Using Iron Ore Ultra-Fines for Hydrogen-Based Fluidized Bed Direct Reduction—A Mathematical Evaluation
Abstract
:1. Introduction
2. Materials and Methods
2.1. Iron Ore Ultra-Fines
2.2. Correlations for the Evaluation of Using Iron Ore Ultra-Fines in a Fluidized Bed
2.2.1. General Classification Diagram of Fluidized Particles
2.2.2. Fluidized State Diagram Following Reh’s Approach
2.2.3. Minimum Fluidization Velocity
3. Results and Discussion
3.1. Classification of Iron Ore Ultra-Fine Powders for a Fluidized Bed
3.2. Operating Field of Iron Ore Ultra-Fines for a Fluidized Bed Reactor
- 1.
- Particle diameters, , in size range of 2 to 90 µm, to account for 95 wt.−%;
- 2.
- Densities of the ore and DRI, , between 5000 and 3500 kg/m3;
- 3.
- Gas densities, , and dynamic viscosities, , for the H2 and H2/H2O mixtures at temperatures of 873 to 1123 K and a pressure of 0.1 barg;
- 4.
- Superficial gas velocity, , between 0.15 and 0.30 m/s.
3.3. Mathematical Case Studies
3.3.1. Assumptions of the Reduction Process for the Mathematical Case Studies
3.3.2. First Case Study: Fluidized Bed Reduction without Sticking
3.3.3. Second Case Study: Fluidized Bed Reduction with Sticking
4. Conclusions
- According to Geldart’s and Goossens’s classification, iron ore ultra-fines are mainly Group A, Group A/C, and Group C materials under ambient conditions and air. For the hydrogen-based reduction at higher temperatures, iron ore ultra-fines are mostly Group A/C and Group C, according to Goossens’s classification;
- The operating field for iron ore ultra-fines needs an extended version of the Reh diagram, and it is not positioned within the general fields of circulating or bubbling fluidized beds;
- Changing process conditions, such as the temperature and gas properties, hardly affects the fluidization conditions or the minimum fluidization velocity;
- Changing the characteristic diameter due to sticking significantly affects the fluidization conditions and the minimum fluidization velocity. Thus, the characteristic particle or agglomerate diameter is the most critical parameter for a stable fluidized bed direct reduction process.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Symbol | Description | Unit |
Archimedes number | – | |
Drag coefficient for a single particle | – | |
Drag coefficient to account for mutual interactions between particles | – | |
Characteristic diameter; i vol.−% underflow | µm | |
Mean particle size | µm | |
Amount of iron in the sample | mol | |
Modified Froude number | – | |
Gravity | m/s2 | |
Gas oxidation degree | – | |
Constant for laminar term | – | |
Constant for turbulent term | – | |
Liatschenko number | – | |
Load factor | – | |
Amount of oxygen in the sample | mol | |
Pressure gauge | barg | |
Reduction degree | % | |
Reynolds number | – | |
Temperature | K | |
Superficial gas velocity in the reactor | m/s | |
Minimum fluidization velocity | m/s | |
Slip velocity | m/s | |
Index to account for the mutual interactions between particles | – | |
Pressure drop caused by gas flow through a packed bed | Pa | |
Void fraction of the bulk material | – | |
Void fraction of the bed material in the fluidized state | – | |
Void fraction of the bed material at the point of incipient fluidization | – | |
Gas utilization | % | |
Dynamic gas viscosity | Pa*s | |
