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

Abstract

The Eulerian advection-dispersion-reaction equation (ADRE) suffers the well-known scaleeffect 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-particletracking (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.

Mixing Ratios With Age: Application to Preasymptotic One‐Dimensional Equilibrium Bimolecular Reactive Transport in Porous Media

“…Very few of these studies have focused on the effects of preasymptotic dispersion on reaction product development under mixing limited conditions. Porta et al (2012), Porta et al (2016), Chiogna and Bellin (2013), Alhashmi et al (2015), Perez et al (2019), and Benson et al (2019) have demonstrated capturing reactant and product concentrations at early time. Perez et al (2019) uses the enhanced stretched lamella approach called dispersive lamella which is able to capture effects of the diffusion on the evolving interface.…”

“…Perez et al (2019) uses the enhanced stretched lamella approach called dispersive lamella which is able to capture effects of the diffusion on the evolving interface. Benson et al (2019) use reactive‐particle‐tracking (RPT) to upscale reactive transport in a Hagen‐Poiseuille flow with a preasymptotic dispersion coefficient similar to that derived by Wang et al (2012). Chiogna and Bellin (2013) use a beta distribution on mixing ratios for an elementary volume resulting in an analytical solution requiring an additional parameter calibration at early time.…”

Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model

“…Incomplete mixing typically results in an overestimation of the amount of reaction that will occur, presenting the need to artificially, and often non-physically, alter the effective reaction rate used in the model to better match observations [19]. This has led to the development of upscaled models that aim to account for subscale concentration fluctuations that limit reaction e.g., [20][21][22]. The correct prediction of reaction rates has many practical implications in the context of porous media and aquifers, e.g., the prediction of contaminant migration [23,24], the remediation of contaminated groundwater [25,26], and the fundamental prediction of naturally occurring geochemical reactions that shape the subsurface below us.…”

A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients

“…and the calculations are analogous for the portions of (32) corresponding to the other subdomains. As in the 1D case, the solutions given in (30) and (32) do not conserve mass if they are used as the WtFunction() in Algorithm 1, but they do conserve mass and generate minimal error if they are used in Algorithm 2.…”