Ignition–extinction analysis of catalytic reactor models
-
Vemuri Balakotaiah
,
Zhe Sun
and
Ram Ratnakar
Upstream Oil & Gas Technology , editorial advisor ofJNGSE and a member of SPE’s advisory committees. He received a BTech from IIT Delhi, India and a PhD from University of Houston, USA, both in chemical engineering. He has authored more than 40 technical papers and contributed significantly in the areas of multiscale modeling, reactive-transport, PVT and new energy.
Abstract
A detailed analysis of the ignition–extinction and hysteresis behavior of the two widely used catalytic reactor models (packed-bed and monolith) for the case of a single exothermic reaction is presented. First, limiting models are used to determine the minimum adiabatic temperature rise and/or catalyst activity needed to observe hysteresis behavior. Next, explicit expressions are provided for estimating the feed temperature or space time at ignition (light-off) and extinction (blow-out) as a function of the adiabatic temperature rise (or inlet concentration of limiting reactant), effective thermal conductivity, time and length scales (reactor, tube/channel diameter, effective diffusion length and pore size), catalyst activity (or dilution) and heat loss. It is shown that various limiting reactor models such as the thin-bed, long-bed, lumped thermal, adiabatic and strongly cooled cases that are defined in terms of various inter- and intraphase heat and mass dispersion time scales can be used to derive scaling relations that are useful in predicting the ignition/extinction loci for both laboratory scale (with heat exchange) and large scale (near adiabatic) reactors.
About the authors
Vemuri Balakotaiah is a professor of chemical and biomolecular engineering and holds the Hugh Roy and Lillie Cranz Cullen Distinguished University Chair at the University of Houston. His research interests are in the areas of chemical and catalytic reaction engineering, multiphase flow, transport phenomena and applied mathematics and computation. He has authored more than 200 research articles, developed and taught many graduate level courses, and served as advisor or coadvisor to more than 50 doctoral students on these topics.
Zhe Sun works as a postdoctoral researcher in Chemical Engineering Department at University of Houston (UH). He received his doctoral degree in chemical engineering from UH in 2019. His doctoral research focuses on mathematical modeling and numerical analysis of chemical reactors. He received his Master’s degree from University of Pennsylvania and his Bachelor’s degree from Beijing University of Chemical Technology (China), both in chemical engineering. He is currently working on the scale-up of autothermal reactors for catalytic partial oxidation reactions.
Ram Ratnakar is a subject matter expert (thermodynamics/PVT) and a researcher in R&D Mathematics & Computation at Shell Int. E&P. He is editor-in-chief of Upstream Oil & Gas Technology, editorial advisor of JNGSE and a member of SPE’s advisory committees. He received a BTech from IIT Delhi, India and a PhD from University of Houston, USA, both in chemical engineering. He has authored more than 40 technical papers and contributed significantly in the areas of multiscale modeling, reactive-transport, PVT and new energy.
Acknowledgments
The senior author (V. B) would like to thank SABIC Americas Inc., especially David H. West, for support of his work on the dynamics of chemical reactors. Additional support was also provided by the University of Houston through the Cullen professorship.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no financial conflicts of interest regarding this article.
