Transport upscaling using multi-rate mass transfer in three-dimensional highly heterogeneous porous media

A methodology for transport upscaling of three-dimensional highly heterogeneous formations is developed and demonstrated. The overall approach requires a prior hydraulic conductivity upscaling using an interblock-centered full-tensor Laplacian-with-skin method followed by transport upscaling. The coarse scale transport equation includes a multi-rate mass transfer term to compensate for the loss of heterogeneity inherent to all upscaling processes. The upscaling procedures for flow and transport are described in detail and then applied to a three-dimensional highly heterogeneous synthetic example. The proposed approach not only reproduces flow and transport at the coarse scale, but it also reproduces the uncertainty associated with the predictions as measured by the ensemble variability of the breakthrough curves.

Research highlights
► A methodology for 3D transport upscaling in highly heterogeneous media is developed.
► An interblock-centered full-tensor Laplacian-with-skin method is used for the hydraulic conductivity upscaling.
► The coarse scale transport equation includes a multi-rate mass transfer term to make up for the loss of heterogeneity.
► The transport upscaling is demonstrated in a 3D synthetic experiment.