1
GDP Formulation of a segmented CDU Swing Cut Model for Refinery Planning
(Performance Analysis)
Department of Chemical EngineeringCarnegie Mellon University
Pittsburgh, PA 15213
Juan P. RuizIgnacio E. Grossmann
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Motivation
• Refinery planning is an active area in process systems that strongly relies on the accuracy of the CDU model that is used
• Rigorous models of CDU units may lead to high computational efforts preventing them from being applied on a regular basis (Barsamian, 2001)
• Current approaches such as fixed yield structure representation or Swing Cut Models (Zhang et al.,2001), although computationally efficient they are not able to capture the actual behavior of CDUs leading to planning solutions that may be suboptimal.
Goal: Find a methodology that considers both, accuracy in quality estimation and computational efficiency
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ATMDIST
VACDIST
REFORMER
CRACKER
ISOMERISATION
DESULPHURISATION
PG98
ES95
F1ORF2
AGO
HGO
HF
REFINERYFUEL
RGLPG
LN
HN
KN
GO1GO2
VGO
VR1
VR2
C1
LPG
LIGHT NAPHTHA
PMS 98
MOGAS 95
JET FUEL
AGOHGO
HFO
RG
LPGR95R100
RG
LPGCN
CGO
RG
Refinery Operation and Management - J.P. Favennec
Crude Distillation Unit (CDU)
Refinery flow chart
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Error
Traditional Swing Cut Model
X =HN
X P =HN
X + X + XHN SC1+ SC2-
HNP X + P X + P XHN SC1 SC2HN SC1+ SC2-
Example : HN cut definition
TBP
LN HN KE
SC1 SC2
LN HN KE
SC1+ SC2-SC1- SC2+
Swing Cuts
Prop
(P) SC1 SC2
PLN
PSC1 P
HN PSC2 P
KE
LN HN KE Mass Fraction (X)
The assumption of a constant property value for each swing cut is themain source of inaccuracy in the property estimation of the CDU cuts
Swing Cut Definition Property Estimation
Mass Fraction (X)
CDU Cuts
Mass Fraction:
Property Value:
How can we improve the accuracy of the estimation?
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Segmented Swing Cut ModelBasic Idea
Prop
SC SCj-1 j
X
P
j
j-1(+1) P j
(-1)
P j
Xj-1(+1) X
j(-1)
x1j x2j
Xj(-1) Xj
(+1)
xij(-1)
xij(+1)
Prop
i=1 i=2
pj1p j2
Estimate the propertyfor each segment
P j(-1)
P j(+1)
Property value ofeach split is more
accurate!
Mass Fraction (X)
Mass Fraction (X)
A natural representation of the above concept is givenby a GDP formulation
Consider a segmentation of the swing cuts
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Segmented Swing Cut ModelFormulation
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
≤≤
−+=
+=
−+=
+=
−
−=
+=
++
−−=
=
−−
−=
+=
+
−−=
=
−
∑
∑
∑
∑
ijij
ijijij
Ik
ikkjkjjj
ijij
ik
kkjkjjj
ijij
Ik
ikkjj
ij
ik
kkjj
ij
xx
pxxpxPX
pxpxPX
xxxX
xxX
Y
j
j
)1(
)1(||
1
)1()1(
)1(1
1
)1()1(
)1(||
1
)1(
)1(1
1
)1(
0
)(
)(
jIi∈∨ j = 1,2,….|J|
)1(1
)1( +−
− ++= jjjj XXXX)1(
111−+= XXX
)1(||1||1||+
++ += JJJ XXX
j = 2,….|J|
Swing Cut Split Definition
Cut Yield Definition
Cut Property Definition)1(
1)1(
1)1()1( +
−+
−−− ++= jjjjjjjj PXPXPXPX
)1(1
)1(11111
−−+= PXPXPX)1(
||)1(
||1||1||1||1||++
++++ += JJJJJJ PXPXPX
j = 2,….|J|
Bilinear
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Perfomance Analysis
* Petroleum Refinery Distillation (Watkins, 1973)
Crude * : Tia Juana LightCountry: Venezuela
Objective: Compare the accuracy of estimation achieved in the Swing Cut Modelwith the Proposed Approach using real crude data
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0.004.730.164.744.73100.0
2.364.584.494.674.4790.0
3.914.408.574.604.2480.0
4.184.1912.104.514.0270.0
3.113.9415.254.413.8360.0
0.033.6417.714.293.6450.0
2.593.5619.164.133.4740.0
4.243.4618.963.943.3230.0
4.833.3216.653.703.1720.0
3.633.1510.893.373.0410.0
0.002.910.002.912.910.0
ErrorEstimatedErrorEstimated
2 Segment ModelTrue%
Proposed Framework
Swing Cut Model
VISCOSITY *
-5.00
0.00
5.00
10.00
15.00
20.00
25.00
0.0 20.0 40.0 60.0 80.0 100.0
% Vol Fraction in Pseudocut
Abs
olut
e Er
ror
Swing Cut Model
2 Segment Model
- The maximum error in Swing Cut Model is 19.16% as opposed to 4.83% in the Proposed Framework using the 2 Segment Model.
