reactord.mix package

Module contents

Mixture module.

class reactord.mix.AbstractMix(substance_list: List[Substance], phase_nature: str, viscosity_mixing_rule: str)

Bases: object

Mixture objects abstract class.

Parameters:

• metaclass (AbstractMix) – Mixture objects interface.

• phase_nature (str) – Liquid or gas.

• substance_list (List[Substance]) – List of substances.

• viscosity_mixing_rule (str) – Viscosity mixing rule method. Options available: “linear”, “grunberg_nissan”, “herning_zipperer”.

names

Names of the mixture’s substances.

Type:

NDArray[str]

molecular_weights

The molecular weights of the mixture’s substances. [g/mol]

Type:

NDArray[np.float64]

normal_boiling_points

The normal boiling points of the mixture’s substances. [K]

Type:

NDArray[np.float64]

normal_melting_points

The normal melting points of the mixture’s substances. [K]

Type:

NDArray[np.float64]

critical_temperatures

The critical temperatures of the mixture’s substances. [K].

Type:

NDArray[np.float64]

critical_pressures

The critical pressures of the mixture’s substances. [Pa]

Type:

NDArray[np.float64]

acentric_factors

The acentric factors of the mixture’s substances.

Type:

NDArray[np.float64]

formation_enthalpies

Standard state molar enthalpies of formation of the mixture’s substances. [J/mol]

Type:

NDArray[np.float64]

formation_enthalpies_ig

Ideal-gas molar enthalpies of formation of the mixture’s substances. [J/mol]

Type:

NDArray[np.float64]

substances: List[Substance] = []

phase_nature: str = 'gas'

viscosity_mixing_rule: str = 'linear'

mole_fractions(moles: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Calculate the mole fractions of the mixture’s substances.

Multiple mixture compositions can be specified by a moles matrix. Each column of the matrix represents each mixture and each row represent each substance’s mole fraction.

\[z_i = \frac {n_i} {\sum_{i=0}^{N} n_i}\]

\(z_i\): mole fraction of the mix’s \(i\)-th substance.

\(n_i\): moles of the mix’s \(i\)-th substance.

\(N\): total number of substances in the mixture.

Parameters:

moles (Union[float, NDArray[np.float64]]) – Mole fractions of each substance specified in the same order as the mix’s substances order.

Returns:

The array of the molar fractions of the mix’s substances. Each column of the matrix represents each mixture and each row represent each substance’s mole fraction.

Return type:

Union[float, NDArray[np.float64]]

mix_molecular_weight(mole_fractions: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Calculate the molecular weight of the mixture.

Multiple mixture compositions can be specified by a mole_fractions matrix. Each column of the matrix represents each mixture and each row represent each substance’s mole fraction. In this case, the return is a 1D array with the molecular weight of each mix.

\[M_{mix} = \sum_{i=0}^{N} M_i z_i\]

\(M_{mix}\): molecular weight of the mixture.

\(N\): total number of substances in the mixture.

\(M_i\): molecular weight of the mix’s \(i\)-th substance.

\(z_i\): mole fraction of the mix’s \(i\)-th substance.

Parameters:

mole_fractions (Union[float, NDArray[np.float64]]) – Mole fractions of each substance specified in the same order as the mix’s substances order.

Returns:

The molecular weight of the mixture. [kg/kmol]

Return type:

Union[float, NDArray[np.float64]]

Requires

molecular_weight defined on each mix’s Substance.

molar_density(mole_fractions: float | ndarray[Any, dtype[float64]], temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Calculate the mixture’s molar density.

Multiple mixture compositions can be specified by a mole_fractions matrix. Each column of the matrix represents each mixture and each row represent each substance’s mole fraction. Also with temperature and pressure vectors following de NumPy broadcasting rules.

\[\rho_{mix} = \frac {1} {v_{(\vec{z}, T, P)}}\]

\(\rho_{mix}\): mix’s molar density.

\(v\): mix’s molar volume.

\(T\): temperature.

\(P\): pressure.

\(\vec{z}\): substances’ mole fractions.

Parameters:

• mole_fractions (Union[float, NDArray[np.float64]]) – Mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

Mixture’s molar density. [mol/m3]

Return type:

Union[float, NDArray[np.float64]]

mass_density(mole_fractions: float | ndarray[Any, dtype[float64]], temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Calculate the mixture’s mass density.

