In this work we examine the dispersion of conservative tracers (bromide and
fluorescein) in an experimentally-constructed three-dimensional dual-porosity
porous medium. The medium is highly heterogeneous (ΟY2β=5.7), and
consists of spherical, low-hydraulic-conductivity inclusions embedded in a
high-hydraulic-conductivity matrix. The bi-modal medium was saturated with
tracers, and then flushed with tracer-free fluid while the effluent
breakthrough curves were measured. The focus for this work is to examine a
hierarchy of four models (in the absence of adjustable parameters) with
decreasing complexity to assess their ability to accurately represent the
measured breakthrough curves. The most information-rich model was (1) a direct
numerical simulation of the system in which the geometry, boundary and initial
conditions, and medium properties were fully independently characterized
experimentally with high fidelity. The reduced models included; (2) a
simplified numerical model identical to the fully-resolved direct numerical
simulation (DNS) model, but using a domain that was one-tenth the size; (3) an
upscaled mobile-immobile model that allowed for a time-dependent mass-transfer
coefficient; and, (4) an upscaled mobile-immobile model that assumed a
space-time constant mass-transfer coefficient. The results illustrated that all
four models provided accurate representations of the experimental breakthrough
curves as measured by global RMS error. The primary component of error induced
in the upscaled models appeared to arise from the neglect of convection within
the inclusions. Interestingly, these results suggested that the conventional
convection-dispersion equation, when applied in a way that resolves the
heterogeneities, yields models with high fidelity without requiring the
imposition of a more complex non-Fickian model.Comment: 27 pages, 9 Figure