Flow through a granular, natural porous media can erode it chemically by dissolving and thus shrinking the solid particles, or mechanically, by removing them. The two-way interplay between the transport of fluids and dissolved solutes and alteration of the porous structure and hence the medium's transport properties is of interest to processes ranging from subsurface energy storage to contamination in groundwater. Here, we conduct a quantitative pore-scale analysis through a combination of numerical simulations and microfluidic experiments. We find that erosion enhances solute dispersion at low Pe (diffusion-dominated) and diminishes it at high Pe. Residence time distribution reveals that mechanical erosion tends to induce non-Fickian transport more than chemical erosion, which we attribute to the differences in their effects on pore size distribution.