INVESTIGADORES
ZABALOY Marcelo Santiago
congresos y reuniones científicas
Título:
A strategy for the computation of complete lines of three-phase equilibria of ternary fluid systems
Autor/es:
G. PISONI; A. BEL; R. COBIAGA; M. CISMONDI; W. REARTES; M.S. ZABALOY
Lugar:
Uberlandia
Reunión:
Congreso; VII Congresso Brasileiro de Termodinâmica Aplicada (CBTermo 2013); 2013
Institución organizadora:
UFU
Resumen:
For ternary fluid systems, a line of three-phase equilibria at, e.g., set temperature or set pressure, provides key information on the phase behavior of the system of interest. A given ternary three-phase line (T-3PL) belongs to a ternary three-phase surface (T-3PS). Possible boundaries of a T-3PS are ternary four-phase equilibrium lines (T-4PLs), ternary critical end lines (T-CELs) and binary three-phase equilibrium lines (B-3PLs). A T-3PS can indefinitely extend towards low temperatures and pressures. In this work, we propose a strategy for computing ternary three-phase equilibrium lines (T-3PLs) applicable when a model is chosen and its parameter values are set. Once a temperature value (or pressure value) is set, the key points of the T-3PL to be computed are obtained from previously computed T-4PLs, T-CELs and B-3PLs. Next, a first point of the T-3PL is calculated by using the Newton-Raphson method. Such first point is initialized in a way that depends on the nature of the key point of the T-3PL which is closest to the mentioned first point. Once the first three-phase equilibrium point is converged, the rest of the T-3PL is computed by applying a numerical continuation method (NCM). Actually, a T-3PL is a line that develops in a multidimensional space, where the variables are pressure, temperature, phase densities and mole fractions of the components of the ternary system. NCMs are able to compute highly nonlinear multi-dimensional lines, throughout their whole domain of existence, in a single run. NCMs thus minimize the need for user intervention. We used two different NCMs in this work. The first one (NCM1), as done in other recent works, makes use, for computing the next point belonging to the T-3PL being built, of a sensitivity vector useful (a) to predict the solution of the three-phase equilibrium system of equations and, (b) to identify the optimum variable to be specified when solving it. We have implemented the NCM1 with the help of a symbolic computation software package. The second NCM used in this work (NCM2) is one of those available in the standard software MatCont (http://www.matcont.ugent.be). We have considered in this work models of the equation of state type over wide ranges of conditions. The ternary systems here studied are highly asymmetric. The resort to known key points makes possible to avoid the use of stability tests when computing T-3PLs.