Design of biochemical reactors mass transfer criteria for simple and complex systems

  • M. Moo-Young
  • H. W. Blanch
Conference paper
Part of the Advances in Biochemical Engineering book series (ABE, volume 19)


Biochemical reactors are treated as heterogeneous catalytic reactors in which physical mass transfer completely or significantly controls the overall rate of the process being promoted in the reactor. The treatment used to develop basic design strategies takes into account the special constraints imposed by biological and biochemical phenomena on the systems.

By identifying the fundamental principles involved, generalized mass transfer criteria for biochemical reactors are developed for both inter-particle and intra-particle pathways in solid-fluid and fluid-fluid contacting systems for such diverse processes as aerobic fermentations, anaerobic fermentations, immobilized enzyme reactions, and insoluble substrate utilization. A wide range of practical operating conditions extending from Theologically simple non-viscous materials to complex viscous non-Newtonian and multiphase systems, and from geometrically simple bubble-column and packed-bed devices to complex stirred-tank and tubular-loop configurations are considered. Recent advancements in the development of correlations for mass transfer coefficients, interfacial areas, and related parameters are reviewed.

The processing energy required to induce and maintain the physical mass transfer pathways in the various reactor systems are also considered. It is shown that with the present state of the art, the application of engineering correlations to the scaling-up of biochemical reactors, especially stirred-tank reactor types, is more difficult than may be generally realized. Finally, attention is drawn to the areas of ignorance which need further exploration to help in the establisment of rational design and operation procedures for biochemical reactors.


Mass Transfer Coefficient Biochemical Reactor Bubble Size Mass Transfer Rate Intraparticle Diffusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

Roman Letters


total interfacial area


specific interfacial area (based on unit volume of dispersion)


non-Newtonian mixing factor


concentration of solute in bulk liquid

\(\bar C\)

concentration of solute in bulk media (as opposed to the interior of a particle)


concentration of component A


initial concentration of solute


heat capacity


nutrient concentration at r


nutrient concentration at R


saturation concentration of solute


critical nutrient concentration


dilution rate; impeller diameter; diffusivity


liquid-phase diffusivity


diffusivity of product in membrane


intra-particle molecular diffusivity


diffusivity of substrate in membrane


tank or column diameter


diameter of particle as an equi-volume sphere


bubble diameter


equilibrium bubble diameter


orifice diameter


fractional approach to equilibrium


ratio between bubble width and bubble height


eddy diffusivity


effectiveness factor


volumetric liquid flow rate feeding reactor


molar gas flow rate (subscript 1 indicates inlet and 2 outlet)


acceleration due to gravity


Henry's law coefficient


liquid height in reactor


total height of dispersion in reactor


heat transfer coefficient


mass flux of component A in B


consistency coefficient of power-law fluids


inhibition constant


Michaelis constant


overall gas phase mass transfer coefficient


Boltzman constant; thermal conductivity


liquid phase mass transfer coefficient


volumetric mass transfer coefficient


impeller blade length; 1/2 membrane thickness in Sect. 4.3


characteristic length; length of terminal eddies; distance from center of membrane in Sect. 4.3


speed of agitator


number of wall baffles in stirred tank


fluid behavior index of power-law fluids; Froude number exponent in Eq. (107)


number of blades on impeller


agitator power requirements for ungassed liquids; product concentration in Sect. 4.3


agitator requirements for gas-liquid dispersions


total pressure

P1, P2

pressure at bottom and top of tank


specific nutrient consumption rate (when nutrient is oxygen — specific, espiration rate at C; volumetric gas flow rate


specific respiration rate in bulk media


maximum value of specific respiration rate at C (within a particle)


universal gas constant; outer radius of a sphere


radius; reaction rate per unit volume


sphere radius of solute


radius within a particle at which a dissolved nutrient becomes zero


reaction rate of substrate


substrate concentration; ratio of cup to bob diameter


concentration of substrate at surface of membrane


surface renewal rate


temperature; tank diameter




characteristic linear velocity


bubble velocity


mean square fluctuating velocity component


liquid velocity


velocity of gas at orifice


terminal velocity of particle


relative particle velocity


volume of fermentor contents


volume of gas


volume of liquid


maximum reaction rate


superficial gas velocity


volume of air per unit volume of medium per minute


width of impeller blade


width of wall baffles


film thickness at the interface


diffusional distance


mole fraction of component in gas phase; dimensionless concentration

\(\bar y\)

mean mole fraction defined by Eq. (48)

Greek Letters

\(\dot \gamma\)

shear rate


diffusion boundary layer thickness (for mass transfer)


momentum boundary layer thickness


Bingham number


ratio of gas velocity just above orifice to initial velocity


viscosity (dynamic)


apparent viscosity (dynamic)


interfacial viscosity


kinematic viscosity of continuous phase


General modulus in Sect. 4.2 \(( = R\sqrt {{{\varrho _m \bar Q} \mathord{\left/{\vphantom {{\varrho _m \bar Q} {2D_r \bar C}}} \right.\kern-\nulldelimiterspace} {2D_r \bar C}})}\)


density of continous phase


density of dispersed phase


density of mycelia


interfacial tension between dispered and continuous phases


shear stress


hold-up of dispersed phase


intra-particle mass transfer rate for a nutrient


fower factor in Eq. (107)







dispersed phase


gas phase






liquid phase




initial condition

equilibrium conditions

Abbreviations for Dimensionless Groups


Deborah number


Froude number


orifice Froude number


Grashof number for mass transfer based on particle-environment density difference


Grashof number for heat transfer


Grashof number for mass transfer based on the momentum boundary layer thickness


aeration number


Nusselt number


Peclet number for mass transfer


Peclet number for bubble swarms


power number


Prandtl number


Reynolds number for moving particles


generalized Reynolds number for power-law fluids


impeller Reynolds number


isotropic turbulence Reynolds number


orifice Reynolds number (based on gas properties)


orifice Reynolds number (based on liquid properties)


Sherwood number


Schmidt number


Weber number


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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • M. Moo-Young
    • 1
  • H. W. Blanch
    • 2
  1. 1.Dept. of Chemical EngineeringUniversity of WaterlooWaterlooCanada
  2. 2.Dept. of Chemical EngineeringUniversity of CaliforniaBerkeleyU.S.A.

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