Impact of solute charge and diffusion coefficient on electromigration and mixing in porous media

Quantifying anomalous chemical diffusion through disordered porous rock materials

Fickian (normal) diffusion models show limitations in quantifying diffusion-controlled migration of solute species through porous rock structures, as observed in experiments. Anomalous diffusion prevails and can be interpreted using a Continuous Time Random Walk (CTRW) framework with a clear mechanistic underpinning. From the associated fractional diffusion equation we derive solutions over a broad range of anomalous diffusion behaviours, from highly anomalous to nearly Fickian, that yield temporal breakthrough curves and spatial concentration profiles of diffusing solutes. We illustrate that these solutions can be tailored to match realistic experimental conditions and resulting measurements that display anomalous diffusion. In particular, our analysis enables clear differentiation between early-time Fickian and anomalous diffusion, which becomes more pronounced over longer durations. It is shown that recent measurements of diffusion in natural rocks display distinct anomalous behaviour, with significant implications for critical assessment of solute migration in diverse geological and engineering applications.

Temperature-dependent dynamics of electrokinetic conservative and reactive transport in porous media: A model-based analysis

Electrokinetic techniques employ direct current electric fields to enhance the transport of amendments in low permeability porous media and have been demonstrated effective for in situ remediation of both organic contaminants and heavy metals. The application of electric potential gradients give rise to coupled chemical, hydraulic and electric fluxes, which are at the basis of the main transport mechanisms: electromigration and electroosmosis. Previous research has highlighted the significant impacts of charge interactions and fluid composition, including temperature-dependent properties such as electrolyte conductivity and density, on these transport phenomena. However, current models of electrokinetic applications often assume isothermal conditions and overlook the production of heat resulting from Joule heating. This study provides a detailed model-based investigation, systematically exploring the effects of temperature on electrokinetic conservative and reactive transport in porous media. By incorporating temperature-dependent material properties and progressively investigating the impact of temperature on each transport mechanism, we analyze the effects of temperature variations in both 1D and 2D systems. The study reveals how temperature dynamically influences the physical, chemical and electrostatic processes controlling electrokinetic transport. A temperature increase results in a higher speed of amendments delivery by both electromigration and electroosmosis and increases the kinetics of degradation reactions. The simulations also reveal a feedback mechanism in which higher aqueous conductivity results in increased Joule heating, leading to a faster temperature rise and, subsequently, to higher electrolyte conductivity. Finally, we estimate the electric energy requirements of the system at varying temperatures and show how these changes impact the rate of contaminant removal.

A new method for assessment of electro-osmotic permeability through the integration of theoretical and experimental ion flux in electrokinetic processes

Electrokinetic (EK) technology is promising for removing heavy metals from contaminated unsaturated soils. It is crucial to accurately determine the unsaturated electro-osmotic permeability for predicting the efficiency of EK treatment, optimizing treatment strategies, and accurately predicting the distribution of contaminant concentrations. However, the current approach of estimating unsaturated electro-osmotic permeability, which involves measuring effective voltage, drainage volume, and performing exponential fitting, fails to address the issue of uneven voltage gradient distribution during EK treatment. Herein, a novel method was presented for estimating the electro-osmotic permeability of unsaturated porous media. This method quantifies the electro-osmotic flow in an unsaturated porous medium by considering the difference in mass-transfer efficiency (MTE) between real (with electro-osmotic flow) and hypothetical cases (without electro-osmotic flow). This difference serves as a metric for estimating the electro-osmotic permeability. Results revealed a linear relationship between the electro-osmotic permeability and the product of volumetric moisture content and tortuosity, with the slope related to the ionic mobility of target ions, hypothetical and actual MTE. To validate this method, hexavalent Cr (Cr(VI)) was selected as the target contaminant and six EK experiments were conducted with varying initial volumetric moisture content. The feasibility of the method was evaluated by fitting the results of these experiments to obtain the specific slope of the porous medium used. Compared to the existing effective voltage-drainage volume-exponential fitting method, the proposed method offers several advantages. First, it effectively addressed the issue of nonuniform voltage distribution during EK treatment in the unsaturated porous medium. Second, it overcame the problem of a nonzero electro-osmotic permeability at zero volumetric moisture content in the exponential empirical formula. Third, the proposed method was based on theoretical derivations instead of relying solely on empirical fitting. Finally, the proposed method does not require a prior estimate of the saturated electro-osmotic permeability of the porous medium.

On the interplay between electromigration and electroosmosis during electrokinetic transport in heterogeneous porous media

Electrokinetic techniques represent a valuable approach to enhance solute transport, reactant delivery and contaminant degradation in complex environmental matrices, such as contaminated soil and groundwater, and have a great potential for the remediation of many organic and inorganic pollutants. This study investigates the complex interplay between the key electrokinetic transport mechanisms, electromigration and electroosmosis, in physically heterogeneous porous media and its impact on tracer distribution, reactant mixing and degradation efficiency. We perform experiments in a multidimensional setup, considering different types of heterogeneities, injected tracers and reactants, as well as background electrolyte pore water with different chemical composition and pH. We show that EK transport is significantly affected by the physical heterogeneities, due to the interaction between electrokinetic and hydraulic processes, and by the pore water chemistry that plays a key role on the magnitude and spatial distribution of electroosmotic fluxes. The latter affect the overall transport of charged and non-charged species, including the migration velocity of injected plumes, their spatial patterns, spreading and mixing with the background groundwater, and the extent of degradation and the spatio-temporal evolution of reactive zones in the heterogeneous porous media. Process-based numerical modeling allowed us to interpret the experimental observations and to disentangle the coupled effects of physical, chemical and electrostatic processes in the multidimensional, heterogeneous setups. Besides elucidating the mechanisms controlling electrokinetic transport, the results of this study have also important implications for practical field implementation of EK approaches in intrinsically heterogeneous subsurface systems.

Diffusion and Sorption Studies of Cs, Sr and Co in Intact Crystalline Rock

Three cationic tracers, Sr2+, Co2+ and Cs+ were tested with a modified electromigration device by applying 2V, 3V and 4V voltage gradients over an intact Grimsel granodiorite rock sample. An ideal plug-flow model and an advection-dispersion model were applied to analyze the breakthrough curves. Matrix characterization by C-14-PMMA autoradiography and scanning electron microscopy showed that in the centimeter scale of Grimsel granodiorite rock, the interconnected matrix porosity forms a well-connected network for diffusion. Micrometer-scale fissures are transecting biotite and chlorite minerals, indicating sorption of the studied cations. The ideal plug-flow model indicated that the effective diffusion coefficients (De values) for Sr2+, Co2+ and Cs+ tracer ions within the Grimsel granodiorite rock were 3.20 × 10−13 m2/s, 1.23 × 10−13 m2/s and 2.25 × 10−12 m2/s, respectively. De values were also derived from the advection-dispersion model, from which 2.86 × 10−13 m2/s, 1.35 × 10−13 m2/s and 2.26 × 10−12 m2/s were calculated. The diffusion speed for the tracers was in the sequence of Cs+ > Sr2+ > Co2+ that is in the same sequence as their diffusion in diluted water. The distribution coefficients (Kd values) calculated from the models covered the range of two magnitudes (from 10−7 m3/kg to 10−5 m3/kg). The result indicated that the sorption process of the studied elements did not reach equilibrium during the electromigration process, mainly due to the too much acceleration of the migration speed by the voltage gradients applied over the rock sample.