# Transport velocity¶

In circulating fluidized bed reactors, particle velocities should exceed the transport velocity to ensure circulation of solids in the system. According to Zhang et al., the transport velocity can be calculated from the following equation

$U_{TR} = \left( \frac{\mu}{\rho_g d_p} \right) \left(3.23 + 0.23 Ar\right)$

where the Archimedes number is defined as

$Ar = \frac{d_p^3 \rho_g (\rho_s - \rho_g) g}{\mu^2}$

## Nomenclature¶

$$Ar$$ - Archimedes number (-)
$$d_p$$ - Particle diameter (m)
$$g$$ - Acceleration due to gravity, 9.81 m/s²
$$\mu$$ - Gas viscosity (kg/(m s))
$$\rho_g$$ - Gas density (kg/m³)
$$\rho_s$$ - Solid particle density (kg/m³)

## Source code¶

chemics.transport_velocity.utr(dp, mu, rhog, rhos)[source]

Determine the transport velocity of particles in a circulating fluidized bed riser. Based on Equation 2 in article by Zhang et al. 1.

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

• mu (float) – Viscosity of gas [kg/(m s)]

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

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

Returns

utr (float) – Transport velocity [m/s]

Example

>>> utr(0.0005, 3.6e-5, 0.44, 1630)
26.0617


References

1

H.L. Zhang, J. Degreve, R. Dewil, and J. Baeyens. Operation diagram of Circulating Fluidized Beds (CFBs). Procedia Engineering, 102, pp. 1092-1103, 2015.