Test for the detection of the retrograde melting phenomenon in computed solid–fluid equilibria of binary asymmetric systems

• Previous criteria for retrograde melting lack general validity.
• Test based on tangent plane distance proposed for detecting retrograde melting (RM).
• Test applied on the boundary between solid–fluid and homogeneous fluid regions.
• Two test types: RM at constant temperature; RM at constant pressure.
• Test applicable to any equation of state.

The phenomenon of retrograde melting at constant temperature takes place when a solid phase is melted, or made to disappear, upon compression. Analogously, retrograde melting at constant pressure happens when a solid phase is melted, or made to disappear, 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 regular or retrograde and, in case of retrograde behavior, whether the melting phenomenon is retrograde with respect to temperature, or to pressure, or to both. The test is based on evaluating, at TSFE and PSFE, the derivatives of the reduced tangent plane distance (tpd  ) with respect to temperature (dtpd*/dT|P,z2)SFE(dtpd*/dT|P,z2)SFE and pressure (dtpd*/dP|T,z2)SFE(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(dtpd*/dT|P,z2)SFE and (dtpd*/dP|T,z2)SFE(dtpd*/dP|T,z2)SFE are evaluated explicitly from the already converged SFE point, i.e., the present test does not require the computation of additional SFE points. 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 regular 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.

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