Development of an equation of state based on thermodynamic perturbation theory (TPT) for mixtures prone to asphaltene precipitation (2021)
We use the molecular theory of liquids to review the Perturbed Chain-Statistical Association Fluid Theory Equation of State (PC-SAFT EoS) and formulate new dispersive and repulsive terms for this model. As a well-known fact in the literature, the original PC-SAFT normally predicts accelerated asphaltene onset pressures (AOPs) in petroleum reservoir fluids and cloud points (CPs) in polymeric systems at low temperatures. This phenomenon was studied in this thesis. Thermodynamic perturbation theories (TPTs) and integral equation theory (IET) are central. By combining these theories, we formulate several effective diameter expressions dependent upon temperature and density to replace the original effective diameter of PC-SAFT, which depends on temperature only. Barker and Henderson´s second-order dispersion term based upon a concept of correlated shells of fluids was introduced into PC-SAFT and its effect was studied, especially at low temperatures. Both the new effective diameters formulated, and the modified second-order dispersion term produce less accelerated AOPs and CPs curves at low temperatures. The original universal constants (called here as GSUCs) in the attractive part PC-SAFT were also analyzed in this work. The main conclusion is that GSUCs should not be used at all, and the set of these constants presented by Liang and Kontogeorgies (LKUCs) are preferred instead. In fact, LKUCs not only correct the defect of PC-SAFT of predicting multiple density roots at low temperatures but also reduces the tendency of PC-SAFT of predicting accelerated AOP and CP curves at low temperatures. The PC-SAFT predictions of HAOP loci at very high pressures were also studied. New phase diagrams at low temperatures are presented in this work. HAOPs are displaced at very low temperatures when the modified second-order dispersion term is used or when the LKUCs are combined with the temperature- and density-dependent effective diameters presented in this thesis. Unfortunately, these HAOPs are not possible of being experimentally tested. Nonetheless, the high densities at which these HAOPs are predicted by the original PC-SAFT represent non-isotropic conditions. Under those conditions, the TPTs for fluids lose validity. The combination of the LKUCs and the temperature-and density-dependent effective diameters presented in this thesis substantially increases the isotropic range, allowing a most robust use of the TPTs, and then of PC-SAFT. The failure of the original PC-SAFT to predict coherent Amagat curves is also amply studied. As a result, the failure was found to be directly related to the soft-core repulsion included in PC-SAFT by the effective diameter. Intermolecular potentials as the square well square shoulder (SWSS) are not “soft” enough to correctly predict these curves. Then, we demonstrate in this dissertation that intermolecular potentials soft enough, like Lennard-Jones one, need to be introduced.