Short Note: Effective Hydraulic Conductivity and Transmissivity for Heterogeneous Aquifers

Regional scale models of groundwater flow and transport often employ domain discretizations with grid blocks larger than typical scales of field data. For heterogeneous formations, this difference in scales is often handled by using effective (upscaled) parameters. We investigate the problem of upscaling hydraulic conductivity and transmissivity from a small scale of measurement to a larger scale of grid blocks. Transmissivity statistics is expressed in terms of statistics of hydraulic conductivity, and expressions for the effective (upscaled) hydraulic conductivity K_eff and transmissivity T_eff for steady state flow in confined heterogeneous aquifers are derived by means of stochastic averaging and perturbation analysis. These expressions reveal that the commonly used relation T_eff = BK_eff, where B is the confined aquifer thickness, is not generally valid.