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A critical assessment of the use of a surface reaction rate equation to correlate biosorption kinetics

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Abstract

A critical assessment of the use of a variable-order, power-law type surface reaction rate equation to correlate biosorption kinetics is presented. The general nth order rate equation with three adjustable parameters was fit to the kinetic data of lead uptake by inactivated cells of Rhodotorula glutinis using a genetic algorithm search method. The uptake process was fast, with apparent equilibrium reached in approximately 30 min. According to the Akaike information criterion test, the three-parameter nth order equation was superior to the much used pseudo second order equation with two fitting parameters. However, the strong fit of the former equation resulted in unrealistic parameter estimates. Parametric sensitivity analysis indicated that the available kinetic data with only limited information content did not allow simultaneous identification of three unknown parameters. As a result, the three-parameter nth order equation was found to be overparameterized with highly correlated parameters. It was, however, possible to retrieve meaningful parameter estimates from the kinetic data when the number of fitting parameters was reduced from 3 to 2.

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References

  • Anderson-Sprecher R (1994) Model comparisons and R 2. Am Stat 48:113–117

    Google Scholar 

  • Bai J, Yao H, Fan F, Lin M, Zhang L, Ding H, Lei F, Wu X, Li X, Guo J, Qin Z (2010) Biosorption of uranium by chemically modified Rhodotorula glutinis. J Environ Radioact 101:969–973

    Article  CAS  Google Scholar 

  • Blanchard G, Maunaye M, Martin G (1984) Removal of heavy metals from waters by means of natural zeolites. Water Res 18:1501–1507

    Article  CAS  Google Scholar 

  • Bolster CH, Hornberger GM (2007) On the use of linearized Langmuir equations. Soil Sci Soc Am J 71:1796–1806

    Article  CAS  Google Scholar 

  • Brouers F, Sotolongo-Costa O (2006) Generalized fractal kinetics in complex systems (application to biophysics and biotechnology). Phys A 368:165–175

    Article  Google Scholar 

  • Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, New York

    Google Scholar 

  • Cho DH, Kim EY (2003) Characterization of Pb2+ biosorption from aqueous solution by Rhodotorula glutinis. Bioprocess Biosyst Eng 25:271–277

    Article  CAS  Google Scholar 

  • Cho DH, Chu KH, Kim EY (2011a) Loss of cell components during rehydration of dried Rhodotorula glutinis and its implications for lead uptake. Eng Life Sci 11:283–290

    Article  CAS  Google Scholar 

  • Cho DH, Chu KH, Kim EY (2011b) Lead uptake and potentiometric titration studies with live and dried cells of Rhodotorula glutinis. World J Microbiol Biotechnol 27:1911–1917

    Article  CAS  Google Scholar 

  • Chu KH, Feng X, Kim EY, Hung Y-T (2011a) Biosorption parameter estimation with genetic algorithm. Water 3:177–195

    Article  CAS  Google Scholar 

  • Chu KH, Kim EY, Feng X (2011b) Batch kinetics of metal biosorption: application of the Bohart–Adams rate law. Sep Sci Technol 46:1591–1601

    Article  CAS  Google Scholar 

  • Haerifar M, Azizian S (2013) Mixed surface reaction and diffusion-controlled kinetic model for adsorption at the solid/solution interface. J Phys Chem C 117:8310–8317

    Article  CAS  Google Scholar 

  • Ho Y-S (2006) Review of second-order models for adsorption systems. J Hazard Mater B136:681–689

    Article  Google Scholar 

  • Kumar KV (2006) A note on the comments by Dr. Y.S. Ho on “Nitrate removal from aqueous solution by adsorption onto various materials”. J Hazard Mater B136:995–996

    Article  Google Scholar 

  • Lang W, Buranaboripan W, Wongchawalit J, Parakulsuksatid P, Vanichsriratana W, Sakairi N, Pathom-aree W, Sirisansaneeyakul S (2013) Biosorption of lead from acid solution using chitosan as a supporting material for spore forming-fungal biomass encapsulation. Int J Environ Sci Technol 10:579–590

    Article  CAS  Google Scholar 

  • Liu Y, Shen L (2008a) From Langmuir kinetics to first- and second-order rate equations for adsorption. Langmuir 24:11625–11630

    Article  CAS  Google Scholar 

  • Liu Y, Shen L (2008b) A general rate law equation for biosorption. Biochem Eng J 38:390–394

    Article  CAS  Google Scholar 

  • Liu Y, Wang Z-W (2008) Uncertainty of preset-order kinetic equations in description of biosorption data. Bioresour Technol 99:3309–3312

    Article  CAS  Google Scholar 

  • McCuen RH, Surbeck CQ (2008) An alternative to specious linearization of environmental models. Water Res 42:4033–4040

