Numerical experiments show that variations of an order of magnitude in transmissivity or hydraulic conductivity can cause significant dispersion even when relatively small values of dispersivity are assumed. Such variations should be represented in a deterministic model of solute transport in order to describe the flow field adequately and to realistically simulate dispersion. In an example of a field application to an alluvial aquifer, a satisfactory match to observed field data was obtained using a small (0.01 m) value of longitudinal dispersivity and a grid spacing fine enough to show field-scale alluvial heterogeneities. When large (~30 m) values of longitudinal dispersivity were used, computed solute concentrations were about half of observed values in parts of the aquifer. Modeling efforts with grid spacings two to six times wider than alluvial channels in the aquifer produced ground-water flow and solute-transport simulations which did not adequately match field data.