Swelling Pressure and Transport Coupling during Hydration and Ion Exchange in Smectites
Laura Lammers, Abdullah Cihan, Yuxin Wu, John Christensen, Marco Voltolini, Ben Gilbert, Christophe Tournassat, Jill Banfield, Carl Steefel
Overview: This effort will develop continuum models for dynamic evolution of swelling pressure, structure and transport due to the expansion and collapse of compacted clay minerals during hydration and ion-exchange reactions. Models for ion exchange will build on a recently developed thermodynamic model (described below) and will be tested against one-dimensional swelling pressure data from a X-ray compatible oedometer. Models for hydration and swelling will build on a recently developed pore–continuum model that will be calibrated using experimental and simulation data and will be tested against oedometer data. Oedometer pressure data will be complemented by structural information from small-angle X-ray scattering and solute transport data from induced polarization measurements. For given swelling states, geochemical models for solute speciation and transport, including the anomalous transport of ions, with be developed that increasingly accurately represents the confined aqueous environment in clay nanopores.
Background
Clay Swelling and Collapse by Hydration and Ion Exchange
The reversible uptake of water into the interlayer regions of expansive clay in response to variations in water activity, or solute activity and identity, is one of the most striking and complex aspects of hydrated layer silicates. Swelling behavior is observed in 2:1 phyllosilicates and is a strong function of layer charge caused by metal substitutions in the octahedral or tetrahedral sheets. An intermediate structural charge, believed to be around 0.3–0.4 e– per O10(OH)2, leads to swelling behavior while uncharged clays (e.g., pyrophyllite) and highly charged clays and mica do not swell. While all expansive clays incorporate discrete water layers (WL) through stepwise transitions between crystalline hydrate states, a fraction of clays, called smectites, can expand further forming osmotic hydrates with continuously variable interlayer spacing (Fig. 1).
Decades of experimental, theoretical and molecular simulation work have established the fundamental interactions driving clay swelling or collapse (Norrish 1954; Laird 2006). For example, water uptake by anhydrous clay is predominantly controlled by the free energy of counterion hydration. Further swelling arises due to a balance between competing interactions that include ion association with charged 2:1 layers, the hydrogen bonding network of interlayer water and electrostatic and van der Waals forces between the layers. Molecular simulations that incorporate these interactions are able to reproduce mean interlayer spacings at fixed water content and to predict clay swelling transitions as a function of water activity (e.g., Smith et al. 2006; Tambach et al. 2006; Teich-McGoldrick et al. 2015). However, we lack a firm understanding of the links between clay composition, crystal structure and swelling behavior.
Moreover, although idealized two-layer models can reproduce swelling behavior, the mesoscale geometry of real clays as seen by cryo-TEM, including the ways that smectite layers stack to form particles called tactoids, and the ways that tactoids aggregate, is complex (Whittaker et al. 2020). Geometric models, molecular, coarse-grained and finite-element simulations have been developed to establish packing configurations and transport pathways in packed clays but lack direct experimental validation.
Structure Evolution during Clay Swelling and Collapse
Clay swelling not only alters the interlayer spacing of smectite but dynamically alters the dimension, aggregation and orientation of smectite particles, called tactoids. These changes to the nano-to-microscale pore structure of clay media alters all transport properties (Melkior et al. 2009; Muurinen, 2009; Tournassat et al. 2016). Geometric models, molecular, coarse-grained and finite-element simulations have been developed to establish packing configurations and transport pathways in packed clays (Ferrage; Underwood). However, these models lack the structural features including smectite layer curvature and defective stacking observed in hydrated smectite particles using cryo-TEM (Fig. 2) (Whittaker 2020).
Solute Transport through Overlapping Electric Double Layers
The interlayers and pores in smectites are regions in which the electric double layers (EDL) at charged clay layers overlap, leading to an array of coupled macro-scale phenomena. For example, the partial or total repulsion of anions from the porosity (Fig. 3) retards anion diffusion and influences cation migration due to electro-neutrality constraints. Further, associated differences in electrolyte concentrations between the clay pores and the connected bulk water creates an osmotic pressure between these two types of water domains (Wilson & Wilson, 2014).
