PSRK

The PSRK equation of state ( Soave - Redlich predictive of English - Kwong equation of state) is an estimation method for the calculation of phase equilibria of mixtures of chemical substances. The original goal was to enable the properties of mixtures which contain over critical components. This class of materials could with the previously developed methods such as UNIFAC, to estimate the activity coefficients can not be calculated.

Principle

The PSRK equation is a group contribution equation of state, a class of estimation, combine the equations of state (usually cubic ) with activity coefficient models. The equation of state is used here for the calculation of the pure component properties, and activity coefficient model is used to describe the mixture properties. The method for calculation of mixture properties from the original used only for clean material properties models is called the rule of mixtures.

By using the PSRK - state equation all thermodynamic relations for constitutive equations can use that will allow, for example, densities, enthalpies, heat capacities, inter alia, m. to calculate.

Equations

PSRK equation of state is based on a combination of the equation of state of Soave - Redlich - Kwong ( SRK equation of state ) with a mixture rule whose parameters are determined by means of the group contribution method UNIFAC.

Equation of state

The Soave - Redlich - Kwong equation of state is:

The original used by Giorgio Soave α function is replaced by the function after Mathias - Copeman.

The parameters of the Mathias - Copeman equation are fitted to experimental saturated vapor pressure data of pure substances. This thus allows a significantly improved description of the saturation vapor pressure. The equation form was chosen because by setting the parameters c2 and c3 to zero again the result of the original Soave approach. In addition, the parameters c1 from the acentric factor can about the relationship

Be determined if no custom Mathias - Copeman parameters are available.

Mixing rule

The PSRK - mixing rule calculates the parameters a (cohesive pressure) and b ( covolume ) of the equation of state for the mixture

And

From the parameters ai and bi of pure substances whose mole fractions xi and the Gibbs excess Gibbs gE. The Gibbs excess Gibbs is calculated using a slightly modified UNIFAC model.

Model parameters

PSRK needed for the equation of state part of the critical temperature and the critical pressure and at least acentric factor. A higher quality can be achieved when the acentric factor is replaced by Mathias Copeman parameter. Mathias - Copeman parameters are adapted to saturated vapor pressure data.

The mixing rule used UNIFAC, which requires a number of UNIFAC - specific parameters. In addition to some model constants are the most important group interaction parameters, which are adjusted to vapor -liquid equilibria.

Experimental data ( pure component saturation vapor pressures and mixture vapor -liquid equilibria ) are thus for a high-quality parameterization to a greater extent necessary. These are usually made ​​of factual databases, such as the Dortmund Data Bank, available. In rare cases, directly required material data despite the associated high costs are determined experimentally, if for no other sources of phase equilibrium data can be found.

The latest available parameters were published in 2005. The further development of the model took over the UNIFAC consortium.

Example calculation

The prediction of a vapor-liquid equilibrium is possible also in mixtures, in which on critical components are included.

The mixture itself, however, must be subcritical. In the example, the carbon dioxide is the supercritical component with Tc = 304.19 K and Pc = 7.475 kPa. The critical point of the mixture is 15 MPa at T = 411 K and P ≈. The composition of the mixture is about 78 mole percent carbon dioxide and 22 mole percent cyclohexane.

PSRK describes this binary mixture in a very good quality, both boiling and Taukurve and also the critical point of the mixture are well taken.

Weaknesses in the model

In a follow-up work PSRK some weaknesses in the model are listed below:

• The course of the α - function for Mathias - Copeman is in the extrapolation to high temperatures without physical basis.
• Although the Soave - Redlich - Kwong equation describes the vapor densities of pure substances and mixtures quite well, but that of the liquid phase only bad.
• In the prediction of vapor -liquid equilibria of mixtures in which the components are of significantly different sizes ( as ethanol, C2H6O, and eicosane, C20H44 ), there is a larger systematic errors.
• Heats of mixing and activity coefficients at infinite dilution are poorly reproduced.