References
Adaje, J. and Sheintuch, M. (1990). Comparison of multiplicity patterns of a single catalytic pellet and a fixed catalytic bed for ethylene oxidation. Chem. Eng. Sci. 45: 1331–1342, https://doi.org/10.1016/0009-2509(90)87125-c.Search in Google Scholar
Agrawal, R., West, D.H., and Balakotaiah, V. (2008). Transport limited pattern formation in catalytic fluid–particle systems. Chem. Eng. Sci. 63: 460–483, https://doi.org/10.1016/j.ces.2007.09.024.Search in Google Scholar
Aris, R. (1969). On stability criteria of chemical reaction engineering. Chem. Eng. Sci. 24: 149–169, https://doi.org/10.1016/0009-2509(69)80017-5.Search in Google Scholar
Aris, R. (1993). Ends and beginnings in the mathematical modelling of chemical engineering systems. Chem. Eng. Sci. 48: 2507–2517, https://doi.org/10.1016/0009-2509(93)80263-p.Search in Google Scholar
Aris, R. and Amundson, N.R. (1958). An analysis of chemical reactor stability and control—II: the evolution of proportional control. Chem. Eng. Sci. 7: 132–147, https://doi.org/10.1016/0009-2509(58)80020-2.Search in Google Scholar
Balakotaiah, V. (1982). Structure of the steady-state solutions of lumped-parameter chemically reacting systems, PhD thesis. Houston: University of Houston.10.1016/0009-2509(82)80030-4Search in Google Scholar
Balakotaiah, V. (1989). Simple runaway criteria for cooled reactors. AIChE J. 35: 1039–1043, https://doi.org/10.1002/aic.690350618.Search in Google Scholar
Balakotaiah, V. (1996). Structural stability of nonlinear convection-reaction models. Chem. Eng. Educ. 30: 234–239.Search in Google Scholar
Balakotaiah, V. (2008). On the relationship between Aris and Sherwood numbers and friction and effectiveness factors. Chem. Eng. Sci. 63: 5802–5812, https://doi.org/10.1016/j.ces.2008.08.025.Search in Google Scholar
Balakotaiah, V. and Chakraborty, S. (2003). Averaging theory and low-dimensional models for chemical reactors and reacting flows. Chem. Eng. Sci. 58: 4769–4786, https://doi.org/10.1016/j.ces.2002.11.002.Search in Google Scholar
Balakotaiah, V. and Chang, H.C. (1995). Dispersion of chemical solutes in chromatographs and reactors. Philos. Trans. R. Soc. London, Ser. A Phys. Eng. Sci. 351: 39–75.10.1098/rsta.1995.0025Search in Google Scholar
Balakotaiah, V., Kodra, D., and Nguyen, D. (1995). Runaway limits for homogeneous and catalytic reactors. Chem. Eng. Sci. 50: 1149–1171, https://doi.org/10.1016/0009-2509(94)00463-2.Search in Google Scholar
Balakotaiah, V. and Luss, D. (1983). Multiplicity features of reacting systems: dependence of the steady-states of a CSTR on the residence time. Chem. Eng. Sci. 38: 1709–1721, https://doi.org/10.1016/0009-2509(83)85028-3.Search in Google Scholar
Balakotaiah, V. and Ratnakar, R.R. (2010). On the use of transfer and dispersion coefficient concepts in low-dimensional diffusion–convection-reaction models. Chem. Eng. Res. Des. 88: 342–361, https://doi.org/10.1016/j.cherd.2009.10.008.Search in Google Scholar
Balakotaiah, V., Sun, Z., Gu, T., and West, D.H. (2021). Scaling relations for autothermal operation of catalytic reactors. Ind. Eng. Chem. Res., https://doi.org/10.1021/acs.iecr.0c05594.Search in Google Scholar
Balakotaiah, V., Sun, Z., and West, D.H. (2019). Autothermal reactor design for catalytic partial oxidations. Chem. Eng. J. 374: 1403–1419, https://doi.org/10.1016/j.cej.2019.05.155.Search in Google Scholar
Bilous, O. and Amundson, N.R. (1955). Chemical reactor stability and sensitivity. AIChE J. 1: 513–521, https://doi.org/10.1002/aic.690010422.Search in Google Scholar
Bird, R.B., Stewart, W.E., and Lightfoot, E.N. (1960). Transport phenomena. New York: Wiley.Search in Google Scholar
Boreskov, G.K. and Matros, Y.S. (1983). Unsteady-state performance of heterogeneous catalytic reactions. Catal. Rev. Sci. Eng. 25: 551–590, https://doi.org/10.1080/01614948308078056.Search in Google Scholar
