- Email: [email protected]
An integrated process optimization model for chemical production at Ibn Zahr
An integrated process optimization model for chemical production at Ibn Zahr S. 0. Duffuaa” Industrial and Operations Engineering
Department,
University of Michigan,
Ann Arbor, MI, USA
In this paper a mathematical optimization model is developedfor several reactors settings. The model integrates several reactors and is stated in a generalform. The model selects the settings for the reactors that maximizes profit subject to operation, selection and environmental constraints. Each setting is determined by a set of operating parameters, which are feed rate, reactor temperature and pressure. The production level and the cost of each setting is determined from the operating parameter and the raw material, labor and fuel cost. It is used to optimize Methyl-Tert-Butyle Ether (MTBE) production at the Ibn Zahr Company in Saudi Arabia. The results in the Ibn Zahr case are consistent and elevated MTBE production. Keywords:
optimization,
operational
research,
chemical
1. Introduction In chemical production reactors settings play a key role. The settings are determined by selecting appropriate input variables, such as temperature, pressure, and raw material feed rate. The levels of input variables affect the quality and quantity of products. For some chemicals, such as methyl-tert-butyl ether (MTBE), their production involves processing material through several reactors. The process of producing MTBE at Ibn Zahr (the company used in this study) has three phases. In the first phase, mixed butane is pumped through a Deisobutanizer to separate pentane from normal butane. Then the butane is dried and passed through the isobutane reactor which is a part of the butamer unit. In this reactor, butane is isomerized to isobutane. In the second phase, isobutane is heated and sent to the isobutylene reactor, which is a part of a dehydrogeneration unit. The reactor in this unit converts isobutane to isobutylene over a catalyst. Then in the third phase the isobutylene is fed to the MTBE unit. In this unit, the isobutylene passes through an ammonia removal tower and prior to entering the MTBE reactor is mixed with methanol. In this reactor isobutylene is converted to MTBE by synthesis with methanol.4 The whole process is known as the hydrocarbon flow scheme and is shown
Address reprint requests to Dr. S. 0. Duffuaa at the Department of Systems Engineering, King Faud University of Petroleum and Minerals, Dhahran 31261, Saudia Arabia. *On Sabbatical from King Fahd University Minerals, Dhahran 31261, Saudi Arabia. Received 28 March January 1995
1994; revised
of Petroleum
22 December
Appl. Math. Modelling 1995, Vol. 19, September 0 1995 by Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010
1994; accepted
and 16
processes
in Figure I. Details about the process is given in Section 2.1 of the paper. In this paper, an optimization model has been developed for the production of MTBE. The model integrates the three reactors used for processing raw and processed material to obtain MTBE (see Figure 1). The model is a zero-one integer program and is of general nature and can easily be adapted for other processes that involve several reactors. The objective of the model is to maximize profit subject to settings selection, input-output, and environmental constraints. The model has resulted in substantial increase in company production. Flanigan et al.’ have developed a linear programming (LP) model for nitric acid production. They obtained their LP model by approximating nonlinear relationships by linear ones using linear regression. In Ref. 2, Boykin developed an economic optimization model for chemical production at Monsanto. The Boykin Model is for a single reactor and is used to select reactor settings that result in the minimum cost operating strategy for a given production target. In Ref. 3, Duffuaa developed an economic optimization model for urea and ammonia production at the Saudi Arabia Fertilizer Company. Again the model in Ref. 3 is for a single reactor. No model in the literature that integrates several reactors and incorporates environmental constraints exists. Such a model is needed since in general chemical production involves several reactors. The objective of this paper is to present a general profit maximization model integrating several reactors, then demonstrate the use of the mode1 in optimizing the production of MTBE. The rest of the paper is organized as follows: Section 2 presents the production process for MTBE and plant operation, Section 3 states the model 0307-904x/95/$10.00 SSDI 0307-904X(95)00016-D
Chemical production
at Ibn Zahr: S. 0. Duffuaa DEHYDROGENERATION
UNIT ISOBIJTYLENE
I
pF!zzq
ISOBUTANE
METHANOL
ISOBUTANE . * BUTAh4ER
MIXED BUTANE
. UNIT m
DEISOBuTi +&J
RECYCLED
Figure
1.
Hydrocarbon flow diagram.
for the case of several reactors, Section 4 presents results and analysis for MTBE, and Section 5 concludes the paper.
