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polykin.properties.thermal_conductivity¤

KVPC_Stiel_Thodos ¤

KVPC_Stiel_Thodos(
    v: float, M: float, Tc: float, Pc: float, Zc: float
) -> float

Calculate the effect of pressure (or density) on the thermal conductivity of pure gases using the method of Stiel and Thodos for nonpolar components.

\[ \left( k-k^{\circ} \right) \Gamma Z_c^5 = f(\rho_r) \]

where \(k\) is the dense gas thermal conductivity, \(k^\circ\) is the low-pressure thermal conductivtiy, \(\Gamma\) is a group of constants, \(Z_c\) is the critical compressibility factor, and \(\rho_r = v_c / v\) is the reduced gas density. This equation is valid in the range \(0 \leq \rho_r < 2.8\).

References

  • RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids 4th edition, 1986, p. 521.
PARAMETER DESCRIPTION
v

Gas molar volume. Unit = m³/mol.

TYPE: float

M

Molar mass. Unit = kg/mol.

TYPE: float

Tc

Critical temperature. Unit = K.

TYPE: float

Pc

Critical pressure. Unit = Pa.

TYPE: float

Zc

Critical compressibility factor.

TYPE: float

RETURNS DESCRIPTION
float

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

Examples:

Estimate the residual thermal conductivity of ethylene at 350 K and 100 bar.

>>> from polykin.properties.thermal_conductivity import KVPC_Stiel_Thodos
>>> v = 1.84e-4 # m³/mol, with Peng-Robinson
>>> k_residual = KVPC_Stiel_Thodos(v=v, M=28.05e-3,
...                                Tc=282.4, Pc=50.4e5, Zc=0.280)
>>> print(f"{k_residual:.2e} W/(m·K)")
1.69e-02 W/(m·K)
Source code in src/polykin/properties/thermal_conductivity/vapor.py 
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def KVPC_Stiel_Thodos(v: float,
                      M: float,
                      Tc: float,
                      Pc: float,
                      Zc: float
                      ) -> float:
    r"""Calculate the effect of pressure (or density) on the thermal
    conductivity of pure gases using the method of Stiel and Thodos for
    nonpolar components.

    $$ \left( k-k^{\circ} \right) \Gamma Z_c^5 = f(\rho_r) $$

    where $k$ is the dense gas thermal conductivity, $k^\circ$ is the
    low-pressure thermal conductivtiy, $\Gamma$ is a group of constants, $Z_c$
    is the critical compressibility factor, and $\rho_r = v_c / v$ is the
    reduced gas density. This equation is valid in the range
    $0 \leq \rho_r < 2.8$.

    **References**

    *   RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
        4th edition, 1986, p. 521.

    Parameters
    ----------
    v : float
        Gas molar volume. Unit = m³/mol.
    M : float
        Molar mass. Unit = kg/mol.
    Tc : float
        Critical temperature. Unit = K.
    Pc : float
        Critical pressure. Unit = Pa.
    Zc : float
        Critical compressibility factor.

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

    Examples
    --------
    Estimate the residual thermal conductivity of ethylene at 350 K and
    100 bar.
    >>> from polykin.properties.thermal_conductivity import KVPC_Stiel_Thodos
    >>> v = 1.84e-4 # m³/mol, with Peng-Robinson
    >>> k_residual = KVPC_Stiel_Thodos(v=v, M=28.05e-3,
    ...                                Tc=282.4, Pc=50.4e5, Zc=0.280)
    >>> print(f"{k_residual:.2e} W/(m·K)")
    1.69e-02 W/(m·K)
    """

    gamma = ((Tc * M**3 * N_A**2)/(R**5 * Pc**4))**(1/6)
    vc = Zc*R*Tc/Pc
    rhor = vc/v

    if rhor < 0.5:
        a = 1.22e-2*(exp(0.535*rhor) - 1)
    elif rhor < 2.0:
        a = 1.14e-2*(exp(0.67*rhor) - 1.069)
    elif rhor < 2.8:
        a = 2.60e-3*(exp(1.155*rhor) + 2.016)
    else:
        raise ValueError("Invalid `rhor` input. Valid range: `rhor` < 2.8.")

    return a/(gamma * Zc**5)