# Temperature Distribution Estimation in a Dwight–Lloyd Sinter Machine Based on the Combustion Rate of Charcoal Quasi-Particles

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## Abstract

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_{2}emission in the sintering process. The purpose of this study was to investigate the combustion rate of a biomass carbon material and to use a sintering simulation model to calculate its temperature profile. The samples were prepared using alumina powder and woody biomass powder. To simplify the experimental conditions, alumina powder, which cannot be reduced, was prepared as a substitute of iron ore. Combustion experiments were carried out in the open at 1073 K~1523 K. The results show that the combustion rates of the biomass carbon material were higher than that of coke. The results were analyzed using an unreacted core model with one reaction interface. The kinetic analysis found that the k

_{c}of charcoal was higher than that of coke. It is believed that the larger surface area of charcoal may affect its combustion rate. The analysis of the sintering simulation results shows that the high temperature range of charcoal was smaller than that of coke because of charcoal’s low fixed carbon content and density.

## 1. Introduction

_{2}emission from Japan’s industrial sector is much higher than that from other sectors. In 2017, it accounted for approximately 37.2% of the total emission. In the industrial sector, the iron and steel-making industry accounts for approximately 39.4% of energy consumption. The steel industry emits approximately 13% of the CO

_{2}in Japan [1]. The demands of global environmental conservation require a greenhouse gas reduction. Currently, approximately 80 million tons of pig iron are produced by blast furnace annually in Japan. Coal and coke are used as reducing materials and heat sources, respectively, and a large amount of CO

_{2}is emitted in the iron-making process. Therefore, the development of innovative technologies is required to reduce the CO

_{2}emission.

## 2. Experimental Sample and Procedure

_{2}atmosphere for 30 mins to remove water, Volatile matter (V.M.) and the binder from the samples. Then, air was passed through the reaction tube. The air flow rate was 4 NL/min. When a weight change in the sample was not observed, the experiment was terminated. It was hypothesized that coke ash did not influence the weight loss of the sample because the amount of coke in every sample stayed the same.

## 3. Results

## 4. Kinetic Analysis

#### 4.1. Unreacted Core Model for Coke

- 1.
- O
_{2}transport from the gas phase to the particle surface through the gas film:$$-{\dot{n}}_{g\cdot {O}_{2}}=4\pi {r}_{0}^{2}{k}_{f}\left({C}_{{O}_{2}}-{C}_{{O}_{2}\cdot s}\right)$$ - 2.
- O
_{2}transport from the particle surface to the reaction interface through the alumina powder layer after coke combustion:$$-{\dot{n}}_{d\cdot {O}_{2}}={({D}_{{O}_{2}})}_{eff}\frac{4\pi {r}_{0}{r}_{i}}{{r}_{0}-{r}_{i}}\left({C}_{{O}_{2}\cdot s}-{C}_{{O}_{2}\cdot i}\right)$$ - 3.
- The combustion reaction at the reaction interface:$$-\dot{R}=4\pi {r}_{i}^{2}{k}_{c}\left({C}_{{O}_{2}\cdot i}-\frac{{C}_{{\mathrm{CO}}_{2}\cdot i}}{K}\right)$$
- 4.
- CO
_{2}transport from the reaction interface to the particle surface through the alumina powder layer after coke combustion:$${\dot{n}}_{d\cdot {\mathrm{CO}}_{2}}={({D}_{{\mathrm{CO}}_{2}})}_{eff}\frac{4\pi {r}_{0}{r}_{i}}{{r}_{0}-{r}_{i}}\left({C}_{{\mathrm{CO}}_{2}\cdot i}-{C}_{{\mathrm{CO}}_{2}\cdot s}\right)$$ - 5.
- CO
_{2}transport from the particle surface to the gas phase through the gas film:$${\dot{n}}_{g\cdot {\mathrm{CO}}_{2}}=4\pi {r}_{0}^{2}{k}_{f}\left({C}_{{\mathrm{CO}}_{2}\cdot s}-{C}_{{\mathrm{CO}}_{2}}\right)$$

_{0}at t = 0 and r = r

_{i}at t = t, Equation(13) is obtained:

_{f}, can be calculated from Ranz–Marshall’s Equation [9]. The value of the effective diffusion coefficient in the alumina layer, D

_{e}, and the interfacial reaction rate coefficient of coke, k

_{C}, was obtained by parameter-fitting using the nonlinear least-squares method to the fractional reaction curves.