Numerical methods for modeling macroscopic transport through clay media, including the effects of overlapping EDLs, have been developed (Revil & Linde 2006; Leroy et al. 2006; Gonçalvès et al. 2007, 2015; Jougnot et al. 2009; Revil et al. 2011). Most of the effort, however, is restricted to simple electrolytes (e.g. NaCl), and steady-state conditions while any event that changes the chemical composition and/or the water activity in clay pores leads to dynamic changes in structure and pressure (Massat et al. 2016; Whittaker et al. 2019). The prediction of transient changes in swelling and transport in response to chemical and mechanical perturbations is necessary for robust modeling of the impacts of swelling clays in a myriad of energy and water relevant rock, soil and engineering settings. Achieving this goal requires the integration of swelling models and reactive transport modeling with the development of a specialized version of the LBNL code CrunchClay (Tournassat & Steefel 2019; Steefel & Tournassat 2019).
Goals
We seek to develop molecular and continuum models for the swelling and transport properties of smectite in the fully saturated state, driven by ion-exchange, and in the partially saturated state, driven by hydration. This effort will validate and integrate recently developed quantitative models for crystalline and osmotic swelling, and address fundamental questions about the applicability of such models to high-density and low-mobility packed clay systems. Geophysical and isotope geochemistry approaches will be developed to quantify coupled ion and solvent transport processes through smectite media.
Proposed Work
Thermodynamic Modeling of Crystalline Hydrate States and Transitions
Geochemical models consider crystalline swelling to proceed through stoichiometrically and energetically well-defined states and are more promising than efforts to account for all the complex interaction forces in the clay interlayer. Geochemical models have been developed for smectite hydration and ion exchange reactions (e.g., Vieillard et al. 2011). However, such efforts have typically relied upon macroscopic thermodynamic data and have inferred an average ideal structural swelling state without having experimental methods capable of microscopic structure determination.
Recently, we developed a thermodynamic model for clay swelling and collapse at low clay mass density that was informed by small-angle X-ray scattering of swelling transition kinetics and cryo-TEM observations of layer ensembles of individual smectite particles (Whittaker et al. 2019). This work discovered that different swelling states can coexist in proportions determined by the solution cation activity ratio. The different swelling states are separated by free energies that are relatively small and thus are dynamically accessible at room temperature provided there are no steric limitations, laying a basis for a geochemical reaction model. Using a nonideal solid-solution model, the work accurately predicted the proportions of 3W vs 2W layer states as a function of the Na:K activity ratio and explains why mechanical compaction increases ion exchange selectivity for low hydration enthalpy ions (cf. Van Loon & Glaus 2008).
The model for ion-exchange and clay swelling will be expanded to (1) test this model for a larger range of homoionic and mixed electrolyte compositions; (2) confirm the cause of clay swelling hysteresis and its effect on the validity of the assumption of dynamic equilibrium; (3) extend the model to compacted clays and investigate whether geometric constraints affect the validity of the assumption of dynamic equilibrium.
Thermodynamic Modeling of Osmotic Hydrate States and Transitions
Although the structural regimes of fully expanded smectite suspensions are well established as a function of clay density and solution composition (Norrish 1954, Michot et al. 2004), and equilibrium structures can be predicted for certain regions of the phase diagram, a comprehensive model for smectite tactoid assembly (i.e., number of layers) and aggregation (i.e., large-scale structure) is lacking. In recent work (Whittaker et al. 2019) we discovered that smectite layer curvature a ubiquitous at room temperature and likely provides a mechanism for the dynamic interlayer expansion and collapse associated with ion exchange. We hypothesize that correctly accounting for smectite layer bending fluctuations is a missing component of the free energy for smectite suspensions.
Oedometer Measurements of Equilibrium and Dynamic Swelling Pressures
In order to test the application of these models to predict swelling under compacted conditions we recently commissioned a small-scale oedometer that is compatible with in-situ small-angle X-ray scattering (SAXS), an approach that is sensitive to microscale and nanoscale porosity (Fig. 4a). The system is based on the design of Massat et al. 2018, constructed by collaborators at the BRGM, and can measure swelling within 1-cm long columns with an internal diameter from 3–9 mm. The cells can be fixed and dismounted from the oedometer for long-term studies and currently six cells are available. Hydration of a packed unsaturated clay takes about 2 days and is accompanied by transients in swelling pressure interpreted to be caused by clay reorganization (Fig. 4b). Preliminary SAXS data acquired during hydration and K-for-Na ion exchange demonstrate that changes in interlayer spacing, the development of preferred orientation and the onset of osmotic hydrate structuring are detectable.
An important goal is the measurement of equilibrium and dynamic swelling pressures for well-characterized swelling and non-swelling layer silicates over a larger range of solution composition than has been previously reported. The experiments will involve (1) the initial hydration phase with water or an electrolyte, (2) ion exchange to achieve a homogenous system, (3) forward ion-exchange reaction and (4) reverse ion-exchange. The work will initially incorporate monovalent and divalent chlorides.
