 Open Access
 Authors : Egemba, Kingsley C, Igbokwe Philomena K
 Paper ID : IJERTV13IS070052
 Volume & Issue : Volume 13, Issue 07 (July 2024)
 Published (First Online): 25072024
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Shortcut Modeling of an Existing Atmospheric Crude Distillation Column
Published by : http://www.ijert.org
International Journal of Engineering Research & Technology (IJERT)
ISSN: 22780181
Vol. 13 Issue 07, July2024
Egemba, Kingsley C, Igbokwe Philomena K.
Department of Chemical Engineering, University of Uyo, Uyo. Nigeria Department of Chemical Engineering, NnamdiAzikiwe University, Awka. Nigeria.
Abstract
A steady state shortcut model was developed for an existing atmospheric distillation column of a refinery in West Africa, which was validated using the plant operating data of the refinery. The model uses a new method to compute key component recoveries appropriate for the column product specifications, and also eliminates the need for stage by stage calculations in the stripping section of the column. The model is implemented by decomposing the atmospheric column into a sequence of thermally coupled simple columns with one net top product and one bottom product, and is capable of predicting flowrates and temperatures of products, column heat duties and true boiling point temperatures(TBP) of fractions. The average
percentage deviations for product flowrates predicted by the model were 1.89%, 3.08%, 1.47%, 4.41%, and 9.98%, while the corresponding values for product temperatures were 2.34%, 2.16%, 0.91%, 3.28% and 3.42% respectively for residue, heavy gas oil, light gas oil, kerosene and naphtha. The developed shortcut model can be used to predict the outputs of the atmospheric column with good accuracy.
Keywords: Distillation Modeling, Shortcut Model, Atmospheric Column, Column Decomposition, Key Component Recoveries.

INTRODUCTION
Refinery crude oil processing is one of the largest applications of distillation as a separation technique in the chemical process industry. Existing refinery distillation units are highly energy intensive and have complex column configurations (Gadalla et al, 2003a). The operating conditions of an existing column affect the efficiency of the distillation occurring in the column and by extension the profitability of the process. The efficiency of an existing crude distillation unit (CDU) column can be improved by applying retrofitting schemes (Gadalla et al, (2003a); Gadalla et al, (2003b)), or by carrying out an operational optimization of the process variables. These procedures require suitable mathematical models relating the variables of the process.
Various rigorous and shortcut models have been proposed and applied to CDU operations. Rigorous models which are more accurate than the shortcut models, have significant convergence problems, and are more difficult to apply in simulation and optimization schemes. Shortcut methods on the other hand, are simple to calculate and robust in convergence (Gadalla et al, 2003b). The Fenske Underwood Gilliland (FUG) model is the most commonly applied shortcut model for multicomponent distillation. The modeling equations for the FUG model were originally derived for simple distillation columns employing reboilers, and hence require modifications for application in CDUs with complex column configurations and employing steam as the stripping agent.
Some researchers have extended the application of the shortcut modeling approach to atmospheric CDU
columns. Many of these models incorporate the Fenske and Underwood equations, and also apply stage by stage calculations in the stripping sections of the steam stripped CDU columns (Liu (2012); Chen (2008); Gadalla et al, (2003b); Suphanit (1999)). Application of the Underwood equations requires iterative procedures, which can result in convergence problems. The underwood equations can have multiple roots with the associated challenges, in cases where some distributed components have volatilities between those of the light and heavy key components. Also, applying stage by stage calculations in the stripping stages of the column makes the method semirigorous. The steady state shortcut modeling approach presented in this work does not employ the Underwood equations, and also does not require a stage by stage computation of the stripping stages, but combines overall column efficiency with an effective viscosity approach to account for the effect of stripping steam on the distillation process.

