1. Introduction to Bioreactors

2. Biochemical Reactor
A device in which living cells or enzyme systems are used to promote biochemical transformation of matter
Uses:
pharmaceutical industries
Chemical industry
Waste treatment
Biomedical applications

3. 2 types:
Microbial fermenter- cell growth is used to produce metabolites, biomass, transformed substrates, or purified solvents
Enzyme reactors (cell free)- immobilized enzymes often used for fluid-fluid and solid-fluid contractors

4. Designing a bioreactor:
The coupled set of mass balance equations which describe the conversion of reactants to products
Ex: Substrate S is converted to cells (X) and Product (P).
Growth of cells… (dX/dT)V = (rx) ( V)
Consumption of substrate… (dS/dT)V = (rs)(V)
Product formation… (dP/dT)V = (rp)(V)

5. Constitutive Rate Expressions for Biological Processes
Model of Microbial Growth
Segregated- cells are different from one another
Non-segregated models lump the population into one biophase interacting with external environment and is one species in solution; they are mathematically simple
External environment influences cell response and can confer new growth characteristics on the cell

6. Unstructured Growth Models
Simple relationships that describe exponential growth
Kinetics of cell growth are described using cell and nutrient concentration profiles
Malthus’s simple model: rx = µX where rx is the increase in dry cell weight and µ(hr-1) is a constant.
dX/dt = kX(1-βX) was proposed as a cell concentration-dependent inhibition term by Verhulst, Pearl, and Reed.

7. Monod Model
Developed by Jaques Monod, exemplifies the effect of nutrient concentration based on E. coli growth are various sucrose concentrations and assumes only the limiting substrate is important in determining the rate of cell proliferation

8. For the Monod Model Cell growth might follow the form
rx = µX = µmaxSX/Ks + S
and batch growth at constant volume
dX/dt = µmaxSX/Ks + S
µmax is max specific growth rate of cells
Ks is value of the limiting nutrient concentration
Two limiting forms:
At high substrate concentrations S>>Ks, µ= µmax
At low substrate concentrations S<<Ks, µ= µmax/KsS

9. Models of Growth and Non-growth Associated Product Formation
Primary metabolites- growth associated; rate of production parallels growth of cell population; Ex: gluconic acid
Secondary metabolites- non-growth associated; kinetics do not depend on culture growth rate; Ex: antibiotics, vitamins
Intermediate products- partially growth associated; Ex: amino acids, lactic acid

10. Mass transfer in Bioreactors
Possible resistances:
In a gas film
At the gas-liquid interface
In a liquid at the gas-liquid interface
In the bulk liquid
In a liquid film surrounding the solid
At the liquid-solid interface
In the solid phase containing the cells
At the sites of biochemical reactions

11. Definition of Mass Transfer Coefficient
Relates transfer rates to concentration terms and is defined as a mass balance for a certain reactant or product species in the reactor…
Na = kLa(Ci x g – CL)
Na= Oxygen transfer rate (through the air bubbles)
CL = local dissolved oxygen concentration in bulk liquid at any time
Cg= oxygen concentration in the liquid at the gas- liquid interface at infinite time
a= interfacial area
kL= local liquid phase mass transfer coefficient

12. Bioreactor types and modes
Bubble Columns
Systems with Stationary Internals
The above take on this correlation:
KLa = constant Vns
where n is in the range in the bubble flow regime
Stirred-Tank Reactors
uses this correlation: KLa = (Pg/V)n (VSr)

13. Power Requirements Air-lift Systems Agitated Un-gassed Systems
The power input through a reactor can be high in larger reactors
The power input is estimated as: Pg = GRT ln (P1/P0)
Agitated Un-gassed Systems
In the turbulent flow regime, P ~ ρn3D5
In the laminar flow regime, P ~ 1/Re P ~ µN2D3
where P is proportional to viscosity but independent of density
Gassed Systems
Power required is less than un-gassed with reduction Pg/P given as PgP = f(NA)

14. Scale-Up Scale-up methods based on… Fixed power input
Fixed mixing time
Fixed oxygen transfer coefficient
Fixed environment
Fixed impeller tip speed

15. Scale-up at fixed KLa
It may be impossible to maintain equal volumetric gas flow rates since the linear velocity through the vessel will increase differently with the scale
It may be possible to decrease the volume of gas per volume of liquid per minute on scale-up while increasing power input by changing reactor geometry and power input per unit volume

16. Scale-up on Flow Basis which becomes: N2 = N1 = (V2/V1)1/3(D1/D2)5/3
Design based on constant input of agitator power per unit reactor volume : P1/V1 = P2/V2
For constant power input in vessels that are geometrically similar
ρN31D51/V1 = ρN32D52/V2
which becomes: N2 = N1 = (V2/V1)1/3(D1/D2)5/3