Catalytic spatiotemporal thermal patterns during CO oxidation on cylindrical surfaces: Experiments and simulations

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Simulations and analysis of transversal patterns in a homogeneous three‐dimensional (3‐D) model of adiabatic or cooled packed bed reactors (PBRs) catalyzing a first‐order exothermic reaction were presented. In the adiabatic case the simulation verify previous criteria, claiming the emergence of such patterns when (ΔTad/ΔTm)/(PeC/PeT) surpasses a critical value larger than unity, where ΔTad and ΔTm are adiabatic and maximal temperature rise, respectively. The reactor radius required for such patterns should be larger than a bifurcation value, calculated here from the linear analysis. With increasing radius new patterned branches, corresponding to eigenfunction of the problem emerge, whereas other branches become unstable. The maximal temperature of the 3‐D simulations may exceed the 1‐D prediction, which may affect design procedures. Cooled reactor may exhibit patterns, usually axisymmetric ones that can be characterized by two anomalies: the peak temperature may exceed the corresponding value of an adiabatic reactor and may increase with wall heat‐transfer coefficient, and the peak temperature in a sufficiently wide reactor need not lie at the center but rather on a ring away from it. In conclusions, we argue that transversal patterns are highly unlikely to emerge in practical adiabatic PBRs with a single exothermic reaction, as in practice PeC/PeT > 1. That eliminates patterns in stationary and downstream‐moving fronts, whereas patterns may emerge in upstream‐moving fronts, as shown here. This conclusion may not hold for microkinetic models, for which stationary modes may be established over a domain of parameters. This suggests that a 1‐D model may be sufficient to analyze a single reaction in an adiabatic reactor and a 2‐D axisymmetric model is sufficient for a cooled reactor. The predictions of a 2‐D cylindrical thin reactor with those of a 3‐D reactor were compared, to show many similarities but some notable differences. © 2012 American Institute of Chemical Engineers AIChE J, 2012

“…13,28,35,36 This conclusion may not hold for two or more competing reactions. This conclusion was justified here for a homogeneous model and for a single reaction.…”

Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Are 3‐D models necessary to simulate packed bed reactors? analysis and 3‐D simulations of adiabatic and cooled reactors

Nekhamkina¹,

Sheintuch²

2012

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“…Similar conclusions apply for oscillatory kinetics. 36,37 (iv) The criterion derived here applies for 3D fixed beds, as we will verify elsewhere by numerical simulations. The linear stability analysis of a 3D model and a cylindrical shell model with respect to transversal perturbations of the form of eigenfunctions [J k (l kn r)exp(ik/) where J k is the Bessel function of the first kind, l kn are the transversal eigenvalues which are defined by boundary conditions dJ k (l kn r)| r¼0 ¼ 0 [25][26][27] ] is similar to that of the 2D shell model.…”

mentioning

confidence: 97%

Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

Nekhamkina

Sheintuch

2011

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We derive a new criterion for transversal instability of planar fronts based on the bifurcation condition dV f /dK| K¼0 ¼ 0, where V f and K are the front velocity and its curvature, respectively. This refines our previously obtained condition, which was formulated as a ¼ (DT ad Pe T )/(DT m Pe C ) [ 1 to a [ 1 þ |d|, where DT ad and DT m are the adiabatic and maximal temperature rise, respectively, Pe C and Pe T are the axial mass and the heat Pe numbers, respectively, and d is a small parameter. The criterion is based on approximate relations for DT m and V f , which account for the local curvature of a propagating front in a packed bed reactor with a first-order activated kinetics. The obtained relations are verified by linear stability analysis of planar fronts. Simulations of a simplified 2D model in the form of a thin cylindrical shell are in good agreement with the critical parameters predicted by dispersion relations. Three types of patterns were detected in simulations: ''frozen'' multiwave patterns, spinning waves, and complex rotating-oscillating patterns. We map bifurcation diagrams showing domains of different modes using the shell radius as the bifurcation parameter. The possible translation of the 2D cylindrical shell model results to the 3D case is discussed. V V C 2010 American Institute of Chemical Engineers AIChE J, 57: 735-748, 2011 Keywords: reactor analysis, simulation, process, fronts, bifurcations, transversal patterns IntroductionHeterogeneous catalysts are extensively used in the chemical and petrochemical industry and for pollution abatement purposes. It is usually assumed that the temperature and concentrations of the reactants at any transversal cross section of an adiabatic packed-bed reactor are uniform. However, various industrial and laboratory experimental observations revealed formation of nonuniform temperature in the reactor cross section. Such patterns may pose severe safety hazards by altering the wall strength and inducing cracks. Ignoring such patterns in design and simulations may lead to erroneous results. Understanding which kinetics may lead to spatiotemporal pattern formation is essential for the development of design and control strategies that circumvent them.Symmetry-breaking leading to either spatial and/or spatiotemporal pattern formation has been observed in many biological, physiological, chemical, and electro-chemical systems [1][2][3][4][5][6][7][8] governed by the interaction of diffusion and reaction processes. Majority of the studies of pattern formation in chemically reacting systems are of homogeneous systems. Pattern formation in heterogeneous catalytic and electrochemical systems, like wires, pellets, and packed bed reactors has been known for 20 years. Recent reviews of the and Krischer. 12 The current knowledge and understanding about the formation of transversal temperature patterns has been reviewed by Viswanathan et al. 13The obtained results are kinetics-dependent 14 and in the present study we focus on kinetics that admits multiple steady sta...

“…The chaotic solutions and the bifurcation scenarios leading to chaos were studied numerically for a three-unit LR by Russo et al 23 and Altimari et al 24 A brief analysis of complex non-frozen solutions in a LR with different N was conducted in our previous works. 20,21 Note, that the complex dynamics emerging in this case is different from that simulated and observed for a packed bed in which an oscillatory reaction proceeds (Barto and Sheintuch, 25 Sheintuch and Nekhamkina, 26 Digilov et al 27 ).…”

Section: Introductionmentioning

confidence: 55%

Structure of operating domains of loop reactors

Nekhamkina

Sheintuch

2008

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A loop reactor (LR), composed as an N‐unit loop with step‐wise shifted inlet and outlet ports, is one of suggested technological solutions for low‐concentration volatile organic compounds (VOC) combustion. Such a scheme ensures a sufficiently high temperature with autothermal behavior and nearly uniform catalytic utilization. The main drawback of the LR is a very narrow window of switching velocities that sustain a stable “frozen” solution that exists if the switching and the pulse velocity are synchronized. In the present work we show the existence of many “finger”‐like domains of complex frequency‐locked solutions that allow to significantly extend the operation domain, rendering the LR scheme more attractive for practical implementation. A brief comparison with the other heat recuperation technologies (reverse flow and circular loop reactors) is presented. © 2008 American Institute of Chemical Engineers AIChE J, 2008