Startseite Parameter estimation in non-linear chemical processes: an opposite point-based differential evolution (OPDE) approach
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Parameter estimation in non-linear chemical processes: an opposite point-based differential evolution (OPDE) approach

  • Swati Yadav und Rakesh Angira EMAIL logo
Veröffentlicht/Copyright: 18. August 2023
Veröffentlichen auch Sie bei De Gruyter Brill
Manuskript einreichen Informationen für Autor*innen
Chemical Product and Process Modeling
Aus der Zeitschrift Chemical Product and Process Modeling Band 18 Heft 6

Abstract

In recent years, evolutionary algorithms have been gaining popularity for finding optimal solutions to non-linear multimodal problems encountered in many engineering disciplines. Differential evolution (DE), an evolutionary algorithm, is a novel optimization method capable of handling nondifferentiable, non-linear, and multimodal objective functions. DE is an efficient, effective, and robust evolutionary optimization method. Still, DE takes large computational time to optimize the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This paper introduces a modification to the original DE that enhances the convergence rate without compromising solution quality. The proposed opposite point-based differential evolution (OPDE) algorithm utilizes opposite point-based population initialization, in addition to random initialization. Such an improvement reduces computational effort. The OPDE has been applied to benchmark test functions and high-dimensional non-linear chemical engineering problems. The proposed method of population initialization accelerates the convergence speed of DE, as indicated by the results obtained using benchmark test functions and non-linear chemical engineering problems.

Keywords: chemical processes; differential evolution; evolutionary algorithms; global optimization; non-linear optimization; parameter estimation
Corresponding author: Rakesh Angira, Process Systems Engineering Laboratory, University School of Chemical Technology, Guru Gobind Singh Indraprastha University, New Delhi, 110078, India, E-mail:

Funding source: Guru Gobind Singh Indraprastha University

Award Identifier / Grant number: GGSIPU/DRC/FRGS/2022/1223/35

Acknowledgments

Authors are thankful to the anonymous reviewers for their valuable suggestions.

  1. Research ethics: Not applicable.

  2. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: No conflict of interest.

  4. Research funding: Financial support from the Guru Gobind Singh Indraprastha University is gratefully acknowledged. The work has been supported under Faculty Research Grant Scheme (FRGS) for the year 2022–23 (F. No. GGSIPU/FRGS/2022/1223/35).

  5. Data availability: Not applicable.

References

1. Michalik, C, Chachuat, B, Marquardt, W. Incremental global parameter estimation in dynamical systems. Ind Eng Chem Res 2009;48:5489–97. https://doi.org/10.1021/ie8015472.Suche in Google Scholar

2. Gau, CY, Brennecke, JF, Stadtherr, MA. Reliable nonlinear parameter estimation in VLE modeling. Fluid Ph Equilibria 2000;168:1–18. https://doi.org/10.1016/s0378-3812(99)00332-5.Suche in Google Scholar

3. Anderson, TF, Abrams, DS, Grens, IIEA. Evaluation of parameters for nonlinear thermodynamic models. AIChE J 1978;24:20–9. https://doi.org/10.1002/aic.690240103.Suche in Google Scholar

4. Chang, JS, Li, CC, Liu, WL, Deng, JH. Two-stage parameter estimation applied to ordinary differential equation models. J Taiwan Inst Chem Eng 2015;000:1–10. https://doi.org/10.1016/j.jtice.2015.05.004.Suche in Google Scholar

5. Khan, AI, Billah, MM, Ying, C, Liu, J, Dutta, P. Bayesian method for parameter estimation in transient heat transfer problem. Int J Heat Mass Tran 2021;166:120746. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120746.Suche in Google Scholar

6. Dua, V. An artificial neural network approximation-based decomposition approach for parameter estimation of system of ordinary differential equations. Comput Chem Eng 2011;35:545–53. https://doi.org/10.1016/j.compchemeng.2010.06.005.Suche in Google Scholar

7. Chang, JS, Deng, JH, Wang, GB. Estimation of kinetic parameters for glycerol/alcohol dehydration reaction systems with incomplete chromatography data set. J Taiwan Inst Chem Eng 2016;60:185–98. https://doi.org/10.1016/j.jtice.2015.11.011.Suche in Google Scholar

