Experimental and Numerical Investigations on Charging Carbon Composite Briquettes in a Blast Furnace

Abstract

In the present research, charging carbon composite briquettes (CCB) in a blast furnace (BF) was investigated. The CCB used contained 29.70 wt.% Fe₃O₄, 39.70 wt.%, FeO, 1.57 wt.% iron, 8.73 wt.% gangue, and 20.30 wt.% carbon. Its reaction kinetics in BF was examined by nonisothermal tests and modeled. Thereafter, the influence of replacing 10% ore with CCB on BF performance was studied by numerical simulations. Results showed that the CCB reaction behavior in BF could be modeled using the previously proposed model under a_gs = 1900 m²·m⁻³. Numerical simulations on a BF with a production of 6250 t hot metal per day (tHM/day) showed that replacing 10% ore with CCB efficiently improved the BF operation for coke saving. In the CCB charging operation, the CCB reached a full iron-oxide reduction above the cohesive zone (CZ) and a carbon conversion of 85%. By charging CCB, the thermal state in the BF upper part was significantly changed while it was not influenced in the BF lower part; the ore reduction was retarded before the temperature reached 1073 K and was prompted after and the local gas utilization tends to increase above the CZ. By the CCB reduction above the CZ, BF top gas temperature was decreased by 8 K, the BF top gas utilization was increased by 1.3%, the BF productivity was decreased by 17 tHM/day, the coke rate was decreased by 52.2 kg/tHM, and ore rate was decreased by 101 kg/tHM. Considering the energy consumption of sintering and coking, charging the CCB could have a significant energy-saving and CO₂-emission-reducing effect for BF iron making.

1. Introduction

The development of the economy and society is increasing the demand and production of iron and steel. In 2019, crude steel production in China reached 996.3 million tons, representing 53.3% of global crude steel production [1,2]. The blast furnace ironmaking-basic oxygen furnace steelmaking (BF-BOF) route is the main route for the production, producing approximately 70% of the total crude steel [3]. Nowadays, the iron and steel industry is facing pressures of energy-saving and CO₂ emission reduction [4,5]. As the BF sector (including coking and sintering) is responsible for approximately 80% of the total energy consumption and generating most CO₂ emissions in the BF-BOF route [6], low-carbon technologies in BF ironmaking have attracted increasing attention from scholars worldwide [7,8].

Charging carbon composite briquettes (CCB) is considered to be a promising technology to improve BF efficiency [9,10]. The CCB refers to carbonaceous materials mixed with iron-bearing materials into agglomerates. Using CCB as a partial charge in BF offers the following benefits of (1) less coking and sintering [11,12,13], (2) utilization of low-grade iron ores or carbon materials [14,15,16], (3) the process is completed faster than that with pellets or sinter [17,18], and (4) energy consumption tends to decrease [19]. Several methods of preparation of CCB for BF have been proposed, including hot briquetting using the thermal plasticity of coal [20], and cold briquetting using cement as a binder [21,22], cold briquetting using coking tar as a binder [23]. The authors of the current study previously proposed to prepare CCB using cold briquetting followed by heat treatment [24,25]. By this method, various noncoking coals and iron-rich metallurgical dust could be used as raw materials, which could significantly reduce the CCB cost. The behavior of a single CCB prepared using this method under simulated BF conditions and in actual BF have been elucidated and the results showed that the CCB reaction in BF includes five stages: reduction by BF gas, partial self-reduction with reduction by BF gas, full self-reduction partial self-reduction with gasification by BF gas and gasification by BF gas [25]. However, to improve BF efficiency, it is more important to understand the influence of charging CCB on BF performance.

The BF ironmaking is a complex process with high temperature, high pressure, and hazardous environment, so conditions of lab-scale experiments could not fully simulate the actual BF in-furnace state and thus results may be unreliable. Nowadays, novel processes involved in BF ironmaking are usually investigated by numerical simulations. Using numerical simulations, investigators can gain very detailed information to examine the feasibility, understand the mechanisms, and optimize operation conditions towards the envisaged BF processes [26,27,28,29]. Simulations on BF operations with CCB charging have been conducted by Chu et al. [30] and Yu et al. [31]. However, in their studies, the reaction model of CCB was significantly simplified and could not reflect the real behavior in BF, which may lead to some misunderstanding in interpreting the influence of CCB charging on BF performance.

In this research, the reaction behavior of CCB under BF conditions was experimentally studied and modeled. Thereafter, BF operation with replacing 10% ore by CCB was investigated by numerical simulations.

2. Experimental

2.1. CCB Sample

The CCB sample used in the present research was the same as that in reference [25]. It was prepared by cold briquetting followed by heat treatment. The raw materials for preparing the CCB sample were hematite fines, quartz fines, and coal fines. The quartz fines were employed as an additive. The hematite fines and the quartz fines were the chemical reagents. The coal fines were provided by the BF PCI (pulverized coal injection) sector. The hematite fines, quartz fines, and coal fines were thoroughly mixed under a mass ratio of hematite:quartz:coal = 67:3:30. After the addition of 10.0% distilled water, 2.0% organic binder, the briquettes were made by pressing these moistened fines using a die under a pressure of 15 MPa. The briquettes were dried in the air followed by drying at 423 K and were then hardened by heat treatment. The heat treatment was carried out under an N₂ atmosphere. The thermal route was the following. The furnace was heated from room temperature to 1073 K at a rate of 5 K/min. After holding for 10 min, the furnace was cooled naturally. The prepared CCB is cylindrical with diameter and height of 14 mm. Its mass is 4.7 g. Its mineralogical composition is listed in

Table 1. Mineralogical composition of CCB: (wt %).

