The present work describes the mass transfer process between a moving fluid and a slightly soluble solid mass buried in a packed bed of small inert particles with uniform voidage, by both advection and diffusion/dispersion. Numerical solutions of the differential equations describing solute mass conservation were undertaken to obtain the concentration profiles, for each concentration level, the width and downstream length of the corresponding contour surface and the mass transfer flux was integrated to give the Sherwood number as a function of the relevant parameters. Mathematical expressions that relate the dependence with the Peclet number and aspect ratio are proposed to describe the approximate size of the diffusion wake downstream of the reactive solid mass.