8. Peric, ND, Paulen, R, Villanueva, ME, Chachuat, B. Set-membership nonlinear regression approach to parameter estimation. J Process Control 2018;70:80–95. https://doi.org/10.1016/j.jprocont.2018.04.002.Suche in Google Scholar

9. Eslick, JC, Akula, PT, Bhattacharyya, D, Miller, DC. Simultaneous parameter estimation in reactive solvent-based processes. Comput Aided Chem Eng 2018;44:901–6.10.1016/B978-0-444-64241-7.50145-2Suche in Google Scholar

10. Stortelder, WJH. Parameter estimation in chemical engineering, a case study for resin production. Sci comput chem eng. Berlin, Heidelberg: Springer; 1996.10.1007/978-3-642-80149-5_27Suche in Google Scholar

11. Erodotou, P, Voutsas, E, Sarimveis, H. A genetic algorithm approach for parameter estimation in vapour-liquid thermodynamic modelling problems. Comput Chem Eng 2020;134:106684. https://doi.org/10.1016/j.compchemeng.2019.106684.Suche in Google Scholar

12. Britt, HI, Luecke, RH. The estimation of parameters in nonlinear, implicit models. Technometrics 1973;15:233–47. https://doi.org/10.1080/00401706.1973.10489037.Suche in Google Scholar

13. Fabries, JF, Renon, H. Method for evaluation and reduction of vapor-liquid equilibrium data of binary mixtures. AIChE J 1975;21:735–43. https://doi.org/10.1002/aic.690210414.Suche in Google Scholar

14. Tjoa, IB, Biegler, LT. Simultaneous solution and optimization strategies for parameter estimation of differential-algebraic equation systems. Ind Eng Chem Res 1991;30:376–85. https://doi.org/10.1021/ie00050a015.Suche in Google Scholar

15. Edgar, TF, Himmelblau, DM, Lasdon, LS. Optimization of chemical processes, 2nd ed. New York: McGraw-Hill; 2001:306–18 pp.Suche in Google Scholar

16. Esposito, WR, Floudas, CA. Global optimization for the parameter estimation of differential-algebraic systems. Ind Eng Chem Res 2000;39:1291–310. https://doi.org/10.1021/ie990486w.Suche in Google Scholar

17. Jaulin, L, Walter, E. Guaranteed nonlinear parameter estimation via interval computations. Interfac Comput 1993;3:61–75.Suche in Google Scholar

18. Dantas, LB, Orlande, HRB, Cotta, RM. An inverse problem of parameter estimation for heat and mass transfer in capillary porous media. Int J Heat Mass Tran 2003;46:1587–98. https://doi.org/10.1016/s0017-9310(02)00424-6.Suche in Google Scholar

19. Sajedi, R, Faraji, J, Kowsary, F. A new damping strategy of Levenberg-Marquardt algorithm with a fuzzy method for inverse heat transfers problem parameter estimation. Int Commun Heat Mass Tran 2021;126:105433. https://doi.org/10.1016/j.icheatmasstransfer.2021.105433.Suche in Google Scholar

20. Walter, E, Kieffer, M. Guaranteed nonlinear parameter estimation in knowledge-based models. J Comput Appl Math 2007;199:277–85. https://doi.org/10.1016/j.cam.2005.07.039.Suche in Google Scholar

21. Abunahman, SS, Santos, LC, Tavares, FW, Kontogeorgis, GM. A computational tool for parameter estimation in EoS: new methodologies and natural gas phase equilibria calculations. Chem Eng Sci 2020;215:115437. https://doi.org/10.1016/j.ces.2019.115437.Suche in Google Scholar

22. Vamos, RJ, Hass, CN. Reduction of ion-exchange equilibria data using an error in variables approach. AIChE J 1994;40:556–69. https://doi.org/10.1002/aic.690400316.Suche in Google Scholar

23. Dao, TT. Investigation on evolutionary computation techniques of a nonlinear system. Model Simulat Eng 2011;2011:1–21. https://doi.org/10.1155/2011/496732.Suche in Google Scholar

24. Sen, S. Chapter 4 – a survey of intrusion detection systems using evolutionary computation. In: Yang X-S, Chien SF, Ting TO, Kaufmann M, editors. Bio-inspired computation in telecommunications. USA: Elsevier Inc.; 2015:73–94 pp.10.1016/B978-0-12-801538-4.00004-5Suche in Google Scholar

