This paper presents the principles underlying a recently developed num
erical technique for modeling transport in heterogeneous porous media.
The method is then applied to derive the concentration mean and varia
nce, the concentration CDF, exceedance probabilites and exposure time
CDF, which are required by various regulatory agencies for risk and pe
rformance assessment calculations. The dependence of the various stati
stics on elapsed travel time, location in space, the dimension of the
detection volume, natural variability and pore-scale dispersion is inv
estigated and discussed.