METHODOLOGY
OVHD
PRODUCT
WATER
LN &HN TOSPLITTER
PA3
44
35
PA2
32
STEAM
KERO
26
PA1
24
STEAM
LAGO
11
CRUDE 6
STEAM
HAGO
STEAM
RESIDUE
PA3 11
5
WATER
STEAM
LN& HNTOSPLITTER
PA2
9
KERO
5
PA1
15
STEAM
LAGO
5
6
STEAM
HAGO
CRUDE
5
STEAM
RESIDUE
The modeled column is the atmospheric distillation column of a refinery in West Africa, which is designed to process 125,000 bpd (830 m3/hr) of crude. The fractionator consists of 46 trays, and is equipped with 3 side strippers (each with 5 trays), 3 pump around circuits and a total condenser. The atmospheric column produces five product fractions, namely distillate (mixture of naphtha and LPG), kerosene (KERO), light atmospheric gas oil (LAGO), heavy atmospheric gas oil (HAGO) and atmospheric residue (see Figure 1).
Figure 1: The decomposition of the existing column into a sequence of simple columns
The topped crude feed to the atmospheric column, was characterized and cut into 31 components, made up of a light end comprising; Methane; Propane; iButane; n Butane; iPentane and nPentane, and 25 pseudocomponents. The Unisim R380 suite simulation package was employed for the characterization, using the
true boiling point (TBP) data of the crude, and selecting Peng Robinson equation as the fluid package, while the light end was auto calculated. The properties and compositions calculated by the simulator for the crude are presented in Table 1.
Table 1: Properties and Compositions of the components of the Characterized Crude
Compo
M.W
Tb (0K)
Tc (0K)
Pc (Bar)
S.G (60/60)
WatsonK
100 (cP)
Molfrac (Xfi)
methane
16.04
111.5
190.6
46.41
0.01150
0.300
19.2323
0.0122
0.0006
propane
44.10
230.9
369.8
42.57
0.15240
0.507
14.3899
0.0898
0.0032
ibutane
58.12
261.3
407.9
36.48
0.18480
0.564
13.7058
0.1563
0.0023
nbutane
58.12
272.5
425.0
37.97
0.20100
0.585
13.2905
0.1480
0.0035
ipentane
72.15
300.9
460.2
33.34
0.22220
0.627
12.9585
0.1906
0.0014
npentane
72.15
309.1
469.5
33.75
0.25390
0.632
13.0570
0.2065
0.0008
hypo 1
74.43
320.8
495.4
36.35
0.22299
0.759
11.6948
0.3195
0.0182
hypo 2
78.43
335.5
511.4
35.14
0.25571
0.766
11.7620
0.3277
0.0162
hypo 3
85.59
350.4
528.6
34.14
0.28155
0.777
11.7504
0.3490
0.0356
hypo 4
95.17
365.7
546.7
33.06
0.30379
0.792
11.6983
0.4057
0.0666
hypo 5
103.65
380.4
563.0
31.56
0.32687
0.804
11.6834
0.4631
0.0666
hypo 6
110.64
392.6
576.3
30.33
0.34709
0.812
11.6798
0.5160
0.0830
hypo 7
117.85
408.1
592.4
28.69
0.37486
0.821
11.7033
0.5790