2. Plant operation The development of “clean fuels” began 15-20 years ago, when environmentalists began to draw attention to the negative effect of lead-based gasoline additives. In order to improve gasoline characteristics, lead alkyls, such as tetra ethyl lead (TEL) and tetra methyl lead (TML), were blended with gasoline. These additives raise the octane number, which is a reference number indicating antiknock properties of a fuel. Unfortunately, the well known harmful properties of lead compounds was having some disturbing effects on the environment, particularly in cities. Methanol-based fuels were seen to offer the possibility of producing an additive that would give equivalent antiknock properties to those of TEL. One such product is MTBE. Realizing the potential market and the availability of raw material, Saudi Arabia decided to construct a plant for MTBE production. Saudi Arabian Basic Industry Corporation (SABIC) joined forces with the Finnish State Oil Corporation CNESTE, OY, ECOFUEL, an affiliate of Italian National Oil Company (ENI), and the Arabian Petroleum Investment Company, APICORP, to form the Saudi European Petrochemical Company, known as Ibn Zahr. The company is established in 1984 and its annual production capacity is 500,000 tons of MTBE mainly marketed outside Saudi Arabia.4 2.1 Plant units and process description The plant has four units. These units are the deisobutanizer, the butamer, the dehydrogeneration, and the MTBE. The purpose of the deisobutanizer is to prepare the feed stock for the butamer unit. In this unit, mixed butane received by pipes is pumped to the main column via a coalescer, which is a type of a mixer and a set of dryers. The main column has 120 trays and is used
532
Appl.
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Modelling,
ISOBUTANE
1995,
Vol. 19, September
to separate the pentane from normal butane. Then the butane goes through a dryer before passing to the butamer feed drum. The purpose of the butamer unit is to produce isobutane, which is used as a feedstock for the dehydrogeneration unit. Normal butane from the deisobutanizer unit flows from the feed drum to the charge heater and then to the reactor (referred to here in Figure I as the isobutane reactor). In the reactor the butane is isomerized to isobutane. The purpose of the dehydrogeneration unit is to partly convert the isobutane coming from the butamer unit into isobutylene. Then the isobutylene is fed to the MTBE unit. Between 45 and 50% of the total feed to the dehydrogeneration unit is converted to isobutylene. The total reactor feed is vaporized by a low pressure stream exchanger. It then passes to an exchanger where the feed is heated by reactor effluent. The feed is raised to the reaction temperature in the charge heater and sent to the reactor. The reactor converts isobutane to isobutylene over a catalyst. This reactor is referred to in Figure 1 as the isobutylene reactor. The purpose of the MTBE unit is to produce the motor gasoline component MTBE. The isobutylene from the dehydrogeneration unit is converted to MTBE by synthesis with methanol.4 The feed, isobutylene, passes through the ammonia removal tower and before entering the reactor is mixed with methanol. The reactor that produces MTBE is accomplished in this unit and is referred to in Figure I as the MTBE reactor. Each reactor can be operated at several settings. The set-up of a reactor is determined by the operating parameters of the reactor. Each of the three reactors has six settings. The parameters that determine the set-up are : 1. Raw materials feed rate; 2. Reactor pressure; 3. Reactor temperature. These three parameters level and cost of operation.
determine Actually
the production given the above
Chemical production three parameters, the production level is specified but the cost can be computed from the cost of raw material, the cost of labor, and the fuel cost. The methodology given in Ref. 3 is employed to compute the cost of each of the settings for the three reactors.
Having constructed the general model in order to use it for the production of MTBE as given in Figure I. The following data are needed.
3.1 Data neededfor The data needed
3. Model formulation The model will be developed for m reactors. The final product comes from reactor m. The production process of MTBE has three reactors as shown in Figure 1. Prior to the statement of the model the following notation is adopted: T Pij lij
Gij Ui Cij P
Production target of reactor m (final reactor) Production level of reactor i at setting j, i= 1,2,..., m,j= 1,2 ,..., n Required input for reactor i at settingj Gas by-product released from reactor i at settingj Pollution limit for reactor i Cost of setting reactor i at setting j Price of final product
Rij
1
if reactor
0
otherwise
i operated
The objective of the model which can be stated as: Max P * T -
f
i
at settingj
is to maximize
profit,
C,R,,
are the constraints
Max P * T -
5 i i=l
each with n settings
CijRij
j=l
subject i
to J’,jR,j
for the model are the following:
Number of settings of each reactor, Feed rate of raw material at each setting, Temperature at each setting, Pressure at each setting, Production level at each setting, Cost of operating at each setting, Pollution release at each setting and set pollution for each reactor, and 8. MTBE price.
