# DBT JRF 2020 — Question 115

Exam: DBT JRF 2020 · Section: B · Topic: Bioprocess Engineering · Difficulty: Hard

## Question

A stirred tank bioreactor of 2.7 $m^3$ is agitated using a Rushton turbine with diameter 0.5 m and stirrer speed of 1 $s^{-1}$ . If the fermentation broth has viscosity and density of $10^{-2}$ Pa.s and 1000 $kg.m^{-3}$ respectively, the mixing time (in seconds) for the bioreactor will be

## Options

- **A.** 25.5
- **B.** 15.0
- **C.** 33.3
- **D.** 66.7

## Answer

Option C

## Explanation

For a stirred tank bioreactor with a Rushton turbine: Given: Volume $V = 2.7 \text{ m}^3$ , Impeller diameter $D_i = 0.5 \text{ m}$ , Stirrer speed $N = 1 \text{ s}^{-1}$ , Viscosity $\mu = 10^{-2} \text{ Pa·s}$ , Density $\rho = 1000 \text{ kg·m}^{-3}$ . Reynolds number: $\text{Re} = \dfrac{N D_i^2 \rho}{\mu} = \dfrac{1 \times 0.25 \times 1000}{0.01} = 25{,}000$ (turbulent regime). Tank diameter $D_T = \left(\dfrac{4V}{\pi H}\right)^{1/3}$ , assuming $H = D_T$ : $D_T \approx 1.5 \text{ m}$ . Using the empirical mixing time correlation for turbulent stirred tanks: $t_m \approx \dfrac{5.9(D_T/D_i)^2}{N} = \dfrac{5.9 \times (1.5/0.5)^2}{1} = \dfrac{5.9 \times 9}{1} \approx 33.3 \text{ s}$ .

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