0.0529
hypo 8
125.70
420.5
605.6
27.63
0.39644
0.830
11.6909
0.6545
0.0574
hypo 9
133.48
435.5
620.8
26.23
0.42480
0.839
11.7092
0.7354
0.0550
hypo 10
142.62
450.3
635.7
25.02
0.45267
0.848
11.7108
0.8414
0.0641
hypo 11
152.98
464.6
650.3
23.98
0.47981
0.858
11.7001
0.9901
0.0620
hypo 12
162.59
478.3
663.8
22.99
0.50670
0.866
11.6995
1.1605
0.0474
hypo 13
173.72
493.5
678.6
21.94
0.53719
0.876
11.7000
1.3884
0.0539
hypo 14
186.55
507.2
692.3
21.15
0.56380
0.885
11.6791
1.7012
0.0659
hypo 15
196.44
520.9
705.1
20.24
0.59316
0.892
11.6915
1.9850
0.0471
hypo 16
209.11
536.0
719.3
19.33
0.62544
0.900
11.6944
2.4138
0.0120
hypo 17
222.82
550.2
732.8
18.57
0.65552
0.908
11.6875
2.9792
0.0084
hypo 18
237.00
564.6
746.3
17.82
0.68663
0.917
11.6834
3.7031
0.0103
hypo 19
252.11
578.8
759.5
17.13
0.71722
0.925
11.6755
4.6773
0.0158
hypo 20
264.04
589.9
769.8
16.60
0.74171
0.931
11.6715
5.6411
0.0192
hypo 21
274.48
604.4
782.2
15.80
0.77779
0.936
11.7009
6.6740
0.0580
hypo 22
283.79
622.5
796.8
14.76
0.82579
0.941
11.7580
7.7465
0.0269
hypo 23
296.23
637.6
809.8
14.05
0.86389
0.947
11.7770
9.6490
0.0190
hypo 24
310.34
650.6
821.4
13.56
0.89437
0.954
11.7717
12.4740
0.0147
hypo 25
329.72
664.3
834.2
13.15
0.92345
0.963
11.7403
17.9233
0.0120
The Fenske equation which was incorporated into the shortcut model being presented was derived for simple distillation columns having one top product and one bottom product. Hence to apply the Fenske equation, the column being modeled was decomposed into a sequence of partially thermally coupled columns, using the
decomposition method of Liebmann cited in Chen (2008) and Liu (2012). The decomposition of the complex column is shown in Figure 1, while the resulting simple columns are depicted in Figure 2. The simple columns were then modeled sequentially to give the model of the fractionator.
v1 L2
(V1L2 =D1 )
6
F1
PA1
V2 L3
(V2 – L3 = D2
15
F2 (D1)
5 5
S1 S2
B1 B2
PA2
COLUMN 1
V3 L4
(V3 – L4 = D3 )
9
COLUMN 2
D41
QC
WATER
D42
PA3
11
F4 (D3 )
5
S4
B4
F3 (D2)
5
S3
B3
COLUMN 3 COLUMN 4
Figure 2: The simple columns showing the distribution of stages in each column section
The pairs of light key (LK) and Heavy key (HK) components used to model the separation occurring in each simple column were determined by a method described in Liu (2012), and is presented in Table 2. In specifying the separation occurring in the columns, the following simplifying assumptions were applied;