In-Situ W/M/SAXS Studies of Porosity and Texture Evolution during Ion Exchange Reactions
The oedometer and control equipment will be shipped to beamline 5-ID-D at the Advanced Photon Source to simultaneously measure 1D profiles in clay structure and swelling pressure through the course of ion-exchange reactions initiated at one end of the packed clay column. It is well established that SAXS measurements can quantitatively determine the distributions of interlayer swelling states (Holmboe et al. 2012) and preliminary analysis of the SAXS data indicate that significantly richer structural information is accessible from the combination of wide-, medium- and small-angle data. In particular, we demonstrated that changes to the mean number of layers per smectite particle, and layer stacking disorder, are detectable through peak profile analysis. We observed changes in clay preferred orientation (during hydration step) through total Bragg intensity changes that we will seek to interpret using recent literature models (Ferrage et al. 2018). In addition, broad scattering features that vary with ionic strength are interpreted as observations of osmotic swelling of particles.
Cryo-TEM Quantification of Smectite Stacking Structures and Energy Differences
Models for clay swelling generally do not explicitly consider whether smectite swelling energetics are affected by layer–layer orientations. Analytical models implicitly assume randomly oriented (turbostratic) stacking while molecular simulations assume crystallographic stacking (i.e., pyrophyllite-like ordering). A trend towards more crystallographic stacking during wetting and drying cycles at high K+ concentration has been documented. In cryo-TEM, crystallographic stacking of water-separated montmorillonite layers can be directly observed (Fig. 5). Even in the presence of Na+, which is widely considered to promote turbostratic stacking (Moore & Reynolds 1997), layers are oriented in one of three unique orientations that are separated by ~60 Å (Whittaker et al. 2020). This stacking arrangement is not turbostratic, but is not readily identifiable via conventional X-ray diffraction techniques. Moreover, by quantifying the proportion of crystallographic vs turbostratic stacking over 100’s of individual smectite particles it is possible to estimate the free energy difference. Non-equilibrium molecular simulations achieve reasonable agreement although underestimated crystallographic stacking energies (Subramanian, Lammers et al. 2020).
The direct imaging of statistically relevant ensembles of smectite particles is a new approach for quantifying the swelling states that underpin our thermodynamic swelling model. The work suggests that turbostratically stacked 3W and 2W states achieve spontaneous dynamic equilibrium at room temperature while the crystallographically stacked 2W state has a higher free-energy barrier for swelling (Subramanian, Lammers et al. 2020). Thus, counterions such as K+ that promote crystallographic stacking likely cause clay swelling hysteresis, and our thermodynamic model must be expanded to account for this effect.
Mesoscale Predictions of Smectite Orientation and Stress State
The effective pressure generated by an aggregate of smectite particles (tactoids), will vary with the tactoid orientation distribution, or texture. In order to quantify this relationship, a mesoscale model will be constructed to predict the equilibrium 3D stress state of a clay aggregates as a function of its microstructure and solution composition.
The basis for the model will be the equilibrium swelling pressure generated by individual tactoids (Fig. 6a). The swelling pressures of endmember 2- and 3- water layer (2W and 3W) hydrates under a range of NaCl + KCl solution compositions will be determined from molecular simulations, while the relative proportion of layer states for given solution composition will be informed by our thermodynamic model.
The mesoscale model is composed from an ensemble of tactoids at different orientations (θi, 𝜙i) (Fig. 6b) according probability distribution functions constrained from above W/M/SAXS studies. The 3D stress state of the aggregate will be calculated from the contributions of each volume element containing a single tactoid. In the first version of the mesoscale model, the aggregate microstructure will not allow for contact between tactoids. A second version will be designed that uses NMM mechanical contact simulations to account for edge-to-face and face-to-face contacts between tactoids. The mesoscale model will yield a 3D stress state for the clay aggregate, and therefore, a macroscopic swelling pressure estimate, whose dependence on tactoid orientation can be explicitly investigated.
Molecular Controls on the Dynamics of Smectite Swelling
In order to develop pore-continuum models that can predict transient changes in smectite swelling state caused by variation in water and ion activities, it is necessary to understand controls on the rates at which clay layers expand and collapse. Molecular simulation will be used to develop a rate law for ion and water transport between the clay particle and the pore fluid that reproduces measured swelling dynamics of clay suspensions and is suitable for inclusion in pore-continuum models.
