Most studies to date have assumed that kinetic processes are extremely fast and hence the adsorption reactions are governed by conditions of local chemical equilibrium; this is often denoted as the 'local equilibrium assumption' (LEA). For nonreactive solutes, unique field-scale effects are well-known to be caused by heterogeneities in the aquifer permeability. Spatial variability manifests itself upon contaminant plume behavior in several ways; for example, field-scale dispersion coefficients are much larger than their laboratory counterparts and they demonstrate a 'scale effect' whereby their value increases with distance from the pollutant source. These phenomena are often referred to collectively as 'macrodispersion'. For the case of adsorbing solutes, both macrodispersive and kinetic processes will contribute to the overall spreading of the solute plume, and therefore LEA validity will depend upon the heterogeneous structure of the aquifer. A numerical modeling approach is being used to examine the issue of LEA validity for transport in randomly heterogeneous aquifers. This paper reviews the computational techniques we have developed and reports some recent results.