Carbon	Fe3O4	FeO	Metallic Iron	Gangue
20.30	29.70	39.70	1.57	8.73

.

2.2. Non-Isothermal Reaction Tests

The experimental setup is detailed elsewhere [25]. The following is an outline. The setup mainly consists of a gas supply system, and a temperature-controlled furnace with an accuracy of ±2 K, and a computer for data acquisition. The furnace was heated using super-canthal (MoSi₂) elements, producing a 50-mm hot zone in the reaction tube (Diameter: 55 mm). The sample holder was made of a heat-resistant alloy (Fe-Cr-Al) wire. In each test, the furnace was heated up to 1073 K and stabilized for 30 min under N₂ atmosphere. A single CCB was loaded at a time. After being preheated for 5 min in the upper part of the tube, the sample was lowered into the constant- temperature zone. The furnace was then heated up under a predetermined heating rate and the gas flow was switched from N₂ to a CO-CO₂-N₂ mixture (CO:CO₂:N₂ = 4:1:5 (volume)). The mass loss of CCB was recorded via a computer. In the test, the total gas flow rate was maintained at 3000 cm³·min⁻¹ (standard temperature and pressure). The test was completed after the temperature reached 1373 K. Pre-experimental results showed that, after heat hardening, volatiles and organic binder could be completely removed from the CCB, so its mass loss fraction at time t (f_m) was calculated by Equation (1).

$$f_{\mathrm{m}}=(m-m_{\mathrm{b}})/(m_{\mathrm{C},0}+m_{\mathrm{O},0})$$

(1)

where, m is the mass of CCB at time t, (g); m_b is the initial mass of CCB, (g); m_C,0 and m_O,0 are the initial mass of carbon and iron-oxide oxygen in CCB, (g), and they are determined according to Table 1 and the initial mass of CCB.

3. Model Development

3.1. Description of BF Operation with CCB Charging

Size of the BF for numerical simulations is given by Tang et al. [32], and its normal operation data is given in

Table 2. BF operation data.

Variable	Value
Productivity (tHM·day−1)	6250
Blast temperature (K)	1523
Blast rate (Nm3·min−1)	4800
Oxygen enrichment (mol%)	4.0
Top absolute pressure (Pa)	2.8 × 105
PC injection rate (kg·tHM−1)	180
Ore rate (kg·tHM−1)	1680
Coke rate (kg·tHM−1)	335
Batch weight of ore (ton)	76
Batch weight of coke (ton)	15
Solid inlet temperature (K)	300
Ore particle property	Composition: TFe: 55.8 wt.%, FeO: 6.8 wt.%, CaO: 4.60, SiO2: 4.97 wt.%, Al2O3: 2.19 wt.%, TiO2: 2.0 wt.% Porosity: 0.35; Bulk density: 1750 kg/m3; Average particle size: 20 mm.
Coke particle property	Composition: Fixed Carbon: 90 wt.%, and Ash: 10 wt.%; Porosity: 0.50; Bulk density: 500 kg/m3; Average particle size: 40 mm.
PC property	Composition: C: 80.0 wt.%, H: 4.0 wt.%, O: 3.5 wt.%, N: 2.0 wt.%, and S: 0.32 wt.%; H2O: 4.0 wt.%, and Ash: 7.0 wt.%.
Liquid phase (molten iron and slag) property	[%C]: 4.0 wt.%, Temperature: 1753 K, Average heat capacity: 1000 J/kg, and Slag rate: approximately 400 kg/tHM

tHM: ton hot metal, PC: pulverized coal.

. In the present investigation, two cases (case A and case B) were simulated and compared. Case A was the BF operation under normal conditions and considered as the base case. Case B was with CCB charging. In case B, 10% (mass) ore was replaced with CCB. In CCB charging of case B, the CCB is assumed to be fully mixed with the ore (sinter, pellet, and lump ore).

3.2. BF Model

The present model is based on a total BF model developed by current authors [32]. The validity of the total BF model was confirmed by the comparison of the simulation results with the averaged industrial data. In the present model, the reaction kinetics of CCB is modeled and is incorporated into the total BF model. The model is two-dimensional, axisymmetric, and steady. In the model, the gas-phase behavior and solid-phase behavior in BF are represented by the conservation of mass, momentum, energy, and species. The computation grid is shown in Figure 1. It is a two-dimensional structure grid, including 780 cells. The computational zone is based on 12 degrees in the circumferential direction. The positions of cohesive zone (CZ), deadman, raceway (RW) are predefined. The porosity of CZ, dripping zone (DZ), and deadman are fixed at 0.15, 0.30, and 0.15, respectively. The Equations involved in the model are listed in

Table 3. Equations involved in BF model.

