The model equations are discretized using a finite volume method, and partial differential equations (PDEs) are turned into a set of differential-algebraic equations (DAEs). We build this DAEs system in Dymola, 2 a Modelica platform. If the column is discretized as 30 equal volumes ("30" is recommended based on both accuracy and efficiency by Haghpanah 1 ), 1220 equations are generated. In numerical solving, Modelica is an objected-oriented modelling language, 3 and all equations are solved simultaneously. Eventually, the DAEs are implemented and numerically integrated by the Dassl solver using the Modelica language in Dymola 2018. The full model of PSA can be the sum of four stages multiplied by corresponding binary variables (Equation S.20). Through varying binary variables [^', ^!, ^", ^J], the four stages of the PSA model can be simulated continuously. >_`= ^'_ 0=. + ^!_ <= + ^"_ AH0( + ^J_ +IA..