Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
Under complete cell washout condition in a chemostat with sterile feed, which of
the following statements is/are correct?
Options:
(A) Biomass concentration in the reactor is maximum
(B) Substrate concentration in the exit stream is less than that in the inlet stream
(C) Substrate concentration in the exit stream is equal to that in the inlet stream
(D) Substrate concentration in the exit stream is zero
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2024 Q.53)**
**1. Governing Concept**:
- **Topic**: Continuous Bioreactor Operation & Chemostat Washout Criterion
- In a continuous stirred tank bioreactor (chemostat) operated with sterile feed ($X_0 = 0$):
- Biomass balance: $\frac{dX}{dt} = (\mu - D) X$.
- At steady state: $\mu = D$.
- As dilution rate $D$ is increased, residual substrate concentration $S$ increases according to Monod kinetics ($S = \frac{K_s D}{\mu_{\max} - D}$).
- When $D \ge D_{\text{crit}} = \frac{\mu_{\max} S_0}{K_s + S_0} \approx \mu_{\max}$, **washout** occurs: cells are removed faster than they can divide ($dX/dt < 0 \implies X \to 0$).
- At complete washout ($X = 0$), substrate is unconsumed, so the exit substrate concentration reaches its maximum possible value, equal to the inlet feed concentration:
$S_{\text{exit}} = S_{\text{in}} = S_0$
**2. Option Analysis**:
- **Option (A) [Exit substrate concentration is zero] is INCORRECT**: At washout, no biomass exists to consume substrate; $S$ reaches its maximum, not zero.
- **Option (B) [Exit biomass concentration is at its maximum] is INCORRECT**: At washout, biomass concentration is zero ($X = 0$).
- **Option (C) [Exit substrate concentration equals inlet substrate concentration] is CORRECT**: Because zero cells remain in the vessel to consume feed substrate, steady-state effluent substrate equals inlet feed ($S = S_0$).
- **Option (D) is INCORRECT**: Dilution rate at washout is at or above critical maximum dilution rate ($D \ge \mu_{\max}$), not zero.
**3. Final Answer**:
- **Correct Option**: **C**
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