79. Doubling the substrate concentration in the inlet of a CSTR (with cells following Monodgrowth
kinetics) will, after reaching the new steady state, lead to:
(a) Higher biomass concentration but unchanged substrate concentration in the outlet
(b) Higher substrate & biomass concentration in the outlet
(c) Higher substrate concentration but unchanged biomass concentration in the outlet
(d) Unchanged substrate & biomass concentration in the outlet

Correct Answer:

(b) Higher substrate & biomass concentration in the outlet

Explanation:

In a Continuous Stirred Tank Reactor (CSTR) with cells following Monod growth kinetics, the relationship between substrate concentration and biomass concentration is crucial in understanding how the system behaves under changes to the substrate input.

Monod Growth Kinetics:

Monod growth kinetics is commonly used to describe the growth of microbial cells in response to the concentration of a limiting substrate. It is defined as:

μ(S)=μmaxSKs+S\mu(S) = \frac{\mu_{\text{max}} S}{K_s + S}μ(S)=Ks​+Sμmax​S​

Where:

• $\mu (S)$ is the specific growth rate of the microorganisms.

• μmax\mu_{\text{max}}μmax​ is the maximum specific growth rate.

• $S$ is the substrate concentration.

• KsK_sKs​ is the half-saturation constant, the substrate concentration at which the growth rate is half of μmax\mu_{\text{max}}μmax​.

According to Monod kinetics:

• As substrate concentration increases, the growth rate of the microorganism increases, but it begins to approach a maximum rate (μmax\mu_{\text{max}}μmax​) when the substrate concentration is much higher than KsK_sKs​.

Impact of Doubling the Substrate Concentration:

When the substrate concentration in the inlet of the CSTR is doubled, several changes occur:

1. Substrate Concentration:

   • As the substrate concentration is increased, the substrate concentration in the outlet will also increase, but it will still be less than the inlet concentration due to the consumption of substrate by the microorganisms.

   • The outlet concentration will be higher than the original steady state, but not as high as the inlet concentration.

2. Biomass Concentration:

   • With the increase in substrate, the growth rate of the microorganisms will increase, leading to a higher biomass concentration in the reactor.

   • This occurs because more substrate allows more microbial cells to grow, as long as the substrate is not saturating the system (i.e., the substrate is not at excessively high levels compared to the half-saturation constant).

Why the Other Options are Incorrect:

• (a) Higher biomass concentration but unchanged substrate concentration in the outlet:
  This is incorrect because while the biomass concentration will indeed increase, the substrate concentration in the outlet will also increase, not stay the same, because more substrate is being provided to the reactor.

• (c) Higher substrate concentration but unchanged biomass concentration in the outlet:
  This is incorrect because while the substrate concentration in the outlet will increase, the biomass concentration will also increase due to the higher growth rate stimulated by the increased substrate concentration.

• (d) Unchanged substrate & biomass concentration in the outlet:
  This is incorrect because doubling the substrate concentration will affect both the substrate and biomass concentrations in the outlet. The system will reach a new steady state with higher concentrations for both.

Conclusion:

When the substrate concentration is doubled in the inlet of a CSTR operating with Monod growth kinetics, the system will reach a new steady state with higher substrate and biomass concentrations in the outlet. Therefore, the correct answer is (b) Higher substrate & biomass concentration in the outlet.