We use temporal moment analysis to examine the effects of nonuniform grain size on the transport of sorbing solute through porous media. We consider the case of advective-dispersive transport with sorption nonequilibrium governed by diffusion into spherical grains. For constant grain radius a and diffusion rate Da, the temporal moments for this problem are well known and have been reported elsewhere. In this paper, we consider the more realistic case, where there exists a distribution of diffusional timescales td≡a2/Da. The first and second temporal moments are unaffected by this distribution, but the third temporal moment is increased by a factor proportional to the variance of the distribution. This result holds regardless of the particular form of the distribution. Higher-order temporal moments depend on the higher-order moments of the distribution of td. Thus, even if the mean diffusion rate is relatively fast, higher-order temporal moments of the solute transport may exhibit significant nonequilibrium effects; hence it may not be possible to decide the validity of the local equilibrium assumption based solely on the second temporal moment. Also, our analysis shows that in simulation of aquifer remediation by pump-and-treat, the appropriate choice for the contaminant desorption rate depends upon the remediation goal. ¿ 1998 American Geophysical Union