Feed = 9070 kg/h
NaOH in Feed = 0.2
NaOH in Product = 0.5
Steam Pressure = 1.37 atm = 138.815 kPa
Vap Pressure = 100 mmHg = 13.33 kPa
U = 1400 W/m2°C
Feed Temperature, Tf = 37.8°C
Overall Material Balance, F = L + V = 9070 = L+V ....(1)
Component balance on NaOH, Fxf = Lxl
9070*0.2 = L *0.5
L = 3628 kg/h
V = 5442 kg/h (from Eq (1))
To determin T1 = Tsat + BPR of 50% concentrated NaOH product, first we obtain Tsat of Pure water from Steam Table. At 13.33 kPa, Tsat = 52°C
From Duhring chart for Tsat = 41.06 & 50% NaOH, boiling point of the solution is, T1 = 93.33°C
BPR = T1-Tsat = 93.33-52 = 41.33°C
From enthalpy concentration chart for superheated steam, Tf = 37.8 °C & xf = 0.2, then hf = 150 kJ/kg
T1 = 93.33°C & Xl = 0.5 then hf = 545 kJ/kg
For saturated steam at 1.37 atm from steam table we get,
Ts = 109.32°C and
= 2231.9 kJ/kg
To get Hv for superheated vapor, first we obtain the enthalpy at T sat = 52°C & P1 = 13.33 kPa, get Hsat = 2594.04kJ/kg
Then using heat capacity of 1.884 kJ/kg K of superheated steam, Hv = Hsat + Cp BPR
Hv = 2594.04 + 1.884 *41.33 = 2671.9 kJ/kg
Substituting in heat balance equation and solving for S,
Fhf + S lambda = Lhl + VHv
9070*150 + S*2231.9 = 3628*545 + 5442*2671.9
S = 6791.196 kg steam / hr
q = S lambda
q = 6791.18*2231.9*1000/3600 = 4210344 W
q = UA(Ts-T1)
A = 4210344 /(1400* (109.32-93.33)
A = 188 m2
Economy = 5442/6791.196
Economy = 0.8