Cited by 180Heat and Mass Transfer in Porous MediaNonlinear Dynamics and Pattern FormationAdvanced Differential Equations and Dynamical Systems

The DOI matches its Crossref record; 86 of the 86 references it cites were found in a registry or an index.

The bifurcation behavior of tubular reactors

Jensen, Klavs F., Ray, W.Harmon·1982·Chemical Engineering Science

DOI 10.1016/0009-2509(82)80155-3

Open this paper in CoChat — free account

Integrity signals

Registry

Crossref · 10.1016/0009-2509(82)80155-3

Cites

86 of 86 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Bifurcation, perturbation of simple eigenvalues, itand linearized stability
Crandall, M. G., & Rabinowitz, P. H. (1973) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00282325 · Cited by 830
On the dynamic behavior of continuous stirred tank reactors
Uppal, A., Ray, W. H., & Poore, A. B. (1974) · Chemical Engineering Science · doi:10.1016/0009-2509(74)80089-8 · Cited by 737
Self-citation
The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
Francis, J. G. F. (1961) · The Computer Journal · doi:10.1093/comjnl/4.3.265 · Cited by 696
Solution of boundary-value problems by orthogonal collocation
Villadsen, J. V., & Stewart, W. E. (1967) · Chemical Engineering Science · doi:10.1016/0009-2509(67)80074-5 · Cited by 673
The QR Transformation--Part 2
Francis, J. G. F. (1962) · The Computer Journal · doi:10.1093/comjnl/4.4.332 · Cited by 384
Orthogonal collocation on finite elements
Carey, G. F., & Finlayson, B. A. (1975) · Chemical Engineering Science · doi:10.1016/0009-2509(75)80031-5 · Cited by 338
The classification of the dynamic behavior of continuous stirred tank reactors—influence of reactor residence time
Uppal, A., Ray, W. H., & Poore, A. B. (1976) · Chemical Engineering Science · doi:10.1016/0009-2509(76)85058-0 · Cited by 284
Self-citation
The Hopf Bifurcation Theorem in infinite dimensions
Crandall, M. G., & Rabinowitz, P. H. (1977) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00280827 · Cited by 181
On the theory and application of the Hopf-Friedrichs bifurcation theory
Poore, A. B. (1976) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00248886 · Cited by 132
Modeling of chemical reactors — XVI Steady state axial heat and mass transfer in tubular reactors An analysis of the uniqueness of solutions
Hlaváček, V., & Hofmann, H. (1970) · Chemical Engineering Science · doi:10.1016/0009-2509(70)85030-8 · Cited by 119

Show all 86 references

Research works printed but not linked: 11

Gilles, 1976, Proc. 4th Int. Symp. Chem. React. Engng Heidelberg, 459
Hlaváček, 1978, Advan. Catal., 27, 59
Butakov, 1973, Dokl. Akad. Nauk. SSSR, 209, 643
Hlaváček, 1974, Int. J. Chem. Engng, 14, 461
Butakov, 1978, Dokl. Akad, Nauk SSSR, 238, 166
Oh, 1978, am. Chem. Soc. Symp. Ser., 65, 461
Paspek, 1980, A.I.Ch.E.J.
Vortmeyer, 1961, Z. Electrochem., 65, 282
McGinnis, 1965, Chem. Engng Prog. Symp. Ser., 55, 2
Sørensen, 1973, A.I.Ch.E.J., 969, 1286
Poore, 1980, A.I.Ch.E. Annual Meeting

