Q.47 A fed batch culture was operated with intermittent addition of
glucose solution at a flow rate of 200 ml h−1.
The values of Ks, μm and D are
0.3 g l−1, 0.4 h−1 and 0.1 h−1,
respectively. Determine the concentration of growth limiting
substrate (g l−1) in the reactor at quasi-steady state.
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Growth-Limiting Substrate Concentration in Fed-Batch Culture
Fed-batch culture is a widely used operation mode in biochemical engineering.
Under quasi-steady state conditions, the microbial growth rate equals the
dilution rate. Using Monod kinetics, the growth-limiting substrate concentration
can be calculated.
Problem Statement
A fed-batch culture was operated with intermittent addition of glucose solution
at a flow rate of 200 ml h−1.
- Ks = 0.3 g l−1
- μmax = 0.4 h−1
- D = 0.1 h−1
Determine the concentration of growth-limiting substrate (g l−1)
at quasi-steady state.
Key Concept
At quasi-steady state in a fed-batch culture:
μ = D
The Monod equation is given by:
μ = μmax × S / (Ks + S)
Step-by-Step Solution
Substituting μ = D:
0.1 = 0.4 × S / (0.3 + S)
Rearranging:
0.1(0.3 + S) = 0.4S
0.03 + 0.1S = 0.4S
0.03 = 0.3S
S = 0.1 g l−1
Correct Answer
Growth-limiting substrate concentration = 0.1 g l−1
Explanation
At substrate concentrations higher than 0.1 g l−1, the growth rate
approaches the maximum value and exceeds the dilution rate. At lower values,
the growth rate becomes insufficient to maintain steady operation.
Therefore, only a substrate concentration of 0.1 g l−1
satisfies the quasi-steady state condition.
Conclusion
Using Monod kinetics and the quasi-steady state assumption, the growth-limiting
substrate concentration in the fed-batch reactor is:
0.1 g l−1