	Reaction	Reaction Rate (kmol·m−3s−1)	Explanation
1	3Fe2O3 (ore, s) + CO(g) = 2Fe3O4(ore, s) + CO2(g)	R1	stepwise reduction of ore (sinter, pellet and lump ore) by CO
2	Fe3O4 (ore, s) + CO(g)=3 FeO(ore, s) + CO2(g)	R2
3	FeO (ore, s) + CO(g) = Fe(ore, s) + CO2(g)	R3
4	C (coke) + CO2 (g) = 2CO (g)	R4	coke solution-loss reaction
5	C (coke) + 1/2O2 (g) = CO (g)	R5	coke combustion
6	3Fe2O3 (CCB, s) + CO (g) = 2Fe3O4 (CCB, s) + CO2 (g)	R6	CCB reactions
7	Fe3O4(CCB, s) + CO(g) = 3FeO(CCB, s) + CO2(g)	R7
8	FeO (CCB, s) + CO (g) = Fe (CCB, s) + CO2 (g)	R8
9	C (CCB) + CO2 (g) = 2CO (g)	R9
10	Fe (ore,s) = Fe (l)	R10	melting reactions of ore
11	FeO (ore,s) = FeO (l)	R11
12	Gangue (ore,s) = Slag (l)	R12
13	Fe (CCB,s) = Fe (l)	R13	melting reactions of CCB
14	FeO (CCB,s) = FeO (l)	R14
15	Gangue (CCB,s) = Slag (l)	R15
16	FeO (l) + C (s) = Fe (l) + CO (g)	R16	direct reduction of molten FeO

. Equations (1)–(3) in Table 3 are CO gaseous reduction of ore, Equations (4) and (5) in Table 3 are coke solution-loss reaction and combustion. Equations (6)–(9) are CCB Equations. Equations (10)–(12) in Table 3 are the melting of the ore. Equations (12)–(15) in Table 3 are the melting of CCB. the melting CCB is assumed to be similar to that of the ore. Rates of Equations (6)–(9) and (16) in Table 3 are given in the following sections, Reaction heats of all Equations and rates of Equations (1)–(5), (10)–(15) in Table 3 are given elsewhere [32].

Behaviors of other phases (molten iron, molten slag, and PC fines) are treated using simplified methods. The PC particles are gasified in the raceway zone reaching a burnout rate of more than 90% within 20 ms. Therefore, the combustion products of the blast and the PC through Equation (5) form the inlet condition for the gas phase in the model. The liquid phase includes the molten iron and the molten slag. Droplets of the molten iron and the molten slag are generated in the cohesive zone with an initial temperature equivalent to the local solid temperature. After generation, they flow down through the dripping zone, acquiring heated by the gas phase and the coke bed and reaching the final tapping temperature in the hearth. On their flowing path, these droplets undergo coalescing, splitting, or flying a short distance with the strong bosh gas, so it is difficult to give precise mathematical descriptions upon the gas-liquid and solid-liquid heat exchanges. In the BF bosh, heat is mainly generated by the combustion of oxygen with coke and PC in the raceway and the gas phase has the highest temperature. As the gas flows upward, the heat is transferred from the gas to the coke bed, and to the liquid droplets; simultaneously, the heat is also transferred from the coke bed to the liquid droplets. This analysis shows that the required heat for the liquid phase could be simplified as an energy source of the gas phase. The temperature of the hearth is considered to be 1753 K, therefore, the overall heat loss rate (Q_l) from the gas-solid system to the liquid phase is Equation (2), Assuming that the heat loss rate is uniformly distributed in the DZ, an enthalpy source Equation (3) is added to energy Equation of the gas phase in the DZ.

$$Q_{\mathrm{l}}={\displaystyle \sum _{\mathrm{i}}^{CZ}\left(M_{\mathrm{Fe}}\right(R_{10}}+R_{13})+M_{\mathrm{FeO}}(R_{11}+R_{14})+M_{\mathrm{Gangue}}(R_{12}+R_{15})\left)C{p}_{\mathrm{l}}{V}_{\mathrm{cell}}\right(1753-T_{\mathrm{S}})$$

(2)

$$E_{\mathrm{gl}}=Q_{\mathrm{l}}/{\displaystyle \sum _i^{\mathrm{DZ}}{V}_{\mathrm{cell}}}$$

(3)

Molten FeO in the slag droplets is reduced fast in the DZ through Equation (9). In the view of the mass balance of molten FeO in CZ and DZ, the rate of Equation (16) in Table 3 is described using Equation (4), in which, Equation (16) is assumed to uniformly proceed in the DZ.

$$R_{16}={\displaystyle \sum _{\mathrm{i}}^{CZ}\left(\right(R_7+R_{14})V_{\mathrm{cell}})/{\displaystyle \sum _{\mathrm{i}}^{\mathrm{D}Z}{V}_{\mathrm{cell}}}}$$

(4)

The above method of treating the behavior of the liquid phase was demonstrated to be helpful for the model to reach a high convergence of the model.

The gas flow is considered to be the flow through the porous bed. The gas phase consists of CO, CO₂, O_2, and N₂, and is considered to be an ideal gas. The general governing Equation of the gas phase is Equation (5), in which, the superficial gas velocity is adopted. Terms to represent ϕ, Γ_ϕ and S_ϕ in Equation (5) are listed in

Table 4. Dependent variables and sources in Equation (5).