Bos, A.N.R., Hof, E., Kuper, W., and Westerterp, K.R. (1993). The behaviour of a single catalyst pellet for the selective hydrogenation of ethyne in ethene. Chem. Eng. Sci. 48: 1959–1969, https://doi.org/10.1016/0009-2509(93)80074-z.Search in Google Scholar
Bremer, J. and Sundmacher, K. (2019). Operation range extension via hot-spot control for catalytic methanation reactors. React. Chem. Eng. 4: 1019–1037, https://doi.org/10.1039/c9re00147f.Search in Google Scholar
Brown, J.R. and Schmitz, R.A. (1989). Multiplicity of states in systems of interacting catalyst particles. Chem. Eng. Commun. 84: 191–215, https://doi.org/10.1080/00986448908940342.Search in Google Scholar
Carr, J. (1982). Applications of centre manifold theory, 35. Springer-Verlag, New York.10.1007/978-1-4612-5929-9Search in Google Scholar
Chakraborty, S. and Balakotaiah, V. (2004). Multi-mode low-dimensional models for non-isothermal homogeneous and catalytic reactors. Chem. Eng. Sci. 59: 3695–3724, https://doi.org/10.1016/j.ces.2004.05.022.Search in Google Scholar
Chakraborty, S. and Balakotaiah, V. (2005). Spatially averaged multi-scale models for chemical reactors. Adv. Chem. Eng. 30: 205–297, https://doi.org/10.1016/s0065-2377(05)30004-4.Search in Google Scholar
Chang, H.C. and Balakotaiah, V. (2003). Hyperbolic homogenized models for thermal and solutal dispersion. SIAM J. Appl. Math. 63: 1231–1258, https://doi.org/10.1137/s0036139901368863.Search in Google Scholar
Chen, L., Pannala, S., Broekhuis, R., Gautam, P., Gu, T., West, D., and Balakotaiah, V. (2020). Three-dimensional CFD simulation of pattern formation in a shallow packed-bed reactor for oxidative coupling of methane. Chem. Eng. J. 400: 125979, https://doi.org/10.1016/j.cej.2020.125979.Search in Google Scholar
Christoforatou, E.L., Balakotaiah, V., and West, D.H. (1998). Runaway limits for adiabatic packed-bed catalytic reactors. AIChE J. 44: 394–404, https://doi.org/10.1002/aic.690440216.Search in Google Scholar
Davy, H. (1816). I. On the fire-damp of coal mines, and on methods of lighting the mines so as to prevent its explosion. Philos. Trans. R. Soc. Lond. 106: 1–22.10.1080/14786441508638577Search in Google Scholar
Davy, H. (1817). VIII. Some new experiments and observations on the combustion of gaseous mixtures, with an account of a method of preserving a continued light in mixtures of inflammable gases and air without flame. Philos. Trans. R. Soc. Lond. 107: 77–85.10.1098/rstl.1817.0009Search in Google Scholar
Deckwer, W.D. (1974). The backflow cell model—applied to non-isothermal reactors. Chem. Eng. J. 8: 135–144, https://doi.org/10.1016/0300-9467(74)85016-1.Search in Google Scholar
Doraiswamy, L.K. and Tajbl, D.G. (1974). Laboratory catalytic reactors. Catal. Rev. Sci. Eng. 10: 177–219, https://doi.org/10.1080/01614947408079629.Search in Google Scholar
Dougherty, R.C., Thygeson, J.R., and Hu, R. (1993). Multiple steady states of adiabatic fixed-bed reactors. Chem. Eng. Commun. 126: 155–177, https://doi.org/10.1080/00986449308936216.Search in Google Scholar
Duarte, S.P., Ferretti, O.A., and Lemcoff, N.O. (1984). A heterogeneous one-dimensional model for non-adiabatic fixed bed catalytic reactors. Chem. Eng. Sci. 39: 1025–1031, https://doi.org/10.1016/0009-2509(84)87011-6.Search in Google Scholar
Eigenberger, G. (1972a). On the dynamic behavior of the catalytic fixed-bed reactor in the region of multiple steady states—I. The influence of heat conduction in two phase models. Chem. Eng. Sci. 27: 1909–1915, https://doi.org/10.1016/0009-2509(72)87049-0.Search in Google Scholar
