Skip to main content
SpringerLink
Log in

Computational modeling of batch stirred tank reactor based on spherical catalyst particles

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

This paper presents a model of a batch stirred tank reactor with spherical catalyst particles as microreactors. The model involves three regions: an array of porous enzyme-loaded microreactors where enzyme reaction as well as mass transfer by diffusion take place, a diffusion limiting region surrounding the particles and a convective region where the substrate is of uniform concentration. The microbioreactors are mathematically modeled by a two-compartment model based on reaction–diffusion equations containing a nonlinear term related to the Michaelis–Menten enzyme kinetics. The influence of the physical and kinetic parameters of the microbioreactors on the transient effectiveness of the bioreactor system is numerically investigated in a wide range of model parameters. The numerical simulation was carried out using the finite difference technique. The simulation results show non-monotonic effect of the initial substrate concentration and nonlinear effects of the internal and external diffusion limitations as well as adsorption capacity of the microreactors on the transient effectiveness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. A.E. Al-Muftah, I.M. Abu-Reesh, Effects of simultaneous internal and external mass transfer and product inhibition on immobilized enzyme-catalyzed reactor. Biochem. Eng. J. 27(2), 167–178 (2005)

    CAS  Google Scholar 

  2. M. Al-Shannag, Z. Al-Qodah, J. Herrero, J.A. Humphrey, F. Giralt, Using a wall-driven flow to reduce the external mass-transfer resistance of a bio-reaction system. Biochem. Eng. J. 38(3), 554–565 (2008)

    Google Scholar 

  3. I. Andrés, Enzyme Biocatalysis: Principles and Applications (Springer, Dordrecht, 2008)

    Google Scholar 

  4. R. Aris, Mathematical Modeling: A Chemical Engineer’s Perspective (Academic Press, London, 1999)

    Google Scholar 

  5. R. Baronas, F. Ivanauskas, J. Kulys, Mathematical modeling of biosensors based on an array of enzyme microreactors. Sensors 6(4), 453–465 (2006)

    CAS  Google Scholar 

  6. R. Baronas, J. Kulys, L. Petkevičius, Modelling the enzyme catalysed substrate conversion in a microbioreactor acting in continuous flow mode. Nonlinear Anal. Model. Control 23(3), 437–456 (2018)

    Google Scholar 

  7. P.N. Bartlett, Bioelectrochemistry: Fundamentals. Experimental Techniques and Applications (Wiley, Chichester, 2008)

    Google Scholar 

  8. L.A. Belfiore, Transport Phenomena for Chemical Reactor Design (Wiley, Hoboken, 2003)

    Google Scholar 

  9. C.M. Bidabehere, J.R. García, U. Sedran, Use of stirred batch reactors for the assessment of adsorption constants in porous solid catalysts with simultaneous diffusion and reaction. Theor. Anal. Chem. Eng. Sci. 61(6), 2048–2055 (2006)

    CAS  Google Scholar 

  10. C.M. Bidabehere, J.R. García, U. Sedran, Transient effectiveness factor in porous catalyst particles. Application to kinetic studies with batch reactors. Chem. Eng. Res. Des. 118, 41–50 (2017)

    CAS  Google Scholar 

  11. C.M. Bidabehere, J.R. García, U. Sedran, Transient effectiveness factor. Simultaneous determination of kinetic, diffusion and adsorption equilibrium parameters in porous catalyst particles under diffusion control conditions. Chem. Eng. J. 345, 196–208 (2018)

    CAS  Google Scholar 

  12. C.M. Bidabehere, U. Sedran, Transient effectiveness factors in the dynamic analysis of heterogeneous reactors with porous catalyst particles. Chem. Eng. Sci. 137, 293–300 (2015)

    CAS  Google Scholar 

  13. J. Biswas, D. Do, P. Greenfield, J.M. Smith, Evaluation of bidisperse diffusivities and tortuosity factors in porous catalysts using batch and continuous adsorbers: a theoretical study. Appl. Catal. 22(1), 97–113 (1986)

    CAS  Google Scholar 

  14. N. Bortone, M. Fidaleo, M. Moresi, Internal and external mass transfer limitations on the activity of immobilised acid urease derivatives differing in enzyme loading. Biochem. Eng. J. 82, 22–33 (2014)

    CAS  Google Scholar 

  15. D. Britz, R. Baronas, E. Gaidamauskaitė, F. Ivanauskas, Further comparisons of finite difference schemes for computational modelling of biosensors. Nonlinear Anal. Model. Control 14(4), 419–433 (2009)

    CAS  Google Scholar 

  16. D. Britz, J. Strutwolf, Digital Simulation in Electrochemistry. Monographs in Electrochemistry, 4th edn. (Springer, Cham, 2016)

    Google Scholar 

  17. N. Casas, P. Blánquez, T. Vicent, M. Sarrà, Mathematical model for dye decoloration and laccase production by Trametes versicolor in fluidized bioreactor. Biochem. Eng. J. 80, 45–52 (2013)

    CAS  Google Scholar 

  18. H.S. Choonia, S. Lele, Kinetic modeling and implementation of superior process strategies for \(\beta \)-galactosidase production during submerged fermentation in a stirred tank bioreactor. Biochem. Eng. J. 77, 49–57 (2013)

    CAS  Google Scholar 

  19. L. Coche-Guerente, P. Labbé, V. Mengeaud, Amplification of amperometric biosensor responses by electrochemical substrate recycling. 3. Theoretical and experimental study of the phenol–polyphenol oxidase system immobilized in laponite hydrogels and layer-by-layer self-assembled structures. Anal. Chem. 73(14), 3206–3218 (2001)

