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move B_mixture and B_pure to properties.pvt
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‎docs/reference/properties/pvt/B_mixture.md‎

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# polykin.properties.pvt
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::: polykin.properties.pvt.virial
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options:
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members:
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- B_mixture

‎docs/reference/properties/pvt/B_pure.md‎

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# polykin.properties.pvt
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::: polykin.properties.pvt.virial
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options:
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members:
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- B_pure

‎docs/reference/properties/pvt/_SUMMARY.md‎

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* [](index.md)
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* [B_mixture](B_mixture.md)
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* [B_pure](B_pure.md)
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* [geometric_interaction_mixing](geometric_interaction_mixing.md)
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* [pseudocritical_properties](pseudocritical_properties.md)
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* [quadratic_mixing](quadratic_mixing.md)

‎docs/reference/thermo/eos/B_mixture.md‎

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‎docs/reference/thermo/eos/B_pure.md‎

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‎docs/reference/thermo/eos/_SUMMARY.md‎

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* [RedlichKwong](RedlichKwong.md)
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* [SoaveRedlichKwong](SoaveRedlichKwong.md)
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* [Virial](Virial.md)
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* [B_mixture](B_mixture.md)
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* [B_pure](B_pure.md)
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* [Z_cubic_roots](Z_cubic_roots.md)

‎src/polykin/properties/pvt/__init__.py‎

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from .mixing_rules import *
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from .tait import *
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from .virial import *
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from .volume import *

‎src/polykin/properties/pvt/virial.py‎

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# PolyKin: A polymerization kinetics library for Python.
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#
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# Copyright Hugo Vale 2025
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import numpy as np
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from numpy import sqrt
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from scipy.constants import R
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from polykin.utils.types import (
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FloatArray,
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FloatSquareMatrix,
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FloatVector,
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)
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__all__ = ["B_pure", "B_mixture"]
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def B_pure(
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T: float | FloatArray,
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Tc: float,
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Pc: float,
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w: float,
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) -> float | FloatArray:
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r"""Estimate the second virial coefficient of a nonpolar or slightly polar
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gas.
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$$ \frac{B P_c}{R T_c} = B^{(0)}(T_r) + \omega B^{(1)}(T_r) $$
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where $B$ is the second virial coefficient, $P_c$ is the critical pressure,
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$T_c$ is the critical temperature, $T_r=T/T_c$ is the reduced temperature,
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and $\omega$ is the acentric factor.
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**References**
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* RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
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4th edition, 1986, p. 40.
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Parameters
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----------
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T : float | FloatArray
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Temperature [K].
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Tc : float
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Critical temperature [K].
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Pc : float
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Critical pressure [Pa].
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w : float
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Acentric factor.
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Returns
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-------
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float | FloatArray
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Second virial coefficient, $B$ [m³/mol].
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"""
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Tr = T / Tc
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B0 = 0.083 - 0.422 / Tr**1.6
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B1 = 0.139 - 0.172 / Tr**4.2
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return R * Tc / Pc * (B0 + w * B1)
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def B_mixture(
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T: float,
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Tc: FloatVector,
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Pc: FloatVector,
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Zc: FloatVector,
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w: FloatVector,
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) -> FloatSquareMatrix:
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r"""Calculate the matrix of interaction virial coefficients using the
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mixing rules of Prausnitz.
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\begin{aligned}
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B_{ij} &= B(T,T_{cij},P_{cij},\omega_{ij}) \\
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v_{cij} &= \frac{(v_{ci}^{1/3}+v_{cj}^{1/3})^3}{8} \\
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k_{ij} &= 1 -\frac{\sqrt{v_{ci}v_{cj}}}{v_{cij}} \\
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T_{cij} &= \sqrt{T_{ci}T_{cj}}(1-k_{ij}) \\
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Z_{cij} &= \frac{Z_{ci}+Z_{cj}}{2} \\
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\omega_{ij} &= \frac{\omega_{i}+\omega_{j}}{2} \\
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P_{cij} &= \frac{Z_{cij} R T_{cij}}{v_{cij}}
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\end{aligned}
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The calculation of the individual coefficients is handled by
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[`B_pure`](B_pure.md).
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**References**
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* RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
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4th edition, 1986, p. 80.
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Parameters
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----------
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T : float
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Temperature [K].
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Tc : FloatVector (N)
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Critical temperatures of all components [K].
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Pc : FloatVector (N)
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Critical pressures of all components [Pa].
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Zc : FloatVector (N)
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Critical compressibility factors of all components.
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w : FloatVector (N)
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Acentric factors of all components.
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Returns
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-------
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FloatSquareMatrix (N,N)
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Matrix of interaction virial coefficients $B_{ij}$ [m³/mol].
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"""
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vc = Zc * R * Tc / Pc
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N = Tc.size
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B = np.empty((N, N), dtype=np.float64)
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for i in range(N):
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for j in range(i, N):
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if i == j:
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B[i, j] = B_pure(T, Tc[i], Pc[i], w[i])
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else:
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vcm = (vc[i] ** (1 / 3) + vc[j] ** (1 / 3)) ** 3 / 8
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km = 1 - sqrt(vc[i] * vc[j]) / vcm
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Tcm = sqrt(Tc[i] * Tc[j]) * (1 - km)
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Zcm = (Zc[i] + Zc[j]) / 2
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wm = (w[i] + w[j]) / 2
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Pcm = Zcm * R * Tcm / vcm
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B[i, j] = B_pure(T, Tcm, Pcm, wm)
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B[j, i] = B[i, j]
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return B