Multiple mixture compositions can be specified by a mole_fractions matrix. Each column of the matrix represents each mixture and each row represent each substance’s mole fraction. Also with temperature and pressure vectors following de NumPy broadcasting rules.

\[\rho_{mix}^{mass} = \rho_{mix}^{mol} M_{mix}\]

\(\rho_{mix}^{mass}\): mix’s masic density.

\(\rho_{mix}^{mol}\): mix’s molar density.

\(M_{mix}\): molecular weight of the mixture.

Parameters:

• mole_fractions (Union[float, NDArray[np.float64]]) – Mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

Mixture’s mass density. [kg/m3]

Return type:

Union[float, NDArray[np.float64]]

Requires

molecular_weight defined on each mix’s Substance.

mix_viscosity(mole_fractions: ndarray[Any, dtype[ScalarType]], temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Evaluate the viscosity of the mixture with the chosen mixing rule.

Multiple mixture compositions can be specified by a moles matrix. Each column of the matrix represents each mixture and each row represents each substance’s mole fractions. Also with temperature and pressure vectors following de NumPy broadcasting rules.

Parameters:

• mole_fractions (NDArray) – Mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

Mixture’s viscosity. [Pa s]

Return type:

Union[float, NDArray[np.float64]]

partial_pressures(mole_fractions: ndarray[Any, dtype[ScalarType]], temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Calculate the partial pressures of the mixture’s substances.

Multiple mixture compositions can be specified by a mole_fractions matrix. Each column of the matrix represents each mixture and each row represent each substance’s mole fraction. Also with temperature and pressure vectors following de NumPy broadcasting rules.

\[P_i = P z_i\]

\(P_i\): partial pressure of the \(i\)-th mix’s substance.

\(P\): total system’s pressure.

\(z_i\): mole fraction of the mix’s \(i\)-th substance.

Parameters:

• mole_fractions (NDArray) – Mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

An array that contains the partial pressures of mix’s substances. Each column of the matrix represents each mixture and each row represent each substance’s partial pressure. [Pa]

Return type:

Union[float, NDArray[np.float64]]

concentrations(mole_fractions: ndarray[Any, dtype[ScalarType]], temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Concentrations of the mixture’s substances.

Multiple mixture compositions can be specified by a moles matrix. Each column of the matrix represents each mixture and each row represents each substance’s mole fractions. Also with temperature and pressure vectors following de NumPy broadcasting rules.

\[C_i = z_i \rho_{mix}\]

\(C_i\): concentration of the mix’s \(i\)-th substance.

\(z_i\): mole fraction of the mix’s \(i\)-th substance.

\(\rho_{mix}\): mix’s molar density.

Parameters:

• mole_fractions (NDArray) – Mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

An array that contains the concentrations of the mixture’s substances. [mol/m³]

Return type:

Union[float, NDArray[np.float64]]

abstract volume(mole_fractions: ndarray[Any, dtype[ScalarType]], temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Return the molar volume of the mixture.

Multiple mixture compositions can be specified by a moles matrix. Each column of the matrix represents each mixture and each row represents each substance’s mole fractions. Also with temperature and pressure vectors following de NumPy broadcasting rules.

Parameters:

• mole_fractions (NDArray) – Mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

Mixture’s molar volume. [m³/mol]

Return type:

Union[float, NDArray[np.float64]]

Raises:

NotImplementedError – Abstract method not implemented.

abstract mix_heat_capacity(mole_fractions: ndarray[Any, dtype[ScalarType]], temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Calculate the mixture’s heat capacity.

Multiple mixture compositions can be specified by a moles matrix. Each column of the matrix represents each mixture and each row represents each substance’s mole fractions. Also with temperature and pressure vectors following de NumPy broadcasting rules.

Parameters:

• mole_fractions (NDArray) – Mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

Mixture’s heat capacity. [J/mol]

Return type:

Union[float, NDArray[np.float64]]

Raises:

NotImplementedError – Abstract method not implemented.

abstract formation_enthalpies_correction(temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float | ndarray[Any, dtype[float64]]

Calculate the correction term for the formation enthalpy.

