Multiscale solute transport upscaling for a three-dimensional hierarchical porous medium

A laboratory-generated hierarchical, fully heterogeneous aquifer model (FHM) provides a reference for developing and testing an upscaling approach that integrates large-scale connectivity mapping with flow and transport modeling. Based on the FHM, three hydrostratigraphic models (HSMs) that capture lithological (static) connectivity at different resolutions are created, each corresponding to a sedimentary hierarchy. Under increasing system lnK variances (0.1, 1.0, 4.5), flow upscaling is first conducted to calculate equivalent hydraulic conductivity for individual connectivity (or unit) of the HSMs. Given the computed flow fields, an instantaneous, conservative tracer test is simulated by all models. For the HSMs, two upscaling formulations are tested based on the advection-dispersion equation (ADE), implementing space versus time-dependent macrodispersivity. Comparing flow and transport predictions of the HSMs against those of the reference model, HSMs capturing connectivity at increasing resolutions are more accurate, although upscaling errors increase with system variance. Results suggest: (1) by explicitly modeling connectivity, an enhanced degree of freedom in representing dispersion can improve the ADE-based upscaled models by capturing non-Fickian transport of the FHM; (2) when connectivity is sufficiently resolved, the type of data conditioning used to model transport becomes less critical. Data conditioning, however, is influenced by the prediction goal; (3) when aquifer is weakly-to-moderately heterogeneous, the upscaled models adequately capture the transport simulation of the FHM, despite the existence of hierarchical heterogeneity at smaller scales. When aquifer is strongly heterogeneous, the upscaled models become less accurate because lithological connectivity cannot adequately capture preferential flows; (4) three-dimensional transport connectivities of the hierarchical aquifer differ quantitatively from those analyzed for two-dimensional systems.