Equation	$\mathit{\varphi }$	${\mathit{S}}_{\mathit{\varphi }}$
Mass	1	$M_{\mathrm{O}}{\displaystyle \sum _{i=1}^3{R}_i}+M_{\mathrm{O}}{\displaystyle \sum _{i=6}^8{R}_i}+M_{\mathrm{C}}(R_4+R_9)+M_{\mathrm{C}}{R}_5+M_{\mathrm{CO}}{R}_{16}$
Momentum	${\stackrel{\rightharpoonup }{U}}_{\mathrm{g}}$	$-\nabla P_g-{\stackrel{\rightharpoonup }{F}}_{\mathrm{gs}}$
Energy	$H_{\mathrm{g}}$	$0.5{\displaystyle \sum _{i=1}^9{R}_{\mathrm{i},}}(-\Delta H_i)-E_{\mathrm{gs}}-E_{\mathrm{gl}}+E_{\mathrm{add}}$
Species	$y_{{\mathrm{O}}_2}$	$M_{{\mathrm{O}}_2}\left(-0.5R_5\right)$
	$y_{\mathrm{CO}}$	$M_{\mathrm{CO}}\left(-R_1-R_2-R_3+2R_4+R_5-R_6-R_7-R_8+2R_9+R_{16}\right)$
	$y_{{\mathrm{CO}}_2}$	$M_{{\mathrm{CO}}_2}\left(R_1+R_2+R_3-R_4+R_6+R_7+R_8-R_9\right)$
	$y_{{\mathrm{N}}_2}$	0

.

$$\mathrm{div}({\rho }_{\mathrm{g}}{\stackrel{\rightharpoonup }{U}}_{\mathrm{g}}\varphi )=\mathrm{div}({\Gamma }_{\varphi }\mathrm{grad}\varphi )+S_{\varphi }$$

(5)

A non-slip wall condition for the gas velocity and an impermeable condition for the gas species are defined on the BF wall. The heat loss of gas phase on the BF wall is calculated by 5.0 (T_g-353) [33]. The PC particles are assumed to be gasified completely in the raceway. Therefore, the combustion products of the blast with the PC through Equation (5) in Table 3 form the inlet conditions for the gas phase. At the gas outlet, a fully-developed gas flow is assumed.

The solid flow is treated as a viscous flow. The CCB is treated as one component of the solid phase. As a consequence, the solid phase consists of coke, ore, and CCB. Each component has its physical properties. Above the CZ, the overall physical properties of the solid phase are calculated by averaging the physical properties of the components based on their volume fractions. Regarding the chemical species, even the same species in CCB and in ore/coke are treated separately because it undergoes different reaction schemes. The general governing Equation of the solid phase is Equation (6), in which, the solid bulk density and the solid physical velocity are adopted. Terms to represent φ, Γ_φ, and S_φ in Equation (6) are listed in

Table 5. Dependent variables and sources in Equation (6).

Equation	$\mathit{\phi }$	${\mathbf{\Gamma }}_{\mathit{\phi }}$	${\mathit{S}}_{\mathit{\phi }}$
Continuity	1	0	$\begin{array}{l}-(M_{\mathrm{O}}{\displaystyle \sum _{i=1}^3{R}_i}+M_{\mathrm{O}}{\displaystyle \sum _{i=6}^8{R}_i})-\left(M_{\mathrm{C}}{R}_9\right)-M_{\mathrm{Fe}}(R_{10}+R_{13})-M_{\mathrm{FeO}}(R_{11}+R_{14})\\ -M_{\mathrm{gangue}}(R_{12}+R_{15})\end{array}$
Momentum	$\stackrel{\rightharpoonup }{V_{\mathrm{s}}}$	${\mu }_{\mathrm{s},\mathrm{eff}}$	$-\nabla P_{\mathrm{s}}$
Energy	$H_{\mathrm{s}}$	${\lambda }_{\mathrm{s},\mathrm{eff}}/C{p}_{\mathrm{s}}$	$0.5{\displaystyle \sum _{i=1}^9(R_{\mathrm{i},}}(-\Delta H_i))+{\displaystyle \sum _{i=10}^{16}(R_{\mathrm{i},}}(-\Delta H_i\left)\right)+E_{\mathrm{gs}}$
Species	$y_{\mathrm{Coke},\mathrm{C}}$	0	0
	$y_{\mathrm{ore}}{}_{{,\mathrm{Fe}}_2{\mathrm{O}}_3}$	0	$M_{{\mathrm{Fe}}_2{\mathrm{O}}_3}\left(-3R_1\right)$
	$y_{{\mathrm{ore},\mathrm{Fe}}_3{\mathrm{O}}_4}$	0	$M_{{\mathrm{Fe}}_3{\mathrm{O}}_4}\left(2R_1-R_2\right)$
	$y_{\mathrm{ore},}{}_{\mathrm{FeO}}$	0	$M_{\mathrm{FeO}}\left(R_2-R_3-R_{11}\right)$
	$y_{\mathrm{ore},}{}_{\mathrm{Fe}}$	0	$M_{\mathrm{Fe}}\left(R_3-R_{10}\right)$
	$y_{\mathrm{CCB},\mathrm{C}}$	0	$M_{\mathrm{C}}\left(-R_9\right)$
	$y_{{\mathrm{CCB},\mathrm{Fe}}_2{\mathrm{O}}_3}$	0	$M_{{\mathrm{Fe}}_3{\mathrm{O}}_4}\left(-3R_6\right)$
	$y_{{\mathrm{CCB},\mathrm{Fe}}_3{\mathrm{O}}_4}$	0	$M_{{\mathrm{Fe}}_2{\mathrm{O}}_3}\left(2R_6-R_7\right)$
	$y_{\mathrm{CCB},\mathrm{FeO}}$	0	$M_{\mathrm{FeO}}(R_7-R_8-R_{14})$
	$y_{\mathrm{CCB},\mathrm{Fe}}$	0	$M_{\mathrm{Fe}}(R_8-R_{13})$
	$y_{\mathrm{CCB},\mathrm{gangue}}$	0	$M_{\mathrm{gangue}}(-R_{15})$

