On the separate treatment of mixing and spreading by the reactive-particle-tracking algorithm: An example of accurate upscaling of reactive Poiseuille flow

• Published in: Advances in water resources 2019-01, Vol.123, p.40-53
• Main Authors: Benson, David A., Pankavich, Stephen, Bolster, Diogo
• Format: Article
• Language: English
• Subjects: Advection; Advection-diffusion-reaction equation; Algorithms; Atoms & subatomic particles; Computational fluid dynamics; Computer simulation; Diffusion; Diffusion coefficient; Diffusion rate; Diffusion-reaction equation; Dispersion; Dye dispersion; Fluids; Laminar flow; Mass transfer; Mathematical analysis; Mathematical models; Molecular diffusion; Numerical methods; Organic chemistry; Particle mass; Particle methods; Random walk; Solutes; Spreading; Tensors; Tracking; Two dimensional models; Velocity; Water resources
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2018.11.001

•Accurate upscaling of reactive transport Poiseuille flow with Reactive Particle Tracking (RPT) model.•RPT model separately simulates mixing with local molecular diffusion and spreading by Taylor macro-dispersion.•Comparison to two semi-analytic upscaling techniques: Volume-averaging and Ensemble Streamtube.•Separate treatment of mixing and spreading makes Lagrangian RPT model more representative than Eulerian advection-dispersion-reaction equation. 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 the streamtube approach (using an effective dispersion coefficient along with macro-dispersion) performs almost exactly the same as RPT.