Modeling of sorption equilibria: state of the art and prospects of models development for heterogeneous sorbents

Cover Page

Cite item

Full Text

Abstract

For many years, adsorption remains one of the most universal and cost-effective approaches to purifying waters of various compositions and extracting valuable components from technological solutions. In addition to affinity, selectivity, and high sorption capacity, the kinetic characteristics of sorbents are of great importance, since they determine the productivity of both industrial sorption columns and small point-of-use filters operating at high flow rates. This review discusses the current state of the art in modeling sorption dynamics and a new approach to analysis of sorption equilibria using the model of sorption/desorption rate constants distribution (RCD) for heterogeneous sorbents developed at the Institute of Crystallography FEB RAS for predictive modeling of breakthrough curves based on the kinetic parameters of sorption centers (RCD functions) calculated from experimental data obtained under static conditions. Using as the example supermacroporous sorbents based on polyethyleneimine, it was shown how the RCD model and its variants, which take into account diffusion limitations and the presence of complexing agents, can be used to optimize conditions for the metal ions concentration and separation under dynamic conditions.

Full Text

Restricted Access

About the authors

А. P. Golikov

Institute of Chemistry, FEB RAS

Email: glk@ich.dvo.ru
ORCID iD: 0000-0002-5306-2542

Candidate of Sciences in Chemistry, Senior Researcher

Russian Federation, Vladivostok

I. A. Malakhova

Institute of Chemistry, FEB RAS

Email: newira94@gmail.com

Candidate of Sciences in Chemistry, Junior Researcher

Russian Federation, Vladivostok

S. Yu. Bratskaya

Institute of Chemistry, FEB RAS

Author for correspondence.
Email: sbratska@ich.dvo.ru
ORCID iD: 0000-0003-4954-0422

