Journal of Applied and Industrial Sciences, 2013, 1 (3): 44-48, ISSN: 2328-4595 (PRINT), ISSN: 2328-4609 (ONLINE)
44
Research Article
A short-Cut Method for Designing Multi-Component
Fractionation Column
Rawia. S.Hassan1 , Gurashi.A. Gasmelseed2, B. A. Karama3, and A.E Musa4
(1)
Faculty of graduate studies, University of Karary, Khartoum – Sudan
Email : rawia.siddig@yahoo.com
(3)
Faculty of graduate studies, University of Karary, Khartoum – Sudan
(2)
Department of Leather Technology, College of Applied and Industrial Sciences, University of Bahri, Khartoum
– Sudan, P.O.Box 1660
Email : gurashigar@hotmail.com
Telephone: +249919634134
(4)
Department of Leather Technology, College of Applied and Industrial Sciences, University of Bahri, Khartoum
– Sudan, P.O.Box 1660
E mail: ali206w@hotmail.com
(Received: June 11, 2013; Accepted: August 14, 2013)

Abstract— Fractionation of multicomponent mixtures into top
and side stream products depends on the relative volatility of the
cut. As the cut consists of more than one component with specific
true boiling point (TBP), its relative volatility can be calculated.
In this method the component with the lowest relative volatility at
the top above the feed tray is designated as a light key component
(lk), all non-light keys,(nlk) are more volatile with volatilities
greater than that of the light key. On the other hand the
components with highest volatility at the bottom below the feed
plate is designated as the heavy key component (hk), all nonheavy keys (nhk), are less volatile with relative volatilities less
than that of the heavy key. Based on these facts, the designated
light and heavy components will be taken as binary and the
column will be designed accordingly. In this study a
multicomponent fractionation column is designed by both the
rigorous multicomponent design method and that of a simple
binary Mc cabe Thiele method for the system C2 to C7 feed
mixture. The results of the design parameters are considered to
be good and in agreement.
Index Terms— Design, Multicomponent, Binary systems.
I. INTRODUCTION
M
ulticomponent hydrocarbons need to be separated into
top and side streams products in a fractionation column
[1]. These streams are separated in cuts depending on their
true boiling point temperature and their relative volatilities.
The design of such columns is tedious and requires
compositions, and physical properties of the top and bottom
products [2]. The important parameter in the design is the
number of theoretical stages which requires the application of
Underwood and Gilly land correlations, the data therefore
require on-line sampling on pilot scale with subsequent scaleup.
A new technique is developed taking into consideration the
more volatile component or cut as the (lk) component and the
less volatile component or cut as the heavy key (hk). The (nlk)
are those which are more volatile than the (lk), while the nonheavy keys (nhk) are those which are less volatile than heavy
keys [2]. The light and heavy are taken to be a binary system
of the two components and the number of theoretical plates are
determined by Mc cabe Thiele graphical method, and so are the
other design parameters. The design parameters determined by
both methods are to be compared and analyzed.
II. MATERIALS AND METHODS
A mixture of hydrocarbons C2 to C7 is taken as a
multicomponent feed entering the fractionators as saturated
liquid at a temperature of 120oC and a pressure of 13 bars. The
equilibrium data are obtained using Antoine equation. The
minimum number of theoretical stages is calculated by Fenske
equation [3]. Compositions of the feed, distillate, bottom, and
relative volatilities are specified and tabulated.
The minimum reflux ratio is determined by Underwood
equation [4] taking q-value equal to one as the feed is
saturated liquid. The flow factor is calculated as well as the
tray space and the column is operated at 85% of the flooding
capacity, the number of theoretical trays is then calculated by
Gilly land equation [6], the overall efficiency is calculated by
O’nell equation[5], and hence the number of actual stages and
the column height. The column down-comer, net, and active
areas are specified as well as the diameter of the column at
85% of the flooding velocity. But as for the new technique, the
equilibrium data are determined for the binary consisting of lk
and hk, and Mc cabe Thiele plot is used to determine the
number of the theoretical plates, other design parameters are
calculated normally [6].