The composition of the crude was assumed to be the same for the period covered by the plant operating data used.

Each pair of LK and HK was fixed for each simple column. Hence, the quality specification for each product
fraction of a simple column was fixed. The shortcut model calculates product flowrates and temperatures, column pumparound and condenser duties, as well as the T10 and T90 true boiling point temperatures (TBP) of HAGO, LAGO and KERO.
Table 2: Fixed Column and Operating Specifications for the Decomposed Simple Columns
Parameter
Column 1
Column 2
Column 3
Column 4
Rectifying Stages
6
15
9
11
Stripping Stages
5
5
5
5
LK Component
Hypo 14
Hypo 14
Hypo 9
Hypo 6
HK Component
Hypo 24
Hypo 24
Hypo 18
Hypo 8


MODEL DEVELOPMENT
The developed shortcut model combines the Fenske equation, material and energy balances in terms of the key component recoveries, a new method for computing key component recoveries, a modified overall column efficiency and energy balances to model the atmospheric column.

Material and Energy Balances:
In the decomposed scheme applied, vapour and liquid leave and enter a column respectively on the same stage. Hence, (Vn Ln+1) can be taken as the effective distillate for column n. If the fractional recoveries of the key components in a column are defined by Equations 1 and 2, then material balances can be written for a simple column n as in Equations 3 to 5.
Dn1 = Dn + Bn 3
LK Component Material Balance:
Dn1xdn1,LKn(RLK,n) = Dnxdn,LKn 4
HK Component Material Balance:
Dn1xdn1,HKn(RHK,n) = Bnxbn,HKn 5
The energy balances (total stream) written for the simple columns are given in Equations 6 to 10.
F1hf1 + S1HS1 = D1hd1 + B1hb1
(column1) 6
D1hd1 + S2HS2 = D2hd2 + B2hb2 + QPA1
(column2) 7
D2hd2 + S3HS3 = D3hd3 + B3hb3 + QPA2
(column3) 8
RLK,n
= DxdLK,n 1
FxfLK,n
BxbHK,n
D3hd3
+ S4HS4
= D41
Hd41
+ B4hb4
+ QPA3
RHK,n =
FxfHK,n
2
D41
Hd41
= D42
hd42
+ Qc
(column4) 10
Total Material Balance:

Estimating relative volatilities of components:
The model computes relative volatilities from component
The discussion on the derivation of these equations is published elsewhere (Igbokwe and Egemba, 2018).
Kvalues, using Equation 11.
Nmin(R)(
Nmin(S))
R = LH
1LH 14
= Ki
11 LK
( Nmin(R) Nmin(S))
ir Kr
1 LH
Nmin(S)
LH
Nmin(R)
Many authors have estimated Kvalues from correlations of
R = LH
(LH
1)
15
the form of Equation 12 (Wilson (1968); Kumar et al,
HK ( Nmin(S) Nmin(R))1
LH LH
(2001); Almehaideb et al, (2002); Fattah (2012)).
i i ri
K = Pci exp[(1 + )f(T )] 12
P
This shortcut model uses a modified form of the Wilsons
correlation given in Equation (13) to compute component Kvalues.
Applying OConnells correlation for efficiency (Sinnot, 2005), with the average viscosity term replaced by an effective viscosity defined as in Equation 16, and setting the minimum number of stages in a column equal to 60% of the equilibrium number of stages (Smith (1963); Sinnot
Pci Ki = ( P
0.745
)
exp [5.37(1 + 0.714) Tci T
0.755
) )]
(2005)), gives the minimum number of stages for the
rectifying and stripping sections as Equations 17 and 18.
(1 (
eff = f(av, S) 16
N = (0.6) (5132.5Log(efLH)) (N )
13

Computation of key component recoveries:
For each pair of selected LK and HK components in a
min (R)
N
100
= (0.6) (5132.5Log(efLH)
ac(R)
17
)
simple column, a new method was used to compute the recoveries of these key components in terms of the minimum number of stages, using Equations 14 and 15.
min (S)
100 ) (Nac(S)
18

Recovery of nonKey components:
(1 RHK
Nmin
Components lighter than the LK component and
R = RHK )iH 19
i 1+ (1 RHK
Nmin
components heavier than the HK component were assumed not to be distributed (King, 1980). The recoveries of the components with volatilities between those of the LK and HK components were estimated from a form of the Fenske equation given in Equation 19.
RHK )iH

Computation of the enthalpy of streams: The model computes the enthalpy of hydrocarbon streams from Equation 20.
H (Kj
Kg
) = Hig
(2.326)RTc M
HigH
[RTc
] 20
The first term on the right hand side of Equation (20) is the ideal gas enthalpy term which was computed using the LeeKesler method (Fahimet al, (2010); API (1997)), while the pressure effect (second term on the right) was computed using the Pitzer and Curl correlation (API,1997). The enthalpy of steam was computed from the correlation of Domijan and Kalpic (2005).
The viscosity and density of hydrocarbon components were determined from procedures
11A4.1 and 6A3.5 of API (1997) respectively. The model determines mixture properties using the mixing rule in Equation 21.
Pmix = xiPi 21
The model was validated by comparing model output with the operating data of the existing atmospheric distillation column.