. In actual BF, the iron-bearing burden is transformed to molten iron and slag, and the coke is completely consumed by combustion, carbon-solution loss reaction, carburization, and other equations. However, the present BF model is developed based on the gas-solid two-phase flow. Therefore, the present BF model needs a solid outlet. For ensuring a stable solid flow, the consumption of coke is not included in Table 5.

$$\mathrm{div}({\rho }_{\mathrm{s}}{\stackrel{\rightharpoonup }{V}}_{\mathrm{S}}\phi )=\mathrm{div}({\Gamma }_{\phi }\mathrm{grad}\phi )+S_{\phi }$$

(6)

A fluid-slip boundary is applied for the solid velocity on the BF wall. Heat loss of the solid phase on the BF wall is not considered. Inlet conditions of the solid phase are established according to BF operation conditions. At the solid outlet, the solid phase reaches a fully-developed flow. As, in actual BF operation, coke is completely consumed in BF, the enthalpy loss owing to the solid flow at the solid outlet is compensated by adding a source (E_add) on the gas enthalpy Equation in RW, which is expressed by Equation (7).

$$E_{\mathrm{add}}=\left(m_{\mathrm{C},\mathrm{coke}}{T}_{\mathrm{s},\mathrm{out}}C{p}_{\mathrm{s}}\right)/{\displaystyle \sum _{\mathrm{i}}^{\mathrm{RW}}{V}_{\mathrm{cell}}}$$

(7)

3.3. CCB Model

The CCB model developed by Tang et al. [34] was used in this research. The following is a brief introduction of the CCB model. The shape of CCB is nearly spherical, so the model is one-dimensional in a radial direction. The model is developed based on mass conservation of gas species, mass conservation of solid species, and mass transfer between CCB and environment. The gas species include CO, CO₂, and N₂, and the solid species are the components in the CCB. The Equations in the CCB model are listed in

Table 6. Equations in CCB model.

No	Reaction	Reaction Rate/(mol·m−3·s−1)
1	3Fe2O3(fine, s) + CO(g) = 2Fe3O4(fine, s) + CO2(g)	$r_i=\frac{(P_{\mathrm{CO}}-P_{{\mathrm{CO}}_2}/K_{\mathrm{i}})/\left(8.314T\right)}{(K_i/(k_i(1+K_i))}{(1-f_i)}^{2/3})a_{\mathrm{gs}}$, (i = 1,2,3), $k_1=\exp (-1.445-6038/T)$, $K_1=\exp (7.255+3720/T)$ $k_2=1.70\exp (2.515-4811/T)$, $K_2=\exp (5.289-4711/T)$ $k_3=\exp (0.805-7385/T)$, $K_3=\exp (-2.946+2744.63/T)$
2	Fe3O4(fine, s) + CO(g) = 3FeO(fine, s) + CO2(g)
3	FeO(fine, s) + CO(g) = Fe(fine, s) + CO2(g)
4	C(fine,s) + CO2(g) = 2CO(g)	$\begin{array}{l}{r}_4={\rho }_{\mathrm{C},0}{k}_4{\left(1-f_4\right)}^{2/3}(P_{{\mathrm{CO}}_2}/1.01\times {10}^5)/M_{\mathrm{C}},\\ k_4=1400\exp (-138000/RT)\end{array}$

. Equations (1)–(3) in Table 6 are the gaseous reductions of iron particles, and Equation (4) in Table 6 is the carbon solution-loss reaction of carbon particles.

The mass conservation of the gas species in the CCB gives Equations (8) and (9).

$$\frac{\partial \left(\alpha P_{{\mathrm{co}}_2}\right)}{\partial t}=\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2{D}_{{\mathrm{CO}}_2{-\mathrm{N}}_2,\mathrm{eff}}\frac{\partial P_{{\mathrm{co}}_2}}{\partial r}\right)+RT(R_1+R_2+R_3-R_4)$$

(8)

$$\frac{\partial \left(\alpha P_{\mathrm{co}}\right)}{\partial t}=\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2{D}_{{\mathrm{CO}-\mathrm{N}}_2,\mathrm{eff}}\frac{\partial P_{\mathrm{co}}}{\partial r}\right)+RT(2R_4-R_1-R_2-R_3)$$

(9)

where, $\alpha =0.5$, $D_{{\mathrm{eff},\mathrm{CO}-\mathrm{N}}_2}=D_{{\mathrm{CO}-\mathrm{N}}_2}{\alpha }^2/\sqrt{3}$, and $D_{{\mathrm{eff},\mathrm{CO}}_2{-\mathrm{N}}_2}=D_{{\mathrm{CO}}_2{-\mathrm{N}}_2}{\alpha }^2/\sqrt{3}$.

