Ion Transport In Porous Media Research Articles

Prediction competitive multi-ions leaching under various flow chemistry conditions: Column studies and unified thermodynamic-kinetic modeling

Current models for inorganic ion transport in porous media describe the adsorption–desorption processes mostly based on empirical adsorption isotherms or simple thermodynamic mechanisms, often overlooking the adsorption kinetics. This study introduces a novel unified reactive solute transport model framework that incorporates well-established surface complexation models to describe the adsorption–desorption of ions in the transport process and takes into full consideration the non-equilibrium adsorption, enabling the use of the same set of thermodynamic-kinetic parameters to accurately describe ion transport under different chemical conditions. To evaluate the constructed model, Cr(VI), P(V), and As(V) column transport experiments were carried out using goethite-coated sand as the porous medium. Kinetic constants derived from single-ion transport experiments accurately predicted the cotransport behaviors of Cr(VI), P(V), and As(V) under various flow chemistry conditions, especially the overshooting phenomena of Cr(VI) under P(V) and As(V) competition. The model framework can be easily incorporated into solute transport models with various surface complexation reactions to predict the fate and transport of ions under complexed chemical conditions without extensive parameterization, and thus is a useful complement to the current reactive transport model.

Confinement Effects on Distribution and Transport of Neutral Solutes in a Small Hydrophobic Nanopore.

Molecular dynamics simulations are used to study confinement effects in small cylindrical silica pores with extended hydrophobic surface functionalization as realized, for example, in reversed-phase liquid chromatography (RPLC) columns. In particular, we use a 6 nm cylindrical and a 10 nm slit pore bearing the same C18 stationary phase to compare the conditions inside the smaller-than-average pores within an RPLC column to column-averaged properties. Two small, neutral, apolar to moderately polar solutes are used to assess the consequences of spatial confinement for typical RPLC analytes with water (W)-acetonitrile (ACN) mobile phases at W/ACN ratios between 70/30 and 10/90 (v/v). The simulated data show that true bulk liquid behavior, as observed over an extended center region in the 10 nm slit pore, is not recovered within the 6 nm cylindrical pore. Instead, the ACN-enriched solvent layer around the C18 chain ends (the ACN ditch), a general feature of hydrophobic interfaces equilibrated with aqueous-organic liquids, extends over the entire pore lumen of the small cylindrical pore. This renders the entire pore a highly hydrophobic environment, where, contrary to column-averaged behavior, neither the local nor the pore-averaged sorption and diffusion of analytes scales directly with the W/ACN ratio of the mobile phase. Additionally, the solute polarity-related discrimination between analytes is enhanced. The consequences of local ACN ditch overlap in RPLC columns are reminiscent of ion transport in porous media with charged surfaces, where electrical double-layer overlap occurring locally in smaller pores leads to discrimination between co- and counterionic species.

Impact of asymmetries in valences and diffusivities on the transport of a binary electrolyte in a charged cylindrical pore

Ion transport in porous media is present in a wealth of technologies, e.g., energy storage devices such as batteries and supercapacitors, and environmental technologies such as electrochemical carbon capture and capacitive deionization. Recent studies on flat plate electrodes have demonstrated that asymmetries in ions properties, such as valences and diffusivities, lead to intriguing and counter-intuitive physical phenomena. Yet, the consequences of such asymmetries to ion transport have seldom been explored in porous geometries. To bridge this knowledge gap, we employ direct numerical simulations to solve Poisson-Nernst-Planck equations inside a cylindrical pore for a binary electrolyte with arbitrary valences and diffusivities. Next, we conduct a perturbation expansion in the limit of small potential and derive equations for charge and salt transport under confinement. We obtain good agreement between the perturbation analysis and the direct numerical simulations. Our analysis reveals that the charge and the salt transport are coupled with each other. Further, the coupling between the charge and salt transport processes is enhanced by an increase in valence and diffusivity asymmetries of ions. We observe that the mismatch of the ionic diffusivities induces a non-trivial salt dynamics, producing either transient depletion or enhancement of salt in the pore. In the regime of high static-diffusion-layer conductance, we obtain an analytical solution to our perturbation model. The solution elucidates how electrolyte asymmetry induces two charging timescales that are set by the relative pore size. In the overlapping-double-layer regime, these timescales reduce to the diffusion times of each ion such that the transport of the two ions appears to be decoupled. Overall, our work underscores that the asymmetry in cation and anion diffusivities fundamentally alters the behavior of ionic transport inside a charged cylindrical pore and opens up new avenues of research on electrolyte transport in porous materials.

