Calculation of complex phase equilibrium isotherms in ternary systems

PISONI, G. O.; CISMONDI DUARTE, M.; CARDOZO-FILHO, L.; ZABALOY, M.

Alicante

Conferencia; EQUIFASE 2015: X Conferencia Iberoamericana sobre Equilibrio entre Fases para el Diseño de Procesos; 2015

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.