A series of molecular dynamics simulations that use a newly developed molecular structure for cis-vacant MMT (Subramanian et al. 2020) will predict the kinetics of coupled ion and water exchange at the clay-pore interface. The simulation domain will contain a single clay tactoid sufficiently large to avoid size effects that is contained on the edges by bulk pore fluid (Fig. 7). The pore fluid composition will be varied over a range of NaCl + KCl compositions for which thermodynamic equilibrium swelling state data are available, and the kinetics of ion and water exchange at the clay edge will be investigated. Simulations will be repeated over a range of normal stresses to investigate the influence of stress on the rates of clay swelling and collapse. The reversibility of each reaction will be studied to identify candidate mechanisms responsible for swelling hysteresis.
In-Situ X-ray Photon Correlation Spectroscopy of Layer Mobility in Compacted Clays
Geochemical models of clay swelling assume the system will attain a dynamic equilibrium, an assumption that requires the smectite layers to possess the mobility to sample chemical and structural configurations. The observation of co-existing swelling states in mixed electrolyte provides strong support for dynamic equilibrium at low clay density but it is unknown how compaction reduces layer mobility. Above approximately 0.2% clay volume fraction clay layers undergo a sol-gel transition in which they lose translational and rotational mobility (Paineau 2011). Slow dynamics in the gel structure result in properties, such as viscosity and shear modulus, can evolve on the timescale of years (Pujala & Bohidar 2019) as layers sample the configuration space.
The dynamics of dense systems can be investigated using X-ray photon correlation spectroscopy (XPCS), an approach that uses coherent X-ray scattering to track spontaneous motions of atoms or particles over a range of timescales. X-ray scattering speckle patterns are collected stroboscopically with a fixed time interval, t (Fig. 8). Autocorrelation of the intensities, g2(Q,t), at each interval and scattering vector, Q, provides both spatial and temporal information about the dynamics of the system. The decay of g2 is typically exponential and the decay exponent is directly related to the characteristic lifetimes of the fluctuations. For systems that are not at equilibrium, the relaxation constants change over time. The two-time correlation function, C(Q,t1,t2), captures the effects of a wide variety of non-equilibrium processes, including temporally inhomogeneous dynamics such as gelling, or intermittent dynamics arising from spontaneous changes in local configurations.
Preliminary observations of Na-Mt and K-Mt in 1 M chloride electrolyte solutions suggest that layer dynamics depend strongly on the identity of the cation. Two-time correlograms (Fig. 8) reveal highly non-equilibrium behavior in Na-Mt suspensions. The decay of correlations is highly nonlinear and depends strongly on the measurement time. There is also an oscillatory aspect of the dynamics, in which correlations diminish and then re-emerge at later times. This contrasts sharply with K-Mt dynamics, which decay rapidly and nearly homogeneously, independent of the measurement time.
Strain and Transport Evolution During Clay Swelling
A goal for clay swelling modeling is the ability to predict the coupling between swelling pressure, pore structure and connectivity, and ion transport properties. The transport of solutes through clay-rich systems is conventionally quantified by measuring the rates of in-diffusion or through-diffusion of ions and neutral molecules. Because ion transport through nanoporous clays is strongly retarded relative to bulk solution, such studies require weeks to months. Here we develop an alternative approach to continuously acquire electromagnetic signals of ion mobility during clay swelling evolution with complementary measurement of one-dimensional observations and three-dimensional maps of strain.
Low-frequency impedance spectroscopy (IS) (10 mHz to 10 kHz) applied to porous media measures the electrochemical response of ions in the pore spaces and associated with surfaces. New versions of the X-ray compatible uniaxial swelling pressure systems will be designed that incorporate IS electrodes.
High-resolution fiber optics based distributed strain sensing (DSS) is capable of measuring spatially resolved strain and stress signals of swelling clay. A new clay swelling column experiment will be constructed incorporating IS and DSS (Fig. 9). The inner sample sleeve will be built with soft plastic or rubber, e.g. Viton or PVC, for its elasticity and ability to expand and deform during clay swelling or collapse. This allows the transfer of swelling induced strain and stress onto the DSS sensor (~5 meters long) that will be densely wrapped helically on the outside of the elastic sample sleeve, providing high spatial resolution, three dimensional measurements of dynamic swelling rate and pressure based on calibrated strain-stress models. The experimental setup will be calibrated for its geometric factor for impedance measurements and strain-stress correlation for DSS measurements. These calibrations will be conducted utilizing the empty cell filled with known electrolytes under different injection pressure conditions.
