Hydrogen Reduction Kinetics of Magnetite Concentrate Particles Relevant to a Novel Flash Ironmaking Process

Abstract

A novel ironmaking technology is under development at the University of Utah. The purpose of this research was to determine comprehensive kinetics of the flash reduction reaction of magnetite concentrate particles by hydrogen. Experiments were carried out in the temperature range of 1423 K to 1673 K (1150 °C to 1400 °C) with the other experimental variables being hydrogen partial pressure and particle size. The nucleation and growth kinetics expression was found to describe the reduction rate of fine concentrate particles and the reduction kinetics had a 1/2-order dependence on hydrogen partial pressure and an activation energy of 463 kJ/mol. Unexpectedly, large concentrate particles reacted faster at 1423 K and 1473 K (1150 °C and 1200 °C), but the effect of particle size was negligible when the reduction temperature was above 1573 K (1300 °C). A complete reaction rate expression incorporating all these factors was formulated.

Appendices

Appendix A: Determination of Residence Time

The value of residence time was calculated from the length of the hot zone, which started from the tip of the powder feeding tube, the linear velocity of the gas, and the terminal falling velocity for the cree** flow region expressed by the Stokes’ law assuming that particles fall at a constant velocity in the isothermal zone. As the gas flows downward after the flow straightener, a change in the flow mode from a plug flow to a fully developed laminar flow is expected in the very short length of the circular tube. From the normalized development length relationship suggested by Durst et al.[31] as indicated in Eq. [A1], it was found that the fully developed state of the flow is reached in less than 5 pct of the hot zone length.

$$ L/D = \left[ {\left( {0.619} \right)^{1.6} + \left( {0.0567\;{Re} } \right)^{1.6} } \right]^{{{1 \mathord{\left/ {\vphantom {1 {1.6}}} \right. \kern-0pt} {1.6}}}} $$

(A1)

where L is the length of the isothermal zone, D the diameter of tubular reactor, and Re is the Reynolds number.

Since the solid particles fall along the centerline, the residence time in this work was calculated by taking the maximum velocity, which is twice the average velocity (=volumetric flow rate divided by cross-sectional area), as the linear velocity of gas. The relevant equations are as follows:

$$ u_{\text{t}} = d_{\text{p}}^{2} g(\rho_{\text{p}} - \rho_{\text{g}} )/18\mu $$

(A2a)

$$ u_{\text{p}} = u_{\text{g}} + u_{\text{t}} $$

(A2b)

$$ t = L/u_{\text{p}} $$

(A2c)

where, all in consistent units, d _p is the particle size, g the gravitational acceleration, ρ _p the particle density, ρ _g the gas density, μ the viscosity of gas, u _p the particle velocity relative to tube wall, u _g the centerline gas velocity at furnace temperature, u _t the terminal velocity of a falling particle, and t is the residence time.

Appendix B: Complete Experimental Data (Excess Hydrogen = 200 pct)

