Development of A Thermodynamically-Consistent Alpha Function for the Patel-Teja-Valderrama Equation of State

Abstract—A new, four-parameter alpha function with thermodynamically consistent parameter values is developed for predicting vapor pressures using the Patel-Teja-Valderrama equation of state. The form of the alpha function was derived by keeping in mind the thermodynamic consistency rules as provided by the limiting conditions in the determination of the generalized parameters in a generic cubic equation of state. Using MATLAB, codes executing a nonlinear program that would minimize errors between DIPPR-estimated vapor pressures between the triple point until the critical point from the alpha function’s vapor pressure prediction has been developed. Thermodynamically consistent parameters were calculated by setting up nonlinear constraints for the derivatives, assuring a monotonically decreasing behavior for the function. The performance of the model was compared with five other models commonly used in industries and process simulation programs and is found to provide better accuracy in comparison when working with polar fluids. Further, its performance is found to be comparable to some models when estimating nonpolar and light fluids. The statistical analyses used to verify the performance of the model in comparison with the other models used in literature include the calculation of the r-squared, adjusted r-squared, predicted r-squared, absolute average deviation, root mean square errors, and by visual inspection. The study also included the determination of thermodynamically consistent parameter values for twenty different fluids commonly used in process simulations.