9.4.6 CSTR Bioreactor Operation

In this section we return to the mass balance equations on the cells [Equation (9-75)] and substrate [Equation (9-76)] and consider the case where the volumetric flow rates in and out are the same and that no live (i.e., viable) cells enter the chemostat. We next define a parameter common to bioreactors called the dilution rate, D. The dilution rate is

and is simply the reciprocal of the space time τ. Dividing Equations (9-75) and (9-76) by V and using the definition of the dilution rate, we have

9-82

9-83

Using the Monod equation, the growth rate is determined to be

9-53

For steady-state operation we have

9-84

and

9-85

We now neglect the death rate, r_d, and combine Equations (9-51) and (9-84) for steady-state operation to obtain the mass flow rate of cells out of the system, .

9-86

After we divide by C_cV,

9-87

An inspection of Equation (9-87) reveals that the specific growth rate of the cells can be controlled by the operator by controlling the dilution rate D. Using Equation (9-52)

9-52

to substitute for μ in terms of the substrate concentration and then solving for the steady-state substrate concentration yields

9-88

Assuming that a single nutrient is limiting, cell growth is the only process contributing to substrate utilization, and that cell maintenance can be neglected, the stoichiometry is

9-89

9-68

Substituting for C_s using Equation (7-87) and rearranging, we obtain

9-90