- Email: [email protected]
Optimal operation of a pyrolysis reactor
Krist V. Gernaey, Jakob K. Huusom and Rafiqul Gani (Eds.), 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering. 31 May – 4 June 2015, Copenhagen, Denmark © 2015 Elsevier B.V. All rights reserved.
Optimal operation of a pyrolysis reactor Aysar T. Jarullaha, Shemaa A. Hameeda, Zina A. Hameeda, and I.M. Mujtabab* a
Chemical Engineering Department, College of Engineering, Tikrit University, IRAQ *School of Engineering, Design and Technology, University of Bradford, Bradford BD7 1DP, UK, E-mail: [email protected]
b
Abstract In the present study, the problem of optimization of thermal cracker (pyrolysis) operation is discussed. The main objective in thermal cracker optimization is the estimation of the optimal flow rates of different feeds (such as, Gas-oil, Propane, Ethane and Debutanized natural gasoline) to the cracking furnace under the restriction on ethylene and propylene production. Thousands of combinations of feeds are possible. Hence the optimization needs an efficient strategy in searching for the global minimum. The optimization problem consists of maximizing the economic profit subject to a number of equality and inequality constraints. Modelling, simulation and optimal operation via optimization of the thermal cracking reactor has been carried out by gPROMS (general PROcess Modelling System) software. The optimization problem is posed as a Non-Linear Programming problem and using a Successive Quadratic Programming (SQP) method for solving constrained nonlinear optimization problem with high accuracy within gPROMS software. New results have been obtained for the control variables and optimal cost of the cracker in comparison with previous studies. Keywords: Thermal Cracking, Mathematical Modeling, Olefins Pyrolysis, SQP.
1. Introduction Hydrocarbon thermal cracking is the most significant operation in the production of olefins. Recently, the worldwide olefins production (mainly ethylene) increases rapidly (around 180 billion lb/yr), and is regarded one of the most important issues for chemical industries where improving its production operation can bring several benefits. Thus, the market demand for olefins production has accelerated the improvement of a more rigorous and reliable thermal cracking model of such process. Its annual industrial production depends on the thermal cracking (pyrolysis) of oil hydrocarbons, where the heart of the process with a massive economic effect is the reactor of the cracking process. Cracking of heavier fuel oils is done to produce mainly high quality (octane number) petrol, olefins (feed for petrochemical industry), coke (by coking) and to reduce the viscosity of fuel oil by visbreaking (Masoumi et al., 2006a, Babu and Angira, 2001). The main parameter of the optimal design of such reactor is the accurate prediction of yield and reactor performance. Each reactant is known to produce a certain distribution of products. When multiple reactants are employed, it is desirable to optimize the amounts of each reactant so that the products satisfy flow and demand constraints. Control systems are designed for achieving several goals, involving product quality, safety, and minimum cost (Masoumi et al., 2006b, Edgar and Himmelblau, 2001). The feed of a thermal cracking furnace can be a variety of components (such as ethane, propane, butane, isobutane, naphtha, and gas oil) and the main factor influencing the product is the feed composition (Lee and Aitani, 1990). The optimal design and operation strategy and purchase decisions for raw materials have become
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main issues in the olefin industries (Joo and Park, 2001). It is extremely difficult to obtain the detailed operation factors in the reactor from direct measurements owing to the limitation of current techniques. Thus, mathematical simulation, as an alternative, has become a powerful tool for predicting control variable distributions and olefin yields. The thermal cracking reactor is the key parameters affecting the economics of the process and the olefin yields (Lan et al., 2007). The main focus in this study is to find the optimal design of pyrolysis reactor (thermal cracker) and objective function of the process (which is the estimation of optimal flow rates of different feeds to the cracking furnace) subject to a number of equality and inequality constraints using an alternative approach to describe the reactor operating conditions as accurately as possible. The optimization problem is posed as a Non-Linear Programming problem and is solved by employing a Successive Quadratic Programming (SQP) method (which is considered to be one of the most promising approaches for solving constrained nonlinear optimization problem in addition to its successful application to many engineering optimization problems) with high accuracy within gPROMS (general PROcess Modelling System) software.
