Nonlinear frequency response analysis of nonisothermal adsorption controlled by macropore diffusion

• NFR method is used to study nonisothermal adsorption governed by macropore diffusion.
• Theoretical first- and second-order FRFs were derived and analyzed.
• The second-order FRF can be used for model identification and discrimination from other kinetic mechanisms.
• A procedure for estimation of kinetic and equilibrium parameters is proposed.

In this work, a nonlinear frequency response (NFR) approach is used for a theoretical study of nonisothermal adsorption controlled by macropore diffusion (NMD). Based on the nonlinear mathematical model on the particle scale for spherical geometry, the theoretical frequency response functions (FRFs) up to the second order have been derived, using the concept of higher-order FRFs. The FRFs for isothermal macropore diffusion model have also been derived for comparison. For the NMD model two series of FRFs define the process: one which relates the sorbate concentration in the particle to the pressure (F) and the other which relates the particle temperature to the pressure (Z). The obtained FRFs were simulated for seven different sets of parameters. The second-order F function exhibits specific bimodal pattern, which enables separation of the diffusional and heat-transfer time constant. The high-frequency asymptotic features of the second-order F function discriminates the NMD mechanism from micropore-macropore diffusion control. Based on the characteristic of the first- and second-order F and Z functions, the new procedure for direct estimation of the diffusional and heat-transfer time constants is proposed. Additionally, some equilibrium parameters, as well as the heat of adsorption, can also be estimated. The NFR approach shows significant advantages regarding analysis of NMD compared to the linear FR method.