Fluid Phase Equilibria 330 (2012) 24–35 Contents lists available at SciVerse ScienceDirect Fluid Phase Equilibria j o ur nal homep age: www.elsevier.com/locate/fluid The iPRSV equation of state T.P. van der Stelt a,∗ , N.R. Nannan b , P. Colonna a a Process and Energy Department, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands b Mechanical Engineering Discipline, Anton de Kom University of Suriname, Leysweg 86, PO Box 9212, Paramaribo, Suriname a r t i c l e i n f o Article history: Received 3 April 2012 Received in revised form 5 June 2012 Accepted 9 June 2012 Available online 21 June 2012 Keywords: Equation of state Peng–Robinson PRSV ˛-Function Discontinuity iPRSV a b s t r a c t The Peng–Robinson cubic equation of state with the Stryjek–Vera modification (PRSV) is widely adopted in scientific studies and engineering. However, it is affected by a discontinuity in all the properties, which is caused by a discontinuity of the ˛-function. Aside of being non-physical, this discontinuity causes robustness and accuracy issues in numerical simulations. The discontinuity in thermodynamic proper- ties is eliminated here without affecting the overall accuracy of the model. In addition, the functional form of ˛(T) is optimized in such a way that it is not required to change the values of the fluid-dependent parameters stored in the many available databases. The performance of the improved equation of state (iPRSV) is assessed by comparing calculated properties with those obtained with the original PRSV equa- tion of state, the Gasem et al. equation of state (PRG), which is also continuous in temperature, a reference multiparameter equation of state, and experimental data. It is shown that the accuracy of the new model approaches the accuracy of the original equation of state and that it performs better than the PRG equa- tion of state. The modified PRSV equation of state solves the issue of the artificial discontinuity in the calculation of properties relevant to scientific and industrial applications, at the cost of a small decrease in overall accuracy. © 2012 Elsevier B.V. All rights reserved. 1. Introduction In order to obtain a better correlation of vapor pressures for a wide variety of fluids, Stryjek and Vera [1,2] proposed to use the Peng-Robinson [4] cubic equation of state (EoS), com- plemented by the Soave [3] ˛-function, but with a different temperature and acentric factor dependence. However, as a result, the Peng–Robinson EoS with the Stryjek–Vera modification (PRSV) features a discontinuity in all the properties in correspondence of the absolute critical temperature, T c , of water and of alcohols, and at T = 0.7 · T c for other fluids. Over the last few decades, numerous modifications to the ˛- function of Soave have been proposed, most of them with the aim of obtaining a more accurate estimate of the pure-compound vapor pressure. In particular, better performance has been sought for reduced temperatures, T r ≡ T/T c , lower than 0.7, for substances with an acentric factor ω greater than 0.5, and for polar fluids like alcohols. Some of the proposed modifications accomplish this goal by introducing one or more component-dependent parame- ters [1,2,5,6]. Other modifications involve changing the functional form of ˛ in terms of either ω or T r , or both. The ˛-function depen- dency can be either linear [7], exponential [8], quadratic [6], or a combination of the aforementioned [5,9]. ∗ Corresponding author. Tel.: +31 15 2785412. E-mail address: T.P.vanderStelt@TUDelft.nl (T.P. van der Stelt). Because in most cases the proposed modifications are aimed at improving only vapor–pressure predictions, merely a handful of researchers investigated the effect of their proposed modifi- cation of the ˛-function on the prediction of all thermodynamic properties, especially those dependent upon first or higher-order derivatives of ˛ in the supercritical region. A number of thermodynamic models [1,7,9] suffer from the reliance on the use of switching functions below and above the critical temperature. These switching functions can cause large dis- continuities in the ˛-function and its derivatives. Gasem et al. [8] addressed the problem of switching functions and proposed an exponential and continuous ˛-function. They determined the first and second-order derivative of the ˛-function with respect to the temperature and compared values of heat capacities predicted by their model with experimental data, for temperatures spanning the range from T r ≈ 0.5 up to values well above the critical point tem- perature for methane and nitrogen, and up to T r = 1.14 for propane. They obtained a significant improvement of the predicted heat capacities with respect to the results from earlier models [3,5,7]. Neau et al. [10,11] analyzed in detail the influence of the functional relation of the EoS and the first and second-order temperature derivatives of the ˛-function on the modeling of enthalpies and heat capacities for reduced temperatures as high as about 3.5. They found that the second-order temperature derivative of the general- ized models for ˛ of Twu et al. [7] and Boston and Mathias [12] also features abnormal extrema and inconsistent break points at the critical temperature, due to the use of different sets of parameters 0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2012.06.007