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Application of a First Principles Mathematical Model of a Mass-Transfer Technological Process to Improve the Accuracy of the Estimation of the End Product Quality

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Abstract

This study addresses the problem of improvement of the accuracy of the estimation of the quality of the end product when the used set of training data segments is small. It is extended with a physically grounded model (first principles model) of a mass-transfer technological process involved in the production of methyl tert-butyl ether (MTBE). It is shown that the proposed approach is superior to other methods for the construction of statistical models (soft sensors) to estimate the quality of the end products, since it makes it possible to take into account physically grounded relationships and characteristics of the technological process, which ultimately leads to an increase in the level of adequacy of the developed model. The feasibility of the use of a first principles model of the mass-transfer process in the algorithm for the development of statistical models to estimate the quality index of the end product are determined under conditions of parametric uncertainty in the Murphree efficiency of mass transfer and the parameters of the binary interaction between isobutylene dimers and components from the MTBE production system. The use of the area of the region of the intersection of output variable distributions between the values in the extended training and test samples is proposed as a criterion for the effectiveness of extension of the training sample.

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REFERENCES

  1. Vairo, T., Reverberi, A.P., Bragatto, P.A., Milazzo, M.F., and Fabiano, B., Predictive model and soft sensors application to dynamic process operative control, Chem. Eng. Trans., 2021, vol. 86, pp. 535–540.

    Google Scholar 

  2. Jiang, Y., Yin, Sh., Dong, J., and Kaynak, O., A review on soft sensors for monitoring, control, and optimization of industrial processes, IEEE Sens. J., 2021, vol. 21, no. 11, pp. 12868–12881.

    Article  Google Scholar 

  3. Shokry, A., Vicente, P., Escudero, G., Pérez-Moya, M., Graells, M., and Espuña, A., Data-driven soft-sensors for online monitoring of batch processes with different initial conditions, Comput. Chem. Eng., 2018, vol. 118, pp. 159–179.

    Article  CAS  Google Scholar 

  4. Lin, B., Recke, B., Knudsen, J.K.H., and Jorgensen, S.B., A systematic approach for soft sensor development, Comput. Chem. Eng., 2007, vol. 31, nos. 5–6, pp. 419–425.

    Article  CAS  Google Scholar 

  5. Niño-Adan, I., Landa-Torres, I., Manjarres, D., Portillo, E., and Orbe, L., Soft-sensor for class prediction of the percentage of pentanes in butane at a debutanizer column, Sensors, 2021, vol. 21, p. 3991.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  6. Kadlec, P., Gabrys, B., and Strandt, S., Data-driven soft sensors in the process industry, Comput. Chem. Eng., 2009, vol. 33, pp. 759–814.

    Article  CAS  Google Scholar 

  7. Fortuna, L., Graziani, S., Rizzo, A., and Xibilia, M.G., Soft Sensors for Monitoring and Control of Industrial Processes, London, UK: Springer, 2007.

    Google Scholar 

  8. Graziani, S. and Xibilia, M.G., On the use of correlation analysis in the estimation of finite-time delay in soft sensors design, IEEE Int. Instrum. Meas. Technol. Conf., 2021, pp. 1–6.

  9. Ge, Zh., Huang, B., and Song, Zh., Mixture semisupervised principal component regression model and soft sensor application, AIChE J., 2014, vol. 60, no. 2, pp. 533–545.

    Article  CAS  Google Scholar 

  10. Sun, K., Tian, P., Qi, H., Ma, F., and Yang, G., An improved normalized mutual information variable selection algorithm for neural network based soft sensors, Sensors, 2019, vol. 19, no. 24, p. 5368.

    Article  PubMed Central  Google Scholar 

  11. Graziani, S. and Xibilia, M.G., Development and Analysis of Deep Learning Architectures (Deep Learning for Soft Sensor Design), Cham, Switzerland: Springer, 2020, Chapter 2.

    Google Scholar 

  12. Sun, Q. and Ge, Zh., A survey on deep learning for data-driven soft sensors, IEEE Trans. Ind. Inf., 2021, vol. 17, no. 9, pp. 5853–5866.

    Article  Google Scholar 

  13. Ge, Zh., Song, Zh., and Kano, M., External analysis-based regression model for robust soft sensing of multimode chemical processes, AIChE J., 2014, vol. 60, no. 1, pp. 136–147.

