Mathematical modeling of catalytic converter lightoff: Single‐pellet studies

Abstract

A detailed mathematical model of a single catalyst pellet has been developed to describe its behavior under transient conditions encountered during the warmup period of automobile exhaust catalytic converters. In contrast to the converter models previously reported in the literature, this model is capable of describing the time-dependent behavior of a composite catalyst pellet, and thus provides a convenient means of examining the effects of poison penetration and various noble metal impregnation strategies in the activity-time (rather than activitytemperature) domain.Extensive calculations were carried out to investigate the effects of various catalyst design parameters and converter operating conditions on the lightoff behavior of a spherical, platinum-alumina catalyst pellet. Due to the complex kinetics of the CO and hydrocarbon oxidation reactions, catalyst lightoff was found to exhibit interesting behavior with respect to variations of the system's design parameters and operating conditions. Graphs are presented to illustrate the parametric sensitivity of these effects. It has been widely recognized that a substantial fraction of the carbon monoxide and hydrocarbon emissions occurs during the first few minutes (i.e., warmup period) of the Federal Test Procedure (FTP) driving cycle. Therefore, it is crucial to improve converter warmup performance in order to meet automotive emission standards which mandate more stringent emission control. Since converter performance is a complex function of operating conditions, converter geometries, and catalyst properties, an empirical approach to the problem can be very costly and time-consuming; thus, mathematical modeling promises to be helpful in the development of catalytic converters with improved warmup performance.There are some important design parameters associated with catalyst pellets used in automobile catalytic converters. For example, the relative locations of noble metals Hegedus, 1978, Hegedus et al., 1979) and their impregnation depths (Hegedus and Summers, 1977) have been shown to have a strong influence on the performance and durability characteristics of automotive catalysts. Converter models previously developed (e.g., Kuo et al., 1971;Ferguson and Finlayson, 1974), however, were not designed to study the effects of the parameters associated with the design of the catalyst pellet.Recently, Becker and Wei (1976, 1977a) investigated the effects of the location of the active layer on the catalyst's activity for negative-order reaction systems, such as the oxidation of carbon monoxide over platinum. They used the isothermal effectiveness factor vs. Thiele modulus plot to compare the lightoff characteristics of catalysts with various impregnation patterns. Although this approach is useful in gaining insight into the change in catalysts' activity as temperature varies, it does not provide information about the time scale of catalyst lightoff. Such information is necessary for estimating time-integrated emissions. For this reason, we decided to explore the...

Mathematical modeling of catalytic converter lightoff. Part II: Model verification by engine‐dynamometer experiments

“…In accord with the results of our previous study (Oh et al, 1980), however, the converter lightoff times (say, the time required for 50% conversion) for CO, C3H6, and Hz were predicted to be very similar because of the kinetic coupling between the species. (In all cases considered, the predicted conversion of methane was negligibly small.)…”

“…11, because the validity of this uniform pellet temperature assumption in converter warmup studies has been demonstrated previously (Oh et al, 1980). It is important to emphasize that Eqs.…”

“…8-13) is given in our earlier paper (Oh et al, 1980). Our approach involved the use of Galerkin's method with piecewise analytic basis functions to approximate the single-pellet equations by a well-structured nonlinear algebraic/ initial value problem in the time domain.…”

“…The converter models previously reported in the literature (e.g., Kuo et al, 1971;Harned, 1972;Bauerle and Nobe, 1973;Ferguson and Finlayson, 1974) were not designed to include details about the catalyst pellets and thus are not well-suited for studying the effects of the parameters associated with catalyst design. In our previous paper (Oh et al, 1980), a detailed mathematical model was developed which describes the behavior of a single catalyst pellet under transient conditions encountered during the warmup period of automobile exhaust catalytic converters. The singlepellet model treated catalyst pellets as composite porous media composed of concentric shells of differing physical and chemical properties.…”

CFD Modelling of 3-Way Catalytic Converters with Detailed Catalytic Surface Reaction Mechanism

“…Chemical reaction kinetics is a key aspect in the modelling of catalyst performance. Models of reaction kinetics for catalytic converters may be divided into two categories: (1) Langmuir-Hinshelwood type with few global reaction steps [2,3,4], (2) detailed catalytic surface reaction mechanism [5,6,7].…”