Journal of Applied and Industrial Sciences, 2013, 1 (3): 44-48, ISSN: 2328-4595 (PRINT), ISSN: 2328-4609 (ONLINE)
Procedure
Vapor -liquid equilibrium is calculated by Antoine equation:
………..1
Where: Pvap= vapor pressure of the component
A, B, C = Antoine constants
T = absolute temperature in Kelvin
For saturation feed at 120°C and 13 bar
Table1
Antoine constants for the system C2 – C7
Component name
Symbol
A
B
Ethane
C2H6
15.9
1580
Propane
C3H8
15.7
1870
Iso butane
C4H10
15.9
2200
Cis butane
C4H8
15.8
2210
i-pentane
C5H12
15.6
2350
Iso prene
C5H8
15.9
2470
Cyclo hexane
C6H12
15.8
2660
Toluene
C7H8
16.3
3240
C
-13.8
-25.1
-29.9
-36.2
-40.2
-39.6
-47.2
-47.2
III. RESULTS AND DISCUSSION
The following data are obtained:
Component
Name
Symbol
Ethane
Propane
Iso butane
Cis butane
i-pentane
Iso prene
Cyclo hexane
Toluene
C2H6
C3H8
C4H10
C4H8
C5H12
C5H8
C6H12
C7H8
Table 2
Equilibrium relationship
Vapor
Distribution
Pressure
Coefficient Ki
Pvi
123292.7
12.64
40256.2
4.13
18477.9
1.89
14598.1
1.5
7480.6
0.767
7265.7
0.745
3246.7
0.333
995.5
0.102
Component
Feed Rate
Kmol/h
0.93
17.09
14.06
18.05
14.93
1.62
12.29
30
Calculate from equilibrium relationship: Ki= Pvi/Pt
Where:
Pvi = vapour pressure of component i
Pt = total pressure
Minimum number of stages
Fenske equation
Table 3
Composition of components C2 – C7
Component
Feed
D ,mole fraction W, mole fraction
name
mole
fraction
Ethane
0.0093
0.0475
0
Propane
0.1709
0.4196
0
Iso butane
0.1406
0.3462
0
Cis butane
0.085
0.1967
0.00105
i-pentane
0.1439
0.0004
0.2530
Iso prene
0.0162
0
0.28
Cyclo hexane
0.1229
0
0.2695
Toluene
0.3
0
0.5107
Where: D= distillate product, W= bottom product
C2= Ethane; C3 = Propane; C4 = Iso butane, Cis butane; C5 =
i-pentane, Iso prene;
C6 = CYCLO HEXANE; C7 = TOLUENE
Table 4
Calculation of Relative volatility of C2 – C7
Component Name
αi = Pi/Pj
Ethane
16.48
Propane
5.38
Iso butane
1.95
Cis butane
2.74
i-pentane
1
Iso prene
0.97
Cyclo hexane
0.43
Toluene
0.13
Pvi = vapour pressure of component i Pj = vapour pressure of
component j
lk = 2.74 , where lk is the relative volatility of the light
key
Table 5
Composition of light (cis-butane) and heavy (i-pentane) keys
in top and bottom:
Lk
Hk
xD,mole fraction
0.1967
0.0004
xB, mole fraction
0.0015
0.253
The mole fraction of XD and XB are experimental data
Determination of minimum number of stages (Nm):
Nm = 12.8 = 13 stages
Minimum Reflux Ratio Rm
Using Underwood equation:
………3
……….2
Where:
Nm = minimum number of stages, xD =composition of the top product
α = relative volatility,
xw=composition of the bottom product
45
For saturation feed condition, q=1,
θ = 1.3 by trial and error
Where: αi = relative volatility of component (i),
XiF =
composition of component ( i) in feed.
