Semipermeable Membrane Behavior Research Articles

Chemical osmosis-induced deformation of mudstone: Nonlinear semipermeable membrane behavior and dimensionless analysis

Mudstones can act as semipermeable membranes that induce osmotic flow and pressure changes which, in turn, cause deformation of mudstones. A numerical model was developed for describing these coupled processes by considering the nonlinear concentration-dependent semipermeable membrane properties and was applied to laboratory-scale experimental results to describe the deformation behavior. The strain behaviors obtained from the laboratory experiments were compared with the type curves obtained from the numerical simulations with constant and nonlinear concentration-dependent reflection coefficients. Both type curves efficiently explained the deformation of the sample in the early stage of the experiment, whereas incremental extension in the latter stage was only explained by the type curves with nonlinear concentration-dependent reflection coefficient. Nonlinear semipermeable membrane behavior should be considered to fully understand the long-term coupled processes observed in mudstones in the presence of a concentration gradient.

Semipermeable membrane behavior of geosynthetic clay liners

The focus of this paper is on providing an overview of the results of the nearly 20 years of research related to the discovery, examination, and potential benefits of semipermeable membrane behavior of bentonite-based geosynthetic clay liners (GCLs) commonly used as barriers or components of barriers in a variety of hydraulic and chemical containment applications, such as water and chemical retention ponds, tailings and coal ash impoundments, and solid waste landfills. First, the concept of solute restriction underlying semipermeable membrane behavior and the development of a solute-restriction or membrane efficiency coefficient (ω) and chemico-osmosis (q π) are described. Second, previously measured values of ω are presented for clays and GCLs for the purpose of illustrating the physical and chemical factors affecting ω. Third, the potential benefits of both ω and q π in terms of hydraulic and chemical containment applications are illustrated, and the relative importance of ω versus q π is described. Finally, some of the remaining issues related to the semipermeable membrane behavior of GCLs, such as the uniqueness of the measured ω and the persistence of ω at high salt concentrations, are discussed.

Assessment of membrane and diffusion behavior of soil-bentonite slurry trench wall backfill consisted of sand and Xanthan gum amended bentonite

The diffusion and semi-permeable membrane behavior are significant for evaluating pollution containment effectiveness of soil-bentonite slurry trench wall backfill (referred to as SB backfill) at contaminated sites. In this study, chemico-osmotic tests were performed on xanthan gum amended SB backfill (referred to as XGSB backfill) and conventional SB backfill utilizing zinc nitrate and lead nitrate solutions as tested liquids. The effective diffusion coefficient (D*), retardation factor (Rd), and chemico-osmotic efficiency coefficient (ω) of the backfills were evaluated. The results revealed that each tested backfill behaved as a semi-permeable membrane material with measured ω ranging from 0.015 to 0.14 and 0.007 to 0.05 when exposed to lead and zinc solutions with concentrations varying from 0.5 to 50 mM, respectively. The ω and Rd values for the backfills decreased with increasing concentrations of the tested solutions, while the D* of heavy metal cations increased, regardless of backfill type and tested solution type. Compared to the SB backfill, the ω and Rd of the XGSB backfill were higher while the D* was lower. The values of ω, D*, and Rd for the XGSB backfill were compared to those for soil-bentonite backfills in previous studies. A linear equation was presented to evaluate the correlation between ω and solute concentration in a semi-logarithmic scale. Finally, the advantages of considering membrane behavior in the design of slurry trench wall was discussed with the aid of an example analysis based on the measured ω and D* for the SB and XGSB backfill.

The role of diffusion induced electro-osmosis in the coupling between hydraulic and ionic fluxes through semipermeable clay soils

