  In this work, the development of a framework for the multi-scale data-driven
parametrization of averaged-scale models is outlined and applied to dispersive
transport. Dispersive transport is a common phenomena included in transport
models at the averaged scale, describing the velocity and geometry dependent
mixing seen at the pore scale. Optimal parameters for the development of
dispersion tensors can be extracted from pore-scale simulations in the form of
an averaged velocity and characteristic length scales. In this work, the
determination of these parameters is outlined and tested first on simple and
later on complex random pore geometries. These parametrizations are then used
to develop a data-driven model extracting optimal parameters from pore
geometries. In order to better understand the relationships between these
parameters and pore geometries, we introduce a series of metrics based on
interfacial geometry, volume ratios, and connectivity. These metrics are then
compared against the parametrizations, and used to develop a metrics based
data-driven model.
