Fluidized bed simulation

solid + fluidizing gas -> heated/reacted solid + gas (indirect, Wen-Yu sized)

Governing equations

The exact equations the solver works for a fluidized bed — the same math shown in the app's "Theory" panel, not a black box.

$Re_{mf}$

Reynolds number at minimum fluidization (Wen-Yu)

$Ar$

Archimedes number — the dimensionless group that decides when the bed lifts

$U_{mf}$

minimum fluidization velocity [m/s] — below this it is a fixed bed, not a fluidized one

$\mu$

gas viscosity [Pa·s]

$d_p$

particle diameter [m]

$\rho_g$

gas density [kg/m³]

$\tau$

solids residence time [s]

$m_{bed}$

bed inventory [kg]

$\dot m$

mass flow [kg/s]

$c_p$

heat capacity [J/kg/K]

$T_{wall}, T_{in}, T_{out}$

wall and solids temperatures [K]

$U$

heat-transfer coefficient [W/m²/K]

$k$

rate constant

$A_0$

pre-exponential

$E_a$

activation energy [J/mol]

$R$

gas constant

$X$

conversion [0..1] — well-mixed, so the kτ/(1+kτ) CSTR form, not the plug-flow one

Parameters

wall_temperature_K + heat_transfer_area_m2 [required, immersed coil]; bed_diameter_m/bed_inventory_kg/gas_velocity_m_s [geometry + hydrodynamics, defaults 2/5000/1], particle_diameter_m [default from the feed's solids payload], particle_density_kg_m3/gas_density_kg_m3/gas_viscosity_pa_s [Wen-Yu Umf inputs], molar_mass_kg_mol [default 0.1, for the mass-based residence time], overall_u_w_m2k [default 250, typical bubbling-bed range 200-500]; same optional reaction params as rotary_kiln (CSTR conversion form instead of plug-flow)

Example flowsheets that use it