ARTICLE pubs.acs.org/IECR
Improvements in Petroleum Refinery Planning: 2. Case Studies Omar J. Guerra† and Galo A. C. Le Roux* Department of Chemical Engineering, University of S~ao Paulo, Av. Prof. Luciano Gualberto trav.3, 380, CEP 05508-900, S~ao Paulo-SP, Brazil ABSTRACT: This paper is the second part of a series of two papers on the recent advances in petroleum refinery planning. In Part 1 (Guerra and Le Roux, Ind. Eng. Chem. Res. 2011, DOI: 10.1021/ie200303m), nonlinear empirical process models for CDUs and a FCC unit were developed. The implementation of these models in two case studies for petroleum refinery planning is presented in this paper. In the first case, the empirical model for CDUs was implemented in the planning model for a small-scale refinery. In the second case, the empirical models for CDUs and a FCC unit were integrated in the planning model for a medium-scale refinery. In both case studies, empirical process models from the literature were adopted for refinery processes that were not considered in Part 1 of this work. In addition, a comparison of the computational performance for three popular nonlinear programming (NLP) solvers is presented in case study 1. The case studies showed that the empirical models developed in Part 1 of this work are computationally adequate for the petroleum refinery planning.
1. INTRODUCTION In a previous paper (Part 1 of this series of papers),1 an overview of recent advances in petroleum refinery planning has been given and empirical models for refinery processes were presented. In addition, it was shown that these models overcome some limitations of empirical process models previously developed by other authors. In this paper, the implementation of nonlinear empirical process models in petroleum refinery planning is presented. The details of the process model formulation can be found in Part 1 of this series of papers.1 First, a solution strategy for nonlinear refinery planning models is presented in section 2. Next, two case studies are presented in section 3. In the first case, the empirical model for CDU developed in Part 11 is implemented in the refinery planning for a small-scale refinery. In the second case, the empirical models for CDU and a FCC unit developed in Part 11 of this work are integrated in the refinery planning for a medium-scale refinery. Finally, conclusions and suggestions for future work are presented in section 4. 2. SOLUTION STRATEGY FOR NONLINEAR REFINERY PLANNING MODELS The empirical refinery process models developed in Part 1 of this work1 involve bilinear, trilinear, and other nonlinear and nonconvex terms. Therefore, refinery planning models based on these process models result in nonconvex nonlinear programming (NLP) optimization problems that are usually solved with NLP algorithms. Nevertheless, these algorithms can lead to infeasible or local optimal solutions, depending on the starting point; consequently, the solution to the NLP problem can be very sensitive to the starting point. Alternatively, global optimization algorithms can be applied in order to overcome the limitations of NLP algorithms. In contrast, the solution of NLP problems using global optimization algorithms requires much more computational effort than using NLP algorithms. r 2011 American Chemical Society
Figure 1. Multistart solution strategy for nonlinear refinery planning models.
Since global optimization algorithms usually lead to large computational times and NLP algorithms may lead to infeasible or local optimal solutions, a solution strategy for nonlinear refinery planning models is proposed in this work. This strategy is based on a multistart procedure using a NLP algorithm for local optimization problems, as described in Figure 1. The main idea of this strategy is to select the best local solution (which may correspond to the global optimum) for a given set of starting points Received: February 12, 2011 Accepted: October 11, 2011 Revised: June 20, 2011 Published: October 11, 2011 13419
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Figure 2. Refinery flow sheet for case study 1 (Li et al.2).
