A continuously operated 1000 liter CSTR is used for production of biomass from glucose provided by
the feed (feed rate of 100l/h and glucose concentration of 10 g/l). The bacteria show Monod type
growth with a maximal specific growth rate of 0.4/h and an affinity towards glucose of 1.5 g/l. The
biomass yield per substrate consumed is 0.5.
a) What is the specific and absolute production rate of biomass at steady-state condition?
b) At which critical dilution rate is wash out expected?
c) Now a biomass recycling system is included into the setup producing a five times higher cell
concentration than at the reactor outlet. What’s the impact on the specific biomass
production rate?
To answer these questions, we need to understand the relationship between growth rate, substrate concentration, and biomass production in a continuously operated CSTR.
a) Specific production rate of biomass at steady-state condition:
The specific production rate of biomass (μ) is given by the Monod equation:
μ = μ_max * (S / (Ks + S))
Where:
- μ_max is the maximal specific growth rate (0.4/h in this case)
- S is the substrate concentration (glucose concentration in this case)
- Ks is the affinity constant for glucose (1.5 g/l in this case)
Given the substrate concentration (S) = 10 g/l, we can calculate the specific production rate of biomass (μ).
μ = 0.4 * (10 / (1.5 + 10))
μ = 0.4 * (10 / 11.5)
μ ≈ 0.3478 g biomass/g cells/h
The specific production rate of biomass is approximately 0.3478 g biomass/g cells/h.
To calculate the absolute production rate of biomass (P), we multiply the specific production rate by the feed rate (F).
P = μ * F
P = 0.3478 * 100
P = 34.78 g biomass/h
The absolute production rate of biomass is 34.78 g biomass/h.
b) Critical dilution rate for wash out:
Washout occurs when the dilution rate (D) exceeds the specific growth rate (μ).
In this case, the maximal specific growth rate (μ_max) is given as 0.4/h.
Therefore, the critical dilution rate for washout is 0.4/h.
c) Impact of biomass recycling on specific production rate:
When a biomass recycling system is introduced, producing a five times higher cell concentration, it means the biomass concentration in the reactor will be higher.
Since the specific production rate of biomass (μ) depends on the biomass concentration, an increase in biomass concentration will result in an increase in the specific production rate of biomass.
Therefore, the specific biomass production rate will be higher when a biomass recycling system is included in the setup.