Sorted by citations

Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations
Tezduyar, T. E., & Park, Y. J. (1986) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(86)90003-4 · Cited by 269
Olefin/paraffin separations by adsorption: π‐Complexation vs. kinetic separation
Rege, S. U., Padin, J., & Yang, R. T. (1998) · AIChE Journal · doi:10.1002/aic.690440405 · Cited by 225
Multiplicities and instabilities in chemically reacting systems — a review
Razón, L. F., & Schmitz, R. A. (1987) · Chemical Engineering Science · doi:10.1016/0009-2509(87)80055-6 · Cited by 193
Tracking control for boundary controlled parabolic PDEs with varying parameters: Combining backstepping and differential flatness
Meurer, T., & Kugi, A. (2009) · Automatica · doi:10.1016/j.automatica.2009.01.006 · Cited by 184
Modelling and adaptive control of nonlinear distributed parameter bioreactors via orthogonal collocation
Dochain, D., Babary, J. P., & Tali-Maamar, N. (1992) · Automatica · doi:10.1016/0005-1098(92)90141-2 · Cited by 151
A heterogeneous dynamic model for the simulation and optimisation of the steam methane reforming reactor
Pantoleontos, G., Kikkinides, E. S., & Georgiadis, M. C. (2012) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2012.02.125 · Cited by 139
“where NLe is Lewis number defined as [59]:”
Background
Bifurcation behavior in homogeneous-heterogeneous combustion: II. Computations for stagnation-point flow
Song, X., Williams, W. R., Schmidt, L. D., & Aris, R. (1991) · Combustion and Flame · doi:10.1016/0010-2180(91)90007-x · Cited by 116
Coupling exothermic and endothermic reactions in adiabatic reactors
Ramaswamy, R. C., Ramachandran, P. A., & Duduković, M. P. (2007) · Chemical Engineering Science · doi:10.1016/j.ces.2007.11.010 · Cited by 109
Operation range extension via hot-spot control for catalytic CO 2 methanation reactors
Bremer, J., & Sundmacher, K. (2019) · Reaction Chemistry & Engineering · doi:10.1039/c9re00147f · Cited by 103
Propane/propylene separation by pressure swing adsorption: sorbent comparison and multiplicity of cyclic steady states
Rege, S. U., & Yang, R. T. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(01)00440-7 · Cited by 93
Feedforward and Feedback Tracking Control of Nonlinear Diffusion−Convection−Reaction Systems Using Summability Methods
Meurer, T., & Zeitz, Μ. (2004) · Industrial & Engineering Chemistry Research · doi:10.1021/ie0495729 · Cited by 84
Wrong‐way behavior of packed‐bed reactors: II. Impact of thermal dispersion
Pinjala, V., Chen, Y. C., & Luss, D. (1988) · AIChE Journal · doi:10.1002/aic.690341010 · Cited by 79
On modelling, monitoring and control of fixed bed bioreactors
Dochain, D., Tali-Maamar, N., & Babary, J. P. (1997) · Computers & Chemical Engineering · doi:10.1016/s0098-1354(96)00370-5 · Cited by 76
Backstepping Control of Coupled Linear Parabolic PIDEs With Spatially Varying Coefficients
Deutscher, J., & Kerschbaum, S. (2018) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2018.2802422 · Cited by 76
“importance for applications. Typical real-world problems originate from chemical and biochemical engineering, whereby chemical ﬁxed-bed and tubular reactors are important examples (see, e. g., [20], [10]). A ﬁrst solution to the backstepping design for coupled diffusion-reaction systems with equal diffusion coefﬁcient…”
Background
Methane auto-ignition delay times and oxidation regimes in MILD combustion at atmospheric pressure
Sabia, P., de Joannon, M., Picarelli, A., & Ragucci, R. (2012) · Combustion and Flame · doi:10.1016/j.combustflame.2012.09.015 · Cited by 68
Nonlinear analysis in process design
Seider, W. D., Brengel, D. D., & Widagdo, S. (1991) · AIChE Journal · doi:10.1002/aic.690370102 · Cited by 62
Spatiotemporal patterns in catalytic systems
Luss, D., & Sheintuch, M. (2005) · Catalysis Today · doi:10.1016/j.cattod.2005.02.043 · Cited by 59
Spatiotemporal patterns in catalytic reactors
Sheintuch, M., & Shvartsman, S. Y. (1996) · AIChE Journal · doi:10.1002/aic.690420416 · Cited by 54
