Abstract
This paper presents a mathematical model of a batch stirred tank reactor based on an array of identical spherical porous microbioreactors loaded with non specific glucose dehydrogenase and oxygen reducing enzyme, i.e. laccase. The model was validated by experimental data. The microreactors (MR) are mathematically modeled by a two-compartment model, based on reaction–diffusion equations containing nonlinear terms related to the Michaelis–Menten kinetics of two enzymatic reactions with addition of the mass transport. The dynamics of oxygen concentration change is analysed numerically using the finite difference technique. The transient effectiveness factor and the process duration are investigated at different initial concentration of carbohydate (lactose) as well as at internal and external diffusion resistances. The simulation results show a non-monotonic effect of the initial concentration of lactose and nonlinear effects of the internal and external diffusion limitations on the transient effectiveness.
Graphic Abstract
Similar content being viewed by others
References
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, 167–178 (2005)
M. Al-Shannag, Z. Al-Qodah, J. Herrero, J.A.C. Humphrey, F. Giralt, Using a wall-driven flow to reduce the external mass-transfer resistance of a bio-reaction system. Biochem. Eng. J. 38, 554–565 (2008)
R. Aris, Mathematical Modeling: A Chemical Engineer’s Perspective (Academic Press, London, 1999)
R. Baronas, F. Ivanauskas, J. Kulys, Modelling a biosensor based on the heterogeneous microreactor. J. Math. Chem. 25, 245–252 (1999)
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, 437–456 (2018)
R. Baronas, J. Kulys, L. Petkevičius, Computational modeling of batch stirred tank reactor based on spherical catalyst particles. J. Math. Chem. 57, 327–342 (2019)
P.N. Bartlett, Bioelectrochemistry: Fundamentals, Experimental Techniques and Applications (Wiley, Chichester, 2008)
L.A. Belfiore, Transport Phenomena for Chemical Reactor Design (Wiley, Hoboken, 2003)
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. Theoretical analysis. Chem. Eng. Sci. 61, 2048–2055 (2006)
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)
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)
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)
R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd edn. (Wiley, New York, 2006)
K. Bizon, B. Tabiś, Dynamics of an isothermal catalyst pellet with simultaneous chemical reaction and adsorption. Chem. Eng. Res. Des. 115, 221–229 (2016)
D. Britz, R. Baronas, E. Gaidamauskaitė, F. Ivanauskas, Further comparisons of finite difference schemes for computational modelling of biosensors. Nonlinear Anal. Model. Control 14, 419–433 (2009)
D. Britz, J. Strutwolf, Digital Simulation in Electrochemistry, 4th edn., Monographs in Electrochemistry (Springer, Cham, 2016)
H.-C. Chang, C.-C. Wu, S.-J. Ding, I.-S. Lin, I.-W. Sun, Measurement of diffusion and partition coefficients of ferrocyanide in protein-immobilized membranes. Anal. Chim. Acta. 532, 209–214 (2005)
D.S. Clark, H.W. Blanch, Biochemical Engineering, 2nd edn. (Marcel Dekker, New York, 1997)
M.E. Davis, R.J. Davis, Fundamentals of Chemical Reaction Engineering (McGraw-Hill, New York, 2003)
P.M. Doran, Bioprocess Engineering Principles, 2nd edn. (Academic Press, Waltham, MA, 2013)
R.F. Fonseca, C.C.B. Melo, B.C.P. Beatriz, V. Sanches, C.S. Bertucci-Neto, W.H.K. Farinas, Modelling of solid-state fermentation over wide operational range for application in process optimization. Can. J. Chem. Eng. 96, 1723–1734 (2018)
J. Iqbal, S. Iqbala, C.E. Müller, Advances in immobilized enzyme microbioreactors in capillary electrophoresis. Analyst 138, 3104–3116 (2013)
B. Kaoui, M. Lauricella, G. Pontrelli, Mechanistic modelling of drug release from multi-layer capsules. Comput. Biol. Med. 93, 149–157 (2018)
