The determination of the existence and composition of azeotropes is important both from theoretical and practical standpoints. An important test of the veracity o f thermodynamic models is whether or not known azeotropes are predicted, and whether or not they are predicted accurately. Model parameters can be ne tuned by comparing the model predictions can be used as starting points for experimental searches for actual azeotropes. These azeotropes often present limitations in process design which m ust be known, and their determination strictly from experiment alone can be expensive.There are two main di culties in solving the problem. The rst is the fact that the equations derived from most thermodynamic models are highly nonlinear, which m a y make nding any azeotrope a nontrivial exercise. In addition, there is the question of whether or not all of the azeotropes have been found, or of being certain that there are no azeotropes if none have been found. Because of these di culties there has been much recent i n terest in the reliable computation of azeotropes, focused primarily on the prediction of homogeneous azeotropes. For example, Fidkowski et al. 1993 have present a homotopy continuation method for the calculation of homogeneous azeotropes. The primary drawback of this technique is that it can not guarantee that all azeotropes have been found. More recently, Harding et al. 1997 have reported a global optimization procedure based on a branch and bound approach using convex underestimation functions that are continuously re ned as the range where azeotropes are possible is narrowed. This technique does provide a guarantee that all azeotropes have been found. Harding et al. 1997 have developed appropriate convex underestimating functions for several speci c thermodynamic models.We describe here a new approach for reliably nding all homogeneous azeotropes of multicomponent mixtures. The technique is based on interval analysis, in particular the use of an interval Newton generalized bisection algorithm. The method can determine with mathematical certainty all azeotropes for any system. The technique is general purpose and can be applied in connection with any thermodynamic models. No model speci c convex underestimating functions need be derived. In this paper, the technique is described in detail, and then tested on several problems. Results of the test problems indicate that the method can e ciently and reliably determine all homogeneous azeotropes for multicomponent mixtures.

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Recently, a robust new computational technique, based on interval analysis, has been developed for solving the difficult nonlinear problems arising in the modeling of phase behavior.This technique can be used, with mathematical and computational guarantees of certainty, to find the global optimum of a nonlinear function or to enclose any and all roots of a system of nonlinear equations. As shown in the applications here to phase stability analysis and to the location of homogeneous azeotropes, it provides a method that can guarantee that the correct result is found, thus eliminating computational problems that may potentially be encountered with currently available techniques. The method is initialization independent; it is also model independent, straightforward to use, and can be applied in connection with any equation of state or activity coefficient model.

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