3.2 Reactors
2 T
setting
Each of the three reactors has six settings. As an example, currently the isobutane reactor is operated at set-up #4. This set-up has the following specifications: (a) (b) (c) (d) (e)
Raw material feed rate (ton hr) is 70 tons of butane, Reactor temperature is 168°C Reactor pressure is 26 kg/cm2, Production level is 68.05 ton/hr, and The cost of set-up 4 is 23,797 SR/hr (SR is Saudi Riyals, 3.75 SR = 1 U.S. dollar)
The cost of a set-up is computed as the sum of raw material, labor, and fuel costs. The cost of butane is 324 SR/ton, the labor cost is 200 SR/hr, and the fuel cost is 917 SR/hr. Therefore the cost of set-up 4 is: C,,
= 324(70) + 200 + 917 = 23,797
Similarly the costs of other settings are computed. The different settings with their corresponding parameters are given in Table 1 for the isobutane reactor. Tables 2 and 3 provide the same data for the isobutylene and the MTBE reactors, respectively. The price of MTBE is 1332 SR/ton and the pollution limit imposed on gas biproduct is 0.665 hr. Using Tables 1-3 and the data about MTBE price and the set pollution limit, the complete statement of the model for the process given in Figure I is given as follows: Maximize
j=l
1332T - 25813R,, i
Pi-
I,jRi-
I,j
-
j$l
IijRij
2
0
j=l i
CijRij I Ui
j=l
i
limit
of the model:
The output of reactor i must meet the input to reactor i + 1. Reactor i feeds reactor i + 1, The selected set-up must satisfy the required pollution limit, One reactor set-up must be selected for each reactor, and The selected set-up for the last reactor must produce a level 7: A general model for m reactors, _ ^._ can be stated as tallows:
the model
1. 2. 3. 4. 5. 6. 7.
i=lj=1
The following
at Ibn Zahr: S. 0. Duffuaa
Rij = 1
j=l
Appl.
Math.
- 26123R,,
- 26461R,,
- 26857R,,
- 27397R3,, - 26173R,,
- 33747R,,
- 33866R,,
- 35284R,,
- 35006R2,
- 34725R,,
- 33399R,,
- 22825R,,
- 23149R,,
- 23473R,,
-23797R,,
- 24121R,,
- 24769R,,
Modelling,
1995,
Vol. 19, September
533
Chemical production Table
1.
ar Ibn Zahr: S. 0. Duffuaa
Operating
parameters
of the Ibn Zahr isobutane Set-up #2
Set-up #3
Set-up #4
Set-up #5
Set-up #6
67 0.009 0.065 164 26.0
68 0.0092 0.067 165 26.0
69 0.009 0.069 166 26.0
70 0.009 0.07 168 26.0
71 0.009 0.075 170 26.0
72 0.009 0.066 169 26.0
66.2
67.08
67.07
68.05
69.4
71.7
Set-up #I
Parameters 1. Raw material Feed rate (ton/hr) Butane Carbon-teterachloride HZ 2. Reactor temp. “C 3. Reactor pressure
reactor.
(kg/cm2)
4. Production of reactor (isobutane) (ton/hr) 5. Gas byproduct (ton/hr) Hydrogen 60% Methane 18% 12% Ethane Propane 6% Butane 4% 6. Liquid byproduct (ton/hr) Butane 10% Pentane 90% 7. Cost of reactor (Whr)
Subject
0.4 0.24 0.072 0.048 0.024 0.016
0.42 0.252 0.0756 0.0504 0.0252 0.0168
0.43 0.258 0.0774 0.0516 0.0258 0.0172
0.45 0.27 0.081 0.034 0.027 0.018
0.6 0.36 0.168 0.072 0.036 0.024
0.5 0.3 0.09 0.06 0.03 0.02
0.4 0.04 0.36
0.5 0.05 0.45
0.6 0.06 0.54
0.7 0.07 0.73
1 0.1 0.9
0.8 0.08 0.72
23,149
22,825
to
57.8R,,
+ 59.1R,,
+ 62R,,
- 36R,,
+ 60R,,
+ 61R,,
2 T
- 37SR,,
- 38R,, + 42.34Y,,
+ 40.55R,,
- 38.5R,,
- 39R,,
+ 40.23R,,
+ 39.62R,,
+ 42.75R,,
+ 33.89R,,
2 0
- 4%6R3,, - 44.2R,,
- 47.OR,,
- 44.8R3,, - 37.9R,,
- 37.6R,,
+ 66.2R,,
+ 67.08R,,
+ 67.07R,,
0.4R,,
+ 68.05R,, 2 0
+ 0.42R,,
+ 0.43R13 + 0.45,,R
+ 0.395R,,
+ 0.3R,,
+ 0.42R,, + 0.37R,,
+ 0.4R,,
+ 0.66R,,
+ 0.42R,,
+ 0.5R,,
+ 0.6R,,
I 0.665
i- R,,
+ R,,
+ R,,
+ R,,
+ R,,
= 1
R,,
+ R,,
+ R,,
+ R,,
+ R,,
+ R,,
= 1
R,,
+ R,,
+ R,,
+ R,,
+ R,,
+ R,,
= 1
Appl.
24,121
24,769
Math.
i = 1, 2, 3,
Modelling,
Using Tables 1-3, the model just given is obtained. The resulting model is solved using the software LINDO (Linear Interactive and Discrete Optimizer) a software marketed by Scientific Press.’ The model is solved and the optimal solution together with the current operation policy is given in Table 4. The table provides the settings for the isobutane, isobutylene, and MTBE reactors and the production levels at each setting. The current operation policy is derived using a production target of 60 tons of MTBE and then uses experience to set the other two reactors. It is evident from the solution in Table 4 that the model provides a systematic approach for process optimization. The optimal solution of the model resulted in an increase in MTBE level of production by 3.3%. Also systematic sensitivity analysis of the production target has been performed and the obtained model settings are stable.