Classification of steady-state and dynamic behavior of distributed reactor models
Subramanian, S., & Balakotaiah, V. (1996) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00261-8 · Cited by 52
Mapping regions with different bifurcation diagrams of a reverse‐flow reactor
Khinast, J., & Luss, D. (1997) · AIChE Journal · doi:10.1002/aic.690430812 · Cited by 50
Data-driven model reduction-based nonlinear MPC for large-scale distributed parameter systems
Xie, W., Bonis, I., & Theodoropoulos, C. (2015) · Journal of Process Control · doi:10.1016/j.jprocont.2015.07.009 · Cited by 48
Convective instability induced by differential transport in the tubular packed-bed reactor
Yakhnin, V. Z., Rovinsky, A. B., & Menzinger, M. (1995) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00114-k · Cited by 45
The growth of pure and simple microbial competitors in a moving distributed medium
Kung, C.-M., & Baltzis, B. C. (1992) · Mathematical Biosciences · doi:10.1016/0025-5564(92)90076-9 · Cited by 44
On the dynamics of the Circulation Loop Reactor—Numerical methods and analysis
Kienle, A., Lauschke, G., Gehrke, V., & Gilles, E. D. (1995) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00112-i · Cited by 43
Modeling the spontaneous ignition of coal stockpiles
Salinger, A. G., Aris, R., & Derby, J. J. (1994) · AIChE Journal · doi:10.1002/aic.690400610 · Cited by 42
Fixed-Bed Reactors
Eigenberger, G. (2000) · Ullmann's Encyclopedia of Industrial Chemistry · doi:10.1002/14356007.b04_199 · Cited by 41
Output Feedback Control of Coupled Linear Parabolic ODE–PDE–ODE Systems
Deutscher, J., & Gehring, N. (2020) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2020.3030763 · Cited by 37
“sor dynamics and ﬁnite-dimensional actuator dynamics. / Remark 2: The class (1) of systems typically appears in the modelling of chemical reactors with actuator and sensor dynamics (see, e. g., [19], [11]). Furthermore, the case in which some of the coefﬁcients i in (2) are equal can also be considered by a simple ext…”
Background
Constructive nonlinear dynamics in process systems engineering
Marquardt, W., & Mönnigmann, M. (2005) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2005.02.009 · Cited by 37
Use of orthogonal collocation on finite elements with moving boundaries for fixed bed catalytic reactor simulation
Laura Gardini, B., Servida, A., Morbidelli, M., & Carrà, S. (1985) · Computers & Chemical Engineering · doi:10.1016/0098-1354(85)87001-0 · Cited by 36
State multiplicity in PFR–separator–recycle polymerization systems
Kiss, A. A., Bîldea, C. S., Dimian, A. C., & Iedema, P. D. (2003) · Chemical Engineering Science · doi:10.1016/s0009-2509(03)00162-3 · Cited by 35
Steady-State Multiplicity and Superadiabatic Extinction Waves in the Oxidation of CO/H2 Mixtures over a Pt/Al2O3-Coated Monolith
Sun, M., Croiset, E., Hudgins, R. R., Silveston, P. L., & Menzinger, M. (2002) · Industrial & Engineering Chemistry Research · doi:10.1021/ie020310l · Cited by 34
A linear model predictive control algorithm for nonlinear large‐scale distributed parameter systems
Bonis, I., Xie, W., & Theodoropoulos, C. (2011) · AIChE Journal · doi:10.1002/aic.12626 · Cited by 34
Reaktorstabilität und sichere Reaktionsführung
Eigenberger, G., & Schüler, H. (1986) · Chemie Ingenieur Technik · doi:10.1002/cite.330580807 · Cited by 33
Mathematics in chemical engineering: A 50 year introspection
Ramkrishna, D., & Amundson, N. R. (2004) · AIChE Journal · doi:10.1002/aic.10002 · Cited by 33
“The bifurcation analysis of stirred-tank reactors was followed by that of tubular reactors by Jensen and Ray (1982).”
Background
An Arnoldi-based iterative scheme for nonsymmetric matrix pencils arising in finite element stability problems
Natarajan, R. (1992) · Journal of Computational Physics · doi:10.1016/0021-9991(92)90315-p · Cited by 33
An algorithm for the computation of Hopf bifurcation points in comparison with other methods