Bulk density | kg/m3 | |
Density of the fluidizing medium | kg/m3 | |
True particle density | kg/m3 | |
Sphericity | – |
Appendix A
Property | 0% RD | 30% RD | 70% RD | 95% RD |
---|---|---|---|---|
Characteristic particle diameter, (µm) | 25 | 25 | 25 | 25 |
Sphericity, (−) | 0.70 | 0.70 | 0.70 | 0.70 |
Gas density, (kg/m3) | 0.112 | 0.044 | 0.040 | 0.021 |
Dynamic gas viscosity, (×10−6 Pas) | 33.0 | 28.3 | 27.4 | 22.0 |
True particle density, (kg/m3) | 5000.0 | 4571.7 | 4000.6 | 3643.7 |
Modified Froude number, Fr (−) | 7.04 × 10−3 | 3.02 × 10−3 | 3.14 × 10−3 | 1.81 × 10−3 |
Reynolds number, Re (−) | 2.72 × 10−2 | 1.25 × 10−2 | 1.17 × 10−2 | 7.65 × 10−3 |
Archimedes number, Ar (−) | 7.88 × 10−2 | 3.85 × 10−2 | 3.27 × 10−2 | 2.42 × 10−2 |
Liatschenko number, M (−) | 2.55 × 10−4 | 5.02 × 10−5 | 4.90 × 10−5 | 1.85 × 10−5 |
Void fraction of the bulk material at (−) | 0.65 | 0.65 | 0.65 | 0.65 |
Minimum fluidization velocity, (m/s) | 0.0024 | 0.0025 | 0.0023 | 0.0026 |
Property | 0% RD | 30% RD | 70% RD | 95% RD |
---|---|---|---|---|
Characteristic particle diameter, (µm) | 25 | 25 | 25 | 25 |
Sphericity, (−) | 0.70 | 0.70 | 0.70 | 0.70 |
Gas density, (kg/m3) | 0.084 | 0.071 | 0.038 | 0.018 |
Dynamic gas viscosity, (×10−6 Pas) | 44.4 | 43.5 | 38.1 | 28.7 |
True particle density, (kg/m3) | 5000.0 | 4571.7 | 4000.6 | 3643.7 |
Modified Froude number, Fr (−) | 5.28 × 10−3 | 4.88 × 10−3 | 2.98 × 10−3 | 1.55 × 10−3 |
Reynolds number, Re (−) | 1.52 × 10−2 | 1.31 × 10−2 | 7.99 × 10−3 | 5.03 × 10−3 |
Archimedes number, Ar (−) | 3.27 × 10−2 | 2.63 × 10−2 | 1.61 × 10−2 | 1.22 × 10−2 |
Liatschenko number, M (−) | 1.07 × 10−4 | 8.51 × 10−5 | 3.18 × 10−5 | 1.04 × 10−5 |
Void fraction of the bulk material at (−) | 0.65 | 0.65 | 0.65 | 0.65 |
Minimum fluidization velocity, (m/s) | 0.0018 | 0.0017 | 0.0017 | 0.0020 |
Property | 0% RD | 30% RD | 70% RD | 95% RD |
---|---|---|---|---|
Characteristic particle diameter, (µm) | 25 | 25 | 250 | 500 |
Sphericity, (−) | 0.70 | 0.70 | 0.85 | 0.85 |
Gas density, (kg/m3) | 0.112 | 0.044 | 0.040 | 0.021 |
Dynamic gas viscosity, (×10−6 Pas) | 33.0 | 28.3 | 27.4 | 22.0 |
True particle/agglomerate density, (kg/m3) | 5000.0 | 4571.7 | 4000.6 | 3643.7 |
Modified Froude number, Fr (−) | 7.04 × 10−3 | 3.02 × 10−3 | 4.49 × 10−4 | 1.29 × 10−4 |
Reynolds number, Re (−) | 2.72 × 10−2 | 1.25 × 10−2 | 1.17 × 10−1 | 1.53 × 10−1 |
Archimedes number, Ar (−) | 7.88 × 10−2 | 3.85 × 10−2 | 3.27 × 10+1 | 1.94 × 10+2 |
Liatschenko number, M (−) | 2.55 × 10−4 | 5.02 × 10−5 | 4.90 × 10−5 | 1.85 × 10−5 |
Void fraction of the bulk material at (−) | 0.65 | 0.65 | 0.65 | 0.65 |
Minimum fluidization velocity, (m/s) | 0.0024 | 0.0025 | 0.2363 | 1.0594 |
Property | 0% RD | 30% RD | 70% RD | 95% RD |
---|---|---|---|---|
Characteristic particle diameter, (µm) | 25 | 25 | 250 | 500 |
Sphericity, (−) | 0.70 | 0.70 | 0.85 | 0.85 |
Gas density, (kg/m3) | 0.084 | 0.071 | 0.038 | 0.018 |
Dynamic gas viscosity, (×10−6 Pas) | 44.4 | 43.5 | 38.1 | 28.7 |
True particle/agglomerate density, (kg/m3) | 5000.0 | 4571.7 | 4000.6 | 3643.7 |
Modified Froude number, Fr (−) | 5.28 × 10−3 | 4.88 × 10−3 | 4.26 × 10−4 | 1.11 × 10−4 |
Reynolds number, Re (−) | 1.52 × 10−2 | 1.31 × 10−2 | 7.99 × 10−2 | 1.01 × 10−1 |
Archimedes number, Ar (−) | 3.27 × 10−2 | 2.63 × 10−2 | 1.12 × 10+1 | 6.83 × 10+1 |
