Upscaling of Mixing‐Limited Bimolecular Chemical Reactions in Poiseuille Flow

Self Cite

We investigate the impact of pore-scale heterogeneity on reactive mixing using experimental data from inert fluid-fluid displacement in a quasi 2-D porous medium. We interpret the invading and defending fluids as the conservative components A + C and B + C of the instantaneous irreversible bimolecular chemical reaction A + B → C and determine the reaction product C. We find strong growth of the reaction rate at short and intermediate times due to deformation of the mixing interface and heterogeneity-induced increase of the mixing area. This behavior is captured by a dispersive lamella approach that quantifies the mixing dynamics at the interface in terms of temporally evolving effective dispersion coefficients. The latter capture the dominant controls on the evolution of the mixing interface, namely, advective heterogeneity and transverse mixing. Reactive transport formulations based on constant hydrodynamic dispersion coefficients are not able to describe the observed behavior due to the lack of complete mixing on the support scale, which is required for these approaches to hold. These results shed some new light on the origins of heterogeneity-induced mixing and reaction dynamics in porous media and their systematic upscaling.

Section: Dynamics Of Reactive Mixingsupporting

confidence: 84%

Assessment and Prediction of Pore‐Scale Reactive Mixing From Experimental Conservative Transport Data

Perez

Hidalgo

Puyguiraud

et al. 2020

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“…Hence, at late times the actual mixing state M AB converges toward the ideal well‐mixed case

M_{AB}^{\overset{normalc}{true}}

and scales with t 1/2 . Looking closely at the log‐log scale plot (Figure 3b), and taking the modeled mixing state M AB as a proxy for the amount of reaction, we see that it does reproduce trends observed in mixing‐limited systems such as simple Poiseuille flows (e.g., Perez et al., 2019, Figure 7).…”

Section: Concentration Fluctuation Dynamicssupporting

confidence: 52%

Lagrangian Modeling of Mixing‐Limited Reactive Transport in Porous Media: Multirate Interaction by Exchange With the Mean

Sole‐Mari

Fernàndez-García

Sánchez-Vila

et al. 2020

The presence of solute concentration fluctuations at spatial scales much below the scale of resolution is a major challenge for modeling reactive transport in porous media. Overlooking small‐scale fluctuations, which is the usual procedure, often results in strong disagreements between field observations and model predictions, including, but not limited to, the overestimation of effective reaction rates. Existing innovative approaches that account for local reactant segregation do not provide a general mathematical formulation for the generation, transport, and decay of these fluctuations and their impact on chemical reactions. We propose a Lagrangian formulation based on the random motion of fluid particles carrying solute concentrations whose departure from the local mean is relaxed through multirate interaction by exchange with the mean (MRIEM). We derive and analyze the macroscopic descriptionof the local concentration covariance that emerges from the model, showing its potential to simulate the dynamics of mixing‐limited processes. The action of hydrodynamic dispersion on coarse‐scale concentration gradients is responsible for the production of local concentration covariance, whereas covariance destruction stems from the local mixing process represented by the MRIEM formulation. The temporal evolution of integrated mixing metrics in two simple scenarios shows the trends that characterize fully resolved physical systems, such as a late‐time power law decay of the relative importance of incomplete mixing with respect to the total mixing. Experimental observations of mixing‐limited reactive transport are successfully reproduced by the model.

“…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. 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).…”

Section: Introductionmentioning

confidence: 99%

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

Gurung

Ginn

2020

Analysis of reactive transport in natural and engineered porous media has benefited from the concept of mixing ratios, in particular as a basis for mathematical separation of transport and reactions processes. General use of solute age has also been recently explored as a way to describe solute mass transfer and/or as a proxy for reaction extent. Age here is defined as exposure time to the flow field. Pairing these concepts, we develop mixing ratio models that are structured on age. One‐dimensional transport is cast in terms of age‐structured mixing ratios in general and compared with conventional formulations of mixing ratio models, demonstrating that age is often a more natural independent variable than absolute time. Using this modeling framework, we then apply age‐structured mixing ratios to the problem of mixing‐limited reactive transport in one‐dimension by explicitly considering unmixed and mixed phases. In order to address mixing limitations under the entirety of transport including the preasymptotic dispersion timeframe, we use the same age variable to define the dispersion coefficient value in a local formulation of transport. Establishing an age‐dependent dispersion coefficient allows simulation of the whole transport time including both preasymptotic and asymptotic dispersion conditions with one model. In our application we explore use of this modeling approach to both synthetic preasymptotic data and experimental asymptotic data pertaining to one famous experiment.