Chemical Papers

, Volume 64, Issue 4, pp 450–460 | Cite as

Comparative evaluation of critical operating conditions for a tubular catalytic reactor using thermal sensitivity and loss-of-stability criteria

  • Gheorghe MariaEmail author
  • Dragoş-Nicolae Ştefan
Original Paper


Optimal operation of a chemical reactor according to various performance criteria often drives the system towards critical boundaries. Thus, precise evaluation of runaway limits in the parametric space becomes a crucial problem not only for the reactor’s safe operation, but also for over-designing the system. However, obtaining an accurate estimate for operating limits is a difficult task due to the limited validity of kinetic models describing complex processes, as well as the inherent fluctuations of the system’s properties (catalyst, raw-material quality). This paper presents a comparison of several effective methods of deriving critical conditions for the case of a tubular fixed-bed catalytic reactor used for aniline production in the vapour phase. Even though the methods being compared are related to one another, the generalised sensitivity criterion of Morbidelli-Varma (MV) seems to be more robust, not depending on a particular parameter being perturbed, when compared to the criteria that detect an incipient loss of system stability in the critical region (i.e., div-methods based on the system’s Jacobian and Green’s function matrix analysis). Combined application of div- and MV criteria allows for an accurate evaluation of the distance from the reactor’s nominal conditions to the safety limits.