For Equations (8) and (9), the boundary conditions are Equations (10)–(12).

$$r=0:\frac{\partial P_{\mathrm{CO}}}{\partial r}=0,\frac{\partial P_{\mathrm{CO}2}}{\partial r}=0$$

(10)

$$r=d/2:D_{\mathrm{eff},{\mathrm{CO}-\mathrm{N}}_2}\frac{\partial P_{\mathrm{CO}}}{\partial r}=\left(D_{{\mathrm{CO}-\mathrm{N}}_2}\right(2.0+0.6{\mathrm{Re}}^{1/2}{\mathrm{Sc}}_{{\mathrm{CO}-\mathrm{N}}_2}^{1/3})/d)(P_{\mathrm{CO}}-P_{\mathrm{CO},\mathrm{e}})$$

(11)

$$r=d/2: D_{{\mathrm{eff}, \mathrm{CO}}_2{-\mathrm{N}}_2}\frac{\partial P_{{\mathrm{CO}}_2}}{\partial r}=\left(D_{{\mathrm{CO}}_2{-\mathrm{N}}_2}\right(2.0+0.6{\mathrm{Re}}^{1/2}{\mathrm{Sc}}_{{\mathrm{CO}}_2{-\mathrm{N}}_2}^{1/3})/d)(P_{{\mathrm{CO}}_2}-P_{{\mathrm{CO}}_2,\mathrm{e}})$$

(12)

where, $\mathrm{Re}=u_{\mathrm{g},\mathrm{e}}{\rho }_{\mathrm{g},\mathrm{e}}d/{\mu }_{\mathrm{g},\mathrm{e}}$, ${\mathrm{Sc}}_{{\mathrm{CO}-\mathrm{N}}_2}={\mu }_{\mathrm{g},\mathrm{e}}/\left({\rho }_{\mathrm{g},\mathrm{e}}{D}_{{\mathrm{CO}-\mathrm{N}}_2}\right)$, and ${\mathrm{Sc}}_{{\mathrm{CO}}_2{-\mathrm{N}}_2}={\mu }_{\mathrm{g},\mathrm{e}}/\left({\rho }_{\mathrm{g},\mathrm{e}}{D}_{{\mathrm{CO}}_2{-\mathrm{N}}_2}\right)$.

For Equations (8)–(9), the initial conditions are provided by Equation (13).

$$t=0, r\in (0,d/2):P_{\mathrm{CO}}=P_{\mathrm{CO},\mathrm{e}} , P_{{\mathrm{CO}}_2}=P_{{\mathrm{CO}}_2,\mathrm{e}}$$

(13)

The mass conservation of the solid species in the CCB gives Equation (14).

$$\partial {\rho }_j/\partial t=S_j$$

(14)

where j = Fe₂O₃, Fe₃O₄, FeO, Fe, and C; $S_{{\mathrm{Fe}}_2{\mathrm{O}}_3}=0.003M_{{\mathrm{Fe}}_2{\mathrm{O}}_3}(-r_1)$, $S_{{\mathrm{Fe}}_3{\mathrm{O}}_4}=0.001M_{{\mathrm{Fe}}_3{\mathrm{O}}_4}(2r_1-r_2)$, $S_{\mathrm{FeO}}=0.001M_{\mathrm{FeO}}(3r_2-r_3)$, $S_{\mathrm{Fe}}=0.001M_{\mathrm{Fe}}{R}_3$, and $S_{\mathrm{C}}=-0.001M_{\mathrm{C}}{r}_4$.

The initial condition for Equation (14) is provided by Equation (15).

$$t=0,r\in (0,d/2):{\rho }_{\mathrm{j}}={\rho }_{\mathrm{j},0}$$

(15)

3.4. Solution Strategy

The simulations were performed using the following strategy. Firstly, the rates of the CCB Equations (6)–(9) in Table 3 were initialized. The BF model Equations (5) and (6) were solved numerically solved using PHOENICS [35] and an in-house developed code. After the BF model reached a primary convergence, the Lagrangian method was used to adjust these reaction rates in all cells. These adjustments continued until the BF model reached the final convergence.

The Lagrangian method to adjust the rates of Equations (6)–(9) in Table 3 is illustrated in Figure 2 and detailed elsewhere [34]. For a given cell, the solid-phase streamline through the cell is determined after the BF model reaches a primary convergence Figure 2a. The CCB reaction behavior along the streamline is calculated using the above CCB model. The descending time of the CCB to reach the cell center is calculated by ${\displaystyle {\int }_0^s(1/\left|\overrightarrow{V_{\mathrm{s}}}\right|})ds$, where, s is the distance from the cell center to the burden surface, (m). The boundary conditions of the CCB model are determined by the corresponding BF variables along the streamline. Thus, the radial distributions of r₁, r₂, r₃, and r₄ of Equations (1)–(4) Table 6 in CCB reaching the cell center are obtained. It is considered that the CCB reaching the cell center is representative of all briquettes in the cell Figure 2b. Therefore, the rates of Equations (6)–(9) in Table 3 in the cell are Equation (16).

$$R_j=0.001{\alpha }_{\mathrm{CCB}}{N}_{\mathrm{CCB}}4\pi {\displaystyle {\int }_0^{d/2}{r}_i{r}^2}dr$$

(16)

where, i = 1, 2, 3, and 4 of the Equations in Table 5 for j = 6, 7, 8, and 9 of the Equations in Table 3, respectively; ${\alpha }_{\mathrm{CCB}}$ is the volume fraction of CCB in the solid burden, (-); and $N_{\mathrm{CCB}}$ is the number density of CCB, (1/m³).

In addition to the examination of the convergence of gas and solid flow fields, the mass balance of the removable element O and of the element Fe are examined and the convergence criteria are Equations (17) and (18).

$$\left|m_{\mathrm{O}}-{\displaystyle \sum M_{\mathrm{O}}(R_1+R_2+R_3+R_6+R_7+R_8)V_{\mathrm{cell}}}\right|/m_{\mathrm{O}}<0.01$$

(17)

$$\left|m_{\mathrm{Fe}}-{\displaystyle \sum M_{\mathrm{Fe}}(R_{10}+R_{11}+R_{13}+R_{14}+R_{16})V_{\mathrm{Cell}}}\right|/m_{\mathrm{Fe}}<0.01$$

(18)

where, m_O is the mass supply rate of the element O in the solid phase at the solid inlet, and m_Fe is the mass supply rate of element Fe in the solid phase at the solid inlet.