Table 1. Specifications for CDU Products
Table 3. Model Size for Case Study 1
products gross overhead (GO) heavy naphtha (HN)
ASTM D86
gap (5 95)
TBP cut
100% (°F)
ASTM (°F)
points (°F)a
260 275 325 400
25
229 244 304 382
light distillate (LD)
550 600
35
530 584
heavy distillate (HD)
650 700
10
645 699
bottom residue (BR)
102
total number of variables
Specifications
variables with only lower bounds
89
variables with lower and upper bounds
13
variables with only upper bounds
0
total number of equality constraints
87
total number of inequality constraints
8
inequality constraints with only lower bounds inequality constraints with lower and upper bounds
2 0
inequality constraints with only upper bounds
5
a
Estimated through the procedure described in section 3.2 of Part 1 of this work.1
Table 2. Price Data for Case Study 1
6 15
degrees of freedom
373
nonlinear elements N-Z
Table 4. Solver Performance price (US$/t)
Convergence
Raw Material MTBE EOC RAT Refinery Products C2 C4 90#G 93#G 10#D 0#D heavy oil
422.34 135.63 145.28 301.67 387.95 408.70 362.00 301.67 181.00
average CPU
average iteration
solver
success
failure
time (s)
number
CONOPT
100/100
0/100
0.08
36
IPOPT
100/100
0/100
0.13
42
MINOS
77/100
23/100
0.13
238
(randomly generated using a uniform distribution) for the decision variables. The starting point for the remaining variables is estimated as a function of the decision variables. Although this 13420
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Table 5. Properties for CDU Products TBP Cut Points (°F) example
profit (US$/day)
GO-HN
Max Profit
77843.2
244
MN
74519.8
229
ML
77157.2
Li et al.2
66577.1
HN-LD
Octane Number
Pour Point (°F)
LD-HD
HD-BR
GO
HN
LD
HD
304
584
699
67.4
46.1
53.4
26.0
382
584
645
68.9
38.8
36.1
16.0
244
304
584
645
67.4
46.1
53.3
16.0
255.9
298.9
588
671
60.9
46.7
51.2
9.7
strategy does not guarantee the convergence to the global optimum, this strategy can lead to a better local solution than those obtained using a local optimization solver and a single starting point. In addition, this strategy can be faster than deterministic global optimization algorithms, and its results can be used as a starting point for deterministic global optimization algorithms.
3. CASE STUDIES In this section, two case studies are presented. These case studies focus on the implementation of the nonlinear empirical process models (presented in Part 1 of this work1) in the petroleum refinery planning (small-scale refinery for case study 1 and medium-scale refinery for case study 2). All case studies were implemented in the modeling language GAMS (version 22.9) on an Intel Core 2 Duo (3.00 GHz, 4.0 GB of RAM) and solved by applying the solution strategy (using 100 starting points) described in section 2. The case studies are described below. 3.1. Case Study 1: Small-Scale Refinery. In this case study, the empirical model for CDUs developed in Part 1 of this work1 was implemented in the production planning model for a smallscale refinery (based on Li et al.2), which includes a CDU, an FCC unit, and a blending system (see Figure 2). Two crude oils— EOCENE (EOC) and RATAWI (RAT)—can be processed in the refinery, where C2 C4, 90# gasoline (90# G), 93# gasoline (93# G), 10# diesel oil ( 10# D), 0# diesel oil (0# D), and heavy oil (TGO, which is not recycled) can be produced; MTBE (with an octane number equal to 101) is available as an additive for gasoline blending. The capacities for the CDU and FCC units are both 400 t/day, the maximum demand for each product, and the availability for each crude oil is 200 t/day. The specifications for gasoline blending are as follows: octane number of g90 for 90# gasoline, and octane number g93 for 93# gasoline. Similarly, the specifications for diesel blending are: pour point of e 10 °C for 10# diesel, and pour point of e0 °C for 0# diesel. The CDU was simulated using the empirical model (without bias factors, since bias factors (in Part 1 of this work1) were estimated for other crude oils) developed in Part 1 of this work;1 the specifications ASTM D86 100% and Gap (5 95) and the TBP cut points (operating variables) for the CDU products are presented in Table 1. In addition, the FCC unit was simulated using the empirical model proposed by Li et al.,2 the ranges for the operating variables are 60% 85% for conversion, and 0 5 for the recycle ratio. The operating cost for the processing units are 2.41 and 13.27 US$/t for the CDU and FCC units, respectively. The prices of the raw materials and refinery products are presented in Table 2. The crude oil prices were estimated using the procedure described by Bacon and Tordo.3 The refinery planning model was formulated on a mass basis, using the generic planning model proposed by Moro et al.4 and described in section 2.1 of Part 1 of this work.1 The planning model for this case study results in a NLP optimization problem with
