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

Abstract

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

Wall Temperature Modulates Transversal Spatiotemporal Pattern Selection in Shallow, Nonadiabatic Packed-Bed Reactors

“…These models predict formation of stable 2-D (transversal) and 3-D spatiotemporal patterns such as band, antiphase, rotating, and pulse motion under adiabatic conditions. 26,[29][30][31]37 The long periods of oscillations predicted in these studies were in agreement with experimental observations. Intricate features of these complex motions have primarily been attributed to strong interactions between several underlying modes.…”

“…Models that use, in addition to local temperature and concentration, detailed rate expressions for the underlying kinetics such as adsorption–desorption and surface microkinetic mechanisms for CO oxidation and a periodic blocking-reactivation mechanism for ethylene hydrogenation − have been considered. These models predict formation of stable 2-D (transversal) and 3-D spatiotemporal patterns such as band, antiphase, rotating, and pulse motion under adiabatic conditions. ,− , The long periods of oscillations predicted in these studies were in agreement with experimental observations. Intricate features of these complex motions have primarily been attributed to strong interactions between several underlying modes.…”

“…Several groups have modeled PBRs and have theoretically predicted formation of transversal spatial and spatiotemporal patterns in different configurations ,− and varying interfacial parameters . Models that use, in addition to local temperature and concentration, detailed rate expressions for the underlying kinetics such as adsorption–desorption and surface microkinetic mechanisms for CO oxidation and a periodic blocking-reactivation mechanism for ethylene hydrogenation − have been considered.…”

Novel Multiplicity and Stability Criteria for Non-Isothermal Fixed-Bed Reactors

“…For this reason, recent works are often motivated to add more physical meaning to their models. This allows to additionally focus on effects of secondary order (e.g., flow maldistributions, localized hot-spots, spatial and spatiotemporal patterns) (Sheintuch, 1997;Trinh and Ramkrishna, 1997;Jaree et al, 2001;Papadias et al, 2001;Marwaha and Luss, 2003;Agrawal et al, 2007;Viswanathan et al, 2008;Nekhamkina and Sheintuch, 2012), which is, however, not object of this work. Similarly, stable oscillatory solutions are also disregarded in this work, since they are unlikely to occur in fixed-bed reactors on an industrial scale due to their high thermal inertia (Jensen and Ray, 1982).…”

Impact of Wall Heat Transport on Formation of Transversal Hot Zones in Shallow, Non-adiabatic Packed-Bed Reactors

“…In this study, we consider the formation of spatiotemporal patterns in non-adiabatic, catalytic packed-bed reactors. Nekhamkina and Sheintuch showed that, for a homogeneous model with first-order exothermic kinetics, under non-adiabatic conditions, at best only axisymmetric patterns such as targets can be obtained. Using a periodic blocking–reactivation kinetic model, we predict formation of a rich variety of spatiotemporal patterns, such as rotating patterns and spirals, in shallow, non-adiabatic packed-bed reactors.…”