VaporLiquid Equilibrium Property Models (Ideal Gas  Nonideal Liquids)#
This property package supports phase equilibrium calucations with a smooth phase transition formulation that makes it amenable for equation oriented optimization. The gas phase is assumed to be ideal and for the liquid phase, the package supports an ideal liquid or a nonideal liquid using an activity coefficient model. To compute the activity coefficient, the package currently supports the Non Random Two Liquid Model (NRTL) or the Wilson model. Therefore, this property package supports the following combinations for gasliquid mixtures for VLE calculations:
Ideal (vapor)  Ideal (liquid)
Ideal (vapor)  NRTL (liquid)
Ideal (vapor)  Wilson (liquid)
Flow basis: Molar
Units: SI units
State Variables:
The state block supports the following two sets of state variables:
Option 1  “FTPz”:
 Total molar flow rate (mol/s) 
flow_mol
 Temperature (K) 
temperature
 Presure (Pa) 
pressure
 Mole fraction of the mixture 
mole_frac_comp
Option 2  “FcTP”:
 Component molar flow rate (mol/s) 
flow_mol_comp
 Temperature (K) 
temperature
 Presure (Pa) 
pressure
The user can specify the choice of state variables while instantiating the parameter block. See the Inputs section for more details.
Support for other combinations of state variables will be made available in the future.
Inputs#
When instantiating the parameter block that uses this particular state block, 2 arguments can be passed:
valid_phase
 "Liq" or "Vap" or ("Liq", "Vap") or ("Vap", "Liq")activity_coeff_model
 "Ideal" or "NRTL" or "Wilson"state_vars
 "FTPz" or "FcTP"
The valid_phase
argument denotes the valid phases for a given set of inlet conditions. For example, if the user knows a priori that the it will only be a single phase (for example liquid only), then it is best not to include the complex flash equilibrium constraints in the model. If the user does not specify any option, then the package defaults to a 2 phase assumption meaning that the constraints to compute the phase equilibrium will be computed.
The activity_coeff_model
denotes the liquid phase assumption to be used. If the user does not specify any option, then the package defaults to assuming an ideal liquid assumption.
The state_vars
denotes the preferred set of state variables to be used. If the user does not specify any option, then the package defaults to using the total flow, mixture mole fraction, temperature and pressure as the state variables.
Degrees of Freedom#
The number of degrees of freedom that need to be fixed to yield a square problem (i.e. degrees of freedom = 0) depends on the options selected. The following table provides a summary of the variables to be fixed and also the corresponding variable names in the model.
Property Model Type 
State variables 
Additional Variables 
Total number of variables 

Ideal (vapor)  Ideal (liquid) 

None 
3 + \(N_{c}\) 
Ideal (vapor)  NRTL (liquid) 


3 + \(N_{c}\) + \(2N_{c}^{2}\) 
Ideal (vapor)  Wilson (liquid) 


