Arithmetic approach for complex PSA cycle scheduling

An algebraic model was derived for obtaining complex pressure swing adsorption (PSA) cycle schedules. This new approach involves a priori specifying the cycle steps, their sequence and any constraints, and then solving a set of analytical equations. The solution identifies all the cycle schedules for a given number of beds, the minimum number of beds required to operate the specified cycle step sequence, the minimum number and location of idle steps to ensure alignment of coupled cycle steps, and a simple screening technique to aid in identifying the best performing cycles that deserve further examination. The methodology was tested successfully against 10, 12 and 16 bed PSA systems in the literature that all utilized the same 13 step cycle sequence that has four pressure equalization steps. It completely resolved all the corresponding cycle schedules for these 13 step multi-bed PSA systems with ease, and showed that the number of cycle schedules was hundreds to thousands of times greater than the few ever reported in the literature for each one. Overall, this new methodology for complex PSA cycle scheduling can be applied to any number of cycle steps, any corresponding cycle step sequence, and any number of constraints, with the outcome being the complete set of cycle schedules for any number of beds greater than or equal to the minimum number it determines.