Residence Time (s)	Temp. [K ( °C)]	Particle Size (μm)	Feeding Rate (mg/min)	Flowrate of H2 (NL/min)	Partial Pressure of H2 (atm)	Reduction Degree (pct)
4.93	1423 (1150)	20 to 25	599	1.933	0.85	54.6
7.39	1423 (1150)	20 to 25	298	0.962	0.85	72
9.27	1423 (1150)	20 to 25	176	0.568	0.85	92.8
12.17	1423 (1150)	20 to 25	60	0.200	0.85	98.4
3.34	1423 (1150)	32 to 38	595	1.920	0.85	62.7
4.07	1423 (1150)	32 to 38	358	1.156	0.85	77.8
4.92	1423 (1150)	32 to 38	169	0.545	0.85	88.1
5.58	1423 (1150)	32 to 38	60	0.200	0.85	96.7
2.23	1423 (1150)	45 to 53	556	1.796	0.85	65.7
2.51	1423 (1150)	45 to 53	330	1.064	0.85	73.1
2.97	1423 (1150)	45 to 53	60	0.194	0.85	88.9
1.64	1473 (1200)	20 to 25	599	1.890	0.2	16.4
3.13	1473 (1200)	20 to 25	298	0.940	0.2	21
6.91	1473 (1200)	20 to 25	117	0.369	0.2	42.8
10.93	1473 (1200)	20 to 25	62	0.196	0.2	81
2.39	1473 (1200)	20 to 25	599	1.890	0.3	24.3
4.46	1473 (1200)	20 to 25	298	0.940	0.3	38.1
6.88	1473 (1200)	20 to 25	176	0.555	0.3	68
9.32	1473 (1200)	20 to 25	117	0.369	0.3	85.4
13.90	1473 (1200)	20 to 25	62	0.196	0.3	96.4
1.53	1473 (1200)	32 to 38	595	1.877	0.2	10
2.80	1473 (1200)	32 to 38	291	0.918	0.2	17.9
4.17	1473 (1200)	32 to 38	169	0.533	0.2	27.3
5.36	1473 (1200)	32 to 38	115	0.363	0.2	45.5
7.34	1473 (1200)	32 to 38	62	0.196	0.2	72
2.17	1473 (1200)	32 to 38	595	1.877	0.3	34.4
3.77	1473 (1200)	32 to 38	291	0.918	0.3	42
5.37	1473 (1200)	32 to 38	169	0.533	0.3	60
8.53	1473 (1200)	32 to 38	62	0.196	0.3	88
1.45	1473 (1200)	45 to 53	556	1.755	0.2	14.6
2.14	1473 (1200)	45 to 53	330	1.040	0.2	17.7
3.34	1473 (1200)	45 to 53	155	0.490	0.2	26.2
4.82	1473 (1200)	45 to 53	60	0.189	0.2	56.9
1.96	1473 (1200)	45 to 53	556	1.755	0.3	26.2
2.75	1473 (1200)	45 to 53	330	1.040	0.3	38.3
3.86	1473 (1200)	45 to 53	167	0.527	0.3	48
5.26	1473 (1200)	45 to 53	60	0.189	0.3	80
0.92	1573 (1300)	20 to 25	542	1.650	0.1	22.9
2.06	1573 (1300)	20 to 25	233	0.709	0.1	25.9
3.66	1573 (1300)	20 to 25	117	0.356	0.1	48
4.77	1573 (1300)	20 to 25	90	0.274	0.1	62
6.56	1573 (1300)	20 to 25	62	0.189	0.1	81
1.58	1573 (1300)	20 to 25	599	1.823	0.2	44.7
3.02	1573 (1300)	20 to 25	298	0.907	0.2	58
4.86	1573 (1300)	20 to 25	176	0.536	0.2	78
6.81	1573 (1300)	20 to 25	117	0.356	0.2	93
2.33	1573 (1300)	20 to 25	599	1.811	0.3	80
4.37	1573 (1300)	20 to 25	298	0.918	0.3	90
6.77	1573 (1300)	20 to 25	176	0.533	0.3	94
9.22	1573 (1300)	20 to 25	117	0.369	0.3	96
1.06	1573 (1300)	32 to 38	427	1.300	0.1	10
1.96	1573 (1300)	32 to 38	219	0.667	0.1	22.4
3.33	1573 (1300)	32 to 38	115	0.350	0.1	45
5.12	1573 (1300)	32 to 38	62	0.189	0.1	72
1.48	1573 (1300)	32 to 38	595	1.811	0.2	24
2.74	1573 (1300)	32 to 38	291	0.886	0.2	45
4.1	1573 (1300)	32 to 38	169	0.514	0.2	70
5.32	1573 (1300)	32 to 38	115	0.350	0.2	82
7.45	1573 (1300)	32 to 38	62	0.189	0.2	97
2.13	1573 (1300)	32 to 38	595	1.811	0.3	56
3.2	1573 (1300)	32 to 38	358	1.090	0.3	75
4.55	1573 (1300)	32 to 38	219	0.667	0.3	85
6.63	1573 (1300)	32 to 38	115	0.350	0.3	99
0.84	1573 (1300)	45 to 53	504	1.534	0.1	10
1.5	1573 (1300)	45 to 53	271	0.826	0.1	14.1
2.92	1573 (1300)	45 to 53	110	0.295	0.1	46
4.52	1573 (1300)	45 to 53	62	0.118	0.1	68
1.43	1573 (1300)	45 to 53	556	1.693	0.2	21
2.12	1573 (1300)	45 to 53	330	1.003	0.2	37
3.35	1573 (1300)	45 to 53	167	0.472	0.2	58
4.90	1573 (1300)	45 to 53	60	0.183	0.2	84
1.94	1573 (1300)	45 to 53	556	1.693	0.3	40
2.74	1573 (1300)	45 to 53	330	1.003	0.3	59
4.02	1573 (1300)	45 to 53	167	0.472	0.3	79
5.38	1573 (1300)	45 to 53	60	0.183	0.3	92
0.79	1673 (1400)	20 to 25	595	1.784	0.1	54.6
2.62	1673 (1400)	20 to 25	169	0.507	0.1	73.1
4.70	1673 (1400)	20 to 25	88	0.264	0.1	94
6.31	1673 (1400)	20 to 25	62	0.186	0.1	98.6
0.76	1673 (1400)	32 to 38	595	1.784	0.1	36.9
1.90	1673 (1400)	32 to 38	219	0.657	0.1	47.6
2.36	1673 (1400)	32 to 38	169	0.507	0.1	54.9
3.22	1673 (1400)	32 to 38	115	0.345	0.1	82.1
5.01	1673 (1400)	32 to 38	62	0.186	0.1	98
1.39	1673 (1400)	45 to 53	556	1.666	0.1	57.4
2.07	1673 (1400)	45 to 53	330	0.987	0.1	75
3.32	1673 (1400)	45 to 53	167	0.464	0.1	90
4.96	1673 (1400)	45 to 53	60	0.180	0.1	98.7