Doctor of Sciences in Chemistry, Chief Researcher

Russian Federation, Vladivostok

References

  1. Nandanwar S.U., Coldsnow K., Utgikar V., Sabharwall P., Eric Aston D. Capture of harmful radioactive contaminants from off-gas stream using porous solid sorbents for clean Environment – A review. Chem. Eng. J. 2016;306:369–381. https://doi.org/10.1016/j.cej.2016.07.073.
  2. Tofik A.S., Taddesse A.M., Tesfahun K.T., Girma G.G. Fe–Al binary oxide nanosorbent: Synthesis, characterization and phosphate sorption property. J. Environ. Chem. Eng. 2016;4:2458–2468. https://doi.org/10.1016/j.jece.2016.04.023.
  3. Bagheri H., Asgharinezhad A.A., Ebrahimzadeh H. Determination of trace amounts of Cd(II), Cu(II), and Ni(II) in food samples using a novel functionalized magnetic Nanosorbent. Food Anal. Methods. 2016;9:876–888. https://doi.org/10.1007/s12161-015-0264-x.
  4. Crini G., Badot P.M. Application of chitosan, a natural aminopolysaccharide, for dye removal from aqueous solutions by adsorption processes using batch studies: A review of recent literature. Prog. Polym. Sci. 2008;33:399–447. https://doi.org/10.1016/j.progpolymsci.2007.11.001.
  5. Tan K.L., Hameed B.H. Insight into the adsorption kinetics models for the removal of contaminants from aqueous solutions. J. Taiwan Inst. Chem. Eng. 2017;74:25–48. https://doi.org/10.1016/j.jtice.2017.01.024.
  6. Alberti G., Amendola V., Pesavento M., Biesuz R. Beyond the synthesis of novel solid phases: Review on modelling of sorption phenomena. Coord. Chem. Rev. 2012;256:28–45. https://doi.org/10.1016/j.ccr.2011.08.022.
  7. Ma A., Abushaikha A., Allen S.J., McKay G. Ion exchange homogeneous surface diffusion modelling by binary site resin for the removal of nickel ions from wastewater in fixed beds. Chem. Eng. J. 2019;358. 135. https://doi.org/10.1016/j.cej.2018.09.135.
  8. Dadwhal M., Ostwal M.M., Liu P.K.T., Sahimi M., Tsotsis T.T. Adsorption of arsenic on conditioned layered double hydroxides: Column experiments and modeling. Ind. Eng. Chem. Res. 2009;48:2076–2084. https://doi.org/10.1021/ie800878n.
  9. Sperlich A., Schimmelpfennig S., Baumgarten B., Genz A., Amy G., Worch E., Jekel M. Predicting anion breakthrough in granular ferric hydroxide (GFH) adsorption filters. Water Res. 2008;42:2073–2082. https://doi.org/10.1016/j.watres.2007.12.019.
  10. Chu K.H. Fixed bed sorption: Setting the record straight on the Bohart–Adams and Thomas models. J. Hazard. Mater. 2010;177:1006–1012. https://doi.org/10.1016/j.jhazmat.2010.01.019.
  11. Lagergren S. Zur Theorie der sogenannten Adsorption Geloster Stoffe. K. Sven. vetensk. akad. handl. 1898;24:1–39.
  12. Khamizov R. KhA pseudo-second order Kinetic equation for sorption processes. Russian Journal of Physical Chemistry A: Focus on Chemisttry. 2020;94:171–176. https://doi.org/10.1134/S0036024420010148.
  13. Douven S., Paez C.A., Gommes C.J. The range of validity of sorption kinetic models. J. Colloid Interface Sci. 2015;448:437–450. https://doi.org/10.1016/j.jcis.2015.02.053.
  14. Malash G.F., El-Khaiary M.I. Piecewise linear regression: A statistical method for the analysis of experimental adsorption Data by the intraparticle-diffusion models. Chem. Eng. J. 2010;163:256–263. https://doi.org/10.1016/j.cej.2010.07.059.
  15. Hu Q., Xie Y., Feng C., Zhang Z. Fractal-like kinetics of adsorption on heterogeneous surfaces in the fixed-bed column. Chem. Eng. J. 2019;358:1471–1478. https://doi.org/10.1016/j.cej.2018.10.165.
  16. Hu Q., Xie Y., Feng C., Zhang Z. Prediction of breakthrough behaviors using logistic, hyperbolic tangent and double exponential models in the fixed-bed column. Sep. Purif. Technol. 2019;212:572–579. https://doi.org/10.1016/j.seppur.2018.11.071.
  17. Chu K.H. Breakthrough curve analysis by simplistic models of fixed bed adsorption: In defense of the century-old Bohart–Adams model. Chem. Eng. J. 2020;380. 122513. https://doi.org/10.1016/j.cej.2019.122513.
  18. Długosz O., Banach M. Sorption of Ag+ and Cu2+ by vermiculite in a fixed-bed column: Design, process optimization and dynamics investigations. Appl. Sci. 2018;8. 2221. https://doi.org/10.3390/app8112221.
  19. Figaro S., Avril J.P., Brouers F., Ouensanga A., Gaspard S. Adsorption studies of molasse’s wastewaters on activated carbon: Modelling with a new fractal kinetic equation and evaluation of kinetic models. J. Hazard. Mater. 2009;161:649–656. https://doi.org/10.1016/j.jhazmat.2008.04.006.
  20. Park H.-J., Tavlarides L.L. Adsorption of chromium(VI) from aqueous solutions using an imidazole functionalized adsorbent. Ind. Eng. Chem. Res. 2008;47:3401–3409. https://doi.org/10.1021/ie7017096.
  21. Marczewski A.W., Deryło-Marczewska A., Słota A. Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons. Adsorption. 2013;19:391–406. https://doi.org/10.1007/s10450-012-9462-7.
  22. Bohart G.S., Adams E.Q. Some aspects of the behavior of charcoal with respect to chlorine. J. Franklin Inst. 1920;189:669. https://doi.org/10.1016/s0016-0032(20)90400-3.
  23. Azizian S. A novel and simple method for finding the heterogeneity of adsorbents on the basis of adsorption kinetic data. J. Colloid Interface Sci. 2006;302:76–81. https://doi.org/10.1016/j.jcis.2006.06.034.
  24. Kuan W.H., Lo S.L., Chang C.M., Wang M.K. A geometric approach to determine adsorption and desorption kinetic constants. Chemosphere. 2000;41:1741–1747. https://doi.org/10.1016/S0045-6535(00)00054-0.
  25. Novak L.T., Adriano D.C. Phosphorus movement in soils: 1. Soil-orthophosphate reaction kinetics. J. Environ. Qual.1975;4:261. https://doi.org/10.2134/jeq1975.00472425000400020028x.
  26. Liu Y., Shen L. From Langmuir kinetics to first- and second-order rate equations for adsorption. Langmuir. 2008;24:11625–11630. https://doi.org/10.1021/la801839b.