‎src/polykin/thermo/eos/virial.py‎

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import functools
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import numpy as np
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from numpy import dot, exp, log, sqrt
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from numpy import dot, exp, log
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from scipy.constants import R
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from polykin.properties.pvt.mixing_rules import quadratic_mixing
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from polykin.properties.pvt.virial import B_mixture
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from polykin.utils.math import convert_FloatOrVectorLike_to_FloatVector
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from polykin.utils.types import (
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FloatArray,
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FloatSquareMatrix,
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FloatVector,
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FloatVectorLike,
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)
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from .base import GasEoS
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__all__ = ["Virial", "B_pure", "B_mixture"]
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__all__ = ["Virial"]
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class Virial(GasEoS):
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) -> FloatSquareMatrix:
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r"""Calculate the matrix of interaction virial coefficients.
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The calculation is handled by [`B_mixture`](B_mixture.md).
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The calculation is handled by [`B_mixture`](../../properties/pvt/B_mixture.md).
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Parameters
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----------
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y = n / nT
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Bm = self.Bm(T, y)
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return -nT * R * T * log((V - nT * Bm) / (nT * v0))
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def B_pure(
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T: float | FloatArray,
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Tc: float,
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Pc: float,
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w: float,
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) -> float | FloatArray:
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r"""Estimate the second virial coefficient of a nonpolar or slightly polar
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gas.
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$$ \frac{B P_c}{R T_c} = B^{(0)}(T_r) + \omega B^{(1)}(T_r) $$
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where $B$ is the second virial coefficient, $P_c$ is the critical pressure,
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$T_c$ is the critical temperature, $T_r=T/T_c$ is the reduced temperature,
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and $\omega$ is the acentric factor.
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**References**
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* RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
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4th edition, 1986, p. 40.
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Parameters
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----------
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T : float | FloatArray
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Temperature [K].
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Tc : float
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Critical temperature [K].
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Pc : float
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Critical pressure [Pa].
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w : float
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Acentric factor.
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Returns
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-------
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float | FloatArray
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Second virial coefficient, $B$ [m³/mol].
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"""
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Tr = T / Tc
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B0 = 0.083 - 0.422 / Tr**1.6
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B1 = 0.139 - 0.172 / Tr**4.2
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return R * Tc / Pc * (B0 + w * B1)
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def B_mixture(
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T: float,
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Tc: FloatVector,
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Pc: FloatVector,
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Zc: FloatVector,
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w: FloatVector,
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) -> FloatSquareMatrix:
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r"""Calculate the matrix of interaction virial coefficients using the
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mixing rules of Prausnitz.
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\begin{aligned}
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B_{ij} &= B(T,T_{cij},P_{cij},\omega_{ij}) \\
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v_{cij} &= \frac{(v_{ci}^{1/3}+v_{cj}^{1/3})^3}{8} \\
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k_{ij} &= 1 -\frac{\sqrt{v_{ci}v_{cj}}}{v_{cij}} \\
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T_{cij} &= \sqrt{T_{ci}T_{cj}}(1-k_{ij}) \\
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Z_{cij} &= \frac{Z_{ci}+Z_{cj}}{2} \\
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\omega_{ij} &= \frac{\omega_{i}+\omega_{j}}{2} \\
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P_{cij} &= \frac{Z_{cij} R T_{cij}}{v_{cij}}
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\end{aligned}
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The calculation of the individual coefficients is handled by
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[`B_pure`](B_pure.md).
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**References**
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* RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
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4th edition, 1986, p. 80.
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Parameters
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----------
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T : float
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Temperature [K].
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Tc : FloatVector (N)
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Critical temperatures of all components [K].
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Pc : FloatVector (N)
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Critical pressures of all components [Pa].
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Zc : FloatVector (N)
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Critical compressibility factors of all components.
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w : FloatVector (N)
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Acentric factors of all components.
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Returns
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-------
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FloatSquareMatrix (N,N)
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Matrix of interaction virial coefficients $B_{ij}$ [m³/mol].
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"""
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vc = Zc * R * Tc / Pc
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N = Tc.size
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B = np.empty((N, N), dtype=np.float64)
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for i in range(N):
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for j in range(i, N):
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if i == j:
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B[i, j] = B_pure(T, Tc[i], Pc[i], w[i])
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else:
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vcm = (vc[i] ** (1 / 3) + vc[j] ** (1 / 3)) ** 3 / 8
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km = 1 - sqrt(vc[i] * vc[j]) / vcm
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Tcm = sqrt(Tc[i] * Tc[j]) * (1 - km)
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Zcm = (Zc[i] + Zc[j]) / 2
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wm = (w[i] + w[j]) / 2
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Pcm = Zcm * R * Tcm / vcm
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B[i, j] = B_pure(T, Tcm, Pcm, wm)
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B[j, i] = B[i, j]
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return B

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