Mixing and Reaction Kinetics in Porous Media: An Experimental Pore Scale Quantification

Abstract

We propose a new experimental set up to characterize mixing and reactive transport in porous media with a high spatial resolution at the pore scale. The analogous porous medium consists of a Hele-Shaw cell containing a single layer of cylindrical solid grains built by soft lithography. On the one hand, the measurement of the local, intrapore, conservative concentration field is done using a fluorescent tracer. On the other hand, considering a fast bimolecular reaction A + B → C occurring as A displaces B, we quantify the rate of product formation from the spatially resolved measurement of the pore scale reaction rate, using a chemiluminescent reaction. The setup provides a dynamical measurement of the local concentration field over 3 orders of magnitude and allows investigating a wide range of Péclet and Damköhler numbers by varying the flow rate within the cell and the local reaction rate. We use it to study the kinetics of the reaction front between A and B. While the advection-dispersion (Fickian) theory, applied at the continuum scale, predicts a scaling of the cumulative mass of product C as MC ∝ √t, the experiments exhibit two distinct regimes in which the produced mass MC evolves faster than the Fickian behavior. In both regimes the front rate of product formation is controlled by the geometry of the mixing interface between the reactants. Initially, the invading solute is organized in stretched lamellae and the reaction is limited by mass transfer across the lamella boundaries. At longer times the front evolves into a second regime where lamellae coalesce and form a mixing zone whose temporal evolution controls the rate of product formation. In this second regime, the produced mass of C is directly proportional to the volume of the mixing zone defined from conservative species. This interesting property is indeed verified from a comparison of the reactive and conservative data. Hence, for both regimes, the direct measurement of the spatial distribution of the pore scale reaction rate and conservative component concentration is shown to be crucial to understanding the departure from the Fickian scaling as well as quantifying the basic mechanisms that govern the mixing and reaction dynamics at the pore scale.

The Impact of Pore Structure Heterogeneity, Transport, and Reaction Conditions on Fluid–Fluid Reaction Rate Studied on Images of Pore Space

“…They demonstrated the impact of pore structure on reaction and showed that the interfacial contact area between fluids is important in determining the amount of pore-scale mixing and thus the amount of reaction. De Anna et al (2014) presented a 2D pore-scale experiment of fluid-fluid reactive transport in a porous medium consisting of circular grains that were randomly distributed. They compared the results against a model based on imperfect mixing to estimate the concentration profile of the product of an irreversible bimolecular reaction.…”

Schlieren imaging of viscous fingering in a horizontal Hele-Shaw cell

“…Other techniques have been used for imaging porous media flows (de Anna et al 2014;Rose and Britton 2013;Wildenschild and Sheppard 2013). For HS cell dynamics, fluorescence (Bunton et al 2014), shadowgraphy (Almarcha et al 2010b), interferometry (Almarcha et al 2010a, Grosfils et al 2009, and Schlieren techniques have also been of growing interest.…”

Hybrid multiscale simulation of a mixing-controlled reaction

“…Of particular note are reactive transport processes in which reaction rates are not limited by fundamental molecular interactions, but instead are controlled by mixing processes (primarily diffusion) at interfaces between fluid and/or solid phases containing the various reactants [44][45][46]. These mixing-controlled reactions are often characterized by sharp local gradients and localized reaction zones; example problems include biologically-mediated natural attenuation of dissolved contaminant plumes [47,48], precipitation/dissolution reactions [10,49,50], incomplete mixing effects on reaction rates [51][52][53][54][55][56][57] and biofilm dynamics [11,58]. There have been many representative pore-scale modeling works on transverse mixing-controlled reactive transport [58][59][60][61][62][63][64][65][66].…”