multistage course chemical engineering

1. MULTISTAGE SEPARATION
PROCESSES
CHE 452
ENG. AMAL MAGDY
SECTION (5)

2. Multistage Distillation
Calculations
• Binary System
• Sorel plate to plate calculations
• Ponchon Sevarit method
• Lewis plate to plate calculations
• McCabe Thiele method

3. Ponchon Savarit method
• To begin calculating the required number of
stages, you should know:
1. The Enthalpy data
2. The equilibrium data
• You may count the number of stages on:
1. The enthalpy curve (the difficult method)
2. The equilibrium curve (the easy method)
Enthalpy
x
y
x

4. General tips
• If the feed enters the column as saturated liquid,
its enthalpy exists on the liquid curve
• If the feed enters the column as saturated vapor,
its enthalpy exists on the vapor curve
• Latent heat calculations
1. 𝜆 = 𝐻 − ℎ
2. From enthalpy-composition curve
Enthalpy
x
0.5
𝜆

5. Ponchon Savarit method
• Calculation steps:
1. OMB  F = D + W
2. CMB  𝑭. 𝒙𝒇 = 𝑫. 𝒙𝑫 +𝑾. 𝒙𝒘
Get D & W
3. 𝑸′ = 𝒉𝑫 + 𝟏 + 𝑹 𝝀𝑫 , 𝜆𝐷 = 𝐻𝐷 − ℎ𝐷
Get 𝑸′
4. 𝒉𝑭 = 𝑪𝑷𝒎𝒊𝒙
∗ 𝑻𝑭 − 𝑻𝒓𝒆𝒇 , 𝐶𝑃𝑚𝑖𝑥
= 𝑥𝑖 ∗ 𝐶𝑃𝑖
5. Match (xD,Q’) with (xF, hF) to get the overall operating
line that ends with (xW, Q”)
Get Q”
This line is called the overall operating line
XF XD
XW
Q’
Q’’
Q’-hD
=(1+R)lD
Qr/W

6. Ponchon Savarit method
• You may get the number of stages using:
1. The enthalpy-composition curve (the difficult
method)
• For the top section
x1
x2
x3
y3
y1
y2
y4
XW XD
XF

7. Ponchon Savarit method
• You may count the number of stages on:
1. The enthalpy-composition curve (the difficult
method)
• For the bottom section
x1
XW XD
XF
yr
y1
x2
y2
x3

8. Ponchon Savarit method
• You may count the number of stages on:
1. The enthalpy-composition curve (the difficult
method)
The final shape will be ….
x1
XW XD
XF
yr
y1
x2
y2
x3
x1
x2
x3
y3
y1
y2
y4
XD
XF

9. Ponchon Savarit method
• You may count the number of stages on:
1. Using the equilibrium curve (the easy method)
XW XD
XF
R

10. Minimum Reflux Ratio
• Rmin Determination methods:
• There are three methods according to the form of
feed:
1. If the feed is saturated liquid:
• Overall operating line at the Rmin conditions is got by
getting the y in equilibrium with xf
XF XD
XW
hF
yF
Q’min

11. Minimum Reflux Ratio
• Rmin Determination methods:
2. If the feed is saturated vapor:
• Overall operating line at the Rmin conditions is got by
getting the x in equilibrium with yf
yF XD
XW
Q’min

12. Minimum Reflux Ratio
• Rmin Determination methods:
3. If the feed is superheated or subcooled or in the
two phase region:
• Overall operating line at the Rmin conditions is got by
Trial and error
XF XD
XW
Trial 1
Incorre
ct
Trial 2
Correct
Q’min