25. Zelinka, I, Davendra, DD, Senkerik, R, Pluhacek, M. Investigation on evolutionary predictive control of chemical reactor. J Appl Logic 2015;13:156–66. https://doi.org/10.1016/j.jal.2014.11.009.Suche in Google Scholar

26. Mallaiah, M, Rao, KR, Venkateswarlu, C. A simulated annealing optimization algorithm based nonlinear model predictive control strategy with application. Evol Syst 2021;12:225–31. https://doi.org/10.1007/s12530-020-09354-1.Suche in Google Scholar

27. Zhang, H, Rangaiah, GP, Petriciolet, AB. Integrated differential evolution for global optimization and its performance for modeling VaporLiquid equilibrium data. Ind Eng Chem Res 2011;50:10047–61. https://doi.org/10.1021/ie200819p.Suche in Google Scholar

28. Bertolino, A, Furst, M, Stagni, A, Frassoldati, A, Pelucchi, M, Cavallotti, C, et al.. An evolutionary, data-driven approach for mechanism optimization: theory and application to ammonia combustion. Combust Flame 2021;229:111366. https://doi.org/10.1016/j.combustflame.2021.02.012.Suche in Google Scholar

29. Rao, KR, Marjan, T, Mohammad, TY, Sahu, JN. Optimization and modelling of methyl orange adsorption onto polyaniline nano-adsorbent through response surface methodology and differential evolution embedded neural network. J Environ Manag 2018;223:517–29. https://doi.org/10.1016/j.jenvman.2018.06.027.Suche in Google Scholar PubMed

30. Rasoulzadeh, H, Dehghani, MH, Sheikhmohammadi, A, Rao, KR, Nabizadeh, R, Nazmara, S, et al.. Parametric modelling of Pb(II) adsorption onto chitosan-coated Fe3O4 particles through RSM and DE hybrid evolutionary optimization framework. J Mol Liq 2020;297:111893. https://doi.org/10.1016/j.molliq.2019.111893.Suche in Google Scholar

31. Ryzhikov, I, Semenkin, E, Panfilov, I. Evolutionary optimization algorithms for differential equation parameters, initial value and order identification. In: Proceedings of the 13th international conference on Informatics in Control, Automation and Robotics (ICINCO 2016). Lisbon, Portugal: SCITEPRESS; 2016, 1:168–76 pp.10.5220/0005979201680176Suche in Google Scholar

32. Gujarathi, AM, Nezhaad, GV, Vatani, M. Optimization of process design problems using differential evolution algorithm. J Eng Res 2016;13:88–101.10.24200/tjer.vol13iss1pp89-102Suche in Google Scholar

33. Saha, C, Agbu, N, Jinks, R, Huda, MN. Review article of the solar PV parameters estimation using evolutionary algorithms. MOJSP 2018;2:63–75.Suche in Google Scholar

34. Dragoi, EN, Curteanu, S. The use of differential evolution algorithm for solving chemical engineering problems. Rev Chem Eng 2016;32:149–80. https://doi.org/10.1515/revce-2015-0042.Suche in Google Scholar

35. Esmailzadeh, A, Rahnamayan, S. Opposition-based differential evolution with protective generation jumping. Paris, France: IEEE Symposium on Differential Evolution (SDE); 2011:1–8 pp.10.1109/SDE.2011.5952059Suche in Google Scholar

36. Rahnamayan, S, Tizhoosh, HR, Salama, MMA. A novel population initialization method for accelerating evolutionary algorithms. Comput Math Appl 2007;53:1605–14. https://doi.org/10.1016/j.camwa.2006.07.013.Suche in Google Scholar

37. Storn, R, Price, K. Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. Berkeley. CA: International Computer Science Institute; 1995. Tech. Rep. TR-95-012.Suche in Google Scholar

38. Storn, R, Price, K. Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 1997;11:341–59. https://doi.org/10.1023/a:1008202821328.10.1023/A:1008202821328Suche in Google Scholar

39. Onwubolu, GC, Babu, BV. New optimization techniques in engineering. Berlin, New York: Springer; 2004.10.1007/978-3-540-39930-8Suche in Google Scholar

40. Zhang, H, Rangaiah, GP. A hybrid global optimization algorithm and its applications to parameter estimation problems. Asia Pac J Chem Eng 2011;6:379–90. https://doi.org/10.1002/apj.548.Suche in Google Scholar

