–134 (1992)CrossRefGoogle Scholar
  53. Shen, C., Huang, Y., Li, B., Jin, Y.: Effects of solution chemistry on straining of colloids in porous media under unfavorable conditions. Water Resour. Res. (2008). doi: 10.1029/2007WR006580 Google Scholar
  54. Shen, C., Lazouskaya, V., Zhang, H., Wang, F., Li, B., Jin, Y., Huang, Y.: Theoretical and experimental investigation of detachment of colloids from rough collector surfaces. Colloids Surf. A 410, 98–110 (2012)CrossRefGoogle Scholar
  55. Song, L., Elimelech, M.: Calculation of particle deposition rate under unfavorable particle-surface interactions. J. Chem. Soc. Faraday Trans. 89(18), 3443–3452 (1993)CrossRefGoogle Scholar
  56. Tang, G.Q., Morrow, N.R.: Oil recovery by waterflooding—invading brine cation valency and salinity. J. Pet. Sci. Eng. 24, 99–111 (1999)CrossRefGoogle Scholar
  57. Tien, C.: Granular Filtration of Aerosols and Hydrosols. Butterworths Series in Chemical Engineering. Butterworths, Boston (1989)Google Scholar
  58. Torkzaban, S., Bradford, S.A., Vanderzalm, J.L., Patterson, B.M., Harris, B., Prommer, H.: Colloid release and clogging in porous media: effects of solution ionic strength and flow velocity. J. Contam. Hydrol. 181, 161–171 (2015)CrossRefGoogle Scholar
  59. Torkzaban, S., Bradford, A.S., Walker, S.L.: Resolving the coupled effects of hydrodynamics and DLVO forces on colloid attachment in porous media. Langmuir 23, 9652–9660 (2007)CrossRefGoogle Scholar
  60. Tosco, T., Bosch, J., Meckenstock, R.U., Sethi, R.: Transport of ferrihydrite nanoparticles in saturated porous media: role of ionic strength and flow rate. Environ. Sci. Technol. 46, 4008–4015 (2012)CrossRefGoogle Scholar
  61. Tripathy, A.: Hydrodynamically and chemically induced in situ kaolin particle release from porous media an experimental study. Adv. Powder Technol. 21, 564–572 (2010)CrossRefGoogle Scholar
  62. Tufenkji, N., Elimelech, M.: Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environ. Sci. Technol. 38, 529–536 (2004)CrossRefGoogle Scholar
  63. Tufenkji, N., Elimelech, M.: Spatial distributions of Cryptosporidium oocysts in porous media: evidence of dual mode deposition. Environ. Sci. Technol. 39(10), 3620–3629 (2005)CrossRefGoogle Scholar
  64. Verwey, E.J.W., Overbeek, J.T.G.: Theory of the Stability of Lyophobic Colloids. Elsevier, Amsterdam (1948)Google Scholar
  65. Wang, H.-Q., Lacroix, M., Massei, N., Dupont, J.-P.: Transport des particules en milieu poreux détermination des paramètres hydrodispersifs et du coefficient de dépôt. Comptes Rendus de l’Académie des Sciences, Sciences de la Terre et des planètes 331, 97–104 (2000)Google Scholar
  66. Xu, S., Gao, B., Saiers, J.E.: Straining of colloidal in saturated porous media. Water Resour. Res. 42, 1–10 (2006)CrossRefGoogle Scholar
  67. Yao, K.M., Habibian, M.T., O’Melia, C.R.: Water and waste water filtration concepts and applications. Environ. Sci. Technol. 5, 1105–1112 (1971)CrossRefGoogle Scholar

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

Personalised recommendations