2. Problem Description The problem presented by Edgar and Himmelblau, (2001) is to obtain the maximum profit of the process, while operating within the reactor and down stream process equipment constraints. Figure 1 shows various feeds and corresponding product distribution for a thermal cracker that produces olefins. The variables to be optimized are the amounts of the four feeds (mainly, Gas-oil, Propane, Ethane and Debutanized natural gasoline (DNG)). This problem will be solved utilizing SQP method within gPROMS package. DNG
Gas Oil
Propane
Ethane
Thermal Cracker
Fuel
Propane
Ethane
Methane
Fuel Oil
Ethylene
Propylene
Butadiene
Gasoline
Figure 1: Pyrolysis Reactor
3. Mathematical Model of the Pyrolysis Reactor Table 1 shows various feeds and the corresponding product distribution for a Pyrolysis reactor that produces olefins (Edgar and Himmelblau, 2001). The possible feeds include ethane, propane, debutanized natural gasoline (DNG), and gas oil, some of which may be fed simultaneously. Based on plant data, eight products are produced in varying proportions according to the following matrix. The capacity to run gas feeds through the cracker is 200,000 Ib/stream hour (total flow based on an average mixture). Ethane uses the equivalent of 1.1 Ib of capacity per pound of ethane; propane 0.9 Ib; gas oil 0.9 Ib/Ib; and DNG 1.0. Downstream processing limits exist of 50,000 Ib/stream hour on the ethylene and 20,000 Ib/ stream hour on the propylene. The fuel requirements to run the cracking system for each feedstock type are listed in Table 2. Methane and fuel oil
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produced by the cracker are recycled as fuel. All the ethane and propane produced is recycled as feed. Heating values are shown in Table 3 (Geddes and Kubera, 2000). Table 1: Yield Structure (wt. fraction) Product Methane Ethane Ethylene Propane Propylene Butadiene Gasoline Fuel oil
Ethane 0.07 0.40 0.50 0.01 0.01 0.01 -
Feed Propane 0.25 0.06 0.35 0.10 0.15 0.02 0.07 -
Gas oil 0.10 0.04 0.20 0.01 0.15 0.04 0.25 0.21
Table 2: Fuel Requirement Feedstock type Ethane Propane Gas oil DNG
DNG 0.15 0.05 0.25 0.01 0.18 0.05 0.30 0.01
Table 3: Heating Values
Fuel requirement (Btu/Ib) 8364 5016 3900 4553
Recycled feed Natural gas Methane Fuel oil
Heat produced (Btu/Ib) 21,520 21,520 18,000
Because of heat losses and the energy requirements for pyrolysis, the fixed fuel requirement is 20.0 × 106 Btu/stream hour and the energy (fuel) cost of $2.50/106 Btu. The price structure on the feeds and products and fuel costs is presented in Table 4 (Edgar and Himmelblau, 2001). Table 4: Feeds and Products Prices Feeds Ethane Propane Gas oil DNG
Price($/Ib) 0.0655 0.0973 0.1205 0.1014
Products Methane Ethane Propylene Butadiene Gasoline Fuel oil
Price($/Ib) 0.0538 (fuel value) 0.1775 0.1379 0.2664 0.0993 0.0450 (fuel value)
The following variables for the flow rates (input and output) of the reactor (in Ib/h) can be defined as: C1 = fresh ethane feed, C2 = fresh propane feed, C3 = gas oil feed, C4 = DNG feed, C5 = ethane recycle, C6 = propane recycle, C7 = fuel added. Objective function (profit). The objective function is the economic profit depending upon the difference between the value of the product and the value of feed and energy cost and all costs are calculated in cents/h. In other words, the profit ƒ is written as: ƒ = Product value – Feed cost – Energy cost Product value: Ethylene:ͳǤͷሺͲǤͷܥଵ ͲǤͷܥହ ͲǤ͵ͷܥଶ ͲǤ͵ͷ ܥ ͲǤʹͲܥଷ ͲǤʹͷܥସ ሻ ………(1) Propylene: ͳ͵ǤͻሺͲǤͲͳܥଵ ͲǤͲͳܥହ ͲǤͳͷܥଶ ͲǤͳͷ ܥ ͲǤͳͷܥଷ ͲǤͳͺܥସ ሻ ……… (2) Butadiene: ʹǤͶሺͲǤͲͳܥଵ ͲǤͲͳܥହ ͲǤͲʹܥଶ ͲǤͲʹ ܥ ͲǤͲͶܥଷ ͲǤͲͷܥସ ሻ ……… (3) Gasoline: ͻǤͻ͵ሺͲǤͲͳܥଵ ͲǤͲͳܥହ ͲǤͲܥଶ ͲǤͲ ܥ ͲǤʹͷܥଷ ͲǤ͵Ͳܥସሻ ……… (4) Total product sales ൌ ͻǤ͵ͻܥଵ ͻǤͷͳܥଶ ͻǤͳܥଷ ͳͳǤʹ͵ܥସ ͻǤ͵ͻܥହ ͻǤͷͳܥ ……… (5) Feed cost: Feed cost (cents/h)ൌ Ǥͷͷܥଵ ͻǤ͵ܥଶ ͳʹǤͷͲܥଷ ͳͲǤͳͶܥସ ……… (6) Energy cost: The fixed heat loss of 20×106 Btu/h can be expressed in terms of methane cost using a heating value of 21,520 Btu/Ib for methane. The fixed heat loss represents a constant cost that is independent of the variables Ci, hence in optimization this factor can be ignored, but in evaluating the final costs this term must be taken into account.
