Stochastic modelling of solute transport by groundwater flow, state of the art

ABSTRACT The inadequacy of the traditional approach of modelling transport in large porous formations by using a deterministic differential equation with a constant dispersivity is first discussed. The apparent variation of dispersivity with distance in field tests and the uncertainty of prediction are emphasized. A stochastic model of transport governed by the large-scale heterogeneity of hydraulic conductivity is outlined. Two scales, the local and the regional are set forth. The local scale is of the order of the aquifer depth and heterogeneity has a three-dimensional structure, with correlation scale of order of metres. The regional scale is of the order of the horizontal extent of the aquifer; variables are averaged over depth and become functions of two variables in the plane. The transmissivity correlat