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polykin.properties.pvt¤

pseudocritical_properties ¤

pseudocritical_properties(
    y: FloatVector,
    Tc: FloatVector,
    Pc: FloatVector,
    Zc: FloatVector,
    w: FloatVector | None = None,
) -> tuple[float, float, float, float, float]

Calculate the pseudocritial properties of a mixture to use in corresponding states correlations.

\[ \begin{aligned} T_{cm} &= \sum_i y_i T_{ci} \\ Z_{cm} &= \sum_i y_i Z_{ci} \\ v_{cm} &= \sum_i y_i \frac{Z_{ci} R T_{ci}}{P_{ci}} \\ P_{cm} &= \frac{Z_{cm} R T_{cm}}{v_{cm}} \\ \omega_{cm} &= \sum_i y_i \omega_{ci} \end{aligned} \]

where the meaning of the parameters is as defined below.

References

  • RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids 4th edition, 1986, p. 76-77.
PARAMETER DESCRIPTION
y

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

TYPE: FloatVector

Tc

Critical temperatures of all components. Unit = K.

TYPE: FloatVector

Pc

Critical pressures of all components. Unit = Pa.

TYPE: FloatVector

Zc

Critical compressibility factors of all components.

TYPE: FloatVector

w

Acentric factors of all components.

TYPE: FloatVector | None DEFAULT: None

RETURNS DESCRIPTION
tuple[float, float, float, float, float]

Tuple of pseudocritial properties, \((T_{cm}, P_{cm}, v_{cm}, Z_{cm}, \omega_{cm})\).
Source code in src/polykin/properties/pvt/mixing_rules.py 
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def pseudocritical_properties(y: FloatVector,
                              Tc: FloatVector,
                              Pc: FloatVector,
                              Zc: FloatVector,
                              w: FloatVector | None = None
                              ) -> tuple[float, float, float, float, float]:
    r"""Calculate the pseudocritial properties of a mixture to use in
    corresponding states correlations.

    $$ \begin{aligned}
        T_{cm} &= \sum_i y_i T_{ci} \\
        Z_{cm} &= \sum_i y_i Z_{ci} \\
        v_{cm} &= \sum_i y_i \frac{Z_{ci} R T_{ci}}{P_{ci}} \\
        P_{cm} &= \frac{Z_{cm} R T_{cm}}{v_{cm}} \\
        \omega_{cm} &= \sum_i y_i \omega_{ci}
    \end{aligned} $$

    where the meaning of the parameters is as defined below.

    **References**

    *   RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
        4th edition, 1986, p. 76-77.

    Parameters
    ----------
    y : FloatVector
        Mole fractions of all components. Unit = mol/mol.
    Tc : FloatVector
        Critical temperatures of all components. Unit = K.
    Pc : FloatVector
        Critical pressures of all components. Unit = Pa.
    Zc : FloatVector
        Critical compressibility factors of all components.
    w : FloatVector | None
        Acentric factors of all components.

    Returns
    -------
    tuple[float, float, float, float, float]
        Tuple of pseudocritial properties,
        $(T_{cm}, P_{cm}, v_{cm}, Z_{cm}, \omega_{cm})$.
    """

    Tc_mix = dot(y, Tc)
    Zc_mix = dot(y, Zc)
    vc = Zc*R*Tc/Pc
    vc_mix = dot(y, vc)
    Pc_mix = R*Zc_mix*Tc_mix/vc_mix

    if w is not None:
        w_mix = dot(y, w)
    else:
        w_mix = -1e99

    return (Tc_mix, Pc_mix, vc_mix, Zc_mix, w_mix)