A simple approximate density-based phase envelope construction method

Abstract

Abstract A new simple density-based method is proposed for approximate phase envelope construction of constant composition multicomponent mixtures. The phase envelope is traced in the molar density-temperature plane (with a unique saturation temperature at given mixture molar density) and the pressure is calculated explicitly from the equation of state (EoS). The computational procedure is very easy to implement and a reduced system of only three equations must be solved for three variables (molar densities of feed and incipient phases and temperature), irrespective of the number of components in the mixture. The EoS must not be solved for volume and the elements of the Jacobian matrix have simple forms; the partial derivatives of fugacity coefficients with respect to compositions are not required. A simple and computationally inexpensive correction procedure highly improves results by updating the reference conditions at each point on the phase envelope. Simple equations for calculation of maximum temperature and pressure points are presented. The proposed method was tested for a variety of mixtures, ranging from natural gases to heavy oils, using a general form of two-parameter cubic EoS. For usual (closed) phase envelopes, the entire phase boundary is remarkably well reproduced. Certain unusual (open-shaped, with a bubble point branch extending to infinity) phase envelopes are also entirely traced up to very high pressures, while in certain cases the method fails at low temperatures (where the approximation of equilibrium constants becomes inadequate), but provides an excellent approximation for a wide temperature range. The proposed method is not dependent of the thermodynamic model (any pressure-explicit EoS can be used), it is recommended for mixtures with many components and it may be particularly attractive for complex EoS.