A simple distillation column is designed to separate an ideal binary mixture to specified distillate and bottoms purities at a given column pressure. If RR$_{\min}$ is the minimum reflux ratio for this separation, select the statement that is NOT CORRECT with regard to the variation in the total annualized cost (TAC) of the column with reflux ratio (RR).
A simple distillation column is designed to separate an ideal binary mixture to specified distillate and bottoms purities at a given column pressure. If RR$_{\min}$ is the minimum reflux ratio for this separation, select the statement that is NOT CORRECT with regard to the variation in the total annualized cost (TAC) of the column with reflux ratio (RR).
Show Hint
- TAC has a minimum with respect to RR
- The sharpest rise in TAC occurs as RR approaches RR$_{\min}$ from above
- The sharpest decrease in TAC occurs as RR approaches RR$_{\min}$ from above
- TAC increases with RR for RR >> RR$_{\min}$
The Correct Option is C
Solution and Explanation
In the design of a distillation column, the reflux ratio (RR) strongly influences both capital cost and operating cost, which together determine the total annualized cost (TAC). As RR increases, the vapor and liquid traffic inside the column increases, leading to larger column diameter and higher energy usage in the reboiler and condenser. Thus, extremely high RR values increase TAC due to higher operating costs. Conversely, when RR approaches RR$_{\min}$, the number of theoretical stages increases sharply, causing a steep rise in the capital cost of the column.
Step 1: Behaviour near RR$_{\min}$
As RR → RR$_{\min}$ from above, the number of stages approaches infinity. This drastically increases column height and capital cost. Therefore, TAC increases sharply near RR$_{\min}$. Hence, option (B) is correct.
Step 2: TAC at intermediate RR
Between RR$_{\min}$ and very high RR, there exists an optimum RR at which TAC is minimized. Option (A) correctly states that TAC has a minimum.
Step 3: TAC at high RR
For RR >> RR$_{\min}$, the column requires a large boil-up rate, increasing utility consumption. This makes TAC rise again, so (D) is correct.
Step 4: Identifying the NOT CORRECT statement
Option (C) states that the "sharpest decrease in TAC occurs as RR approaches RR$_{\min}$ from above," which is incorrect because TAC increases sharply in that region, not decreases. Therefore, (C) is the NOT CORRECT option.
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