# DBT JRF 2022 — Question 93

Exam: DBT JRF 2022 · Section: B · Topic: Bioprocess Engineering › Fed-Batch Reactor & Growth Kinetics · Difficulty: Medium

## Question

A concentrated feed of substrate is added at a constant rate in a fed-batch reactor. If all the substrate is utilized, the specific growth rate (μ) pattern will be:

## Options

- **A.** Exponential growth with constant μ
- **B.** Exponential growth with increasing μ
- **C.** Growth with decreasing μ
- **D.** Growth with fluctuating μ

## Answer

Option C

## Explanation

Specific growth rate (μ) in fed-batch culture with constant feed rate: In a fed-batch fermentation with a CONSTANT feed rate F into a vessel of increasing volume V: $F = \text{constant}$ , but $V$ increases over time as feed is added. The dilution rate: $D = \frac{F}{V(t)}$ As V increases over time (while F stays constant), D DECREASES over time. At steady state in fed-batch: $\mu \approx D = \frac{F}{V(t)}$ As the fermentation progresses: • Volume V increases → dilution rate D decreases → specific growth rate $\mu$ DECREASES over time. • The culture is NOT at steady state — it slows progressively. Answer: In fed-batch with constant feed rate, $\mu$ (specific growth rate) decreases over time as culture volume increases.

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