Eigenberger, G. (1972b). On the dynamic behavior of the catalytic fixed-bed reactor in the region of multiple steady states—II. The influence of the boundary conditions in the catalyst phase. Chem. Eng. Sci. 27: 1917–1924, https://doi.org/10.1016/0009-2509(72)87050-7.Search in Google Scholar
Eigenberger, G. and Nieken, U. (1988). Catalytic combustion with periodic flow reversal. Chem. Eng. Sci. 43: 2109–2115, https://doi.org/10.1016/0009-2509(88)87091-x.Search in Google Scholar
Eigenberger, G. and Ruppel, W. (2012). Catalytic fixed-bed reactors. Ullmann’s Encycl. Ind. Chem. 1–66, https://doi.org/10.1002/14356007.b04_199.Search in Google Scholar
Endo, I., Furusawa, T., and Matsuyama, H. (1978). Stability of catalytic reactors: a critical review. Catal. Rev. Sci. Eng. 18: 297–335, https://doi.org/10.1080/03602457808081870.Search in Google Scholar
Froment, G.F., Bischoff, K.B., and De Wilde, J. (2010). Chemical reactor analysis and design, 3rd ed. New York: Wiley.Search in Google Scholar
Golubitsky, M. and Keyfitz, B.L. (1980). A qualitative study of the steady-state solutions for a continuous flow stirred tank chemical reactor. SIAM J. Math. Anal. 11: 316–339, https://doi.org/10.1137/0511030.Search in Google Scholar
Gu, T. and Balakotaiah, V. (2016). Impact of heat and mass dispersion and thermal effects on the scale-up of monolith reactors. Chem. Eng. J. 284: 513–535, https://doi.org/10.1016/j.cej.2015.09.005.Search in Google Scholar
Gundlapally, S.R. and Balakotaiah, V. (2011). Heat and mass transfer correlations and bifurcation analysis of catalytic monoliths with developing flows. Chem. Eng. Sci. 66: 1879–1892, https://doi.org/10.1016/j.ces.2011.01.045.Search in Google Scholar
Gundlapally, S.R. and Balakotaiah, V. (2013). Analysis of the effect of substrate material on the steady-state and transient performance of monolith reactors. Chem. Eng. Sci. 92: 198–210, https://doi.org/10.1016/j.ces.2013.01.051.Search in Google Scholar
Hegedus, L.L., Oh, S.H., and Baron, K. (1977). Multiple steady states in an isothermal, integral reactor: the catalytic oxidation of carbon monoxide over platinum-alumina. AIChE J. 23: 632–642, https://doi.org/10.1002/aic.690230503.Search in Google Scholar
Heinemann, R.F. and Poore, A.B. (1981). Multiplicity, stability, and oscillatory dynamics of the tubular reactor. Chem. Eng. Sci. 36: 1411–1419, https://doi.org/10.1016/0009-2509(81)80175-3.Search in Google Scholar
Hickman, D.A., Degenstein, J.C., and Ribeiro, F.H. (2016). Fundamental principles of laboratory fixed bed reactor design. Curr. Opin. Chem. Eng. 13: 1–9, https://doi.org/10.1016/j.coche.2016.07.002.Search in Google Scholar
Hlaváček, V. and Hofmann, H. (1970a). Modeling of chemical reactors—XVI steady state axial heat and mass transfer in tubular reactors an analysis of the uniqueness of solutions. Chem. Eng. Sci. 25: 173–185.10.1016/0009-2509(70)85030-8Search in Google Scholar
Hlaváček, V. and Hofmann, H. (1970b). Modeling of chemical reactors—XVII Steady state axial heat and mass transfer in tubular reactors numerical investigation of multiplicity. Chem. Eng. Sci. 25: 187–199.10.1016/0009-2509(70)85031-XSearch in Google Scholar
Hlaváček, V., Hofmann, H., Votruba, J., and Kubíček, M. (1973). Modeling of chemical reactors—XXVII. Steady state axial heat and mass transfer in tubular reactors. Effect of different values of Peclet numbers on the region of multiplicity. Chem. Eng. Sci. 28: 1897–1900.10.1016/0009-2509(73)85073-0Search in Google Scholar
Hlaváček, V. and van Rompay, P. (1981). Current problems of multiplicity, stability and sensitivity of states in chemically reacting systems. Chem. Eng. Sci. 36: 1587–1597.10.1016/0009-2509(81)80002-4Search in Google Scholar
Huang, D.J. and Varma, A. (1981). Steady-state multiplicity of a nonadiabatic bubble column with fast reactions. AIChE J. 27: 111–120, https://doi.org/10.1002/aic.690270116.Search in Google Scholar