Roose, D. (1985) · Journal of Computational and Applied Mathematics · doi:10.1016/0377-0427(85)90045-7 · Cited by 32
Off-line model reduction for on-line linear MPC of nonlinear large-scale distributed systems
Xie, W., Bonis, I., & Theodoropoulos, C. (2011) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2011.01.023 · Cited by 31
Steady states and oscillations in homogeneous—heterogeneous reaction systems
Song, X., Schmidt, L. D., & Aris, R. (1991) · Chemical Engineering Science · doi:10.1016/0009-2509(91)85049-4 · Cited by 31
Reaction front propagation in nonadiabatic exothermic reaction flow systems
Gatica, J. E., Puszynski, J. A., & Hlaváček, V. (1987) · AIChE Journal · doi:10.1002/aic.690330515 · Cited by 30
Global Hopf bifurcation of two-parameter flows
Fiedler, B. (1986) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00278243 · Cited by 28
Fixed Bed Reactor Dynamics and Control - A Review
Jørgensen, S. B. (1986) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)59393-3 · Cited by 27
Feedforward and feedback tracking control of diffusion-convection-reaction systems using summability methods
Meurer, T. (2005) · OPUS Publication Server of the University of Stuttgart (University of Stuttgart) · doi:10.18419/opus-4075 · Cited by 27
Nonstandard finite difference schemes based on Green's function formulations for reaction–diffusion–convection systems
Hernández‐Martínez, E., Puebla, H., Valdés‐Parada, F. J., & Álvarez‐Ramírez, J. (2013) · Chemical Engineering Science · doi:10.1016/j.ces.2013.03.001 · Cited by 26
Dynamic responses of packed bed reactors
Menzinger, M., Yakhnin, V. Z., Jaree, A., Silveston, P. L., & Hudgins, R. R. (2004) · Chemical Engineering Science · doi:10.1016/j.ces.2004.05.031 · Cited by 26
Design of tubular reactors in recycle systems
Bîldea, C. S., Dimian, A. C., Cruz, S. C., & Iedema, P. D. (2003) · Computers & Chemical Engineering · doi:10.1016/s0098-1354(03)00170-4 · Cited by 25
“Coupled with the nonlinearity of the reaction rate, the positive feedback can lead to state multiplicity even in stand-alone reactors (Jensen & Ray, 1982; Weisz & Hicks, 1962).”
Background
Multiplicity of conversion in a cascade of imperfectly stirred tank reactors
Lo, S. N., & Cholette, A. (1983) · Chemical Engineering Science · doi:10.1016/0009-2509(83)80155-9 · Cited by 25
Catalytic reactions and reactors: A surface science approach
Doraiswamy, L. K. (1991) · Progress in Surface Science · doi:10.1016/0079-6816(91)90017-x · Cited by 24
Evaluation of Hopf bifurcation points in parabolic equations describing heat and mass transfer in chemical reactors
Kubı́ček, M., & Holodniok, M. (1984) · Chemical Engineering Science · doi:10.1016/0009-2509(84)80055-x · Cited by 24
Intelligent Process Control with Supervisory Knowledge-Based Systems
Kendra, S. J., Basila, M. R., & Çınar, A. (1997) · Springer eBooks · doi:10.1007/978-94-011-5498-7_5 · Cited by 23
Dynamics and stability analysis of solid catalyzed gas-phase polymerization of olefins in continuous stirred bed reactors
Gorbach, A., Naik, S. D., & Ray, W. H. (2000) · Chemical Engineering Science · doi:10.1016/s0009-2509(00)00080-4 · Cited by 23
Self-citation
Studies on the analysis of nonlinear processes via functional expansions—I. Solution of nonlinear ODEs
Batıgün, A., Harris, K. R., & Palazoğlu, A. (1997) · Chemical Engineering Science · doi:10.1016/s0009-2509(97)00117-6 · Cited by 23
Ignition and extinction of homogeneous-heterogeneous combustion: CH4 and C3H8 oxidation on PT
Song, X., Williams, W. R., Schmidt, L. D., & Aris, R. (1991) · Symposium (International) on Combustion · doi:10.1016/s0082-0784(06)80372-3 · Cited by 22
Intelligent process control with supervisory knowledge-based systems
Kendra, S. J., Basila, M. R., & Çınar, A. (1994) · IEEE Control Systems · doi:10.1109/37.291458 · Cited by 22
The bifurcation behavior of an autothermal packed bed tubular reactor
Adomaitis, R. A., & Çınar, A. (1988) · Chemical Engineering Science · doi:10.1016/0009-2509(88)80085-x · Cited by 22
Bifurcation analysis of chemical reactors and reacting flows
