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A new method for fast approximate calculation of quasi-steady states of cyclic processes is presented. The method is based on the concept of higher-order frequency response functions. The system input is represented in the form of Fourier series, whereas the output is presented in the form of Volterra series. For practical applications, both the input and the output series are approximated by finite-length sums. In this way, the approximate periodic quasi-steady state of the system output is calculated directly, without long numerical integrations. Cyclic operation of an adsorption column with periodic fluctuations of the inlet concentration or/and adsorbent temperature is used as a case study for testing the new method. The necessary frequency response functions (FRFs), up to the third order, are derived, based on the equilibrium dispersion model. The method is tested for sinusoidal and rectangular input changes. The approximate solutions based on the FRFs, up to the third order, and a finite number of input harmonics, are calculated for different input frequencies and amplitudes and compared with the numerical solutions. Very good agreement is obtained.

Mathematical modeling of an Electric-Swing Adsorption (ESA) system (adsorption cycle with electrothermal desorption step, performed by direct heating of the adsorbent particles by passing electric current through them), with annular, radial-flow, cartridge-type fixed-bed and invessel condensation, is performed by using Comsol Multiphysics™ software. Three multiphysics models are built, in order to describe three stages of a compete ESA cycle: adsorption, electrothermal desorption before the start of condensation and electrothermal desorption with in-vessel condensation. In order to describe the complete ESA cycle the models for the three stages are integrated, by using a combination of Comsol Multiphysics™ and Matlab™. The models were successfully used for simulation of separate stages of the process and of the complete ESA cycles, as well as for investigation of the influences of the main operational parameters on the process performance.

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