Upscaling hydraulic conductivities in heterogeneous media: An overview

Hydraulic conductivity upscaling is a process that transforms a grid of hydraulic conductivities defined at the scale of the measurements, into a coarser grid of block conductivity tensors amenable for input to a numerical flow simulator. The need for upscaling stems from the disparity between the scales at which measurements are taken and the scale at which aquifers are discretized for the numerical solution of flow and transport. The techniques for upscaling range from the simple averaging of the heterogeneous values within the block to sophisticated inversions, after the solution of the flow equation at the measurement scale within an area embedding the block being upscaled. All techniques have their own advantages and limitations. Recently, the definition of the geometry of the grid has been intimately linked to the upscaling problem; promising results have been obtained using elastic gridding. Also, recently, the need to perform Monte-Carlo analysis, involving many realizations of hydraulic conductivity, has steered the development of methods that generate directly the block conductivities in accordance with the rules of upscaling, yet conditional to the measurement data.