Temperature optimization model to inhibit zero-order kinetic reactions
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Januardi Januardi
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Aditya Sukma Nugraha
Abstract
Originally, the Arrhenius parameters were used to estimate the rate of chemical reactions. This article aims to develop the optimal temperature to inhibit specific zero-order kinetic reactions. The model extends the use of the Arrhenius equation and heat capacity modeling to derive the optimal temperature solution. Specifically, the Arrhenius equation, which connects temperature to reaction rates, and the heat equation are formulated to create a comprehensive heat accumulation model. Analytical modeling is utilized through a derivative process to provide optimization. According to a case study of carotene oxidation, the derivative solution proposes −1.73 °C and can extend the reaction time by 206,160.29 days compared to a solution with no temperature change. The derivative solution also offers higher advantages in practical application than setting the lowest temperature limit due to the high initial energy requirement. The temperature derivative solution exhibits a global optimum property because of its high heat accumulation and slower kinetic reactions. These slower kinetic reactions can prevent reactant substances from deteriorating, making them valuable for maintaining a chemical’s shelf life. The temperature solutions offer valuable insights for devising an effective temperature strategy to inhibit specific chemical processes and verifying the relationship between temperature and heat accumulation with curvature.
Acknowledgements
The first author gives his gratitude to Dr. Sugiarto, Prof. Endang Warsiki, Dr. Indah Yuliasih, and the late Dr. Ade Iskandar from Institut Pertanian Bogor for the knowledge of Agricultural Quality Deteriorations and Kinetic Reactions. Their perspective encourages the first author to pursue different subject for optimization application in Agricultural Process Engineering.
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Research ethics: Not applicable.
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Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Competing interests: The authors states no conflict of interest.
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Research funding: None declared.
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Data availability: Not applicable.
References
1. Olvera Astivia, OL, Gadermann, A, Guhn, M. The relationship between statistical power and predictor distribution in multilevel logistic regression: a simulation-based approach. BMC Med Res Methodol 2019;19:1–20. https://doi.org/10.1186/s12874-019-0742-8.Suche in Google Scholar PubMed PubMed Central
2. Chakraborty, S, Uppaluri, R, Das, C. Optimization of ultrasound-assisted extraction (UAE) process for the recovery of bioactive compounds from bitter gourd using response surface methodology (RSM). Food Bioprod Process 2020;120:114–22. https://doi.org/10.1016/j.fbp.2020.01.003.Suche in Google Scholar
3. Erihemu, Wang, M, Zhang, F, Wang, D, Zhao, M, Cui, N, et al.. Optimization of the process parameters of ultrasound on inhibition of polyphenol oxidase activity in whole potato tuber by response surface methodology. Lwt 2021;144:111232. https://doi.org/10.1016/j.lwt.2021.111232.Suche in Google Scholar
4. Stokes, Z, Mandal, A, Wong, WK. Using Differential Evolution to design optimal experiments. Chemometr Intell Lab Syst 2020;199:103955. https://doi.org/10.1016/j.chemolab.2020.103955.Suche in Google Scholar PubMed PubMed Central
5. Mooney, DD, Swift, RJ. A course in mathematical modeling. American Mathematical Society; 2021, 13.Suche in Google Scholar
6. Tripathi, D, Edla, DR, Bablani, A, Shukla, AK, Reddy, BR. Experimental analysis of machine learning methods for credit score classification. Prog Artif Intell 2021;10:217–43. https://doi.org/10.1007/s13748-021-00238-2.Suche in Google Scholar
7. Abedeen, I, Rahman, MA, Prottyasha, FZ, Ahmed, T, Chowdhury, TM, Shatabda, S. FracAtlas: a dataset for fracture classification, localization and segmentation of musculoskeletal radiographs. Sci Data 2023;10:1–8. https://doi.org/10.1038/s41597-023-02432-4.Suche in Google Scholar PubMed PubMed Central
8. Muthappa, R, Purushothaman, BK, Meera Sheriffa Begum, KM, Maheswari, PU. Kinetic modeling and optimization of the release mechanism of curcumin from folate conjugated hybrid BSA nanocarrier. Chem Prod Process Model 2020;15:20190026. https://doi.org/10.1515/cppm-2019-0026.Suche in Google Scholar