Detailed gas and solid inlet conditions of cases A and B are shown in

Table 7. Gas and solid inlet conditions of cases A and B (1/30 BF volume).

Condition	Variable	Case A	Case B
Solid inlet conditions	Ore supply rate (kg/s)	4.05	3.64
	CCB supply rate (kg/s)	0	0.41
	Coke supply rate (kg/s)	0.81	-
	Solid temperature (K)	300
Gas inlet conditions	Gas supply rate (kg/s)	3.88
	Gas composition (mass fraction, -)	CO: 20, O2:13, N2:67
	Gas temperature (K)	2350

. The results of case A are kept as reference values for case B. In case B, the coke supply rate is determined by trial and error, and the convergence criteria for the mass balance of element C in the coke is Equation (19).

$$\left|m_{\mathrm{C},\mathrm{coke}}-{\displaystyle \sum M_{\mathrm{C}}(R_4+R_5+R_9+R_{16})V_{\mathrm{cell}}-m_{\mathrm{Fe}}[\%\mathrm{C}]/(1.0-[\%\mathrm{C}])-m_{\mathrm{C},\mathrm{other}}}\right|/m_{\mathrm{C},\mathrm{coke}}<0.01$$

(19)

where, $m_{\mathrm{C},\mathrm{coke}}$ and $m_{\mathrm{Fe}}$ are the mass supply rates of element C in the coke, and element Fe in the solid burden, respectively; [%C] is the carbon content in molten iron; and $m_{\mathrm{C},\mathrm{other}}$ is the rate of carbon consumed by other Equations (e.g., silica and manganese oxide reductions), which is determined by case A.

4. Results and Discussion

4.1. Determination of Parameter in CCB Model

In this case, a_gs in the reaction rates of Equations (1)–(3) in Table 6 was difficult to determine owing to the sintering of iron-oxide particles [25]. Different from CCB reduction in some direct reduction processes (e.g., rotary hearth furnace), CCB in BF undergoes slow heating. During the heating, its self-reduction and Equations with BF gas proceed. Under the BF environment, changes in CCB volume and porosity become obvious with the increase of temperature [34,36]. Therefore, compared to the isothermal tests, the nonisothermal tests under simulated BF environment are more suitable to determine the CCB model parameters. The value of a_gs was determined by trial and error. The experimental data points for fitting are shown in Figure 3a. They were selected at time intervals of 300 s on the curve of 2 K·min⁻¹, 120 s on the curve of 5 K·min⁻¹, and 60 s on the curve of 10 K·min⁻¹. Five values of a_gs (1000 m²·m⁻³, 1300 m²·m⁻³, 1600 m²·m⁻³, 1900 m²·m⁻³, and 2200 m²·m⁻³) were examined. the fitness of each value was evaluated by MSE, which is expressed by Equation (20).

$$MSE=\left({\displaystyle \sum _i^{N_P}{(v_{\mathrm{sim}}-v_{\exp })}^2}\right)/N_{\mathrm{P}}$$

(20)

where, v_sim is model-predicted value, v_exp is experimental value, and N_P is the total number of data points in Figure 3a.

The fitting results showed that, under a_gs = 1000 m²·m⁻³, MSE = 0.064; under a_gs = 1300 m²·m⁻³, MSE = 0.058; under a_gs = 1600 m²·m⁻³, MSE = 0.055; under a_gs = 1900 m²·m⁻³, MSE = 0.054, and under a_gs = 2200 m²·m⁻³, MSE = 0.055. Thus, it was considered that a_gs = 1900 m²·m⁻³ was optimal. Measured mass-loss curves and optimal model-predicted ones are plotted in Figure 3b. It could be seen in Figure 3b that the model predictions agree well with the experimental measurements.

4.2. CCB Behavior in BF

The simulation results of CCB behavior in case B are shown in Figure 4. Figure 4a shows that the CCB iron oxide starts reduction at approximately 673 K, and it reaches a full reduction at approximately 1123 K, reflecting that the CCB reducibility is high. Figure 4b shows that the CCB carbon starts gasification at approximately 923 K. Above the CZ, its overall conversion is 85%, indicating that 15% of the CCB carbon would enter the BF lower part. In the present investigation, the influence of the ungasified CCB carbon in the BF lower part was not considered as its behavior has not been distinctly disclosed so far [37].

Figure 5 shows the behavior of a single CCB along a solid flowing path in the BF. The path is near the BF mid-radius Figure 5a. From Figure 5b, it can be seen that, in the temperature range from 923 K to 1123 K, self-reduction occurs in the CCB. However, the CO potential ($P_{\mathrm{CO}}/(P_{\mathrm{CO}}+P_{{\mathrm{CO}}_2})$) in CCB becomes higher than that in BF gas after the temperature reaches 1083 K.

4.3. Influence on BF in-Furnace State

The influence of CCB charging on the BF thermal state is shown in Figure 6 and Figure 7. In Figure 6, compared to case A, lines 873 K and 1073 K move downward in case B. These tendencies are also displayed in Figure 7. In CCB charging operation, the CCB self-reduction is a strongly endothermic reaction and needs more heat than the ore gaseous reduction or the coke gasification. The CCB self-reduction occurs in the temperature range from 923 K to 1123 K Figure 5a, so the gas-solid heat transfer is enhanced there, and the gas-solid heat transfer is weakened above, resulting in a considerable change of thermal state in the BF upper part. After 1273 K, the CCB Equations are finished, so the influence on the BF thermal state becomes negligible. It is observed that, in Figure 6, locations of line 1273 K in both cases are nearly the same, and the heights of CZ in both cases don’t show a significant difference. Furthermore, in Figure 7, gas temperature profiles in both cases exhibit similar patterns in the BF lower part.

