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Modelling the Competitive Sorption Process of Multiple Solutes During their Transport in Porous Media

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Abstract

A general mathematical model to solve the advection–dispersion transport equation for multiple solutes was developed, where the dual porosity mobile–immobile mass transfer, the two-site non-equilibrium model and first-order transformation reactions were included. The two-site model was expressed with an equilibrium sorption term and a kinetic term. One of three kinetic models could be used: the non-linear, the bilinear and the pore diffusion model. The traditional Freundlich or Langmuir isotherms were employed to simulate no-interaction between the solutes, but with the extended Freundlich or extended Langmuir isotherms, a competitive sorption could be simulated. The transport equation was solved with the Moving Concentration Slope method. The mathematical model was tested and further simplified by using real data from soil column experiments, with 1,2-cis-dichloroethene and trichloroethene as model contaminants and silica gel and real soil samples as porous medium.

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References

  1. Allen-King, R. M., Groenevelt, H., James Warren, C., & Mackay, D. M. (1996). Non-linear chlorinated-solvent sorption in four aquitards. Journal of Contaminant Hydrology, 22, 203–221. doi:10.1016/0169-7722(95)00089-5.

    Article  CAS  Google Scholar 

  2. Ball, W. P., & Roberts, P. V. (1991). Long-term sorption of halogenated organic chemicals by aquifer material. 2. Intraparticle diffusion. Environmental Science & Technology, 25, 1237–1249. doi:10.1021/es00019a003.

    Article  CAS  Google Scholar 

  3. Broughton, D. B. (1948). Adsorption isotherms for binary gas mixtures. Industrial & Engineering Chemistry, 40, 1506–1508. doi:10.1021/ie50464a036.

    Article  CAS  Google Scholar 

  4. Brusseau, M. L., Jessup, R. E., & Rao, P. S. C. (1992). Modeling solute transport influenced by multiprocess nonequilibrium and transformation reactions. Water Resources Research, 28, 175–182. doi:10.1029/91WR02497.

    Article  CAS  Google Scholar 

  5. Carta, G., & Cincotti, A. (1998). Film model approximation for non-linear adsorption and diffusion in spherical particles. Chemical Engineering Science, 53, 3483–3488. doi:10.1016/S0009-2509(98)00156-0.

    Article  CAS  Google Scholar 

  6. Coats, K. H., & Smith, B. D. (1964). Dead-end pore volume and dispersion in porous media. Society of Petroleum Engineers Journal, 4, 73–84.

    Article  Google Scholar 

  7. Connaughton, D. F., Stedinger, J. R., Lion, L. W., & Shuler, M. L. (1993). Description of time-varying desorption kinetics: Release of naphthalene from contaminated soils. Environmental Science & Technology, 27, 2397–2403. doi:10.1021/es00048a013.

    Article  CAS  Google Scholar 

  8. Crank, J. (1979). The mathematics of diffusion. Oxford: Oxford University Press.

    Google Scholar 

  9. Danckwerts, P. V. (1953). Continuous flow systems: Distribution of residence times. Chemical Engineering Science, 2, 1–13. doi:10.1016/0009-2509(53)80001-1.

    Article  CAS  Google Scholar 

  10. Do, D. D. (1998). Adsorption analysis: Equilibria and kinetics. London: Imperial College Press.

    Google Scholar 

  11. Fetter, C. W. (1993). Contaminant hydrology. Upper Saddle River: Prentice-Hall.

    Google Scholar 

  12. Glueckauf, E. (1955). Theory of chromatography. Part 10.— Formulae for diffusion into spheres and their application to chromatography. Transactions of the Faraday Society, 51, 1540–1551. doi:10.1039/tf9555101540.

    Article  CAS  Google Scholar 

  13. Gu, T. (1995). Mathematical modeling and scale-up of liquid chromatography. Heidelberg: Springer.

    Google Scholar 

  14. Gu, T., Tsai, G.-J., Tsao, G. T., & Ladisch, M. R. (1990). Displacement effect in multicomponent chromatography. AIChE, 36, 1156–1162. doi:10.1002/aic.690360805.

    Article  CAS  Google Scholar 

  15. Helfferich, F., & Klein, G. (1970). Multicomponent chromatography. Theory of interference. New York: Marcel Dekker.

    Google Scholar 

  16. Helfferich, F. G. (1997). Non-linear waves in chromatography III. Multicomponent langmuir and langmuir-like systems. Journal of Chromatography A, 768, 169–205. doi:10.1016/S0021-9673(96)00573-0.

    Article  CAS  Google Scholar 

  17. Kaczmarski, K., Mazzotti, M., Storti, G., & Morbidelli, M. (1997). Modeling fixed-bed adsorption columns through orthogonal collocations on moving finite elements. Computers & Chemical Engineering, 21, 641–660. doi:10.1016/S0098-1354(96)00300-6.

    Article  CAS  Google Scholar 

  18. Knudsen, J. G., Hottel, H. C., Sarofim, A. F., Wankat, P. C., & Knaebel, K. S. (1997). Heat and mass transfer. In R. Perry, & D. Green (Eds.), Perry’s chemical engineers’ handbook (pp. 72–74). USA: McGraw Hill.