3 + \(N_{c}\) + \(2N_{c}^{2}\) 
Please refer to reference 3 for recommended values for tau
.
VLE Model with Smooth Phase Transition#
The flash equations consists of the following equations depending on the choice of state variables selected by the user.
If the state variables are total flow, mole fraction, temperature, and pressure, then the following constraints are implemented:
If the state variables are component flow rates, temperature, and pressure, then the following constraints are implemented:
The equilibrium condition, the fugacity of the vapor and liquid phase are defined as follows:
The equilibrium constraint is written as a generic constraint such that it can be extended easily for nonideal gases and liquids. As this property package only supports an ideal gas, the fugacity coefficient (\(\phi_{i}\)) for the vapor phase is 1 and hence the expression reduces to \(y_{i}P\). For the liquid phase, if the ideal option is selected then the activity coefficient (\(\nu_{i}\)) is 1. If an activity coefficient model is selected then corresponding constraints are added to compute the activity coefficient.
Typically, the flash calculations are computed at a given temperature, \(T\). However, the flash calculations become trivial if the given conditions do not fall in the two phase region. For simulation only studies, the user may know a priori the condition of the stream but when the same set of equations are used for optimization, there is a high probability that the specifications can transcend the phase envelope and hence the flash equations included may be trivial in the single phase region (i.e. liquid or vapor only). To circumvent this problem, property packages in IDAES that support VLE will compute the flash calculations at an “equilibrium” temperature \(T_{eq}\). The equilibrium temperature is computed as follows:
where \(T_{eq}\) is the equilibrium temperature at which flash calculations are computed, \(T\) is the stream temperature, \(T_{1}\) is the intermediate temperature variable, \(T_{bubble}\) is the bubble point temperature of mixture, and \(T_{dew}\) is the dew point temperature of the mixture. Note that, in the above equations, approximations are used for the max and min functions as follows:
where \(\epsilon_1\) and \(\epsilon_2\) are smoothing parameters(mutable). The default values are 0.01 and 0.0005 respectively. It is recommended that \(\epsilon_1\) > \(\epsilon_2\). Please refer to reference 4 for more details. Therefore, it can be seen that if the stream temperature is less than that of the bubble point temperature, the VLE calucalations will be computed at the bubble point. Similarly, if the stream temperature is greater than the dew point temperature, then the VLE calculations are computed at the dew point temperature. For all other conditions, the equilibrium calculations will be computed at the actual temperature.
Additional constraints are included in the model to compute the thermodynamic properties such as component saturation pressure, enthalpy, specific heat capacity. Please note that, these constraints are added only if the variable is called for when building the model. This eliminates adding unnecessary constraints to compute properties that are not needed in the model.
The saturation or vapor pressure (pressure_sat
) for component \(i\) is computed using the following correlation[1]:
where \(P_c\) is the critical pressure, \(T_c\) is the critical temperature of the component and \(T_{eq}\) is the equilibrium temperature at which the saturation pressure is computed. Please note that when using this expression, \(T_{eq}<T_{c}\) is required and when violated it results in a negative number raised to the power of a fraction.
The specific enthalpy (enthalpy_comp_liq
) for component \(i\) is computed using the following expression for the liquid phase:
The specific enthalpy (enthalpy_comp_vap
) for component \(i\) is computed using the following expression for the vapor phase:
The mixture specific enthapies (enthalpy_liq
& enthalpy_vap
) are computed using the following expressions for the liquid and vapor phase respectively:
Similarly, specific entropies are calculated as follows. The specific entropy (entropy_comp_liq
) for component \(i\) is computed using the following expression for the liquid phase:
The specific entropy (entropy_comp_vap
) for component \(i\) is computed using the following expression for the vapor phase:
Please refer to references 1 and 2 to get parameters for different components.
Activity Coefficient Model  NRTL#
The activity coefficient for component \(i\) is computed using the following equations when using the NonRandom Two Liquid model [3]:
where \(\alpha_{ij}\) is the nonrandomness parameter and \(\tau_{ij}\) is the binary interaction parameter for the NRTL model. Note that in the IDAES implementation, these are declared as variables that allows for more flexibility and the ability to use these in a parameter estimation problem. These NRTL model specific variables need to be either fixed for a given component set or need to be estimated from VLE data.
The bubble point is computed by enforcing the following condition:
Activity Coefficient Model  Wilson#
The activity coefficient for component \(i\) is computed using the following equations when using the Wilson model [3]:
where \(v_{i}\) is the molar volume of component \(i\) and \(\tau_{ij}\) is the binary interaction parameter. These are Wilson model specific variables that either need to be fixed for a given component set or need to be estimated from VLE data.
The bubble point is computed by enforcing the following condition:
List of Variables#
Variable Name 
Description 
Units 


Total molar flow rate 
mol/s 

Mixture mole fraction indexed by component 
None 

Temperature 
K 

Pressure 
Pa 

Molar flow rate indexed by phase 
mol/s 

Mole fraction indexed by phase and component 
None 

Saturation or vapor pressure indexed by component 
Pa 

Molar density indexed by phase 
mol/m3 

Molar entropy of vaporization 
J/mol.K 

Liquid molar enthalpy indexed by component 
J/mol 

Vapor molar enthalpy indexed by component 
J/mol 

Liquid phase enthalpy 
J/mol 

Vapor phase enthalpy 
J/mol 

Liquid molar entropy indexed by component 
J/mol 

Vapor molar entropy indexed by component 
J/mol 

Liquid phase entropy 
J/mol 

Vapor phase entropy 
J/mol 

Bubble point temperature 
K 

Dew point temperature 
K 

Temperature at which the VLE is calculated 
K 
Variable Name 
Description 
Units 


Nonrandomness parameter indexed by component and component 
None 

Binary interaction parameter indexed by component and component 
None 

Activity coefficient indexed by component 
None 
Variable Name 
Description 
Units 