  27. Zhang J. Physical insights into kinetic models of adsorption. Sep. Purif. Technol. 2019;229. 115832. https://doi.org/10.1016/j.seppur.2019.115832.
  28. Salvestrini S. Analysis of the Langmuir rate equation in its differential and integrated form for adsorption processes and a comparison with the pseudo first and pseudo second order models. React. Kinet. Mech. Catal. 2018;123:455–472. https://doi.org/10.1007/s11144-017-1295-7.
  29. Svitel J., Balbo A., Mariuzza R.A., Gonzales N.R., Schuck P. Combined affinity and rate constant distributions of ligand populations from experimental surface binding kinetics and equilibria. Biophys. J. 2003;84:4062–4077. https://doi.org/10.1016/S0006-3495(03)75132-7.
  30. Kirchner G., Baumgartner D. Migration rates of radionuclides deposited after the Chernobyl Accident in various North German soils. Analyst. 1992;117:475. https://doi.org/10.1039/an9921700475.
  31. Garnier J.-M., Ciffroy P., Benyahya L. Implications of short and long term (30 days) sorption on the desorption kinetic of trace metals (Cd, Zn, Co, Mn, Fe, Ag, Cs) associated with river suspended matter. Sci. Total Environ. 2006;366:350–360. https://doi.org/10.1016/j.scitotenv.2005.07.015.
  32. Choi H., Al-Abed S.R. PCB congener sorption to carbonaceous sediment components: Macroscopic comparison and characterization of sorption kinetics and mechanism. J. Hazard. Mater. 2009;165:860–866. https://doi.org/10.1016/j.jhazmat.2008.10.100.
  33. Monazam E.R., Shadle L.J., Miller D.C., Pennline H.W., Fauth D.J., Hoffman J.S., Gray M.L. Equilibrium and kinetics analysis of carbon dioxide capture using immobilized amine on a mesoporous silica. AIChE J. 2013;59:923–935. https://doi.org/10.1002/aic.13870.
  34. Warrinnier R., Goossens T., Braun S., Gustafsson J.P., Smolders E. Modelling heterogeneous phosphate sorption kinetics on iron oxyhydroxides and soil with a continuous distribution approach. Eur. J. Soil Sci. 2018;69:475–487. https://doi.org/10.1111/ejss.12549.
  35. Scott K.F. Extraction of rate constant distributions from heterogeneous chemical kinetics. J. Chem. Soc. Faraday Trans. 1. Phys. Chem. Condens. Phases.1980;76:2065–2079. https://doi.org/10.1039/F19807602065.
  36. Rudzinski W., Panczyk T. The Langmuirian adsorption kinetics revised: A farewell to the XXth century theories? Adsorption. 2002;8:23–34. https://doi.org/10.1023/A:1015214406179.
  37. Rietsch E. On an Alleged Breakdown of the Maximum-Entropy Principle. In: Maximum-Entropy and Bayesian Methods in Inverse Problems. Dordrecht: Springer Netherlands; 1985. P. 67–82.
  38. Phillips D.L.L.D. A technique for the numerical solution of certain integral equations of the first kind. J. ACM. 1962; 9:84–97. https://doi.org/10.1145/321105.321114.
  39. Golikov A., Malakhova I., Azarova Y., Eliseikina M., Privar Y., Bratskaya S. Extended Rate Constant Distribution model for sorption in heterogeneous systems. 1: Application to kinetics of metal ion sorption on polyethyleneimine cryogels. Ind. Eng. Chem. Res. 2020;59:1123–1134. https://doi.org/10.1021/acs.iecr.9b06000.
  40. Malakhova I., Golikov A., Azarova Y., Bratskaya S. Extended Rate Constants Distribution (RCD) model for sorption in heterogeneous systems. 2. Importance of diffusion limitations for sorption kinetics on cryogels in batch. Gels. 2020;6. 15. https://doi.org/10.3390/gels6020015.
  41. Golikov A., Malakhova I., Privar Y., Parotkina Y., Bratskaya S. Extended Rate Constant Distribution model for sorption in heterogeneous systems. 3. From batch to fixed-bed application and predictive modeling. Ind. Eng. Chem. Res. 2020;59:19415–19425. https://doi.org/10.1021/acs.iecr.0c03516.
  42. Golikov A., Privar Y., Balatskiy D., Polyakova N., Bratskaya S. Extended Rate Constants Distribution (RCD) model for sorption in heterogeneous systems. 4. Kinetics of metal ions sorption in the presence of complexing agents – application to Cu(II) sorption on polyethyleneimine cryogel from acetate and tartrate solutions. Int. J. Mol. Sci. 2023;24. 12385. https://doi.org/10.3390/ijms241512385.
  43. Malakhova I., Privar Y., Azarova Y., Eliseikina M., Golikov A., Skatova A., Bratskaya S. Supermacroporous monoliths based on polyethyleneimine: Fabrication and sorption Properties under static and dynamic conditions. J. Environ. Chem. Eng. 2020;8. 104395. https://doi.org/10.1016/J.JECE.2020.104395.
  44. Malakhova I.A. Macroporous monolith materials based on polyethyleneinine. Dissertation (Candidate of Sciences, Chemistry). Vladivostok; 2022. (In Russ.).
  45. Lozinsky V.I., Galaev I.Y., Plieva F.M., Savina I.N., Jungvid H., Mattiasson B. Polymeric cryogels as promising materials of biotechnological Interest. Trends Biotechnol. 2003;21:445–451. https://doi.org/10.1016/j.tibtech.2003.08.002.
  46. Baimenov A., Berillo D.A., Poulopoulos S.G., Inglezakis V.J. A review of cryogels synthesis, characterization and applications on the removal of heavy metals from aqueous solutions. Adv. Colloid Interface Sci. 2020;276. 102088. https://doi.org/10.1016/j.cis.2019.102088.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Kinetic curves of Ni(II) ion sorption on PEI granules at the sorbent:solution ratio of 1:1000 (4), 1:1500 (3), 1:2000 (2), 1:4000 (1): dots – experimental data; lines – RKS model (a). Scheme of distribution of sorption centers by sorption rate and affinity and isolines of Ni(II) distribution by PEI sorption centers at the end point of the kinetic curve at the sorbent:solution ratio of 1:4000 (b). Distributions of PEI sorption centers in the space of logarithms of sorption (Ks) and desorption (Kd) rate constants (c) and logarithms of affinity constants (KAFF) (d)