9. Tallam, A, Bairy, SR, Kalakuntala, R, Naga Prapurna, PV, Suranani, S. Kinetic modeling of Citrullus lanatus (watermelon) peel using thermo gravimetric analysis. Chem Prod Process Model 2020;15:1–8. https://doi.org/10.1515/cppm-2019-0076.Suche in Google Scholar
10. Tylinski, M, Smith, RS, Kay, BD. Structure and desorption kinetics of acetonitrile thin films on Pt(111) and on graphene on Pt(111). J Phys Chem C 2020;124:2521–30. https://doi.org/10.1021/acs.jpcc.9b10579.Suche in Google Scholar
11. Cano-Pleite, E, Rubio-Rubio, M, Riedel, U, Soria-Verdugo, A. Evaluation of the number of first-order reactions required to accurately model biomass pyrolysis. Chem Eng J 2021;408:127291. https://doi.org/10.1016/j.cej.2020.127291.Suche in Google Scholar
12. Calligaris, S, Manzocco, L, Anese, M, Nicoli, MC. Accelerated shelf life testing. In: Food quality and shelf life. Elsevier; 2019, vol 52:359–92 pp.10.1016/B978-0-12-817190-5.00012-4Suche in Google Scholar
13. Mauro, JC. Materials kinetics: transport and rate phenomena. Elsevier; 2020.Suche in Google Scholar
14. Wu, W, Cronjé, P, Verboven, P, Defraeye, T. Unveiling how ventilated packaging design and cold chain scenarios affect the cooling kinetics and fruit quality for each single citrus fruit in an entire pallet. Food Packag Shelf Life 2019;21:100369. https://doi.org/10.1016/j.fpsl.2019.100369.Suche in Google Scholar
15. Salazar-González, C, Fuenmayor, CA, Díaz-Moreno, C, Stinco, CM, Heredia, FJ. Stability and shelf life modeling of natural colorant from bee pollen. Food Packag Shelf Life 2023;40. https://doi.org/10.1016/j.fpsl.2023.101169.Suche in Google Scholar
16. Zang, J, Qing, M, Chi, Y, Chi, Y. Predicting quality of the whole egg powder during storage: based on Arrhenius and radial basis function model. J Food Compos Anal 2023;124:105666. https://doi.org/10.1016/j.jfca.2023.105666.Suche in Google Scholar
17. Ji, S, Liu, Z, Pan, H, Li, X. Energy, exergy, environmental and exergoeconomic (4E) analysis of an ultra-low temperature cascade refrigeration system with environmental-friendly refrigerants. Appl Therm Eng 2024;248:123210. https://doi.org/10.1016/j.applthermaleng.2024.123210.Suche in Google Scholar
18. Holubec, V, Ye, Z. Maximum efficiency of low-dissipation refrigerators at arbitrary cooling power. Phys Rev 2020;101:1–10. https://doi.org/10.1103/PhysRevE.101.052124.Suche in Google Scholar PubMed
19. Rodríguez-Aragón, LJ, López-Fidalgo, J. Optimal designs for the Arrhenius equation. Chemometr Intell Lab Syst 2005;77:131–8. https://doi.org/10.1016/j.chemolab.2004.06.007.Suche in Google Scholar
20. Schwaab, M, Pinto, JC. Optimum reference temperature for reparameterization of the Arrhenius equation. Part 1: problems involving one kinetic constant. Chem Eng Sci 2007;62:2750–64. https://doi.org/10.1016/j.ces.2007.02.020.Suche in Google Scholar
21. Munson-Mcgee, SH. D- and G-optimal experimental designs for the partition coefficient in freeze concentration. J Food Eng 2014;121:80–6. https://doi.org/10.1016/j.jfoodeng.2013.08.018.Suche in Google Scholar
22. Kucinskis, G, Bozorgchenani, M, Feinauer, M, Kasper, M, Wohlfahrt-Mehrens, M, Waldmann, T. Arrhenius plots for Li-ion battery ageing as a function of temperature, C-rate, and ageing state – an experimental study. J Power Sources 2022;549:232129. https://doi.org/10.1016/j.jpowsour.2022.232129.Suche in Google Scholar
23. Hayat, T, Khan, SA, Ijaz Khan, M, Alsaedi, A. Theoretical investigation of Ree–Eyring nanofluid flow with entropy optimization and Arrhenius activation energy between two rotating disks. Comput Methods Progr Biomed 2019;177:57–68. https://doi.org/10.1016/j.cmpb.2019.05.012.Suche in Google Scholar PubMed
24. Pfitzner, M, Klein, M. A near-exact analytic solution of progress variable and pdf for single-step Arrhenius chemistry. Combust Flame 2021;226:380–95. https://doi.org/10.1016/j.combustflame.2020.12.007.Suche in Google Scholar
25. Leipold, J, Seidel, C, Nikolic, D, Seidel-Morgenstern, A, Kienle, A. Optimization of methanol synthesis under forced periodic operation in isothermal fixed-bed reactors. Comput Chem Eng 2023;175:108285. https://doi.org/10.1016/j.compchemeng.2023.108285.Suche in Google Scholar
26. Marion, G, & Lawson, D (2008). An introduction to mathematical modelling: Bioinformatics and statistics Edinburgh, Scotland, University of Bristol.Suche in Google Scholar
27. Laidler, KJ. Reaction kinetics: homogeneous gas reactions. Elsevier; 2013, vol 1.Suche in Google Scholar
28. Tavella, P, Milton, MJT, Inguscio, M. Metrology: from physics fundamentals to quality of life. IOS Press; 2018, vol 196.Suche in Google Scholar
29. Smith, WR. A precise, simple and general Basic Le Châtelier Principle based on elementary calculus: what Le Châtelier had in mind? J Math Chem 2020;58:1548–70. https://doi.org/10.1007/s10910-020-01140-3.Suche in Google Scholar
