Blast furnace process and oxidation of metallurgical coke
There are two main process routes in steel making. There are the integrated steel making route and electrical arc steel making route, see Figure 5.
In the integrated steel production route, the blast furnace process main objective is to produce liquid pig iron by the reduction of iron ores. A blast furnace can produce approximately 1200 tons of liquid pig iron per day and use approximately 85-90% of all the heat that is produced in the process. .
The blast furnace process is a continuous process where the input materials such as iron ore, slag formers and metallurgical coke are charged at the top of the blast furnace while the end products, liquid iron and slag, are tapped from tap holes in the bottom of the furnace.
The input material passes through different temperature zones inside the blast furnace and after several chemical reactions turns into the end products. The temperature zones are zones with different temperatures and therefore have chemical reactions with different kinetic conditions. The temperature zones in the blast furnace, from the top to the bottom of the furnace, are listed below.
It is possible to find natural deposits graphite at some places in the world such as China and South America . In this study focus is on synthetic graphite, which includes both so called carbon graphite and electro graphite. Therefore, this study do not involve any more information regarding so called natural graphite.
Synthetic graphite is produced mainly from special types of carbon sources which are made into a specific powder. The carbon sources mainly originates from petroleum coke, pitch coke and carbon black. The carbon sources may also originate from secondary graphite, re-used graphite.   During the powder preparation, see Figure 8, the carbon sources are first separated and stored in silos. Then the carbon sources are mixed, crushed and pulverized in order to obtain a fine powder, also known as carbon powder. The carbon powder is then screened in order to obtain the right particles sizes and particle size distribution. The particles which fail to pass the required demands on particles size is returned back to the crushing and pulverizing step. When the carbon powder has obtained the right particle sizes and particle size distribution, the carbon powder is mixed together with a binder. The binder usually consist of coal tar pitch or synthetic resins. The binder provides some enhancement to the mechanical properties of the green body.
The effect of the temperature on the graphite oxidation rate
The graphite oxidation rate is, to a very high degree, temperature dependent. The temperature dependence of the graphite oxidation rate is manifested into three different temperature zones or regimes where the graphite oxidation rate has different rate-limiting steps . The name of these temperature regimes can be seen below. The temperature regimes are listed from low temperature to high temperature.
1) The chemical regime.
2) The in-pore diffusion regime.
3) Boundary layer controlled regime.
The schematics of the effect of the temperature regimes on the oxygen concentration adjacent to the graphite surface can be seen in Figure 9.
In the chemical regime, the graphite oxidation rate is relatively low due to relatively high activation energy for the oxidation reaction. As the name of the temperature regime implies, the graphite oxidation rate is limited by the chemical reaction between the oxygen and the reactive carbon in the graphite. The relatively low graphite oxidation rate allows the oxygen to diffuse deep into the graphite porous network before reacting at an active site. The result of the deeper diffusion is that the graphite oxidation becomes much more homogenously distributed within the graphite  . An increase in porosity and pore size is seen in the chemical regime as a consequence of the homogenous oxidation. No major changes of the geometry is found in this regime since the graphite is oxidized and consumed mainly by pore formation in the interior part of the graphite. 
When the temperature reaches approximately 800-1050°C, see Table 1, the oxidation enters into the last temperature regime which is the boundary layer controlled regime. In the boundary layer controlled regime the reaction rate is very high and the graphite oxidation rate reaches saturation, small or no increase in graphite oxidation rate with higher temperature . The oxidation reactions are limited to the graphite surface and therefore there is almost no oxygen diffusion into the porous network. In the boundary layer controlled regime the gas diffusion or the mass transport to the graphite surface is the rate-limiting step since the oxidation reactions are occurring very rapidly when the oxygen comes in contact with the graphite.
When the temperature is between the interval of the chemical regime and the boundary layer controlled regime, the graphite oxidation enters in to the in-pore diffusion regime. The in-pore diffusion regime is a mixture between the chemical regime and the boundary layer controlled regime. In the in-pore diffusion regime the reaction rate is relatively higher than in the chemical rate regime , the reactions occur more frequently relative to the chemical rate regime. In the in-pore diffusion regime the rate-limiting step is a combination of both the chemical reaction and the mass diffusion. The oxidation reaction occurs closer to the graphite surface than in the chemical regime but the diffusion into the porous network are still occurring. The limitation of the diffusing depth makes it more difficult for the oxygen to oxidize the inner parts of the graphite.
