Straightforward computation of loci of local extrema of fluid-fluid equilibria for binary mixtures

J. I. RAMELLO; M. CISMONDI; M. S. ZABALOY

Uberlandia

Congreso; VII Congresso Brasileiro de Termodinâmica Aplicada (CBTermo 2013); 2013

UFU

The cricondenbar (CCB) and cricondentherm (CCT) points are important key points for the characterization of a multicomponent or binary mixture of given overall composition. The CCB is the maximum pressure at which the mixture can be heterogeneous. Analogously, the CCT is the maximum temperature at which the mixture can be heterogeneous. A mixture isopleth is made of the phase envelope and of the heterogeneous region. Both, the CCB and CCT points, belong to the phase envelope of the isopleth. For a binary mixture, a locus of, e.g., CCB points, can be generated by computing a number of phase equilibrium isopleths within a given composition range. This requires, however, to search for the CCB point for each calculated isopleth. In this work we show that it is possible to directly compute, in a single run, a full CCB (or CCT) locus avoiding the computation of isopleths. For that, we first obtain, through implicit differentiation, the mathematical conditions valid at a CCB (and/or CCT) point. Next, we solve such conditions in a composition range by resorting to a numerical continuation method (NCMs). NCMs are the methods of choice for the straightforward computation of highly non-linear lines, which are made of points defined by several coordinates. CCB and CCT loci are characteristic lines of binary systems. These lines can be plotted together with critical lines, azeotropic lines and liquid-liquid-vapor lines, to more completely characterize the behavior of a binary system as represented by a model of the equation of state type, at set values for the model parameters. We present calculated CCB and CCT loci for systems of type I and III in the classification of van Konynenburg and Scott. The mathematical CCB and CCT conditions considered in this work are those of local extrema (not just local maxima). In other words, the CCB and CCT conditions in this work encompass a wider range of situations than the conventional CCB and CCT definitions.