Journal of Applied and Industrial Sciences, 2013, 1 (3): 44-48, ISSN: 2328-4595 (PRINT), ISSN: 2328-4609 (ONLINE)
Table 6
Calculation of Rm for separation of C2 – C7
Component name
Component name
Ethane
Propane
Iso butane
Cis butane
0.052
0.553
1.03
0.37
i-pentane
Iso prene
Cyclo hexane
Toluene
TOTAL
-0.0013
0
0
0
1.78
Where:
ρv = density of the vapor phase
ρl= density of the liquid phase
Densities at the top of the distillation column
ρv= 3.67 Kg/m3
ρl= 738 Kg/m3
Densities at the bottom of distillation column
ρv= 2.16 Kg/m3
ρl= 578 Kg/m3
Taking tray spacing = 0.6 m
Flow factor at the top = 0.03
Flow factor at the bottom = 0.02
KT = 0.18
KB = 0.16
Rm= 0.78
R actual = 1.5 * Rm = 1.18
Where R actual = R
X = (R-Rm) /(R+ 1) …………..4 [7]
Y = 1- X0.33 ………5
N = (Nmin + Y)/(1-Y) = 21.5 = 22 stages
Column Efficiency
EO= 51 – 32.1 log (αi* μi) …….6
μi = average viscosity= ∑ μi xi,
αi = relative volatility of light key
E0= 65.4 Na = 22/0.654= 34 stages
Height of the column
Ht = (Na – 1 ) *C + (Na /10) * C + 0.1 Ht ….7
Where: KT and KB are constants at the top and bottom
respectively
Velocity at the top = 2.8 m/s
Velocity at the bottom = 2.3 m/s
Operation at 85% flooding rate
Velocity at the top = 2.38m/s
Velocity at the bottom = 1.9 m/s
Calculation of volumetric flow rates
At the top =41900/3.67/3600 = 3.17 m3/s
At the bottom 41900 /2.17 / 3600= 3.7 m3/s
Area of the column
Top = 3.17/ 2.38= 1.33 m2
Bottom = 3.7/1.98 = 1.8 m2
Column cross sectional area
TOP = 1.33 / 0.88 = 1.5 m2
Bottom 1.8/0.88 =2.04 m2
Diameter of column:
Where: Ht = Height of the column.
C = tray Space = 0.6
[8]
Ht = 24 m
Flow Rates: Feed = 160 Ton/h.
Top Product = 20.94 T/h.
Bottom Product = 139.06 T/h
Vapor rate = D (1+R) = 41.9 T/h
LT = DR = 21.06 T/h
LB = F + LT
L / V (top) = 0.5 L / V (bottom) = 2.5
Column diameter: The column diameter must be selected so
that flooding does not occur, however at the same time vapor
velocities that are high for greater plate are needed. In these
calculations, operation at 85% of flooding velocity is taken,
this velocity determined from equation
………. (8)
Flow Factor
…………….9
………..10
DT = 1.38m, DB = 1.61 m
Where: DT = column diameter at the top, DB = column
diameter at the bottom
Column diameter = 1.61 m
Column area = 2 m2
Down comer area (12 % Ac) = 0.24 m2
Net Area = 2.5 – 0.3 = 1.8 m2
Active area = Ac – 2Ad = 1.56 m2
Hole area (10% Aa) = 0.156 m2
Hole diameter = 5 mm
Plate thickness = 5 mm
Area of one hole = 1.96*10-5
Number of holes = 7945 holes
Binary Design Method: this is Mc.Thiele Method
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Journal of Applied and Industrial Sciences, 2013, 1 (3): 44-48, ISSN: 2328-4595 (PRINT), ISSN: 2328-4609 (ONLINE)
LK
HK
Table 7
Identification of Light and Heavy component
Component name
xf
xD
xW
Cis- butane
0.085
0.1967
0.00105
I-pentane
0.1493 0.0004
0.2530
Where: xf = composition in feed
Data for vapor-liquid equilibrium curve in term of relative volatility
..................11
x 0
Y 0
0.05
0.123
0.1
0.23
Relative volatility for light component = 2.74
0.2
0.3
0.4
0.5
0.6
0.7
0.4 0.53 0.64 0.73 0.8 0.86
