# PENG ROBINSON CUBIC EQUATION OF STATE

EQ-COMP uses Peng-Robinson equation  to calculate multicomponent vapor-liquid equilibrium properties automatically at the click of a button. EQ-COMP  is a complex combination of macros written in MS Excel using Visual Basic for Application programming language. Peng-Robinson cubic equation state is the preferred equation for calculating vapor-liquid equilibrium properties for non-polar and mildly polar hydrocarbons

The Peng-Robinson Equation of State was developed in 1976 in order to satisfy the following goals

1. The parameters of state should be expressible in terms of the critical properties and the acentric factor.

2. The model should provide reasonable accuracy near the critical point, particularly for calculations of the compressibility factor and liquid density.

3. The mixing rules should not employ more than a single binary interaction parameter, which should be independent of temperature, pressure and composition.

4. The equation of state should be applicable to all calculations of all fluid properties in natural gas processes.

For the most part, the Peng-Robinson Cubic Equation of State exhibits performance similar to the Soave equation, although it is generally superior in predicting the liquid densities of many materials, especially non-polar ones.

The Peng-Robinson Cubic Equation of State is given below:

In polynomial form:

where, w is the acentric factor of the species and R is the universal gas constant.

Van der Waals mixing rule is applied for mixtures and mixture parameters are calculated as given below

Where: a and b = the interaction energy and molecular size parameters for the mixture

ai, bi = a and b parameters for component i in the mixture
xi = composition (mol fraction) for component i in the mixture
kij = binary interaction parameter
n = number of component in the mixture

A common correlation to estimate the binary interaction parameter is used which is given below:

In the above equation, νci and νcj represent the critical volumes of components i and j, respectively.

The default value of exponent n is normally set to 1.2 but it can be used as a tuning parameter to match the experimentally measured dew point.

EQ-COMP software uses modified version of Peng-Robinson cubic equation of state given in 1978.

Apart from the constant values of binary interaction parameters derived using critical volumes of interacting components given above, EQ-COMP can include any other binary interaction parameters in its calculations in case the same are provided by the user. EQ-COMP can also include temperature dependent binary interaction parameters as per Predictive Peng Robinson 78 (PPR 78) equation given by Dr. Jaubert and his colleagues in its calculations. These parameters are supposed to increase the accuracy of prediction of VLE properties over constant parameters or no use of parameters. Temperature dependent binary interaction parameters are used in EQ-COMP to calculate water dew point temperature values where it provides accurate results comparable to CPA (cubic plus association) equation of state. Further EQ-COMP uses statistical thermodynamic model for clathrates  developed by Van der Waals and Platteeuw in 1959 to predict hydrate dissociation curve for hydrocarbon mixtures.

The results of various VLE calculators of EQ-COMP software calculated using Peng-Robinson cubic equation of state can be requested from VLE CALCULATOR page.