Discussion on Question 6 of the 2011 Case Analysis

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6. A distillation column is used to separate a binary mixture A and B; the top of this column is equipped with a fractional condenser and a total condenser. The liquid from the fractional condenser is used as reflux for the column, while the gas phase is condensed in the total condenser as the product. It is known that the feed is in a saturated state, with a feed rate of 100 kmol/h; the concentration of the light component A is 0.5 (mole fraction, the same hereafter). The operating reflux ratio is 2.0. It is required that the concentration of component A in the top product be 0.95, and the concentration of component B in the bottom product be 0.94. The latent heat of condensation for the vapor at the tower top is 21,800 kJ/kmol, while the latent heat of vaporization for the liquid at the tower bottom is 21,900 kJ/kmol. What are the values of the heat load on the fractional distiller (kJ/h) and the heat load on the reboiler (kJ/h)? (A) 2.16×106, 3.25×106 (B) 2.23×106, 3.25×106 (C) 2.16×106, 2.25×106 (D) 3.23×106, 4.25×106
Solution: xW = 1 – 0.94 = 0.06
D/F = (xF – xW) / (xD – xW) = (0.5 – 0.06) / (0.95 – 0.06) = 0.4944
D = 0.4944 × F = 0.4944 × 100 = 49.44
L = RD = 2 × 49.44 = 98.88
Q1 = rDL = 21800 × 98.88 = 2.16×106 (kJ/h)
q = 1 – V’ = (R + 1)D – (1 – q)F = (2 + 1) × 49.44 – 0 = 148.3
Q’ = rWV’ = 21900 × 148.3 = 3.25×106 (kJ/h)
How should this problem be solved if it is asking for the load on the entire condenser?