I 0.665
R,,
Rij = 0 or 1,
534
+ 0.6R,,
< 0.665
+ 0.33R,, 0.2R,,
+ 69.40R15
+ 71.7R,,
+ 0.5R,, 0.53R,,
23,797
4. Results and analysis + 58.4R,,
- 37R,,
23,473
1995,
j=l,2,...,6
Vol. 19, September
5. Conclusion The production process of MTBE has been studied, and a general model for reactors setting selection has been developed. The model is of a general nature and can be easily adapted to other chemical processes. The model is used to optimize the production of MTBE at Ibn Zahr. The results of the model are compared with current reactor, settings and the model offers a systematic
Chemical production at Ibn Zahr: S. 0. Duffuaa Table 2.
Operating
parameters of the Ibn Zahr isobutylene Set-up #l
Parameters 1. Raw material Feed rate (ton/hr) isobutane 2. Reactor temp. “C 3. Reactor pressure (kg/cm*) 4. Production of reactor (isobutylene) (ton/hr) 5. Gas byproduct (ton/hr) Hydrogen 80% Methane 8% Ethane 7% Propane 3% Pentane 2% 6. lsobutane (ton/hr) 7. Reactor cost (SR/hr)
Table 3.
Set-up #2
82.4 645 30
Set-up #3
82.7 640 30
42.34
33,747
33,866
33.89
0.33 0.26 0.26 0.0231 0.0099 0.0066
0.37 0.294 0.294 0.0257 0.011 0.0073
47.0
40.80
35,284
81.50 632 30
39.62
0.42 0.338 0.338 0.0295 0.0127 0.0084
39.3
Set-up #6
84.9 633 30
40.55
0.42 0.338 0.338 0.0296 0.0127 0.0085
38.50
Set- up #5
85.6 645 30
42.75
0.395 0.316 0.316 0.0217 0.0119 0.0079
34.8
Set-up #4
86.3 647 30
40.23
0.53 0.424 0.424 0.037 0.0159 0.0106
Operating
reactor.
35,006
43.90
34,725
33,399
parameters of the Ibn Zahr reactor (MTBE).
Parameters 1. Raw material feed rate (ton/hr) Methanol lsobutylene lsobutane Reactor temp. “C Reactor pressure (kg/cm*) Production of reactor (MTBE) (ton/hr) Gas byproduct (ton/hr) TBE 50% MBE 50% 6. lsobutane (ton/hr) 7. Reactor cost (SR/hr)
Set-up #l
Set-up #2
Set-up #3
Set-up #4
Set-up #5
Set-up #6
21 37 34.8 65 16
21.2 37.5 38.5 66 16
21.5 38 39.3 67 16
22 38.5 40.8 68 16
23 39 48.6 70 16
24 36 44.0 71 16
57.8
58.4
59.1
60
61
62
0.2 0.1 0.1
0.4 0.2 0.2
0.5 0.25 0.25
0.66 0.33 0.33
38.9
39.3
40.8
48.6
41 .o
25,813
26,123
26,461
26,857
27,397
26,173
TBE = tert-butyle-ether;
and MBE = methyle-butyle-ether.
Model optimal settings and current settings. Model optimal settings and production
Current settings and production Reader product lsobutane lsobutylene MTBE
0.6 0.3 0.3
34.8
MTBE = methyle-tert-butyle-ether;
Table 4.
0.3 0.19 0.19
Setting
Production
Setting
Production
Set-up #4 Set-up #5 Set-up #4
68.05 40.55 60
Set-up # 1 Set-up # 1 Set-up #6
66.2 43.34 62
Appl.
Math.
Modelling,
1995,
Vol. 19, September
535
Chemical
production
at Ibn Zahr: S. 0. Duffuaa
approach for setting the reactors involved in the MTBE production. In addition, MTBE production is increased by 3.3%.
References
Acknowledgment
2
The author would like to acknowledge the support provided by King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, for conducting this research. Also, thanks to one referee whose comments improved an earlier version of the paper.
3
536
Appl.
Math.