0.8
0.92
0.9
0.96
1.0
1
Figure 1: Mccabe Thiele graphical method
Where y axis is the composition of light key in vapor phase and x axis is the composition of light key in liquid phase
Design parameter
N
Eo
Na
Ht
D
At
Ad
An
Aa
Ah
Plate thickness
Hole diameter
Number of holes
Table 8
Comparison of multicomponent and binary design methods
Multi component method
Mc Thiele method
22stages
19 stages
65.4%
62.3%
34 stages
31 stages
24m
22 m
1.5 m2
1.7 m2
2
2m
2.3 m2
2
0.24 m
0.27 m2
2
1.8 m
2.02 m2
2
1.56m
1.76 m2
0.156
0.176 m2
0.5mm
0.5mm
0.5 mm
0.5 mm
7945
8963
Percent deviation
-15.7
-4.9
-9.7
-9.0
11.7
13
11.1
10.8
11.3
11.3
0
0
11.3
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Journal of Applied and Industrial Sciences, 2013, 1 (3): 44-48, ISSN: 2328-4595 (PRINT), ISSN: 2328-4609 (ONLINE)
From figure 1
= 0.29
Number of theoretical stages = 19 stages
Column Efficiency
EO= 51 – 32.1 log (αi* μi)
μi = average viscosity
E0= 62.3%
N = 19/0.623 = 29 stages
Height of the column
Ht = (Na – I ) *C + (Na /10) * C + 0.1 Ht
Where: Na= Actual number of stages
Ht = Height of
the column
C = tray Space = 0.6
Ht = 22 m
Flow Rates- Feed = 160 Ton/h
Top Product = 20.94 T/h
Bottom Product = 139.06 T/h
Vapor rate = D (12+2.2) = 67 T/h.
LT = DR=46T/h, LB = F + LT = 206 T/h
L / VT = 0.69,
L / VB= 2.8
Where: LT, LB = liquid rate at the top and bottom
VT, VB = vapor rate at the top and bottom
Column diameter
Column cross sectional area
AT=1.76 / 0.88=2 m AB =2.04 /0.88 =2.3m2
Diameter of the column
DT = 1.59 m
DB = 1.7m
Column area = 2.3 m2
Down comer area (12 % Ac) = 0.27 m2
Net Area = 2.02 m2
Active area = Ac – 2Ad = 1.76 m2
Hole area (10% Aa) = 0.176 m2
Hole diameter = 5m Plate thickness = 5mm
Number of holes = 9677 holes
IV. CONCLUSIONS
The multicomponent method using the (lk) and (hk) as binaries
is comparatively similar to the method of Mccabe Thiele for
binary graphical method. It is observed that the maximum
deviations is 15% in the number of theoretical stages, other
deviations fall between 11.7% and 0.0% which is acceptable
for the design. The new method is simple, saves time and
accurate.
It is recommended that more case studies have to be designed
and compared to confirm and verify the new design technique.
Acknowledgement
Flow Factor
The authors wish to thank the University of Karary, Faculty of
graduate studies for supporting this work for Ph.D Thesis in
chemical engineering.
REFERENCES
Densities at the top of distillation column
ρv= 2.54Kg/m3
ρl= 641Kg/m3
Densities at the bottom distillation
ρv= 2.44 Kg/m3
ρl= 626 Kg/m3
Taking tray spacing = 0.6 m
Flow factor at the top = 0.04.
Flow factor at the bottom = 0.17
KT = 0.19
KB = 0.17
Velocity at the top = 3.0 m/s
Velocity at the bottom = 2.7 m/s
For 85% flooding
Velocity at the top = 3.0 * 0.85 = 2.55 m/s
Velocity at the bottom=2.7* 0.85 = 2.3 m/s
Volumetric flow metric rates
At the top =41900/2.54 /3600 = 4.5 m3/s
At the bottom 41900/2.441/ 3600= 4.7 m3/s
Area of the column
Top = 4.5/2.55 = 1.76 m2
Bottom = 4.7 / 2.3 = 2.04 m2
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