41. Price, KV. An introduction to differential evolution. In: Corne, D, Dorigo, M, Glover, F, editors. New ideas in optimization. London, UK: McGraw-Hill; 1999:79–108 pp.Suche in Google Scholar

42. Ali, M, Pant, M. Improving the performance of differential evolution algorithm using Cauchy mutation. Soft Comput 2011;15:991–1007. https://doi.org/10.1007/s00500-010-0655-2.Suche in Google Scholar

43. Storn, R. On the usage of differential evolution for function optimization. In: Proceedings: NAFIPS 1996. Berkeley, CA, USA; 1996:519–23 pp.Suche in Google Scholar

44. Sarker, RA, Elsayed, SM, Ray, T. Differential evolution with dynamic parameters selection for optimization problems. IEEE Trans Evol Comput 2014;18:689–707. https://doi.org/10.1109/tevc.2013.2281528.Suche in Google Scholar

45. Das, S, Mullick, SS, Suganthan, PN. Recent advances in differential evolution-an updated survey. Swarm Evol Comput 2016;27:1–30. https://doi.org/10.1016/j.swevo.2016.01.004.Suche in Google Scholar

46. Rahnamayan, S, Tizhoosh, HR, Salama, MMA. Opposition-based differential evolution for optimization of noisy problems. In: 2006 IEEE int. conf. evol. comput.; 2006:1865–72 pp.10.1109/CEC.2006.1688534Suche in Google Scholar

47. Rahnamayan, S, Tizhoosh, HR, Salama, MMA. Opposition-based differential evolution. IEEE Trans Evol Comput 2008;12:64–79. https://doi.org/10.1109/tevc.2007.894200.Suche in Google Scholar

48. Ozer, AB. CIDE: chaotically initialized differential evolution. Expert Syst Appl 2010;37:4632–41. https://doi.org/10.1016/j.eswa.2009.12.045.Suche in Google Scholar

49. Melo, VV, Delbem, ACB. Investigating smart sampling as a population initialization method for differential evolution in continuous problems. Inf Sci 2012;193:36–53. https://doi.org/10.1016/j.ins.2011.12.037.Suche in Google Scholar

50. Zhu, W, Tang, Y, Fang, JA, Zhang, W. Adaptive population tuning scheme for differential evolution. Inf Sci 2013;223:164–91. https://doi.org/10.1016/j.ins.2012.09.019.Suche in Google Scholar

51. Poikolainen, I, Neri, F, Caraffini, F. Cluster-based population initialization for differential evolution frameworks. Inf Sci 2015;297:216–35. https://doi.org/10.1016/j.ins.2014.11.026.Suche in Google Scholar

52. Bajer, D, Martinovic, G, Brest, J. A population initialization method for evolutionary algorithms based on clustering and Cauchy deviates. Expert Syst Appl 2016;60:294–310. https://doi.org/10.1016/j.eswa.2016.05.009.Suche in Google Scholar

53. Ali, MZ, Awad, NZ, Suganthan, PN, Reynolds, RG. An adaptive multipopulation differential evolution with dynamic population reduction. IEEE Trans Cybern 2016;47:2768–79. https://doi.org/10.1109/tcyb.2016.2617301.Suche in Google Scholar

54. Mustafi, D, Sahoo, G. A hybrid approach using genetic algorithm and the differential evolution heuristic for enhanced initialization of the k-means algorithm with applications in text clustering. Soft Comput 2019;23:6361–78. https://doi.org/10.1007/s00500-018-3289-4.Suche in Google Scholar

55. Liu, WL, Gong, YJ, Chen, WN, Liu, Z, Wang, H, Zhang, J. Coordinated charging scheduling of electric vehicles: a mixed-variable differential evolution approach. IEEE Trans Intell Transport Syst 2020;21:5094–109. https://doi.org/10.1109/tits.2019.2948596.Suche in Google Scholar

56. Zhao, F, He, X, Mang, L. A two-stage cooperative evolutionary algorithm with problem-specific knowledge for energy-efficient scheduling of no-wait flow-shop problem. IEEE Trans Cybern 2021;51:5291–303. https://doi.org/10.1109/tcyb.2020.3025662.Suche in Google Scholar

