Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media.

We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion, namely, the smoothing of intrapore velocity contrasts, the increase of the tortuosity of particle paths, and the setting of a maximum time for particle transitions. Based on these mechanisms, we derive a theory that predicts anomalous and normal hydrodynamic dispersion in terms of the characteristic pore length, Eulerian velocity distribution, and Péclet number.

Self-averaging and weak ergodicity breaking of diffusion in heterogeneous media.

Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency R_{n}, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in q≥2 dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.

Erratum: Self-averaging and ergodicity of subdiffusion in quenched random media [Phys. Rev. E 93, 010101(R) (2016)].

This corrects the article DOI: 10.1103/PhysRevE.93.010101.

Self-averaging and ergodicity of subdiffusion in quenched random media.

We study the self-averaging properties and ergodicity of the mean square displacement m(t) of particles diffusing in d dimensional quenched random environments which give rise to subdiffusive average motion. These properties are investigated in terms of the sample to sample fluctuations as measured by the variance of m(t). We find that m(t) is not self-averaging for d<2 due to the inefficient disorder sampling by random motion in a single realization. For d≥2 in contrast, the efficient sampling of heterogeneity by the space random walk renders m(t) self-averaging and thus ergodic. This is remarkable because the average particle motion in d>2 obeys a CTRW, which by itself displays weak ergodicity breaking. This paradox is resolved by the observation that the CTRW as an average model does not reflect the disorder sampling by random motion in a single medium realization.

Diversity and geochemical structuring of bacterial communities along a salinity gradient in a carbonate aquifer subject to seawater intrusion.

In aquifers subject to saline water intrusion, the mixing zone between freshwater and saltwater displays strong physico-chemical gradients. Although the microbial component of these specific environments has been largely disregarded, the contribution of micro-organisms to biogeochemical reactions impacting water geochemistry has previously been conjectured. The objective of this study was to characterize and compare bacterial community diversity and composition along a vertical saline gradient in a carbonate coastal aquifer using high throughput sequencing of 16S rRNA genes. At different depths of the mixing zone, stable geochemical and hydrological conditions were associated with autochthonous bacterial communities harboring clearly distinct structures. Diversity pattern did not follow the salinity gradient, although multivariate analysis indicated that salinity was one of the major drivers of bacterial community composition, with organic carbon, pH and CO2 partial pressure. Correlation analyses between the relative abundance of bacterial taxa and geochemical parameters suggested that rare taxa may contribute to biogeochemical processes taking place at the interface between freshwater and saltwater. Bacterial respiration or alternative metabolisms such as sulfide oxidation or organic acids production may be responsible for the acidification and the resulting induced calcite dissolution observed at a specific depth of the mixing zone.

X-ray microtomography characterization of porosity, permeability and reactive surface changes during dissolution.

Numerical programs for simulating flow and reactive transport in porous media are essential tools for predicting reservoir properties changes triggered by CO(2) underground injection. At reservoir scale, meshed models in which equations are solved assuming that constant macroscopic properties can be defined in each cells, are widely used. However, the parameterization of the dissolution-precipitation problem and of the feedback effects of these processes on the flow field is still challenging. The problem arises from the mismatch between the scales at which averaged parameters are defined in the meshed model and the scale at which chemical reactions occur and modify the pore network geometry. In this paper we investigate the links between the dissolution mechanisms that control the porosity changes and the related changes of the reactive surface area and of the permeability. First, the reactive surface area is computed from X-ray microtomography data obtained before and after a set of dissolution experiments of pure calcite rock samples using distinctly different brine-CO(2) mixtures characterizing homogeneous to heterogeneous dissolution regimes. The results are used to validate the power law empirical model relating the reactive surface area to porosity proposed by Luquot and Gouze (2009). Second, we investigate the spatial distribution of the effective hydraulic radius and of the tortuosity, two structural parameters that control permeability, in order to explain the different porosity-permeability relationships observed for heterogeneous and homogeneous dissolution regimes. It is shown that the increase of permeability is due to the decrease of the tortuosity for homogeneous dissolution, whereas it is due to the combination of tortuosity decrease and hydraulic radius increase for heterogeneous dissolution. For the intermediate dissolution regime, identified to be the optimal regime for increasing permeability with small changes in porosity, the increase of permeability results from a large increase in the mean effective hydraulic radius of the sample.

Effective non-local reaction kinetics for transport in physically and chemically heterogeneous media.

The correct characterization of the effective reactive transport dynamics is an important issue for modeling reactive transport on the Darcy scale, specifically in situations in which reactions are localized, that is when different reactions occur in different portions of the porous medium. Under such conditions the conventional approach of homogenizing only the porous medium chemistry is not appropriate. We consider here reactive transport in a porous medium that is characterized by mass transfer between a mobile and a distribution of immobile regions. Chemical and physical heterogeneities are reflected by distributions of kinetic reaction rate constants and residence times in the immobile zones. We derive an effective reactive transport equation for the mobile solute that is characterized by non-local physical mass transfer and reaction terms. Specifically, chemical heterogeneity is upscaled in terms of a reactive memory function that integrates both chemical and physical heterogeneity. Mass transfer limitations due to physical heterogeneity yield effective kinetic rate coefficients that can be much smaller than the volumetric average of the local scale coefficients. These results help to explain and quantify the often reported discrepancy between observed field reaction rate constants and the ones obtained under well mixed laboratory conditions. Furthermore, these results indicate that transport under physical and chemical heterogeneity cannot be upscaled separately.

General database for ground water site information.

In most cases, analysis and modeling of flow and transport dynamics in ground water systems require long-term, high-quality, and multisource data sets. This paper discusses the structure of a multisite database (the H+ database) developed within the scope of the ERO program (French Environmental Research Observatory, http://www.ore.fr). The database provides an interface between field experimentalists and modelers, which can be used on a daily basis. The database structure enables the storage of a large number of data and data types collected from a given site or multiple-site network. The database is well suited to the integration, backup, and retrieval of data for flow and transport modeling in heterogeneous aquifers. It relies on the definition of standards and uses a templated structure, such that any type of geolocalized data obtained from wells, hydrological stations, and meteorological stations can be handled. New types of platforms other than wells, hydrological stations, and meteorological stations, and new types of experiments and/or parameters could easily be added without modifying the database structure. Thus, we propose that the database structure could be used as a template for designing databases for complex sites. An example application is the H+ database, which gathers data collected from a network of hydrogeological sites associated with the French Environmental Research Observatory.