    Article  CAS  Google Scholar 

  14. Bakirov, R., Gabrys, B., and Fay, D., Multiple adaptive mechanisms for data-driven soft sensors, Comput. Chem. Eng., 2017, vol. 96, pp. 42–54.

    Article  CAS  Google Scholar 

  15. Zhu, J., Ge, Z., Song, Z., and Gao, F., Review and big data perspectives on robust data mining approaches for industrial process modeling with outliers and missing data, Annu. Rev. Control, 2018, vol. 46, pp. 107–133.

    Article  Google Scholar 

  16. Xie, R., Jan, N.M., Hao, K., Chen, L., and Huang, B., Supervised variational autoencoders for soft sensor modeling with missing data, IEEE Trans. Ind. Inf., 2019, vol. 16, no. 4, pp. 2820–2828.

    Article  Google Scholar 

  17. Kaneko, H. and Funatsu, K., Classification of the degradation of soft sensor models and discussion on adaptive models, AIChE J., 2013, vol. 59, no. 7, pp. 2339–2347.

    Article  CAS  Google Scholar 

  18. Hsiao, Y.-D., Kang, J.-L., and Wong, D.S.-H., Development of robust and physically interpretable soft sensor for industrial distillation column using transfer learning with small datasets, Processes, 2021, vol. 9, p. 667.

    Article  CAS  Google Scholar 

  19. Napoli, G. and Xibilia, M.G., Soft sensor design for a topping process in the case of small datasets, Comput. Chem. Eng., 2011, vol. 35, no. 11, pp. 2447–2456.

    Article  CAS  Google Scholar 

  20. Chang, C.-J., Li, D.-C., Huang, Y.-H., and Chen, C.-C., A novel gray forecasting model based on the box plot for small manufacturing data sets, Appl. Math. Comput., 2015, vol. 265, pp. 400–408.

    Google Scholar 

  21. Andrijić, Ž.U., Cvetnić, M., and Bolf, N., Soft sensor models for a fractionation reformate plant using small and bootstrapped data sets, Braz. J. Chem. Eng., 2018, vol. 35, pp. 745–756.

    Article  CAS  Google Scholar 

  22. Urhan, A., Ince, N.G., Bondy, R., and Alakent, B., Soft-sensor design for a crude distillation unit using statistical learning methods, Comput.-Aided Chem. Eng., 2018, vol. 44, pp. 2269–2274.

    Article  CAS  Google Scholar 

  23. Chen, Z.-S., Zhu, B., He, Y.-L., and Yu, L.-A., A PSO based virtual sample generation method for small sample sets: Applications to regression datasets, Eng. Appl. Artif. Intell., 2017, vol. 59, pp. 236–243.

    Article  Google Scholar 

  24. He, Y.L., Wang, P.J., Zhang, M.Q., Zhu, Q.X., and Xu, Y., A novel and effective nonlinear interpolation virtual sample generation method for enhancing energy prediction and analysis on small data problem: A case study of ethylene industry, Energy, 2018, vol. 147, pp. 418–427.

    Article  Google Scholar 

  25. Di Girolamo, M., Lami, M., Marchionna, M., Pescarollo, E., Tagliabue, L., and Ancillotti, F., Liquid-phase etherification/dimerization of isobutene over sulfonic acid resins, Ind. Eng. Chem. Res., 1997, vol. 36, pp. 4452–4458.

    Article  CAS  Google Scholar 

  26. Rehfinger, A. and Hoffmann, U., Kinetics of methyl-tertiary-butyl ether liquid phase synthesis catalyzed by ion exchange resin intrinsic rate expression in liquid phase activities, Chem. Eng. Sci., 1990, vol. 45, no. 6, pp. 1605–1617.

    Article  CAS  Google Scholar 

  27. Esbensen, K., Multivariate Data Analysis: Selected Chapters, Barnaul: Altai. Gos. Univ., 2003.

    Google Scholar 

  28. Wold, S., Sjöström, M., and Eriksson. L., PLS-regression: A basic tool of chemometrics, Chemom. Intell. Lab. Syst., 2001, vol. 58, pp. 109–130.

    Article  CAS  Google Scholar 

  29. De Jong, S., SIMPLS: An alternative approach to partial least squares regression, Chemom. Intell. Lab. Syst., 1993, vol. 18, pp. 251–263.