30. Lee, JHS, Ramamurthi, K. Fundamentals of Thermodynamics. CRC Press; 2022, vol 59.10.1201/9781003224044Suche in Google Scholar
31. Farrukh, MA. Advanced Chemical Kinetics. Rijeka, Croatia: InTech; 2018. https://doi.org/10.5772/68089.Suche in Google Scholar
32. Thompson, PW, Silverman, J. The concept of accumulation in calculus. Making the connection: research and teaching in undergraduate mathematics; 2008, vol 73:43–52 pp.10.5948/UPO9780883859759.005Suche in Google Scholar
33. Bittinger, ML, Ellenbogen, D, Surgent, SA, Kramer, GF. Calculus and its applications, 10th ed. Pearson Education; 2012.Suche in Google Scholar
34. Kythe, PK. Elements of concave analysis and applications. CRC Press; 2018.10.1201/9781315202259Suche in Google Scholar
35. Zeb, A. Oxidation and formation of oxidation products of β-carotene at boiling temperature. Chem Phys Lipids 2012;165:277–81. https://doi.org/10.1016/j.chemphyslip.2012.02.005.Suche in Google Scholar PubMed
36. Tagliavini, G, Defraeye, T, Carmeliet, J. Multiphysics modeling of convective cooling of non-spherical, multi-material fruit to unveil its quality evolution throughout the cold chain. Food Bioprod Process 2019;117:310–20. https://doi.org/10.1016/j.fbp.2019.07.013.Suche in Google Scholar
37. Selvnes, H, Allouche, Y, Manescu, RI, Hafner, A. Review on cold thermal energy storage applied to refrigeration systems using phase change materials. Therm Sci Eng Prog 2021;22:100807. https://doi.org/10.1016/j.tsep.2020.100807.Suche in Google Scholar
38. Melillo, JH, Swenson, J, Cerveny, S. Influence of ice formation on the dynamic and thermodynamic properties of aqueous solutions. J Mol Liq 2022;356:119039. https://doi.org/10.1016/j.molliq.2022.119039.Suche in Google Scholar
39. Fang, Z, Fan, C, Yan, G, Yu, J. Performance evaluation of a modified refrigeration cycle with parallel compression for refrigerator-freezer applications. Energy 2019;188:116093. https://doi.org/10.1016/j.energy.2019.116093.Suche in Google Scholar
40. Erihemu, Wang, M, Zhang, F, Wang, D, Zhao, M, Cui, N, et al.. Optimization of the process parameters of ultrasound on inhibition of polyphenol oxidase activity in whole potato tuber by response surface methodology. Lwt 2021;144:111232. https://doi.org/10.1016/j.lwt.2021.111232.Suche in Google Scholar
41. Sur, A, Sah, RP, Pandya, S. Milk storage system for remote areas using solar thermal energy and adsorption cooling. Mater Today Proc 2020;28:1764–70. https://doi.org/10.1016/j.matpr.2020.05.170.Suche in Google Scholar
42. Revell, LE, Williamson, BE. Why are some reactions slower at higher temperatures? J Chem Educ 2013;90:1024–7. https://doi.org/10.1021/ed400086w.Suche in Google Scholar
43. Azad, ZRAA, Ahmad, MF, Siddiqui, WA. Food spoilage and food contamination. Health and safety aspects of food processing technologies; 2019:9–28 pp.10.1007/978-3-030-24903-8_2Suche in Google Scholar
44. Bashir, S, Li, R, Song, S, Zheng, F, Ramirez, GA, Houf, W, et al.. Interactive nanomaterials for energy storage and conversion. In: Nanostructured materials for sustainable energy: design, evaluation, and applications. ACS Publications; 2022:27–81 pp.10.1021/bk-2022-1421.ch002Suche in Google Scholar
45. Owolabi, KM, Hammouch, Z. Mathematical modeling and analysis of two-variable system with noninteger-order derivative. Chaos 2019;29. https://doi.org/10.1063/1.5086909.Suche in Google Scholar PubMed
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
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Artikel in diesem Heft
- Frontmatter
- Review
- Computational chemistry unveiled: a critical analysis of theoretical coordination chemistry and nanostructured materials
- Research Articles
- Reducing sludge formation by enhancing biological decay of biomass: a mathematical model
- Numerical investigation of discharge pressure effect on steam ejector performance in renewable refrigeration cycle by considering wet steam model and dry gas model
- Natural pigment indigoidine production: process design, simulation, and techno-economic assessment
- Energy efficiency in cooling systems: integrating machine learning and meta-heuristic algorithms for precise cooling load prediction
- A parametric study on syngas production by adding CO2 and CH4 on steam gasification of biomass system using ASPEN Plus
- Temperature optimization model to inhibit zero-order kinetic reactions
- Multi-objective Bonobo optimisers of industrial low-density polyethylene reactor
- Assessment the thermal performance of square twisted double tube heat exchanger with Al2O3 nanofluid
- Short Communication
- Layouts and tips for a typical final-year chemical engineering graduation project
