USE OF TEMPORAL MOMENTS TO INVESTIGATE THE EFFECTS OF NONUNIFORM GRAIN-SIZE DISTRIBUTION ON THE TRANSPORT OF SORBING SOLUTES

We use temporal moment analysis to examine the effects of nonuniform g rain size on the transport of sorbing solute through porous media. We consider the case of advective-dispersive transport with sorption none quilibrium governed by diffusion into spherical grains. For constant g rain radius a and diffusion rate D-a, the temporal moments for this pr oblem 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 t(d) = a(2)/D-a. The first and second tempo ral moments are unaffected by this distribution, but the third tempora l moment is increased by a factor proportional to the variance of the distribution. This result holds regardless of the particular form of t he distribution. Higher-order temporal moments depend on the higher-or der moments of the distribution of t(d). Thus, even if the mean diffus ion rate is relatively fast, higher-order temporal moments of the solu te 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 ana lysis shows that in simulation of aquifer remediation by pump-and-trea t, the appropriate choice for the contaminant desorption rate depends upon the remediation goal.