Download (176KB)
Indexing metadata
3. Fig. 2. Output curves of Cu(II) ion sorption on PEI, adsorbate concentration – 100 mg/l, column diameter – 0.48 cm, height – 6 cm: dots – experimental data, solid lines – RCS model (a). Distributions of PEI sorption centers by affinity constants with respect to Cu(II) ions (b)

Download (87KB)
Indexing metadata
4. Fig. 3. Kinetic curves of Cu(II) ion sorption on PEI granules at the sorbent:solution ratio of 1:1000 (4), 1:1500 (3), 1:2000 (2), 1:4000 (1): dots – experimental data; dashed lines – RKS model, solid lines – RKS-D model (a). Model kinetic curves of Cu(II) ion sorption obtained using the RKS model and RKS function for granules (1) and fine fraction (2) and the RKS-D model and RKS function for the fine fraction of PEI (3); the parameters for modeling (sorbent mass, column volume, adsorbate concentration) correspond to the sorption conditions in dynamics in Fig. 2, a (b)

Download (74KB)
Indexing metadata
5. Fig. 4. Output curves of Cu(II) (a) and Cd(II) (b) ions sorption on monolithic PEI cryogel: dots are experimental data, lines are model curves calculated within the RCS model. Sorption conditions (adsorbate concentration and flow rate): a – 1.56 mM, 41 k.v./h (1); 3.15 mM, 17 k.v./h (2); 6.25 mM, 17 k.v./h (3); b – 0.45 mM, 8 k.v./h (1); 0.90 mM, 17 k.v./h (2); 0.90 mM, 41 k.v./h (3). Distributions of sorption centers of PEI cryogel by sorption rate constants for Cu(II) and Cd(II) ions, calculated using the RKS-D function obtained from the kinetic curves of sorption under static conditions (c)

Download (130KB)
Indexing metadata

Copyright (c) 2024 Russian Academy of Sciences