Most of the experimental research conducted to date has provided evidence on the semipermeable membrane behaviour of smectite-rich clay soils, the extent of which is typically quantified through the reflection coefficient, when the permeant (electrolyte) solution contains a single monovalent or divalent salt. Under such conditions, the osmotic flow of solution is controlled to a great extent by the different accessibility of ions and water molecules to the soil porosity, which is referred to as the chemico-osmotic effect. However, theoretical simulations of coupled solute and solvent transport suggest that, when two or more cations that diffuse in water at different rates are present simultaneously in the permeant solution, the electro-osmotic effect, which stems from the condition of null electric current density through the porous medium, can be enhanced compared to the case of a single salt to such an extent that it becomes comparable to or even greater than the chemico-osmotic effect. An original closed-form analytical solution to the problem of calculating the diffusion potential, which in turn controls the magnitude of the electro-osmotic effect, is here illustrated, and the relative importance of the aforementioned contributions to multi-electrolyte systems is examined through the interpretation of laboratory test results from the literature pertaining to a bentonite amended clay soil in equilibrium with aqueous mixtures of potassium chloride (KCl) and hydrochloric acid (HCl). The proposed mechanistic model is shown to be able to quantitatively capture the impact of both chemico-osmosis and electro-osmosis on the measured reflection coefficient of smectite clays, thereby breaking new ground in the experimental and theoretical research on the osmotic properties of engineered clay barriers in contact with mixed aqueous electrolyte solutions.

Heavy metals containment by vertical cutoff walls backfilled with novel reactive magnesium-activated slag-bentonite-sand: Membrane and diffusion behavior

This study aims to investigate the membrane and diffusion behavior of a novel vertical cutoff wall backfill comprised of reactive magnesium-activated slag, bentonite and sand (referred as MSBS backfill) for the containment of heavy metals in groundwater. The MSBS backfill specimens were subjected to a series of multi-stage chemico-osmotic tests using Pb(NO3)2 and Zn(NO3)2 solutions at different concentrations. Chemico-osmotic efficiency coefficient, effective diffusion coefficient, and retardation factor of the backfills were computed. For computing chemico-osmotic efficiency coefficient, the theoretical chemico-osmotic pressure differences were computed using both van't Hoff equation and water activity method. The results showed that the MSBS backfill exhibited semipermeable membrane behavior in tested solutions. The chemico-osmotic efficiency coefficients of the backfills decreased, whereas effective diffusion coefficients of heavy metal cations remained nearly constant, and retardation factors of heavy metal cations increased slightly with the increase of metal concentration. For the range of concentrations of Zn(NO3)2 in this study, the maximum percent error of theoretical chemico-osmotic pressure difference calculated using van't Hoff equation relative to that calculated using water activity method was 14.4%. A comparative assessment of reported chemico-osmotic efficiency coefficient, effective diffusion coefficient, and retardation factor values for various soil-bentonite backfills and geosynthetic clay liners with those for MSBS backfill was performed. Overall, the results are useful to assess containment performance of MSBS vertical cutoff walls at metal-contaminated groundwater sites.

Modelling non-isothermal volume change and solute transport behaviours of a semi-permeable clay soil under the combined influence of mechanical loading, chemical-osmosis, and thermo-osmosis

Clays are widely used in geotechnical and geoenvironmental engineering applications and it is crucial to understand its behaviour for the dynamic field conditions. The presence of a temperature gradient across clayey soils that exhibit semi-permeable membrane (or osmotic) behaviour may promote a number of complex processes, including thermal expansion or consolidation, thermally induced osmosis, thermal diffusion, along with other flow and deformation processes. Chemical-osmosis and chemico-osmotic consolidation that are significant in isothermal conditions are also affected by temperature. Publications on chemical-osmosis, and to some extent thermo-osmosis behaviour of semi-permeable clays under coupled conditions are widely available. However, studies that include the influence of both thermo-osmosis and chemical-osmosis together are rare. In this paper, a fully coupled numerical model is presented to study the effects of both osmotic processes on thermo-hydro-mechanical-chemical behaviour of semi-permeable clays. Solute spread in a landfill clay liner is investigated under the combined influence of mechanical, thermal, and chemical loading. Model results show that the clay deformation is sensitive to thermo-osmosis; and the effects of thermo-osmotic consolidation, excess pore water dissipation, and the overall settlement increases with temperature. Variation of the source temperature from 40 °C to 80 °C yielded an increase of 11.3% of the peak soil settlement. Significant contribution of thermo-osmosis on solute transport is noticed in this study and ignoring the process substantially deviate from the realism. Up to 80% overprediction of cadmium spread is observed in the clay liner when the thermo-osmotic processes are neglected.

