고온 분해로의 kinetic 모델링과 모사

주 은정, 최 인석*, 박 선원

한국과학기술원 화학공학과

삼성엔지니어링(주) 기술연구소*

Kinetic Modeling and Simulation of cracking furnaces

Eunjung Joo , Inseok Choi*, and Sunwon Park

Dept. of Chemical Engineering, KAIST

Samsung Engineering co., R&D center*

Introduction

The large capacity of olefins plants justifies interest in accurate and reliable models to optimize furnace design and operating conditions in order to maximize the yields of particular products, typically ethylene and propylene. The industrial production of olefins from various hydrocarbon feedstocks is carried out in the steam cracking furnace, which is schematically represented in Figure 1. The heart of a pyrolysis plant is considered to be the thermal cracking furnace, with its main components, the thermal cracking reactors. All the products of the plant are formed here, so the performance of the cracking process is the key to the efficient operation of the entire facility. The classical thermal cracking reactor is designed as a coil, having a high length to diameter ratio. The rising needs of accuracy in predicting the reactor effluents under a wider range of feedstocks and different reactor coils demand models even more flexible and more detailed than the best ones actually available.

In high temperature cracking furnaces, the long molecules crack to form smaller olefins and chain radical reactions are the dominant mechanism. The first difficulty in characterizing these complex systems is related to the large number of feed components, intermediate and final products. So the first attempt towards the modelling of ethylene furnaces relied on empirical (molecular) models with drastically simplified kinetic schemes. But empirical and semi-empirical models were revealed not to be suitable for the description of furnaces, thus reliable mechanistic kinetic schemes appeared. The large number of chemical species involved, the number and type of reactions and the uncertainties of some kinetic constants make the first two steps of the chemical reactions modelling activity(i.e., setup of the reactions network and quantitative assessment of the associated kinetic scheme) critical in establishing the acceptable degree of simplification. Finally, the unavailability of efficient numerical algorithms to handle the numerous equations has been a further critical element imposing restrictions on the reaction scheme even at the expense of possible oversimplification.

Figure . Schematic diagram of furnace.

In this study, ethane cracking reactors were simulated through simplified free radical chain reaction mechanism and naphtha cracking reactors were simulated through simplified molecular reaction mechanism because of its great number of feedstocks, intermediate species, and reactions involved.

Model formulation and mathematical tools

The model for the cracking coil is a set of differential and algebraic equations in mathematical terms as follows:

The objective of cracking coil modeling by solving these equations is to find the temperature, pressure and the product distribution along the coil and particularly at the outlet of the coil.

Because of the stiffness, a simple algorithm for integration of the differential equation such as Runge-Kutta is not suitable or even not possible. The physical origin of stiffness is that concentrations of molecules vary in the rates that differ by orders of magnitude from those of the radicals. This arises from the fact that the radicals are more reactive than the molecules. In this study, DASSL which is based on the backward difference formula by Gear was used and showed reasonable results.

Ethane cracking reaction mechanism and simulation

The cracking of hydrocarbons occurs through a free-radical chain mechanism. Table 1 illustrates this chain mechanism with a very simplified scheme of ethane cracking.

The major geometry of the coil and operation conditions are shown in table 2. The simulation results are shown in figures 2 and 3. The simulation results are consistent with the published literature data.

Table . Ethane cracking reaction chain mechanism

Reaction	Ea(J/mol)	A(1/s or m3/s mol)
(1) C2H6 □ 2CH3□	3.726 E5	1.1 E17
(2) CH3□ + C2H6 □ C2H5□ + CH4	4.983 E4	1.5 E5
(3) C2H5□□ C2H4 + H□	1.717 E5	7.9 E13
(4) H□+ C2H6 □ C2H5□ + H2	3.350 E4	1.1 E8
(5) 2C2H5□□ C4H10	0	2.0 E6
(6) C2H5□ + C2H4 □ C3H6 + CH3□	7.955 E4	3.0 E6
(7) C2H4 + H□□ C2H5□	8.374 E3	1.0 E8

Table 2. Operating conditions and coil geometry

Temperature (K)	855-1160
Pressure (105 Pa)	2.84 - 3.04
H2O/C2H6 (kg kg-1)	0.4
Total feed flow rate ( mol s-1 )	10
( kg s-1 )	0.252
Reactor diameter (m)	0.113
Reactor length (m)	10

Figure 3. Ethane cracking simulation results(radicals)

Figure 2. Ethane cracking simulation results(molecules)

Naphtha cracking reaction mechanism and simulation

In naphtha cracking reactions, the numbers of species involved and reactions occurring are so great that considering the radical reaction mechanisms is really a difficult job even for a simplified case. Thus to know just the trend, 22 molecular reactions and 17 species are considered and a simulation study was carried out using  the conditions in table 3. To calculate the equilibrium constant for the reversible reactions, GAMS was used to regress it. The results are shown in figures 4 and 5.

Table 3. Operating conditions and coil geometry

Temperature (K)	993 - 1073
Pressure (105 Pa)	2.84 - 3.04
H2O/naphtha (kg kg-1)	0.71 - 1.43
Total feed flow rate (mol s-1)	10
Reactor diameter (m)	0.113
Reactor length (m)	10

Figure 5. Naphtha cracking simulation results(radicals and aromatics)

Figure 4. Naphtha cracking simulation results(molecules)

Conclusions

An accurate model of ethylene plant can be used for the advanced control and optimization of the plant, and the large capacity of the plant justifies the importance and interest of the model. The key part, thermal cracking furnace was simulated for the ethane and naphtha cases. This study can be used further to develop advanced control tasks or optimization tools for ethylene plants.

Acknowledgment

This work was supported (in part) by the Korean Science and Engineering Foundation (KOSEF) through the Automation Research Center at POSTECH and by the Korea Ministry of Trade, Industry and Energy through RaCER.

References

1. Dente, M., S.Pierucci, E.Ranzi, and G.Bussani, "New improvements in modeling kinetic schemes for hydrocarbons pyrolysis reactors," Chem.Eng.Sci., vol. 47, pp.2629-2634, 1992

2. Wagner, E.S., O.A. Hamid, E.M. Sohn, and R.F. Preston, "Pyrotec's ethylene plant furnace modeling technology coupled with aspentech's real-time optimization system provides off-line and on-line benefits," ASPEN WORLD 97, Boston, 1997

3. Benson, S.W., "Thermochemical kinetics," 2nd ed. Wiley. New York, 1976