# Project Materials

## Mathematical Model on a Three Way Catalytic Converter: A Comparative Study of Gas Phase Concentration and Temperature

ABSTRACT

We comparatively studied gas phase concentration and gas temperature of three way catalytic converter models. We considered channel level models and provided concise solutions for them.

Solutions to the models were graphically represented and we found that gas phase temperature increases with time and gas phase concentration of gaseous species attain light-off at temperature above 600K.

OF S

Title page…………………………………………………………………………………….i
Certification …………………………………………………………………………………ii
Dedication …………………………………………………………………………………..iii
Acknowledgement ……………… ………………………………………………………….iv
Abstract..…………………………………………………………………………………….vii
CHAPTER ONE
1.1 Introduction ……………………………………………………………………………..1
1.2 Motivation for the study …………………………………………………………………2
1.3 Objectives of the study ………………………………………………………………….2
1.4 Scope of the study ………………………………………………………………………3
CHAPTER TWO
2.1 Review ……………………………………………………………………….4
CHAPTER THREE
3.1 of catalytic converter…………………………………………………….…7
3.2 Levels of catalytic converter ……………………………………………………………..8
3.3 Phenomena involved in a 3wcc operation………………………………………………..13
3.4 Challenges of catalytic converter…………………………………………………………16
3.5 Catalytic converter/system technologies………………………………………………….20
CHAPTER FOUR
4.1 Channel model formulation………………………………………………………………23
4.2Solutions of the model……………………………………………………………………26
4.3 Graphical analysis of the reactions of Cj(z) and Tg(z)……………………………………30
CHAPTER FIVE
5.1 Discussion………………………………………………………………….. 33
5.2 Conclusion ……………………………………………………………………33
5.3 Recommendations ……………………………………………………………34
S

CHAPTER ONE

INTRODUCTION

The Combustion of fuel in the engine always releases some harmful by-products which are majorly hydrocarbon, carbon monoxides and oxides of nitrogen. These dangerous gases emitted by the exhaust engine have been a major source of air pollution. The alarming increase in the number of automobiles due to economic growth in some developing countries has also aided the increase of these pollutants which have been causing so much damage to nature and human life. Efforts to combat this menace has been on for more than three decades.

In the early 1950’s when the reality of pollution began to dun on the world. The federal carried out a research to determine its course and found that automobiles are one of the biggest sources of emissions. This led to the enactment of different laws to enforce pollution control from automobiles according to Agency, (1994). For instance, the clean Air Act of 1970 gave the environmental protection agency (EPA) authority to regulate vehicles pollution.

equently, EPA dictated allowed quantity of each species emitted which is presented in Agency,(1994) and Chorkendorff and Niemantsverdriet,(2007).The first federal legislation regarding emission limits in the United States also came in 1975. These laws have necessitated the use of a three- way catalytic converter by the automobile companies. This device located in line with the exhaust system has been used to cause a desirable chemical reaction in the exhaust flow by completing the oxidation process for hydrocarbon (HC) and carbon monoxides (CO) to carbon dioxide and water; and Oxides of Nitrogen (NOx) back to Simple Nitrogen.

Due to the ever increasing stringent safety measures, there has been need for the improvement of the existing three-way catalytic converters. Efforts are being made to optimize the converter geometry, substrates selection and wash coat materials and the converter location in the exhaust system and a great understanding of the gaseous flow through the thin channels of the monolith while the gases are reacting which largely depends on the concentration of the gaseous species and the exhaust gas temperature as they flow will help in designing monolith that can function efficiently at any temperature. In other to minimize the cost and time that will be wasted in design, mathematical modelling is best suited for this optimization.

1.2 FOR THE STUDY

There has been a growing interest in using mathematical models for the improvements of the existing three-way catalytic converters. Several approaches exist for the modelling of mass transport which completely neglects the washcoat diffusion for simplicity although evidence of diffusion is important according to Massing et al(2000) and Hayes and Kolaczkowski(1994). We want to look into channel level modeling which accounts for the gas-phase concentration and the exhaust gas temperature to provide simple solution to the model and compare the effect of concentration and temperature to the light-off ofa catalytic converter.

1.3 OBJECTIVES OF THE STUDY

The aims/objectives of the study are:

a) To provide a concise solution to the channel level models.

b) To use the solution we obtained to investigate the effect of gas-phase concentration and exhaust gas temperature on the conversion efficiency of catalytic converter.

1.4 SCOPE OF THE STUDY

This study will focus on formulating a model for the expression of gas-phase concentration and exhaust gas temperature using channel level modeling. We shall not consider other levels of modeling of catalytic converter and there complexities.

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