# 3. Elaboration Question 2

Course subject(s) 3. Biological treatment

### Question 2: Impact of temperature on microbial growth

Temperature is one of the key factors that influence microbial growth. Given that the average summer temperature is 20°C and the average winter temperature is 7°C, draw a graph representing the average heterotrophic bacteria growth rate for summer and winter using the information given below.

The Monod equation for bacterial growth is defined as :

$$\dfrac{dX}{dt}=\mu\cdot X\text{ with }\mu = \mu_{max}\dfrac{s}{(K_{s}+s)}$$

With:

• X = Biomass concentration
• S = Substrate concentration
• Ks = Monod coefficient (substrate affinity)
• μ = Growth rate
• μmax = temperature dependent and the relationship represented in the equation below:
• $$\mu_{max,T}=\mu_{max,20}\theta^{(T-20)}$$

The different parameters are given in the table below.

ParameterValueUnits
$$K_{s}$$ 5 g BOD/m3
At 20 °C: $$\mu_{max}$$ 6 g VSS/g Vss.d
At 20 °C: $$\theta$$ for calculating: $$\mu_{max,T}$$ 1.07 -