The temperature intervals for the temperature regimes for some common graphite grades can be seen in Table 1.
The effect of the gas flow rate on the graphite oxidation rate
The effect of the gas flow rate on the graphite oxidation rate has been investigated and studied by several previous studies. In a study conducted by Chi et al.  An investigation of the gas flow rate effect on graphite oxidation concerning the graphite grades NBG-18 and NBG-25 was conducted. The experiments were conducted in a vertical tube furnace (VTF) from ASTM with several flow rates within the interval of 1-10 L/min. It was concluded from their study that the effect of the gas flow arte on the graphite oxidation rate is temperature dependent and the gas flow rate generally increases the graphite oxidation rate when the temperature is higher than 700°C.
The gas flow rate has been seen to have an impact on the thickness of the boundary layer which forms in the boundary layer controlled regime. A high flow rate will make the boundary layer thinner since the bulk flow will mechanically force the product gas away, thus the high flow rate of the inlet gas influences the transportation and removal of product gases away from the surface of the graphite.
Another study was conducted by Takahashi et al.  in which the oxidation behavior of the graphite grade IG-110 was investigated. It was observed that the graphite oxidation rate increases with higher gas flow rate relative to the lower gas flow rate. The gas velocity also seemed to effect the rate at which carbon monoxide were formed in respect to temperature.
The off-gas composition
When graphite is oxidized by oxygen there are several chemical compounds which can form, carbon monoxide, carbon dioxide and surface oxide complexes. According to previous studies, both carbon monoxide and carbon dioxide are considered to be primary products and that the ratio between then mainly dependents on the temperature, burn-off degree and oxygen concentration in the atmosphere or carrier gas . According several previous studies, the off-gas composition is also affected by the gas pressure and the gas flow rate.
At higher temperatures the main compound found in the off-gas is carbon monoxide  . There are some indications that the Boudouard reactions is partially responsible for the graphite oxidation at high temperatures.
Guldbransen et al.  conducted online off-gas analysis during a graphite oxidation experiments by using mass spectrometry to analyze the off-gas composition. It was concluded that study that at 1200°C, with a total pressure of 5-9 torr, the off-gas mainly consisted of carbon monoxide when injecting both commercial oxygen gas and air to react with graphite. According to the result of the study, when the temperature is lower than 1000°C and the oxygen concentration is relatively high, carbon dioxide formation is favored over carbon monoxide formation. Thus, a high fraction of carbon monoxide is obtained when the temperature is elevated above a specific critical temperature. The same phenomena is also seen from the results of Takahashi et al . where several oxidation experiments on the nuclear graphite grade IG-110 were made and gas analysis of the off-gas were conducted by using gas chromatography. From their experimental result a maximum peak of the carbon dioxide content was detected at approximately 800°C, when having a gas flow velocity of 6.63 m/s with a carrier gas containing He-1.37mol% O2. At temperatures above 800°C the carbon dioxide content rapidly decreases while the carbon monoxide increases with constant slope until the carbon monoxide content reaches a saturation point at 1000°C. Another interesting phenomena is that both the oxygen concentration, in the carrier gas, and the gas flow rate seams to effect the maximum carbon dioxide content.
There are several previous studies that have constructed empirical models for predicting the fraction between produced carbon monoxide and carbon dioxide in respect to temperature when oxidizing graphite. The empirical models and their temperature intervals is displayed in Table 2.
Mathematical and CFD-modeling of graphite oxidation
There are some previous studies that have used results from graphite oxidation experiments and fundamental theories to construct mathematical models. Those models have later been benchmarked by using numerical simulations. These numerical simulations were conducted with the use of computational fluid dynamics software’s or by using numerical methods in order to solve multi-dimensional flows, mass transport and heat transport equations.
