• Severe cryogenic conditions require high reliability on thermodynamic models. • Reliable models allow to avoid overdesigns and energy dissipations. • Different numerical techniques for bubble/dew problems have been analyzed. • Proposed approach can be generally extended to non-cubic Equations of State. • An improvement in algorithm robustness and efficiency have been proven. High accuracy in Equations of State (EoSs) is becoming a more and more critical aspect for design and operational purposes in different areas of chemical and process engineering. It is well-known that improper predictions of mixture properties provide large deviations in process simulations, process control actions, estimation of operative conditions, assessment of performance indexes and optimal unit/process design. These deviations are strongly emphasized when typical operating conditions appear rather severe. One of the most challenging application sectors is represented by cryogenic separations and especially in case their nominal operating conditions approach the critical point. Air Separation Units (ASUs) are the ideal application field to demonstrate these criticisms. In addition, dedicated EoSs sometimes lacks in implementation details and thermodynamic parameters, making the reliability target impossible to be achieved. The present paper is aimed at bridging the current gaps in the implementation of Bender EoS for the reliable prediction of air mixture properties as well as the reliable simulation of ASU plants. The implementation requires the description of robust and efficient algorithms. At last, a quantitative comparison between the proposed approach and the existing solutions is provided.