The continuum media approach continues to dominate the methodologies used to model flow and advective transport in natural formations. This approach converts measurements of natural systems into hydraulic conductivity estimates for the formations. These estimates are used to predict flow and advective transport in aquifers. To date, no systematic study has been conducted to evaluate the errors generated by these averaging techniques to determine the best averages to use in geologically heterogeneous media. This study evaluates commonly used averaging techniques from core, well and regional conductivity measurements to test their predictions of “average” flow and advective transport using numerical analysis. The model system is a two-layer heterogeneous system consisting of two homogeneous layers where the true average flow and transport conductivities can be solved. Using the conductivities that result from averaging the known system, the core, well, and regional averaging techniques are tested against the model system. The results show that error in the current averaging techniques for flow are due only to measurement errors, but that significant error exists in transport velocity estimate methods. The results suggest that continuum models predict artificially low transport velocities and can be greatly improved in strongly heterogeneous systems by using discrete models of advective transport.