Assessment of averaged 1D models for column adsorption with 3D computational experiments

Abstract

In the present manuscript, we formulate a 3D mathematical model describing the capture of a contaminant in an adsorption column. The novelty of our approach involves the description of mass transfer by adsorption via a nonlinear evolution equation defined on the surface of the porous media, while Stokes flow and an advection-diffusion equation describe the contaminant transport through the interstices. Simulations of 3D models with varying microstructures but identical porosity reveal a minimal impact of the microstructure on contaminant distribution within the column, particularly in the radial direction. Using homogenization theory and a periodic microstructure, we rigorously derive a 1D adsorption model that matches the standard form that is found in the literature, but contains two effective coefficients, the dispersion and the permeability, that explicitly incorporate microstructural details of the porous medium. The 1D model closely reproduces 3D results, the 1D concentration profiles closely match the cross-section averaged 3D profiles, and the outlet breakthrough curves are nearly identical. We also demonstrate how the 3D simulations converge to the solution of the 1D model as the microstructure is refined. Consequently, our model offers a theoretical foundation for the widely used 1D model, confirming its reliability for investigating, optimizing, and aiding in the design of column adsorption processes for practical applications.