    Article  CAS  Google Scholar 

  30. Van Kollenburg, G.H., Van Es, J., Gerretzen, J., Lanters, H., Bouman, R., Koelewijn, W., Davies, A.N., Buydens, L.M.C., Van Manen, H.-J., and Jansen, J.J., Understanding chemical production processes by using PLS path model parameters as soft sensors, Comput. Chem. Eng., 2020, vol. 139, pp. 1–8.

    Article  CAS  Google Scholar 

  31. Kaneko, H., Arakawa, M., and Funatsu, K., Development of a new soft sensor method using independent component analysis and partial least squares, AIChE J., 2009, vol. 55, no. 1, pp. 87–98.

    Article  CAS  Google Scholar 

  32. Jin, H., Chen, X., Yang, J., and Wu, L., Adaptive soft sensor modeling framework based on just-in-time learning and kernel partial least squares regression for nonlinear multiphase batch processes, Comput. Chem. Eng., 2014, vol. 71, pp. 77–93.

    Article  CAS  Google Scholar 

  33. Si, Y., Wang, Y., and Zhou, D., Key-performance-indicator-related process monitoring based on improved kernel partial least squares, IEEE Trans. Ind. Electron. Control Instrum., 2020, vol. 68, no. 3, pp. 2626–2636.

    Article  Google Scholar 

  34. Deng, X., Chen, Y., Wang, P., and Cao, Y., Soft sensor modeling for unobserved multimode nonlinear processes based on modified kernel partial least squares with latent factor clustering, IEEE Access, 2020, vol. 8, pp. 35864–35872.

    Article  Google Scholar 

  35. Schwaab, M., Biscaia, E.C., Monteiro, J.L., and Pinto, J.C., Nonlinear parameter estimation through particle swarm optimization, Chem. Eng. Sci., 2008, vol. 63, no. 6, pp. 1542–1552.

    Article  CAS  Google Scholar 

  36. Ourique, C.O., Biscaia, E.C., and Pinto, J.C., The use of particle swarm optimization for dynamical analysis in chemical processes, Comput. Chem. Eng., 2002, vol. 26, no. 12, pp. 1783–1793.

    Article  CAS  Google Scholar 

  37. Prata, D.M., Schwaab, M., Lima, E.L., and Pinto, J.C., Nonlinear dynamic data reconciliation and parameter estimation through particle swarm optimization: application for an industrial polypropylene reactor, Chem. Eng. Sci., 2009, vol. 64, no. 18, pp. 3953–3967.

    Article  CAS  Google Scholar 

  38. Fredenslund, A., Jones, R.L., and Prausnitz, J.M., Group-contribution estimation of activity coefficients in nonideal liquid mixtures, AIChE J., 1975, vol. 21, no. 6, pp. 1086–1099.

    Article  CAS  Google Scholar 

  39. Abrams, D.S. and Prausnitz, J.M., Statistical thermodynamics of liquid mixtures: a new expression for the excess gibbs energy of partly or completely miscible systems, AIChE J., 1975, vol. 21, no. 1, pp. 116–128.

    Article  CAS  Google Scholar 

  40. Sundmacher, K., Uhde, G., and Hoffmann, U., Multiple reactions in catalytic distillation processes for the production of the fuel oxygenates MTBE and TAME: Analysis by rigorous model and experimental validation, Chem. Eng. Sci., 1999, vol. 54, pp. 2839–2847.

    Article  CAS  Google Scholar 

  41. On the Empirical Determination of the Distribution, Prokhorov, Yu.V., Ed., Moscow: Nauka, 1986.

    Google Scholar 

  42. Samotylova, S.A. and Torgashov, A.Y., Developing a soft sensor for MTBE process based on a small sample, Avtom. Telemekh., 2020, vol. 81, no. 11, pp. 2132–2142.

    Google Scholar 

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Funding

This study was partially supported by RFBR and NSFC, project no. 21-57-53005.

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Correspondence to S. A. Samotylova.

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The authors declare that they have no conflicts of interest.

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Translated by O. Kadkin

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Samotylova, S.A., Torgashov, A.Y. Application of a First Principles Mathematical Model of a Mass-Transfer Technological Process to Improve the Accuracy of the Estimation of the End Product Quality. Theor Found Chem Eng 56, 371–387 (2022). https://doi.org/10.1134/S0040579522020117

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