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There has been many methods for calculation and analysis of chemical engineering problems. Number of phases in equilibrium and mole content of each component in existing phases has been one of the most important subjects of research in recent years. Among all conventional methods in phase stability analysis the Michelsen (1982) Stability Analysis
Method" is of much interest. Regardless of what Method(s) is (are) being used for calculation of engineering problems, the key operation is solving the set of generated Equations. Presence of complicated empirical and theoretical equations, which are usually non-linear, mostly leads the solution to multiple roots for dominating set of equations. The conventional mathematical algorithms are not of enough robustness to yield all co-existing roots for these sets of equations. Number of coexisting roots is not predictable.
Uncertainty about number of phases in equilibrium is a further problem. Therefore
the importance of a robust method to yield all co-existing phases in equilibrium together with the mole contents of each phase is obvious. The idea of this paper is to describe Homotopy continuation method,
as a solution and extend the capability of this method to complex domain.