COMPUTING AZEOTROPES IN MULTICOMPONENT MIXTURES

The problem of computing the temperatures and compositions of all azeo tropes predicted by thermodynamic models for nonideal, multicomponent mixtures can be formulated as a multi-dimensional root-finding problem . This problem is complicated by the presence of multiple solutions, c onstraints on the compositions and the complexity of realistic vapor-l iquid equilibrium descriptions. We describe a homotopy method which, t ogether with an arc length continuation, gives an efficient and robust scheme for finding solutions. The homotopy begins with a hypothetical ideal mixture described by Raoult's Law for which all of the solution s to the problem are known trivially, since they are simply the pure c omponents. There are as many solution branches for the homotopy as the re are pure components, and one or more of the branches shows a bifurc ation when azeotropes are present in the mixture. Solutions for the az eotropes are found from the limiting behavior of the homotopy and we s how that azeotropes containing c components can be found from a series of c-1 bifurcations in the solution branches of lower dimensions. The re is no restriction on the dimension of the problems other than the a vailability of an accurate thermodynamic model; examples containing up to five components are described.