Influence of Variable Membrane Behavior of Clay on Solute Transport

It is well established that clays can exhibit semipermeable membrane behavior and osmotic efficiency is used to describe the membrane behavior of clays. Several experimental results have already verified that osmotic efficiency is not constant when pore-fluid chemistry changes. In this article, based on the mechanical balance, generalized Darcy's law and the principle of mass conservation, an improved fully coupled hydro-chemo-mechanical model is proposed for saturated clayey materials, in which osmotic efficiency is treated as a variable that depends on the solute concentration, grain density, porosity of soil, and cation exchange capacity. Numerical simulations are conducted to investigate the influence of variable osmotic efficiency on solute transport. The results show that solute transport is very sensitive to osmotic efficiency and when the transport time is 10 years, the difference in influence depth reaches about 13.6 cm with constant (0.069) and variable (initially 0.069) osmotic efficiencies, this indicates that semipermeable membrane behavior of clays with variable osmotic efficiency restricts the solute transport effectively and slows down the solute movement strongly. The difference in breakthrough time reaches 15.8 years with osmotic efficiency (0.069). The proposed coupled model can be used to guide the design of clay liners and evaluate their service performance.

A novel transient gravimetric monitoring technique implemented to GCL osmotic suction control

A modified osmotic suction control technique for monitoring apparent transient weight changes was successfully adapted to the wetting and drying paths of geosynthetic clay liners (GCLs). Reasonable control was possible, enabling suction equilibrium to be achieved without disruption to the test. The results provide unique insight into the time-dependent changes in water retention properties and the semi-permeable membrane behaviour of the bentonite component in GCLs. The stages of suction equilibrium, related to the tri-modal pore structure of GCLs and the point of capillary break, could also be monitored. While the osmotic method has been traditionally used to control matric suction (up to 10 MPa) in soils, the overall results presented in this paper indicate that its application for total suction control in GCLs is largely due to the membrane behaviour of their bentonite component. Furthermore, because of capillary break between the GCL and the osmotic solution at the water entry (or residual) suction value of a GCL, an upper limit of 2.8 MPa suction is recommended for the application of the osmotic method to measure the water retention properties of GCLs.

Membrane Behavior of Unsaturated Sodium Bentonite

AbstractChemical containment barriers comprising sodium bentonite (Na-bentonite) have been shown to exhibit semipermeable membrane behavior under saturated conditions. Since membrane behavior resul...

Membrane behavior of compacted sand–bentonite mixture

Semi-permeable membrane behavior contributes to the containment function of engineered barriers used for waste containment by restricting the migration of dissolved chemical species (solutes) such as aqueous-phase contaminants. The existence of membrane behavior has been demonstrated extensively for virtually all categories of bentonite-based containment barriers except compacted sand–bentonite mixtures. Accordingly, membrane tests were conducted on two specimens of a compacted sand–bentonite mixture comprising 15% bentonite (dry weight) with sufficiently low hydraulic conductivity (i.e., ≤1.0 × 10−9 m/s) to be suitable for use as a waste containment barrier. Despite the imposition of relatively complex chemical conditions, including the use of tap water versus de-ionized water as a circulating liquid and incomplete flushing (leaching) of soluble salts from the specimens prior to membrane testing, the results were in good agreement with those previously reported for other bentonite-based engineered barriers when exposed to similar or the same types of salts and salt concentrations. Also, both compacted soil–bentonite specimens exhibited similar magnitudes of membrane behavior, with measured membrane efficiencies ranging from 0.395 ± 0.053 to 0.063 ± 0.012 when exposed to source KCl solutions with concentrations ranging from 5 to 80 mmol/L, respectively. Thus, compacted sand–bentonite mixtures suitable for use as engineered containment barriers can exhibit semi-permeable membrane behavior, thereby potentially enhancing the containment function of the barriers.

