Phase equilibrium with external fields: Application to confined fluids

This work addresses the problem of finding the equilibrium spatial segregation of components in systems that have multiple regions, each of them subject to the effect of external fields. The specifications are the temperature, region volumes, component amounts, and additional variables that characterize the effect of such fields. The formulation leads to the mathematical problem of minimizing the Helmholtz energy of the system, subject to constraints that represent component mass balances and volume conservation equations applied to each region. Among other uses, the approach is suitable for determining the equilibrium conditions in batch adsorption. The formulation is general but the focus of this work is on the compositional segregation in isothermal reservoirs due to gravity and the spatial segregation of components close to pore walls. Calculations using the Steele and DRA potentials to model fluid-wall interactions demonstrate the formulation, and its solution procedure provides results that are generally in very good agreement with experimental data and simulations reported in the literature. The formulation enables the prediction of meaningful trends for local composition profiles for fluids inside pores, at a coarser level than those from molecular simulations, but with much smaller computational load.