Thermodiffusion of ions in nanoconfined aqueous electrolytes

Understanding of thermal effects on ion transport in porous media is very important for environmental applications. The movement of ions along a temperature gradient is named thermophoresis or thermodiffusion. In nanoporous media, where the interaction of ions with solid–liquid interfaces has a significant influence on their migration, the theoretical understanding of thermodiffusion is still incomplete. Herein, we present experimental results for the thermodiffusion of cations in saturated nanoporous silica by the through-diffusion method. Both the experimental data and theoretical analysis indicate that the temperature-induced polarization of surface charges strongly influences ionic transport. Stated simply, the electric field in a liquid electrolyte confined in nanopores changes when the applied temperature gradients are altered, thereby affecting the motion of the nanoconfined ionic species. By applying an external temperature field, the gradient of the surface charge density leads to the charged aqueous species exhibiting strong temperature gradient-dependent electrophoretic mobility. When the thickness of the electrical double layer is comparable to the size of the nanopores, the theory used herein indicates that this kind of nonisothermal ionic mobility is up to one order of magnitude larger than classical thermophoretic mobility. This study improves the understanding of the underlying mechanisms that govern the transport of ions in nanoporous media, which could set the stage for diffusional metamaterials induced by specific thermal fields.

Experimental Study of Natural Ions and Rock Interactions for Seawater Breakthrough Percentage Monitoring during Offshore Seawater Flooding

Summary Seawater breakthrough percentage monitoring is critical for offshore oil reservoirs because seawater fraction is an important parameter for estimating the severity of many flow assurance issues caused by seawater injection and further developing effective strategies to mitigate the impact of those issues on production. The validation of using natural ions as a tracer to calculate the seawater fraction was investigated systematically by studying the natural chemical composition evolution in porous media using coreflood tests and static bottle tests. The applicable range of ions was discussed based on the interaction between ion and rock. The barium sulfate reactive model was improved by integrating interaction between ions and rock as well as fluid flow effect. The results indicate that chloride and sodium interact with rock, but the influence of the interaction can be minimized to a negligible level because of the high concentrations of chloride and sodium. Thus, chloride and sodium can be used as conservative tracers during the seawater flooding process. However, adsorption/desorption may have a large influence on chloride and sodium concentrations under the scenario that both injection water and formation water have low chloride and sodium content. Bromide shows negligible interaction with rock even at low concentrations and can be regarded as being conservative. The application of a barium and sulfate reaction model in coreflood tests does not work as well as in bottle tests because fluid flow in porous media and ion interaction with rock is not taken into account. Although sulfate and barium adsorption on clay is small, it should not be neglected. The barium sulfate reaction model was improved based on the simulation of ion transport in porous media. Cations (magnesium, calcium, and potassium) are involved in the complicated cation-exchange process, which causes large deviation. Therefore, magnesium, calcium, and potassium are not recommended to calculate seawater fraction. Boron, which exists as anions in formation water and is used as a conservative tracer, has significant interactions with core matrix, and using boron in an ion tracking method directly can significantly underestimate the seawater fraction. The results give guidelines on selecting suitable ions as tracers to determine seawater breakthrough percentages under different production scenarios.

Experimental investigation on the effects of clay colloid-facilitated ammonium transport through saturated porous media under variable transport conditions

Ammonium contamination is one of the major environmental issues in subsurface contamination and groundwater which in turn poses risks to human health. Predicting and formulating desirable situations is necessary for the study of NH4+ ion adsorption and transport in the environment. The purpose of the present paper is to assess the influence of various factors, such as different colloidal concentration, different size of porous media and different flow rates on colloid-facilitated NH4+ ion transport. In order to understand the influence of colloid concentration on NH4+ ion transport in porous media, few soil column experiments were performed in laboratory scale. Different clay colloidal concentrations with NH4+ ion solution as contaminant were supplied to the soil column and the leached out solution was tested using UV–vis spectrophotometer to find the concentration of NH4+ ion; 500ppm clay colloidal concentration in fine sand medium at 5ml/min flow rate has been identified as most suitable condition for NH4+ ion subsurface adsorption with highest cumulative NH4+ ion adsorption of 1.9mg/g, whereas 200ppm clay colloidal solution had least cumulative NH4+ ion adsorbed values than other solutions. TherefoZhangre, 200ppm colloid solution was found to be most efficient for NH4+ ion transport. The efficiency of NH4+ ions transport in all the solutions in the study was doubled at a flow rate of 15ml/min than at 5ml/min. The outflow NH4+ ion concentration was lower for fine sand than medium sand in all the cases in the study. The results illustrated that variable factors in the study can either facilitate or retard ammonium ion adsorption.