Hunt, L.B. (1958). The ammonia oxidation process for nitric acid manufacture. Platin. Met. Rev. 2: 129–134.Search in Google Scholar
Jensen, K.F. and Ray, W.H. (1982). The bifurcation behavior of tubular reactors. Chem. Eng. Sci. 37: 199–222, https://doi.org/10.1016/0009-2509(82)80155-3.Search in Google Scholar
Joshi, S.Y., Harold, M.P., and Balakotaiah, V. (2009). Low-dimensional models for real time simulations of catalytic monoliths. AIChE J. 55: 1771–1783, https://doi.org/10.1002/aic.11794.Search in Google Scholar
Kalthoff, O. and Vortmeyer, D. (1980). Ignition/extinction phenomena in a wall cooled fixed bed reactor: experiments and model calculations including radial porosity and velocity distributions. Chem. Eng. Sci. 35: 1637–1643, https://doi.org/10.1016/0009-2509(80)80056-x.Search in Google Scholar
Kapteijn, F. and Moulijn, J.A. (2008). Laboratory catalytic reactors: aspects of catalyst testing. In: Ertl, G., Knőzinger, H., Schűth, F., and Weitkamp, J. (Eds.), Handbook of heterogeneous catalyst, 2nd ed. Wiley-VCH, pp. 1361–1398.Search in Google Scholar
Kubíčekt, M., Hofmann, H., and Hlaváček, V. (1979). Modelling of chemical reactors-XXXII: nonisothermal nonadiabatic tubular reactor. One dimensional model-detailed analysis. Chem. Eng. Sci. 34: 593–600.10.1016/0009-2509(79)85104-0Search in Google Scholar
Kumar, P., Gu, T., Grigoriadis, K., Franchek, M., and Balakotaiah, V. (2014). Spatio-temporal dynamics of oxygen storage and release in a three-way catalytic converter. Chem. Eng. Sci. 111: 180–190, https://doi.org/10.1016/j.ces.2014.02.014.Search in Google Scholar
Kumar, P., Makki, I., Kerns, J., Grigoriadis, K., Franchek, M., and Balakotaiah, V. (2012). A low-dimensional model for describing the oxygen storage capacity and transient behavior of a three-way catalytic converter. Chem. Eng. Sci. 73: 373–387, https://doi.org/10.1016/j.ces.2011.12.001.Search in Google Scholar
Liljenroth, F.G. (1918). Starting and stability phenomena of ammonia-oxidation and similar reactions. Chem. Metall. Eng. 19: 287–293.Search in Google Scholar
Liu, S.L. and Amundson, N.R. (1962). Stability of adiabatic packed bed reactors. An elementary treatment. Ind. Eng. Chem. Fundam. 1: 200–208, https://doi.org/10.1021/i160003a008.Search in Google Scholar
Lovo, M. and Balakotaiah, V. (1992). Multiplicity features of adiabatic autothermal reactors. AIChE J. 38: 101–115, https://doi.org/10.1002/aic.690380111.Search in Google Scholar
Luss, D. (1971). Uniqueness criteria for lumped and distributed parameter chemically reacting systems. Chem. Eng. Sci. 26: 1713–1721, https://doi.org/10.1016/0009-2509(71)86059-1.Search in Google Scholar
Luss, D. (1980). Steady-state multiplicity and uniqueness criteria for chemically reacting systems. In: Stewart, W.E., Ray, W.H., and Conley, C.C. (Eds.), Dynamics and modeling of reactive systems, 1st ed. Academic Press, pp. 131–159.10.1016/B978-0-12-669550-2.50009-9Search in Google Scholar
Luss, D. and Balakotaiah, V. (1984). Steady-state multiplicity features of chemical reactors. Front. Chem. React. Eng. 1: 66–84.Search in Google Scholar
Mariani, N.J., Keegan, S.D., Martínez, O.M., and Barreto, G.F. (2012). Thermal behavior of laboratory-scale catalytic packed beds. Chem. Eng. J. 198: 397–411, https://doi.org/10.1016/j.cej.2012.05.101.Search in Google Scholar
Mikuš, O., Puszynski, J., and Hlaváček, V. (1979). Experimental observation of multiple steady states and temperature fields in a laboratory tubular reactor. Chem. Eng. Sci. 34: 434–436.10.1016/0009-2509(79)85082-4Search in Google Scholar
Pirie, J.M. (1958). The manufacture of hydrocyanic acid by the Andrussow process. Platin. Met. Rev. 2: 7–11.Search in Google Scholar
