Mixture Cubic Equation of State Class

class cubicm(mix, c1, c2, oma, omb, alpha_eos, mixrule)[source]

Bases: object

Mixture Cubic EoS Object

This object have implemeted methods for phase equilibrium as for interfacial properties calculations.

Parameters:
  • mix (object) – mixture created with mixture class
  • c2 (c1,) – constants of cubic EoS
  • omb (oma,) – constants of cubic EoS
  • alpha_eos (function) – function that gives thermal funcionality to attractive term of EoS
  • mixrule (function) – computes mixture attactive and cohesive terms
Tc

critical temperture [K]

Type:array_like
Pc

critical pressure [bar]

Type:array_like
w

acentric factor

Type:array_like
cii

influence factor for SGT polynomials [J m5 mol-2]

Type:array_like
nc

number of components of mixture

Type:int
Mw

molar weight of the fluids [g mol-1]

Type:array_like
secondorder

True if dlogfugef and dlogfugef_aux methods are available

Type:bool
secondordersgt

True if dmuad and dmuad_aux methods are available

Type:bool
temperature_aux: computes temperature dependent parameters.
a_eos : computes the attractive term of cubic eos.
Zmix : computes the roots of compressibility factor polynomial.
density : computes density of mixture.
logfugef : computes effective fugacity coefficients.
logfugmix : computes mixture fugacity coeficcient.
dlogfugef: computes effective fugacity coefficients and its

composition derivatives.

a0ad : computes dimensionless Helmholtz density energy.
muad : computes dimensionless chemical potential.
dmuad : computes dimensionless chemical potential and its

composition derivatives.

dOm : computes dimensionless Thermodynamic Grand Potential.
ci : computes influence parameters matrix for SGT.
sgt_adim : computes dimensionless factors for SGT.
beta_sgt : method that incorporates the beta correction for SGT.
EntropyR : computes residual Entropy.
EnthalpyR: computes residual Enthalpy.
CvR : computes residual isochoric heat capacity.
CpR : computes residual isobaric heat capacity.
speed_sound : computes the speed of sound.
CpR(X, T, P, state, v0=None, T_Step=0.1)[source]

Cpr(X, T, P, state, v0, T_step)

Method that computes the residual heat capacity at given composition, temperature and pressure.

Parameters:
  • X (array_like) – molar fraction array
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase and ‘V’ for vapour phase
  • v0 (float, optional) – initial guess for volume root [cm3/mol]
  • T_step (float, optional) – Step to compute the numerical temperature derivates of Helmholtz free energy
Returns:

Cp – residual heat capacity [J/mol K]
Return type:

float
CvR(X, T, P, state, v0=None, T_Step=0.1)[source]

Cpr(X, T, P, state, v0, T_step)

Method that computes the residual isochoric heat capacity at given composition, temperature and pressure.

Parameters:
  • X (array_like) – molar fraction array
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase and ‘V’ for vapour phase
  • v0 (float, optional) – initial guess for volume root [cm3/mol]
  • T_step (float, optional) – Step to compute the numerical temperature derivates of Helmholtz free energy
Returns:

Cv – residual isochoric heat capacity [J/mol K]
Return type:

float
EnthalpyR(X, T, P, state, v0, T_step)[source]

Method that computes the residual enthalpy at given composition, temperature and pressure.

Parameters:
  • X (array_like) – molar fraction array
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase and ‘V’ for vapour phase
  • v0 (float, optional) – initial guess for volume root [cm3/mol]
  • T_step (float, optional) – Step to compute the numerical temperature derivates of Helmholtz free energy
Returns:

Hr – residual enthalpy [J/mol]
Return type:

float
EntropyR(X, T, P, state, v0, T_step)[source]

Method that computes the residual entropy at given composition, temperature and pressure.

Parameters:
  • X (array_like) – molar fraction array
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase and ‘V’ for vapour phase
  • v0 (float, optional) – initial guess for volume root [cm3/mol]
  • T_step (float, optional) – Step to compute the numerical temperature derivates of Helmholtz free energy
Returns:

Sr – residual entropy [J/mol K]
Return type:

float
Zmix(X, T, P)[source]

Method that computes the roots of the compressibility factor polynomial at given mole fractions (X), Temperature (T) and Pressure (P)

Parameters:
  • X (array_like) – mole fraction vector
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
Returns:

Z – roots of Z polynomial
Return type:

array_like
a0ad(roa, T)[source]

Method that computes the dimensionless Helmholtz density energy at given density and temperature.

Parameters:
  • rhoa (array_like) – dimensionless density vector [rhoa = rho * b[0]]
  • T (float) – absolute temperature [K]
Returns:

a0ad – dimensionless Helmholtz density energy
Return type:

float
a_eos(T)[source]

Method that computes attractive term of cubic eos at fixed T (in K)

Parameters:T (float) – absolute temperature [K]
Returns:a – attractive term array [bar cm6 mol-2]
Return type:array_like
beta_sgt(beta)[source]

Method that allow asigning the beta correction for the influence parameter in Square Gradient Theory.

Parameters:beta (array_like) – beta corrections for influence parameter
ci(T)[source]

Method that evaluates the polynomials for the influence parameters used in the SGT theory for surface tension calculations.