RESULTS AND DISCUSSION
The flowrates and temperatures of product fractions predicted by the model were compared with plant values and presented in Tables 3 and 4 respectively. The column heat duties and the product TBPs computed by the model were not presented here because the plant operating data for these parameters were not available for comparison.
Table 3: Comparison of plant data and model predicted product flowrates
Test No 
RESDF (m3/hr) 
HAGOF (m3/hr) 
LAGOF (m3/hr) 
KEROF (m3/hr) 
NAPHF (m3/hr) 

PV 
MV 
%DV 
PV 
MV 
%DV 
PV 
MV 
%DV 
PV 
MV 
%DV 
PV 
MV 
%DV 

1 
151.1 
153.3 
1,46 
26.5 
26.6 
0.53 
124.9 
121.8 
2.48 
91.0 
87.0 
4.40 
86.6 
77.8 
10.16 
2 
152.3 
153.4 
0.72 
25.7 
26.6 
3.50 
123.9 
122.0 
1.53 
91.0 
87.1 
4.29 
86.7 
77.8 
10.27 
3 
154.2 
153.7 
0.32 
26.0 
26.6 
2.27 
125.0 
121.9 
2.48 
91.0 
87.0 
4.40 
83.4 
77.7 
6.83 
4 
143.7 
154.2 
7.31 
25.7 
26.6 
3.70 
120.7 
122.2 
1.24 
95.0 
87.3 
8.11 
91.4 
78.1 
14.55 
5 
152.3 
154.0 
1.12 
27.2 
26.7 
1.80 
123.1 
122.4 
0.57 
91.0 
87.6 
3.74 
87.6 
783 
10.62 
6 
155.7 
155.2 
0.32 
28.0 
26.9 
3.83 
124.8 
123.2 
1.28 
91.0 
87.9 
3.41 
86.8 
78.6 
9.45 
7 
151.8 
154.8 
1.98 
26.8 
26.9 
0.56 
125.0 
123.1 
1.52 
91.0 
87.9 
3.41 
86.9 
78.5 
9.67 
8 
151.6 
153.9 
1.52 
27.9 
26.7 
4.13 
125.0 
122.2 
2.24 
91.0 
87.3 
4.07 
85.8 
78.0 
9.09 
9 
158.0 
153.4 
2.91 
27.4 
26.6 
2.74 
122.9 
122.1 
0.65 
91.0 
87.2 
4.18 
87.4 
77.5 
11.33 
10 
154.3 
156.3 
1.30 
25.4 
27.4 
7.75 
125.0 
125.9 
0.72 
91.0 
89.7 
1.43 
86.2 
79.4 
7.89 
Avg 
1.89 
3.08 
1.47 
4.14 
9.98 
PV: Plant value; MV: Model value; %DV: Percentage absolute deviation
Table 4: Comparison of plant data and model predicted product temperatures
Tes t No 
RESDT (OC) 
HAGOT (OC) 
LAGOT (OC) 
KEROT (OC) 
NAPHT (OC) 

PV 
MV 
%D V 
PV 
MV 
%D V 
PV 
MV 
%D V 
PV 
MV 
%D V 
PV 
MV 
%D V 

1 
338. 6 
348. 1 
334. 6 
339. 9 
284. 9 
287. 7 
192. 0 
199. 2 
136. 7 
141. 4 

2.81 
1.58 
0.98 
3.75 
3.44 

2 
339. 4 
348. 4 
333. 6 
341. 2 
284. 0 
288. 5 
192. 4 
200. 0 
136. 5 
141. 6 

2.65 
2.28 
1.58 
3.95 
3.74 

3 
339. 3 
347. 8 
332. 9 
339. 2 
285. 9 
286. 8 
192. 1 
197. 2 
134. 8 
139. 2 

2.51 
1.89 
0.31 
2.65 
3.26 

4 
338. 6 
344. 7 
328. 3 
334. 2 
287. 5 
283. 7 
192. 1 
194. 5 
133. 7 
137. 1 