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The value for C7 depends on the amount of fuel oil and methane produced in the cracker (C7 provides for any deficit in products recycled as fuel). Equation (5) and (6) is combined to get the objective function, which is ƒ ൌ ʹǤͺͶܥଵ Ȃ ͲǤʹʹܥଶ Ȃ ͵Ǥ͵͵ܥଷ ͳǤͲͻܥସ ͻǤ͵ͻܥହ ͻǤͷͳܥ
………(7)
ܿݎܥൌ ͳǤͳܥଵ ͲǤͻܥଶ ͲǤͻܥଷ ͳǤͲܥସ ͳǤͳܥହ ͲǤͻ ܥ ʹͲͲǡͲͲͲ
………(8)
݄ݐܧൌ ͲǤͷܥଵ ͲǤ͵ͷܥଶ ͲǤʹͷܥଷ ͲǤʹͷܥସ ͲǤͷܥହ ͲǤ͵ͷ ܥ ͷͲǡͲͲͲ
……… (9)
Process limitations: 1- Cracker capacity of 200,000 Ib/h
2- Ethylene processing limitation of 50,000 Ib/h
3- Propylene processing limitation of 20,000 Ib/h
ܲ ݎൌ ͲǤͲͳܥଵ ͲǤͳͷܥଶ ͲǤͳͷܥଷ ͲǤͳͺܥସ ͲǤͲͳܥହ ͲǤͳͷ ܥ ʹͲǡͲͲͲ
……… (10)
ݎ݄ݐܧൌ ܥହ ൌ ͲǤͶܥଵ ͲǤͶܥହ ͲǤͲܥଶ ͲǤͲ ܥ ͲǤͲͶܥଷ ͲǤͲͷܥସ
……… (11)
ݎ݄ݐܧൌ ͲǤͶܥଵ ͲǤͲܥଶ ͲǤͲͶܥଷ ͲǤͲͷܥସ െ ͲǤܥହ ͲǤͲ ܥൌ Ͳ
……… (12)
ܲ ݎݎൌ ͲǤͳܥଶ ͲǤͲͳܥଷ ͲǤͲͳܥସ െ ͲǤͻ ܥൌ Ͳ
……… (13)
4- Ethane recycle
By rearranging equation (11), we get 5- Propane recycle
6- Heat constraint. The total fuel heating value (THV) in (Btu/h) is given by fuel
methane from cracker
fuel oil from cracker
ܶ ܸܪൌ ʹͳǡͷʹͲ ܥ ʹͳǡͷʹͲሺͲǤͲܥଵ ͲǤʹͷܥଶ ͲǤͳͲܥଷ ͲǤͳͷܥସ െ ͲǤͲܥହ ͲǤʹͷ ܥሻ ͳͺǡͲͲͲሺͲǤʹͳܥଷ ͲǤͲͳܥସ ሻ ൌ ͳͷͲǤͶܥଵ ͷ͵ͺͲܥଶ ͷͻ͵ʹܥଷ ͵ͶͲͺܥସ ͳͷͲǤͶܥହ ͷ͵ͺͲ ܥ ʹͳǡͷʹͲܥ ……… (14)
The required fuel for cracking (Btu/h) is ethane
propane
gas oil
DNG
ͺ͵Ͷሺܥଵ ܥହ ሻ ͷͲͳሺܥଶ ܥሻ ͵ͻͲͲܥଷ Ͷͷͷ͵ܥସ ൌ ͺ͵Ͷܥଵ ͷͲͳܥଶ ͵ͻͲͲܥଷ Ͷͷͷ͵ܥସ ………(15) ͺ͵Ͷܥହ ͷͲͳܥ Thus the sum of eq. (15) + 20,000,000 Btu/h is equal to the THV from eq. (14), which gives the constraint ܥܪൌ െͺͷǤܥଵ ͵Ͷܥଶ ʹͲ͵ʹܥଷ െ ͳͳͶͷܥସ െ ͺͷǤܥହ ͵Ͷ ܥ ʹͳǡͷʹͲ ܥൌ ʹͲǡͲͲͲǡͲͲͲ ..… (16)
3.1. Optimization Problem Formulation The optimal design problem is to obtain the optimal flow rate of different feeds giving maximum economic profits from the reactor operation corresponding to different constraints. Mathematically, the optimization problem can be stated as: Max f Ci (i=1 – 7) s.t y(x, u, q) = 0, (model, equality constraints) Ci L ≤ Ci ≤ Ci U , Crc ≤ Crc * , Eth ≤ Eth * (inequality constraints) Pro ≤ Pro * , Ethr = Ethr * , Pror = Pror*, Hc = Hc * (inequality constraints) The model equations can be written in compact form as: y(x, u, q) = 0, where x gives the set of all algebraic variables, u is the control variables, and q represents the design variables and the function y is assumed to be continuously differentiable with respect to all its arguments (Jarullah et al., 2011, Jarullah et al., 2012 ). L and U are the lower and upper bounds, respectively. The optimization solution method utilized by gPROMS is a two-steps method known as feasible path approach. The first step performs the simulation to converge all the equality constraints and to satisfy the inequality constraints. The second step performs the optimization (updates the values of the optimization parameters).
