180. In a plug flow bioreactor running at steady state, 12.5% cells are recycled back to the inlet. If the cells grow
at μmax=1 h-1 throughout the length of the reactor (L=124 cm), then the flow velocity should be
1. 0.5 cm/min
2. 1cm/min
3. 1.5 cm/min
4. 2cm/min
Introduction: Understanding the flow velocity in a plug flow bioreactor is essential for optimizing the conditions for cell growth, especially in processes where cell recycling is involved. This article explains how to calculate the flow velocity for a bioreactor running at steady state with cell recycling.
Step-by-Step Calculation of Flow Velocity:
Problem Overview: You are given the following parameters for a plug flow bioreactor:
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Cell recycling: 12.5% of cells are recycled back to the inlet.
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Maximum growth rate (μmax): 1 h^-1.
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Reactor length (L): 124 cm.
The goal is to calculate the flow velocity (v) that ensures steady-state conditions while accounting for the cell recycling factor.
Key Concept:
In a plug flow bioreactor, cells are subject to a growth process described by the Michaelis-Menten kinetics or Monod kinetics, but for simplicity, we are assuming exponential growth here. Given the recycling rate, the effective growth rate is influenced by both the cell’s growth rate and the recycling process.
Formula for Flow Velocity:
The flow velocity in a plug flow bioreactor is determined by the rate at which cells grow and the reactor length. In this case, the growth rate of cells is given as μmax, and the recycling rate (12.5%) will influence the flow velocity.
Effective Growth Rate Calculation: The effective growth rate, accounting for the recycling of 12.5% of the cells, will affect the steady-state biomass concentration within the reactor.
The effective growth rate, considering the cell recycling, is given by:
μeff=μmax×(1+Recycling Fraction)\mu_{\text{eff}} = \mu_{\text{max}} \times (1 + \text{Recycling Fraction})
For recycling of 12.5%, the effective growth rate is:
μeff=1 h−1×(1+0.125)=1.125 h−1\mu_{\text{eff}} = 1 \, \text{h}^{-1} \times (1 + 0.125) = 1.125 \, \text{h}^{-1}
Flow Velocity:
The flow velocity (v) is determined using the relationship between the reactor length (L) and the growth rate:
v=μeffLv = \frac{\mu_{\text{eff}}}{L}
Plugging in the values:
v=1.125 h−1124 cm=0.0091 cm/minv = \frac{1.125 \, \text{h}^{-1}}{124 \, \text{cm}} = 0.0091 \, \text{cm/min}
Thus, the calculated flow velocity is approximately 0.0091 cm/min.
Conclusion:
Given the assumptions in this example, the flow velocity based on the described parameters seems very low. However, for practical applications, you would need to adjust these parameters to align with the expected flow rates for industrial-scale bioreactors. Given the provided options, it appears that the ideal flow velocity might vary depending on further context or constraints not fully described in this simplified calculation.
