During sterilization of a fermentation medium in a given bioreactor,
Vheating = 12.56,
Vcooling = 7.48 and the total value of
V required for the whole sterilization process is
52, where V is the design criteria.
Q.55 What is the holding period (min) at a
k value of 3.36 min-1?
- (A) 10.6
- (B) 9.5
- (C) 8.4
- (D) 7.2
Fermentation Medium Sterilization: Holding Period Calculation at k=3.36 min-1
Step-by-Step Calculation
The design criterion ∇ represents the sterilization value, where total ∇ = ∇heating + ∇holding + ∇cooling. Given ∇heating = 12.56, ∇cooling = 7.48, and total ∇ = 52, solve for ∇holding.
∇holding = 52 – 12.56 – 7.48 = 31.96
Holding time t relates to ∇holding by t = ∇holding / k. With k = 3.36 min-1, t = 31.96 / 3.36 ≈ 9.51 minutes, which rounds to 9.5 minutes.
This matches option (B) as the standard answer in bioprocess engineering references.
Options Analysis
| Option | Value (min) | Explanation |
|---|---|---|
| (A) | 10.6 | Overestimates by using incorrect ∇holding ≈ 35.6 (e.g., total ∇ misread as 55). 35.6 / 3.36 ≈ 10.6; incorrect subtraction. |
| (B) | 9.5 | Correct: ∇holding = 31.96, t = 31.96 / 3.36 = 9.51 ≈ 9.5 min. |
| (C) | 8.4 | Underestimates with ∇holding ≈ 28.2 (e.g., subtracting extra losses). 28.2 / 3.36 ≈ 8.4; wrong ∇holding. |
| (D) | 7.2 | Lowest error, perhaps ∇holding = 24.2 and k misread as 3.36 as 3.0. Incorrect inputs. |
Bioreactor Sterilization Context
In microbial fermentation, sterilization follows first-order kinetics where k is the specific death rate constant at holding temperature (typically 121°C). Heating and cooling phases contribute partial ∇ due to varying temperatures, but holding at peak temperature dominates lethality.
∇ integrates the lethal effect: ∇ = ∫ k dt over time. For constant k in holding, it simplifies to k × t. This ensures <10-6 contaminant probability for safe media prep in biotech processes.
