A cryogenic air separation unit produces large volumes of high-purity oxygen, nitrogen, and argon through distillation. Such a complex process with a heat-coupling design, a high purity requirement, and a large-scale feature is difficult to analyze and optimize. In this study, a complete equation-oriented (EO) model, which includes a unit model and a thermodynamic model, is developed for cryogenic air separation involving a low-pressure column, a high-pressure column, and an argon side arm column. The EO approach is then applied to deal with the following three issues in air separation: thermodynamic parameter estimation, process analysis with heat-coupling design, and process optimization with varying load demands. The proposed EO method is superior to traditional sequential modular based commercial software in terms of convergence performance.