    Google Scholar 

  19. Krishna, R., & Taylor, R. (1993). Multicomponent mass transfer. USA: Wiley.

    Google Scholar 

  20. Lee, P. H., & Kozak, J. J. (1987). Calculation of the tortuosity factor in single-phase transport through a structured medium. The Journal of Chemical Physics, 86, 4617–4627. doi:10.1063/1.452703.

    Article  CAS  Google Scholar 

  21. Lee, L. S., Rao, P. S. C., Brusseau, M. L., & Ogwada, R. A. (1988). Nonequilibrium sorption of organic contaminants during flow through columns of aquifer materials. Environmental Toxicology and Chemistry, 7, 779–793. doi:10.1897/1552-8618(1988)7[779:NSOOCD]2.0.CO;2.

    Article  CAS  Google Scholar 

  22. Lim, B.-G., Ching, C.-B., & Tan, R. B. H. (1995). Determination of competitive adsorption isotherms of enantiomers on a dual-site adsorbent. Separations Technology, 5, 213–228. doi:10.1016/0956-9618(95)00126-3.

    Article  CAS  Google Scholar 

  23. Ma, Z., Katti, A., Lin, B., & Guiochon, G. (1990). Simple wave effects in two-component nonlinear liquid chromatography: Application to the measurement of competitive adsorption isotherms. Journal of Physical Chemistry, 94, 6911–6922. doi:10.1021/j100380a069.

    Article  CAS  Google Scholar 

  24. Markham, E. C., & Benton, A. F. (1931). The adsorption of gas mixtures by silica. Journal of the American Chemical Society, 53, 497–507. doi:10.1021/ja01353a013.

    Article  CAS  Google Scholar 

  25. Mauran, S., Rigaud, L., & Coudevylle, O. (2001). Application of the Carman–Kozeny correlation to a high-porosity and anisotropic consolidated medium: The compressed expanded natural graphite. Transport in Porous Media, 43, 355–376. doi:10.1023/A:1010735118136.

    Article  Google Scholar 

  26. Moldrup, P., Yamaguchi, T., Hansen, J. A., & Rolston, D. E. (1992). An accurate and numerically stable model for one-dimensional solute transport in soils. Soil Science, 153, 261–273.

    CAS  Google Scholar 

  27. Moldrup, P., Yamaguchi, T., Rolston, D. E., Vestergaard, K., & Hansen, J. A. (1994). Removing numerically induced dispersion from finite difference models for solute and water transport in unsaturated soils. Soil Science, 157, 153–161.

    CAS  Google Scholar 

  28. Moon, H., & Kook-Lee, W. (1986). A lumped model for multicomponent adsorptions in fixed beds. Chemical Engineering Science, 41, 1995–2004. doi:10.1016/0009-2509(86)87116-0.

    Article  CAS  Google Scholar 

  29. Morbidelli, M., Servida, A., Storti, G., & Carra, S. (1982). Simulation of multicomponent adsorption beds. Model analysis and numerical solution. Industrial & Engineering Chemistry Fundamentals, 21, 123–131. doi:10.1021/i100006a005.

    Article  CAS  Google Scholar 

  30. Myers, T. E., Townsend, D. M., & Hill, C. B. (1998). Application of a semianalytical model to TNT transport in laboratory soil columns. U. S. Army Engineer Waterways Experiment Station.

  31. Neville, C. J., Ibaraki, M., & Sudicky, E. A. (2000). Solute transport with multiprocess nonequilibrium: A semi-analytical solution approach. Journal of Contaminant Hydrology, 44, 141–159. doi:10.1016/S0169-7722(00)00094-2.

    Article  CAS  Google Scholar 

  32. Nkedi-Kizza, P., Brusseau, M. L., Rao, P. S. C., & Hornsby, A. G. (1989). Nonequilibrium sorption during displacement of hydrophobic organic chemicals and calcium-45 through soil columns with aqueous and mixed solvents. Environmental Science & Technology, 23, 814–820. doi:10.1021/es00065a009.

    Article  CAS  Google Scholar 

  33. Pignatello, J. J., & Xing, B. (1996). Mechanisms of slow sorption of organic chemicals to natural particles. Environmental Science & Technology, 30, 1–11. doi:10.1021/es940683g.

    Article  CAS  Google Scholar 

  34. Rahman, M., Amiri, F., & Worch, E. (2003). Application of the mass transfer m.odel for describing nonequilibrium transport of HOCs through natural geosorbents. Water Research, 37, 4673–4684. doi:10.1016/S0043-1354(03)00430-5.

    Article  CAS  Google Scholar 

  35. Rhee, H.-K., Aris, R., & Amundson, N. R. (1989a). First-order partial. Differential equations, 1. Theory and application of single equations. Mineola: Dover.

    Google Scholar 

  36. Rhee, H.-K., Aris, R., & Amundson, N. R. (1989b). First-order partial. Differential equations, 2. Theory and application of hyperbolic systems of quasilinear equations. Mineola: Dover.