Liatschenko number, M (−) | 1.07 × 10−4 | 8.51 × 10−5 | 4.54 × 10−5 | 1.49 × 10−5 |
Void fraction of the bulk material at (−) | 0.65 | 0.65 | 0.65 | 0.65 |
Minimum fluidization velocity, (m/s) | 0.0018 | 0.0017 | 0.1701 | 0.8178 |
Deviation and Trend | (µm) Increase | (kg/m3) Decrease | (kg/m3) Decrease | (kg/ms) Decrease | (−) Increase | (−) Increase |
---|---|---|---|---|---|---|
0.0 | 25.0 | 5000 | 0.122 | 3.30 × 10−5 | 0.55 | 0.65 |
2.5 | 25.6 | 4875 | 0.119 | 3.22 × 10−5 | 0.56 | 0.67 |
5.0 | 26.3 | 4750 | 0.116 | 3.14 × 10−5 | 0.58 | 0.68 |
7.5 | 26.9 | 4625 | 0.113 | 3.05 × 10−5 | 0.59 | 0.70 |
10.0 | 27.5 | 4500 | 0.110 | 2.97 × 10−5 | 0.61 | 0.72 |
12.5 | 28.1 | 4375 | 0.107 | 2.89 × 10−5 | 0.62 | 0.73 |
15.0 | 28.8 | 4250 | 0.104 | 2.81 × 10−5 | 0.63 | 0.75 |
17.5 | 29.4 | 4125 | 0.101 | 2.72 × 10−5 | 0.65 | 0.76 |
20.0 | 30.0 | 4000 | 0.098 | 2.64 × 10−5 | 0.66 | 0.78 |
22.5 | 30.6 | 3875 | 0.095 | 2.56 × 10−5 | 0.67 | 0.80 |
25.0 | 31.3 | 3750 | 0.092 | 2.48 × 10−5 | 0.69 | 0.81 |
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Property | Sample A | Sample B | Sample C | Sample D | Sample E |
---|---|---|---|---|---|
d10 (µm) | 3.0 | 4.2 | 5.1 | 4.6 | 5.3 |
d50 (µm) | 16.1 | 20.0 | 25.0 | 25.2 | 31.1 |
d90 (µm) | 36.9 | 44.0 | 54.2 | 53.5 | 73.8 |
Maximum particle size (µm) | 90.0 | 90.0 | 125.0 | 90.0 | 125.0 |
True particle density, (kg/m3) | 4990 | 4980 | 4980 | 4870 | 4930 |
Bulk density, (kg/m3) | 1925 | 1988 | 2117 | 1996 | 2093 |
Void fraction of the bulk material, (−) | 0.61 | 0.60 | 0.57 | 0.59 | 0.58 |
Sphericity, (−) | 0.75 | 0.65 | 0.60 | 0.70 | 0.60 |
Fetot (wt.−%) | 68.06 | 69.76 | 69.09 | 67.31 | 66.96 |
FeO (wt.−%) | 23.25 | 30.03 | 27.30 | 27.60 | 25.70 |
SiO2 (wt.−%) | 2.84 | 2.32 | 3.78 | 6.65 | 2.33 |
CaO (wt.−%) | 0.13 | 0.15 | 0.01 | 0.01 | 0.93 |
Al2O3 (wt.−%) | 1.68 | 0.04 | 0.08 | 0.01 | 0.69 |
MgO (wt.−%) | 0.27 | 0.19 | 0.49 | 0.42 | 0.56 |
Property | 0% RD | 30% RD | 70% RD | 95% RD |
---|---|---|---|---|
Temperature, T (K) | 1173/873 | 1173/873 | 1173/873 | 1173/873 |
Pressure gauge, p (barg) | 0.1 | 0.1 | 0.1 | 0.1 |
Superficial gas velocity, (m/s) | 0.25 | 0.25 | 0.25 | 0.25 |
Void fraction of the bulk material, (−) | 0.78 | 0.78 | 0.78 | 0.78 |
Slip velocity, (m/s) | 0.321 | 0.321 | 0.321 | 0.321 |
Gas utilization, (%) | 80 | 80 | 80 | 20 |
Gas composition for 1173 K, xH2O (−) | 0.8 (1 × 0.8) | 0.66 (0.83 × 0.8) | 0.29 (0.37 × 0.8) | 0.07 (0.37 × 0.2) |
Gas composition for 873 K, xH2O (−) | 0.8 (1 × 0.8) | 0.24 (0.30 × 0.8) | 0.20 (0.25 × 0.8) | 0.05 (0.25 × 0.2) |
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Wolfinger, T.; Spreitzer, D.; Schenk, J. Using Iron Ore Ultra-Fines for Hydrogen-Based Fluidized Bed Direct Reduction—A Mathematical Evaluation. Materials 2022, 15, 3943. https://doi.org/10.3390/ma15113943
Wolfinger T, Spreitzer D, Schenk J. Using Iron Ore Ultra-Fines for Hydrogen-Based Fluidized Bed Direct Reduction—A Mathematical Evaluation. Materials. 2022; 15(11):3943. https://doi.org/10.3390/ma15113943
Chicago/Turabian StyleWolfinger, Thomas, Daniel Spreitzer, and Johannes Schenk. 2022. "Using Iron Ore Ultra-Fines for Hydrogen-Based Fluidized Bed Direct Reduction—A Mathematical Evaluation" Materials 15, no. 11: 3943. https://doi.org/10.3390/ma15113943