runaway boundaries tubular reactor aniline sensitivity stability 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adrover, A., Creta, F., Giona, M., & Valorani, M. (2007) Explosion limits and runaway criteria: A stretching-based approach. Chemical Engineering Science, 62, 1171–1183. DOI: 10.1016/j.ces.2006.11.007.CrossRefGoogle Scholar
  2. Alós, M. A., Nomen, R., Sempere, J. M., Strozzi, F., & Zaldívar, J. M. (1998) Generalized criteria for boundary safe conditions in semi-batch processes: simulated analysis and experimental results. Chemical Engineering and Processing, 37, 405–421. DOI: 10.1016/S0255-2701(98)00048-8.CrossRefGoogle Scholar
  3. Balakotaiah, V., & Luss, D. (2004) Explicit runaway criterion for catalytic reactors with transport limitations. AIChE Journal, 37, 1780–1788. DOI: 10.1002/aic.690371203.CrossRefGoogle Scholar
  4. Bonvin, D. (1998) Optimal operation of batch reactors-a personal view. Journal of Process Control, 8, 355–368. DOI: 10.1016/S0959-1524(98)00010-9.CrossRefGoogle Scholar
  5. Bosch, J., Kerr, D. C., Snee, T. J., Strozzi, F., & Zaldívar, J. M. (2004) Runaway detection in a pilot-plant facility. Industrial & Engineering Chemistry Research, 43, 7019–7024. DOI: 10.1021/ie049540l.CrossRefGoogle Scholar
  6. Chen, M. S. K., Erickson, L. E., & Fan, L. (1970) Consideration of sensitivity and parameter uncertainty in optimal process design. Industrial & Engineering Chemistry Process Design and Development, 9, 514–521. DOI: 10.1021/i260036a004.CrossRefGoogle Scholar
  7. Doraiswamy, L. K., & Sharma, M. M. (1984) Heterogeneous reactions: Analysis, examples, and reactor design (Vol. 1). New York, NY, USA: Wiley.Google Scholar
  8. Fotopoulos, J., Georgakis, C., & Stenger, H. G., Jr. (1994) Uncertainty issues in the modeling and optimization of batch reactors with tendency models. Chemical Engineering Science, 49, 5533–5547. DOI: 10.1016/0009-2509(94)00336-X.CrossRefGoogle Scholar
  9. Froment, G. F., & Bischoff, K. B. (1990) Chemical reactor analysis and design. New York, NY, USA: Wiley.Google Scholar
  10. Grewer, T. (1994). Thermal hazards of chemical reactions. Amsterdam, The Netherlands: Elsevier.Google Scholar
  11. Hedges, R. M., Jr., & Rabitz, H. (1985) Parametric sensitivity of system stability in chemical dynamics. Journal of Chemical Physics, 82, 3674–3684. DOI: 10.1063/1.448903.CrossRefGoogle Scholar
  12. Maria, G., & Stefan, D.-N. (2010) Variability of operating safety limits with catalyst within a fixed-bed catalytic reactor for vapour-phase nitrobenzene hydrogenation. Journal of Loss Prevention in the Process Industries, 23, 112–126. DOI: 10.1016/j.jlp.2009.06.007.CrossRefGoogle Scholar
  13. Mönnigmann, M. (2004) Constructive nonlinear dynamics for the design of chemical engineering processes. PhD Thesis, RWTH Aachen, Germany: VDI Verlag.Google Scholar
  14. Mönnigmann, M., & Marquardt, W. (2003) Steady-state process optimization with guaranted robust stability and feasibility. AIChE Journal, 49, 3110–3126. DOI: 10.1002/aic.690491212.CrossRefGoogle Scholar
  15. Morbidelli, M., & Varma, A. (1988) A generalized criterion for parametric sensitivity: Application to thermal explosion theory. Chemical Engineering Science, 43, 91–102. DOI: 10.1016/0009-2509(88)87129-X.CrossRefGoogle Scholar
  16. Quina, M. M. J., & Quinta Ferreira, R. M. (1999) Thermal runaway conditions of a partially diluted catalytic reactor. Industrial & Engineering Chemistry Research, 38, 4615–4623. DOI: 10.1021/ie9807295.CrossRefGoogle Scholar
  17. Rihani, D. N., Narayanan, T. K., & Doraiswamy, L. K. (1965) Kinetics of catalytic vapor-phase hydrogenation of nitrobenzene to aniline. Industrial & Engineering Chemistry Process Design and Development, 4, 403–410. DOI: 10.1021/i260016a012.CrossRefGoogle Scholar
  18. Ruppen, D., Bonvin, D., & Rippin, D. W. T. (1997) Implementation of adaptive optimal operation for a semi-batch reaction system. Computers & Chemical Engineering, 22, 185–199. DOI: 10.1016/S0098-1354(96)00358-4.CrossRefGoogle Scholar
  19. Satterfield, C. N. (1970) Mass transfer in heterogeneous catalysis. Cambridge, MA, USA: MIT Press.Google Scholar
  20. Seinfeld, J., & McBride, W. L. (1970) Optimization with multiple performance criteria. Application to minimization of parameter sensitivities in a refinery model. Industrial & Engineering Chemistry Process Design and Development, 9, 53–57. DOI: 10.1021/i260033a010.CrossRefGoogle Scholar
  21. Srinivasan, B., Bonvin, D., Visser, E., & Palanki, S. (2002) Dynamic optimization of batch processes: II. Role of measurements in handling uncertainty, Computers & Chemical Engineering, 27, 27–44. DOI: 10.1016/S0098-1354(02)00117-5.CrossRefGoogle Scholar
  22. Stefan, D. N., & Maria, G. (2009) Derivation of operating region runaway boundaries for the vapour phase catalytic reactor used for aniline production. Revista de Chimie, 60, 949–956.Google Scholar
  23. Stoessel, F. (2008). Thermal safety of chemical processes. Risk assessment and process design. Weinheim, Germany: Wiley-VCH.CrossRefGoogle Scholar
  24. Strozzi, F., & Zaldívar, J. M. (1994) A general method for assessing the thermal stability of batch chemical reactors by sensitivity calculation based on Lyapunov exponents. Chemical Engineering Science, 49, 2681–2688. DOI: 10.1016/0009-2509(94)E0067-Z.CrossRefGoogle Scholar
  25. Strozzi, F., Zaldívar, J. M., Kronberg, A. E., & Westerterp, K. R. (1999) On-line runaway detection in batch reactors using chaos theory techniques. AIChE Journal, 45, 2429–2443. DOI: 10.1002/aic.690451116.CrossRefGoogle Scholar
  26. Trambouze, P., Van Landeghem, H., & Wauquier, J. P. (1988) Chemical reactors: Design, engineering, operation. Paris, France: Editions Technip.Google Scholar
  27. Vajda, S., & Rabitz, H. (1992) Parametric sensitivity and self-similarity in thermal explosion theory. Chemical Engineering Science, 47, 1063–1078. DOI: 10.1016/0009-2509(92)80232-2.CrossRefGoogle Scholar
  28. Varma, A., Morbidelli, M., & Wu, H. (1999). Parametric sensitivity in chemical systems. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  29. Watanabe, N., Nishimura, Y., & Matsubara, M. (1973) Optimal design of chemical processes involving parameter uncertainty. Chemical Engineering Science, 28, 905–913. DOI: 10.1016/0009-2509(77)80025-0.CrossRefGoogle Scholar
  30. Westerterp, K. R., & Molga, E. J. (2006) Safety and runaway prevention in batch and semibatch reactors-A review. Chemical Engineering Research and Design, 84, 543–552. DOI: 10.1205/cherd.05221.CrossRefGoogle Scholar
  31. Westerterp, K. R., & Molga, E. J. (2004) No more runaways in fine chemical reactors. Industrial & Engineering Chemistry Research, 43, 4585–4594. DOI: 10.1021/ie030725m.CrossRefGoogle Scholar
  32. Wen, C. Y., & Chang, M. T. (1968) Optimal design of systems involving parameter uncertainty. Industrial & Engineering Chemistry Process Design and Development, 7, 49–53. DOI: 10.1021/i260025a010.CrossRefGoogle Scholar
  33. Zaldívar, J. M., Cano, J., Alós, M. A., Sempere, J., Nomen, R., Lister, D., Maschio, G., Obertopp, T., Gilles, E. D., Bosch, J., & Strozzi, F. (2003) A general criterion to define runaway limits in chemical reactors. Journal of Loss Prevention in the Process Industries, 16, 187–200. DOI: 10.1016/S0950-4230(03)00003-2.CrossRefGoogle Scholar
  34. Zaldívar Comenges, J. M., Strozzi, F., & Bosch Pagans, J. (2005) Divergence as a goal function for control and on-line optimization. AIChE Journal, 51, 678–681. DOI: 10.1002/aic.10339.CrossRefGoogle Scholar
  35. Zaldívar, J.-M., & Strozzi, F. (2010) Phase-space volume based control of semibatch reactors. Chemical Engineering Research and Design, 88, 320–330. DOI: 10.1016/j.cherd.2009.04.008.CrossRefGoogle Scholar

Copyright information

© Institute of Chemistry, Slovak Academy of Sciences 2010

Authors and Affiliations

  1. 1.Department of Chemical EngineeringUniversity Politehnica of BucharestBucharestRomania

Personalised recommendations