Modelling,
1995,
Vol. 19, September
1
4 5
Flanigan, O., Wilson, W. W. and Sale, D. R. Process-cost reduction through linear programming. Chem. Eng. 1972, 79, 6G73 Boykin, R. F. Optimizing chemical nroduction at Monsanto. rnterf~ces 1985, l$l), 88-9-5 Dufluaa, S. A mathematical optimization model for chemical production at Saudi Arabian Fertilizer Company. Appl. Math. Model&g 1991, 15, 652-656 Ibn-Zahr Company. Al-Nasser Press, Saudi Arabia, 1986 Schrage, L. Linear, integer and quadratic programming with Lindo, 3rd edition. The Scientific Press, 1986
Department,
University of Michigan,
Ann Arbor, MI, USA
In this paper a mathematical optimization model is developedfor several reactors settings. The model integrates several reactors and is stated in a generalform. The model selects the settings for the reactors that maximizes profit subject to operation, selection and environmental constraints. Each setting is determined by a set of operating parameters, which are feed rate, reactor temperature and pressure. The production level and the cost of each setting is determined from the operating parameter and the raw material, labor and fuel cost. It is used to optimize Methyl-Tert-Butyle Ether (MTBE) production at the Ibn Zahr Company in Saudi Arabia. The results in the Ibn Zahr case are consistent and elevated MTBE production. Keywords:
optimization,
operational
research,
chemical
1. Introduction In chemical production reactors settings play a key role. The settings are determined by selecting appropriate input variables, such as temperature, pressure, and raw material feed rate. The levels of input variables affect the quality and quantity of products. For some chemicals, such as methyl-tert-butyl ether (MTBE), their production involves processing material through several reactors. The process of producing MTBE at Ibn Zahr (the company used in this study) has three phases. In the first phase, mixed butane is pumped through a Deisobutanizer to separate pentane from normal butane. Then the butane is dried and passed through the isobutane reactor which is a part of the butamer unit. In this reactor, butane is isomerized to isobutane. In the second phase, isobutane is heated and sent to the isobutylene reactor, which is a part of a dehydrogeneration unit. The reactor in this unit converts isobutane to isobutylene over a catalyst. Then in the third phase the isobutylene is fed to the MTBE unit. In this unit, the isobutylene passes through an ammonia removal tower and prior to entering the MTBE reactor is mixed with methanol. In this reactor isobutylene is converted to MTBE by synthesis with methanol.4 The whole process is known as the hydrocarbon flow scheme and is shown
Address reprint requests to Dr. S. 0. Duffuaa at the Department of Systems Engineering, King Faud University of Petroleum and Minerals, Dhahran 31261, Saudia Arabia. *On Sabbatical from King Fahd University Minerals, Dhahran 31261, Saudi Arabia. Received 28 March January 1995
1994; revised
of Petroleum
22 December
Appl. Math. Modelling 1995, Vol. 19, September 0 1995 by Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010
1994; accepted
and 16
processes
in Figure I. Details about the process is given in Section 2.1 of the paper. In this paper, an optimization model has been developed for the production of MTBE. The model integrates the three reactors used for processing raw and processed material to obtain MTBE (see Figure 1). The model is a zero-one integer program and is of general nature and can easily be adapted for other processes that involve several reactors. The objective of the model is to maximize profit subject to settings selection, input-output, and environmental constraints. The model has resulted in substantial increase in company production. Flanigan et al.’ have developed a linear programming (LP) model for nitric acid production. They obtained their LP model by approximating nonlinear relationships by linear ones using linear regression. In Ref. 2, Boykin developed an economic optimization model for chemical production at Monsanto. The Boykin Model is for a single reactor and is used to select reactor settings that result in the minimum cost operating strategy for a given production target. In Ref. 3, Duffuaa developed an economic optimization model for urea and ammonia production at the Saudi Arabia Fertilizer Company. Again the model in Ref. 3 is for a single reactor. No model in the literature that integrates several reactors and incorporates environmental constraints exists. Such a model is needed since in general chemical production involves several reactors. The objective of this paper is to present a general profit maximization model integrating several reactors, then demonstrate the use of the mode1 in optimizing the production of MTBE. The rest of the paper is organized as follows: Section 2 presents the production process for MTBE and plant operation, Section 3 states the model 0307-904x/95/$10.00 SSDI 0307-904X(95)00016-D
Chemical production
at Ibn Zahr: S. 0. Duffuaa DEHYDROGENERATION
UNIT ISOBIJTYLENE
I
pF!zzq
ISOBUTANE
METHANOL
ISOBUTANE . * BUTAh4ER
MIXED BUTANE
. UNIT m
DEISOBuTi +&J
RECYCLED
Figure
1.
Hydrocarbon flow diagram.
for the case of several reactors, Section 4 presents results and analysis for MTBE, and Section 5 concludes the paper.
