  The Eulerian advection-dispersion-reaction equation (ADRE) suffers the
well-known scale-effect of reduced apparent reaction rates between chemically
dissimilar fluids at larger scales (or dimensional averaging). The dispersion
tensor in the ADRE must equally and simultaneously account for both solute
mixing and spreading. Recent reactive-particle-tracking (RPT) algorithms can,
by separate mechanisms, simulate 1) smaller-scale mixing by inter-particle mass
transfer, and 2) mass spreading by traditional random walks. To test the
supposition that the RPT can accurately track these separate mechanisms, we
upscale reactive transport in Hagen-Poiseuille flow between two plates. The
simple upscaled 1-D RPT model with one velocity value, an upscaled Taylor
macro-dispersivity, and the local molecular diffusion coefficient matches the
results obtained from a detailed 2-D model with fully described velocity and
diffusion. Both models use the same thermodynamic reaction rate, because the
rate is not forced to absorb the loss of information upon upscaling. Analytic
and semi-analytic upscaling is also performed using volume averaging and
ensemble streamtube techniques. Volume averaging does not perform as well as
the RPT, while ensemble streamtubes (using an effective dispersion coefficient
along with macro-dispersion) perform almost exactly the same as RPT.
