R.E. Hayes

Mass and heat transfer effects in catalytic monolith reactors

Abstract Numerical simulations of catalytic oxidation in monolith reactors are performed in order to develop criteria for mass transfer limitation. A two-dimensional finite-element simulator previously developed is used to examine previously reported studies of propane and carbon monoxide combustion in excess oxygen. The Sherwood and Nusselt numbers computed from the two-dimensional simulation results are compared to numbers derived experimentally. The results from the simulations are much higher than results which have been reported in the literature for experimental work. Simulation results agree well with numbers obtained analytically and experimentally for non-reacting flow in circular tubes, and also with other correlations for reacting flows based on numerical work. The reason for the discrepancy between experimental and simulated results is explained. For first-order reactions, a dimensionless catalytic reaction number is proposed, which may be used to evaluate whether or not the rate is mass transfer controlled. For the oxidation of CO, multiple steady states are possible and the variation in Nusselt and Sherwood numbers under transient conditions is discussed. The influence of diffusion in a real monolith washcoat is also examined. In square monolith channels of dimension 1 mm, low effectiveness factors are obtained for temperatures above 700 K, and much of the catalyst is not utilised. It is shown that care needs to be taken in the extension of relatively low-temperature kinetic data to the elevated temperatures encountered in real operating conditions.

Finite-element model for a catalytic monolith reactor

Abstract The development of a comprehensive 2-D finite-element model for a single channel of a honeycomb type monolith catalytic reactor is described. This includes a description of the weak variational form of the heat and mole balance equations derived using the Galerkin method. A description of the complex nonlinear boundary conditions is given and various schemes are compared for dealing with the convection term, including the method of characteristics, the standard Galerkin method and the Petrov—Galerkin method. The best results were obtained using a standard quadratic discretization for both temperature and concentration. For the transient case, several time discretization schemes were tested, including implicit Gear and Euler methods, the Crank—Nicholson method, as well as a fourth-order Runga—Kutta scheme. The Runga—Kutta scheme gave the most stable solution. The effects of radiation, homogeneous reaction, heterogeneous reaction and solid-phase conduction are addressed. Radiation and conduction were found to affect the outlet temperature, with axial conduction being more significant.

A study of Nusselt and Sherwood numbers in a monolith reactor

Abstract A two-dimensional model of a single channel of a monolith reactor is used to evaluate the values of the Nusselt and Sherwood numbers under reaction conditions. The circular channel is assumed to have axisymmetry with a first-order reaction occurring at the wall. The values of the Nusselt and Sherwood numbers do not correlate uniquely with the Graetz number but rather depend on the reaction rate at the wall. Hence they depend on such variables as gas velocity, inlet temperature and reactant concentration.

Modelling the three-way catalytic converter with mechanistic kinetics using the Newton–Krylov method on a parallel computer

Abstract A mathematical model for an automotive three-way catalytic converter based on experimental mechanistic kinetics is developed. The transient model includes a one-space dimension discretization for the gas phase and a two-dimensional discretization for the solid phase is comprised of the washcoat and substrate. Axi-symmetry is assumed. The combination of the complex kinetic model and the associated transport equations generates a large system of non-linear equations that is solved using the Newton–Krylov method based on a pre-conditioned GMRES algorithm. Simulated light-off curves for cold start operation illustrate the importance of including dynamic adsorption process in the model for this type of operating condition. Diffusion limitation in the washcoat is shown to be very significant even at relatively low operating temperatures. From the numerical standpoint, the importance of the choice of pre-conditioner is demonstrated. The use of parallel computing at a fine grain level on vector–vector and vector–matrix operation is shown to provide a large degree of speedup, which increases as the number of grid points increases.

The palladium catalysed oxidation of methane: reaction kinetics and the effect of diffusion barriers

Abstract The combustion of methane on a palladium catalyst was examined in a monolith reactor. The rate equation was determined and showed an approximately first order dependence in methane concentration and zero order dependence on oxygen concentration. Significant inhibition by water was observed, and inhibition by carbon dioxide was negligible. At high water concentrations the order with respect to water is approximately minus one. A significant reduction in both activity and activation energy was observed above temperatures of approximately 820 K with a dry feed. Significant diffusion limitation in the washcoat was observed. The intrinsic volumetric rate constant was found to be directly proportional to the palladium loading of the washcoat. The effect on the reaction rate of layers of inert washcoat placed on top of the active catalyst was investigated. These diffusion barriers reduced the reaction rate. The reactor performance was modelled using a two-dimensional finite element single channel model that included washcoat diffusion. The effect of diffusion barriers was compared to the effect of using a less active catalyst for steady state and transient modes of operation at values of the Lewis number. At low Lewis number the diffusion barrier was effective at reducing the temperature rise at the entrance to the reactor for large inlet reactant concentration.