4. Results and Discussion The purpose of this study is to obtain the optimal design of thermal cracking reactor via optimal flow rates of different hydrocarbons feeds (namely, Gas-oil, Propane, Ethane and Debutanized natural gasoline) to get maximum profit. The modelling, simulation and optimization process has been carried out by using gPROMS software and the
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optimization problem based on a Non-Linear Programming (NLP) problem, which is solved using Successive Quadratic Programming (SQP) method. The optimal parameters obtained for two cases: case1 at maximum ethylene production of 50000 lb/hr and 100000 lb/hr for case2, are shown in Table 5. As noticed from the results presented in this Table that the maximum possible amount of ethylene is produced for both cases. Where, the optimal feed flow rate in lb/hr of ethane, ethane recycle and the fuel that should be added is 60000, 40000 and 32795.5 for case 1 and 109091, 72727.3 and 58867.9 for case 2, respectively with no feed of propane, gas oil, DNG and propane recycle for both cases. This means that the process depends mainly on the ethane (fresh feed as well as ethane recycle) in addition to the fuel. The maximum objective function (economic profit) is 5460 $/h for case 1 and 9927.28 $/h for case2 with satisfying all the inequality constraints. It has also been observed as the ethylene production constraint is relaxed, the objective function value increases. Once the constraint is raised above 90909.15 lb/hr, the objective function remains constant for whole process. Table 5: Optimization Results for Pyrolysis Reactor Control Variables
C1 (Fresh Ethane Feed) C2 (Fresh Propane Feed) C3 (Gas Oil Feed) C4 (DNG Feed) C5 (Ethane Recycle) C6 (Propane Recycle) C7 (Fuel Added) Objective function($/h)
Optimized value (lb/hr) Case 1
Case 2
60000 0.0 0.0 0.0 40000 0.0 32795.5 5460.0
109091 0.0 0.0 0.0 72727.3 0.0 58867.9 9927.28
Process Constraints Crc Eth Pro Ethr Pror Hc
Values (lb/hr) Case 1
Case 2
110000 50000 1000 0.0 0.0 2×107
200000 90909.15 1818.183 0.0 0.0 2×107
In order to describe the performance of the pyrolysis reactor, the simulation of such reactor is necessary. The simulation results for the products obtained by thermal cracking reactor for both cases are presented in Table 6. It is noted from this table that the highest favourable product (the main target), which is ethylene is achieved at 50000 lb/h for case 1 and 90909.15 lb/h for case 2 (whole process) among all products. Table 6: Simulation Results for Stream Pyrolysis Reactor Product (lb/hr) Ethylene Propylene Butadiene Gasoline Methane Fuel Oil
Simulation Results Case 1 50000 1000 1000 1000 7000 0.0
Case 2 90909.15 1818.183 1818.183 1818.183 12727.28 0.0
Table 7 shows the comparison results obtained from this study and those obtained by last studies. It is clearly observed from this Table that the new approach (SQP) used in this work to maximize the process profit related to thermal cracking reactor is better than the methods used with all previous works (that used different solution methods for maximizing the objective function to get the optimal design of pyrolysis reactor in this field). Where, the economic profit of the process is increased by 47% for both cases and the CPU-time was reduced by 86% for case 1 compared with last studies. This new result obtained can be attributed to the SQP approach employed in the present work (has high accuracy in evaluating the control variables of the process) within gPROMS package. Furthermore, this approach is a highly trusted method for solution of such mathematical models.
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A.T. Jarullah et al. Table 7: Comparison results between this work and last studies
Authors
Edgar &Himmelblau (2001) Babu & Angira (2007) Babu & Angira (2007) This work (2015)
Solution method
LP LP Simplex DE with GA SQP
CPU-time (sec) – Case1
Objective function ($/h) Case 1
Case 2
--------0.113 0.015625
3695.6 3695.6 3695.6 5460.0
----6760.18 6760.18 9927.28
5. Conclusions In this paper, an optimal design of thermal cracking (pyrolysis) reactor is studied. The optimization framework has been presented to tackle the optimal design and operation problem of pyrolysis reactor. The optimization problem formulation has been presented to give maximum economic index of such process. It has been carried out using a new alternative approach (the optimization problem was posed as a Non-linear programming (NLP) problem and was solved using a SQP method within gPROMS software). Based on the results obtained from this study using two cases (based upon ethylene production), it can be concluded that the operation depends mainly on the ethane and the fuel under process restriction to get maximum profit and maximum yield. As well as, the accurate process model of such reactor is namely depends on the solution methods in evaluating the control variables of the process so that the model can be effectively used for simulation, optimization and control. SQP is the most efficient in terms of function evaluations in dealing with process constraint problems. Finally, SQP method has been demonstrated to be able to give accurate results of feed flow rates with corresponding economic profit of 9927.28 $/h for whole process and gave highest profit (increased by 47%) and lowest CPU-time (reduced by 86%) in comparison with those obtained by previous studies.
References B.V. Babu, R. Angira, 2001, In Proceeding of International Symposium & 54th Annual Section of IICHE, Chennai. T.F. Edgar, D.M. Himmelblau, 2001, Optimization of Chemical Processes, McGraw-Hill Science. D. Geddes, T. Kubera, 2000, Integration of planning and real-time optimization in olefins production, Comput. Chem. Eng., 2-7, 24, 1645-1649. A.T. Jarullah, I.M. Mujtaba, A.S. Wood, 2011, Kinetic Model Development and Simulation of Simultaneous Hydrodenitrogenation and Hydrodemetallization of Crude Oil in a Trickle-Bed Reactor, Fuel, 90, 2165-2181. A.T. Jarullah, I.M. Mujtaba, A.S. Wood, 2012, Improving Fuel Quality by Whole Crude Oil Hydrotreating:A Kinetic Model for Hydrodeasphaltenization in a Trickle Bed Reactor, Applied Energy, 94, 182-191. E. Joo, S. Park, M. Lee, 2001, Pyrolysis Reaction Mechanism for Industrial Naphtha Cracking Furnaces, Ind. Eng. Chem. Res., 40, 11, 2409-2415. X. Lan, J. Gao, C. Xu, H. Zhang, 2007, Numerical simulation of transfer and reaction process in ethylene furnaces, Trans. IChemE, 85, A12, 1565-1579. A.K.K. Lee, A.M. Aitani, 1990, Saudi ethylene plants move toward more feed flexibility, Oil & Gas J. 88, 60-63. M. Masoumi, M. Shahrokhi, M. Sadrameli, J. Towfighi, 2006a, Modeling and Control of a naphtha Thermal Cracking Pilot Plant, Ind. Eng. Chem. Res., 45, 10, 3574-3582. M. Masoumi, S.M. Sadrameli, J. Towfighi, A. Niaei, 2006b, Simulation, Optimization and Control of Thermal Cracking Pilot Plant Furnace, Energy, 31, 4, 516-527.
