Multi-effect Evaporators: Example Problem

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Example Problem 1

A 5.0 wt% sugar solution at 110°C and 2.0 bar is fed to a double-effect evaporator. The first effect operates at 1.0-bar pressure and concentrates the sugar to 8.0 wt%. It is heated by saturated steam at 140°C; the condensate leaves evaporator 1 as saturated liquid. The second effect operates at 0.12-bar pressure. The overall heat transfer coefficient is 2.0 kJ/(m2 s K) for the first effect and 1.6 kJ/(m2 s K) for the second effect. The heat transfer area is 56 m2 in each effect. The results of mass and energy balances on the first evaporator: the feed rate of 5.0 wt% sugar solution is 5.61 kg/s, the steam feed rate is 2.10 kg/s, the rate that water is evaporated is 2.11 kg/s, and the 8.0 wt% stream flow rate is 3.51 kg/s.
What is the sugar concentration leaving the second effect? What is the steam economy for the system (kg water evaporated per kg of steam condensed)?