P. Substrate concentration inside the chemostat is equal to that in the exit stream
Q. Optimal dilution rate is lower than critical dilution rate
R. Biomass concentration increases with increase in dilution rate
S. Cell recirculation facilitates operation beyond critical dilution rate
Ideal Chemostat Analysis
This solution analyzes the provided statements regarding the operation of an ideal chemostat.
Statement P Analysis
Statement P: Substrate concentration inside the chemostat is equal to that in the exit stream.
In an ideal chemostat operating at steady state, continuous inflow and outflow with perfect mixing ensure that the concentration of all components, including substrate, is uniform throughout the reactor and identical in the exit stream. Therefore, statement P is correct.
Statement Q Analysis
Statement Q: Optimal dilution rate is lower than critical dilution rate.
The critical dilution rate ($D_c$) is the maximum dilution rate at which the biomass can maintain steady state without washout. The optimal dilution rate is typically chosen based on specific objectives like maximizing productivity ($D \times X$) or yield. These optimal rates are generally maintained below $D_c$ to ensure stable operation and prevent washout. Therefore, statement Q is correct.
Statement R Analysis
Statement R: Biomass concentration increases with increase in dilution rate.
In an ideal chemostat, the steady-state biomass concentration ($X$) is related to the substrate consumed. Using the Monod model, $X = Y_{X/S} (S_f - S)$, where $S = \frac{K_m D}{\mu_{max} - D}$. As the dilution rate ($D$) increases towards the maximum specific growth rate ($\mu_{max}$), the residual substrate concentration ($S$) decreases. This leads to a decrease, not an increase, in biomass concentration ($X$) in this range. Therefore, statement R is incorrect.
Statement S Analysis
Statement S: Cell recirculation facilitates operation beyond critical dilution rate.
Cell recirculation, often achieved using filtration or centrifugation, retains cells within the reactor. This increases the effective cell residence time, allowing the chemostat to sustain a culture at dilution rates ($D$) higher than the critical dilution rate ($D_c$) without washout, as the cells are prevented from exiting the system. Therefore, statement S is correct.
Conclusion
Based on the analysis, statements P, Q, and S are always correct for an ideal chemostat.
Important Questions from Batch Fed Batch and Continuous Processes
- Under complete cell washout condition in a chemostat with sterile feed, which of the following statements is/are correct?
A fed batch process is running at quasi-steady state with respect to substrate and biomass concentration. At $2 \text{ h}$, the culture volume is $500 \text{ L}$ with a constant sterile inlet feed at $50 \text{ L } h^{-1}$ of glucose. The culture kinetic parameters $ \mu_m$ and $K_s$ are $0.2 \text{ } h^{-1}$ and $0.1 \text{ } g \text{ } L^{-1}$, respectively.
The substrate concentration in the reactor will be ________ $g \text{ } L^{-1}$ (rounded off to one decimal place).
The following schematic diagram shows a chemostat with cell recycle
where $F_0$ and $F_r$ are the volumetric flow rates (in $L.h^{-1}$) of feed and recycle streams, respectively. $X_1$, $X_0$ and $X$ are the cell concentrations (in $g.L^{-1}$) in the reactor, recycle-stream and product-stream, respectively. If $\frac{X_0}{X_1}=1.5$, $\frac{F_r}{F_0}=0.7$ and $X_1$ is $7.3 g.L^{-1}$, the value of $X$ (in $g.L^{-1}$, rounded off to one decimal place) is ________
A $2 \text{ L}$ bioreactor is being operated as a chemostat, at a flow rate of $0.8 \text{ L/h}$ and sterile feed of $10 \text{ g/L}$ substrate. The bacterial growth follows Monod kinetics at a maximum specific growth rate of $0.6 \text{ h}^{-1}$ with a Monod constant of $0.5 \text{ g/L}$ and a biomass yield coefficient of $0.4 \text{ g/g}$. The exit biomass concentration is __________ $\text{g/L}$.
(Round off to one decimal place)
- The amount of biomass in a reactor at the end of the batch process is 50 g. Fed- batch operation is initiated by feeding the substrate solution at a constant rate of $1 \text{ L h}^{-1}$. The concentration of substrate in the feed is $50 \text{ g L}^{-1}$. The maximum biomass yield ($Y_{XS}^M$) is $0.4 \frac{\text{g biomass}}{\text{g substrate}}$. Assuming the system is at quasi-steady state, the maximum amount of biomass after 5 h of feeding is ________________ g.
