Equilibrium Calculations

Internal TEA equilibrium calculations

The only internal equilibrium calculation (or flash calculation) method supported is the VLE equilibrium method. The VLE equilibrium method only calculates vapor-liquid equilibria.

The logFugacityCoefficient property must be present and configured if the VLE equilibrium model is selected.

To calculate an equilibrium, the following CAPE-OPEN version 1.0 specifications are supported:

• TP: pressure and temperature must be specified
• TVF: temperature and vapor fraction must be specified
• PVF: pressure and vapor fraction must be specified
• PH: pressure and enthalpy must be specified
• TH: temperature and enthalpy must be specified
• HVF: enthalpy and vapor fraction must be specified
• PS: pressure and entropy must be specified
• TS: temperature and entropy must be specified
• SVF: entropy and vapor fraction must be specified
• PHF: pressure and enthalpyF must be specified
• THF: temperature and enthalpyF must be specified
• HFVF: enthalpyF and vapor fraction must be specified
• PSF: pressure and entropyF must be specified
• TSF: temperature and entropyF must be specified
• SFVF: entropyF and vapor fraction must be specified
• PU: pressure and internal energy must be specified
• TU: temperature and internal energy must be specified
• UVF: internal energy and vapor fraction must be specified

The reversed specifiers are also supported, e.g. PT, VFT, VFP, HP, HT, VFH, SP, ST, VFS, HFP, HFT, VFHF, SFP, SFT, VFSF, UP, UT and VFU.

Note: no additional flash types are currently supported for enthalpyNF and entropyNF. However, the internal VL equilibrium server will be able to calculate equilibria involving these properties when using version 1.1 thermo, when using internal calculation routines for properties enthalpyNF and entropyNF

For CAPE-OPEN version 1.1, all combinations of specifications equivalent to the above are supported. For the equilibrium type argument, only 'Unspecified' is currently supported.

Numeric details of the VLE equilibrium server

Primary calculations

Most of the equilibrium calculations are first attempted with the inside-out flash algorithms, based on:

• Boston and Britt, "A radically different formulation and solution of the single-stage flash problem", Computers and chemical engineering, vol 2 pp 109-122 (1978)
• Parekh and Mathias, "Efficient flash calculations for chemical process design - extension to the Boston-Britt Inside-Out flash algorithm to extreme conditions and new flash types", Computers and chemical engineering, vol 22 pp 1371-1380 (1998)

If the primary calculation method fails, a backup calculation method will be attempted.

Backup calculation method

The backup method of calculation equilibria is based on a full Newton approach to solving all equilibrium equations simultaneously. On the Options page of the property package configuration, one can select either of the following initialization methods:

• None: initialization uses the Wilson Ideal Solution model for K-values, but no iteration is performed. The Wilson Ideal Solution model:
  
• Wilson Ideal Solution Model: initialization uses the Wilson Ideal Solution model for K-values. The equilibrium is first calculated using K-values with the Wilson model, and then with the actually selected models.
• Saturated Vapor Pressures: initialization uses the K-values based on:
  
  When using the backup methods, the equilibrium is first calculated using these K-values, and then with the actually selected models.
  The backup equilibrium calculation is not used if the mixture contains solid-only compounds or if mass-based vapor fraction is part of the flash constraints.

For the backup equilibrium calculation methods, during calculations with estimation of K-values, simplified models for enthalpies and entropies calculations are used for phases that use a cubic equation of state.

For enthalpy, the Ideal Enthalpy model is used. For entropy, the Ideal Entropy model is used. In both cases, a default model is applied for the liquid heat capacity and heat of vaporization.

Cubic equations of state and pseudo properties

When using cubic equations of state, and when evaluating properties of a phase outside of its region of existence, properties are returned that belong to the other phase. I.e. gas phase properties are returned for the liquid phase in regions where liquid does not exist and vice versa. This may lead to equilibrium calculation divergence or to invalid trivial solutions.

To prevent this from happening, cubic equations can return pseudo property values for these regions. These pseudos properties (enabled by default) can be turned on or off from the property package configuration window, on the Options page.

The pseudo property calculations for cubic equations of state are only applied during:

• equilibrium calculations performed by an external equilibrium routine
• equilibrium calculations performed by the internal equilibrium routine in case of multiple compounds

External equilibrium calculations

TEA supports loading a CAPE-OPEN version 1.1 stand-alone ICapeThermoEquilibriumRoutine, or a CAPE-OPEN version 1.1 property package (stand-alone or from a property package manager) as equilibrium calculation server. To do so, click Import on the Equilibrium page of the property package configuration window.

All phases exported by the equilibrium routine will be exported by TEA. Only one vapor phase is allowed. Internal TEA phase identifiers will be mapped to those as exported by the external routine on each call.

All TEA compounds must be known by the external routine. If the external routine does not export compounds, all compounds are assumed to be known. If it does export compounds, compounds will automatically be mapped between TEA internal names and those as exported by the external routine, at each call.

If the object selected as external equilibrium calculation routine exports properties as well, these property calculations can be selected by using calculation routine "Equilibrium server". This is subsequently the default routine for all properties supported by the external routine.

Phase identifiers

When using internal or external equilibrium calculations, the exported identifiers can be modified. Select a phase on the Equilibrium page, and click the Rename button. If the property package that you are modifying will ever be used using the CAPE-OPEN version 1.0 standard, it is advised to name the vapor phase "Vapor", the liquid phases "Liquid", "Liquid1", etc, and the solid phases "Solid", "Solid1", etc. The only phase identifiers officially supported by the CAPE-OPEN version 1.0 standard are "Vapor", "Liquid" and "Solid".