(321e) Describing the Global Thermodynamic Properties of Chain Fluids Using a Crossover Perturbed-Chain Statistical Associating Fluid Theory

The true thermodynamic behavior in the critical region is a consequence of long-range density fluctuations. Classical equations of state perform well in the regime where the correlation length is small (far from the critical region), where only correlations between a few molecules make significant contributions to the free energy. However, as the critical point is approached, the correlation length increases and larger numbers of molecules make significant contributions to the free energy. Here, the large correlation lengths imply that the system is not homogenous near the critical point and the long-wavelength density fluctuations become important. Most mean-field theories are not capable of accurately describing correlations between large numbers of molecules. As a result, long-wavelength density fluctuations are neglected, providing reason why these classical equations fail near the critical point.

The development of an equation of state that is accurate in describing thermodynamic properties of fluids both near to and far from the critical region is of much interest in the chemical industry. Technology within industry that utilizes such information includes separation processes where critical conditions are encountered. Such processes are encountered in natural gas and gas-condensates production, for supercritical extraction and fractionation of petroleum. In this work, the perturbed-chain statistical associating theory (PC-SAFT) equation of state is extended to include a crossover treatment that accounts for these long-wavelength density fluctuations. Here the crossover PC-SAFT provides the needed corrections due to density fluctuations as the critical point is approached, and reduces to the original equation of state far from the critical region. This method is based on the renormalization group work by White [Fluid Phase Equilib. 75, 53 (1992); J. Chem. Phys. 96, 4559 (1992)]. The advantage of White's method is the addition of only a few parameters, thereby making the theory more meaningful physically and more predictable than other scaling techniques. Results for the pure n-alkane family are in excellent agreement with experimental vapor-liquid equilibrium data. The scaling parameters follow trends with molecular weight, thereby providing the ability to extrapolate the parameters for heavier n-alkanes.