    Article  CAS  Google Scholar 

  • Morais WA, Fernandes ALP, Dantas TNC, Pereira MR, Fonseca JLC (2007) Sorption studies of a model anionic dye on crosslinked chitosan. Colloids Surf A: Physicochem Eng Asp 310:20–31

    Article  CAS  Google Scholar 

  • Motulsky H, Christopoulos A (2004) Fitting models to biological data using linear and nonlinear regression: a practical guide to curve fitting. Oxford University Press, Oxford

    Google Scholar 

  • Naja G, Volesky B (2011) The mechanism of metal cation and anion biosorption. In: Kotrba P, Mackova M, Macek T (eds) Microbial biosorption of metals. Springer, Dordrecht, pp 19–58

    Chapter  Google Scholar 

  • Özer A (2007) Removal of Pb(II) ions from aqueous solutions by sulphuric acid-treated wheat bran. J Hazard Mater 141:753–761

    Article  Google Scholar 

  • Park D, Yun Y-S, Park JM (2010) The past, present, and future trends of biosorption. Biotechnol Bioprocess Eng 15:86–102

    Article  CAS  Google Scholar 

  • Pipíška M, Horník M, Remenárová L, Augustín J, Lesný J (2010) Biosorption of cadmium, cobalt and zinc by moss Rhytidiadelphus squarrosus in the single and binary component systems. Acta Chim Slov 57:163–172

    Google Scholar 

  • Plazinski W, Rudzinski W, Plazinska A (2009) Theoretical models of sorption kinetics including a surface reaction mechanism: a review. Adv Colloid Interface Sci 152:2–13

    Article  CAS  Google Scholar 

  • Praus P, Turicová M (2007) A physico-chemical study of the cationic surfactants adsorption on montmorillonite. J Braz Chem Soc 18:378–383

    Article  CAS  Google Scholar 

  • Qiu H, Lv L, Pan B-C, Zhang Q-J, Zhang W-M, Zhang Q-X (2009) Critical review in adsorption kinetic models. J Zhejiang Univ Sci A 10:716–724

    Article  CAS  Google Scholar 

  • Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, Chichester

    Google Scholar 

  • Suazo-Madrid A, Morales-Barrera L, Aranda-García E, Cristiani-Urbina E (2011) Nickel(II) biosorption by Rhodotorula glutinis. J Ind Microbiol Biotechnol 38:51–64

    Article  CAS  Google Scholar 

  • Usunoff E, Winzettel P, Dietrich S (2009) Sorption of fluoride by quartz sand: batch tests. Geoacta 34:9–17

    Google Scholar 

  • Volesky B, Naja G (2007) Biosorption technology: starting up an enterprise. Int J Technol Transf Commer 6:196–211

    Google Scholar 

  • Zamani AA, Shokri R, Yaftian MR, Parizanganeh AH (2013) Adsorption of lead, zinc and cadmium ions from contaminated water onto Peganum harmala seeds as biosorbent. Int J Environ Sci Technol 10:93–102

    Article  CAS  Google Scholar 

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Acknowledgments

K.H.C. acknowledges partial support from the State Key Laboratory of Heavy Oil Processing at China University of Petroleum through the Open Project Funding Program under Agreement No. 2012-1-01.

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Authors and Affiliations

  1. Department of Chemical Engineering, The University of Seoul, Seoul, 130-743, Korea

    D. H. Cho & E. Y. Kim

  2. Honeychem, Nanjing Chemical Industry Park, Nanjing, 210047, China

    K. H. Chu

Authors
  1. D. H. Cho
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  2. K. H. Chu
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  3. E. Y. Kim
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Corresponding author

Correspondence to E. Y. Kim.

Nomenclature

C i

Initial solution phase concentration (mg/L)

j

Index

k 2

Pseudo second order rate coefficient (g/mg min)

k n

nth order rate coefficient [(mg/g)1−n/min]

m

Number of observations

n

Surface reaction order

p

Parameter value

q

Biosorbent phase concentration (mg/g)

q cal,j

Model-calculated q value for observation j (mg/g)

q e

Equilibrium biosorbent phase concentration (mg/g)

q exp,j

Measured q value for observation j (mg/g)

q max

Observed maximum q value (mg/g)

\(\bar{q}_{ \exp }\)

Average of measured q values (mg/g)

S p

Dimensionless sensitivity coefficient

t

Time (min)

w

Number of adjustable parameters

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Cho, D.H., Chu, K.H. & Kim, E.Y. A critical assessment of the use of a surface reaction rate equation to correlate biosorption kinetics. Int. J. Environ. Sci. Technol. 12, 2025–2034 (2015). https://doi.org/10.1007/s13762-014-0590-3

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  • DOI: https://doi.org/10.1007/s13762-014-0590-3

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