Q.64 An industrial fermentor containing 10,000 L of medium needs to be sterilized.
The initial spore concentration in the medium is 10⁶ spores mL⁻¹.
The desired probability of contamination after sterilization is 10⁻³.
The death rate of spores at 121 °C is 4 min⁻¹.
Assume that there is no cell death during heating and cooling phases.
The holding time of the sterilization process is ________ min (rounded off to the nearest integer).

Sterilization holding time in fermentors follows first-order spore death kinetics, where the goal is to reduce contamination probability to a specified low level like 10^-3. This GATE-style problem requires calculating the holding time at 121°C based on initial spore load, volume, death rate constant, and target survival probability, ignoring heating/cooling effects.

Problem Breakdown

The fermentor holds 10,000 L (10⁷ mL) of medium with initial spore concentration N₀ = 10⁶ spores mL^-1, yielding total initial spores N_0,total = 10⁷ mL × 10⁶ spores mL^-1 = 10¹³ spores.

The desired probability of contamination P = 10^-3 means the expected surviving spores should be 0.001 for that risk level. With first-order kinetics, spore survival follows N = N₀ e^-kt, where k = 4 min^-1 is the death rate constant at 121°C.

Step-by-Step Calculation

Target surviving spores N_t = P × N_0,total = 10^-3 × 10¹³ = 10¹⁰ spores.

Apply the survival equation: N_t / N_0,total = e^-kt, so ln(N_t / N_0,total) = -kt.

Here, N_t / N_0,total = 10¹⁰ / 10¹³ = 10^-3, so ln(10^-3) = -6.907 = -kt.

Thus, t = 6.907 / k = 6.907 / 4 ≈ 1.727 min.

This seems low; recheck total spores—yes, 10,000 L = 10⁷ mL confirms 10¹³ total. But probability interpretation targets expected survivors = P = 10^-3, so N_t = 10^-3. Then ln(10^-3/10¹³) = ln(10^-16) ≈ -36.84 = -kt, t = 36.84 / 4 ≈ 9.21 min, rounds to 9 min.

Final Holding Time

The holding time is 9 min (nearest integer). This matches standard solutions for similar GATE BT 2019 problems, ensuring <0.1% contamination risk.

Industrial fermentor sterilization ensures aseptic conditions for biotechnology processes by killing spores via moist heat at 121°C. This fermentor sterilization holding time calculation addresses an industrial 10,000 L fermentor with 10⁶ spores mL^-1 initial concentration, targeting 10^-3 contamination probability using a 4 min^-1 spore death rate, assuming no death in heating/cooling.

Core Kinetics

First-order death kinetics govern spore inactivation: N = N₀ e^-kt, where k = 4 min^-1. Total initial spores: 10,000 L = 10⁷ mL × 10⁶ spores mL^-1 = 10¹³.

Probability Design

Target: Probability of ≥1 survivor ≈ expected survivors = 10^-3 (Poisson approximation for rare events). Thus, N_t = 10^-3.

Derivation

ln(N_t / N₀) = -kt → ln(10^-3 / 10¹³) = ln(10^-16) = -36.841 = -4t → t = 9.21 min ≈ 9 min.

This fermentor sterilization holding time calculation prevents contamination in bioprocesses like antibiotic production, aligning with GATE Biotechnology standards.