New Alpha Functions for the Peng-Robinson Cubic Equation of State.

Area of Science:

• Chemical Engineering
• Thermodynamics
• Physical Chemistry

Background:

• The alpha function significantly impacts the accuracy of cubic equations of state (EoS), particularly the attractive term.
• Accurate prediction of thermodynamic properties is crucial for chemical process design and optimization.

Purpose of the Study:

• To propose and evaluate four novel alpha functions for the Peng-Robinson (PR) equation of state.
• To assess the predictive capabilities of these new alpha functions for various thermodynamic properties of pure compounds.

Main Methods:

• Developed four new alpha functions (Alpha Function-1 to Alpha Function-4) for the Peng-Robinson (PR) EoS.
• Verified thermodynamic consistency of the proposed alpha functions and their derivatives.
• Predicted vapor pressure, enthalpy of vaporization, liquid volume, and liquid isobaric heat capacity for multiple compounds using the PR EoS with the new alpha functions.

Main Results:

• Alpha Function-4 achieved the lowest average relative deviation (ARD) for vapor pressure prediction (0.38%).
• Alpha Function-4 showed ARDs of 1.46% for enthalpy of vaporization, 7.54% for liquid volume, and 7.59% for liquid isobaric heat capacity.
• Three-parameter alpha functions outperformed two-parameter functions for vapor pressure and enthalpy of vaporization predictions.
• All tested alpha functions exhibited significant deviations in estimating liquid volume and isobaric heat capacity within the PR EoS framework.

Conclusions:

• The proposed alpha functions, especially Alpha Function-4, enhance the accuracy of the Peng-Robinson equation of state for predicting vapor pressure and enthalpy of vaporization.
• While improvements were noted, the accurate estimation of liquid volume and isobaric heat capacity remains a challenge for current alpha functions within the PR EoS.