Effect of reflux ratio — As the reflux ratio in a distillation column is increased from its minimum value, which overall trend is correct?
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AThe slope of the stripping-section operating line decreases steadily
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BThe required number of plates decreases very slowly at first and then more and more rapidly
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CThe total annual cost first decreases (as plates fall) and then increases (as utilities rise), giving an optimum
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DLiquid flow increases while vapor flow decreases for the same separation
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EThe minimum number of plates is reached at minimum reflux
Answer
Correct Answer: The total annual cost first decreases (as plates fall) and then increases (as utilities rise), giving an optimum
Explanation
Introduction:Reflux ratio is a key design and operating variable in distillation. Moving away from minimum reflux reduces the number of equilibrium stages, but also increases internal flows and energy use. Understanding these trade-offs is crucial for selecting an economical design point.
Given Data / Assumptions:
- Constant product specifications.
- Feasible range: from minimum reflux (infinite stages) to very high reflux (near total reflux, minimal stages).
- Typical cost structure: capital linked to plate count/size; operating linked to reboiler/condenser duties.
Concept / Approach:As reflux increases from the minimum, the number of stages decreases sharply at first and then with diminishing returns. Capital cost initially falls (fewer trays/shorter column), but energy and utility costs rise due to increased internal liquid and vapor rates. The combined total annual cost therefore shows a shallow minimum at an intermediate reflux ratio.
Step-by-Step Solution:At minimum reflux: N → very large, capital high, energy low.Increase reflux slightly: N drops rapidly; capital decreases.Further increases: N decreases slowly; utilities rise significantly.Result: a cost optimum where total annual cost is minimized.
Verification / Alternative check:Gilliland correlations (or modern simulators) show diminishing returns in stage reduction at high reflux, consistent with the cost-tradeoff curve.
Why Other Options Are Wrong:
- (a) The stripping-line slope is not the primary monotonic trend with reflux; rectifying line slope increases.
- (b) Trend is opposite: decrease is rapid at first, then slower.
- (d) Both internal liquid and vapor generally increase with reflux for fixed separation.
- (e) Minimum plates occur at very high (approaching total) reflux, not at minimum reflux.
Common Pitfalls:Assuming linear trade-offs; ignoring condenser and reboiler size impacts at high reflux.
Final Answer:The total annual cost first decreases (as plates fall) and then increases (as utilities rise), giving an optimum