Transient modeling of a catalytic converter to reduce nitric oxide in automobile exhaust

Abstract

Mathematical models m e developed to study the catalytic reduction of nitric oxide contained in $utomobile exhaust in which the temperature, flow rate, and concentrations of various species vary widely with time. The quasi-static approximatio$ is compared to the fully dynamic model. In the quasi-static model all prQcesses are steady state except for the solid temperature and inlet condiGons. Suggestions are given for deciding a priori if the quasi-static model is appropriate. Suggestions are also given for integrating the quasi-sta6c equations in order to minimize errors compared to the dynamic model. The exhaust gas from an automobile contains nitric oxide which must be reduced to nitrogen in order to meet Federal pollution standards. The problem is compIicated because the temperaturg, flow rate, and concentrations of different species vary in time over wide ranges. We develop transient ma*ematical models for a catalytic muffler applicable to this situation. The mathematical model is then used to examine the performance of three different catalysts.The inIet conditions correspond to those encountered when an automobile is operated in the Federal Test Procedure. The automobili: begins cold, and as it operates the catalyst bed graduglly warms up. The one feature of interest is to compare aatalysts having different properties so that they warm up at different rates. Furthermore, as the automobile changes driving modes the exhaust properties (or their time rates of change) may change discontinuously.The mathematical npodels employ a mixing-cell model for the packed bed aqd consider the reduction of nitric oxide with two catalyFic reactions. The reaction rate of nitric oxide with carb+ monoxide is closely coupled with the reaction rate of qitric oxide with hydrogen because nitric oxide is reacted essentially completely inside the catalyst. Thus one new feature of this model is the inability to construct pl@ts of effectiveness factor vs. Thiele modulus a priori, due )to the coupling of the two reaction rates. Rather, the problem of diffusion and reaction inside the catalyst pellet must be solved at each time for each mixing cell, and the orthogonal collocation method is used to do this efficiently.Three models are developed. The main model employs the quasi-static approximation which recognizes that the time response of the system is governed by the thermal response of the packing. All other processes are assumed to occur so fast that they are essentially steady state. A dynamic model is also used to test the conditions under which the quasi-static model is inappropriate. In the dynamic model all processes are allowed to be transient. Due to the wide difference in time constants for the system, the dynamic model leads to stiff ordinary differential equations, which necessitate small integration time steps. The comparison of the two models is interesting because the quasi-static model is frequently used but seldom tested. An even simpler model results when, in the quasistatic model, the reaction rate expression is assu...

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

“…11 and 12) at all times. This quasistatic assumption is valid under typical converter operating conditions because the characteristic response time for the intrapellet gas-phase concentration is much smaller than that of the pellet thermal response (Kuo et al, 1971;Ferguson and Finlayson, 1974).…”

“…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.…”

“…Note that the accumulation of mass in the catalyst pellet is neglected here in view of its small time constant (Ferguson and Finlayson, 1974). Also, the radial dependence of a ( r ) is explicitly shown in Eq.…”

“…Notice that the quasistatic approximation was again invoked in deriving Eqs. 14 and 15 (Ferguson and Finlayson, 1974). Also, the temperature dependence of the gas volumetric flow rate is accounted for in Eq.…”

Start-up and wrong-way behavior in a tubular reactor: dilution effect of the catalytic bed

“…The transient heterogeneous models are based on some common assumptions: the catalyst particle was considered isothermal (Hansen, 1971(Hansen, , 1973, and the concentration pro"les inside the catalyst were assumed to be in pseudo-steady-state (Ferguson & Finlayson, 1974;Quinta Ferreira et al, 1992. The catalyst particle was assumed to have slab geometry, where in addition to the intraparticle di!usion, the mass transport by convection could also be accounted for.…”