Computational Analysis of The Performance of Shaft Furnaces with Partial Replacement of The Burden with Self-Reducing Pellets Containing Biomass

Elisa Pinto da Rocha ^**e-mail elisa.procha@gmail.com

Universidade Federal do Rio de Janeiro, Av. Aluizio da Silva Gomes, 50, CEP 27930-560, Novo Cavaleiros, Macaé, Rio de Janeiro, RJ, Brasil

José Adilson de Castro

Universidade Federal Fluminense, Av. dos Trabalhadores 420, CEP 27255-125, Vila Sta. Cecília, Volta Redonda, RJ, Brasil

Leonardo Silva

Universidade Federal Fluminense, Av. dos Trabalhadores 420, CEP 27255-125, Vila Sta. Cecília, Volta Redonda, RJ, Brasil

Rayla de Souza Caldas

Universidade Federal Fluminense, Av. dos Trabalhadores 420, CEP 27255-125, Vila Sta. Cecília, Volta Redonda, RJ, Brasil

% Compounds	Fe₂O₃	FeO	SiO₂	Al₂O₃	CaO	MgO	ZnO	P	S	MnO	PbO	C_fix	Vol.	Ash.
SRP	53.5	0.41	1.12	0.29	8.07	1.32	3.43	0.02	0.32	0.71	0.05	11.24	6.52	2.2
DRI^* * Composition of DRI was obtained from author 10,11,19.	96.71	0.39	1.5	0.42	0.84	0.11	0	0	0	0	0	0	0	0
Charcoal	0	0	0	0	0	0	0	0	0.2	0	0	56.2	32.6	11
Ashes	0.24	0	9.21	0.51	0.47	0.47	0	0.19	0	0	0	0	0	0

Granular classes; momentum conservation

(2)

\frac{\partial (ρ_{i} ɛ_{i} u_{i, k} u_{i, j})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (μ_{s} \frac{\partial u_{i, j}}{\partial x_{k}}) + F_{j}^{i - l} + F_{i}^{l}

Mass conservation of solid fractions

(3)

\frac{\partial (ρ_{i} ɛ_{i} u_{i, k})}{\partial x_{k}} = \sum_{m = 1}^{Nreacts} M_{n} r_{m}

Enthalpy balance of solid fractions

(4)

\frac{\partial (ρ_{i} ɛ_{i} u_{i, k} H_{i})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (\frac{k_{i}}{C_{p, i}} \frac{\partial H_{i}}{\partial x_{k}}) + E_{}^{i - l} + \sum_{m = 1}^{Nreacts} Δ H_{m} r_{m}

Chemical species of solid phases

(5)

\frac{\partial (ρ_{i} ɛ_{i} u_{i, k} \emptyset_{i})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (D_{n}^{eff} \frac{{\partial \emptyset}_{n}}{\partial x_{k}}) - \sum_{m = 1}^{Nreacts} M_{n} r_{m}

Gas momentum transfer

(6)

\frac{\partial (ρ_{g} ɛ {gu}_{g, k} u_{g, j})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (μ_{s} \frac{\partial u_{g, j}}{\partial x_{k}}) - \frac{\partial P}{\partial x_{j}} F_{j}^{i - j}

Mass conservation of the gas phase

(7)

\frac{\partial (ρ_{g} ɛ_{g} u_{g, k})}{\partial x_{k}} = \sum_{m = 1}^{Nreacts} M_{n} r_{m}

Enthalpy conservation in the gas phase

(8)

\frac{\partial (ρ_{g} ɛ_{g} u_{g, k} H_{g})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (\frac{k_{g}}{C_{pg}} \frac{\partial H_{g}}{\partial x_{k}}) - E_{}^{g - p} - \sum_{m = 1}^{Nreacts} Δ H_{m} r_{m}

Chemical species

(9)

\frac{\partial (ρ_{g} ɛ_{g} u_{g, k} \emptyset_{n})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (D_{n}^{eff} \frac{{\partial \emptyset}_{n}}{\partial x_{k}}) - \sum_{m = 1}^{Nreacts} M_{n} r_{m}

Semi empirical relations for the gas-solid momentum transfer

(10)

\begin{matrix} F_{j}^{g - i} = [1.75 ρ_{g} + \frac{150 μ_{g}}{| {\underset{U}{\to}}_{g} - {\underset{U}{\to}}_{i} |} (\frac{ɛ_{i}}{d_{i} ϕ_{i}})] \\ (\frac{ɛ_{i}}{{(1 - ɛ_{i})}^{3} d_{i} ϕ_{i}}) | {\underset{U}{\to}}_{g} - {\underset{U}{\to}}_{i} | (u_{g, j} - u_{i, j}) \end{matrix}

Effective energy transferred between the solid and gaseous phases

(11)

\begin{matrix} F_{j}^{g - i} = [1.75 ρ_{g} + \frac{150 μ_{g}}{|{\vec{U}}_{g} - {\vec{U}}_{i}|} (\frac{ε_{i}}{d_{i} ϕ_{i}})] \\ (\frac{ε_{i}}{{(1 - ε_{i})}^{3} d_{i} ϕ_{i}}) |{\vec{U}}_{g} - {\vec{U}}_{i}| (u_{gj} - u_{ij}) \end{matrix}

