Reactive transport upscaling at the Darcy scale: A new flow rate based approach raises the unsolved issue of porosity upscaling

Abstract This article demonstrates that permeability upscaling, which can require complex techniques, is not necessary to significantly decrease the CPU time in reactive transport modeling. CPU time depends more on the geochemistry than the flow calculation. Flow rate upscaling is proposed as an alternate method to permeability upscaling, which is more suited to time-consuming flow resolution. To apply this method, a finite volume approach is most convenient. Considering the equality of flow as the equivalence criterion, when the coarse grid overlays the fine grid, flow rate upscaling leads, by construction, to the exact results, whereas the accuracy of permeability upscaling methods often depends on specific conditions. Some focus is put on the limitations of a common permeability upscaling technique, the simplified renormalization. In stationary flow, the gain in CPU time is the same for both flow rate upscaling and permeability upscaling. In transient flow, flow rate upscaling is slightly less time-efficient but the ratio between both CPU times decreases when the geochemistry is more complex. Working with an accurate flow rate field in the upscaled case reveals that porosity upscaling is a surprisingly tricky issue. Solution mixing is induced and residence times can be significantly affected. These changes have potentially important consequences on reactive transport modeling. They are not specific to the flow rate upscaling method; they are a general issue. Some simplified cases, assuming a homogeneous mineralogy, are examined. At this stage, a simple heuristic method is proposed, which yields reliable results under particular conditions (high heterogeneity). Porosity upscaling remains an open research field.