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polykin.properties.thermal_conductivity¤

KVMXPC_Stiel_Thodos ¤

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

Calculate the effect of pressure (or density) on the thermal conductivity of gas mixtures using the method of Stiel and Thodos for nonpolar components, combined with the mixing rules of Yorizane.

References

  • RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids 4th edition, 1986, p. 536.
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

w

Acentric factors of all components.

TYPE: FloatVectorLike

RETURNS DESCRIPTION
float

Residual thermal conductivity, \((k_m - k_m^{\circ})\). Unit = W/(m·K).

Examples:

Estimate the residual thermal conductivity of a 50 mol% ethylene/propylene mixture at 350 K and 100 bar.

>>> from polykin.properties.thermal_conductivity import KVMXPC_Stiel_Thodos
>>> import numpy as np
>>> v = 1.12e-4  # m³/mol, with Peng-Robinson
>>> y = [0.5, 0.5]
>>> M = [28.05e-3, 42.08e-3]  # kg/mol
>>> Pc = [50.4e5, 46.0e5]     # Pa
>>> Tc = [282.4, 364.9]       # K
>>> Zc = [0.280, 0.274]
>>> w = [0.089, 0.144]
>>> k_residual = KVMXPC_Stiel_Thodos(v, y, M, Tc, Pc, Zc, w)
>>> print(f"{k_residual:.2e} W/(m·K)")
3.82e-02 W/(m·K)
Source code in src/polykin/properties/thermal_conductivity/vapor.py 
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def KVMXPC_Stiel_Thodos(v: float,
                        y: FloatVectorLike,
                        M: FloatVectorLike,
                        Tc: FloatVectorLike,
                        Pc: FloatVectorLike,
                        Zc: FloatVectorLike,
                        w: FloatVectorLike
                        ) -> float:
    r"""Calculate the effect of pressure (or density) on the thermal
    conductivity of gas mixtures using the method of Stiel and Thodos for
    nonpolar components, combined with the mixing rules of Yorizane.

    **References**

    *   RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
        4th edition, 1986, p. 536.

    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.
    w : FloatVectorLike
        Acentric factors of all components.

    Returns
    -------
    float
        Residual thermal conductivity, $(k_m - k_m^{\circ})$. Unit = W/(m·K).

    Examples
    --------
    Estimate the residual thermal conductivity of a 50 mol% ethylene/propylene
    mixture at 350 K and 100 bar.
    >>> from polykin.properties.thermal_conductivity import KVMXPC_Stiel_Thodos
    >>> import numpy as np
    >>> v = 1.12e-4  # m³/mol, with Peng-Robinson
    >>> y = [0.5, 0.5]
    >>> M = [28.05e-3, 42.08e-3]  # kg/mol
    >>> Pc = [50.4e5, 46.0e5]     # Pa
    >>> Tc = [282.4, 364.9]       # K
    >>> Zc = [0.280, 0.274]
    >>> w = [0.089, 0.144]
    >>> k_residual = KVMXPC_Stiel_Thodos(v, y, M, Tc, Pc, Zc, w)
    >>> print(f"{k_residual:.2e} W/(m·K)")
    3.82e-02 W/(m·K)
    """

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

    vc = Zc*R*Tc/Pc

    # The loop could be simplified because
    # sum_i sum_j y_i y_j V_{ij} = sum_i y_i^2 V_{ii} + 2 sum_i sum_{j>i} y_i y_j V_ij
    vc_mix = 0.
    Tc_mix = 0.
    N = len(y)
    for i in range(N):
        for j in range(N):
            if i == j:
                vc_ = vc[i]
                Tc_ = Tc[i]
            else:
                vc_ = (1/8)*(vc[i]**(1/3) + vc[j]**(1/3))**3
                Tc_ = sqrt(Tc[i]*Tc[j])
            vc_term = y[i]*y[j]*vc_
            vc_mix += vc_term
            Tc_mix += vc_term*Tc_
    Tc_mix /= vc_mix

    w_mix = dot(y, w)
    Zc_mix = 0.291 - 0.08*w_mix
    Pc_mix = Zc_mix*R*Tc_mix/vc_mix
    M_mix = dot(y, M)

    return KVPC_Stiel_Thodos(v, M_mix, Tc_mix, Pc_mix, Zc_mix)