2. Plant operation The development of “clean fuels” began 15-20 years ago, when environmentalists began to draw attention to the negative effect of lead-based gasoline additives. In order to improve gasoline characteristics, lead alkyls, such as tetra ethyl lead (TEL) and tetra methyl lead (TML), were blended with gasoline. These additives raise the octane number, which is a reference number indicating antiknock properties of a fuel. Unfortunately, the well known harmful properties of lead compounds was having some disturbing effects on the environment, particularly in cities. Methanol-based fuels were seen to offer the possibility of producing an additive that would give equivalent antiknock properties to those of TEL. One such product is MTBE. Realizing the potential market and the availability of raw material, Saudi Arabia decided to construct a plant for MTBE production. Saudi Arabian Basic Industry Corporation (SABIC) joined forces with the Finnish State Oil Corporation CNESTE, OY, ECOFUEL, an affiliate of Italian National Oil Company (ENI), and the Arabian Petroleum Investment Company, APICORP, to form the Saudi European Petrochemical Company, known as Ibn Zahr. The company is established in 1984 and its annual production capacity is 500,000 tons of MTBE mainly marketed outside Saudi Arabia.4 2.1 Plant units and process description The plant has four units. These units are the deisobutanizer, the butamer, the dehydrogeneration, and the MTBE. The purpose of the deisobutanizer is to prepare the feed stock for the butamer unit. In this unit, mixed butane received by pipes is pumped to the main column via a coalescer, which is a type of a mixer and a set of dryers. The main column has 120 trays and is used
532
Appl.
Math.
Modelling,
ISOBUTANE
1995,
Vol. 19, September
to separate the pentane from normal butane. Then the butane goes through a dryer before passing to the butamer feed drum. The purpose of the butamer unit is to produce isobutane, which is used as a feedstock for the dehydrogeneration unit. Normal butane from the deisobutanizer unit flows from the feed drum to the charge heater and then to the reactor (referred to here in Figure I as the isobutane reactor). In the reactor the butane is isomerized to isobutane. The purpose of the dehydrogeneration unit is to partly convert the isobutane coming from the butamer unit into isobutylene. Then the isobutylene is fed to the MTBE unit. Between 45 and 50% of the total feed to the dehydrogeneration unit is converted to isobutylene. The total reactor feed is vaporized by a low pressure stream exchanger. It then passes to an exchanger where the feed is heated by reactor effluent. The feed is raised to the reaction temperature in the charge heater and sent to the reactor. The reactor converts isobutane to isobutylene over a catalyst. This reactor is referred to in Figure 1 as the isobutylene reactor. The purpose of the MTBE unit is to produce the motor gasoline component MTBE. The isobutylene from the dehydrogeneration unit is converted to MTBE by synthesis with methanol.4 The feed, isobutylene, passes through the ammonia removal tower and before entering the reactor is mixed with methanol. The reactor that produces MTBE is accomplished in this unit and is referred to in Figure I as the MTBE reactor. Each reactor can be operated at several settings. The set-up of a reactor is determined by the operating parameters of the reactor. Each of the three reactors has six settings. The parameters that determine the set-up are : 1. Raw materials feed rate; 2. Reactor pressure; 3. Reactor temperature. These three parameters level and cost of operation.
determine Actually
the production given the above
Chemical production three parameters, the production level is specified but the cost can be computed from the cost of raw material, the cost of labor, and the fuel cost. The methodology given in Ref. 3 is employed to compute the cost of each of the settings for the three reactors.
Having constructed the general model in order to use it for the production of MTBE as given in Figure I. The following data are needed.
3.1 Data neededfor The data needed
3. Model formulation The model will be developed for m reactors. The final product comes from reactor m. The production process of MTBE has three reactors as shown in Figure 1. Prior to the statement of the model the following notation is adopted: T Pij lij
Gij Ui Cij P
Production target of reactor m (final reactor) Production level of reactor i at setting j, i= 1,2,..., m,j= 1,2 ,..., n Required input for reactor i at settingj Gas by-product released from reactor i at settingj Pollution limit for reactor i Cost of setting reactor i at setting j Price of final product
Rij
1
if reactor
0
otherwise
i operated
The objective of the model which can be stated as: Max P * T -
f
i
at settingj
is to maximize
profit,
C,R,,
are the constraints
Max P * T -
5 i i=l
each with n settings
CijRij
j=l
subject i
to J’,jR,j
for the model are the following:
Number of settings of each reactor, Feed rate of raw material at each setting, Temperature at each setting, Pressure at each setting, Production level at each setting, Cost of operating at each setting, Pollution release at each setting and set pollution for each reactor, and 8. MTBE price.
