Chemostat Performance — If biomass yield is constant over the operating range, how does biomass productivity vary with dilution rate D (before washout)?
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AIt always decreases monotonically as D increases.
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BIt increases with D up to a maximum just below washout (then collapses at washout).
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CIt remains constant and does not depend on D at all.
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DIt decreases with D until washout in every case, without any increase.
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EIt is independent of yield and only a function of reactor volume.
Answer
Correct Answer: It increases with D up to a maximum just below washout (then collapses at washout).
Explanation
Introduction:Biomass productivity in a chemostat is the product of dilution rate and biomass concentration (PX = D * X). Understanding how PX depends on D under constant yield assumptions is central to selecting an operating point that maximizes throughput without risking washout.
Given Data / Assumptions:
- Single limiting substrate; yield Yx/s is approximately constant.
- Monod kinetics with μ = μm * S / (Ks + S).
- Steady state below washout: μ = D < μm.
Concept / Approach:
As D increases from low values, μ increases and substrate concentration rises, but biomass concentration X tends to decrease. The product D * X typically exhibits a maximum at a D near, but safely below, the washout point D ≈ μm. This is analogous to classical continuous-flow reactor optimization for growth-associated production.
Step-by-Step Solution:
Use steady-state: μ = D.Substrate balance with constant yield gives X = Yx/s * (Sf − S).As D increases, S rises and X falls, but D increases linearly.Compute PX = D * X; differentiate with respect to D to find an interior maximum below μm.Verification / Alternative check:
Plotting PX versus D using typical μm, Ks, Sf, and Yx/s shows a dome-shaped curve peaking below washout, confirming the expected trend.
Why Other Options Are Wrong:
A and D: Ignore the initial rise in PX with D. C: Contradicts dependence of X on D. E: Yield and kinetics are essential determinants, not just volume.
Common Pitfalls:
Operating too close to washout risks instability; choose D with safety margin to account for disturbances and parameter uncertainty.
Final Answer:
It increases with D up to a maximum just below washout (then collapses at washout).