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

TY - JOUR

T1 - Are 3-D models necessary to simulate packed bed reactors? analysis and 3-D simulations of adiabatic and cooled reactors

AU - Nekhamkina, Olga

AU - Sheintuch, Moshe

PY - 2012/11

Y1 - 2012/11

N2 - 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 (ΔT ad/ΔT m)/(Pe C/Pe T) surpasses a critical value larger than unity, where ΔT ad and ΔT m 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 Pe C/Pe T > 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

AB - 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 (ΔT ad/ΔT m)/(Pe C/Pe T) surpasses a critical value larger than unity, where ΔT ad and ΔT m 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 Pe C/Pe T > 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

KW - Bifurcations

KW - Fronts

KW - Process

KW - Reactor analysis

KW - Simulation

KW - Transversal patterns

UR - http://www.scopus.com/inward/record.url?scp=84867233194&partnerID=8YFLogxK

U2 - 10.1002/aic.13752

DO - 10.1002/aic.13752

M3 - 文章

AN - SCOPUS:84867233194

SN - 0001-1541

VL - 58

SP - 3494

EP - 3503

JO - AICHE Journal

JF - AICHE Journal

IS - 11

ER -