Modeling exhaust gas pollution abatement: Part I — single hydrocarbon propylene

Abstract

The one-dimensional models for catalytic converters are used to account for the reduction of pollutants like hydrocarbons (HC), carbon monoxide (CO) and nitric oxide (NO). The proposed model considers both gaseous as well as solid phase reactions of only one gas propylene that could possibly be occurring in the converter channels. Metal substrates were considered, as the better heat conducting solid material. The Runge-Kutta method and backward implicit schemes were employed to solve the coupled ordinary and partial differential equations.

Numerical methods for a coupled system of differential equations arising from a thermal ignition problem

“…i,n } converges monotonically from below to a minimal solution (u i,n , v i,n ) of (4. 3), and this solution is also the minimal solution of (2.1) for as long as v i,n ≤ ρ. Moreover, the minimal solution (u i,n , v i,n ) of (2.1) blows up at some n * if v i,n * > ρ at some i = i * for every ρ < ∞.…”

“…This concern and many others lead to various mathematical models for the study of interphase heat-transfer problems in catalytic converters (cf. [1][2][3][4][5][6][7][8][9][10][11]17]). One of the mathematical models is suggested by Leighton and Chang in [7] where the vehicle temperature T g and the converter temperature T s are governed by a coupled system of a first-order partial differential equation and an ordinary differential equation which is given in the form…”

“…However, most of discussions in the literature are devoted to mechanical experimentation and numerical simulation (cf. [2][3][4][5][6][7][8][9][10][11]). Although the authors in [7] proposed the coupled system in (1.0) their investigation is for a simplified version which is given by the following scalar initial boundary value problem:…”

Modeling Catalytic Converter for Oxidation of Hydrocarbon in the Exhaust Gas

“…where γ 3 = C g 0 a L 2 (-ΔH ) k cat / λ s T g 0 α 33 = 4 h L 2 / λ s d and δ 3 = ρ s C ps L 2 / λ s t 0 Initial and boundary conditions: The above partial differential equations are solved by Backward Implicit finite difference numerical scheme [7].…”

Modeling Catalytic and Homogenous Combustion of Hydrocarbons in Monolithic Converters

“…A one-dimensional model is used to simulate the conversion and thermal characteristics of the gas mixture introduced in a single converter channel (Chauhan and Srivastava, 2008). The converter is considered to be cylindrical and only the axial gradients are accounted for.…”