Apparatus for Measuring Coupled Membrane and Diffusion Behavior of Unsaturated Sodium Bentonite

Core Ideas Coupled membrane and diffusion behavior was measured in unsaturated Na‐bentonite. A new testing apparatus advances the state of the art for coupled processes in clays. The membrane efficiency of Na‐bentonite increased as the degree of saturation decreased. Sodium bentonite (Na‐bentonite) has been shown to exhibit semipermeable membrane behavior—the ability to selectively restrict the migration of dissolved chemical species through the pores of the clay. However, experimental research to date has focused on the membrane behavior of Na‐bentonite almost exclusively under water‐saturated conditions (i.e., degree of saturation S = 1), even though membrane behavior under unsaturated conditions is expected to be more significant. Further, the limited number of studies that have been performed to evaluate membrane behavior in unsaturated soils have used only open systems to quantify membrane efficiency (ω), despite the testing advantages of using closed systems (e.g., more accurate measurement of ω, easier control of boundary conditions). Thus, a closed‐system testing apparatus capable of measuring coupled membrane and diffusion behavior in unsaturated Na‐bentonite was developed and then used to measure ω and salt diffusion in Na‐bentonite with S of 0.84 and 1.0. For a source solution (concentration difference) of 20 mM KCl, ω increased from 0.61 to 0.71 as S decreased from 1.0 to 0.84, which is consistent with the current conceptual understanding of membrane behavior and trends in the literature. In contrast, the effective diffusion coefficient for Cl− was essentially the same (i.e., ∼1.8 × 10−10 m2 s−1) for both specimens due to the small difference in S. The development of the testing apparatus advances the state of the art for laboratory measurement of coupled membrane and diffusion behavior in unsaturated clays commonly used as chemical containment barriers.

Limiting membrane and diffusion behavior of a geosynthetic clay liner

Bentonite based geosynthetic clay liners (GCLs) are commonly used as chemical containment barriers to minimize liquid flow and contaminant transport. The preference for GCLs relative to other materials for chemical containment include economy of use and superior engineering properties, including low hydraulic conductivity (k) and the ability to exhibit semipermeable membrane behavior that restricts the migration of solutes through the bentonite. In the case of low k (e.g., ≤10−10 m/s), diffusion is likely to be a significant, if not dominant, mechanism of chemical transport. The objective of this study was to evaluate the membrane and diffusion behavior of a GCL in the limit as the salt (KCl) concentration increased to the extent that any observed membrane behavior was destroyed. The results indicated that the observed membrane behavior for the GCL was essentially destroyed when the average KCl concentration across the GCL specimen, Cave, reached 200 mM KCl, which was greater than the value of Cave that would have been predicted on the basis of previous results. The results also indicated that the value of the effective diffusion coefficient, D*, for Cl− at this limiting value for Cave of 200 mM KCl was greater than the value of D* that would have been predicted on the basis of the use of lower values of Cave. However, the differences between the measured and predicted values of D* were relatively minor (≤11.3%), such that the differences likely would be insignificant for most practical applications.

Restricted salt diffusion in a geosynthetic clay liner

The influence of semipermeable membrane behaviour on salt diffusion through a geosynthetic clay liner (GCL) was investigated by conducting multi-stage membrane tests on four GCL specimens at different effective stresses (σ′ = 34·5–242 kPa) in flexible-wall cells. Each test was conducted by circulating five source potassium chloride solutions, sequentially from lowest to highest concentration (Co = 3·9, 6·0, 8·7, 20, 47 mM), across the top specimen boundary, while circulating de-ionized water across the bottom boundary. Membrane efficiency coefficients (ω) were determined from differential pressure measurements, and effective salt-diffusion coefficients [Formula: see text] were inferred from boundary electrical conductivities. Increases in [Formula: see text] with increasing Co were observed for all specimens and were correlated to decreases in ω. In each case, [Formula: see text] decreased linearly toward zero as ω → 1, regardless of the applied σ′. These results support the hypothesis from pore-scale physical modelling that [Formula: see text] for GCLs exhibiting membrane behaviour may be expressed as a linear function of the quantity 1 − ω.