Balakotaiah, V., Dommeti, S. M. S., & Gupta, N. (1999) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.166377 · Cited by 21
Optimisation and Linear Control of Large Scale Nonlinear Systems: A Review and a Suite of Model Reduction-Based Techniques
Theodoropoulos, C. (2010) · Lecture notes in computational science and engineering · doi:10.1007/978-3-642-14941-2_3 · Cited by 21
“The tubular reactor where an exothermic reaction A ! B occurs [ 49 ] was used as an illustrative case study to demonstrate the capabilities of RPRH since it has a rich parametric behaviour including a number of bifurcations (turning points, Hopf points), instabilities and multiple steady states making the optimisation…”
Method
Multiple Model Predictive Control of Dissipative PDE Systems
Bonis, I., Xie, W., & Theodoropoulos, C. (2013) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2013.2270182 · Cited by 21
“The model for the reactor consists of two parabolic PDEs [25] ∂x1 ∂ t = 1 Pe1 ∂2x1 ∂y2 − ∂x1 ∂y − Da · x1 exp ( γ x2 1 + x2 ) ∂x2 ∂ t = 1 Pe2 ∂2x2 ∂y2 − ∂x2 ∂y + C Da · x1 exp ( γ x2 1 + x2 ) +β(x2w − x2) (22) where y is the dimensionless longitudinal coordinate, r is the recycle ratio, Da is the Damköhler number, Pe1…”
MethodInfluential
Amplification of inlet temperature disturbances in a packed-bed reactor for CO oxidation over Pt/Al2O3
Jaree, A., Hudgins, R. R., Budman, H. M., Silveston, P. L., Yakhnin, V. Z., & Menzinger, M. (2003) · Chemical Engineering Science · doi:10.1016/s0009-2509(02)00614-0 · Cited by 21
A data-driven reduced-order model of nonlinear processes based on diffusion maps and artificial neural networks
Koronaki, E. D., Νίκας, Α., & Boudouvis, A. G. (2020) · Chemical Engineering Journal · doi:10.1016/j.cej.2020.125475 · Cited by 20
Flatness of Semilinear Parabolic PDEs—A Generalized Cauchy–Kowalevski Approach
Schörkhuber, B., Meurer, T., & Jüngel, A. (2013) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2013.2256013 · Cited by 20
“, [33] for model details and to [12] for the considered normalization process.”
Background
Moving hot spots and resonance in adiabatic packed‐bed reactors
Yakhnin, V. Z., & Menzinger, M. (1998) · AIChE Journal · doi:10.1002/aic.690440521 · Cited by 20
Kinetically induced multiplicity of steady states in integral catalytic reactors
Nibbelke, R. H., Hoebink, J. H. B. J., & Marin, G. B. (1998) · Chemical Engineering Science · doi:10.1016/s0009-2509(98)00055-4 · Cited by 19
Phase transition and steady-state multiplicity in a trickle-bed reactor
Kheshgi, H. S., Reyes, S. C., Hu, R., & Ho, T. C. (1992) · Chemical Engineering Science · doi:10.1016/0009-2509(92)85024-6 · Cited by 19
Differential flow instability of the exothermic standard reaction in a tubular cross-flow reactor
Yakhnin, V. Z., Rovinsky, A. B., & Menzinger, M. (1994) · Chemical Engineering Science · doi:10.1016/0009-2509(94)00143-x · Cited by 19
Model predictive control of a non-isothermal axial dispersion tubular reactor with recycle
Khatibi, S., Ozorio Cassol, G., & Dubljevic, S. (2021) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2020.107159 · Cited by 18
Backstepping-Forwarding Designs for Doubly- Distributed Delay-PDE-ODE Systems
Xu, X., Liu, L., Krstić, M., & Feng, G. (2024) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2024.3383802 · Cited by 18
Efficient modeling of the nonlinear dynamics of tubular heterogeneous reactors
Badillo-Hernández, U., Álvarez, J., & Álvarez-Icaza, L. A. (2019) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2019.01.018 · Cited by 18
Operating zone segregation of chemical reaction systems based on stability and non-minimum phase behavior analysis
Yuan, Z., Wang, H., Chen, B., & Zhao, J. (2009) · Chemical Engineering Journal · doi:10.1016/j.cej.2009.06.036 · Cited by 18
Enabling stability analysis of tubular reactor models using PDE/PDAE integrators
Koronaki, E. D., Boudouvis, A. G., & Kevrekidis, I. G. (2003) · Computers & Chemical Engineering · doi:10.1016/s0098-1354(03)00004-8 · Cited by 18
