PRMIX

This function initializes a Peng-Robinson mixture EOS using mixture composition, critical properties, and optional binary interaction parameters.

With two of temperature, pressure, and molar volume specified, it solves the mixture state and returns key phase, volume-root, and fugacity outputs.

Excel Usage

=PRMIX(critical_temperatures, critical_pressures, omegas, zs, kijs, temperature, pressure, molar_volume, fugacities, only_liquid, only_vapor)
  • critical_temperatures (list[list], required): Critical temperatures for all components (K).
  • critical_pressures (list[list], required): Critical pressures for all components (Pa).
  • omegas (list[list], required): Acentric factors for all components (-).
  • zs (list[list], required): Overall component mole fractions (-).
  • kijs (list[list], optional, default: null): Binary interaction matrix as an n by n range (-).
  • temperature (float, optional, default: null): Temperature (K).
  • pressure (float, optional, default: null): Pressure (Pa).
  • molar_volume (float, optional, default: null): Molar volume (m^3/mol).
  • fugacities (bool, optional, default: true): Whether to calculate fugacity properties.
  • only_liquid (bool, optional, default: false): If true, keep only liquid root properties.
  • only_vapor (bool, optional, default: false): If true, keep only vapor root properties.

Returns (list[list]): 2D array with phase label, solved state variables, roots, and fugacity vectors.

Example 1: Binary PR mixture EOS with temperature and pressure

Inputs:

critical_temperatures critical_pressures omegas zs kijs temperature pressure
126.1 190.6 3394000 4604000 0.04 0.011 0.5 0.5 0 0 115 1000000
0 0

Excel formula:

=PRMIX({126.1,190.6}, {3394000,4604000}, {0.04,0.011}, {0.5,0.5}, {0,0;0,0}, 115, 1000000)

Expected output:

Property Value
phase l/g
T 115
P 1000000
V_l 0.0000362574
V_g 0.000700666
fugacities_l [793860.8382114592, 73468.55225303891]
fugacities_g [436530.9247009118, 358114.638275324]
Example 2: Binary PR mixture EOS without explicit kijs

Inputs:

critical_temperatures critical_pressures omegas zs temperature pressure
126.1 190.6 3394000 4604000 0.04 0.011 0.5 0.5 115 1000000

Excel formula:

=PRMIX({126.1,190.6}, {3394000,4604000}, {0.04,0.011}, {0.5,0.5}, 115, 1000000)

Expected output:

Property Value
phase l/g
T 115
P 1000000
V_l 0.0000362574
V_g 0.000700666
fugacities_l [793860.8382114592, 73468.55225303891]
fugacities_g [436530.9247009118, 358114.638275324]
Example 3: Binary PR mixture EOS with temperature and volume

Inputs:

critical_temperatures critical_pressures omegas zs kijs temperature molar_volume
126.1 190.6 3394000 4604000 0.04 0.011 0.5 0.5 0 0 115 0.00070066592313
0 0

Excel formula:

=PRMIX({126.1,190.6}, {3394000,4604000}, {0.04,0.011}, {0.5,0.5}, {0,0;0,0}, 115, 0.00070066592313)

Expected output:

Property Value
phase g
T 115
P 1000000
V_l
V_g 0.000700666
fugacities_l None
fugacities_g [436530.92470264115, 358114.63827627915]
Example 4: Binary PR mixture EOS with pressure and volume

Inputs:

critical_temperatures critical_pressures omegas zs kijs pressure molar_volume
126.1 190.6 3394000 4604000 0.04 0.011 0.5 0.5 0 0 1000000 0.00070066592313
0 0

Excel formula:

=PRMIX({126.1,190.6}, {3394000,4604000}, {0.04,0.011}, {0.5,0.5}, {0,0;0,0}, 1000000, 0.00070066592313)

Expected output:

Property Value
phase g
T 115
P 1000000
V_l
V_g 0.000700666
fugacities_l None
fugacities_g [436530.9247004668, 358114.6382742559]

Python Code

Show Code 
from thermo.eos_mix import PRMIX as thermo_prmix

def prmix(critical_temperatures, critical_pressures, omegas, zs, kijs=None, temperature=None, pressure=None, molar_volume=None, fugacities=True, only_liquid=False, only_vapor=False):
    """
    Solve Peng-Robinson mixture EOS and return key phase and fugacity metrics.

