Abstract
A three-dimensional mathematical model was developed to simulate the distributions of electrical potential, heat release, temperature, and velocity in the slag and matte in a six-in-line 36 MVA capacity furnace for smelting nickel calcine. From Part I of this series, it was found that there was a substantial electrical potential drop at the electrode surface, likely due to arcing through evolved carbon monoxide. The incorporation of this phenomenon into the model permitted accurate calculation of the current, power, and temperature distributions in the slag and matte. The slag was found to be thermally homogenized due to the evolved gas, and to a lesser extent by natural convection. In contrast, the matte was thermally stratified; this finding was attributed to poor momentum transfer across the slag/matte interface. Ninety percent of the electrical energy was used in smelting reactions in the calcine; to simulate the heat transfer from the slag to the calcine, a heat transfer coefficient was deduced from plant data. The implications of these findings for stable furnace operation are discussed.
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Abbreviations
- C p :
-
heat capacity (J/kg/K)
- D e :
-
electrode diameter (m)
- E :
-
electric field intensity (V/m)
- g :
-
gravitational acceleration (m/s2)
- h :
-
heat transfer coefficient (W/m2/K)
- H e :
-
immersion of the electrode in slag (m)
- I :
-
electrical current (A)
- J :
-
conduction current density (A/m2) or flux in Eq. [2]
- k :
-
thermal conductivity (W/m/K)
- L :
-
length scale (m)
- P :
-
electrical power input of the furnace (MW)
- p :
-
power generation rate per unit volume (W/m3)
- Pr:
-
Prandtl Number, v/α (—)
- q sw :
-
heat flux at the side wall (W/m2)
- Q c :
-
calcine feeding rate (tonne/h)
- R s :
-
electrical resistance of slag (ohm)
- Re m :
-
magnetic Reynolds number, LU/α m (—)
- S :
-
source term in conservation equations
- t :
-
time (s)
- T :
-
temperature (K)
- V :
-
electrical potential (V)
- V e :
-
electrical potential applied to the electrode (V)
- V s :
-
electrical potential experienced by the slag (V)
- U, V, W :
-
velocities (m/s)
- x, y, z :
-
coordinates (m)
- α :
-
thermal diffusivity (m2/s) or gas void fraction (—)
- α m :
-
magnetic diffusivity, 1/σ e μ m (m2/s)
- β :
-
coefficient of thermal expansion (K−1)
- μ :
-
viscosity (Pa s)
- μ m :
-
magnetic permeability (Henry/m)
- v:
-
kinematic viscosity (m2/s)
- ρ m :
-
density of the slag-gas mixture (kg/m3)
- ρ s :
-
density of the slag (kg/m3)
- ρ g :
-
density of the gas (kg/m3)
- σ 0 :
-
surface tension (J/m)
- σ s :
-
electrical conductivity of slag (mho/m)
- τ :
-
shear stress (J/m2)
- φ:
-
transportable variable
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Sheng, Y.Y., Irons, G.A. & Tisdale, D.G. Transport phenomena in electric smelting of nickel matte: Part II. Mathematical modeling. Metall Mater Trans B 29, 85–94 (1998). https://doi.org/10.1007/s11663-998-0010-5
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DOI: https://doi.org/10.1007/s11663-998-0010-5