    CAS  PubMed  Google Scholar 

  20. M.E. Davis, R.J. Davis, Fundamentals of Chemical Reaction Engineering (McGraw-Hill, New York, 2003)

    Google Scholar 

  21. D.D. Do, P.F. Greenfield, The concept of an effectiveness factor for reaction problems involving catalyst deactivation. Chem. Eng. J. 27(2), 99–105 (1983)

    CAS  Google Scholar 

  22. P.M. Doran, Bioprocess Engineering Principles, 2nd edn. (Academic Press, Waltham, 2013)

    Google Scholar 

  23. D.A. Edwards, B. Goldstein, D.S. Cohen, Transport effects on surface-volume biological reactions. J. Math. Biol. 39(6), 533–561 (1999)

    CAS  PubMed  Google Scholar 

  24. E. Fossas, R.M. Ros, J. Fabregat, Sliding mode control in a bioreactor model. J. Math. Chem. 30(2), 203–218 (2001)

    CAS  Google Scholar 

  25. B. Godongwana, Effectiveness factors and conversion in a biocatalytic membrane reactor. PLoS ONE 11(4), e0153,000 (2016)

    Google Scholar 

  26. I. Grubecki, External mass transfer model for hydrogen peroxide decomposition by terminox ultra catalase in a packed-bed reactor. Chem. Process Eng. 38(2), 307–319 (2017)

    CAS  Google Scholar 

  27. J. Iqbal, S. Iqbala, C.E. Müller, Advances in immobilized enzyme microbioreactors in capillary electrophoresis. Analyst 138(11), 3104–3116 (2013)

    CAS  PubMed  Google Scholar 

  28. E. Jones, K. McClean, S. Housden, G. Gasparini, I. Archer, Biocatalytic oxidase: batch to continuous. Chem. Eng. Res. Des. 90, 726–731 (2012)

    CAS  Google Scholar 

  29. V. Kasche, A. Kapune, H. Schwegler, Operational effectiveness factors of immobilized enzyme systems. Enzyme Microb. Technol. 1(1), 41–46 (1979)

    CAS  Google Scholar 

  30. G. Marroquín, J. Ancheyta, C. Esteban, A batch reactor study to determine effectiveness factors of commercial HDS catalyst. Catal. Today 104(1), 70–75 (2005)

    Google Scholar 

  31. V.M. PonRani, L. Rajendran, Mathematical modelling of steady-state concentration in immobilized glucose isomerase of packed-bed reactors. J. Math. Chem. 50(5), 1333–1346 (2012)

    CAS  Google Scholar 

  32. J.K. Poppe, R. Fernandez-Lafuente, R.C. Rodrigues, M.A.Z. Ayub, Enzymatic reactors for biodiesel synthesis: present status and future prospects. Biotechnol. Adv. 33(5), 511–525 (2015)

    CAS  PubMed  Google Scholar 

  33. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edn. (Cambridge University Press, Cambridge, 2007)

    Google Scholar 

  34. J.B. Rawlings, J.G. Ekerdt, Chemical Reactor Analysis and Design Fundamentals, 2nd edn. (Nob Hill Publishing, LLC, Madison, 2015)

    Google Scholar 

  35. U. Rinas, H. El-Enshasy, M. Emmler, A. Hille, D.C. Hempel, H. Horn, Model-based prediction of substrate conversion and protein synthesis and excretion in recombinant Aspergillus niger biopellets. Chem. Eng. Sci. 60(10), 2729–2739 (2005)

    CAS  Google Scholar 

  36. A. Sagiv, Exact solution of mass diffusion into a finite volume. J. Membr. Sci. 186(2), 231–237 (2001)

    CAS  Google Scholar 

  37. D. Schäpper, M.N.H.Z. Alam, N. Szita, A.E. Lantz, K.V. Gernaey, Application of microbioreactors in fermentation process development: a review. Anal. Bioanal. Chem. 395(3), 679–695 (2009)

    PubMed  Google Scholar 

  38. T. Skybová, M. Přibyl, P. Hasal, Mathematical model of decolourization in a rotating disc reactor. Biochem. Eng. J. 93, 151–165 (2015)

    Google Scholar 

  39. M. Velkovsky, R. Snider, D.E. Cliffel, J.P. Wikswo, Modeling the measurements of cellular fluxes in microbioreactor devices using thin enzyme electrodes. J. Math. Chem. 49(1), 251–275 (2011)

    CAS  PubMed  Google Scholar 

  40. J. Villadsen, J. Nielsen, G. Lidén, Bioreaction Engineering Principles. Monographs in Electrochemistry, 3rd edn. (Springer, New York, 2011)

    Google Scholar 

  41. H.J. Vos, P.J. Heederik, J.J.M. Potters, K.C.A.M. Luyben, Effectiveness factor for spherical biofilm catalysts. Bioprocess Eng. 5(2), 63–72 (1990)

    CAS  Google Scholar 

Download references

Acknowledgements

The work of R. Baronas and L. Petkevičius was supported by the Research Council of Lithuania under Grant No. S-MIP-17-98.

Author information

Authors and Affiliations

  1. Institute of Computer Science, Vilnius University, Didlaukio Str. 47, 08303, Vilnius, Lithuania

    Romas Baronas & Linas Petkevičius

  2. Institute of Biochemistry, Life Sciences Center, Vilnius University, Sauletekio Av. 7, 10257, Vilnius, Lithuania

    Juozas Kulys

Authors
  1. Romas Baronas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juozas Kulys
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Linas Petkevičius
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Romas Baronas.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Baronas, R., Kulys, J. & Petkevičius, L. Computational modeling of batch stirred tank reactor based on spherical catalyst particles. J Math Chem 57, 327–342 (2019). https://doi.org/10.1007/s10910-018-0954-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-018-0954-x

Keywords

Search

Navigation