COMPUTING AZEOTROPES IN MULTICOMPONENT MIXTURES

The problem of computing the temperatures and compositions of all azeotropes 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, constraints on the compositions and the complexity of realistic vapor-liquid equilibrium descriptions. We describe a homotopy method which, together 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 solutions to the problem are known trivially, since they are simply the pure components. There are as many solution branches for the homotopy as there are pure components, and one or more of the branches shows a bifurcation when azeotropes are present in the mixture. Solutions for the azeotropes are found from the limiting behavior of the homotopy and we show that azeotropes containing c components can be found from a series of c-1 bifurcations in the solution branches of lower dimensions. There is no restriction on the dimension of the problems other than the availability of an accurate thermodynamic model; examples containing up to five components are described.