Mathematical modeling of monolithic catalysts

Abstract

Mathematical models are developed which account for simultaneous heat transfer, mass transfer, and chemical reaction in the oxidation of carbon monoxide over platinum containing monoliths. A two-dimensional model is shown to predict unusual behavior of the Nusselt number in the presence of rapid reaction. However, a simpler one-dimensional model is adequate for predicting monolith behavior. Department of Chemical EngineeringUniversity of Delaware Newark, Delaware 1971 1 SCOPEThe oxidation of carbon monoxide and hydrocarbons is the principal reaction in an automobile catalytic converter. Half of the 1975 automobiles are equipped with monolithic converters in which platinum and palladium catalysts are deposited on the walls of a bundle of parallel ceramic tubes. The oxidation kinetics exhibits a negative reaction order with respect to carbon monoxide concentration, and the reactions are highly exothermic.This paper describes a theoretical analysis of these unusual kinetics in monoliths. Steady state and transient temperature and concentration profiles are investigated, with numerical techniques used to solve the partial differential equations. The effects of inlet carbon monoxide concentration, inlet gas temperature, gas velocity, tube geometry, and diameter are investigated.Young and Finlayson (1974) have shown that there is a significant difference between a one-dimensional model, where only axial gradients are considered, and a twodimensional model, where both axial and radial gradients are considered. They have shown that in the two-dimensional model the Nusselt number shows an unusual behavior in the presence of rapid reactions. It would appear that the far more time consuming two-dimensional model must be used for the monolithic catalyst.Overheating of the monolith in road use is often observed, to temperatures above the melting point of the ceramic material (about 1 4OO0C), even when the adiabatic flame temperature of the inlet gas is far below this temperature. An explanation for this phenomenon is needed. CONCLUSIONS AND SIGN I FICANCEThis study confirmed the unusual behavior of the Nusselt number when the wall cools the gas in one section but heats the gas in a subsequent section. Despite this spectacular variation in the Nusselt number, the one-and two-dimensional models predict similar performance of the monolithic reactor (measured by the concentration profile). Thus, the simpler one-dimensional model is adequate for predicting monolith behavior during the crucial warm-up of an automobile from a cold start.The monolithic reactor behavior is dominated by the position of the light-off point, where the catalytic wall temperature takes an upward leap, the wall concentration falls to zero, and the reaction becomes mass transport limited. In a typical 1975 automobile, with a rich exhaust during idle or deceleration, the position of the light-off point is dominated by the inlet gas temperature. At a sufficiently low inlet temperature, light-off does not occur, and the conversion is very low. For a very narrow...

Adequacy of lumped parameter models for SCR reactors with monolith structure

“…Analysis of these conditions, which are not typical of SCR reactors, is beyond the scope of this work. Nevertheless, it may be relevant to recall a result reported by Heck et al (1976), who compared one-and two-dimensional models of cylindrical monolithic reactors for automobile catalytic converters. These authors found that a satisfactory match between the two models was achieved when the gas-solid transport coefficients were evaluated from the Graetz solutions for constant wall flux prior to the light-off (ignition) of the combustion reaction (in the region of flow kinetics) and from the solutions for constant wall temperature thereafter (in the region of fast kinetics).…”

“…Brauer and Schluter (1965) showed that a finite rate of reaction at the wall of a catalytic wall tubular reactor can influence significantly the values of the Sherwood number. Relevant results in this respect are contained in a pioneering work by Heck et al (1976), who compared one-and twodimensional models of nonisothermal cylindrical monolith reactors for automobile catalytic converters. They found that the two models would yield very similar results provided that appropriate boundary conditions of the Graetz-Nusselt problem were used when invoking the analogy between heat and mass transfer.…”

Adaptive Global Carbon Monoxide Kinetic Mechanism over Platinum/Alumina Catalysts

“…For these expressions, Heck came to the conclusion that Nusselt and Sherwood numbers should correspond to constant heat flux conditions up until light-off and then correspond to the constant wall temperature condition afterwards [34,35]. This is because up until light-off, the region is kinetically controlled; hence, the heat flux is relatively low and approximately constant [32].…”

Light‐off location and front diffusion in a catalytic monolith reactor

“…Mathematical models of varying degrees of complexity (in terms of the geometric dimensionality of the model, flow modeling, washcoat diffusion modeling, and chemical kinetics modeling) have been in use over the last 2-3 decades. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] In particular, the onedimensional two-phase (gas-solid) model 26,27 which differentiates between the gas and solid phase concentrations and temperatures has been found to describe these processes in a monolith reactor quite satisfactorily. 28,29 The ability to determine the light-off location and the thickness of the light-off front in a monolith reactor is particularly desirable in a TWC to be able to predict its performance and minimize cold-start emissions.…”