A mathematical model is developed to describe the performance of a three-phase¯uidized bed reactor utilizing a transverse magnetic ®eld. The model is based on the axially dispersed plug¯ow model for the bulk of liquid phase and on the Michaelis-Menten kinetics. The model equations are solved by the explicit ®nite difference method from transient to steady state conditions. The results of the numerical simulation indicate that the magnetic ®eld increases the degree of bioconversion. The mathematical model is experimentally veri®ed in a threephase¯uidized bed reactor with Penicillium chrysogenum immobilized on magnetic beads. The experimental results are well described by the developed model when the reactor operates in the stabilized regime. At low and relatively high magnetic ®eld intensities certain discrepancy in the model solution is observed when the model over estimates the product concentration.
List of symbolsB magnetic ®eld intensity, mT C dimensionless substrate concentration in the bulk of the liquid C b substrate concentration in the bulk of the liquid, kg/m 3 C p Penicillin concentration, kg/m 3 C f substrate concentration in the bio®lm, kg/m 3 C o substrate concentration in the bulk of the liquid, kg/m 3 C s substrate concentration at the surface of the bead, kg/m 3 C x biomass dry density, kg/m 3 D aw molecular diffusivity of lactose in water, m/s D e effective diffusivity of lactose in the bio®lm, m 2 /s D l axial dispersion coef®cient, m 2 /s d p Particle diameter, m K m saturation constant, kg/m 3 K s external mass transfer coef®cient for the transport of glucose, m/s L bed height, m L o bed height, m M s saturation magnetic intensity, mT Pe Peclet number R radius of the magnetic bead, m Re Reynolds number r distance inside the bio®lm, m r s radius of the magnetic support, m S dimensionless substrate concentration inside the bio®lm U g gas velocity, m/s U l liquid velocity, m/s V max maximum reaction rate, kg lactose/kg cell X v cell density in the bio®lm, kg/m 3 X dimensionless radius Y max maximum yield coef®cient, kg/kg Y x/s growth yield coef®cient, kg/kg Z dimensionless length z length, mGreek letters q b bulk density of the magnetic particles, kg/m 3 q s molded density of the magnetic particles, kg/m 3 ebed porosity e f bio®lm porosity e gb gas holdup e l liquid holdup e so initial solid holdup l max maximum growth rate, s )1 aParameter, (K s A s L/(e l U l ) h dimensionless time, U l t/L d bio®lm thickness, m
IntroductionWhole cell immobilization technology has generated considerable interest in the ®eld of bioreactor design and operation. It has lead to the design of new reactor con®gurations to accommodate the resulting immobilized cell conformation in the form of relatively large spherical particles. Currently,¯uidized bed bioreactors are being considered as promising reactor con®gurations that are suitable to carry out bioprocesses with immobilized whole cells. The reactors are characterized by low shear stresses compared to mechanically stirred vessels and good mixing conditions, whic...