Using the Method of Referred Derivatives to simulate the dynamics of systems in vapour-liquid equilibrium

Abstract

Two-phase systems in vapour-liquid equilibrium are common features of chemical and power plant and have the characteristic that the vapour and liquid temperatures equalise very quickly compared with the response speed of the rest of the plant. It is normal for the control modeller to assume the equalisation process is instantaneous, which leads to a set of nonlinear simultaneous equations, making such systems candidates for the Method of Referred Derivatives. The paper describes how this technique provides a framework for calculating directly the evaporation or condensation rates needed to keep the two phases in equilibrium. The mass and temperature derivatives may then be found and integrated numerically in a straightforward time-marching manner to trace the transient behaviour of the system. The paper considers both single component and multicomponent boiling and condensing, and, in an appendix, offers advice on suitable forms of thermodynamic functions for use with the method.