Hydrodynamic Dispersion: Upscaling From the Pore to Darcy Scales

The development of Darcy-scale models for hydrodynamic dispersion by directly upscaling the pore-scale equations for conservation of mass and momentum have been in development since the early 1950s. Except for simple geometries (i.e., Taylor-Aris dispersion in a tube), the description of hydrodynamic dispersion has not been tractable via analytical methods alone. Recent advances in computational hardware have finally made it possible to begin to examine the dispersion process at the pore level, and to validate the theoretical frameworks that have been developed over the past 50 years. The focus of this talk will be primarily (1) the development of computational solutions of the closure problem for predicting the dispersion tensor using simple 3D unit cells, and (2) ongoing efforts for extending this analysis to highly complex porous media structures obtained via experimental measurements. The importance of inertial terms- which have generally been neglected in analyses of dispersion in porous media- will be discussed. This discussion will include the relevance of these terms to porous media systems, and will include some motivational examples obtained via numerical computation.