Point to point detection of solid-fluid retrograde melting within computed segments of binary solid-fluid equilibrium isopleth envelopes

S.B. RODRIGUEZ-REARTES; MARTÍN CISMONDI; MARCELO S ZABALOY

Puerto Varas

Conferencia; IX Iberoamerican Conference on Phase Equilibria and Fluid Properties for Process Design; 2012

Universidad de Concepción

The phenomenon of retrograde melting at constant temperature takes place when a solid phase is melted upon compression. Analogously, retrograde melting at constant pressure happens when a solid phase is melted upon cooling. In this work, we propose a test that makes possible to establish for a calculated, already converged, binary solid-fluid equilibrium (SFE) point (of temperature TSFE, pressure PSFE, and fluid phase composition z2.), whether the behavior is normal or retrograde and, in case of retrograde behavior, whether the solidification is retrograde with respect to temperature, or to pressure, or to both. The test consists of evaluating, at TSFE and PSFE, the derivatives of the reduced tangent plane distance (tpd) with respect to temperature (dtpd∗/ dT|P,z2 )SFE and pressure (dtpd∗/ dP|T,z2 )SFE , for a tested phase of composition z2, and a trial phase consisting of the pure heavy component in solid state at TSFE and PSFE. The distinguishing feature of the present test is that the derivatives (dtpd∗/ dT|P,z2 )SFE and (dtpd∗/ dP|T,z2 )SFE are evaluated explicitly from the already converged SFE point, i.e., the present test does not require additional iterative calculations. Consequently, the test is fast and can be used for all points of a calculated SFE segment of an isopleth envelope. This leads to the eventual identification of points along the computed SFE segment where transitions from retrograde to normal behavior occur. We present results for a couple of highly asymmetric systems with the help of a model that uses an equation of state for describing the fluid phases, and a standard equation for describing the fugacity of the pure heavy component as a function of temperature and pressure.