- The average error in the Swing Cut Model is 11.2% while the Proposed Framework presents an average error of 2.65% using the 2 Segment Model.
Perfomance AnalysisViscosity Estimation of HD
* Blending estimation by using ASTM index
Estimation Error
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0.0161.070.0061.060.0061.0661.06100.0
0.0461.530.1261.480.3461.3561.5691.7
0.1062.040.2561.950.7161.6662.1083.3
0.0562.600.2862.461.0062.0062.6375.0
0.0063.220.3163.031.3262.3963.2266.7
0.0963.710.1663.661.4962.8163.7658.3
0.1964.250.0064.381.6863.2964.3850.0
0.1064.870.2164.801.6963.8464.9341.7
0.0065.570.4465.291.6964.4665.5733.3
0.1266.080.4765.851.4765.1866.1525.0
0.2566.670.5066.501.2266.0266.8316.7
0.1367.360.2767.270.6667.0167.458.3
0.0068.200.0068.200.0068.2068.200.0
ErrorEstimatedErrorEstimatedErrorEstimated
3 Segment Model2 Segment ModelTrue%
Proposed Framework
Swing Cut Model
OCTANE NUMBER
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
0.0 20.0 40.0 60.0 80.0 100.0
% Vol Fraction in Pseudocut
Abs
olut
e Er
ror
Swing Cut Model
2 Segment Model
3 Segment Model
- The maximum error in Swing Cut Model is 1.7% as opposed to 0.25% in the Proposed Frameworkusing the 3 Segment Model.
- The average error in the Swing Cut Model is 1.02% while the Proposed Framework presents an average error of 0.23% and 0.08% using the 2 and 3 Segment Model respectively.
Perfomance AnalysisOctane Number Estimation of GO
Estimation Error
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0.000.150.000.150.000.150.15100.0
0.590.141.170.142.970.140.1491.7
1.300.132.590.136.570.140.1383.3
0.720.122.860.129.440.130.1275.0
0.000.113.190.1212.980.130.1166.7
0.970.111.770.1115.340.120.1058.3
2.190.100.000.1018.300.110.1050.0
1.220.092.140.0919.110.110.0941.7
0.000.084.820.0920.130.100.0833.3
0.970.084.990.0817.740.090.0825.0
2.180.075.200.0814.750.080.0716.7
1.220.072.900.078.220.070.078.3
0.000.060.000.060.000.060.060.0
ErrorEstimatedErrorEstimatedErrorEstimated
3 Segment Model2 Segment ModelTrue
Proposed Framework
Swing Cut Model
%
SULFUR CONTENT
-5.00
0.00
5.00
10.00
15.00
20.00
25.00
0.0 20.0 40.0 60.0 80.0 100.0
% Vol Fraction in Pseudocut
Abs
olut
e Er
ror
Swing Cut Model
2 Segment Model
3 Segment Model
- The maximum error in Swing Cut Model is 20.13% as opposed to 2.19% in the Proposed Frameworkusing the 3 Segment Model.
- The average error in the Swing Cut Model is 11.2% while the Proposed Framework presents an average error of 2.43% and 0.87% using the 2 and 3 Segment Model respectively.
Perfomance AnalysisSulfur Content Estimation of LD
Estimation Error
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GO
HN
LD
HD
Resid
FEED
Test Problem I:Maximize LD yield with a limit in the sulfur content concentration of 0.086 % for the Tia
Juana Light crude
19.0018.8717.97LD % VolFraction
RigorousProposed
(2 Segments)Swing Cut
Less than 1% error in the solution
Test Problem II:Maximize GO yield with a limit in the ON of
HN 49.2 for the Tia Juana Light crude
7.07.28.0GO % VolFraction
RigorousProposed
(2 Segments)Swing Cut
CDU
More than 10% more accurate
Perfomance AnalysisImpact of the proposed model under an optimization framework
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Remarks and Conclusions
• A more accurate representation of the quality of the swing cut can be obtained if a segmentation is performed.
• A segmentation of the swing cut leads to a GDP that is still linear (and hence its MIP reformulation) under the same assumptions of the Swing Cut Model.
• If a particular value representing the quality of the product is necessary in the model individually, such as Pj (e.g. splitting and blending operations downstream) it is clear that a bilinear GDP arises.
• Strategies to solve Bilinear GDPs efficiently have been developed (Ruiz & Grossmann, 2007)
General:
From the performance analysis:
• The accuracy of the property estimation for the different cuts of crude improves significantly by using the proposed approach.
• The increase in the complexity of the model (i.e. number of discrete variables added) to achieve good results, is not significant (e.g. adding only 1 discrete variable per swing cut has shown a good performance in the estimation)
