In this paper, new thermodynamic limits on the performance of irreversible separation processes are derived, including work of separation in finite time (a generalization of Van't Hoff reversible work of separation for finite rate processes), maximal productivity of heat-driven separation process (an analogue of Novikov-Curzon-Ahlborn maximal power of a heat engine), and the minimal possible dissipation in an irreversible distillation column, the ideal operating line, for which this dissipation level is achieved, the profile of heat supply/removal that realizes the ideal operating line, and the distillation column's maximal productivity.