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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)

Abstract

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.

Keywords

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

A

total interfacial area

a

specific interfacial area (based on unit volume of dispersion)

B

non-Newtonian mixing factor

C

concentration of solute in bulk liquid

\(\bar C\)

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

CA

concentration of component A

CO

initial concentration of solute

Cp

heat capacity

Cr

nutrient concentration at r

CR

nutrient concentration at R

Cs

saturation concentration of solute

CT

critical nutrient concentration

D

dilution rate; impeller diameter; diffusivity

DL

liquid-phase diffusivity

Dp

diffusivity of product in membrane

Dr

intra-particle molecular diffusivity

Ds

diffusivity of substrate in membrane

DT

tank or column diameter

d

diameter of particle as an equi-volume sphere

dB

bubble diameter

dBe

equilibrium bubble diameter

d0

orifice diameter

E

fractional approach to equilibrium

El

ratio between bubble width and bubble height

ED

eddy diffusivity

Ef

effectiveness factor

F

volumetric liquid flow rate feeding reactor

G

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

g

acceleration due to gravity

H

Henry's law coefficient

HL

liquid height in reactor

HT

total height of dispersion in reactor

h

heat transfer coefficient

JA

mass flux of component A in B

K

consistency coefficient of power-law fluids

Ki

inhibition constant

Km

Michaelis constant

KG

overall gas phase mass transfer coefficient

k

Boltzman constant; thermal conductivity

kL

liquid phase mass transfer coefficient

kLa

volumetric mass transfer coefficient

L

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

l

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

N

speed of agitator

Nb

number of wall baffles in stirred tank

n

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

nB

number of blades on impeller

P

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

Pg

agitator requirements for gas-liquid dispersions

Ps

total pressure

P1, P2

pressure at bottom and top of tank

Q

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

-Q

specific respiration rate in bulk media

Q'mas

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

R

universal gas constant; outer radius of a sphere

r

radius; reaction rate per unit volume

ro

sphere radius of solute

rp

radius within a particle at which a dissolved nutrient becomes zero

r(s)

reaction rate of substrate

S

substrate concentration; ratio of cup to bob diameter

Si

concentration of substrate at surface of membrane

s

surface renewal rate

T

temperature; tank diameter

t

time

U

characteristic linear velocity

UB

bubble velocity

Ūd2

mean square fluctuating velocity component

UL

liquid velocity

Uo

velocity of gas at orifice

UT

terminal velocity of particle

u

relative particle velocity

V

volume of fermentor contents

VG

volume of gas

VL

volume of liquid

Vm

maximum reaction rate

Vs

superficial gas velocity

VVM

volume of air per unit volume of medium per minute

W

width of impeller blade

Wb

width of wall baffles

X

film thickness at the interface

x

diffusional distance

y

mole fraction of component in gas phase; dimensionless concentration

\(\bar y\)

mean mole fraction defined by Eq. (48)

Greek Letters

\(\dot \gamma\)

shear rate

δ0

diffusion boundary layer thickness (for mass transfer)

δM

momentum boundary layer thickness

ε

Bingham number

η

ratio of gas velocity just above orifice to initial velocity

μ

viscosity (dynamic)

μa

apparent viscosity (dynamic)

μs

interfacial viscosity

ν

kinematic viscosity of continuous phase

ξ

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

ϱ

density of continous phase

ϱd

density of dispersed phase

ϱm

density of mycelia

σ

interfacial tension between dispered and continuous phases

τ

shear stress

φ

hold-up of dispersed phase

φm

intra-particle mass transfer rate for a nutrient

Φ

fower factor in Eq. (107)

Δ

difference

Subscripts

B

bubble

d

dispersed phase

G

gas phase

I

impeller

i

interfacial

L

liquid phase

s

surface

o

initial condition

equilibrium conditions

Abbreviations for Dimensionless Groups

De

Deborah number

Fr

Froude number

Fro

orifice Froude number

Gr

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

GrH

Grashof number for heat transfer

Grδ

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

NA

aeration number

Nu

Nusselt number

Pe

Peclet number for mass transfer

Pesw

Peclet number for bubble swarms

Po

power number

Pr

Prandtl number

Re

Reynolds number for moving particles

Re′

generalized Reynolds number for power-law fluids

Ret

impeller Reynolds number

Ree

isotropic turbulence Reynolds number

Re0

orifice Reynolds number (based on gas properties)

Re0L

orifice Reynolds number (based on liquid properties)

Sh

Sherwood number

Sc

Schmidt number

We

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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