Optimal operation of a pyrolysis reactor Aysar T. Jarullaha, Shemaa A. Hameeda, Zina A. Hameeda, and I.M. Mujtabab* a
Chemical Engineering Department, College of Engineering, Tikrit University, IRAQ *School of Engineering, Design and Technology, University of Bradford, Bradford BD7 1DP, UK, E-mail: [email protected]
b
Abstract In the present study, the problem of optimization of thermal cracker (pyrolysis) operation is discussed. The main objective in thermal cracker optimization is the estimation of the optimal flow rates of different feeds (such as, Gas-oil, Propane, Ethane and Debutanized natural gasoline) to the cracking furnace under the restriction on ethylene and propylene production. Thousands of combinations of feeds are possible. Hence the optimization needs an efficient strategy in searching for the global minimum. The optimization problem consists of maximizing the economic profit subject to a number of equality and inequality constraints. Modelling, simulation and optimal operation via optimization of the thermal cracking reactor has been carried out by gPROMS (general PROcess Modelling System) software. The optimization problem is posed as a Non-Linear Programming problem and using a Successive Quadratic Programming (SQP) method for solving constrained nonlinear optimization problem with high accuracy within gPROMS software. New results have been obtained for the control variables and optimal cost of the cracker in comparison with previous studies. Keywords: Thermal Cracking, Mathematical Modeling, Olefins Pyrolysis, SQP.
1. Introduction Hydrocarbon thermal cracking is the most significant operation in the production of olefins. Recently, the worldwide olefins production (mainly ethylene) increases rapidly (around 180 billion lb/yr), and is regarded one of the most important issues for chemical industries where improving its production operation can bring several benefits. Thus, the market demand for olefins production has accelerated the improvement of a more rigorous and reliable thermal cracking model of such process. Its annual industrial production depends on the thermal cracking (pyrolysis) of oil hydrocarbons, where the heart of the process with a massive economic effect is the reactor of the cracking process. Cracking of heavier fuel oils is done to produce mainly high quality (octane number) petrol, olefins (feed for petrochemical industry), coke (by coking) and to reduce the viscosity of fuel oil by visbreaking (Masoumi et al., 2006a, Babu and Angira, 2001). The main parameter of the optimal design of such reactor is the accurate prediction of yield and reactor performance. Each reactant is known to produce a certain distribution of products. When multiple reactants are employed, it is desirable to optimize the amounts of each reactant so that the products satisfy flow and demand constraints. Control systems are designed for achieving several goals, involving product quality, safety, and minimum cost (Masoumi et al., 2006b, Edgar and Himmelblau, 2001). The feed of a thermal cracking furnace can be a variety of components (such as ethane, propane, butane, isobutane, naphtha, and gas oil) and the main factor influencing the product is the feed composition (Lee and Aitani, 1990). The optimal design and operation strategy and purchase decisions for raw materials have become
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main issues in the olefin industries (Joo and Park, 2001). It is extremely difficult to obtain the detailed operation factors in the reactor from direct measurements owing to the limitation of current techniques. Thus, mathematical simulation, as an alternative, has become a powerful tool for predicting control variable distributions and olefin yields. The thermal cracking reactor is the key parameters affecting the economics of the process and the olefin yields (Lan et al., 2007). The main focus in this study is to find the optimal design of pyrolysis reactor (thermal cracker) and objective function of the process (which is the estimation of optimal flow rates of different feeds to the cracking furnace) subject to a number of equality and inequality constraints using an alternative approach to describe the reactor operating conditions as accurately as possible. The optimization problem is posed as a Non-Linear Programming problem and is solved by employing a Successive Quadratic Programming (SQP) method (which is considered to be one of the most promising approaches for solving constrained nonlinear optimization problem in addition to its successful application to many engineering optimization problems) with high accuracy within gPROMS (general PROcess Modelling System) software.