Molar volume of component indexed by component 
None 

Binary interaction parameter indexed by component and component 
None 

Activity coefficient indexed by component 
None 
Initialization#
 class idaes.models.properties.activity_coeff_models.activity_coeff_prop_pack.ActivityCoeffInitializer(**kwargs)[source]#
Initializer for Activity Coefficient property packages.
This Initializer uses a hierarchical routine to initialize the property package using the Pyomo solve_strongly_connected_components method is used at each step to converge the problem.
Note that for systems without vaporliquid equilibrium the generic BlockTriangularizationInitializer is probably sufficient for initializing the property package.
 constraint_tolerance
Tolerance for checking constraint convergence
 output_level
Set output level for logging messages
 solver
Solver to use for initialization
 solver_options
Dict of options to pass to solver
 calculate_variable_options
Dict of options to pass to calc_var_kwds argument in solve_strongly_connected_components method. NOTE: models involving ExternalFunctions must set ‘diff_mode=differentiate.Modes.reverse_numeric’
Config Block Documentation#
 class idaes.models.properties.activity_coeff_models.activity_coeff_prop_pack.ActivityCoeffParameterBlock(*args, **kwds)#
 Parameters:
rule (function) – A rule function or None. Default rule calls build().
concrete (bool) – If True, make this a toplevel model. Default  False.
ctype (class) –
Pyomo ctype of the block. Default  pyomo.environ.Block
Config args
 default_arguments
Default arguments to use with Property Package
 activity_coeff_model
Flag indicating the activity coefficient model to be used for the nonideal liquid, and thus corresponding constraints should be included, default  Ideal liquid. Valid values: { “NRTL”  Non Random Two Liquid Model, “Wilson”  Wilson Liquid Model,}
 state_vars
Flag indicating the choice for state variables to be used for the state block, and thus corresponding constraints should be included, default  FTPz Valid values: { “FTPx”  Total flow, Temperature, Pressure and Mole fraction, “FcTP”  Component flow, Temperature and Pressure}
 valid_phase
Flag indicating the valid phase for a given set of conditions, and thus corresponding constraints should be included, default  (“Vap”, “Liq”). Valid values: { “Liq”  Liquid only, “Vap”  Vapor only, (“Vap”, “Liq”)  Vaporliquid equilibrium, (“Liq”, “Vap”)  Vaporliquid equilibrium,}
initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries with config arguments as keys.
idx_map (function) – Function to take the index of a BlockData element and return the index in the initialize dict from which to read arguments. This can be provided to override the default behavior of matching the BlockData index exactly to the index in initialize.
 Returns:
(ActivityCoeffParameterBlock) New instance
 class idaes.models.properties.activity_coeff_models.activity_coeff_prop_pack.ActivityCoeffStateBlock(*args, **kwds)#
 Parameters:
rule (function) – A rule function or None. Default rule calls build().
concrete (bool) – If True, make this a toplevel model. Default  False.
ctype (class) –
Pyomo ctype of the block. Default  pyomo.environ.Block
Config args
 parameters
A reference to an instance of the Property Parameter Block associated with this property package.
 defined_state
Flag indicating whether the state should be considered fully defined, and thus whether constraints such as sum of mass/mole fractions should be included, default  False. Valid values: { True  state variables will be fully defined, False  state variables will not be fully defined.}
 has_phase_equilibrium
Flag indicating whether phase equilibrium constraints should be constructed in this state block, default  True. Valid values: { True  StateBlock should calculate phase equilibrium, False  StateBlock should not calculate phase equilibrium.}
initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries with config arguments as keys.
idx_map (function) – Function to take the index of a BlockData element and return the index in the initialize dict from which to read arguments. This can be provided to override the default behavior of matching the BlockData index exactly to the index in initialize.
 Returns:
(ActivityCoeffStateBlock) New instance
References#
“The properties of gases and liquids by Robert C. Reid”
“Perry’s Chemical Engineers Handbook by Robert H. Perry”.
H. Renon and J.M. Prausnitz, “Local compositions in thermodynamic excess functions for liquid mixtures.”, AIChE Journal Vol. 14, No.1, 1968.
AP Burgard, JP Eason, JC Eslick, JH Ghouse, A Lee, LT Biegler, DC Miller. “A Smooth, Square Flash Formulation for Equation Oriented Flowsheet Optimization”, Computer Aided Chemical Engineering 44, 871876, 2018