_{e}, and k

_{C}can be expressed by substituting the coefficients in Arrhenius’ equation as shown:

_{c}. The values of k

_{c}are at the same level in all samples.

_{c}is expressed as

Coke | (−125 μm) | k_{c} = 6.02 × 10^{−2} exp(−9.32 × 10^{3}/RT) | (m/s) |

(125~250 µm) | k_{c} = 4.51 × 10^{−2} exp(−5.12 × 10^{3}/RT) | (m/s) |

_{e}. The temperature dependence of D

_{e}can be expressed as

Coke | (−125 μm) | D_{e} = 1.79 × 10^{−}^{3} exp(−36.4 × 10^{3}/RT) | (m/s) |

(125~250 µm) | D_{e} = 3.06 × 10^{−3} exp(−36.6 × 10^{3}/RT) | (m/s) |

#### 4.2. Chemical Reaction Control Step for Charcoal

_{2}transportation rate in the alumina layer will be large. Therefore, the reaction is based on the chemical reaction control step.

_{0}at t = 0 and r = r

_{i}at t = t, and this gives Equation (19):

_{c}was determined using the unreacted core model [3].

_{C}can be substituted in Arrhenius’ equation as shown by Equation (14) which also can be transformed as Equation (16).

_{c}.

_{c}can be expressed as

Coke | (−125 μm) | kc = ${8.24\times 10}^{-3}\mathrm{exp}\left({-10.6\text{}\times \text{}10}^{3}/RT\right)$ | (m/s) |

(125~250 µm) | kc = ${8.54\times 10}^{-3}\mathrm{exp}\left({-10.3\text{}\times \text{}10}^{3}/RT\right)$ | (m/s) |

## 5. Sintering Simulation Model

#### 5.1. Simulation Method

_{3}, the evaporation and condensation of water, and the formation and solidification of calcium ferrite melt according to Ohno’s model [10].

_{e}depends on coke distribution.

_{e}has a value of 10

^{8}because the resistance of the diffusion can be ignored.

_{2}, O

_{2}, CO

_{2}and H

_{2}respectively, can be expressed as follows:

#### 5.2. Calculation Conditions

#### 5.3. Calculation Results

## 6. Conclusions

- Compared with coke, the reaction curves of charcoal combustion show that the combustion reaction of charcoal is faster.
- The interfacial chemical reaction rate coefficient of charcoal for the experimental data was calculated as follows:

Coke | (−125 μm) | kc = ${8.24\times 10}^{-3}\mathrm{exp}\left({-10.6\text{}\times \text{}10}^{3}/RT\right)$ | (m/s) |

(125~250 µm) | kc = ${8.54\times 10}^{-3}\mathrm{exp}\left({-10.3\text{}\times \text{}10}^{3}/RT\right)$ | (m/s) |

- Calculations using the rate equation obtained in the sintering simulation model found that the high temperature range of charcoal is smaller than that of coke due to charcoal’s low fixed carbon content and density.
- If the fixed carbon content of charcoal is the same as that of coke, which means that the combustion heat of carbon materials is the same, a temperature profile of the same level can be obtained.
- The sintering simulation results suggest that there are probabilities that biomass carbon materials can replace coke in the sintering process.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A_{(kc,De)} | Frequency factor (m/s) |

C_{(O2, CO2)} | O_{2} or CO_{2} concentration in the gas phase (mol/m^{3}) |

C_{(O2, CO2)}_{·i} | O_{2} or CO_{2} concentration at the reaction interface (mol/m^{3}) |

C_{(O2, CO2)}_{·s} | O_{2} or CO_{2} concentration at the particle surface (mol/m^{3}) |

C_{p} | Specific heat (J/kg/K) |

d | Particle size (m) |

D_{e} | Effective diffusion coefficient in the Al_{2}O_{3} powder layer (m^{2}/s) |

(D_{O2, CO2})_{eff} | Effective diffusion coefficient of O_{2} or CO_{2} in the Al_{2}O_{3} powder layer (m^{2}/s) |

