Pure Cubic Equation of State Class

class cpure(pure, c1, c2, oma, omb, alpha_eos)

Bases: object

Pure component Cubic EoS Object

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

Parameters:

• pure (object) – pure component created with component 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

Tc

critical temperture [K]

Type:float

Pc

critical pressure [bar]

Type:float

w

acentric factor

Type:float

cii

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

Type:array_like

Mw

molar weight of the fluid [g mol-1]

Type:float

a_eos : computes the attractive term of cubic eos.

psat : computes saturation pressure.

tsat : computes saturation temperature

density : computes density of mixture.

logfug : computes fugacity coefficient.

a0ad : computes dimensionless Helmholtz density energy

muad : computes dimensionless chemical potential.

dOm : computes dimensionless Thermodynamic Grand Potential.

ci : computes influence parameters matrix for SGT.

sgt_adim : computes dimensionless factors 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(T, P, state, v0=None, T_Step=0.1)

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

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

Parameters:

• 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(T, P, state, v0=None, T_Step=0.1)

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

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

Parameters:

• 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(T, P, state, v0, T_step)

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

Parameters:

• 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(T, P, state, v0, T_step)

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

Parameters:

• 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

a0ad(ro, T)

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

Parameters:

• ro (float) – dimensionless density vector [rho = rho * b]
• T (float) – absolute dimensionless temperature [Adim]

Returns:

a0ad – dimensionless Helmholtz density energy [Adim]

Return type:

float

a_eos(T)

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

Parameters:T (float) – absolute temperature [K] Returns:a – atractive term array [bar cm6 mol-2] Return type:float

ci(T)

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

Parameters:T (float) – absolute temperature [K] Returns:ci – influence parameters [J m5 mol-2] Return type:float

dOm(roa, T, mu, Psat)

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

Parameters:

• roa (float) – dimensionless density vector [rho = rho * b]
• T (floar) – absolute dimensionless temperature [Adim]
• mu (float) – dimensionless chemical potential at equilibrium [Adim]
• Psat (float) – dimensionless pressure at equilibrium [Adim]

Returns:

Out – Thermodynamic Grand potential [Adim]

Return type:

float

density(T, P, state)

Method that computes the density of the mixture at given temperature and pressure.

Parameters:

• T (float) – absolute temperature [K]
• P (float) – pressure [bar]
• state (string) – ‘L’ for liquid phase and ‘V’ for vapour phase

Returns:

density – molar density [mol/cm3]

Return type:

float

logfug(T, P, state)

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

Parameters:

• T (float) – absolute temperature [K]
• P (float) – pressure [bar]
• state (string) – ‘L’ for liquid phase and ‘V’ for vapour phase

Returns:

• logfug (float) – fugacity coefficient
• v (float) – volume of the fluid [cm3/mol]

muad(ro, T)

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

Parameters:

• roa (float) – dimensionless density vector [rho = rho * b]
• T (float) – absolute dimensionless temperature [adim]

Returns:

muad – chemical potential [Adim]

Return type:

float

pressure(v, T)

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

Parameters:

• T (float) – absolute temperature [K]
• v (float) – molar volume [cm3/mol]

Returns:

P – pressure [bar]

Return type:

float

psat(T, P0)

Method that computes saturation pressure at given temperature

Parameters:

• T (float) – absolute temperature [K]
• P0 (float, optional) – initial value to find saturation pressure [bar], None for automatic initiation

Returns:

• psat (float) – saturation pressure [bar]
• vl (float) – saturation liquid volume [cm3/mol]
• vv (float) – saturation vapor volume [cm3/mol]

sgt_adim(T)

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

Parameters:

• T (float) –
• temperature [K] (absolute) –

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(T, P, state, v0, T_step, CvId, CpId)

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:

• 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

tsat(P, T0, Tbounds)

Method that computes saturation temperature at given pressure

Parameters:

• P (float) – pressure [bar]
• T0 (float, optional) – Temperature to start iterations [K]
• Tbounds (tuple, optional) – (Tmin, Tmax) Temperature interval to start iterations [K]

Returns:

• tsat (float) – saturation pressure [bar]
• vl (float) – saturation liquid volume [cm3/mol]
• vv (float) – saturation vapor volume [cm3/mol]