Adapting the Heat and Mass Transfer Analogy to Model Performance of Automotive Catalytic Converters

Abstract

Using theory for mass transfer of a diffusing specie with very low concentration, rate equations and a mass-balance equation can be combined to derive a differential equation for mass transfer in an automotive catalytic converter. A closed-form solution to this equation shows conversion efficiency to be a function of the dimensionless size of the converter, or the number of transfer units, Ntum. This mass-transfer-limited analysis does not include catalyst kinetics; hence it is limited to fully warm, fresh catalyst performance. However, a technique is developed to model lightoff of a catalytic converter by combining convective heat transfer when warming up with mass-transfer-limited conversion when fully warm. Realistic assessment of the merit of a catalytic converter must also include the influence of size and shape on flow pressure drop. Accordingly the size and shape of square-cell monoliths and packed-sphere bead beds are correlated with both conversion performance and pressure drop. Applications of these correlations are shown to compare realistically the size versus performance characteristic of monoliths with that for bead beds, in spite of drastically different flow patterns for the two converters. Model predictions are confirmed by engine-dynamometer and vehicle test results.