Double retrograde vaporization is a phase behavior phenomenon that occurs dose to the critical point of binary mixtures and characterized by wide relative difference of volatility between its components. In general, the phenomenon occurs in a very narrow composition range, making the prediction of the molar fraction and pressure of the phase equilibrium problem a challenging problem. Here we employ sophisticated modem numerical methodology to untangle the geometry of this complex phenomenon, based on the robust methodology of inversion of functions. The objective of this work is to evaluate the system that describes the phenomenon dose to the singularity points of the problem, especially with respect to the degeneration of solutions. The method used offers an effective framework for the qualitative analysis of systems of nonlinear equations. We study an application of this methodology in the binary system formed by ethane + limonene, at three different configurations (four dew points, three dew points and only one dew point). The results indicate a very complex structure of the function in the neighborhood of the phenomenon.