Reactive dispersion process in packed tube flow with wall adsorption and desorption

Taylor dispersion theory is widely applied in environmental engineering problems such as gas chromatography column optimization and groundwater remediation. However, existing research has insufficiently addressed the coupled system of porous medium-filled tubes and reversible adsorption walls. The multiscale analysis method cannot adequately characterize early transient behaviors or analyze skewness and kurtosis, hindering accurate reflection of solute transport patterns in specific engineering applications. This study employs a porous-medium-packed tube with reversible adsorption walls. Based on the Barton concentration moment framework and Edgeworth expansion, concentration moments up to the fourth order were calculated, and the analytical solutions were validated via Brownian dynamics simulation. The regulating effects of porous media parameters, reversible adsorption rate, adsorption–desorption coefficient ratio, and initial release position were investigated. Results show that an increase in comprehensive property parameters of porous media suppresses solute dispersion while accelerating downstream drift of the solute cloud. When wall adsorption is stronger than desorption, the amount of solute at the final equilibrium state decreases. Due to the reduction in the number of particles in the fluid, the distance drifted downstream also shortens. Additionally, the coupling effect between the reversible adsorption wall and the porous medium significantly enhances the asymmetry of the solute concentration distribution. Finally, for initial release positions inside the packed tube, wall-mediated release and equilibrium-state release significantly influence the early-stage dispersion process. This study reveals the solute dispersion patterns in packed tubes under the coupling of porous media and reversible adsorption, filling the gap in quantifying transient variations and non-Gaussian characteristics of this model. It provides theoretical support for issues such as assessing pollutant dispersion in environmental engineering.