HESS Opinions: Chemical transport modeling in subsurface hydrological systems – space, time, and the “holy grail” of “upscaling”

Abstract

Extensive efforts over decades have focused on quantifying chemical transport in subsurface geological formations, from microfluidic laboratory cells to aquifer field scales. Outcomes of resulting models have remained largely unsatisfactory, however, largely because domain heterogeneity – characterized for example by porosity, hydraulic conductivity and geochemical properties – is present over multiple length scales, and “unresolved”, practically unmeasurable heterogeneities and preferential pathways arise at virtually every scale. While spatial averaging approaches are effective when considering overall fluid flow, wherein pressure propagation is essentially instantaneous, purely spatial averaging approaches are far less effective for chemical transport essentially because well-mixed conditions do not prevail. We assert here that an explicit accounting of temporal information, under uncertainty, is an additional but fundamental component in an effective modeling formulation. As an outcome, we further assert that “upscaling” of chemical transport equations – in the sense of attempting to develop and apply chemical transport equations at large length scales, based on measurements and model parameter values obtained at significantly smaller length scales – can be considered an unattainable “holy grail”. Rather, we maintain that it is necessary to formulate, calibrate and apply models using measurements at similar scales of interest.