Multiple Unit Balance

Question

Potassium dichromate (K2Cr2O7) is to be recovered from 25 wt % aqueous solution. The solution is joined by a recycle stream and fed to a crystallizer/centrifuge where enough water is removed so the solution is 85 wt % water. Exiting the crystallizer are the crystals with 10 % of the solution, and the remaining solution which forms the recycle stream. The filter cake, which contains 85 wt% crystals and the rest solution is fed to a dryer. The remaining water is evaporated, leaving pure potassium dichromate crystals. For a production rate of 1000 kg/h of potassium dichromate crystals, Calculate, a) water evaporated in the crystallizer/centrifuge b) mass flow rate of the recycle stream

Answer 1

Mass Balance Problem: Potassium Dichromate Recovery

Given:

1. Feed solution: 25 wt% potassium dichromate (K2Cr2O7), 75 wt% water
2. The solution is combined with a recycle stream and sent to a crystallizer
3. In the crystallizer, water is removed so that the exiting solution is 85 wt% water (15 wt% K2Cr2O7)
4. Crystals leave the crystallizer with 10% of the total solution; the rest is recycled
5. Filter cake from the crystallizer is 85 wt% crystals and 15 wt% solution
6. The dryer removes all remaining water, producing pure K2Cr2O7 crystals
7. The final product rate is 1000 kg/h of pure K2Cr2O7

We are to calculate:

1. Water evaporated in the crystallizer
2. Mass flow rate of the recycle stream

Step 1: Determine mass of filter cake

Since the final product is 1000 kg/h of pure K2Cr2O7 and the filter cake is 85% crystals:

Filter cake = 1000 / 0.85 = 1176.47 kg/h

Solution in the filter cake = 15% of 1176.47 = 176.47 kg/h

Step 2: Determine total solution from crystallizer

Crystals leave the crystallizer with 10% of the total solution.

So, 176.47 = 10% of total solution

Total solution (L) = 176.47 / 0.10 = 1764.7 kg/h

Recycle stream is 90% of total solution:

Recycle = 0.90 × 1764.7 = 1588.2 kg/h

Step 3: Potassium dichromate balance

Let F = feed flow rate.

Feed is 25% K2Cr2O7, Recycle is 15% K2Cr2O7.

Crystals = 1000 kg/h of K2Cr2O7

Solution from crystallizer = 15% of 1764.7 = 264.71 kg/h of K2Cr2O7

Total K2Cr2O7 out = 1000 + 264.71 = 1264.71 kg/h

Input K2Cr2O7 = 0.25 × F + 0.15 × 1588.2

0.25F + 238.23 = 1264.71

F = (1264.71 - 238.23) / 0.25 = 4090 kg/h

Step 4: Water balance

Water from feed = 75% of 4090 = 3067.5 kg/h

Water from recycle = 85% of 1588.2 = 1340.97 kg/h

Total water in = 3067.5 + 1340.97 = 4408.47 kg/h

Water out (in recycle solution only) = 85% of 1764.7 = 1499 kg/h

Water in filter cake (150 kg/h) is removed by dryer, not counted in crystallizer output

Water evaporated = 4408.47 - 1499 = 2909.47 kg/h

Final Answers:

(a) Water evaporated in the crystallizer: 2909.5 kg/h

(b) Mass flow rate of the recycle stream: 1588.2 kg/h