57. Zhao, F, Ma, R, Wang, L. A self-learning discrete Jaya algorithm for multiobjective energy-efficient distributed no-idle flow-shop scheduling problem in heterogeneous factory system. IEEE Trans Cybern 2022;52:12675–86.10.1109/TCYB.2021.3086181Suche in Google Scholar PubMed

58. Zhou, S, Xing, L, Zheng, X, Du, N, Wang, L, Zhang, Q. A self-adaptive differential evolution algorithm for scheduling a single batch-processing machine with arbitrary job sizes and release times. IEEE Trans Cybern 2021;51:1430–42. https://doi.org/10.1109/tcyb.2019.2939219.Suche in Google Scholar

59. Ahmad, MF, Isa, NAM, Lim, WH, Ang, KM. Differential evolution with modified initialization scheme using chaotic oppositional based learning strategy. Alex Eng J 2022;61:11835–58. https://doi.org/10.1016/j.aej.2022.05.028.Suche in Google Scholar

60. Ahandani, MA, Alavi-Rad, H. Opposition-based learning in the shuffled differential evolution algorithm. Soft Comput 2012;16:1303–37. https://doi.org/10.1007/s00500-012-0813-9.Suche in Google Scholar

61. Dhahri, H, Alimi, AM. Opposition-based differential evolution for beta basis function neural network. In: IEEE cong. evol. comput.; 2010:1–8 pp.10.1109/CEC.2010.5585970Suche in Google Scholar

62. Peng, L, Wang, Y. Differential evolution using uniform-quasi opposition for initializing the population. Inf Technol J 2010;9:1629–34. https://doi.org/10.3923/itj.2010.1629.1634.Suche in Google Scholar

63. Rahnamayan, S, Tizhoosh, HR, Salama, MMA. Opposition-based differential evolution (ODE) with variable jumping rate. Honolulu, In: IEEE Symp Foun Comput Intell. FOCI 2007; 2007:81–8 pp.10.1109/FOCI.2007.372151Suche in Google Scholar

64. Rahnamayan, S, Tizhoosh, HR, Salama, MMA. Quasi-oppositional differential evolution. In: IEEE cong. evol. comput. (CEC’07). Singapore: IEEE; 2007:2229–36 pp.10.1109/CEC.2007.4424748Suche in Google Scholar

65. Thangaraj, R, Pant, M, Chelliah, TR, Abraham, A. Opposition based chaotic differential evolution algorithm for solving global optimization problems. In: 4th world cong. NaBIC’12. Mexico City: IEEE; 2012:1–7 pp.10.1109/NaBIC.2012.6402168Suche in Google Scholar

66. Wang, H, Wu, Z, Rahnamayan, S. Enhanced opposition-based differential evolution for solving high-dimensional continuous optimization problems. Soft Comput 2011;15:2127–40. https://doi.org/10.1007/s00500-010-0642-7.Suche in Google Scholar

67. Wang, H, Wu, Z, Rahnamayan, S, Wang, J. Diversity Analysis of opposition-based differential evolution-an experimental study. In: Cai, Z, Hu, C, Kang, Z, Liu, Y, editors. Adv. comput. intell. Springer Berlin, Heidelberg; 2010:95–102 pp.10.1007/978-3-642-16493-4_10Suche in Google Scholar

68. Wang, J, Wu, Z, Wang, H. Hybrid differential evolution algorithm with chaos and generalized opposition-based learning. In: Cai, Z, Hu, C, Kang, Z, Liu, Y, editors. Adv. comput. intell. Springer Berlin/Heidelberg; 2010:103–11 pp.10.1007/978-3-642-16493-4_11Suche in Google Scholar

69. Wu, Y, Zhao, B, Guo, J, Su, TJ, Luo, AR, Fan, RJ, et al.. A fast opposition-based differential evolution with cauchy mutation. In: Glob congress intell. sys.; 2012:72–5 pp.10.1109/GCIS.2012.91Suche in Google Scholar

70. Tjoa, IB, Biegler, LT. Reduced successive quadratic programming strategy for errors-in-variables estimation. Comput Chem Eng 1992;16:523–33. https://doi.org/10.1016/0098-1354(92)80064-g.Suche in Google Scholar