2. Problem Description The problem presented by Edgar and Himmelblau, (2001) is to obtain the maximum profit of the process, while operating within the reactor and down stream process equipment constraints. Figure 1 shows various feeds and corresponding product distribution for a thermal cracker that produces olefins. The variables to be optimized are the amounts of the four feeds (mainly, Gas-oil, Propane, Ethane and Debutanized natural gasoline (DNG)). This problem will be solved utilizing SQP method within gPROMS package. DNG
Gas Oil
Propane
Ethane
Thermal Cracker
Fuel
Propane
Ethane
Methane
Fuel Oil
Ethylene
Propylene
Butadiene
Gasoline
Figure 1: Pyrolysis Reactor
3. Mathematical Model of the Pyrolysis Reactor Table 1 shows various feeds and the corresponding product distribution for a Pyrolysis reactor that produces olefins (Edgar and Himmelblau, 2001). The possible feeds include ethane, propane, debutanized natural gasoline (DNG), and gas oil, some of which may be fed simultaneously. Based on plant data, eight products are produced in varying proportions according to the following matrix. The capacity to run gas feeds through the cracker is 200,000 Ib/stream hour (total flow based on an average mixture). Ethane uses the equivalent of 1.1 Ib of capacity per pound of ethane; propane 0.9 Ib; gas oil 0.9 Ib/Ib; and DNG 1.0. Downstream processing limits exist of 50,000 Ib/stream hour on the ethylene and 20,000 Ib/ stream hour on the propylene. The fuel requirements to run the cracking system for each feedstock type are listed in Table 2. Methane and fuel oil
Optimal operation of a pyrolysis reactor
829
produced by the cracker are recycled as fuel. All the ethane and propane produced is recycled as feed. Heating values are shown in Table 3 (Geddes and Kubera, 2000). Table 1: Yield Structure (wt. fraction) Product Methane Ethane Ethylene Propane Propylene Butadiene Gasoline Fuel oil
Ethane 0.07 0.40 0.50 0.01 0.01 0.01 -
Feed Propane 0.25 0.06 0.35 0.10 0.15 0.02 0.07 -
Gas oil 0.10 0.04 0.20 0.01 0.15 0.04 0.25 0.21
Table 2: Fuel Requirement Feedstock type Ethane Propane Gas oil DNG
DNG 0.15 0.05 0.25 0.01 0.18 0.05 0.30 0.01
Table 3: Heating Values
Fuel requirement (Btu/Ib) 8364 5016 3900 4553
Recycled feed Natural gas Methane Fuel oil
Heat produced (Btu/Ib) 21,520 21,520 18,000
Because of heat losses and the energy requirements for pyrolysis, the fixed fuel requirement is 20.0 × 106 Btu/stream hour and the energy (fuel) cost of $2.50/106 Btu. The price structure on the feeds and products and fuel costs is presented in Table 4 (Edgar and Himmelblau, 2001). Table 4: Feeds and Products Prices Feeds Ethane Propane Gas oil DNG
Price($/Ib) 0.0655 0.0973 0.1205 0.1014
Products Methane Ethane Propylene Butadiene Gasoline Fuel oil
Price($/Ib) 0.0538 (fuel value) 0.1775 0.1379 0.2664 0.0993 0.0450 (fuel value)
The following variables for the flow rates (input and output) of the reactor (in Ib/h) can be defined as: C1 = fresh ethane feed, C2 = fresh propane feed, C3 = gas oil feed, C4 = DNG feed, C5 = ethane recycle, C6 = propane recycle, C7 = fuel added. Objective function (profit). The objective function is the economic profit depending upon the difference between the value of the product and the value of feed and energy cost and all costs are calculated in cents/h. In other words, the profit ƒ is written as: ƒ = Product value – Feed cost – Energy cost Product value: Ethylene:ͳǤͷሺͲǤͷܥଵ ͲǤͷܥହ ͲǤ͵ͷܥଶ ͲǤ͵ͷ ܥ ͲǤʹͲܥଷ ͲǤʹͷܥସ ሻ ………(1) Propylene: ͳ͵ǤͻሺͲǤͲͳܥଵ ͲǤͲͳܥହ ͲǤͳͷܥଶ ͲǤͳͷ ܥ ͲǤͳͷܥଷ ͲǤͳͺܥସ ሻ ……… (2) Butadiene: ʹǤͶሺͲǤͲͳܥଵ ͲǤͲͳܥହ ͲǤͲʹܥଶ ͲǤͲʹ ܥ ͲǤͲͶܥଷ ͲǤͲͷܥସ ሻ ……… (3) Gasoline: ͻǤͻ͵ሺͲǤͲͳܥଵ ͲǤͲͳܥହ ͲǤͲܥଶ ͲǤͲ ܥ ͲǤʹͷܥଷ ͲǤ͵Ͳܥସሻ ……… (4) Total product sales ൌ ͻǤ͵ͻܥଵ ͻǤͷͳܥଶ ͻǤͳܥଷ ͳͳǤʹ͵ܥସ ͻǤ͵ͻܥହ ͻǤͷͳܥ ……… (5) Feed cost: Feed cost (cents/h)ൌ Ǥͷͷܥଵ ͻǤ͵ܥଶ ͳʹǤͷͲܥଷ ͳͲǤͳͶܥସ ……… (6) Energy cost: The fixed heat loss of 20×106 Btu/h can be expressed in terms of methane cost using a heating value of 21,520 Btu/Ib for methane. The fixed heat loss represents a constant cost that is independent of the variables Ci, hence in optimization this factor can be ignored, but in evaluating the final costs this term must be taken into account.