“…reaction for which the equations of the pseudohomogeneous axial dispersion model are two coupled nonlinear parabolic PDEs which, in dimension-less form are (Jensen & Ray, 1982): with boundary conditions: Here x 1 and x 2 are the con v ersion and the dimension-less temperature, respecti v ely.”
BackgroundMethod
Steady state multiplicity behavior of an isothermal axial dispersion fixed-bed reactor with nonuniformly active catalyst
Lee, C. K., Morbidelli, M., & Varma, A. (1987) · Chemical Engineering Science · doi:10.1016/0009-2509(87)80164-1 · Cited by 18
Closed-loop monitoring systems for detecting impending instability
Abed, E. H., & Kim, T. (2000) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.886978 · Cited by 18
“Examples include electric power system voltage collapse [18], chemical reactor runaway [ 12 ], jet engine stall [13], aircraft stall at high angle-of-attack [5], and laser system instability [8].”
Background
Front initiation on microdesigned composite catalysts
Li, X., Kevrekidis, I. G., Pollmann, M., Papathanasiou, A. G., & Rotermund, H. H. (2002) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.1452739 · Cited by 17
An off-line Model Reduction-based Technique for On-line Linear MPC Applications for Nonlinear Large-Scale Distributed Systems
Xie, W., & Theodoropoulos, C. (2010) · Computer-aided chemical engineering/Computer aided chemical engineering · doi:10.1016/s1570-7946(10)28069-0 · Cited by 16
A Heterogeneous Multiscale Dynamic Model for Simulation of Catalytic Reforming Reactors
Pantoleontos, G., Skevis, G., Karagiannakis, G. P., & Konstandopoulos, A. G. (2016) · International Journal of Chemical Kinetics · doi:10.1002/kin.20985 · Cited by 16
Optimization Strategies in a Fixed-Bed Reactor for HCl Oxidation
Till, Z., Varga, T., Réti, J., & Chován, T. (2017) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.7b00750 · Cited by 16
The Differential Flow Instabilities
Menzinger, M., & Rovinsky, A. B. (1995) · Springer eBooks · doi:10.1007/978-94-011-1156-0_11 · Cited by 16
An Input/Output Model Reduction-Based Optimization Scheme for Large-Scale Systems
Luna‐Ortiz, E., & Theodoropoulos, C. (2005) · Multiscale Modeling and Simulation · doi:10.1137/040604716 · Cited by 16
“This system exhibits a highly nonlinear behavior, as shown in [22], and its rich parametric space leads to D ow nl oa de d 01 /0 4/ 13 to 1 29 .”
BackgroundMethod
Model reduction-based optimization using large-scale steady-state simulators
Bonis, I., & Theodoropoulos, C. (2011) · Chemical Engineering Science · doi:10.1016/j.ces.2011.09.033 · Cited by 15
Novel Multiplicity and Stability Criteria for Non-Isothermal Fixed-Bed Reactors
Bremer, J., & Sundmacher, K. (2021) · Frontiers in Energy Research · doi:10.3389/fenrg.2020.549298 · Cited by 15
A study of temperature sensor location based on fractal analysis for cascade control schemes in tubular reactors
Ramírez-Castelán, C. E., Moguel‐Castañeda, J. G., Puebla, H., & Hernández‐Martínez, E. (2015) · Chemical Engineering Science · doi:10.1016/j.ces.2015.10.036 · Cited by 15
Complex Nonlinear Behavior in the Full-Scale High-Impact Polystyrene Process
Flores‐Tlacuahuac, A., Zavala-Tejeda, V., & Saldívar‐Guerra, E. (2005) · Industrial & Engineering Chemistry Research · doi:10.1021/ie049418m · Cited by 15
Model inversion of boundary controlled parabolic partial differential equations using summability methods
Meurer, T., & Zeitz, Μ. (2008) · Mathematical and Computer Modelling of Dynamical Systems · doi:10.1080/13873950701844873 · Cited by 14
“Well-known examples concern (bio-)chemical tubular and ﬁxed-bed reactors for production or degradation with complex dynamical behaviour and multiple steady states [1,2].”
Background
Identification of low-order parameter-varying models for large-scale systems
Wattamwar, S. K., Weiland, S., & Backx, T. (2009) · Journal of Process Control · doi:10.1016/j.jprocont.2009.11.010 · Cited by 14
Input constrained adaptive tracking for a nonlinear distributed parameter tubular reactor
