Modeling of equilibration times at high pressure for multicomponent vapor–liquid diffusional processes

Abstract

Isothermal multicomponent diffusion in a vapor–liquid system at high pressure is analyzed. It is assumed that there are no composition gradients in the bulk vapor due to mixing; diffusion takes place only in the liquid phase and in a thin film near the interface on the vapor side. This model is of value in the analysis of the supercritical drying of porous media and approach to phase equilibrium in a closed system at high pressure. The principle model used is the Fick's Law in one-dimensional form, which is a second order partial differential equation with respect to time and a spatial dimension. The change in the position of the interface is taken into account as an ordinary differential equation. The Fick diffusivities are estimated through the Maxwell–Stefan approach, which decouples the drag effects from the thermodynamic non-ideality effects. The model equations are solved using a fixed grid finite difference formulation. The effects of temperature, pressure, diameter to height ratio of the autoclave, mixing in the vapor phase, the starting mole fraction of the liquid and the initial liquid composition on the equilibration times and equilibrium compositions are analyzed. It is found that for uniform bulk vapor compositions, equilibration times are in the order of hours, while they increase at least one order of magnitude when there is no mixing in the vapor phase. Also, when the starting mole fraction of liquid increases, the equilibration times and the equilibrium position of the interface change significantly.