13. SHEET (4)

14. Example (4)
2080 lb/h of an aqueous solution containing 31 mass% ethanol is to be fractionated
under pressure of 1 atmosphere to produce a distillate of 88 mass% ethanol and
bottom product of 3.5 mass% ethanol. The feed is liquid at 140°F.
a. If R=1.25 Rmin, How many theoretical plates are required?
b. If total condenser of duty 106 BTU/h is used. How many theoretical plates are required?
c. What are the reboiler duties in all cases?
Knowing that:
𝐶𝑃𝑤𝑎𝑡𝑒𝑟
= 1 Btu/Ib.°F
𝐶𝑃𝐸𝑡ℎ𝑎𝑛𝑜𝑙
= 0.64 Btu/Ib.°F
Values of enthalpy are calculated based on reference temperature of 32 °F

15. Example (4)
The enthalpy and equilibrium data are given in
the following tables:
T, °F
Weight fraction of Ethanol
x y
212 0 0
210.1 0.01 0.103
208.5 0.02 0.192
207 0.03 0.263
204.8 0.04 0.325
197.2 0.1 0.527
189.2 0.187 0.636
184.5 0.3 0.713
181.7 0.4 0.746
179.6 0.5 0.771
177.8 0.6 0.794
176.2 0.7 0.822
174.3 0.8 0.858
173 0.9 0.912
171 1 1
Wt. % of Ethanol hL, BTU/lb Hv, BTU/lb
0 180.1 1158.4
10 159.8 1085
20 144.3 1012.2
30 135 942
40 128 873
50 122.9 804
60 117.5 734
70 111.1 646
80 100 589
90 96.6 526
100 89 457.5

16. Solution (4)
Givens:
F = 2080 Ib/h , 𝑃 = 1 𝑎𝑡𝑚 & 𝑇 = 140°𝐹
𝑥𝑓 = 0.31 , 𝑥𝐷 = 0.88 & 𝑥𝑤 = 0.035
Answer:
F = D + W
D + W = 2080  (1)
𝑭. 𝒙𝒇 = 𝑫. 𝒙𝑫 +𝑾. 𝒙𝒘
2080 ∗ 0.31 = 0.88 𝐷 + 0.035 𝑊  (2)
From (1) & (2)
D = 676.92 Ib/h
W = 1403.08 Ib/h

17. Solution (4)
a. If R=1.25 Rmin, How many theoretical plates are
required?
𝑪𝑷𝒎𝒊𝒙
= 𝒙𝒊 ∗ 𝑪𝑷𝒊
= 0.31* 0.64+(1-0.31)*1 = 0.89 Btu/Ib.°F
𝒉𝑭 = 𝑪𝑷𝒎𝒊𝒙
∗ 𝑻𝑭 − 𝑻𝒓𝒆𝒇 = 0.89* (140 – 32) = 96.12 Btu/Ib
From Graph:
𝝀F = 800 Btu/Ib
hD = 95 Btu/lb
hW = 170 Btu/lb
𝝀D = 450 Btu/lb
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-400
-200
0
200
400
600
800
1000
1200
1400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
XF XD
XW

18. Solution (4)
a. If R=1.25 Rmin, How many theoretical plates are
required?
Feed is neither saturated liquid nor saturated vapor so Rmin is got by
trial and error.
From graph:
𝑸𝒎𝒊𝒏
′
= 800 𝐵𝑡𝑢/𝐼𝑏
𝑸𝒎𝒊𝒏
′
= 𝒉𝑫 + 𝟏 + 𝑹𝒎𝒊𝒏 𝝀𝑫
𝑹𝒎𝒊𝒏 = 0.556
R = 1.25 𝑅𝑚𝑖𝑛 = 0.708
𝑸′
= 𝒉𝑫 + 𝟏 + 𝑹 𝝀𝑫 = 864 Btu/Ib
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-500
-400
-300
-200
-100
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
XF XD
XW
Q’mi
n

19. Solution (4)
b. If total condenser of duty 106 BTU/h is used. How many theoretical plates are required?
𝑸′
= 𝒉𝑫 +
𝑸𝑪
𝑫
= 96.12 +
106
676.92
= 1573.4 Btu/Ib
Using hf and Q’ get the overall operating line, then calculate the required theoretical plates
c. What are the reboiler duties in all cases?
By knowing the flowrate of residue determine Qr