Mesoscale Clay Swelling and Reaction with CrunchClay
This task aims to develop mesoscale models for clay swelling and ion transport at the representative elementary volume scale in order to predict Hydrological-Mechanical-Chemical (HMC) couplings in transient and stationary stages, while taking into account the full geochemical complexity of natural systems.
Because of the charge imbalance in the diffuse layer solution and the requirement of the absence of charge transport (no current condition), the modeling of transport processes in clay media cannot be achieved consistently by considering classical Darcy and Fick’s equation. For diffusion processes, it is necessary to take into account the electrophoretic processes corresponding to the coupling between the charge imbalance in the diffuse layer, the differences in concentration gradients for each species having different charges and thus also different accumulation factors in the diffuse layer, together with the diffusion coefficient of each individual species. This can be done by using the Nernst-Plank equation, which makes the fundamental hypothesis that equilibrium between the diffuse layer composition with the bulk water composition occurs. With this assumption, it is possible to relate the diffusive flux within the diffuse layer with an equation having the same form as the Nernst-Planck equation for the bulk porosity. The number of reactive transport codes that can solve the Nernst-Planck equation is rather limited (Rasouli et al. 2015; Steefel et al. 2015), and, amongst them, only two of them include the capability to solve it for a dual-continuum: PHREEQC and CrunchClay (Steefel et al. 2015; Tournassat & Steefel, 2019).
Advanced macroscopic models for the prediction of clay swelling forces as a function of clay dry density and pore water composition are currently based on the evaluation of the crystalline swelling contribution and the osmotic swelling contribution. For both contributions, some parameters must be estimated based on independent measurements of macroscopic properties on the sample of interest, such as the water sorption isotherm data. As a consequence, model parameters cannot easily be made generic . In addition, this type of model does not take into account the presence of several layer hydrates as observed by XRD (Holmboe et al. 2012), but conceptualizes the hydration of interlayers with a single separation distance between the unit layers within the smectite particles. In nature, therefore, these models are limited to the evaluation of an equilibrium state attained after spatial reorganization of the clay particles following the build-up of the swelling pressure (Massat et al. 2016). The development of swelling models that take into account the evolution of the distribution of the different type of porosities is a necessary step to model transient swelling conditions. This type of approach have been explored successfully in the framework of phenomenological models such as the Barcelona models (Alonso et al. 1990, 1999). These existing models, however, do not make it possible to include the effect of transient chemical conditions on the swelling response of the systems of interest. To achieve this goal, it is necessary to calculate the swelling forces from microstructural considerations and a basic knowledge of surface hydration and osmotic forces in the diffuse layer, for which an increasing body of work is available at the clay layer or molecular scales (Ngouana Wakou and Kalinichev 2014; Sun et al. 2015; Teich-McGoldrick et al. 2015; Tester et al. 2016).
First, we propose that the dual continuum model briefly presented in the previous section should be enhanced to a multi-continuum model including bulk water and a range of diffuse layer porosities and interlayer porosities in which different accumulation factors, and hence fundamental equations, are considered. For example, the Poisson-Boltzmann equation may be appropriate to model the ionic distribution in clay pore size larger than 3 water layer hydrates, but not for 2 water layer hydrates in which complete anion exclusion is expected (Chagneau et al. 2015; Tournassat et al. 2016a; Wigger & Van Loon 2017). Second, we propose to incorporate chemical osmosis resulting from the dynamic redistribution of water between the different types of porosity as a function of changes in chemical conditions. Finally, additional experimental constraints, in which coupled chemical, mechanical and fluid and solute transport processes are explored, are necessary to test the model predictions.
In the framework of this BES task, we intend to develop a fully coupled multicontinuum model to deal with changes in microstructure at the representative elementary volume scale. Theoretical and numerical aspects have been published in part as a result of on-going effort on the previous BES project (Tournassat & Steefel 2019, 2020; Tournassat et al. 2020). The future work will be focused on the full derivation of coupled advective transport theoretical equations in the presence of a diffuse layer and on their full implementation in the reactive transport code CrunchClay. In parallel, we will develop a swelling pressure model that avoids the empirical parameters used in the simpler continuum scale swelling models. Preliminary work indicated that it can at least for the osmotic swelling regime by coupling information on swelling pressure and anion exclusion available in the literature. Inputs from molecular simulations and from TEM and from coupled nanotomography / swelling pressure characterization, which are in progress at LBL, will help to further constrain our model parameters. The swelling pressure model will then be fully coupled to CrunchClay, and the model prediction will be tested against experimental data obtained with oedometer tests in the presence of salt in-diffusion and out-diffusion conditions.
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