A new technique to measure the effective diffusivity in a catalytic monolith washcoat

A method is described for measuring the flux of a diffusing species through a multiple cell structure cut from a catalytic monolith honeycomb. One- and two-dimensional mathematical models are used to calculate the effective diffusivity in the catalyst/washcoat layer. This method is suitable for porous monolith supports, e.g. cordierite, but it is unsuitable for metal monoliths. To illustrate the technique the diffusion of CO in nitrogen is studied using a modified form of a Wicke–Kallenbach type of diffusion cell. The inlet concentration of the diffusing component is 2.4% CO in nitrogen, and experiments are performed at ambient temperature and pressures between 106 and 150 kPa on a catalytic monolith with 62 cells cm −2 . The technique can be applied in many areas where catalytic monoliths are used, e.g. catalytic converters, catalytic combustion reactors, SCR catalysts and many other applications. The method shows good agreement with the results obtained using other methods.

Modelling a reverse flow reactor for the catalytic combustion of fugitive methane emissions

This paper describes the development and validation of a computer simulator for the modelling of a reverse flow catalytic reactor for the combustion of lean mixtures of methane in air. The simulator uses a heterogeneous two dimensional model for the reactor. The reactor uses a packed bed for catalytic sections and ceramic monoliths for inert sections, although the simulator is written in a general fashion so that any combination of packing can be used, in any desired variety. Validation is performed using a 200 mm internal diameter reactor over various flowrates and methane concentrations. The reverse flow reactor is observed to yield stable auto-thermal operation even for low methane concentrations. Higher methane concentrations are observed to give dual temperature peaks in the reactor. The transfer of energy is observed to be a significant factor in the reactor operation, which is shown by comparison of the heterogeneous model to a pseudo-homogeneous reactor model. The simulator can model the pilot reactor in real time for typical operating conditions.

Flow reversal reactor for the catalytic combustion of lean methane mixtures

This paper describes an experimental investigation of a pilot scale reverse flow reactor for the catalytic destruction of lean mixtures of methane in air. It was found that using reverse flow it was possible maintain elevated reactor temperatures which were capable of achieving high methane conversion of methane in air streams at methane concentrations as low as 0.19% by volume. The space velocity, cycle time and feed concentration are all important parameters that govern the operation of the reactor. Control of these parameters is important to prevent the trapping of the thermal energy within the catalyst bed, which can limit the amount of energy that can be usefully extracted from the reactor.

Reversing flow catalytic converter for a natural gas/diesel dual fuel engine

Abstract An experimental and modelling study was performed for a reverse flow catalytic converter attached to a natural gas/diesel dual fuel engine. The catalytic converter had a segmented ceramic monolith honeycomb substrate and a catalytic washcoat containing a predominantly palladium catalyst. A one-dimensional single channel model was used to simulate the operation of the converter. The kinetics of the CO and methane oxidation followed first-order behaviour. The activation energy for the oxidation of methane showed a change with temperature, dropping from a value of 129 to 35 kJ / mol at a temperature of 874 K . The reverse flow converter was able to achieve high reactor temperature under conditions of low inlet gas temperature, provided that the initial reactor temperature was sufficiently high.

Modelling Foamy Oil Flow in Porous Media

This paper describes a dynamic model for the simulation of foamy oil flow in porous media. The model includes expressions for the rate processes of nucleation, bubble growth and disengagement of dispersed gas bubbles from the oil. The model is used to simulate experimental results pertaining to primary depletion tests conducted in a sand pack. Using the model to interpret experimental results indicated that, although the lifetimes of supersaturation and dispersed gas bubbles may be short, supersaturated conditions are likely to exist, and dispersed gas bubbles are likely to be present during the entire production period, as long as the pressure continues to decline at a high rate. The model developed in this paper gave better agreement with experimental data than other proposed models. The effect of foamy oil flow increases as the rate of pressure decline increases.