Puszyński, J., Šnita, D., Hlaváček, V., and Hofmann, H. (1981). A revision of multiplicity and parametric sensitivity concepts in nonisothermal nonadiabatic packed bed chemical reactors. Chem. Eng. Sci. 36: 1605–1609.10.1016/0009-2509(81)80004-8Search in Google Scholar
Ramanathan, K., Balakotaiah, V., and West, D.H. (2003). Light-off criterion and transient analysis of catalytic monoliths. Chem. Eng. Sci. 58: 1381–1405, https://doi.org/10.1016/s0009-2509(02)00679-6.Search in Google Scholar
Ratnakar, R.R. and Balakotaiah, V. (2015a). Reduced order multimode transient models for catalytic monoliths with micro-kinetics. Chem. Eng. J. 260: 557–572, https://doi.org/10.1016/j.cej.2014.09.008.Search in Google Scholar
Ratnakar, R.R. and Balakotaiah, V. (2015b). Reduced-order transient models for describing thermal gradients in catalytic monoliths. Ind. Eng. Chem. Res. 54: 10260–10274, https://doi.org/10.1021/acs.iecr.5b01377.Search in Google Scholar
Ratnakar, R.R. and Balakotaiah, V. (2017). Bifurcation analysis of index infinity DAE parabolic models describing reactors and reacting flows. AIChE J. 63: 295–305, https://doi.org/10.1002/aic.15568.Search in Google Scholar
Ratnakar, R.R., Bhattacharya, M., and Balakotaiah, V. (2012). Reduced order models for describing dispersion and reaction in monoliths. Chem. Eng. Sci. 83: 77–92, https://doi.org/10.1016/j.ces.2011.09.056.Search in Google Scholar
Ratnakar, R.R., Dadi, R.K., and Balakotaiah, V. (2018). Multi-scale reduced order models for transient simulation of multi-layered monolith reactors. Chem. Eng. J. 352: 293–305, https://doi.org/10.1016/j.cej.2018.04.053.Search in Google Scholar
Razon, L.F. and Schmitz, R.A. (1987). Multiplicities and instabilities in chemically reacting systems—a review. Chem. Eng. Sci. 42: 1005–1047, https://doi.org/10.1016/0009-2509(87)80055-6.Search in Google Scholar
Rink, J., Mozaffari, B., Tischer, S., Deutschmann, O., and Votsmeier, M. (2017). Real-time simulation of dual-layer catalytic converters based on the internal mass transfer coefficient approach. Top. Catal. 60: 225–229, https://doi.org/10.1007/s11244-016-0602-2.Search in Google Scholar
Root, R.B. and Schmitz, R.A. (1969). An experimental study of steady state multiplicity in a loop reactor. AIChE J. 15: 670–679, https://doi.org/10.1002/aic.690150509.Search in Google Scholar
Sarkar, B., Ratnakar, R.R., and Balakotaiah, V. (2020). Multi-scale coarse-grained continuum model for bifurcation and transient analysis of coupled homogeneous-catalytic reactions in monoliths. Chem. Eng. J., https://doi.org/10.1016/j.cej.2020.126500 (Epub ahead of print).Search in Google Scholar
Sarsani, S., West, D., Liang, W., and Balakotaiah, V. (2017). Autothermal oxidative coupling of methane with ambient feed temperature. Chem. Eng. J. 328: 484–496, https://doi.org/10.1016/j.cej.2017.07.002.Search in Google Scholar
Schmitz, R.A. (1975). Multiplicity, stability and sensitivity of states in chemically reacting systems-a review. Adv. Chem. Eng. 148: 156–211, https://doi.org/10.1021/ba-1975-0148.ch007.Search in Google Scholar
Sinkule, J., Votruba, J., Hlaváček, V., and Hofmann, H. (1976a). Modeling of chemical reactors—XXX: steady-state analysis of combined axial and gas-to-solid heat and mass transfer in a tubular adiabatic reactor. Chem. Eng. Sci. 31: 23–29, https://doi.org/10.1016/0009-2509(76)85004-x.Search in Google Scholar
Sinkule, J., Hlaváček, V., and Votruba, J. (1976b). Modeling of chemical reactors—XXXI: the one-phase backflow cell model used for simulation of tubular adiabatic reactors. Chem. Eng. Sci. 31: 31–36, https://doi.org/10.1016/0009-2509(76)85005-1.Search in Google Scholar
Subramanian, S. and Balakotaiah, V. (1996). Classification of steady-state and dynamic behavior of distributed reactor models. Chem. Eng. Sci. 51: 401–421, https://doi.org/10.1016/0009-2509(95)00261-8.Search in Google Scholar
