Numerical models of solute transport in water-saturated porous media a
re routinely used to make regulatory and design decisions. For many co
ntaminants, decisions are based on concentrations of 5 parts per billi
on (ppb) or less. This ''action level' is usually a small fraction (<0
.01) of the concentrations near a source of contamination. Two one-dim
ensional example problems are used to demonstrate that modeling errors
using classical numerical methods are largest where concentrations ar
e lowest. This implies that in regions of low dimensionless concentrat
ion, that is near the action level, large relative errors can be expec
ted. Hence, decisions based on numerical model solutions at low concen
trations must be taken cautiously. Modern numerical methods for the so
lution of transport equations provide better behavior, in this sense,
than classical methods.