A parametrical analysis on solute transport in a packed pipe with first-order wall reaction based on the method of Gill's series solution is presented. The main contribution of this work is to demonstrate the dispersion of solute cloud in different superficial flow in porous media, in particular, the evolution of the solute cloud in large times. The results show the dependence of some characteristic coefficients of the dispersion process on both the damping factor of the porous media flow and wall reaction rate. This work offers an insight into the effect of porous media on solute migration with wall reaction, the effect turns out to be of monotonous regularity. (C) 2015 Elsevier Ltd. All rights reserved.