Abstract
The highly exothermic nature of the low-density polyethylene (LDPE) polymerization process and the heating-cooling prerequisite in tubular reactor can lead to various problems particularly safety and economic. These issues complicate the monomer conversion maximization approaches. Consequently, the dynamic optimization study to obtain maximum conversion of the LDPE is carried out. A mathematical model has been developed and validated using industrial data. In the dynamic optimization study, maximum monomer conversion (XM) is considered as the objective function, whereas the constraint and bound consists of maximum reaction temperature and product melt flow index (MFI). The orthogonal collocation (OC) on finite elements is used to convert the original optimization problems into Nonlinear Programming (NLP) problems, which are then solved using sequential quadratic program (SQP) methods. The result shows that five interval numbers produce better optimization result compared to one and two intervals.
Funding source: Ministry of Higher Education, Malaysia
Award Identifier / Grant number: 203/PJKIMIA/6071368
Acknowledgment
The financial support from Kementerian Pengajian Tinggi (KPT) through Grant No. 203/PJKIMIA/6071368 and MyBrain15's Fund to the first author are greatly acknowledged.
- List of symbols
- Bb
Backbiting
- Fx
Mass flow rate of x component (kg/h)
- I
Initiator
- M
Monomer
- px
Input variable of x component
- P(x)
Live radical with chain length x
- R(x)
Live radical with chain length x
- S
Solvent
- T
Temperature (°C)
- Tin
Reactor inlet temperature (°C)
- TJ
Reactor jacket temperature (°C)
- Tmax
Maximum reaction temperature (°C)
- U
Overall heat transfer coefficient (cal/cm2.s.K)
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Employment or leadership: None declared.
Honorarium: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
1. Asteasuain M, Pereda S, Lacunza MH, Ugrin PE, Brandolin A. Industrial high pressure ethylene polymerization initiated by peroxide mixtures: a reduced mathematical model for parameter adjustment. Polym Eng Sci 2001;41:711–26. https://doi.org/10.1002/pen.10767.Search in Google Scholar
2. Agrawal N. Modeling, simulation and multi-objective optimization of an industrial, low-density polyethylene reactor. National University of Singapore, PhD Thesis; 2008.Search in Google Scholar
3. Muhammad D, Ahmad Z, Aziz N. Modeling and nonlinearity studies of low density polyethylene (LDPE) tubular reactor. Mater Today: Proc 2018;5:21612–19. https://doi.org/10.1016/j.matpr.2018.07.010.Search in Google Scholar
4. Yao F Z. Modeling, simulation and optimal control of ethylene polymerization in a high-pressure tubular reactors. Nanchang University, Thesis; 2004.10.2202/1542-6580.1152Search in Google Scholar
5. Azmi A, Aziz N. Comparison Study of Model Based Industrial Low-Density Polyethylene Production in Tubular Reactor. Chem Eng Trans 2017;56:751–6. https://doi.org/10.3303/CET1756126.Search in Google Scholar
6. Hafele M, Kienle A, Boll M, Schmidt C U, Schwibach M. Dynamic simulation of a tubular reactor for the production of low-density polyethylene using adaptive method of lines. J Comput Appl Math 2006;183:288–300. https://doi.org/10.1016/j.cam.2004.12.033.Search in Google Scholar
7. Rangaiah GP. Multi-objective Optimization: techniques and Applications in Chemical Engineering. Adv Proc Syst Eng 2009;1. https://onlinelibrary.wiley.com/doi/book/10.1002/9781118341704.10.1142/10240Search in Google Scholar
8. Erdeghem P M M V, Logist F, Heughebaert M, Dittrich C, Impe J F V. Conceptual modelling and optimization of jacketed tubular reactors for the production of LDPE. 9th IFAC Symposium on Dynamics and Control of Process Systems, 43. IFAC Proceedings Volumes 2010;433–438. https://doi.org/10.3182/20100705-3-BE-2011.00072.Search in Google Scholar
9. Vallerio M, Logist F, Erdeghem P V, Dittrich C, Impe J V. Model-Based Optimization of the Cooling System of an Industrial Tubular LDPE Reactor. Ind Eng Chem Res 2013;52:1656–66. https://doi.org/10.1021/ie3013709.Search in Google Scholar
10. Peters N, Guay M, DeHaan D. Real-time dynamic optimization of batch systems. J. Proc Contr 2007;17:261–71. https://doi.org/10.1016/j.jprocont.2006.11.005.Search in Google Scholar
11. Azmi A, Aziz N. Simulation studies of low-density polyethylene production in a tubular reactor Procedia Eng 2016;148:1170–6. https://doi.org/10.1016/j.proeng.2016.06.620.Search in Google Scholar
12. Cizniar M. Dynamic optimisation of processes, diploma work, Slovak Technical University in Bratislava; 2005.Search in Google Scholar
13. Cuthrell J E, Biegler L T. On the optimization of differential-algebraic process systems, AIChE J 1987;33:1257–70. https://doi.org/10.1002/aic.690330804.Search in Google Scholar
14. Arpornwichanop A, Shomchoam N. Studies on optimal control approach in a Fed-batch Fermentation Kor J Chem Eng 2007;24:11–15. https://doi.org/10.1007/s11814-007-5002-7.Search in Google Scholar
15. Rohman FS. Online dynamic optimization studies of catalyzed esterification of propionic anhydride with 2-butanol in the presence of disturbance and uncertainty. Universiti Sains Malaysia, PhD Thesis; 2015.Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