The influence of charging CCB on gas and solid reaction behaviors is shown in Figure 8, Figure 9, Figure 10 and Figure 11. By charging CCB, the ore reduction is retarded in the BF upper part (e.g., in Figure 8, in comparison to case A, the distance between lines 0.1 and 0.2 in case B increases). This is mainly attributed to the delay of solid temperature increase. However, after the solid temperature reaches 1073 K, the ore reduction is prompted (e.g., in Figure 8, comparing cases A and B, lines of 0.2 and 0.9 are closer in case B, and, in the mid radius zone, the distance between line 0.9 and CZ decreases in case B). This is attributed to the increase of CO potential in BF gas by CCB (Figure 5a). As a result, charging CCB has a positive effect on the overall ore reduction above CZ. Before the temperature reaches 1073 K, the CCB reduces the CO potential in BF gas (Figure 5b), leading to a decrease of CO volume fraction. After the temperature reaches 1073 K, the ore reduction is intensified by CCB, thus, CO volume fraction above CZ tends to decrease by charging CCB (e.g., in Figure 9, compared to case A, lines of 0.25 and 0.40 move downward in case B), and CO₂ volume fraction above CZ tends to increase (Figure 10). Accordingly, local gas utilization ($P_{{\mathrm{CO}}_2}/(P_{\mathrm{CO}}+P_{{\mathrm{CO}}_2})$) increases above CZ (e.g., in Figure 11, compared to case A, lines of 0.4 and 0.5 in case B move downward).

4.4. Coke-Saving Analysis

Table 8. Simulation results of some BF indices.

Index	Case A	Case B
Productivity (tHM·day−1)	6250	6233
Top gas temperature (K)	463	455
Top gas utilization (%)	51.3	52.6
Fuel rate (kg·tHM−1)	PC: 180 Coke:335, CCB carbon: 0	PC: 180.5, Coke:282.8, CCB carbon gasified above CZ: 30 above CZ:30.0 PC:180.5, and CCB carbon gasified above CZ:30.0

lists some operation indices for cases A and B. By replacing 10% ore with CCB, the BF top gas temperature is decreased by 8 K, the BF top gas utilization is increased by 1.3%, BF productivity is decreased by 17 tHM/day, and the coke rate is decreased by 52.2 kg/tHM (this decrease is only with the consideration of gasification of CCB carbon above CZ).

The BF ironmaking process includes sintering, coking, and ironmaking. Replacing 10% ore with CCB, the CCB rate is 179 kg/tHM and the ore rate is decreased to 1579 kg/tHM, Therefore, in the CCB charging operation, 101 kg sinter and 52.2 kg could be saved to produce one-ton hot metal. Considering the energy consumption of sintering and coking, the CCB charging operation could have a significant energy-saving and CO₂-emission-reducing effect for BF ironmaking.

Distributions of coke consumption in cases A and B are listed in

Table 9. Distributions of coke consumption in cases A and B (kg/tHM).

Item	Case A	Case B
Combustion	175.0	175.5
Carbon solution loss in upper BF	56.8	42.5
Direct reduction of molten FeO in lower BF	49.2	10.8
Carburization of molten iron	45.0	45.0
Other reactions	9.0	9.0
Total	335.0	282.8

. From Table 9, it is known that in the total coke-rate reduction by charging CCB, 14.3 kg/tHM is from the carbon solution loss reaction of coke, 38.4 kg/tHM from the direct reduction of molten FeO. These findings indicate that charging CCB can suppress the coke solution-loss reaction and significantly reduce the coke consumption in the direct reduction of molten FeO.

5. Conclusions

In this study, the CCB for BF application was prepared using cold briquetting followed by heat treatment. The CCB contained 29.70 wt.% Fe₃O₄, 39.70 wt.% FeO, 1.57 wt.% Fe, 8.73 wt.% gangue, and 20.30 wt.% carbon. its reduction kinetics in BF conditions were examined by nonisothermal tests and modeled. The BF operation with replacing 10% ore with CCB was investigated by numerical simulations. Some conclusions were obtained.

• The CCB reaction behavior in BF could be modeled using the previously proposed model by the current authors. Under a_gs = 1900 m²·m⁻³, the agreement between experimental measurements and model predictions was satisfying.
• In the CCB charging operation, the CCB reached a full iron-oxide reduction and a carbon conversion of 85% above CZ.
• By charging CCB, the thermal state in the BF upper part was significantly changed; however, the BF thermal state in the BF lower part was inconsiderably influenced.
• By charging CCB, the ore reduction was retarded before the temperature reached 1073 K and was prompted after; and the local gas utilization tended to increase above the CZ.
• By the CCB reduction above the CZ, the BF top gas temperature was decreased by 8 K, the BF top gas utilization was increased by 1.3%, the BF productivity was decreased by 17 tHM/day, 101 kg sinter and 52.8 kg could be saved to produce one-ton hot metal. Considering the energy consumption of sintering and coking, charging the CCB could have a significant energy-saving and CO₂-emission-reducing effect for BF iron making.