After completing four stages, re-initialize the cycle time (@ (?(@A ) as 0 and then start the simulation of another one cycle of PSA. Consequently, the PSA cycle is simulated iteratively until a cyclic steady state (CSS) is reached. Theoretically, when a CSS is reached, the column profile is expected to be the same between the same step in two subsequent cycles. In the mathematical language, when ax(t) -x(t + t KLKMN )a < δ, PSA is deemed to be under CSS. The dynamic simulation of PSA can be found in Figure . A full dynamic simulation can contain much more results than what has been shown here, but those results might not be relevant in the process analysis and optimization. This is a motivation to develop a reduced-order surrogate.