As mentioned earlier, graphite oxidation is a complex phenomenon. In order to make an accurate model of this phenomenon a large number of different parameters needs to be known. Some of those includes molecular diffusion rate of oxygen in graphite, activation energies for the reactions, surface active sites, impurities effect etc.
The oxidation mechanism for the reaction between oxygen and carbon needs to be addressed properly in order to build a proper graphite oxidation model. Despite the extensive work done in the field of graphite oxidation there are still diverse views on the primary oxidation steps, since the oxidation mechanism is complex and that the reaction rate depends on many factors. The modelling of such a reaction mechanism requires extensive knowledge of different types of parameters and their effect on the oxidation. Important kinetic parameters such as activation energies and order of reaction can be found in previous experimental studies.
In study made by El-Genk et al.  a numerical approach was suggested and a mathematic model constructed in order numerically simulate graphite oxidation. The mathematical model was benchmarked against several previous oxidation experiments on the graphite grades NGB-18 and IG- 110. El-Genk et al. suggested that the activation energy for the desorption of carbon atoms from the basal planes of the graphite are not constant but it follows a normal distribution function. The main reason for this is due to the produced organic surface oxide complexes such as alcohols, ethers and ketones etc which have different affinities to oxygen. Four governing graphite oxidation equations were suggested which describes the transport of oxygen In this mathematical model, important phenomena’s were taken in to account such as the burn-off degree and change in ASA over time. The model was benchmarked against experimental data. The model was tested by using the numerical software Matlab and the commercial CFD-software Star-ccm+. The model displayed a good match to the experimental result of the previous oxidation experiments.
Other studies has been conducted where CFD-models, created from commercial CFD-software’s, were benchmarked against controlled graphite oxidation experiments . Amongst these studies there are some who used commercial CFD-software’s to simulate the event of air ingress accidents in a high temperature gas-cooled reactor (HTGR) in the nuclear energy field. Graphite oxidation, during air ingress accidents, is an important factor since it can result in damage of the interior reactor and thus result in shortage in expected reactor lifetime. In a study conducted by Kadak and Zhai  , the commercial CFD-software Fluent was benchmarked against several air ingress experiments conducted by the Japanese atomic energy research institute (JAERI) and by the Julius research center in Germany at the NACOK facility, where NACOK stands for “Naturzug Im Core Mit Korrosion”  . The output data from the numerical simulations regarding the off-gas composition over time matches that of the experimental result to a high degree. The main gas compounds of the off-gas consisted of residual oxygen, helium, nitrogen, carbon monoxide and carbon dioxide. The gas compounds of the off-gas were measured as mole fraction over time. Kadak and Zhai  were able to show that the commercial CFD-software Fluent could successfully be used to numerically simulate the different phenomena or events in air ingress accidents. The numerical simulations results regarding the experiments conducted at NACOK facility also displayed a good match between the experimental data and the output data obtained from the numerical simulations.
In a study by Ferng and Chi  , a CFD-model was constructed in order to simulate air ingress phenomena in a HTGR. Although, this study focused on the graphite oxidation of the high-temperature reactor core. The commercial CFD-software Fluent was used as the numerical tool to investigate the oxidation distribution within a high temperature reactor core A study which involved both graphite oxidation experiments and a numerical simulations were conducted by Kim and No . Graphite oxidation experiments were conducted on the graphite grade IG-110 over a wide temperature interval, 700-1500°C, and with various oxygen concentrations. From the graphite oxidation experiments kinetic parameters such as activation energy and order of reaction were determined. The concentrations of the produced carbon monoxide and carbon dioxide were monitored and an empirical model of the fractions between as a function of the temperature were obtained. A numerical model was constructed by using commercial CFD-software Fluent in order to determine the initial graphite oxidation rate at zero burn-off degree. The experimentally obtained kinetic-parameters and the fraction between carbon monoxide and carbon dioxide were used as input data in the numerical simulations. The output data from the numerical simulations matched the experimental results to a high degree. A semi-empirical model, based on the experimental results, was also suggested.
