Question

Data are presented in the figure below for an evaporator. What is the recycle stream in kg per hour? H2O Feed Evaporator 300-F R 10,000 kg/hr 20% KNO, soln. Recycle 100 F saturated soln. 0.6 kg KNO) 50% kg 120 Crystallizer crystals cany of 4% H2O (4% H20 per kg total crystal + H2O) с

Answer 1

Given

Feed 1,0 F= 10,000 kg/ha 20°/. ENo 2 29. H26 EVAPORATOR M 50°, KNO, 50, H,0 IR Recycte stream 0.6 kg KNO, ka 1,0 'RYSTALLIZER C ч°lH, о 9ь , KNo3

Feed flow rate , F = 10,000 kg/hr

M is the flow rate of solution coming out of evaporator that fed to crystallized.

W is the flow rate of water evaporated from evaporator.

C is the crystal flow rate .

R is the recycle stream flow rate

Let K denote KNO_{​​​​3}

Mass fraction of KNO_​3​​​ in Feed , W_{​​​​​​​​​​​​K,F} = 0.20

Mass fraction of KNO_{​​​​3} in M , W​​​​​_{​​​​​​K,M} = 0.50

Mass fraction of KNO_​3​​​ in C , W_{​​​​​​K,C} = 1 - 0.04 = 0.96

Mass ratio of KNO_{​​​​3}​​​ to H_{​​​​2}O in Recycle stream = 0.6

Now convert the mass ratio in to mass fraction

Mass fraction of KNO_{​​​​3}​​​ in Recycle , W_{​​​​​​K,R} = 0.6/(1+0.6)=0.375

Consider overall material balance : F = W + C

Now KNO_{​​​​3}​​​ Balance : 0.20*F = 0.96*C

0.20*10000 = 0.96*C

C = 2083.33 kg and W = F - C = 10000 - 2083.33 = 7916.67 kg

Now consider balance over crystallizer

Overall mass balance : M = C + R

M = 2083.33 + R

M - R = 2083.33 ----------(1)

KNO_​3  Balance : 0.50*M = 0.96*C + 0.375*R

0.50*M = 0.96*2083.33 + 0.375*R

0.50*M - 0.375*R = 1999.9968 ------------(2)

Solving the above two equation we get

M = 9749.9844 kg

R = 7666.6544 kg

Flow rate of Recycle stream, R = 7666.6544 kg/hr