Beniich, N., Bouhtouri, A. E., & Dochain, D. (2009) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.1127 · Cited by 14
Numerical Computation of Hopf Bifurcation Points for Parabolic Diffusion-Reaction Differential Equations
Roose, D., & Hlaváček, V. (1983) · SIAM Journal on Applied Mathematics · doi:10.1137/0143070 · Cited by 13
“Varma and Amundson [9], Jensen and Ray [6], Margolis [11] and Hlavacek, Hofmann and Kubicek [10] observe oscillations for "diffusion-convection-reaction" problems.”
BackgroundMethod
Closed-loop monitoring systems for detecting incipient instability
Kim, T., & Abed, E. H. (2002) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.1998.757958 · Cited by 13
“Examples include electric power system voltage collapse [ll], chemical reactor runaway [ 6 ], jet engine stall [7], aircraft stall at high angle-of-attack [2], and laser system instability [4].”
Background
Ignition–extinction analysis of catalytic reactor models
Balakotaiah, V., Sun, Z., & Ratnakar, R. R. (2021) · Reviews in Chemical Engineering · doi:10.1515/revce-2020-0113 · Cited by 12
Control of an exothermic packed-bed tubular reactor
Nájera, I., Álvarez, J., Baratti, R., & Gutiérrez, C. D. G. (2016) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2016.07.282 · Cited by 12
Steady-state multiplicity analysis of the heterogeneous axial dispersion fixed-bed reactor
Juncu, G., Bîldea, C. S., & Floarea, O. (1994) · Chemical Engineering Science · doi:10.1016/0009-2509(94)85039-9 · Cited by 12
Comparison of multiplicity patterns of a single catalytic pellet and a fixed catalytic bed for ethylene oxidation
Adaje, J., & Sheintuch, M. (1990) · Chemical Engineering Science · doi:10.1016/0009-2509(90)87125-c · Cited by 12
Exploring the Steady Operation of a Continuous Pilot Plant for the Di‐Nitration Reaction
Sharma, M. K., Acharya, R. B., & Kulkarni, A. A. (2019) · Chemical Engineering & Technology · doi:10.1002/ceat.201900140 · Cited by 11
Estimating spectral properties of the thermal instability in packed-bed reactors
Yakhnin, V. Z., & Menzinger, M. (2007) · Chemical Engineering Science · doi:10.1016/j.ces.2007.11.031 · Cited by 10
Forced periodic operation of tubular reactors
Özgülşen, F., & Çınar, A. (1994) · Chemical Engineering Science · doi:10.1016/0009-2509(94)00152-9 · Cited by 10
Transient linear stability of a Simons-process gas–liquid electrochemical flow reactor using numerical simulations
Drake, J. A., Radke, C. J., & Newman, J. (2001) · Chemical Engineering Science · doi:10.1016/s0009-2509(01)00268-8 · Cited by 10
Deactivation of the preferential oxidation of CO in packed bed reactor by 3D modelling and near-infrared tomography
Alzahrani, F., Rusi, H., Assabumrungrat, S., Fernandes, D. L. A., & Aiouache, F. (2019) · Chemical Engineering Journal · doi:10.1016/j.cej.2019.122082 · Cited by 9
On the Pseudomultiplicity of Pressure Swing Adsorption Periodic States
Sundaram, N., & Yang, R. T. (1998) · Industrial & Engineering Chemistry Research · doi:10.1021/ie970522w · Cited by 9
Absolute instability of a tubular packed-bed reactor with recycling
Yakhnin, V. Z., Rovinsky, A. B., & Menzinger, M. (1995) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00007-r · Cited by 9
A Reduced Input/Output Dynamic Optimisation Method for Macroscopic and Microscopic Systems
Theodoropoulos, C., & Luna‐Ortiz, E. (2006) · Springer eBooks · doi:10.1007/3-540-35888-9_24 · Cited by 9
“It is a tubular reactor with pseudohomogeneous axial dispersion, where a simple exothermic irreversible first order reaction, A → B, occurs [67].”
Background
The role of surface inhomogeneities in pattern formation on catalytic surfaces
Jensen, K. F. (1983) · Chemical Engineering Science · doi:10.1016/0009-2509(83)80006-2 · Cited by 9
Self-citation
Deactivation models by fitting the progression of temperature profiles – Coking model for the MTG process in adiabatic reactors
Sørensen, M. D. P. (2013) · Chemical Engineering Science · doi:10.1016/j.ces.2013.11.012 · Cited by 8