Appendix C: Derivation of Appropriate Average Driving Force

Case 1: The Reaction is 1st-Order with Respect to H₂ Partial Pressure

The change in $p_{{{\text{H}}_{2} }}$ is proportional to the rate of reaction and thus can be expressed by the following equation in which A is a term containing the rate constant and independent of $p_{{{\text{H}}_{2} }}$ and $p_{{{\text{H}}_{2} {\text{O}}}}$:

$$ \frac{{dp_{{{\text{H}}_{2} }} }}{dt} = - A\left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right) $$

(C1)

Similarly,

$$ \frac{{dp_{{{\text{H}}_{2} {\text{O}}}} }}{dt} = + A\left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right) $$

(C2)

Multiplying Eq. [C2] by (−1/K _E) and adding to [C1], we get

$$ \frac{{d(p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} )}}{dt} = - A(1 + 1/K_{\text{E}} )\;(p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} ) $$

(C3)

Integration from $t_{1}$ to $t_{2}$ results in

$$ {\text{Ln}} \left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)_{2} - {\text{Ln}}\left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)_{1} = - A(1 + 1/K_{\text{E}} )\;(t_{2} - t_{1} ) $$

(C4)

The appropriate average driving force is a constant term that can replace the term on the right-hand side of Eq. [C3], made up of the known parameters, as follows:

$$ \frac{{d(p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} )}}{dt} = - A(1 + 1/K_{\text{E}} )\;(p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} )_{\text{avg}} $$

(C5)

which upon integration yields

$$ \left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)_{2} - \left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)_{1} = - A(1 + 1/K_{\text{E}} )\;(p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} )_{\text{avg}} \;(t_{2} - t_{1} ) $$

(C6)

Eliminating $(t_{2} - t_{1} )$ from Eqs. [C4] and [C6], we get

$$ \left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)_{\text{avg}} = \frac{{(p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} )_{2} - \left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)_{1} }}{{{\text{Ln}} \left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)_{2} - {\text{Ln}}\left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)_{1} }} = \left( {p_{{{\text{H}}_{2} }} - p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)_{\text{lm}} $$