1.80 
1.80 
1.32 
1.25 
2.54 

5 
338. 5 
347. 8 
334. 0 
339. 9 
285. 1 
287. 9 
193. 5 
200. 1 
137. 1 
142. 0 

2.75 
1.77 
0.98 
3.41 
3.57 

6 
340. 1 
348. 0 
333. 2 
340. 0 
285. 6 
287. 2 
192. 6 
198. 2 
135. 3 
139. 9 

2.32 
2.04 
0.56 
2.91 
3.40 

7 
339. 8 
348. 5 
333. 5 
341. 0 
287. 0 
288. 6 
193. 1 
199. 9 
136. 3 
141. 2 

2.56 
2.25 
0.56 
3.52 
3.60 

8 
339. 8 
347. 9 
332. 4 
339. 4 
286. 8 
287. 2 
192. 6 
198. 4 
135. 6 
140. 7 

2.38 
2.11 
0.14 
3.01 
3.76 

9 
339. 9 
347. 0 
332. 4 
339. 7 
287. 4 
288. 0 
193. 0 
199. 0 
134. 0 
138. 3 

2.09 
2.20 
0.21 
3.11 
3.21 

10 
339. 9 
345. 0 
332. 8 
345. 0 
286. 4 
293. 3 
193. 8 
203. 9 
134. 8 
139. 7 

1.50 
3.67 
2.41 
5.21 
3.64 

Av g 
2.34 
2.16 
0.91 
3.28 
3.42 
PV: Plant value; MV: Model value; %DV: Percentage absolute deviation
The absolute deviations of the predicted flowrates for residue, heavy atmospheric gas oil, light atmospheric gas oil and kerosene were all below 10%, while the maximum percentage deviation for naphtha was 14.55%. The average percentage deviations were 1.89%, 3.08%, 1.47%, 4.14% and 9.98% for residue, heavy atmospheric gas oil, light atmospheric gas oil, kerosene and naphtha flowrates respectively. The product fractions temperatures predicted by the model had maximum percentage deviations of 2.81%, 3.67%, 2.41%, 5.21%, and 3.76% for residue, heavy atmospheric gas oil, light atmospheric gas oil, kerosene and naphtha respectively, while the corresponding average values were 2.34%, 2.16%, 0.91%, 3.28%, and 3.42%. The absolute deviations for the predicted temperatures were also generally below 10OC. A percentage deviation of 10% or less is considered acceptable. The low values of the deviations observed for the model outputs is an indication that the model can be used to predict product flowrates and temperatures in an existing atmospheric crude distillation column of a refinery.
5.0 CONCLUSION
A shortcut model of an existing refinery atmospheric crude distillation column has been developed. A new method for determining key component recoveries, which was incorporated into the model, was able to transform industry specifications into appropriate key component and their recoveries required for the implementation of the model on the column. The model does not require initial guesses to compute component recoveries, nor require stage by stage calculations in the stripping section of the atmospheric column. The average percentage deviations predicted by the model for product flowrates and temperatures when compared with plant values were below 10%. The deviations for temperatures were also generally below 10OC. Hence the developed shortcut model can be used to predict the product flowrates and temperatures of the existing CDU column with sufficient accuracy. A MATLAB code was written to execute the shortcut model on the existing refinery atmospheric column.
Notations
h Enthalpy of liquid
H Enthalpy of vapour HK Heavy key component LK Light key component
Nac Actual number of stages in a column
Nmin(i) Minimum number of stages in section i of a column
Pc Critical pressure
P Total pressure
QC Condenser duty
QPAi Heat duty of pump around i Ri Recovery of component i
T Temperature of stream
Tc Critical temperature
Tr Reduced temperature
xbi Mole fraction of component i in bottom product
xdi Mole fraction of component i in top product
xfi Mole fraction of component i in feed
Accentric factor
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