Analysis of the boundary conditions for the simulation of the pressure equalization step in PSA cycles

In this work, the physical validity of Danckwerts boundary conditions (original and modified) for simulating the connection of two beds in the pressure equalization step of a PSA cycle with a dynamic model including axial dispersion is analyzed. A model of this kind has been employed to simulate the separation of a carbon dioxide/methane mixture with silicalite as the adsorbent using a Skarstrom PSA cycle including a pressure equalization step before the pressurization step of each bed. It is demonstrated that both kinds of boundary conditions can lead to unrealistic results (either mass and heat flux are not conserved or molar fraction and temperature are not continuous in both beds) if the contribution of dispersion to axial mass flow is important, which occurs for long equalization times. To overcome these problems, the continuity of both dependent variables and fluxes as boundary conditions is proposed, which lead to the expected results for very long equalization times (the flux of each component is conserved and flat and continuous spatial profiles of all the dependent variables are obtained in both beds). These boundary conditions, unlike the ones proposed in the literature, can be the same regardless of the direction of flow. The impact of the different kind of boundary conditions on the performance results of the selected PSA process at the cyclic steady state is also analyzed.