Simulation of Combustion and Thermal-flow inside a Petroleum Coke Rotary Calcining Kiln, Part 1: Process Review and Modeling

Calcined coke is an important material for making carbon anodes for smelting of alumina to aluminum. Calcining is an energy intensive industry and a significant amount of heat is wasted in the calcining process. Efficiently managing this energy resource is tied to the profit margin and survivability of a calcining plant. To help improve the energy efficiency of the calcining process, a 3-D computational model is developed to gain insight of the thermal-flow and combustion behavior in the calciner. Comprehensive models are employed to simulate the moving petocke bed with moisture evaporation, devolatilization, and coke fines combustion with a conjugate radiation-convection-conduction calculation. NOMENCLATURE a Local speed of sound (m/s) c Concentration (mass/volume, moles/volume) cp, cv Specific heat at constant pressure, volume (J/kg-K) Dij Mass diffusion coefficient (m/s) E Total energy, activation energy (J) f Mixture fraction (dimensionless) g Gravitational acceleration (m/s) H Total enthalpy (energy/mass, energy/mole) h Heat transfer coefficient (W/m-K) h Species enthalpy (energy/mass, energy/mole) h0 Standard state enthalpy of formation (energy/mass, energy/mole) I Radiation intensity (energy per area of emitting surface per unit solid angle) J Mass flux; diffusion flux (kg/m-s) K Equilibrium constant = forward rate constant / backward rate constant (units vary) k Kinetic energy per unit mass (J/kg) k Reaction rate constant, e.g., k1, k-1, kf;r, kb;r (units vary) k Thermal conductivity (W/m-K) kB Boltzmann constant (1.38×10 J/mole-K) k, kc Mass transfer coefficient (units vary) l, L Length scale (m, cm) m Mass (kg) m& Mass flow rate (kg/s, kg/hr, metric ton/hr) Mw Molecular weight (kg/kgmol) M Mach number Nu Nusselt number ≡ hL/k (dimensionless) p Pressure (Pa, atm) Pr Prandtl number = α/ν (dimensionless) Q Flow rate of enthalpy (W) q" Heat flux (W/m) R Gas-law constant (8.31447×10 J/kgmol-K) r Radius (m) R Reaction rate (units vary) Re Reynolds number ≡ UL/ν (dimensionless) S Total entropy (J/K) s Specific entropy(J/K-kg) s0 Standard state entropy (J/K) Sc Schmidt number = ν/D (dimensionless) Sij Mean rate-of-strain tensor (s) T Temperature (K, °C) t Time (s) t Thickness (m) u, v, w Velocity components (m/s); also written with directional sub-scripts (e.g., vx, vy, vz, vr) U Free-stream velocity (m/s) V Volume (m) V Volume flow rate (SCFM) v Overall velocity vector (m/s) X Mole fraction (dimensionless) Y Mass fraction (dimensionless) Greek Letters α Permeability, or flux per unit pressure difference (L/m-hr-atm) α Volume fraction (dimensionless) α Thermal diffusivity (m/s) β Coefficient of thermal expansion (K) γ Specific heat ratio, cp/cv (dimensionless) δ Delta function Δ Change in variables) ε Emissivity (dimensionless) ε Turbulent dissipation rate (m/s) η′,η′′ Rate exponents for reactants, products (dimensionless) θr Radiation temperature (K) ν Kinematic viscosity (m/s) 2 μ Dynamic viscosity (Pa-s) ν′,ν′′ Stoichiometric coefficients for reactants, products ρ Density (kg/m) σ Stefan-Boltzmann constant (5.67×10 W/m-K) σs Scattering coefficient (m) τ Stress tensor (Pa) τ Shear stress (Pa) τ Time scale, e.g., τc, τp (s) Φ Equivalence ratio (dimensionless) Φ Diameter (m)