4. Circulation of a working fluid. The most common example of this application is the refrigeration cycle used in household refrigerators and air conditioners. In these devices, a single material is reused indefinitely, with only small makeup quantities being added to the system to replenish working fluid that may be lost through leaks.
Part 1 of the next example presents a detailed material balance calculation for a separation process that involves recycle. Part 2 of the problem shows what would happen if the recycle were omitted and, in doing so, illustrates one of the reasons for recycling.
An Evaporative Crystallization Process
The flowchart of a steady-state process to recover crystalline potassium chromate ($K_2CrO_4$) from an aqueous solution of this salt is shown below.
4500 kg/h
33.3% $K_2CrO_4$
EVAPORATOR
49.4% $K_2CrO_4$
Filtrate
36.4% $K_2CrO_4$ solution
Filter cake
CRYSTALLIZER $K_2CrO_4$ (solid crystals)
AND FILTER 36.4% $K_2CrO_4$ solution
(the crystals constitute
95% by mass of the
filter cake)
4.5 Recycle and Bypass 113
Forty-five hundred kilograms per hour of a solution that is one-third $K_2CrO_4$ by mass is joined by a recycle stream containing 36.4% $K_2CrO_4$, and the combined stream is fed into an evaporator.
The concentrated stream leaving the evaporator contains 49.4% $K_2CrO_4$; this stream is fed into a crystallizer in which it is cooled (causing crystals of $K_2CrO_4$ to come out of solution) and then filtered. The filter cake consists of $K_2CrO_4$ crystals and a solution that contains 36.4% $K_2CrO_4$ by mass; the crystals account for 95% of the total mass of the filter cake. The solution that passes through the filter, also 36.4% $K_2CrO_4$, is the recycle stream.
1. Calculate the rate of evaporation, the rate of production of crystalline $K_2CrO_4$, the feed rates that the evaporator and the crystallizer must be designed to handle, and the recycle ratio (mass of recycle)/(mass of fresh feed).
2. Suppose that the filtrate were discarded instead of being recycled. Calculate the production rate of crystals. What are the benefits and costs of the recycling?