3.2 Reactors
2 T
setting
Each of the three reactors has six settings. As an example, currently the isobutane reactor is operated at set-up #4. This set-up has the following specifications: (a) (b) (c) (d) (e)
Raw material feed rate (ton hr) is 70 tons of butane, Reactor temperature is 168°C Reactor pressure is 26 kg/cm2, Production level is 68.05 ton/hr, and The cost of set-up 4 is 23,797 SR/hr (SR is Saudi Riyals, 3.75 SR = 1 U.S. dollar)
The cost of a set-up is computed as the sum of raw material, labor, and fuel costs. The cost of butane is 324 SR/ton, the labor cost is 200 SR/hr, and the fuel cost is 917 SR/hr. Therefore the cost of set-up 4 is: C,,
= 324(70) + 200 + 917 = 23,797
Similarly the costs of other settings are computed. The different settings with their corresponding parameters are given in Table 1 for the isobutane reactor. Tables 2 and 3 provide the same data for the isobutylene and the MTBE reactors, respectively. The price of MTBE is 1332 SR/ton and the pollution limit imposed on gas biproduct is 0.665 hr. Using Tables 1-3 and the data about MTBE price and the set pollution limit, the complete statement of the model for the process given in Figure I is given as follows: Maximize
j=l
1332T - 25813R,, i
Pi-
I,jRi-
I,j
-
j$l
IijRij
2
0
j=l i
CijRij I Ui
j=l
i
limit
of the model:
The output of reactor i must meet the input to reactor i + 1. Reactor i feeds reactor i + 1, The selected set-up must satisfy the required pollution limit, One reactor set-up must be selected for each reactor, and The selected set-up for the last reactor must produce a level 7: A general model for m reactors, _ ^._ can be stated as tallows:
the model
1. 2. 3. 4. 5. 6. 7.
i=lj=1
The following
at Ibn Zahr: S. 0. Duffuaa
Rij = 1
j=l
Appl.
Math.
- 26123R,,
- 26461R,,
- 26857R,,
- 27397R3,, - 26173R,,
- 33747R,,
- 33866R,,
- 35284R,,
- 35006R2,
- 34725R,,
- 33399R,,
- 22825R,,
- 23149R,,
- 23473R,,
-23797R,,
- 24121R,,
- 24769R,,
Modelling,
1995,
Vol. 19, September
533
Chemical production Table
1.
ar Ibn Zahr: S. 0. Duffuaa
Operating
parameters
of the Ibn Zahr isobutane Set-up #2
Set-up #3
Set-up #4
Set-up #5
Set-up #6
67 0.009 0.065 164 26.0
68 0.0092 0.067 165 26.0
69 0.009 0.069 166 26.0
70 0.009 0.07 168 26.0
71 0.009 0.075 170 26.0
72 0.009 0.066 169 26.0
66.2
67.08
67.07
68.05
69.4
71.7
Set-up #I
Parameters 1. Raw material Feed rate (ton/hr) Butane Carbon-teterachloride HZ 2. Reactor temp. “C 3. Reactor pressure
reactor.
(kg/cm2)
4. Production of reactor (isobutane) (ton/hr) 5. Gas byproduct (ton/hr) Hydrogen 60% Methane 18% 12% Ethane Propane 6% Butane 4% 6. Liquid byproduct (ton/hr) Butane 10% Pentane 90% 7. Cost of reactor (Whr)
Subject
0.4 0.24 0.072 0.048 0.024 0.016
0.42 0.252 0.0756 0.0504 0.0252 0.0168
0.43 0.258 0.0774 0.0516 0.0258 0.0172
0.45 0.27 0.081 0.034 0.027 0.018
0.6 0.36 0.168 0.072 0.036 0.024
0.5 0.3 0.09 0.06 0.03 0.02
0.4 0.04 0.36
0.5 0.05 0.45
0.6 0.06 0.54
0.7 0.07 0.73
1 0.1 0.9
0.8 0.08 0.72
23,149
22,825
to
57.8R,,
+ 59.1R,,
+ 62R,,
- 36R,,
+ 60R,,
+ 61R,,
2 T
- 37SR,,
- 38R,, + 42.34Y,,
+ 40.55R,,
- 38.5R,,
- 39R,,
+ 40.23R,,
+ 39.62R,,
+ 42.75R,,
+ 33.89R,,
2 0
- 4%6R3,, - 44.2R,,
- 47.OR,,
- 44.8R3,, - 37.9R,,
- 37.6R,,
+ 66.2R,,
+ 67.08R,,
+ 67.07R,,
0.4R,,
+ 68.05R,, 2 0
+ 0.42R,,
+ 0.43R13 + 0.45,,R
+ 0.395R,,
+ 0.3R,,
+ 0.42R,, + 0.37R,,
+ 0.4R,,
+ 0.66R,,
+ 0.42R,,
+ 0.5R,,
+ 0.6R,,
I 0.665
i- R,,
+ R,,
+ R,,
+ R,,
+ R,,
= 1
R,,
+ R,,
+ R,,
+ R,,
+ R,,
+ R,,
= 1
R,,
+ R,,
+ R,,
+ R,,
+ R,,
+ R,,
= 1
Appl.
24,121
24,769
Math.
i = 1, 2, 3,
Modelling,
Using Tables 1-3, the model just given is obtained. The resulting model is solved using the software LINDO (Linear Interactive and Discrete Optimizer) a software marketed by Scientific Press.’ The model is solved and the optimal solution together with the current operation policy is given in Table 4. The table provides the settings for the isobutane, isobutylene, and MTBE reactors and the production levels at each setting. The current operation policy is derived using a production target of 60 tons of MTBE and then uses experience to set the other two reactors. It is evident from the solution in Table 4 that the model provides a systematic approach for process optimization. The optimal solution of the model resulted in an increase in MTBE level of production by 3.3%. Also systematic sensitivity analysis of the production target has been performed and the obtained model settings are stable.