A blind benchmarking of the air ingress experiments from NACOK experimental facility in Germany was conducted by Brudieu.  The main goal of this study was to examine the commercial CFD-software Fluent ability to simulate the phenomenon of natural convection, graphite oxidation and distribution of heat generated by the exothermal reactions etc in a HTGR. A parameters study were conducted regarding reaction kinetics, solver, mesh and fluid flow etc in order to find the most suitable numerical model.
Similar numerical treatments of the graphite oxidation studies of the JAERI and NACOK experiments were conducted by Zhai  and by Lim and No .
The graphite oxidation experiment by Kim and No 
As mentioned earlier, Kim and No  conducted both graphite oxidation experiments and numerical CFD-simulations. The study was conducted in order to investigate graphite oxidation related to the air ingress of a HTGR. The study was conducted by experimentally investigating the impact of parameters such as oxygen concentration and temperature on the initial graphite oxidation rate.
The experimental setup and experimental apparatus, which were used to conduct the graphite oxidation experiments, are displayed in Figure 12.
Suggesting experimental apparatus and setup
In order to determine which experimental apparatus and setup that were best suited in providing the needed experimental data, for the benchmarking of the dynamic coupling approach, some basic requirements were set.
The experimental apparatus and setup should be able to:
1) Provide continuous information regarding the sample mass loss over time and the sample mass loss rate.
2) Control parameters such as temperature and furnace atmosphere.
3) Conduct isothermal experiments.
4) Use and inject gases into the furnace with a controlled mass flow rate.
5) Use a simple furnace geometry.
6) Analyze the off-gases produced during oxidation.
Main assumptions and boundary conditions
In this numerical study the initial graphite oxidation rate at zero burn-off degree was investigated. The main assumptions for the numerical simulation are listed below.
1) Burn-off degree was not taken into account since the experimental data of Kim and No are only valid for the initial graphite oxidation rate with no or very little burn-off degree.
2) The surface temperature of the graphite was assumed to be constant since no information regarding the surface temperature variation was given.
3) The graphite was assumed to be non-porous since only the surface reactions are taken into account.
4) Post-combustion of carbon monoxide and Boudouards reaction were not taken into account since no carbon dioxide was used as reactive gas and the post-combustion reaction is not a surface reaction.
5) A steady-state solution was assumed since there should not be any major change in graphite oxidation rate over time at the initial moment of the experiment.
The inlet was set as a mass flow inlet while the outlet was set to a pressure outlet.
The mass flow rate was calculated by using equation 41 and equation 42.
Table of contents :
1.1 Metallurgical Coke
1.1.1 Manufacturing process
1.1.2 Blast furnace process and oxidation of metallurgical coke
1.2.1 Manufacturing process
1.2.2 Graphite oxidation
1.2.3 The effect of the temperature on the graphite oxidation rate
1.2.4 The effect of the gas flow rate on the graphite oxidation rate
1.2.5 The off-gas composition
1.3 Mathematical and CFD-modeling of graphite oxidation
1.4 Previous studies regarding the experimental setup for oxidation experiments
1.4.1 Thermogravimetric analysis
1.4.2 The graphite oxidation experiment by Kim and No 
2.1 Suggesting experimental apparatus and setup
2.2 Numerical setup
2.2.1 Computational domain and mesh
2.2.2 Surface reaction model and governing equations
2.2.3 Graphite oxidation model and kinetic parameters
2.2.4 Main assumptions and boundary conditions
3.1 Suggested experimental setup
3.1.1 Experimental equipment’s
3.1.2 Sample material
3.1.3 Experimental gases and gas flow rates
3.1.4 Experimental procedure
3.2 Numerical study
3.2.1 Calculated numerical parameters
3.2.2 Graphite oxidation simulation
4.1 Experimental apparatus and setup
4.1.1 Temperature measurements
4.1.2 Off-gas measurements
4.1.3 Sample attachment
4.2 Numerical simulations
4.2.1 The graphite oxidation rate dependence on the oxygen concentration and surface temperature
4.2.2 The graphite oxidation rate dependence on the mass diffusion and the gas flow rate
4.2.3 The graphite oxidation rate dependence on the kinetic parameters