A Closer Look: High-Resolution Pore-Scale Simulations of Solute Transport and Mixing Through Porous Media Columns

Abstract

Mixing is pivotal to conservative and reactive transport behaviors in porous media. Methods for investigating mixing processes include mathematical models, laboratory experiments and numerical simulations. The latter have been historically limited by the extreme computational resources needed for solving flow and transport at the microscopic scale within the complex pore structure of a three-dimensional porous medium, while dealing with a sufficiently large domain in order to generate meaningful emergent continuum-scale observables. We present the results of such a set of virtual column experiments, which have been conducted by taking advantage of modern High-Performance Computing infrastructure and Computational Fluid Dynamics software capable of massively parallel simulations. The computational approach has important advantages such as full control over the experimental conditions as well as high spatial and temporal resolution of measurements. We study the roles of Péclet number and grain size variability on emergent conservative and reactive transport behaviors. Hydrodynamic dispersion results agree with the empirical and theoretical literature and link dispersivity to median grain size, while elucidating the impact of grain-size variability on the critical Péclet number. Reactive transport results also indicate that the relative degree of incomplete mixing is related to the granular material's mean hydraulic radius, and not to the median grain size. When compared to a well-known laboratory experiment with similar configuration, less incomplete mixing is observed in our simulations. We offer a partial explanation for this discrepancy, by showing how an apparent non-linear absorbance-concentration relationship may induce laboratory measurement error in the presence of local concentration fluctuations. KeywordsMixing • Porous media • Column • Experiment • Computational Fluid Dynamics Article Highlights • High-resolution numerical simulation experiments were conducted to study fluid-fluid mixing in porous (granular) media.• Results unravel the roles of Péclet number and grain-size variability on emergent conservative and reactive transport.• Non-linear light attenuation and local concentration fluctuations could cause measurement errors in physical experiments.

Solute Front Shear and Coalescence Control Concentration Gradient Dynamics in Porous Micromodel

“…Their magnitude generally increases with Pe. Several concentration gradient lamellae are found within a single pore (Figure 1b), indicating a strong variation of concentrations within it and the persistence of incomplete solute mixing at the pore scale, which is more evident at higher Pe (Sole‐Mari et al., 2022).…”

“…Solute mixing controls reaction rates in a range of processes when the typical reaction time is shorter than the typical mixing time (Chiogna et al., 2012; Engdahl et al., 2014; Rolle & Le Borgne, 2019; Valocchi et al., 2019), including groundwater contaminant transport and degradation (Kang et al., 2019), mineral dissolution and precipitation rates (Al‐Khulaifi et al., 2019; Cil et al., 2017), mineral transformation at bacterial hot spots, bacterial growth rates and chemotaxis (Bochet et al., 2020; de Anna et al., 2021; Hubert et al., 2020), and CO 2 sequestration (Gilmore et al., 2020; MacMinn et al., 2012). An important feature of reactive transport by porous media flow is that often chemical species exhibit incomplete mixing at the pore scale, meaning that their concentrations are not uniform within individual pores (de Anna, Jiménez‐Martínez et al., 2014; Gramling et al., 2002; Puyguiraud et al., 2020; Sole‐Mari et al., 2022). This leads to discrepancies between reaction rates measured in laboratory batch systems and in porous media (Botella Espeso et al., 2021).…”

Impact of Oil Viscosity on Dispersion in the Aqueous Phase of an Immiscible Two‐Phase Flow in Porous Media: An X‐Ray Tomography Study

“…Under high‐viscosity‐contrast conditions (Figures 4d–4f), both the longitudinal and transverse concentration distributions became strongly asymmetric over time with earlier arrival and much longer tailing than their counterparts with lower viscosity contrast. A heterogeneous flow field is generated according to the skewed concentration profile, similar to that in a disordered porous media (Sole‐Mari et al., 2022). Simultaneous compression perpendicular to the main direction of elongation may counteract diffusion (Jiménez‐Martínez et al., 2017).…”

“…The results indicate that dispersion can be enhanced to a more considerable degree in complex hydraulic conductivity fields, which leads to greater streamline compression and expansion due to the increase in heterogeneity of the velocity field. In heterogeneous porous media, anomalous and normal hydrodynamic dispersion is determined by the characteristic grain (pore) size (Puyguiraud et al., 2021; Sole‐Mari et al., 2022), grain orientation (Willingham et al., 2008), dimensionality (Le Borgne et al., 2010; Rolle et al., 2012), and Péclet number (De Dreuzy et al., 2012; Majdalani & Guinot, 2023; Puyguiraud et al., 2021; Sole‐Mari et al., 2022). The structural disorder of porous media enforces the overlap of lamellae (streamline or layer) within the dispersion area, resulting in the folding and coalescence of segregated solutes and enhancing mixing (Le Borgne et al., 2013).…”

Intrapore Geometry and Flow Rate Controls on the Transition of Non‐Fickian to Fickian Dispersion

“…Thus, many studies had to rely on simplified pore models (Bijeljic et al., 2004; Bolster et al., 2009; Cardenas, 2009; Crevacore et al., 2016; Le Borgne et al., 2011; Sund et al., 2015). Recent advances in digital rock physics allow testing impacts of naturally found complex pore structures (Bijeljic et al., 2013; Gouze et al., 2021; Puyguiraud et al., 2021; Sole‐Mari et al., 2022) on the transport phenomenon; however, these studies are limited to testing a few rock types and cannot study length‐scale dependent dispersivity due to their shorter domain lengths (∼1 cm 3 ). Thus, there remains a need to study the impact of pore structures, starting from its most fundamental unit, that is, intrapore geometry, on the emergence of flow‐rate‐dependent hydrodynamic dispersion and length‐scale dependence of dispersivity.…”