I 0.665
R,,
Rij = 0 or 1,
534
+ 0.6R,,
< 0.665
+ 0.33R,, 0.2R,,
+ 69.40R15
+ 71.7R,,
+ 0.5R,, 0.53R,,
23,797
4. Results and analysis + 58.4R,,
- 37R,,
23,473
1995,
j=l,2,...,6
Vol. 19, September
5. Conclusion The production process of MTBE has been studied, and a general model for reactors setting selection has been developed. The model is of a general nature and can be easily adapted to other chemical processes. The model is used to optimize the production of MTBE at Ibn Zahr. The results of the model are compared with current reactor, settings and the model offers a systematic
Chemical production at Ibn Zahr: S. 0. Duffuaa Table 2.
Operating
parameters of the Ibn Zahr isobutylene Set-up #l
Parameters 1. Raw material Feed rate (ton/hr) isobutane 2. Reactor temp. “C 3. Reactor pressure (kg/cm*) 4. Production of reactor (isobutylene) (ton/hr) 5. Gas byproduct (ton/hr) Hydrogen 80% Methane 8% Ethane 7% Propane 3% Pentane 2% 6. lsobutane (ton/hr) 7. Reactor cost (SR/hr)
Table 3.
Set-up #2
82.4 645 30
Set-up #3
82.7 640 30
42.34
33,747
33,866
33.89
0.33 0.26 0.26 0.0231 0.0099 0.0066
0.37 0.294 0.294 0.0257 0.011 0.0073
47.0
40.80
35,284
81.50 632 30
39.62
0.42 0.338 0.338 0.0295 0.0127 0.0084
39.3
Set-up #6
84.9 633 30
40.55
0.42 0.338 0.338 0.0296 0.0127 0.0085
38.50
Set- up #5
85.6 645 30
42.75
0.395 0.316 0.316 0.0217 0.0119 0.0079
34.8
Set-up #4
86.3 647 30
40.23
0.53 0.424 0.424 0.037 0.0159 0.0106
Operating
reactor.
35,006
43.90
34,725
33,399
parameters of the Ibn Zahr reactor (MTBE).
Parameters 1. Raw material feed rate (ton/hr) Methanol lsobutylene lsobutane Reactor temp. “C Reactor pressure (kg/cm*) Production of reactor (MTBE) (ton/hr) Gas byproduct (ton/hr) TBE 50% MBE 50% 6. lsobutane (ton/hr) 7. Reactor cost (SR/hr)
Set-up #l
Set-up #2
Set-up #3
Set-up #4
Set-up #5
Set-up #6
21 37 34.8 65 16
21.2 37.5 38.5 66 16
21.5 38 39.3 67 16
22 38.5 40.8 68 16
23 39 48.6 70 16
24 36 44.0 71 16
57.8
58.4
59.1
60
61
62
0.2 0.1 0.1
0.4 0.2 0.2
0.5 0.25 0.25
0.66 0.33 0.33
38.9
39.3
40.8
48.6
41 .o
25,813
26,123
26,461
26,857
27,397
26,173
TBE = tert-butyle-ether;
and MBE = methyle-butyle-ether.
Model optimal settings and current settings. Model optimal settings and production
Current settings and production Reader product lsobutane lsobutylene MTBE
0.6 0.3 0.3
34.8
MTBE = methyle-tert-butyle-ether;
Table 4.
0.3 0.19 0.19
Setting
Production
Setting
Production
Set-up #4 Set-up #5 Set-up #4
68.05 40.55 60
Set-up # 1 Set-up # 1 Set-up #6
66.2 43.34 62
Appl.
Math.
Modelling,
1995,
Vol. 19, September
535
Chemical
production
at Ibn Zahr: S. 0. Duffuaa
approach for setting the reactors involved in the MTBE production. In addition, MTBE production is increased by 3.3%.
References
Acknowledgment
2
The author would like to acknowledge the support provided by King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, for conducting this research. Also, thanks to one referee whose comments improved an earlier version of the paper.
3
536
Appl.
Math.
Modelling,
1995,
Vol. 19, September
1
4 5
Flanigan, O., Wilson, W. W. and Sale, D. R. Process-cost reduction through linear programming. Chem. Eng. 1972, 79, 6G73 Boykin, R. F. Optimizing chemical nroduction at Monsanto. rnterf~ces 1985, l$l), 88-9-5 Dufluaa, S. A mathematical optimization model for chemical production at Saudi Arabian Fertilizer Company. Appl. Math. Model&g 1991, 15, 652-656 Ibn-Zahr Company. Al-Nasser Press, Saudi Arabia, 1986 Schrage, L. Linear, integer and quadratic programming with Lindo, 3rd edition. The Scientific Press, 1986