Authors: Jensen, K. F., & Ray, W. H.
Affiliations: University of Wisconsin–Madison (US)
Corresponding author: Ray, W.Harmon
ORCID: Jensen, Klavs F.
Venue: Chemical Engineering Science
Publisher: Elsevier BV
Published: 1982
Volume: 37
Issue: 2
Pages: 199-222
ISSN: 0009-2509 (ISSN-L)
DOI: 10.1016/0009-2509(82)80155-3
OpenAlex: W2065214383
Cited by: 180
References: 86
Citations by year: 2026: 2 · 2025: 5 · 2024: 5 · 2022: 3 · 2021: 4 · 2020: 4 · 2019: 5 · 2018: 3 · 2017: 4 · 2016: 3 · 2015: 6 · 2014: 1 · 2013: 7 · 2012: 2
FWCI: 5.55
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
www.elsevier.com/legal/tdmrep-license (tdm)
Locations: Chemical Engineering Science (publishedVersion)
Defense Technical Information Center (DTIC) (submittedVersion)
Topics: Physical Sciences › Engineering › Computational Mechanics › Heat and Mass Transfer in Porous Media
Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Dynamics and Pattern Formation
Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
Keywords: tubular reactor, bifurcation analysis, Hopf bifurcation, steady-state profiles, axial dispersion, first-order irreversible reaction, multiple steady states, periodic solutions, Lewis number, Peclet number, fixed-bed reactor, reaction-diffusion systems, two-phase model

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

The bifurcation behavior of tubular reactors

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks