System Modelling

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System Modelling

Assignment, Question 1

By

Kevin Gan Kwan Yew

Department of Chemical Engineering
School of Engineering
The University of Birmingham
18th January 2018

Table of Contents

Contents

Table of Contents        2

Abstract        3

1.0        Introduction        4

1.1 Solid oxide fuel cells        4

1.2 Interconnects        4

1.3 Chromium Vaporization        4

1.4 Aim and Objectives        5

2.0        Theory        5

2.1 Ficks second law        5

2.2 Boundary conditions        8

2.3 Parameters        8

3.0        Discussion        9

4.0        Methods        10

5.0        Conclusion        10

6.0 References        10

Abstract

Chromium is now widely used commercially as part of the steel used as interconnects. This is because the oxidation of chromium produces a layer of chromium oxide scale that has a protective function. However the oxidation causes the chromium to deplete over time . The oxidation also increases the electrical resistance of the interconnects. By modifying the Deal-Grove model given, and using the flux obtained throughout, a new model could be obtained where the optimum oxide growth as well as the chromium depletion could be found. Using the model an equation based on the growth of oxide over time could be found which is  Furthermore by using Fick’s second law and differential equations as well as forward,backward and central differences, a relationship of dc/dt was obtained.[pic 2]

1. Introduction

1.1 Solid oxide fuel cells

Solid oxide fuel cells (SOFC) are electrochemical devices that generate electricity in the most efficient way using various fuel cells such as methane, hydrogen and even natural gas without any combustion or mechanical processes. (SOFC) also generates high quality byproduct heat while also generating very low amount of pollutants which shows the importance of SOFC in the past and also the future. (W.Z.ZhuS.C.Deevi ,2003)[pic 3]

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1.2 Interconnects

The importance of solid oxide fuel cells (SOFC) has brought many modifications to further improve it where an interconnect component is installed which can be seen in figure 1. The interconnect is a critical component in any SOFC as the role of interconnect as it operates in both oxidizing and reducing atmosphere where it: (Joelle C.W Mah,2016)

• Prevents the fuel electrode material from contacting with oxidizing atmosphere of the oxidant electrode side.
• Connects the cathode and anode to provide electrical connection
• Acts as a barrier in between the air electron material and the reducing environment of the fuel electrode

1.3 Chromium Vaporization

Almost all metals undergo oxidation when it is exposed to oxygen in air. Negative oxygen ions which forms penetrates into the metal causing a growth of oxide surface. When the oxide layer grows the rate of electron transfer decreases. An example of oxidation can be seen in the equation below where chromium is oxidized

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https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1992/illpres/oxidation.html

Recently, chromium rich steel have been used as interconnects for its many advantages such as they act as a good electric conductor, have a body centered cubic (BCC) structure which is suitable with CTE as well as lower cost compared to ceramics. One of the main importance of this is the thickness control of the interfacial chromia, Cr2O3. This is because it provides resistance of alloys against high temperature

1.4 Aim and Objectives

For silicon, silicon oxide could be well expressed by the Deal-Grove model. However, for chromium, there is an unstable Cr/Cr2O3 interface, making it doubtful to follow the silicon oxidation kinetics therefore a modified version of the Deal-Grove model would be done where the oxide film thickness, weight gain as well as the chromium depletion could be calculated.

1. Theory

Consider that the interconnect steel begins with no oxide layers. There are a few assumptions that needs to be made such that the chemical reactions that occur are at steady state with first order kinetics. It can be assumed that the oxidation process is by the outward moment from the steel where it undergoes the following stages:

1. The chromium is diffused into chromia forming a layer of oxide,chromia.
2. Chromium diffuse across the oxide layer towards the air.
3. Chromia reacts with the water in the oxidant

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2.1 Ficks second law

There are a few models that can be used to further understand these processes. Using Fick’s 2nd law of diffusion, the mass transfer of chromium into an external surface could be determined.( J. Andrews,2017)

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There is another approach to modelling where reaction oxidation kinetics is used. By modifying the Deal-Grove model and assuming that reactions occur at the air-oxide interface which can be seen by the X mark on figure 2, the different fluxes could be found and expressed as:

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