Journal of Mathematical Chemistry

, Volume 54, Issue 6, pp 1221–1232 | Cite as

Impact of convective transport and inert membrane on action of the bio-catalytic filter

  • Feliksas Ivanauskas
  • Pranas Katauskis
  • Valdas Laurinavicius
Original Paper


We describe two types of enzyme-containing filters. The first type consists of a semi-permeable membrane with immobilized enzyme covered with inert membrane, permeable for the substrate and badly permeable for the product. The second filter type is a semi-permeable enzyme containing a membrane where substrate is pumping through the membrane. The first type is described by a system of two reaction–diffusion equations. The diffusion is described by Fick’s law, and the reaction is described by the Michaelis–Menten term. We obtain mathematical expression of the effectiveness of the bio-catalytic active filters to generate flux of the product and parameter describing permeability of the bio-catalytic filter for substrate. An inert membrane leads to the increase of the product flow through the bio-catalytic membrane about three times and possesses the optimal thickness of the later. Decreasing permeability of inert membrane for product decreases the product flow back, and increases product flow forward about six times. The second-type filter is described by a system of two reaction–diffusion–convection equations. The included convection term is a principal innovation of the research. The convection term increases the transport of the substrate and restricts the flux of the product in the back direction. The convection term increases both rate of the product generation and the capacity to consume the substrate more than 12 times.


Membrane reactors Immobilized enzymes Porous membranes Mathematical modeling 


  1. 1.
    W. Tisher, F. Wedekind, Immobilized enzymes: methods and applications, in Biocatalysis: From Discovery to Application, Topics in Current Chemistry, vol. 200, ed. by W.-D. Fessner, et al. (Springer, Berlin, 1999), pp. 95–126CrossRefGoogle Scholar
  2. 2.
    G.M. Rios, M.P. Belleville, D. Paolucci, J. Sanchez, Progress in enzymatic membrane reactors: a review. J. Membr. Sci. 242, 189–196 (2004)CrossRefGoogle Scholar
  3. 3.
    D.M.F. Prazeres, J.M.S. Cabral, Enzymatic membrane bioreactors and their application. Enzyme Microb. Technol. 16, 738–750 (1994)CrossRefGoogle Scholar
  4. 4.
    L. Giorno, E. Drioli, Biocatalytic membrane reactors: applications and perspectives. Trends Biotechnol. 18, 339–349 (2000)CrossRefGoogle Scholar
  5. 5.
    R. Mazzei, L. Giorno, E. Piacentini, S. Mazzuca, E. Drioli, Kinetic study of a biocatalytic membrane bioreactor containing immobilized \(\upbeta \)-galactosidase for the hydrolysis of oleuropein. J. Membr. Sci. 339, 215–223 (2009)CrossRefGoogle Scholar
  6. 6.
    F.I. Hai, L.D. Nghiem, O. Modin, Biocatalytic membrane reactors for the removal of recalcitrant and emerging pollutants from wastewater, in Handbook of Membrane Reactors: Reactor Types and Industrial Applications, ed. by A. Basile (Woodhead Publishing Ltd., Cambridge, 2013), pp. 763–806CrossRefGoogle Scholar
  7. 7.
    J. Fischer, C.Z. Guidini, L.N. Soares Santana, M.M. de Resende, V.L. Cardoso, E.J. Ribeiro, Optimization and modeling of lactose hydrolysis in a packed bed system using immobilized \(\upbeta \)-galactosidase from Aspergillus oryzae. J. Mol. Catal. B Enzym. 85–86, 178–186 (2013)CrossRefGoogle Scholar
  8. 8.
    G. Catapano, G. Iorio, E. Drioli, M. Filosa, Experimental analysis of cross-flow membrane bioreactor with intrapped whole cels: influence of trans-membrane preasure and substrate feed concentration of reactor performance. J. Membr. Sci. 35, 325–338 (1988)CrossRefGoogle Scholar
  9. 9.
    Y. Yurekli, S.A. Altinkaya, Catalytic performances of chemically immobilized urease under static and dynamic conditions: a comparative study. J. Mol. Catal. B Enzym. 71, 36–44 (2011)CrossRefGoogle Scholar
  10. 10.
    E. Nagy, Mathematical modeling of biochemical membrane reactors, in Membrane Operations: Innovative Separations and Transformations, ed. by E. Drioli, L. Giorno (Wiley, Weinheim, 2009), pp. 309–334CrossRefGoogle Scholar
  11. 11.
    V. Calabro, S. Curcio, G. Iorio, A theoretical analysis of transport phenomena in hollow fiber membrane bioreactor with immobilized biocatalyst. J. Membr. Sci. 206, 217–241 (2002)CrossRefGoogle Scholar
  12. 12.
    D.E. Steinmeyer, M.L. Shuller, Mathematical modelling and simulations of membrane bioreactor extractive fermentations. Biotechnol. Prog. 6, 362–369 (1990)CrossRefGoogle Scholar
  13. 13.
    R. Baronas, F. Ivanauskas, J. Kulys, The influence of the enzyme membrane thickness on the response of amperometric biosensors. Sensors 3, 248–262 (2003)CrossRefGoogle Scholar
  14. 14.
    P.N. Bartlett, R.G. Whitaker, Electrochemical immobilization of enzymes. Part 1. Theory. J. Electroanal. Chem. 224, 27–35 (1987)CrossRefGoogle Scholar
  15. 15.
    T. Schulmeister, Mathematical modeling of the dynamic behavior of amperometric enzymes electrodes. Sel. Electrode Rev. 12, 203–260 (1990)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Feliksas Ivanauskas
    • 1
  • Pranas Katauskis
    • 1
  • Valdas Laurinavicius
    • 2
  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Vilnius University Institute of BiochemistryVilniusLithuania

Personalised recommendations