# Bed expansion factor¶

The bed expansion factor can be used to estimate the expanded bed height of a bubbling fluidized bed reactor. Two equations are given in the Souza-Santos book based on the diameter of the bed.

For $$d_D < 0.0635$$ m:

$f_{bexp} = 1 + \frac{1.032\,(U-U_{mf})^{0.57}\;\rho_{GA}^{0.083}}{\rho_p^{0.166}\,U_{mf}^{0.063}\,d_D^{0.445}}$

For $$d_D \geq 0.0635$$ m:

$f_{bexp} = 1 + \frac{14.314\,(U-U_{mf})^{0.738}\;d_p^{1.006}\,\rho_p^{0.376}}{\rho_{GA}^{0.126}\;U_{mf}^{0.937}}$

## Nomenclature¶

$$d_D$$ - Diameter of the bed (m)
$$d_p$$ - Diameter of the bed particle (m)
$$f_{bexp}$$ - Bed expansion factor (-)
$$\rho_{GA}$$ - Gas density (kg/m³)
$$\rho_p$$ - Particle density (kg/m³)
$$U$$ - Gas superficial velocity (m/s)
$$U_{mf}$$ - Minimimum fluidization velocity (m/s)

## Source code¶

chemics.bed_expansion_factor.fbexp(db, dp, rhog, rhos, umf, us)[source]

Bed expansion factor for calculating expanded bed height of a bubbling fluidized bed reactor. See equations 14.7 and 14.8 in Souza-Santos 1.

Parameters
• db (float) – Diameter of the bed [m]

• dp (float) – Diameter of the bed particle [m]

• rhog (float) – Density of gas [kg/m^3]

• rhos (float) – Density of bed particle [kg/m^3]

• umf (float) – Minimum fluidization velocity [m/s]

• us (float) – Superficial gas velocity [m/s]

Returns

fbx (float) – Bed expansion factor [-]

Example

>>> umf = 0.1157
... us = 3.0*umf
... fbexp(0.05232, 0.0004, 0.4413, 2500, 0.1157, us)
1.4864


References

1

Marcio de Souza-Santos. Solid Fuels Combustion and Gasification: Modeling, Simulation, and Equipment Operations. CRC Press, Taylor and Francis Group, 2nd edition, 2010.