(352n) Approximate Density-Based Phase Envelope Construction Including Capillary Pressure

Phase equilibrium including capillarity effects became a hot topic in the last few years. The phase envelopes of confined fluids are modified by the capillary pressure induced by highly curved interfaces; the bubble point pressures are suppressed and the dew point locus is expanded, with an increase of the cricondentherm temperature. Moreover, if geometrical confinement is taken into account, the critical points are displaced and the phase envelopes are shrinking.

In this work, a recently proposed approximate density-based phase envelope construction method (Nichita, Fluid Phase Equilib. 499, 112245, 2019) is adapted to account for capillary and geometrical confinement effects. A reduced system of only three equations (as in the bulk fluid case) must be solved for three variables (temperature and molar densities of feed and incipient phase) to trace the phase envelope in the molar density-temperature plane; the pressure is calculated explicitly from the equation of state (EoS). The EoS must not be solved for volume and a simple scaling equation relates approximate incipient phase compositions to the exact composition at some reference conditions (which are updated along the phase envelope with no additional computational cost).The additional partial derivatives of capillary terms have very simple expressions due to the form of the interfacial tension model (explicit in molar density). Geometrical confinement is considered by altering pure component critical properties. The new method is easy to implement, by adding the capillary terms to the Jacobian matrix and residual functions to the bulk fluid formulation and it is not dependent of the thermodynamic model. Simple equations allow the calculation of maximum temperature and pressure conditions.

The proposed method was applied to various hydrocarbon mixtures, ranging from lean gases to heavy oils and the entire phase boundary is remarkably well reproduced in all cases (with very small absolute deviations of approximate saturation pressures at fixed temperature). The computational procedure proved to be robust, smoothly crossing the critical region (where interfacial tensions are very low) and unproblematic even at very large capillary pressures (of the order of hundreds bar in some test examples) and at important negative pressures (the latter case cannot be handled by conventional pressure-based approaches).