The purpose of this study is to upscale nonlinearly reactive transport from the pore scale to a heterogeneous porous medium with the aid of a sufficiently large three-dimensional pore network model. We consider a porous medium that is chemically homogeneous (sorption reactivity is constant in space) but physically heterogeneous, as it has a spatially variable pore size. Our numerical experiments aim to assess whether traveling wave (TW) behavior develops and to assess how large a network is required to be to allow our conclusions. This study revealed that for this purpose the network should include more than a million pore units and that this size varies with the degree of heterogeneity. This assertion is based on temporal changes of the moments of a migrating front of nonlinearly adsorbing solute. In networks of equal sized pores, TW behavior occurs, and concentration distributions can be predicted by an analytical solution. For increasing physical heterogeneity the balance between the dispersive and adsorptive forces remains absent because the second central moment continues to grow as a function of time. The growth rate of this moment is a function of pore-scale heterogeneity.