Table 6. Optimal Product Flow Rates for Case Study 1 Flow Rate (t/day) example
MTBE
C2 C4
90#G
93#G
Max Profit MN
71.95 156.03
75.38 80.67
68.95 181.32
200 200
66.88
80.63
75.28
157.56
60.18
143.53
ML Li et al.2
10#D
0#D
107.69 72.70
0 0
200
89.64
0
200
137.92
0
15 degrees of freedoms, as described in Table 3. This optimization problem was solved with CONOPT (Version 3.14), IPOPT (Version 3.5), and MINOS (Version 5.51), CONOPT and MINOS are based on the generalized reduced gradient (GRG) algorithm, while IPOPT is based on an interior point algorithm. The performance of these solvers using the refinery profit as the objective function is presented in Table 4. All solvers were run with the default settings. As can be seen from Table 4, the best solver performance was achieved by CONOPT and IPOPT (in that order) while MINOS failed to converge to any local optimal solution for 20 of the 100 starting points. On the other hand, IPOPT and MINOS required more CPU time and iterations than CONOPT. All local optimal solutions were found to be the same. The base case from Li et al.2 was solved with the same personal computer, using CONOPT with a single starting point. The CPU time for the solution of this planning model was 0.072 s, and the number of iterations was 14. The results for case study 1 are summarized in Tables 5 and 6; the objective function used in the base case from Li et al.2 corresponds to the maximized profit, as in the original work. The properties of CDU products are listed in Table 5, and the refinery product flow rates are presented in Table 6. In example MN, the TBP cut points between CDU fractions are fixed in order to maximize the flow rate of heavy naphtha. Similarly, in example ML, the TBP cut points are fixed in order to maximize the flow rate of light distillate. It can be observed from Table 5 that the optimization of TBP cut points represents an increase of 1213048 and 250364 US$/yr in the refinery profit, relative to examples MN and ML, respectively. On the other hand, in all of the examples, the refinery was operated at its maximum capacity, processing 200 t/day of each crude oil. In addition, the optimal operating variables in the FCC unit were a conversion of 73.3 wt % and a recycle ratio of 0.406 . Finally, in Table 6, it can be observed that, in all cases, the refinery produces 200 t/day of 93# gasoline, which corresponds to the maximum demand for this product. This situation arises because this gasoline is the mostvaluable product. The opposite situation occurs with 0# diesel, because the price of this product is lower than that of 90# G, 93# G, and 10# D. 3.2. Case Study 2: Medium-Scale Refinery. In this case study, the empirical model for the CDUs and a FCC unit 13421
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Figure 3. Refinery flow sheet for case study 2 (Zhang and Zhu5).
Table 7. Process Capacity for Case Study 2
Table 8. Demands and Specifications for Refinery Products refinery product
Process Capacity (kbpd) unit
low limit
high limit
ADU
120
200
VDU
75
120
DCU
30
60
CRU
8
50
FCC
50
80
NHU DHU
6 30
12 50 1
developed in Part 1 of this work are integrated in the planning model for a medium-scale refinery (based on Zhang and Zhu5), which includes an atmospheric distillation unit (ADU), a vacuum distillation unit (VDU), a delayed coking unit (DCU), a FCC unit, a naphtha hydrotreating unit (NHU), a diesel hydrotreating unit (DHU), a catalytic reforming unit (CRU), and a blending system (see Figure 3). Two crude oils—Tia Juana Light (TJL) and Arabian Heavy (ARH)—can be processed at the refinery to produce liquefied petroleum gas (LPG), regular gasoline (REG), premium gasoline (PRG), jet fuel (JET), diesel oil (DSL), light fuel oil (LFO), and heavy fuel oil (HFO). The availability for each crude oil is 120 kbpd; the capacities for the process units are presented in Table 7. The demands, as well as the specifications, for refinery products are presented in Table 8; additional information about the specifications for the refinery products can be found in the norms for jet fuel (ASTM D1655), diesel oil (ASTM
LPG demand (kbpd) REG demand (kbpd) octane (OCN = (RON +MON)/2) sulfur (wt %) PRG demand (kbpd) octane (OCN = (RON + MON)/2) sulfur (wt %) JET demand (kbpd) specific gravity sulfur (wt %) smoke point (mm) DSL demand (kbpd) sulfur (wt %) cetane index LFO demand (kbpd) sulfur (wt %) kinematic viscosity @ 100 °C (mm2/s) HFO demand (kbpd) kinematic viscosity @ 100 °C (mm2/s) 13422
lower bound
upper bound
0
100
10 85
30 88 0.05
10 90
100 0.05
0 0.7758
100 0.8408 0.3
25 40
60 0.05
40 0
100 1.0 14.9
0
100 50
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Table 9. Price Data for Case Study 2a average price,
standard deviation,
2008 (US$/bbl)
2008 (US$/bbl)
TJL
95.69
28.39
ARH
89.81
26.92
Crude oil
Refinery product
a
GLP
96.26
6.47
REG
136.31
30.90
PRG JET
146.39 128.08
30.47 32.22
DSL
123.29
31.66
LFO
93.46
21.96
HFO
79.77
22.40
Data taken from ref 11.
