Introduction
The Phosphorus Producing Process
General Model Construction
Model Characteristics
Operation Data of the Industrial Furnace
Scenario | Energy Input | Pellets | Silica Gravel | Coke | Outlet Temp | P2O5(slag)
|
---|---|---|---|---|---|---|
MW | t/8 h | t/8 h | t/8 h | K | Wt Pct | |
1 | 37.9 | 180 | 52 | 27 | 699 | 1.3 |
2 | 41.3 | 189 | 58 | 30 | 711 | 1.3 |
3 | 45.4 | 209 | 62 | 32 | 728 | 1.6 |
4 | 48.5 | 229 | 69 | 36 | 734 | 1.6 |
5 | 50.6 | 248 | 73 | 38 | 748 | 1.9 |
Compound | Wt Pct | Compound | Wt Pct |
---|---|---|---|
Ca10(PO4)6OH2
| 25 | MgO | 0.8 |
Ca10(PO4)6F2
| 24.4 | K2O | 0.2 |
C | 10 | Na2O | 0.6 |
SiO2
| 28.4 | ZnO | 0.3 |
Fe2O3
| 0.6 | CaO | 4.0 |
Al2O3
| 1.3 | CaSiO3
| 4.3 |
Furnace Dimensions, Structure and Computational Grid
Material Type | Material Properties | |
---|---|---|
kcond W/m × K | ρ kg/m3 | |
Chamotte | k = 2.31 × 10−10T3 − 4.76 × 10−7T2 + 4.85 × 10−4T + 1.04 | 2050 |
Concrete | k = 1.85 × 10−4T + 0.562 | 2300 |
Carbon | k = 0.0017T + 7.041; (273 K − 1540 K (0 °C − 1813 °C)) k = 1.12 × 10−4T2 − 0.344T + 274; (1540 K − 1773 K (1813 °C − 2046 °C)) k = 15; (>1773K (>2046 °C)) | 1570 |
Electrode | k = 23 | 1570 |
Reactant and Product Material Properties
Reactant Type | Bulk Density | Porosity |
---|---|---|
ρ kg/m3 | ε Pct | |
Apatite pellets | 1714 | 44 |
Coke | 1230 | 32 |
Silica gravel | 2600 | — |
Product Type | Density | Thermal Conductivity | Heat Capacity |
---|---|---|---|
ρ kg/m3 | W/m × K | Cp J/kg × K | |
Slag | 2964 | 0.5 | 1260 |
Ferrophosphorus | 5000 | 15 | 850 |
Gaseous product | Ideal gas law | (above the packed bed); 0.06 (inside the packed bed); user-developed model 4 | Cp = 1 × 10−8T3 − 9.4 × 10−5T2 + 0.3T + 818 |
Input Conditions
Energy Input | Type of Energy Input | Value | |
---|---|---|---|
MW | |||
1 | Electrodes (Q
elec) | Positive source | 45.4* (Table I) |
2 | New Moeller fed under gravity (Q
newfeed) | Negative source | Integral (Eq. [2]) |
Boundary Conditions
Boundary Condition | Value | |
---|---|---|
[MW] | ||
1 | Bottom furnace cooling water | −1.1* |
2 | Side furnace cooling water | −0.5* |
3 | Exposed furnace surface | See below |
4 | Electrode cooling water | −5.0†
|
5 | Heating the Moeller from 313 K (40 °C) to 573 (300 °C) K** | −2.75 (see below) |
Exposed Furnace Surface
Heating the Moeller from 313 K to 573 K (40 °C to 300 °C)
Mass Flow
Physical Models
Turbulence Model
Radiation Model
User-Developed Model Construction
User-Developed Model 1: Mass Source Generation
Defining a Scalar Value for P2O5 Concentration
Formation of a New Transport Equation for the Scalar (P2O 5 S )
P2O5 Consumption and Gaseous Product Generation
Additional Mass Sources
Energy Distribution Ratio
User-Developed Model 2: Chemical Reaction Energy
User-Developed Model 3: Heating and Melting Energy
User-Developed Model 4: Particle–Particle Radiation and Effective Thermal Conductivity Model
Results and Model Validation
Base Case Model Results
Reduction Zone and P2O5 Consumption
Temperature and Pressure Distributions
Gas Formation and Flow Characterization
Energy Distribution Within the Furnace
Base Case Model Validation
The Radial Furnace Lining Temperature
The Vertical Furnace Lining Temperature B
The Gaseous Outlet Temperatures
The Slag Temperature
The P2O5(slag) Analysis from the Laboratory
The Specific Power Consumption (SPC)
Actual Value | Model Value | ||
---|---|---|---|
1 | Radial temperature of one temperature probe in the refractory lining | 585 K (312 °C) (±61 K (±61 °C)) | 660 K (387 °C) |
2 | Vertical temperature difference in the refractory lining | 70 K (70 °C) (±35 K (±35 °C)) | 30 K (30 °C) |
3 | Gaseous outlet temperature | 728 K (455 °C) (±126 K (126 °C)) | 832 K (559 °C) |
4 | Slag temperature | 1750 K (1477 °C) (±50 K (±50 °C)) | 1813 K (1540 °C) |
5 | P2O5(slag)
| 1.6 wt pct | 2.8 wt pct |
6 | SPC | 14.3 MWh/P4
| 15.3 MWh/P4
|