Further Validation of the Quartic Concentration Profile Approximation for Describing Intraparticle Transport in Cyclic Adsorption Processes

Abstract

Models developed previously by the authors that describe nonlinear adsorption, and simultaneous pore and surface diffusion in a single particle, that are based on intraparticle quartic and parabolic concentration profile approximations, and that utilize the summation of the gas and adsorbed phases approach in the material balance formulations, were further validated under more diverse, yet more realistic, cycling conditions. Periodic square, sinusoidal and triangular wave functions were used to more accurately represent the periodic boundary conditions that the external surface of an adsorbent particle may be exposed to during repeated adsorption and desorption cycles in a fixed bed adsorber. Analytical solutions that describe the periodic uptake and release of the adsorbate by the adsorbent were obtained for all three periodic wave functions, and for both the quartic and parabolic profile approximations. By comparing the predictions obtained from both models with the exact numerical solution, the superiority of the quartic model over the parabolic model was clearly demonstrated for all wave functions, and for a wide range of adsorbate-adsorbent systems and bulk concentrations. Excellent agreement between the quartic and exact models was obtained in most cases. In general, the predictions improved as the wave function changed more gradually with time (triangular more gradual than sinusoidal and sinusoidal more gradual than square), as the degree of mathematical linearity of the adsorbate-adsorbent system increased, and as the maximum external surface concentration decreased (an isotherm nonlinearity effect). Subtle differences in the predictive ability of the new approximate models, stemming from the use of the different wave functions, were exposed. Overall, these results exemplify the importance of comparing the predictive ability of new approximate models that describe intraparticle transport under more diverse cycling conditions than are typically utilized in the literature, which has been dominated by the square wave function.