Method that calculates the correction term for the formation enthalpies of the pure substances from 298.15 K and 101325 Pa to the given temperature and pressure. Multiple temperatures and pressures may be specified following de NumPy broadcasting rules.

Parameters:

• temperature (Union[float, NDArray[np.float64]]) – Temperature at which formation enthalpies are to be calculated. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure at which formation enthalpies are to be calculated. [Pa]

Returns:

Formation enthalpies correction for each mix’s substance. [J/mol/K]

Return type:

Union[float, NDArray[np.float64]]

Raises:

NotImplementedError – Abstract method not implemented.

abstract get_formation_enthalpies() → float | ndarray[Any, dtype[float64]]

Calculate the formation enthalpy of the mixture’s substances.

Returns:

Formation enthalpies of the mixture’s substances. [J/mol]

Return type:

Union[float, NDArray[np.float64]]

Raises:

NotImplementedError – Abstract method not implemented.

class reactord.mix.IdealGas(substance_list: List[Substance], viscosity_mixing_rule: str = 'herning_zipperer')

Bases: AbstractMix

IdealGas object class.

This class should be used when the mixture is considered an ideal gas.

Parameters:

• substance_list (list[Substance]) – list of substance objects

• viscosity_mixing_rule (str, optional) – Viscosity mixing rule method. Options available: “linear”, “grunberg_nissan”, “herning_zipperer”., by default “herning_zipperer”

phase_nature

gas.

Type:

str

substances

List of substances.

Type:

List [Substance]

viscosity_mixing_rule

Viscosity mixing rule method.

Type:

str

volume(mole_fractions: ndarray, temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float

Return the molar volume of the mixture.

Multiple mixture compositions can be specified by a moles matrix. Each column of the matrix represents each mixture and each row represents each substance’s mole fractions. Also with temperature and pressure vectors following de NumPy broadcasting rules.

\[v = \frac {R T} {P}\]

\(v\): mix’s molar volume.

\(R\): Ideal gas constant = 8.31446261815324 \(\frac {m^3 Pa} {K mol}\)

\(T\): temperature.

\(P\): pressure.

Parameters:

• mole_fractions (NDArray[np.float64]) – mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

Mixture’s molar volume. [m³/mol]

Return type:

Union[float, NDArray[np.float64]]

mix_heat_capacity(mole_fractions: ndarray, temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float

Calculate the mixture’s heat capacity [J/mol].

Multiple mixture compositions can be specified by a moles matrix. Each column of the matrix represents each mixture and each row represents each substance’s mole fractions. Also with temperature and pressure vectors following de NumPy broadcasting rules.

\[C_{p_{mix}} = \sum_{i=0}^{N} z_i C_{p_i}\]

\(C_{p_{mix}}\): mix’s heat capacity.

\(N\): total number of substances in the mixture.

\(C_{p_i}\): ideal gas heat capacity of the mix’s \(i\)-th substance.

\(z_i\): mole fraction of the mix’s \(i\)-th substance.

Parameters:

• mole_fractions (np.ndarray [float]) – mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

• Union[float, NDArray[np.float64]] – Mixture’s heat capacity. [J/mol]

• Requires

• ——– – heat_capacity_gas defined on each mix’s Substance.

formation_enthalpies_correction(temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]])

Calculate the correction term for the formation enthalpy.

Method that calculates the correction term for the formation enthalpies of the pure substances from 298.15 K and 101325 Pa to the given temperature and pressure.

\[ \begin{align}\begin{aligned}\Delta H_{f T_{(g)}} = \Delta H_{f 298.15_{(g)}}^0 + \sum_{i=0}^{N} \int_{298.15}^{T} v_i C_{p_i} dT\\CT = \sum_{i=0}^{N} \int_{298.15}^{T} v_i C_{p_i} dT\end{aligned}\end{align} \]

\(\Delta H_{f T_{(g)}}\): reaction enthalpy.

\(\Delta H_{f 298.15_{(g)}}^0\): ideal gas standard reaction enthalpy.

\(N\): total number of substances in the mixture.

\(C_{p_i}\): ideal gas heat capacity of the mix’s \(i\)-th substance.

\(z_i\): mole fraction of the mix’s \(i\)-th substance.

\(v_i\): stoichiometric coefficient of the mix’s \(i\)-th substance.

\(CT\): correction term.