A.Y. Khan, S.B. Noronha, R. Bandyopadhyaya, Glucose oxidase enzyme immobilized porous silica for improved performance of a glucose biosensor. Biochem. Eng. J. 91, 78–85 (2014)
J. Kulys, The development of new analytical systems based on biocatalysts. Anal. Lett. 14, 377–397 (1981)
J. Leszczynski, Handbook of Computational Chemistry (Springer, Dordrecht, 2012)
M.F. Luna, E.C. Martínez, Optimal design of dynamic experiments in the development of cybernetic models for bioreactors. Chem. Eng. Res. Des. 136, 334–346 (2018)
G. Maria, Enzymatic reactor selection and derivation of the optimal operation policy, by using a model-based modular simulation platform. Comput. Chem. Eng. 36, 325–341 (2012)
E. Nagy, Survey on biocatalytic membrane reactor and membrane aerated biofilm reactor. Curr. Org. Chem. 21, 1713–1724 (2017)
E. Papadakis, S. Pedersen, A.K. Tula, M. Fedorova, J.M. Woodley, R. Gani, Model-based design and analysis of glucose isomerization process operation. Comput. Chem. Eng. 98, 128–142 (2017)
S. Petronis, M. Stangegaard, C.B.V. Christensen, M. Dufva, Transparent polymeric cell culture chip with integrated temperature control and uniform media perfusion. Biotechniques 40, 368–376 (2006)
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)
D. Ratautas, L. Marcinkevičienė, R. Meškys, J. Kulys, Mediatorless electron transfer in glucose dehydrogenase/laccase system adsorbed on carbon nanotubes. Electrochim. Acta 174, 940–944 (2015)
D. Ratautas, E. Ramonas, L. Marcinkevičienė, R. Meškys, J. Kulys, Wiring gold nanoparticles and redox enzymes: a self-sufficient nanocatalyst for the direct oxidation of carbohydrates with molecular oxygen. ChemCatChem 10, 971–974 (2018)
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, 2729–2739 (2005)
A. Sagiv, Exact solution of mass diffusion into a finite volume. J. Membr. Sci. 186, 231–237 (2001)
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, 679–695 (2009)
S. Skoneczny, M. Cioch-Skoneczny, Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods. Chem. Eng. Res. Des. 139, 309–320 (2018)
W. Tischer, F. Wedekind, Immobilized enzymes: methods and applications, in Biocatalysis-From Discovery to Application, vol. 200, Topics in Current Chemistry. Topics in Current Chemistry, ed. by W.D. Fessner, et al. (Springer, Berlin, 1999), pp. 95–126
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, 251–275 (2011)
G. Vidriales-Escobar, R. Rentería-Tamayo, F. Alatriste-Mondragón, O. González-Ortega, Mathematical modeling of a composting process in a small-scale tubular bioreactor. Chem. Eng. Res. Des. 120, 360–371 (2017)
J. Villadsen, J. Nielsen, G. Lidén, Bioreaction Engineering Principles, 3rd edn., Monographs in Electrochemistry (Springer, New York, 2011)
H.J. Vos, P.J. Heederik, J.J.M. Potters, K.C.A.M. Luyben, Effectiveness factor for spherical biofilm catalysts. Bioprocess Eng. 5, 63–72 (1990)
S. Whitaker, The Method of Volume Averaging, vol. 13 (Springer, Berlin, 2013)
L.-T. Zhu, W.-Y. Ma, Z.-H. Luo, Influence of distributed pore size and porosity on MTO catalyst particle performance: modeling and simulation. Chem. Eng. Res. Des. 137, 141–153 (2018)
Acknowledgements
The work of R. Baronas and L. Petkevičius was supported by the Research Council of Lithuania under Grant No. S-MIP-17-98. J. Kulys thanks to Eimantas Ramonas for the CPG modification and the performance of the oxygen consumptions experiments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Baronas, R., Kulys, J. & Petkevičius, L. Modeling carbohydrates oxidation by oxygen catalyzed by bienzyme glucose dehydrogenase/laccase system immobilized into microreactor with carbon nanotubes. J Math Chem 59, 168–185 (2021). https://doi.org/10.1007/s10910-020-01187-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-020-01187-2