Stochastic Averaging and Estimate of Effective

Numerical models for groundwater flow and transport on a regional scale require the assignment of hydraulic parameters to grid blocks of a size larger than typical scales of available field data. Most natural formations are heterogeneous with hydraulic properties varying on a multiplicity of scales. This difference in scales is often handled by using effective (upscaled) parameters. Here we investigate the problem of upscaling hydraulic conductivity and transmissivity from the small scale of measurement to the larger scale of a grid block by means of stochastic averaging and perturbation analysis. We start by deriving the statistics of a random transmissivity field from that of a conductivity field, and proceed by establishing the relationship between effective conductivity and transmissivity derived from the same data set.