Table 10. Operating Cost for Processing Units processing unit
operating cost (US$/bbl)
ADU
0.49
VDU DCU
0.31 1.09
CRU
2.31
FCC
1.79
NHU
0.91
DHU
2.06
Table 11. Model Size for Case Study 2 total number of variables variables with only lower bounds variables with lower and upper bounds variables with only upper bounds total number of equality constraints
363 328 33 0 336
total number of inequality constraints
0
inequality constraints with only lower bounds inequality constraints with lower and upper bounds
0 0
inequality constraints with only upper bounds degrees of freedom nonlinear elements N-Z
0 27 769
D975), and both light and heavy fuel oils (ASTM D396). The properties that involve highly nonlinear mixing rules (i.e., pour point, flash point, viscosity, etc.) are converted to blending indices, using the index correlations presented in Part 1 of this work.1 The distillation unit (ADU and VDU) and the FCC unit were simulated using the empirical models developed in Part 1 of this work;1 the bias factors calculated in Part 11 were considered for the simulation of the ADU. The specification for ADU products are the same as those used in case study 1 (see Table 1). Moreover, the range for the TBP cut point between vacuum gas oil (VGO) and vacuum residue (VRE) was set from 1075 °F to 1125 °F, as recommended by Watkins.6 On the other hand, the limits for operating variables in the FCC unit are 3.85 6.8 for the catalystto-oil ratio and 956 1000 °F for the reaction temperature. The DCU was simulated through the procedure based on a microcoker (pilot plant) model and a scale-up method proposed by
Volk et al.7 This procedure was validated by the authors using industrial plant data, the results showed that this procedure is more accurate than the empirical model for delayed coking process previously proposed by other authors (Castiglioni8 and Gary and Handwerk9). In addition, the hydrotreating units were simulated using a constant sulfur removal of 85 and 92.5 wt % for HNU € um10). Finally, the CRU and DHU, respectively (Speight and Oz€ was simulated using the procedure described by Gary and Handwerk;9 the severity was set to 94 RON (RON = research octane number). The prices for crude oils and refinery products were taken as the average value for the period from January 2008 to December 2008 (Energy Information Administration (EIA11)). The average values, as well as the standard deviation, for the price of crude oils and refinery products are presented in Table 9. On the other hand, the operating costs for the processing units were estimated as the cost of utility consumption. The unitary utility consumption for processing units were adopted from Gary and Handwerk,9 and the unitary cost for utilities was estimated following the procedure proposed by Ulrich and Vasudevan.12 The operating costs are presented in Table 10. The refinery planning model was formulated on a volume basis using the same generic planning model used in case study 1, resulting in a NLP optimization problem with 27 degrees of freedom, as described in Table 11. This optimization problem was solved with CONOPT (Version 3.14). The two examples were evaluated using two different objective functions: maximize the entire refinery profit (Max Profit), called Example 1 and maximize the volumetric flow rate of premium gasoline (Max PRG), denominated as Example 2. The results are presented in Tables 12 14. Four local optimal solutions (LOP1, LOP2, LOP3 and LOP4) were identified for Example 1; the average CPU time for the solution of this example was 0.164 s, and the average number of iterations was 105. CONOPT failed