INVESTIGADORES
CISMONDI DUARTE Martin
congresos y reuniones científicas
Título:
Calculation of complex phase equilibrium isotherms in ternary systems
Autor/es:
PISONI, G. O.; CISMONDI DUARTE, M.; CARDOZO-FILHO, L.; ZABALOY, M.
Lugar:
Alicante
Reunión:
Conferencia; EQUIFASE 2015: X Conferencia Iberoamericana sobre Equilibrio entre Fases para el Diseño de Procesos; 2015
Resumen:
Ref [1] describes an approach for computing binary (phase equilibrium) Txy and Pxy diagrams using, as starting point, information on previously computed univariant lines: critical and three-phase lines, and pure compound vapor pressure curves. Key points, relevant to the set temperature (or set pressure), are obtained from such lines. The key points are the limits of the isothermal (or isobaric) equilibrium phase envelope/envelopes, and/or the limits between the segments (liquid-liquid or vaporliquid) that make a phase envelope up. In such approach [1], the use of stability tests is minimized. In this work, an analogous methodology is tested for the case of ternary systems held at constant temperature [ternary isotherm (TI)]. First, key points are obtained, and then proper phase equilibrium lines are computed. The goal is to test the performance of the methodology for a case of particularly complex ternary phase behavior.Key Points in Ternary Phase Equilibrium Isotherms We understand by TI a set of ternary equilibrium objects whose variables have values which become defined once the temperature and some other intensive variable (e.g., pressure) are specified (divariant objects). Thus, e.g., a ternary two-phase equilibrium does not contribute to a TI because it requires three specifications rather than two. To obtain the key points of a TI, the system?s phase equilibrium Ternary Characteristic Map (T-CM) [2, 3] has to be known. Ref [2] presents a methodology for computing T-CMs. Examples of ternary univariant lines (T-ULs) that contribute to the T-CM are ternary critical end lines (T-CELs) and ternary four-phase equilibrium lines (T-4PLs). The TI keypoints are found by searching, along every T-UL (and also along binary and unary ULs), for the points at which the temperature equals that of the TI, i.e., by intersecting a constant temperature line (or plane) with all univariant lines of the already computed T-CM. It should be clear that once the temperature of the TI is set, then, the key points become defined. The TI key points (from which it is possible to start off the construction of the lines, or hyper-lines, that make a TI up) are, e.g., Binary Critical Points (B-CPs), Ternary Critical end Points (T-CEPs) and Ternary Four Phase Points (T-4PPs). Eventually, the TI could also contain invariant points, such as a ternary tricritical point (TTCP). A known computed key point is used to produce a first converged point of a given line, such as Ternary Three Phase Lines (T-3PL) and Ternary Critical Lines (T-CL). Next, the line is computed using a numerical continuation method [2]. A line may be limited by two endpoints, or it may have a single endpoint and extend indefinitely towards either high or low pressures.