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The value for C7 depends on the amount of fuel oil and methane produced in the cracker (C7 provides for any deficit in products recycled as fuel). Equation (5) and (6) is combined to get the objective function, which is ƒ ൌ ʹǤͺͶܥଵ Ȃ ͲǤʹʹܥଶ Ȃ ͵Ǥ͵͵ܥଷ ͳǤͲͻܥସ ͻǤ͵ͻܥହ ͻǤͷͳܥ
………(7)
ܿݎܥൌ ͳǤͳܥଵ ͲǤͻܥଶ ͲǤͻܥଷ ͳǤͲܥସ ͳǤͳܥହ ͲǤͻ ܥ ʹͲͲǡͲͲͲ
………(8)
݄ݐܧൌ ͲǤͷܥଵ ͲǤ͵ͷܥଶ ͲǤʹͷܥଷ ͲǤʹͷܥସ ͲǤͷܥହ ͲǤ͵ͷ ܥ ͷͲǡͲͲͲ
……… (9)
Process limitations: 1- Cracker capacity of 200,000 Ib/h
2- Ethylene processing limitation of 50,000 Ib/h
3- Propylene processing limitation of 20,000 Ib/h
ܲ ݎൌ ͲǤͲͳܥଵ ͲǤͳͷܥଶ ͲǤͳͷܥଷ ͲǤͳͺܥସ ͲǤͲͳܥହ ͲǤͳͷ ܥ ʹͲǡͲͲͲ
……… (10)
ݎ݄ݐܧൌ ܥହ ൌ ͲǤͶܥଵ ͲǤͶܥହ ͲǤͲܥଶ ͲǤͲ ܥ ͲǤͲͶܥଷ ͲǤͲͷܥସ
……… (11)
ݎ݄ݐܧൌ ͲǤͶܥଵ ͲǤͲܥଶ ͲǤͲͶܥଷ ͲǤͲͷܥସ െ ͲǤܥହ ͲǤͲ ܥൌ Ͳ
……… (12)
ܲ ݎݎൌ ͲǤͳܥଶ ͲǤͲͳܥଷ ͲǤͲͳܥସ െ ͲǤͻ ܥൌ Ͳ
……… (13)
4- Ethane recycle
By rearranging equation (11), we get 5- Propane recycle
6- Heat constraint. The total fuel heating value (THV) in (Btu/h) is given by fuel
methane from cracker
fuel oil from cracker
ܶ ܸܪൌ ʹͳǡͷʹͲ ܥ ʹͳǡͷʹͲሺͲǤͲܥଵ ͲǤʹͷܥଶ ͲǤͳͲܥଷ ͲǤͳͷܥସ െ ͲǤͲܥହ ͲǤʹͷ ܥሻ ͳͺǡͲͲͲሺͲǤʹͳܥଷ ͲǤͲͳܥସ ሻ ൌ ͳͷͲǤͶܥଵ ͷ͵ͺͲܥଶ ͷͻ͵ʹܥଷ ͵ͶͲͺܥସ ͳͷͲǤͶܥହ ͷ͵ͺͲ ܥ ʹͳǡͷʹͲܥ ……… (14)
The required fuel for cracking (Btu/h) is ethane
propane
gas oil
DNG
ͺ͵Ͷሺܥଵ ܥହ ሻ ͷͲͳሺܥଶ ܥሻ ͵ͻͲͲܥଷ Ͷͷͷ͵ܥସ ൌ ͺ͵Ͷܥଵ ͷͲͳܥଶ ͵ͻͲͲܥଷ Ͷͷͷ͵ܥସ ………(15) ͺ͵Ͷܥହ ͷͲͳܥ Thus the sum of eq. (15) + 20,000,000 Btu/h is equal to the THV from eq. (14), which gives the constraint ܥܪൌ െͺͷǤܥଵ ͵Ͷܥଶ ʹͲ͵ʹܥଷ െ ͳͳͶͷܥସ െ ͺͷǤܥହ ͵Ͷ ܥ ʹͳǡͷʹͲ ܥൌ ʹͲǡͲͲͲǡͲͲͲ ..… (16)
3.1. Optimization Problem Formulation The optimal design problem is to obtain the optimal flow rate of different feeds giving maximum economic profits from the reactor operation corresponding to different constraints. Mathematically, the optimization problem can be stated as: Max f Ci (i=1 – 7) s.t y(x, u, q) = 0, (model, equality constraints) Ci L ≤ Ci ≤ Ci U , Crc ≤ Crc * , Eth ≤ Eth * (inequality constraints) Pro ≤ Pro * , Ethr = Ethr * , Pror = Pror*, Hc = Hc * (inequality constraints) The model equations can be written in compact form as: y(x, u, q) = 0, where x gives the set of all algebraic variables, u is the control variables, and q represents the design variables and the function y is assumed to be continuously differentiable with respect to all its arguments (Jarullah et al., 2011, Jarullah et al., 2012 ). L and U are the lower and upper bounds, respectively. The optimization solution method utilized by gPROMS is a two-steps method known as feasible path approach. The first step performs the simulation to converge all the equality constraints and to satisfy the inequality constraints. The second step performs the optimization (updates the values of the optimization parameters).