    Google Scholar 

  37. Ruthven, D. M. (1984). Principles of adsorption and adsorption processes. USA: Wiley.

    Google Scholar 

  38. Rüttinger, S., Tobschall, H. J., Breiter, R., Hirsch, K., Salaices Avila, M. A., Neeße, T., et al. (2006). Natural Attenuation-Untersuchungen an einem mit LCKW kontaminierten Altdeponiestandort. Grundwasser, 11, 184–193. doi:10.1007/s00767-006-0144-9.

    Article  CAS  Google Scholar 

  39. Salaices Avila, M. A. (2005). Experiment and modelling of the competitive sorption and transport of chlorinated ethenes in porous media. Goettingen: Cuvillier.

    Google Scholar 

  40. Salaices Avila, M. A., Breiter, R., & Mott, H. (2007). Development of a simple, accurate SPME-based method for assay of VOCs in column breakthrough experiments. Chemosphere, 66, 18–29. doi:10.1016/j.chemosphere.2006.05.069.

    Article  CAS  Google Scholar 

  41. Santacesaria, E., Morbidelli, M., Servida, A., Storti, G., & Carra, S. (1982). Separation of xylenes on Y zeolites. 2. Breakthrough curves and their interpretation. Industrial & Engineering Chemistry Process Design and Development, 21, 446–451. doi:10.1021/i200018a017.

    Article  CAS  Google Scholar 

  42. Schaefer, C. E., Schuth, C., Werth, C. J., & Reinhard, M. (2000). Binary desorption isotherms of TCE and PCE from silica gel and natural solids. Environmental Science & Technology, 34, 4341–4347. doi:10.1021/es000875d.

    Article  CAS  Google Scholar 

  43. Sheindorf, C., Rebhun, M., & Sheintuch, M. (1981). A Freundlich-type multicomponent isotherm. Journal of Colloid and Interface Science, 79, 136–142. doi:10.1016/0021-9797(81)90056-4.

    Article  CAS  Google Scholar 

  44. Sheindorf, C., Rebhun, M., & Sheintuch, M. (1983). Prediction of breakthrough curves from fixed-bed adsorbers with Freundlich-type multisolute isotherm. Chemical Engineering Science, 38, 335–342. doi:10.1016/0009-2509(83)85017-9.

    Article  CAS  Google Scholar 

  45. Starr, J. L., & Parlange, J.-Y. (1979). Dispersion in soil columns: The snow plow effect. Soil Science Society of America Journal, 43, 448–450.

    CAS  Google Scholar 

  46. Starr, J. L., Parlange, J.-Y., & Braddock, R. D. (1982). Dispersion in soil columns: The precursor effect. Soil Science, 133, 111–115. doi:10.1097/00010694-198202000-00004.

    Article  CAS  Google Scholar 

  47. Tobschall, H. J., Neeße, T., Rüttinger, S., Breiter, R., Poggel, K., & Salaices Avila, M. A. (2003). Teilprojekt 3: LHKW-Belastung am Standort “Im Reis”, Lauf an der Pegnitz. Gesellschaft zur Altlastensanierung in Bayern (GAB) mbH, München.

  48. Toride, N., Leij, F. J., & van Genuchten, M. T. (1999). The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments. Version 2.1. Research Report No. 137. U.S. Salinity laboratory, USDA, ARS, Riverside, CA.

  49. Travis, C. C., & Etnier, E. (1981). A survey of sorption relationships for reactive solutes in soil. Journal of Environmental Quality, 10, 8–17.

    Article  CAS  Google Scholar 

  50. van Genuchten, M. T. (1981). Non-equilibrium solute transport parameters from miscible displacement experiments, version 1.0. Research Report No. 119. U.S. Salinity laboratory, USDA, ARS, Riverside, CA.

  51. van Genuchten, M. T., & Wierenga, P. J. (1976). Mass transfer studies in sorbing porous media 1. Analytical solutions. Soil Science Society of America Journal, 40, 473–480.

    Google Scholar 

  52. Wilke, C. R., & Chang, P. (1955). Correlation of diffusion coefficients in dilute solutions. AIChE, 1, 264–270. doi:10.1002/aic.690010222.

    Article  CAS  Google Scholar 

  53. Zheng, C., & Bennett, G. D. (2002). Applied contaminant transport modeling. USA: Wiley.

    Google Scholar 

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Acknowledgments

The research is part of the Bavarian Network-Project “Sustainable Management of Contaminated Sites in Consideration of Natural Attenuation”. It is funded by the Bavarian State Ministry of the Environment, Public Health and Consumer Protection. The authors also wish to thank the financial support from the DAAD in Germany.

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Correspondence to Roman Breiter.

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Salaices Avila, M.A., Breiter, R. Modelling the Competitive Sorption Process of Multiple Solutes During their Transport in Porous Media. Environ Model Assess 14, 615–629 (2009). https://doi.org/10.1007/s10666-008-9168-0

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