(C7)

It is noted that

$$ p_{{{\text{H}}_{2} }} + p_{{{\text{H}}_{2} {\text{O}}}} = p_{\text{T}} $$

(C8)

The total pressure $p_{\text{T}}$ is constant because the total number of the mole does not change upon reaction. Substituting Eq. [C8] in [C7], the average driving force can be expressed in terms of just $p_{{{\text{H}}_{2} }}$.

$$ \left( {p_{{{\text{H}}_{2} }} - \frac{{p_{{{\text{H}}_{2} {\text{O}}}} }}{{K_{\text{E}} }}} \right)_{\text{avg}} = (1 + 1/K_{\text{E}} ) \cdot \frac{{(p_{{{\text{H}}_{2} }} )_{2} - (p_{{{\text{H}}_{2} }} )_{1} }}{{{\text{Ln}} \left( {p_{{{\text{H}}_{2} }} - p_{\text{T}} /(1 + K_{\text{E}} )} \right)_{2} - {\text{Ln}} \left( {p_{{{\text{H}}_{2} }} - p_{\text{T}} /(1 + K_{\text{E}} )} \right)_{1} }} $$

(C9)

Case 2: The Reaction is 1/2-Order with Respect to H₂ Partial Pressure

In this case,

$$ \frac{{d(p_{{{\text{H}}_{2} }} )}}{dt} = - B\left[ {\left( {p_{{{\text{H}}_{2} }} } \right)^{1/2} - \left( {p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} } \right)^{1/2} } \right] $$

(C10)

Here, we need to take advantage of the fact that $(p_{{{\text{H}}_{2} {\text{O}}}} /K_{\text{E}} )^{1/2}$ is typically much smaller than $(p_{{{\text{H}}_{2} }} )^{1/2}$, and thus

$$ \frac{{d(p_{{{\text{H}}_{2} }} )}}{dt} = - B\left( {p_{{{\text{H}}_{2} }} } \right)^{1/2} $$

(C11)

Integration from $t_{1}$ to $t_{2}$ yields

$$ 2 \cdot \left[ {\left( {p_{{{\text{H}}_{2} }} } \right)_{2}^{\frac{1}{2}} - \left( {p_{{{\text{H}}_{2} }} } \right)_{1}^{\frac{1}{2}} } \right] = - B \cdot (t_{2} - t_{1} ) $$

(C12)

Again, in terms of an average driving force,

$$ \frac{{d(p_{{{\text{H}}_{2} }} )}}{dt} = - B\left[ {\left( {p_{{{\text{H}}_{2} }} } \right)^{1/2} } \right]_{\text{avg}} $$

(C13)

which gives, upon integration,

$$ \left[ {\left( {p_{{{\text{H}}_{2} }} } \right)^{1/2} } \right]_{\text{avg}} = \frac{1}{ - B}\;\frac{{(p_{{{\text{H}}_{2} }} )_{2} - (p_{{{\text{H}}_{2} }} )_{1} }}{{t_{2} - t_{1} }} $$

(C14)

Eliminating $(t_{2} - t_{1} )$ from Eqs. [C12] and [C14], we get

$$ \left[ {\left( {p_{{{\text{H}}_{2} }} } \right)^{1/2} } \right]_{\text{avg}} = \frac{{\left( {p_{{{\text{H}}_{2} }} } \right)_{2} - \left( {p_{{{\text{H}}_{2} }} } \right)_{1} }}{{2\left[ {\left( {p_{{{\text{H}}_{2} }} } \right)_{2}^{1/2} - \left( {p_{{{\text{H}}_{2} }} } \right)_{1}^{1/2} } \right]}} = \frac{{\left( {p_{{{\text{H}}_{2} }} } \right)_{2}^{1/2} + \left( {p_{{{\text{H}}_{2} }} } \right)_{1}^{1/2} }}{2} = \left[ {\left( {p_{{{\text{H}}_{2} }} } \right)^{1/2} } \right]_{\text{am}} $$

(C15)