Parameters:

• temperature (Union[float, NDArray[np.float64]]) – Temperature at which formation enthalpies are to be calculated. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure at which formation enthalpies are to be calculated. [Pa]

Returns:

Formation enthalpies of each substance (J/mol/K)

Return type:

Union[float, NDArray[np.float64]]

get_formation_enthalpies()

Return the ideal gas formation enthalpies in an ordered ndarray.

Method that read the ideal gas formation enthalpies of the mix class and returns them in an ordered ndarray.

Returns:

Ideal gas formation enthalpies of each substance [J/mol/K]

Return type:

Union[float, NDArray[np.float64]]

class reactord.mix.IdealSolution(substance_list: List[Substance], viscosity_mixing_rule: str = 'grunberg_nissan')

Bases: AbstractMix

IdealSolution object class.

This class should be used when the mixture is considered an ideal solution.

Parameters:

• substance_list (list [float]) – list of substance objects

• viscosity_mixing_rule (str, optional) – Viscosity mixing rule method. Options available: “linear”, “grunberg_nissan”, “herning_zipperer”., by default “grunberg_nissan”

phase_nature

liquid.

Type:

str

substances

List of substances.

Type:

List [Substance]

viscosity_mixing_rule

Viscosity mixing rule method.

Type:

str

volume(mole_fractions: List[float], temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]]) → float

Return the molar volume of the mixture.

Multiple mixture compositions can be specified by a moles matrix. Each column of the matrix represents each mixture and each row represents each substance’s mole fractions. Also with temperature and pressure vectors following de NumPy broadcasting rules.

\[v = \sum z_i {v_i}_{(T,P)}\]

\(v\): mix’s molar volume.

\(z_i\): mole fraction of the mix’s \(i\)-th substance.

\({v_i}_{(T,P)\): liquid molar volume of the mix’s \(i\)-th substance.

\(T\): temperature.

\(P\): pressure.

Parameters:

• mole_fractions (np.Union[float, NDArray[np.float64]]) – mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

Mixture’s molar volume. [m³/mol]

Return type:

float

Requires

volume_liquid defined on each mix’s Substance.

mix_heat_capacity(mole_fractions: List[float], temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]])

Calculate the mixture’s heat capacity [J/mol].

Multiple mixture compositions can be specified by a moles matrix. Each column of the matrix represents each mixture and each row represents each substance’s mole fractions. Also with temperature and pressure vectors following de NumPy broadcasting rules.

\[C_{p_{mix}} = \sum_{i=0}^{N} z_i C_{p_i}\]

\(C_{p_{mix}}\): mix’s heat capacity.

\(N\): total number of substances in the mixture.

\(C_{p_i}\): ideal gas heat capacity of the mix’s \(i\)-th substance.

\(z_i\): mole fraction of the mix’s \(i\)-th substance.

Parameters:

• mole_fractions (np.Union[float, NDArray[np.float64]]) – mole fractions of each substance specified in the same order as the mix’s substances order.

• temperature (Union[float, NDArray[np.float64]]) – Temperature. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure. [Pa]

Returns:

Mixture’s heat capacity. [J/mol]

Return type:

float

Requires

heat_capacity_liquid defined on each mix’s Substance.

formation_enthalpies_correction(temperature: float | ndarray[Any, dtype[float64]], pressure: float | ndarray[Any, dtype[float64]])

Calculate the correction term for the formation enthalpy.

Method that calculates the correction term for the formation enthalpies of the pure substances from 298.15 K and 101325 Pa to the given temperature and pressure using Kirchhoff’s equation. If the substance is a solid at a temperature > 298.15 K, this method also takes it into account.

Parameters:

• temperature (Union[float, NDArray[np.float64]]) – Temperature at which formation enthalpies are to be calculated. [K]

• pressure (Union[float, NDArray[np.float64]]) – Pressure at which formation enthalpies are to be calculated. [Pa]

Returns:

correction_enthalpies – Formation enthalpies correction for each substance (J/mol/K)

Return type:

Union[float, NDArray[np.float64]]

get_formation_enthalpies()

Return the formation enthalpies in a ordered ndarray.

Method that read the formation enthalpies of mix and returns them in a ordered ndarray.

Returns:

Formation enthalpies of each substance

Return type:

Union[float, NDArray[np.float64]]