Model reduction techniques can be used to reduce the computational burden associated with nonlinear model predictive control (NMPC). In our recent work, we introduced the transient nonlinear wave propagation model (TWPM) for reduced dynamic modeling of multi-component distillation columns with variable holdup, and demonstrated its suitability for optimization and control of single-section distillation columns and simple air separation units [Caspari et al., J. Process Control, 2020]. We show here that the TWPM is well-suited for reduced modeling of multi-sectional ultra-high-purity distillation columns and enables real-time capable NMPC of complex process flowsheets with tight operational constraints. To demonstrate its performance and accuracy, we apply the TWPM for NMPC of an ultra-high-purity nitrogen air separation unit. We perform an in-silico closed-loop case study comprising a series of load changes. Our approach reduces CPU time by 84%, enabling NMPC in real time.