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polykin.properties.viscosity¤

MUVMXPC_Dean_Stiel ¤

MUVMXPC_Dean_Stiel(
    v: float,
    y: FloatVectorLike,
    M: FloatVectorLike,
    Tc: FloatVectorLike,
    Pc: FloatVectorLike,
    Zc: FloatVectorLike,
) -> float

Calculate the effect of pressure (or density) on the viscosity of gas mixtures using the method of Dean and Stiel for nonpolar components.

\[ (\mu_m -\mu_m^\circ)\xi = f(\rho_r) \]

where \(\mu_m\) is the dense gas mixture viscosity, \(\mu_m^\circ\) is the low-pressure gas mixture viscosity, \(\xi\) is a group of constants, and \(\rho_r = v_c / v\) is the reduced gas density. This equation is valid in the range \(0 \le \rho_r < 2.5\).

References

  • Dean, D., and Stiel, L. "The viscosity of nonpolar gas mixtures at moderate and high pressures." AIChE Journal 11.3 (1965): 526-532.
PARAMETER DESCRIPTION
v

Gas molar volume. Unit = m³/mol.

TYPE: float

y

Mole fractions of all components. Unit = mol/mol.

TYPE: FloatVectorLike

M

Molar masses of all components. Unit = kg/mol.

TYPE: FloatVectorLike

Tc

Critical temperatures of all components. Unit = K.

TYPE: FloatVectorLike

Pc

Critical pressures of all components. Unit = Pa.

TYPE: FloatVectorLike

Zc

Critical compressibility factors of all components.

TYPE: FloatVectorLike

RETURNS DESCRIPTION
float

Residual viscosity, \((\mu_m - \mu_m^\circ)\). Unit = Pa·s.

Examples:

Estimate the residual viscosity of a 50 mol% ethylene/propylene mixture t 350 K and 100 bar.

>>> from polykin.properties.viscosity import MUVMXPC_Dean_Stiel
>>> v = 1.12e-4  # m³/mol, with Peng-Robinson
>>> y = [0.5, 0.5]
>>> M = [28.05e-3, 42.08e-3] # kg/mol
>>> Tc = [282.4, 364.9]      # K
>>> Pc = [50.4e5, 46.0e5]    # Pa
>>> Zc = [0.280, 0.274]
>>> mu_residual = MUVMXPC_Dean_Stiel(v, y, M, Tc, Pc, Zc)
>>> print(f"{mu_residual:.2e} Pa·s")
2.32e-05 Pa·s
Source code in src/polykin/properties/viscosity/vapor.py 
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def MUVMXPC_Dean_Stiel(v: float,
                       y: FloatVectorLike,
                       M: FloatVectorLike,
                       Tc: FloatVectorLike,
                       Pc: FloatVectorLike,
                       Zc: FloatVectorLike,
                       ) -> float:
    r"""Calculate the effect of pressure (or density) on the viscosity of
    gas mixtures using the method of Dean and Stiel for nonpolar components.

    $$ (\mu_m -\mu_m^\circ)\xi = f(\rho_r) $$

    where $\mu_m$ is the dense gas mixture viscosity, $\mu_m^\circ$ is the
    low-pressure gas mixture viscosity, $\xi$ is a group of constants, and
    $\rho_r = v_c / v$ is the reduced gas density. This
    equation is valid in the range $0 \le \rho_r < 2.5$.

    **References**

    *   Dean, D., and Stiel, L. "The viscosity of nonpolar gas mixtures at
        moderate and high pressures." AIChE Journal 11.3 (1965): 526-532.

    Parameters
    ----------
    v : float
        Gas molar volume. Unit = m³/mol.
    y : FloatVectorLike
        Mole fractions of all components. Unit = mol/mol.
    M : FloatVectorLike
        Molar masses of all components. Unit = kg/mol.
    Tc : FloatVectorLike
        Critical temperatures of all components. Unit = K.
    Pc : FloatVectorLike
        Critical pressures of all components. Unit = Pa.
    Zc : FloatVectorLike
        Critical compressibility factors of all components.

    Returns
    -------
    float
        Residual viscosity, $(\mu_m - \mu_m^\circ)$. Unit = Pa·s.

    Examples
    --------
    Estimate the residual viscosity of a 50 mol% ethylene/propylene mixture
    t 350 K and 100 bar.

    >>> from polykin.properties.viscosity import MUVMXPC_Dean_Stiel
    >>> v = 1.12e-4  # m³/mol, with Peng-Robinson
    >>> y = [0.5, 0.5]
    >>> M = [28.05e-3, 42.08e-3] # kg/mol
    >>> Tc = [282.4, 364.9]      # K
    >>> Pc = [50.4e5, 46.0e5]    # Pa
    >>> Zc = [0.280, 0.274]
    >>> mu_residual = MUVMXPC_Dean_Stiel(v, y, M, Tc, Pc, Zc)
    >>> print(f"{mu_residual:.2e} Pa·s")
    2.32e-05 Pa·s
    """

    y = np.asarray(y)
    M = np.asarray(M)
    Tc = np.asarray(Tc)
    Pc = np.asarray(Pc)
    Zc = np.asarray(Zc)

    # Mixing rules recommended in paper
    M_mix = dot(y, M)
    Tc_mix, Pc_mix, vc_mix, _, _ = pseudocritical_properties(y, Tc, Pc, Zc)

    rhor = vc_mix/v
    # xi = 1e3*Tc_mix**(1/6)/(sqrt(M_mix*1e3)*(Pc_mix/101325)**(2/3))
    xi = 6.87e4*Tc_mix**(1/6)/(sqrt(M_mix)*(Pc_mix)**(2/3))
    a = 10.8e-5*(exp(1.439*rhor) - exp(-1.111*rhor**1.858))

    return a/xi