71. Floudas, CA, Adjiman, CS, Esposito, WR, Gümüş, ZH, Harding, ST, Klepeis, JL, et al.. Handbook of test problems in local and global optimization, 1st ed. New York, NY: Springer; 1999, vol. 33:167–76 pp.10.1007/978-1-4757-3040-1_5Suche in Google Scholar

72. Esposito, WR, Foudas, CA. Global optimization in parameter estimation of nonlinear algebraic models via the error-in-variables approach. Ind Eng Chem Res 1998;37:1841–58. https://doi.org/10.1021/ie970852g.Suche in Google Scholar

73. Esposito, WR, Foudas, CA. Parameter estimation in nonlinear algebraic models via global optimization. Comput Chem Eng 1998;22:S213–20. https://doi.org/10.1016/s0098-1354(98)00217-8.Suche in Google Scholar

74. Rod, V, Hancil, V. Iterative estimati1on of model parameters when measurements of all variables are subject to error. Comput Chem Eng 1980;4:33–8. https://doi.org/10.1016/0098-1354(80)80011-1.Suche in Google Scholar

75. Moore, R, Hansen, E, Ledere, A. Rigorous methods for global optimization. In: Recent advances for global optimization. Pri1nceton: Princeton University Press; 2014:321–42 pp.10.1515/9781400862528.321Suche in Google Scholar

76. Valko, P, Vajda, S. An extended marquardt-type procedure for fitting error-in-variables models. Comput Chem Eng 1987;11:37–43. https://doi.org/10.1016/0098-1354(87)80004-2.Suche in Google Scholar

77. Kim, IW, Liebman, MJ, Edgar, TF. Robust error-in-variables estimation using nonlinear programming techniques. AIChE J 1990;36:985–93. https://doi.org/10.1002/aic.690360703.Suche in Google Scholar
Received: 2022-08-23
Accepted: 2023-07-20
Published Online: 2023-08-18

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Research Articles
  3. Tuning of PID controllers for unstable first-order plus dead time systems
  4. Oxygen excess ratio control of PEM fuel cell: fractional order modeling and fractional filter IMC-PID control
  5. Proposal and energy/exergy/economic analyses of a smart heat recovery for distillation tower of the Naphtha Hydrotreating Unit of the Petrochemical Plant; designing a low-carbon plant
  6. Three-dimensional CFD study on thermo-hydraulic behaviour of finned tubes in a heat exchange system for heat transfer enhancement
  7. A simulation and thermodynamic improvement of the methanol production process with economic analysis: natural gas vapor reforming and utilization of carbon capture
  8. Optimization of hydrogel composition for effective release of drug
  9. Mathematical modelling of water-based biogas scrubber operating at digester pressure
  10. COCO, a process simulator: methane oxidation simulation & its agreement with commercial simulator’s predictions
  11. Hydrodynamics of shear thinning fluid in a square microchannel: a numerical approach
  12. Parameter estimation in non-linear chemical processes: an opposite point-based differential evolution (OPDE) approach
https://doi.org/10.1515/cppm-2022-0044
Schlagwörter für diesen Artikel
chemical processes; differential evolution; evolutionary algorithms; global optimization; non-linear optimization; parameter estimation

Artikel in diesem Heft

  1. Frontmatter
  2. Research Articles
  3. Tuning of PID controllers for unstable first-order plus dead time systems
  4. Oxygen excess ratio control of PEM fuel cell: fractional order modeling and fractional filter IMC-PID control
  5. Proposal and energy/exergy/economic analyses of a smart heat recovery for distillation tower of the Naphtha Hydrotreating Unit of the Petrochemical Plant; designing a low-carbon plant
  6. Three-dimensional CFD study on thermo-hydraulic behaviour of finned tubes in a heat exchange system for heat transfer enhancement
  7. A simulation and thermodynamic improvement of the methanol production process with economic analysis: natural gas vapor reforming and utilization of carbon capture
  8. Optimization of hydrogel composition for effective release of drug
  9. Mathematical modelling of water-based biogas scrubber operating at digester pressure
  10. COCO, a process simulator: methane oxidation simulation & its agreement with commercial simulator’s predictions
  11. Hydrodynamics of shear thinning fluid in a square microchannel: a numerical approach
  12. Parameter estimation in non-linear chemical processes: an opposite point-based differential evolution (OPDE) approach
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 30.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/cppm-2022-0044/pdf?lang=de
Button zum nach oben scrollen