E_{a(kc,De)} | Activation energy (J/mol) |

F | Reaction ratio (–) |

H | Reaction heat of each reaction (J/mol) |

h | Convection heat transfer coefficient (J/m^{2}/s/K) |

K | Equilibrium constant (–) |

k_{C} | Interfacial chemical reaction rate coefficient (m/s) |

k_{f} | Mass transfer coefficient in the gas film (m/s) |

k | Heat conductivity (J/m/s/K) |

k’ | Overall reaction rate (m/s) |

n_{(Coke, Quasi-particle, Lime, Ore)} | The amount of coke, quasi-particle, lime and ore among unit volume (-) |

ΔP | Pressure loss (atm) |

r_{0} | Initial radius (m) |

r_{i} | Radius of the non-reaction nucleus (m) |

r_{i,x} * | Generation rate of the component x in the number i cell (kg/s/m^{3}) |

r_{Quasi-particle} | Distance from the left of the particle to the reaction interface of the quasi-particle (m) |

r * | Reaction ratio of the component in the sample (–) |

r *_{Quasi-particle} | Reaction rate per one particle of the quasi-particle (mol/s) |

T_{g} | Temperature of gas in the control volume (K) |

T_{s} | Temperature of solid in the control volume (K) |

Δw_{t} | Sample weight change (kg) |

U | Superficial velocity (m/s) |

u | Gas flow rate (m/s) |

W | Weight change of the sample during the experiment (kg) |

ΔZ | Length of the control volume (m) |

P_{x} | Density of component x (kg/m^{3}) |

ρ_{Cm} | Carbon concentration in the sample (mol/m^{3}) |

ρ_{N2, O2,CO2, H2O} | Density of gas in the sample(kg/m^{3}) |

ε_{a} | Porosity (-) |

Φ | (Surface area of a ball which has the same volume with the particle)/(Surface area of the particle) (-) |

μ_{g} | Viscosity of gas (Pa·s) |

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Ash (mass %) | V.M. (mass %) | Fix.C. (mass %) | Specific Surface Area (m^{2}/g) | |
---|---|---|---|---|

Charcoal (−125 μm) | 1.84 | 29.2 | 69.0 | 61.0 |

Charcoal (125~250 μm) | 28.5 | |||

Coke (−125 μm) | 10.1 | 1.71 | 88.2 | 2.59 |

Coke (125~250 μm) | 0.92 |

▪Sinter Bed | |

Bed depth | 450 mm |

Porosity of sinter bed | 35% |

▪Composition of Raw materials | |

Hematite | 85.0 mass % |

Lime (CaO) | 10.0 mass % |

Moisture | 5.0 mass % |

Coke, Charcoal | 4.0 mass % (additionally) |

Charcoal | 5.1 mass % (additionally) |

▪Diameter of Raw Materials | |

Hematite | 2.5 mm:0.25 mm ≈ 88.6:11.4 |

Lime (CaO) | 2.0 mm |

▪Others | |

Initial temperature | 298 K |

Ignition temperature | 1573 K |

Ignition time | 90 s |

Gas flow rate (outlet) | 0.6 m/s |

Calculation cell | 5 mm |

Time step | 0.001 s |

Courant number | 0.2 |

Existing State of Coke (%) | Total | Amount of Coke and Charcoal in Sinter Bed (%) | ||
---|---|---|---|---|

S’-Type | C-Type | P-Type | ||

40.0 | 30.0 | 30.0 | 100 | 4.0, 5.1 |

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**MDPI and ACS Style**

Wang, Z.; Ohno, K.-i.; Nonaka, S.; Maeda, T.; Kunitomo, K.
Temperature Distribution Estimation in a Dwight–Lloyd Sinter Machine Based on the Combustion Rate of Charcoal Quasi-Particles. *Processes* **2020**, *8*, 406.
https://doi.org/10.3390/pr8040406

**AMA Style**

Wang Z, Ohno K-i, Nonaka S, Maeda T, Kunitomo K.
Temperature Distribution Estimation in a Dwight–Lloyd Sinter Machine Based on the Combustion Rate of Charcoal Quasi-Particles. *Processes*. 2020; 8(4):406.
https://doi.org/10.3390/pr8040406

**Chicago/Turabian Style**

Wang, Ziming, Ko-ichiro Ohno, Shunsuke Nonaka, Takayuki Maeda, and Kazuya Kunitomo.
2020. "Temperature Distribution Estimation in a Dwight–Lloyd Sinter Machine Based on the Combustion Rate of Charcoal Quasi-Particles" *Processes* 8, no. 4: 406.
https://doi.org/10.3390/pr8040406