1. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Bacteria (cell) growth
LAG PHASE: Growth is slow at first, while the cells acclimate to the food and nutrients in their new habitat.
LOG PHASE: Once the metabolic machinery is running, they start multiplying exponentially, doubling in number every few minutes.
STATIONARY PHASE: As more and
more cells are competing for food and
nutrients, booming growth stops and the
number of bacteria stabilizes.
DEATH PHASE: Toxic waste products
build up, food is depleted and the cells
begin to die.

2. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Growth cycle for batch cultivation
Exponential growth phase
The exponential growth phase can be represented by;
Eq. 3 shows the increase of the number of cells exponentially with respect to time.

3. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Growth cycle for batch cultivation
Exponential growth phase
The time required to double the population, called the doubling time (td), can be estimated from Eq. 3 by setting Cn=2Cno and to=0 and solving for t:
The doubling time is inversely proportional to the specific growth rate and is equal to the reciprocal of the division rate.

4. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Growth cycle for batch cultivation
Factors affecting the specific growth rate
Substrate Concentration:
Usually Monod equation to describe the effect of the substrate concentration CS on the specific growth rate (µ).
Monod equation is an empirical equation based on the form of equation normally associated with enzyme kinetics or gas adsorption:

5. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Growth cycle for batch cultivation
Factors affecting the specific growth rate
Substrate Concentration:
Graphically Monod equation can be shown in Fig.
According to Monod equation, further increase in the nutrient concentration after µ reaches µmax does not affect the µ , see Fig.
It has been observed that the µ decrease as the CS is increased beyond a certain level.

6. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Growth cycle for batch cultivation
Factors affecting the specific growth rate
Substrate Concentration:
Several other models have been proposed to improve the Monod equation, of these models;
If several substrates can limit the growth of a microorganism. The following model can be employed;

7. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Growth cycle for batch cultivation
Factors affecting the specific growth rate
Product Concentration:
As cell grow they produce metabolic by-products which can accumulate in the medium. The growth of microorganisms is usually inhibited by these products, whose effect can be added to the Monod equation as follows;
Where Cpm = the maximum product concentration above which cells cannot grow due to product inhibition.

8. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Growth cycle for batch cultivation
Factors affecting the specific growth rate
Other Conditions:
The specific growth rate (µ) of microorganisms is also affected by;
Medium pH
Temperature
Oxygen supply
The optimum pH and temperature differ from one microorganism to another.

9. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Stirred-tank Fermenter
Fermenter = bioreactor employing living cells
Enzyme bioreactor = bioreactor which employ enzymes.
In laboratories, cell are usually cultivated in Erlenmeyer flasks on a shaker. The gentle shaking in a shake flask is very effective to suspend the cells, to enhance the oxygenation through the liquid surface, and also to aid the mass transfer of nutrients without damaging the structure of cells.

10. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Stirred-tank Fermenter
For a large-scale operation, the stirred-tank fermenter (STF) is the most widely used in industrial fermentation.
It can be employed for both aerobic or anaerobic fermentation of a wide range of cells including microbial, animal, and plant cells.
The mechanical agitation and aeration are effective for suspension of cells, oxygenation, mixing of medium, and heat transfer.
The STF can be also used for high viscosity media.
Since STF is usually built with stainless steel and operated in mild operating conditions, the life expectancy of the fermenter is also long.
Disadvantage of the STF, is that the agitator consumes a large amount of power and can damage a shear-sensitive cell system .

11. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Stirred-tank Fermenter
Certai.

13. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Plug-Flow Fermenter v v

14. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Stirred-tank or Plug-Flow Fermenter
An ideal stirred fermenter is assumed to be well mixed so that the contents are uniform in composition at all times.
Another ideal fermenter is the plug-flow fermenter, the analysis of which is analogous to the ideal batch fermenter.

15. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Batch Stirred-tank Fermenter
Batch or Plug-flow fermenter
The growth rate of the cell in a batch fermenter is;
To derive the performance equation of a batch fermentation, we need to integrate Eq.1 to get;
From Eq.2, the batch growth time t- to is the area under the 1/rx versus Cx curve between Cxo and Cx as shown in Fig.

16. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Batch Stirred-tank Fermenter
Batch or Plug-flow fermenter
Substitute Monod kinetics in the above Eq. to obtain;
The amount of cell mass produced is proportional to the amount of a limiting substrate consumed. The growth yield (Yx/s) is defined as;
Substitute Eq, into Eq. and integration of the resulting equation gives a relationship which shows how the cell concentration change with respect to time:

17. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Batch Stirred-tank Fermenter
Batch or Plug-flow fermenter
Certai.

18. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Batch Stirred-tank Fermenter
Batch or Plug-flow fermenter
We can calculate the change of Cx and Cs with respect to time by solving the following equations;

19. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Batch Stirred-tank Fermenter

20. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Stirred-tank Fermenter
Ideal Continuous Stirred- tank Fermenter
Fig below shows a continuous stirred-tank fermenter (CSTR).
Continuous culture system can be operated as chemostat or as turbidostat.
Chemostat the flow rate is set at a particular value and the rate of growth of the culture adjusts to this flow rate.
Turbidostat the turbidity is set at a constant level by adjusting the flow rate.
It is easier to operate chemostat than turbidostat, because the chemostat can be done by setting the pump at a constant flow rate, while the turbidostat requires an optical sensing device and controller.

21. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Stirred-tank Fermenter
Ideal Continuous Stirred- tank Fermenter
Material balance;
For microorganisms in a CSTR
At steady state
The shorter residence time in reaching a certain cell concentration, the more effective the fermenter.
If the input stream sterile (Cxi=0), and the cells in a CSTR are growing exponentially (rx=miu Cx), Eq. becomes steady state

22. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Stirred-tank Fermenter
Ideal Continuous Stirred- tank Fermenter
Material balance; For microorganisms in a CSTR
If the input stream sterile (Cxi=0), and the cells in a CSTR are growing exponentially (rx=miu Cx), the above Eq. becomes steady state

23. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Ideal Continuous Stirred- tank Fermenter
Material balance;
For microorganisms in a CSTR
Eqn is valid only if Ʈmµm >>1.
If the growth rate yield (Yx/s) is constant, then
Material balances for the substrate and product concentration can also be obtained in the same way.

24. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Ideal Continuous Stirred- tank Fermenter
Evaluation of Monod Kinetic Parameters
By rearranging Eq. 6.30, a linear relationship can be obtained as follows;
Eq. 6.30, can be rearranged to give the following equations, instead of Eq.(6.35) for better estimation of the parameters in certain cases.
To prevent washout of the cells, the cell concentration should be maintained so that it will be >0. Which means µ > D=F/V. The range of the flow rate to prevent washout of the cells must be controlled to do that. 24

25. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Ideal Continuous Stirred- tank Fermenter
Evaluation of Monod Kinetic Parameters
Example: A chemostat study was performed with yeast. The medium flow rate was varied and the steady-state concentration of cells and glucose in the fermenter were measured and recorded. The inlet concentration of glucose was set at 100 g/ l. The volume of the fermenter contents was 500 ml. The inlet stream was sterile.
a. Find the rate equation for cell growth.
b. What should be the range of the flow rate to prevent washout of the cells? 25

26. Bioreactors Engineering Cell Kinetics and Fermenter Design
Ideal Continuous Stirred- tank Fermenter
Evaluation of Monod Kinetic Parameters
The rate equation of cell growth is,
b. To prevent washout of the cells, the cell concentration should be maintained so that it will be >0. Which means µ > D=F/V. The range of the flow rate to prevent washout of the cells must be controlled to do that. 26

27. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Alternative fermentors

28. Bioreactors Engineering
Cell Kinetics and Fermenter Design
Alternative fermentors