Sun, Z., Kota, A., Sarsani, S., West, D.H., and Balakotaiah, V. (2018). Bifurcation analysis of methane oxidative coupling without catalyst. Chem. Eng. J. 343: 770–788, https://doi.org/10.1016/j.cej.2018.02.004.Search in Google Scholar
Sun, Z., West, D.H., and Balakotaiah, V. (2019). Bifurcation analysis of catalytic partial oxidations in laboratory-scale packed-bed reactors with heat exchange. Chem. Eng. J. 377: 119765, https://doi.org/10.1016/j.cej.2018.08.151.Search in Google Scholar
Sun, Z., West, D.H., Gautam, P., and Balakotaiah, V. (2020). Scale-up analysis of autothermal operation of methane oxidative coupling with catalyst. AIChE J. 66: e16949, https://doi.org/10.1002/aic.16949.Search in Google Scholar
Tu, M., Ratnakar, R. and Balakotaiah, V. (2020). Reduced order models with local property dependent transfer coefficients for real time simulations of monolith reactors. Chem. Eng. J. 383: 123074, https://doi.org/10.1016/j.cej.2019.123074.Search in Google Scholar
Uppal, A., Ray, W.H., and Poore, A.B. (1976). The classification of the dynamic behavior of continuous stirred tank reactors—influence of reactor residence time. Chem. Eng. Sci. 31: 205–214, https://doi.org/10.1016/0009-2509(76)85058-0.Search in Google Scholar
Van Heerden, C. (1953). Autothermic processes. Ind. Eng. Chem. 45: 1242–1247, https://doi.org/10.1021/ie50522a030.Search in Google Scholar
Van Heerden, C. (1958). The character of the stationary state of exothermic processes. Chem. Eng. Sci. 8: 133–145, https://doi.org/10.1016/0009-2509(58)80044-5.Search in Google Scholar
Varma, A. and Amundson, N.R. (1973). The non-adiabatic tubular reactor: stability considerations. Can. J. Chem. Eng. 51: 459–467, https://doi.org/10.1002/cjce.5450510411.Search in Google Scholar
Varma, A., Morbidelli, M., and Wu, H. (2005). Parametric sensitivity in chemical systems. Cambridge University Press, New York.Search in Google Scholar
Vejtasa, S.A. and Schmitz, R.A. (1970). An experimental study of steady state multiplicity and stability in an adiabatic stirred reactor. AIChE J. 16: 410–419, https://doi.org/10.1002/aic.690160318.Search in Google Scholar
Votruba, J., Hlaváček, V., and Sinkule, J. (1976). Experimental observation of multiple steady-states for diluted and blended catalyst beds. Chem. Eng. Sci. 31: 971–974, https://doi.org/10.1016/0009-2509(76)87050-9.Search in Google Scholar
Votruba, J., Kubíček, M., and Hlaváček, V. (1974). Modeling of chemical reactors—XXVIII. Steady state operation of tubular adiabatic fixed bed reactor with piston flow and external heat and mass transfer. Chem. Eng. Sci. 29: 2333–2338, https://doi.org/10.1016/0009-2509(74)80010-2.Search in Google Scholar
West, D.H. (2019). Progress and challenges in the autothermal oxidative coupling of methane. In: 4th North American symposium on chemical reaction engineering, Houston, Texas.Search in Google Scholar
Zeldovich, I.A., Barenblatt, G.I., Librovich, V.B., and Makhviladze, G.M. (1985). Mathematical theory of combustion and explosions. Springer, USA.10.1007/978-1-4613-2349-5Search in Google Scholar
Zeldovich, Y.B. and Zysin, U.A. (1941). On the theory of thermal intensity-performance of an exothermic reaction in a jet. J. Tech. Phys. 11: 501–8.Search in Google Scholar
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- In this issue
- Ignition–extinction analysis of catalytic reactor models
- A comprehensive and updated review of studies on the oxidation of cyclohexane to produce ketone-alcohol (KA) oil
- Polyoxadiazoles as proton exchange membranes for fuel cell application
- Synthesis and applications of surface-modified magnetic nanoparticles: progress and future prospects
- Advances in absorbents and techniques used in wet and dry FGD: a critical review
- Carbomer microgels as model yield-stress fluids