to converge to a feasible solution for 4 of the 100 starting points used for Example 1. Zhang and Zhu5 solved a planning model for the same refinery, using a decomposition strategy and nonlinear empirical models for the refinery processes; the authors state that the problem was solved on a personal computer within a matter of minutes using GAMS (the solver was not specified). The crude oil selection for both examples is presented in Table 12, the refinery operates at a maximum capacity in the local optimal solutions LOP1 (the best local solution for Example 1) and LOP2 of Example 1 and in the best local solution of Example 2. The best local solution (with the higher value of refinery profit) was found from most of the starting points (59%) for Example 1. The other local solutions have a negative deviation from the refinery profit equal or higher than 3.01%. This negative deviation is ∼1.13 US $/bbl (US$ 82 490 000 per year), with respect to the best local solution for Example 2 (the obvious optimization strategy). Moreover, the maximum available quantity of TJL crude oil is purchased in both examples. The feed flow rate for process units vary, depending on the local solution reported by the solver (see Table 13); it can be observed that the CDU, FCC unit, and NHU are operated at (or close to) their maximum capacity. In addition, it can be seen that the TBP cut points in the CDU have a direct impact in the refinery profit. For instance, in Example 2, the TBP cut point between light naphtha and heavy naphtha was set to 327.9 °F, whereas in Example 1, it was set to 304.0 °F. On the other hand, the FCC conversion changes from 55.02 wt % to 76.24 wt %, according to the local solution reported by the solver. 13423
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Table 12. Crude Oil Selection for Case Study 2 Example 1: Max Profit (US$/day) Local Solutions LOP1
LOP2
frequency
59/100
17/100
relative change in profit
0.0%
LOP3
LOP4
9/100
3.01%
Example 2: Max PRG (kbpd)a
11/100
4.43%
10.20%
3.35% ( 1.13 US$/bbl)
respect to LOP1 (%) flow rate (kbpd)
crude oil
a
TJL
120.00
120.00
120.00
120.00
120.00
ARH total
80.00 200.00
80.00 200.00
64.90 184.90
63.84 183.84
80.00 200.00
Results for the best local solution.
Table 13. Feed Flow Rates and Process Operation for Case Study 2 Example 1: Max Profit (US$/day) Local Solutions LOP4
Example 2: Max PRG (kbpd)a
processing unit
LOP1
LOP2
LOP3
ADU
200.00
200.00
184.90
183.84
200.00
VDU
100.98
106.35
96.67
97.14
105.77
DCU
34.23
34.23
30.70
30.00
34.23
CRU
39.17
38.96
38.12
35.97
44.26
FCC
80.00
76.71
80.00
80.00
80.00
NHU
10.98
10.55
12.00
12.00
12.00
DHU
43.25
38.61
45.25
33.10
40.00
Feed Flow Rate (kbpd)
TBP Cut Points between Adjacent Products (°F) adjacent products
LOP1
LOP2
LOP3
LOP4
Example 2: Max PRG (kbpd)a
LN-HN
244.0
244.0
244.0
244.0
244.0
HN-LD
304.0
304.0
304.0
304.0
327.9
LD-HD
530.0
530.0
530.0
584.0
530.0
HD-BR
674.8
645.0
651.4
645.0
648.2
FCC Conversion (wt %)
a
variable
LOP1
LOP2
LOP3
LOP4
Example 2: Max PRG (kbpd)a
X
75.62
76.24
68.54
55.02
76.02
Results for the best local solution.
Table 14 presents the production plan and the active property specifications for both examples; it can be observed that the flow rate of regular gasoline is at its minimum demand in all of the solutions. This is because this product is less expensive than the premium gasoline that has similar specifications and both products can be produced from the same set of intermediate streams. The flow rate for premium gasoline in Example 2 is higher than that for Example 1, as expected. Furthermore, the flow rate of total fuel oil (LFO plus HFO) is
