Upscaling hydraulic conductivity: theory and examples from geohydrological studies

This paper presents an overview of the theory of upscaling hydraulic conductivity and describes two case studies in which some of this theory has been applied. The representative hydraulic conductivity of a numerical model block ('block conductivity' for short) is defined in terms of smaller scale hydraulic conductivities, Also, using elementary examples, some general properties of block conductivities are given. Analytical solutions for the block conductivity are presented that were derived by various authors for uniform flow conditions both in a deterministic and in a stochastic setting. Some results of the hydraulic upscaling theory are illustrated by two case studies from the Netherlands. The first case study deals with deriving the representative hydraulic conductivity tensor of a clay layer. Upscaling results are compared with traditional harmonic averaging. In the second case study the upscaling is used to derive the three-dimensional distribution of block conductivities for a numerical groundwater model of a confining layer of complex deposits. Here stochastic upscaling is used together with a geostatistical simulation approach. The simulated block conductivities are used in a numerical groundwater model and results are compared with pumping tests. When the upscaling is ignored groundwater flow through the deposits is predicted wrongly.