SAFT; unbonded sites; compressibility roots; surfactant
Equations of states are used to model fluid behavior. At a given temperature and pressure, for example, a mixture of water and alcohol might form a liquid and vapor phase, with the vapor phase being richer in alcohol and the liquid phase richer in water. In many industrial processes, such as distillation or extraction where mixtures of different compounds need to be separated, knowing how the fluid mixture will behave at various conditions helps make the operations more efficient and economical. While many equations of state exist, they differ in their accuracy in modeling systems and in their mathematical complexity. In particular, the Statistical Association Fluid Theory (SAFT) equation is a model that holds great promise as a predictive model because of its basis in statistical mechanics. Unlike many other equations of state, it is able to account for non-spherical shaped molecules, attraction and repulsion between molecules and site-site interactions. But while it has been able to successfully model a wide range of fluid systems where other models have failed, the SAFT equation is also mathematically complicated. This work focuses on the numerical difficulties and issues that arise in using the SAFT equation, and how they can be resolved. Numerical difficulties encountered in calculation of compressibility roots, mole fraction of unbonded sites, partial derivatives of the association term, and phase equilibria are addressed. Implications of simplifying assumptions about association strengths on different sites are also discussed. From the work done, it has been found that strategies making use of physically sound quantities in the SAFT model were successful in overcoming computational difficulties, which supports the predictive capabilities of the model. Current work is thus aimed at using the SAFT equation to model more complicated fluids, such as self-assembling surfactant systems, where it is expected that correct use of the sound physical basis of the model will lead to accurate results.