    See: https://thermo.readthedocs.io/thermo.eos_mix.html#thermo.eos_mix.PRMIX

    This example function is provided as-is without any representation of accuracy.

    Args:
        critical_temperatures (list[list]): Critical temperatures for all components (K).
        critical_pressures (list[list]): Critical pressures for all components (Pa).
        omegas (list[list]): Acentric factors for all components (-).
        zs (list[list]): Overall component mole fractions (-).
        kijs (list[list], optional): Binary interaction matrix as an n by n range (-). Default is None.
        temperature (float, optional): Temperature (K). Default is None.
        pressure (float, optional): Pressure (Pa). Default is None.
        molar_volume (float, optional): Molar volume (m^3/mol). Default is None.
        fugacities (bool, optional): Whether to calculate fugacity properties. Default is True.
        only_liquid (bool, optional): If true, keep only liquid root properties. Default is False.
        only_vapor (bool, optional): If true, keep only vapor root properties. Default is False.

    Returns:
        list[list]: 2D array with phase label, solved state variables, roots, and fugacity vectors.
    """
    try:
        def to_list(x):
            if isinstance(x, list):
                out = []
                for row in x:
                    if isinstance(row, list):
                        for val in row:
                            if val is not None and val != "":
                                out.append(float(val))
                    elif row is not None and row != "":
                        out.append(float(row))
                return out
            if x is None or x == "":
                return []
            return [float(x)]

        def to_matrix(x):
            if x is None:
                return None
            if not isinstance(x, list):
                return None
            matrix = []
            for row in x:
                if isinstance(row, list):
                    clean_row = []
                    for val in row:
                        if val is None or val == "":
                            clean_row.append(0.0)
                        else:
                            clean_row.append(float(val))
                    if len(clean_row) > 0:
                        matrix.append(clean_row)
            return matrix if len(matrix) > 0 else None

        tc_vals = to_list(critical_temperatures)
        pc_vals = to_list(critical_pressures)
        omega_vals = to_list(omegas)
        z_vals = to_list(zs)
        kij_vals = to_matrix(kijs)

        n = len(z_vals)
        if n == 0 or len(tc_vals) != n or len(pc_vals) != n or len(omega_vals) != n:
            return "Error: critical_temperatures, critical_pressures, omegas, and zs must be non-empty and have the same length"

        specified = 0
        for value in [temperature, pressure, molar_volume]:
            if value is not None:
                specified += 1
        if specified < 2:
            return "Error: At least two of temperature, pressure, and molar_volume must be provided"

        eos = thermo_prmix(Tcs=tc_vals, Pcs=pc_vals, omegas=omega_vals, zs=z_vals, kijs=kij_vals, T=temperature, P=pressure, V=molar_volume, fugacities=fugacities, only_l=only_liquid, only_g=only_vapor)

        return [
            ["Property", "Value"],
            ["phase", str(getattr(eos, "phase", ""))],
            ["T", getattr(eos, "T", None)],
            ["P", getattr(eos, "P", None)],
            ["V_l", getattr(eos, "V_l", None)],
            ["V_g", getattr(eos, "V_g", None)],
            ["fugacities_l", str(getattr(eos, "fugacities_l", None))],
            ["fugacities_g", str(getattr(eos, "fugacities_g", None))]
        ]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Critical temperatures for all components (K).
Critical pressures for all components (Pa).
Acentric factors for all components (-).
Overall component mole fractions (-).
Binary interaction matrix as an n by n range (-).
Temperature (K).
Pressure (Pa).
Molar volume (m^3/mol).
Whether to calculate fugacity properties.
If true, keep only liquid root properties.
If true, keep only vapor root properties.