Transport in Lithium Ion Batteries: Reconciling Impedance and Structural Analysis

Diffusion simulations, electrochemical impedance spectroscopy, and fractal-based random walk analysis can give different values for ion transport in porous media. Comparing results from these different techniques can be used to understand the impact of electrolyte selection, ion–surface interactions, and specific structural features on rate performance of electrochemical devices so that the microstructure and chemistry can be systematically optimized.

Effective Ion Diffusion in Charged Nanoporous Materials

Multiscale models of ion transport in porous media relate microscopic material properties (e.g., pore size distribution and pore connectivity) to their macroscopic counterparts (e.g., porosity, effective diffusion coefficient and effective electrical conductivity). We derive a macroscopic model of ion transport in electrically charged nanoporous materials, and the corresponding effective diffusion coefficient, electric conductivity and transference numbers, that explicitly account for dynamic changes in electrical double layer (EDL) and possible overlap of EDLs in nanopores. The general equations comprising this model reduce to a model of an electrical double layer capacitor (EDLC) used to interpret measurements of the EDLC voltage response to charging. While the original representation relies on empirical coefficients (e.g., Bruggeman’s relation), our effective coefficients are derived from the first principles and vary with a range of electrochemical conditions (e.g., initial concentration of ions in the electrolyte). The resulting model predictions of the EDLC voltage response match the experimental data better than the original model does.

Role of non-ideality for the ion transport in porous media: Derivation of the macroscopic equations using upscaling

This paper is devoted to the homogenization (or upscaling) of a system of partial differential equations describing the non-ideal transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. Realistic non-ideal effects are taken into account by an approach based on the mean spherical approximation (MSA) model which takes into account finite size ions and screening effects. We first consider equilibrium solutions in the absence of external forces. In such a case, the velocity and diffusive fluxes vanish and the equilibrium electrostatic potential is the solution of a variant of the Poisson–Boltzmann equation coupled with algebraic equations. Contrary to the ideal case, this nonlinear equation has no monotone structure. However, based on invariant region estimates for the Poisson–Boltzmann equation and for small characteristic value of the solute packing fraction, we prove existence of at least one solution. To our knowledge this existence result is new at this level of generality. When the motion is governed by a small static electric field and a small hydrodynamic force, we generalize O’Brien’s argument to deduce a linearized model. Our second main result is the rigorous homogenization of these linearized equations and the proof that the effective tensor satisfies Onsager properties, namely is symmetric positive definite. We eventually make numerical comparisons with the ideal case. Our numerical results show that the MSA model confirms qualitatively the conclusions obtained using the ideal model but there are quantitative differences arising that can be important at high charge or high concentrations.

Mapping Li(+) Concentration and Transport via In Situ Confocal Raman Microscopy.

We demonstrate confocal Raman microscopy as a general, nonperturbative tool to measure spatially resolved lithium ion concentrations in liquid electrolytes. By combining this high-spatial-resolution technique with a simple microfluidic device, we are able to measure the diffusion coefficient of lithium ions in dimethyl carbonate in two different concentration regimes. Because lithium ion transport plays a key role in the function of a variety of electrochemical devices, quantifying and visualizing this process is crucial for understanding device performance. This method for detecting lithium ions should be immediately useful in the study of lithium-ion-based devices, ion transport in porous media, and at electrode-electrolyte interfaces, and the analytical framework is useful for any system exhibiting a concentration-dependent Raman spectrum.

Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients

In this work, we undertake a numerical study of the effective coefficients arising in the upscaling of a system of partial differential equations describing transport of a dilute N-component electrolyte in a Newtonian solvent through a rigid porous medium. The motion is governed by a small static electric field and a small hydrodynamic force, around a nonlinear Poisson–Boltzmann equilibrium with given surface charges of arbitrary size. This approach allows us to calculate the linear response regime in a way initially proposed by O’Brien. The O’Brien linearization requires a fast and accurate solution of the underlying Poisson–Boltzmann equation. We present an analysis of it, with the discussion of the boundary layer appearing as the Debye–Huckel parameter becomes large. Next, we briefly discuss the corresponding two-scale asymptotic expansion and reduce the obtained two-scale equations to a coarse scale model. Our previous rigorous study proves that the homogenized coefficients satisfy Onsager properties, namely they are symmetric positive definite tensors. We illustrate with numerical simulations several characteristic situations and discuss the behavior of the effective coefficients when the Debye–Huckel parameter is large. Simulated qualitative behavior differs significantly from the situation when the surface potential is given (instead of the surface charges). In particular, we observe the Donnan effect (exclusion of co-ions for small pores).

Enhancement of ion transport in porous media by the use of a continuously reoriented electric field

Electromigration in porous media is enhanced by a new type of electrokinetic processing. Compared with a single-oriented electric field, a continuously reoriented electric field was proven to sharply enhance mass transport of several heavy metals in kaolin. The initial concentration of the metals was: Cd: 250 mg/kg; Cu: 250 mg/kg; Ni: 250 mg/kg; Zn: 900 mg/kg. Electric field reorientation was obtained by the use of a fixed anode and a cathode that rotated at different frequencies (0, 0.25, 1.00, 1.25, 2.00, 5.00 and 10.00 r/m). Mass transport evidently increased from 0 r/m to 1.25 r/m, and then decreased as the rotation speed reached 10 r/m. From 0 r/m to 1.25 r/m, mass transport increased 2.87 times for Cd, 3.17 times for Cu, 2.11 times for Ni, and 4.13 times for Zn. We suggest that continuous reorientation of the electric field facilitates the advance of ions through kaolin pores, minimizing the retardation effect caused by media tortuosity.

Electroosmosis law via homogenization of electrolyte flow equations in porous media

By the homogenization approach we justify a two-scale model of ion transport in porous media for one-dimensional horizontal steady flows driven by a pressure gradient and an external horizontal electrical field. By up-scaling, the electroosmotic flow equations in horizontal nanoslits separated by thin solid layers are approximated by a homogenized system of macroscale equations in the form of the Poisson equation for induced vertical electrical field and Onsager's reciprocity relations between global fluxes (hydrodynamic and electric) and forces (horizontal pressure gradient and external electrical field). In addition, the two-scale approach provides macroscopic mobility coefficients in the Onsager relations.

An Ion Diffusion Model in Semi-Permeable Clay Materials

Clay materials typically contain negative surface charges that induce electrostatic fields (or diffuse double layers) in electrolytes. During ion diffusion in a porous medium of clay materials, ions dynamically interact with the electrostatic fields associated with individual clay grains by depressing or expanding the electrostatic double layers, which subsequently affects ionic fluxes. Current theory of ion transport in porous media, however, cannot explicitly account for the dynamic interactions. Here we proposed a model by coupling electrodynamics and nonequilibrium thermodynamics (EDNT) to describe ion diffusion in clay materials as a complex function of factors including clay surface charge density, tortuosity, porosity, chemicoosmotic coefficient, and ion self-diffusivity. The model was validated by comparing the calculated and measured apparent ion diffusion coefficients in clay materials as a function of ionic strength. At transitional states, ion diffusive fluxes are dynamically related to the electrostatic fields, which shrink or expand as ion diffusion occurs. At steady states, the electrostatic fields are time-invariant and ion diffusive fluxes conform to flux and concentration gradient relationships; and apparent diffusivity can be approximated by the ion diffusivity in bulk electrolytes corrected by a tortuosity factor and macroscopic concentration discontinuities at the interfaces between clay materials and bulk solutions.

Ion transport in porous media studied by NMR

Moisture and salt transport in masonry can give rise to damages. Therefore a detailed knowledge of the moisture and salt transport is essential for understanding the durability of masonry. A special NMR apparatus has been made allowing quasi-simultaneous measurements of both moisture and Na profiles in porous building materials. Using this apparatus both the absorption of a 4 M NaCl solution in a calcium silicate brick and the drying of a 3 M NaCl capillary saturated fired-clay brick have been studied. It was found that during the absorption process the Na ions clearly stay behind, which this is caused by adsorption of these ions to the pore surface. For the drying it was found that at the beginning of the drying process the ions accumulate near the surface. As the drying rate decreases, diffusion becomes dominant and the ion profile levels off again.