4. Results and Discussion The purpose of this study is to obtain the optimal design of thermal cracking reactor via optimal flow rates of different hydrocarbons feeds (namely, Gas-oil, Propane, Ethane and Debutanized natural gasoline) to get maximum profit. The modelling, simulation and optimization process has been carried out by using gPROMS software and the
Optimal operation of a pyrolysis reactor
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optimization problem based on a Non-Linear Programming (NLP) problem, which is solved using Successive Quadratic Programming (SQP) method. The optimal parameters obtained for two cases: case1 at maximum ethylene production of 50000 lb/hr and 100000 lb/hr for case2, are shown in Table 5. As noticed from the results presented in this Table that the maximum possible amount of ethylene is produced for both cases. Where, the optimal feed flow rate in lb/hr of ethane, ethane recycle and the fuel that should be added is 60000, 40000 and 32795.5 for case 1 and 109091, 72727.3 and 58867.9 for case 2, respectively with no feed of propane, gas oil, DNG and propane recycle for both cases. This means that the process depends mainly on the ethane (fresh feed as well as ethane recycle) in addition to the fuel. The maximum objective function (economic profit) is 5460 $/h for case 1 and 9927.28 $/h for case2 with satisfying all the inequality constraints. It has also been observed as the ethylene production constraint is relaxed, the objective function value increases. Once the constraint is raised above 90909.15 lb/hr, the objective function remains constant for whole process. Table 5: Optimization Results for Pyrolysis Reactor Control Variables
C1 (Fresh Ethane Feed) C2 (Fresh Propane Feed) C3 (Gas Oil Feed) C4 (DNG Feed) C5 (Ethane Recycle) C6 (Propane Recycle) C7 (Fuel Added) Objective function($/h)
Optimized value (lb/hr) Case 1
Case 2
60000 0.0 0.0 0.0 40000 0.0 32795.5 5460.0
109091 0.0 0.0 0.0 72727.3 0.0 58867.9 9927.28
Process Constraints Crc Eth Pro Ethr Pror Hc
Values (lb/hr) Case 1
Case 2
110000 50000 1000 0.0 0.0 2×107
200000 90909.15 1818.183 0.0 0.0 2×107
In order to describe the performance of the pyrolysis reactor, the simulation of such reactor is necessary. The simulation results for the products obtained by thermal cracking reactor for both cases are presented in Table 6. It is noted from this table that the highest favourable product (the main target), which is ethylene is achieved at 50000 lb/h for case 1 and 90909.15 lb/h for case 2 (whole process) among all products. Table 6: Simulation Results for Stream Pyrolysis Reactor Product (lb/hr) Ethylene Propylene Butadiene Gasoline Methane Fuel Oil
Simulation Results Case 1 50000 1000 1000 1000 7000 0.0
Case 2 90909.15 1818.183 1818.183 1818.183 12727.28 0.0
Table 7 shows the comparison results obtained from this study and those obtained by last studies. It is clearly observed from this Table that the new approach (SQP) used in this work to maximize the process profit related to thermal cracking reactor is better than the methods used with all previous works (that used different solution methods for maximizing the objective function to get the optimal design of pyrolysis reactor in this field). Where, the economic profit of the process is increased by 47% for both cases and the CPU-time was reduced by 86% for case 1 compared with last studies. This new result obtained can be attributed to the SQP approach employed in the present work (has high accuracy in evaluating the control variables of the process) within gPROMS package. Furthermore, this approach is a highly trusted method for solution of such mathematical models.
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Authors
Edgar &Himmelblau (2001) Babu & Angira (2007) Babu & Angira (2007) This work (2015)
Solution method
LP LP Simplex DE with GA SQP
CPU-time (sec) – Case1
Objective function ($/h) Case 1
Case 2
--------0.113 0.015625
3695.6 3695.6 3695.6 5460.0
----6760.18 6760.18 9927.28
5. Conclusions In this paper, an optimal design of thermal cracking (pyrolysis) reactor is studied. The optimization framework has been presented to tackle the optimal design and operation problem of pyrolysis reactor. The optimization problem formulation has been presented to give maximum economic index of such process. It has been carried out using a new alternative approach (the optimization problem was posed as a Non-linear programming (NLP) problem and was solved using a SQP method within gPROMS software). Based on the results obtained from this study using two cases (based upon ethylene production), it can be concluded that the operation depends mainly on the ethane and the fuel under process restriction to get maximum profit and maximum yield. As well as, the accurate process model of such reactor is namely depends on the solution methods in evaluating the control variables of the process so that the model can be effectively used for simulation, optimization and control. SQP is the most efficient in terms of function evaluations in dealing with process constraint problems. Finally, SQP method has been demonstrated to be able to give accurate results of feed flow rates with corresponding economic profit of 9927.28 $/h for whole process and gave highest profit (increased by 47%) and lowest CPU-time (reduced by 86%) in comparison with those obtained by previous studies.
References B.V. Babu, R. Angira, 2001, In Proceeding of International Symposium & 54th Annual Section of IICHE, Chennai. T.F. Edgar, D.M. Himmelblau, 2001, Optimization of Chemical Processes, McGraw-Hill Science. D. Geddes, T. Kubera, 2000, Integration of planning and real-time optimization in olefins production, Comput. Chem. Eng., 2-7, 24, 1645-1649. A.T. Jarullah, I.M. Mujtaba, A.S. Wood, 2011, Kinetic Model Development and Simulation of Simultaneous Hydrodenitrogenation and Hydrodemetallization of Crude Oil in a Trickle-Bed Reactor, Fuel, 90, 2165-2181. A.T. Jarullah, I.M. Mujtaba, A.S. Wood, 2012, Improving Fuel Quality by Whole Crude Oil Hydrotreating:A Kinetic Model for Hydrodeasphaltenization in a Trickle Bed Reactor, Applied Energy, 94, 182-191. E. Joo, S. Park, M. Lee, 2001, Pyrolysis Reaction Mechanism for Industrial Naphtha Cracking Furnaces, Ind. Eng. Chem. Res., 40, 11, 2409-2415. X. Lan, J. Gao, C. Xu, H. Zhang, 2007, Numerical simulation of transfer and reaction process in ethylene furnaces, Trans. IChemE, 85, A12, 1565-1579. A.K.K. Lee, A.M. Aitani, 1990, Saudi ethylene plants move toward more feed flexibility, Oil & Gas J. 88, 60-63. M. Masoumi, M. Shahrokhi, M. Sadrameli, J. Towfighi, 2006a, Modeling and Control of a naphtha Thermal Cracking Pilot Plant, Ind. Eng. Chem. Res., 45, 10, 3574-3582. M. Masoumi, S.M. Sadrameli, J. Towfighi, A. Niaei, 2006b, Simulation, Optimization and Control of Thermal Cracking Pilot Plant Furnace, Energy, 31, 4, 516-527.