or;
(74)
When K 1 and K 2 are both significant, the product mass balance is given by the mixed
growth model:
(75)
REFERENCES
Aris, R. (1957) On shape factors for irregular particles—I. The steady state problem. Diffusion and
reaction. Chem. Eng. Sci., 6, 262–268.
Fan, L.T. and Lee Y.-H. (1983) Kinetic studies of enzymatic hydrolysis of insoluble cellulose:
derivation of a mechanistic kinetic model. Biotechnol. Bioeng., 25, 2707–2733.
Fullbrook, P.D. (1983) Kinetics. In Industrial Enzymology, edited by T.Godfrey and J.Reicht, pp.
8–110. New York: The Nature Press.
Horvath, C. and Engasser J.-M. (1974) External and internal diffusion in heterogeneous enzyme
systems. Biotechnol. Bioeng., 16, 909–923.
Lee, Y.Y., Fratzke, A.R., Wun, K. and Tsao G.T. (1976) Glucose isomerase immobilized on porous
glass. Biotechnol. Bioeng., 18, 389–413.
López-Sántin, J., Solà, C. and Lema J.M. (1982) Substrate and product inhibition significance in
the kinetics of sucrose hydrolysis by invertase. Biotechnol. Bioeng., 24, 2721–2724.
Moo-Young, M. and Kobayashi T. (1972) Effectiveness factors for immobilized-enzyme reactions.
Can. J. Chem. Eng., 50, 162–167.
Olsen, H.S. (1995) Enzymes in food processing. In Biotechnology, 2nd edn, edited by H.-J. Rehm,
G.Reed, A.Püller and P.Stadler, Vol. 9, pp. 665–736. Weinheim: VCH.
Pialis, P. and Saville B.A. (1998) Production of L-DOPA from tyrosinase immobilized on nylon
6,6: enzyme stability and scaleup. Enzyme Microb. Technol, 22, 261–268.
Oliveira, S.C. (1999) Evaluation of effectiveness factor of immobilized enzymes using Runge-
Kutta-Gill method: how to solve mathematical undetermination at particle center point?.
Bioprocess Eng., 20, 185–187.
Smith, J.M. (1981) Chemical Engineering Kinetics, 3rd edn. Singapore, McGraw-Hill Book Co.
Villadsen, J.V. and Stewart W.E. (1967) Solution of boundary-value problems by orthogonal
collocation. Chem. Eng. Sci., 22, 1483–1501.
Vos, H.J., Heederik, P.J., Potters, J.J.M. and Luyben K.Ch.A.M. (1990) Effectiveness factor for
spherical biofilm catalysts. Bioprocess Eng., 5, 63–72.
Design and modelling of immobilised biocatalytic reactors 121