Parameters:T (float) – absolute temperature [K]
Returns:cij – matrix of influence parameters with geometric mixing rule [J m5 mol-2]
Return type:array_like
dOm(roa, T, mu, Psat)[source]

Method that computes the dimensionless Thermodynamic Grand potential at given density and temperature.

Parameters:
  • rhoa (array_like) – dimensionless density vector [rhoa = rho * b[0]]
  • T (float) – absolute temperature [K]
  • mu (array_like) – dimensionless chemical potential at equilibrium [adim]
  • Psat (float) – dimensionless pressure at equilibrium [adim]
Returns:

dom – Thermodynamic Grand potential [Adim]
Return type:

float
density(X, T, P, state, rho0=None)[source]

Method that computes the molar concentration (molar density) of the mixture at given composition (X), temperature (T) and pressure (P)

Parameters:
  • X (array_like) – mole fraction vector
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase and ‘V’ for vapor phase
Returns:

density – Molar concentration of the mixture [mol/cm3]
Return type:

float
dlogfugef(X, T, P, state)[source]

Method that computes the effective fugacity coefficients and its composition derivatives at given composition, temperature and pressure.

Parameters:
  • X (array_like) – mole fraction vector
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase, ‘V’ for vapour phase
  • v0 (float, optional) – initial volume to iterate [cm3/mol]
Returns:

  • logfug (array_like) – effective fugacity coefficients
  • dlogfug (array_like) – composition derivatives of effective fugacity coefficients
  • v (float) – volume of phase [cm3/mol]
dmuad(rhoa, T)[source]

muad(roa, T)

Method that computes the dimensionless chemical potential and its derivatives at given density and temperature.

Parameters:
  • rhoa (array_like) – dimensionless density vector [rhoa = rho * b[0]]
  • T (float) – absolute temperature [K]
Returns:

  • muad (array_like) – dimensionless chemical potential vector
  • dmuad (array_like) – dimensionless derivatives of chemical potential vector
logfugef(X, T, P, state)[source]

Method that computes the effective fugacity coefficients at given composition, temperature and pressure.

Parameters:
  • X (array_like,) – mole fraction vector
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase, ‘V’ for vapour phase
  • v0 (float, optional) – initial volume to iterate [cm3/mol]
Returns:

  • logfug (array_like) – effective fugacity coefficients
  • v (float) – volume of the mixture [cm3/mol]
logfugmix(X, T, P, state)[source]

Method that computes the mixture fugacity coefficient at given composition, temperature and pressure.

Parameters:
  • X (array_like) – mole fraction vector
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase and ‘V’ for vapour phase
Returns:

  • lofgfug (array_like) – effective fugacity coefficients
  • v (float) – volume of phase [cm3/mol]
muad(roa, T)[source]

Method that computes the dimensionless chemical potential at given density and temperature.

Parameters:
  • rhoa (array_like) – dimensionless density vector [rhoa = rho * b[0]]
  • T (float) – absolute temperature [K]
Returns:

muad – dimensionless chemical potential vector
Return type:

array_like
muad_aux(rhoa, temp_aux)[source]

muad(roa, T)

Method that computes the dimensionless chemical potential at given density and temperature.

Parameters:
  • rhoa (array_like) – dimensionless density vector [rhoa = rho * b[0]]
  • T (float) – absolute temperature [K]
Returns:

muad – dimensionless chemical potential vector
Return type:

array_like
pressure(X, v, T)[source]

Method that computes the pressure at given composition X, volume (cm3/mol) and temperature T (in K)

Parameters:
  • X (array_like) – mole fraction vector
  • v (float) – molar volume in [cm3/mol]
  • T (float) – absolute temperature [K]
Returns:

P – pressure [bar]
Return type:

float
sgt_adim(T)[source]

Method that evaluates dimensionless factors for temperature, pressure, density, tension and distance for interfacial properties computations with SGT.

Parameters:T (absolute temperature [K]) –
Returns:
  • Tfactor (float) – factor to obtain dimentionless temperature (K -> adim)
  • Pfactor (float) – factor to obtain dimentionless pressure (bar -> adim)
  • rofactor (float) – factor to obtain dimentionless density (mol/cm3 -> adim)
  • tenfactor (float) – factor to obtain dimentionless surface tension (mN/m -> adim)
  • zfactor (float) – factor to obtain dimentionless distance (Amstrong -> adim)
speed_sound(X, T, P, state, v0, T_step, CvId, CpId)[source]

Method that computes the speed of sound at given temperature and pressure.

This calculation requires that the molar weight [g/mol] of the fluid has been set in the component function.

By default the ideal gas Cv and Cp are set to 3R/2 and 5R/2, the user can supply better values if available.

Parameters:
  • X (array_like) – molar fraction array
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase and ‘V’ for vapour phase
  • v0 (float, optional) – initial guess for volume root [cm3/mol]
  • T_step (float, optional) – Step to compute the numerical temperature derivates of Helmholtz free energy
  • CvId (float, optional) – Ideal gas isochoric heat capacity, set to 3R/2 by default [J/mol K]
  • CpId (float, optional) – Ideal gas heat capacity, set to 3R/2 by default [J/mol K]
Returns:

w – speed of sound [m/s]
Return type:

float