Question

(chemical engineering)

4500 Kg/h of a solution that is one-third K₂CrO₄ by mass is joined by a recycle stream containing 36.4% K₂CrO_4, and the combined stream is fed into an evaporator. The concentrated stream leaving the evaporator contains 49.4% K₂CrO₄; this stream is fed into a crystallizer in which it is cooled and then filtered. The filter cake consists of  K₂CrO₄ crystals and a solution that contains 36.4% K₂CrO₄ 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% K₂CrO₄ is the recycle stream.

1- Calculate the rate of evaporation

2- calculate the rate of production of crystalline K₂CrO₄

3- calculate the feed rates that the evaporator and the crystallizer must be designed to handle

4- calculate the recycle ratio (mass of recycle/mass of fresh feed)

5- Suppose that the filtrate was discarded instead of being recycled. calculate the production rate of crystals.

Answer 1

From lets do the mass balance:

For the total mass:

From the two above:

   (1)

For the K2CrO4

(2)

(3)

By substituing equiation 1 in 3 and then solving for Me you get:

(4)

and the use for to solve 1 for Mr:

Mr=5157.6 kg/h

The rate of evaporation is Mp, first using 4 you solve for Me=6628kg/h, then using 1 for Mc=1470.36kg/h and then using 0 for Mp=3029.64kg/h

1) 3029.64kg/h

2 production of crystals is 0.95*Mc=1396.84kg/h

3) the feed rate for the evaporator is Mr+4500=9657.6kg/h

the feed rate for the crystallizer is Me=6627.96kg/h

4)Mr/4500=1.15

5)

Now the mass balance is:

Solving the three eqautions yields:

Mr=2362.8kg/h<----mass discarded

Mc=673.6kg/h<----production rate of crystals