polykin.transport.flow

DP_packed_bed

DP_packed_bed(
    G: float,
    L: float,
    Dp: float,
    eps: float,
    rho: float,
    mu: float,
) -> float

Calculate the pressure drop in a packed bed.

In a packed bed, the pressure drop due to friction is given by:

\[ \Delta P = \frac{G^2 (1 - \epsilon) f_p}{\rho D_p \epsilon^3} L \]

where \(G\) is the mass flux, \(D_p\) is the particle diameter, \(\epsilon\) is the bed porosity, \(L\) is the packed bed length, and \(\rho\) is the fluid density. The packing friction factor \(f_p\) is estimated using the Sato and Tallmadge correlation:

\[ f_p = \frac{150}{Re_p} + \frac{4.2}{Re_p^{1/6}} \]

where \(Re_p=D_p G/(\mu (1-\epsilon))\) is the packing Reynolds number.

References

• Walas, S. M., "Chemical Process Equipment: Selection and Design", Singapore: Butterworths, 1988.

PARAMETER	DESCRIPTION
G	Mass flux (kg/m²·s). TYPE: float
L	Packed bed length (m). TYPE: float
Dp	Particle diameter (m). TYPE: float
eps	Bed porosity. TYPE: float
rho	Fluid density (kg/m³). TYPE: float
mu	Fluid viscosity (Pa·s). TYPE: float

RETURNS	DESCRIPTION
float	Pressure drop (Pa).

Examples:

Calculate the pressure drop in a packed bed reactor under the conditions specified below.

>>> from polykin.transport import DP_packed_bed
>>> DP = DP_packed_bed(G=50., L=2., Dp=1e-2, eps=0.45, rho=800., mu=0.01)
>>> print(f"DP = {DP:.1e} Pa")
DP = 1.4e+04 Pa

Source code in src/polykin/transport/flow.py

def DP_packed_bed(G: float,
                  L: float,
                  Dp: float,
                  eps: float,
                  rho: float,
                  mu: float
                  ) -> float:
    r"""Calculate the pressure drop in a packed bed.

    In a packed bed, the pressure drop due to friction is given by:

    $$ \Delta P = \frac{G^2 (1 - \epsilon) f_p}{\rho D_p \epsilon^3} L $$

    where $G$ is the mass flux, $D_p$ is the particle diameter, $\epsilon$ is
    the bed porosity, $L$ is the packed bed length, and $\rho$ is the fluid
    density. The packing friction factor $f_p$ is estimated using the Sato and
    Tallmadge correlation:

    $$ f_p = \frac{150}{Re_p} + \frac{4.2}{Re_p^{1/6}} $$

    where $Re_p=D_p G/(\mu (1-\epsilon))$ is the packing Reynolds
    number.

    **References**

    * Walas, S. M., "Chemical Process Equipment: Selection and Design",
      Singapore: Butterworths, 1988.

    Parameters
    ----------
    G : float
        Mass flux (kg/m²·s).
    L : float
        Packed bed length (m).
    Dp : float
        Particle diameter (m).
    eps : float
        Bed porosity.
    rho : float
        Fluid density (kg/m³).
    mu : float
        Fluid viscosity (Pa·s).

    Returns
    -------
    float
        Pressure drop (Pa).

    Examples
    --------
    Calculate the pressure drop in a packed bed reactor under the conditions
    specified below.
    >>> from polykin.transport import DP_packed_bed
    >>> DP = DP_packed_bed(G=50., L=2., Dp=1e-2, eps=0.45, rho=800., mu=0.01)
    >>> print(f"DP = {DP:.1e} Pa")
    DP = 1.4e+04 Pa
    """
    Rep = Dp*G/(mu*(1 - eps))
    fp = 150/Rep + 4.2/Rep**(1/6)
    return G**2*(1 - eps)*fp*L/(rho*Dp*eps**3)