Phase	Chemical Species
Gas		CO, CO₂, O₂, H₂, H₂O, N₂
Solid	Iron Ore	Fe₂O₃, Fe₃O₄, FeO, Fe, CaO, Al₂O₃, MgO, SiO₂, H₂O, gang
	DRI Pellet	Fe₂O₃, Fe₃O₄, FeO, Fe, CaO, Al₂O₃, MgO, SiO₂, H₂O, gang
	SRP	C, Volatiles, Fe₂O₃, Fe₃O₄, FeO, Fe, CaO, Al₂O₃, MgO, SiO₂, H₂O, gang
	Coke	C, Volatiles, SiC, SiO₂, Al₂O₃, CaO, MgO, H₂O, gang
	CEG	C, Volatiles, SiC, SiO₂, Al₂O₃, CaO, MgO, H₂O, ganga
Slag		FeO, SiO₂, Al₂O₃, CaO, MgO, gang

	Cases
Parameters	Base	Case A	Case B	Case C	Case D	Case E	Case F
Self-reducing charge	100% DRI	5%	15%	20%
Decrease in height in the reduction zone	x	x	x	15%	30%	40%	40%
Composition in the cooled zone	x	x	50% CH₄ reduction	50% CH₄ reduction	x	x	x
Composition of bustle gas	x	x	2.5% O₂ addition	2.5% O₂ addition	ΔP recuperation	ΔP recuperation	No recuperation of ΔP

Parameters	Operational range
Height and volume of the reduction zone	5.0 – 7.5 m and 100 – 140 m³
Flow rate of the reducing gas	40 – 60 NL/min
Fraction of self-reducing charge	0 – 20%
Size of the pellets	4 – 18 mm

		Cases
Parameters		Base	Case D	Case E	Case F
Productivity (ton/m³/dia)		11.85	13.41	14.53	13.09
Metallization (%)		93.66%	95.34%	94.80%	94.76%
Average residence time (h)		5 h 57 min	3 h 46 min	3 h 09 min	3 h 29 min
Carbon Emission (kgC/tonDRI)		34.55	37.39	37.36	37.39
Composition of gas bustle (kg/tonDRI)	CH₄	19.92	21.92	22.11	22.02
	H₂	54.07	57.32	57.8	57.55
	N₂	7.23	7.97	8.03	7.99
	CO	466.03	513.09	517.33	515.17
	CO₂	32.78	36.1	36.39	36.24
	H2O	51.89	57.14	57.61	57.37
Composition of top gas (Nm³/tonDRI)	CH₄	9.6×10^-6	5.42×10^-4	1.04×10^-3	6.18×10^-4
	H₂	19.47	25.72	26.05	25.84
	N₂	0.51	0.49	0.49	0.49
	CO	24.34	27.37	27.36	27.39
	CO₂	10.21	10.02	10.00	10.00
	H₂O	43.79	33.29	32.96	33.16

\underset{Transient Term}{\underset{︸}{\frac{\partial (p_{i} ε_{i} ϕ_{k})}{\partial t}}} + \underset{Convective Term}{\underset{︸}{div (p_{i} ε_{i} {\vec{U}}_{i} ϕ_{k})}} = \underset{Difusive Term}{\underset{︸}{div (Γ_{φ k} grand (ϕ_{k}))}} + \underset{Source Term}{\underset{︸}{S_{ϕ k}}}

\frac{\partial (ρ_{i} ɛ_{i} u_{i, k} u_{i, j})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (μ_{s} \frac{\partial u_{i, j}}{\partial x_{k}}) + F_{j}^{i - l} + F_{i}^{l}

\frac{\partial (ρ_{i} ɛ_{i} u_{i, k} H_{i})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (\frac{k_{i}}{C_{p, i}} \frac{\partial H_{i}}{\partial x_{k}}) + E_{}^{i - l} + \sum_{m = 1}^{Nreacts} Δ H_{m} r_{m}

\frac{\partial (ρ_{i} ɛ_{i} u_{i, k} \emptyset_{i})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (D_{n}^{eff} \frac{{\partial \emptyset}_{n}}{\partial x_{k}}) - \sum_{m = 1}^{Nreacts} M_{n} r_{m}

\frac{\partial (ρ_{g} ɛ {gu}_{g, k} u_{g, j})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (μ_{s} \frac{\partial u_{g, j}}{\partial x_{k}}) - \frac{\partial P}{\partial x_{j}} F_{j}^{i - j}

\frac{\partial (ρ_{g} ɛ_{g} u_{g, k} H_{g})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (\frac{k_{g}}{C_{pg}} \frac{\partial H_{g}}{\partial x_{k}}) - E_{}^{g - p} - \sum_{m = 1}^{Nreacts} Δ H_{m} r_{m}

\frac{\partial (ρ_{g} ɛ_{g} u_{g, k} \emptyset_{n})}{\partial x_{k}} = \frac{\partial}{\partial x_{k}} (D_{n}^{eff} \frac{{\partial \emptyset}_{n}}{\partial x_{k}}) - \sum_{m = 1}^{Nreacts} M_{n} r_{m}

\begin{matrix} F_{j}^{g - i} = [1.75 ρ_{g} + \frac{150 μ_{g}}{| {\underset{U}{\to}}_{g} - {\underset{U}{\to}}_{i} |} (\frac{ɛ_{i}}{d_{i} ϕ_{i}})] \\ (\frac{ɛ_{i}}{{(1 - ɛ_{i})}^{3} d_{i} ϕ_{i}}) | {\underset{U}{\to}}_{g} - {\underset{U}{\to}}_{i} | (u_{g, j} - u_{i, j}) \end{matrix}

\begin{matrix} F_{j}^{g - i} = [1.75 ρ_{g} + \frac{150 μ_{g}}{|{\vec{U}}_{g} - {\vec{U}}_{i}|} (\frac{ε_{i}}{d_{i} ϕ_{i}})] \\ (\frac{ε_{i}}{{(1 - ε_{i})}^{3} d_{i} ϕ_{i}}) |{\vec{U}}_{g} - {\vec{U}}_{i}| (u_{gj} - u_{ij}) \end{matrix}