Polymer-treated bentonite clay for chemical-resistant geosynthetic clay liners

ABSTRACT: The purpose of hydraulic barriers, such as geosynthetic clay liners (GCLs), is to isolate waste liquids from the environment. Bentonite clay is widely used in GCLs because of its elevated sealing capacity in the presence of water and its ability to restrict the migration of solutes (chemico-osmotic efficiency or semi-permeable membrane behaviour). However, exposure to high concentrations of inorganic solutions can change the clay fabric increasing its hydraulic conductivity and degrading its membrane behaviour, with a consequent harm to the environment. The aim of this research was to study the hydraulic and chemico-osmotic performance of amended clays. For this purpose, an engineered clay (HYPER clay) was developed through treatment of a natural bentonite with an anionic polymer and the results were compared with two amended clay materials (multi-swellable bentonite (MSB) and a dense prehydrated GCL (DPH GCL)). To demonstrate the potential benefits of polymer treatment, material characterisation through X-ray diffraction analysis, density of solid particles, Atterberg limits, and swelling tests was performed on treated and untreated samples. Subsequently, hydraulic conductivity and chemico-osmotic tests were performed with CaCl2 solutions on treated and untreated clays, to evaluate the modified clays resistance to chemical attack. The results of this research showed that the present amendment technology has a great potential for future GCL applications. X-ray diffraction analysis demonstrated the intercalation of the polymer in the interlayer region of the clay inducing a dispersed clay structure. The swell index and the liquid limit of the clay increased with increasing polymer dosage suggesting a potential benefit of the polymer on preserving the hydraulic performance of the clay. Unlike the untreated clay, HYPER clay treatment maintained low hydraulic conductivity of the clay to CaCl2 even in the long term and protected the clay against the destructive role of diffusion, maintaining the initial osmotic efficiency in the long term. Test results were also compared with other amended clays MSB and DPH GCL. These two amended clay materials displayed a chemico-osmotic behaviour at the steady state similar to that observed on untreated clay. On the other hand, the preservation of the chemico-osmotic efficiency of the HYPER clay with time suggests that the carboxymethyl cellulose was not flushed out during the long period of permeation with deionised water.

The ISSMGE Kerry Rowe Lecture: The role of diffusion in environmental geotechnics

Diffusion of contaminants can play a significant if not dominant role in many applications encountered within the field of environmental geotechnics. The objective of this paper is to provide an overview of the important role diffusion plays in such applications. The presentation proceeds from a historical perspective, beginning with the recognition in the late 1970s to early 1980s that diffusion may be an important process in assessing contaminant migration through low-permeability barriers in waste containment applications. Data from the literature and simplified model simulations are used to illustrate under what conditions diffusion is important, and the significance of diffusion is illustrated with respect to different barrier components and types of barriers used in waste containment applications. The barriers considered include natural clays, compacted clay liners, geomembranes, geosynthetic clay liners, composite liners, vertical cutoff walls, subaqueous caps for contaminated sediments, and highly compacted bentonite buffers for high-level radioactive waste containment. The significance of semi-permeable membrane behavior on liquid-phase diffusion through bentonite-based barriers also is highlighted. The potential importance of matrix diffusion as an attenuation mechanism for contaminant transport is illustrated, and the roles of both liquid-phase and gas-phase diffusion under unsaturated conditions are discussed. Finally, the role of diffusion in terms of remediation applications is illustrated via an example analysis illustrating the impact of reverse matrix or back diffusion on the effectiveness of pump-and-treat remediation, as well as via a summary of several diffusion-based models commonly used to describe the leaching of contaminants from a variety of stabilized–solidified waste forms.

Membrane behavior of bentonite-amended compacted clay

The performance of landfill liners can be enhanced if they exhibit a semipermeable membrane behavior, which restricts the migration of contaminants. Consequently, enhancing the membrane property of clays used for liners is becoming increasingly important. As bentonite has already proven to be an excellent additive for improving the membrane behavior of clay, the hydraulic conductivities and membrane behaviors of a locally available clay, known as Fukakusa clay, amended with different amounts of dry bentonite (5%, 10%, 15%, and 20%) were herein evaluated. The chemico-osmotic efficiency coefficient, ω, was obtained under different concentration differences of KCl solution (0.5, 1, 5, 10, and 50mM) for specimens in rigid-wall cells. The test results show that the ω of unamended clay is very low and can be ignored unless amended with bentonite, and that hydraulic conductivity k is suitably low (1.58×10−9m/s). Additionally, ω decreased as the KCl concentration increased, which is consistent with the theory that increasing concentration causes progressively greater shrinkage of the diffuse-double layers of the clay particles. Furthermore, the mechanisms that influence the membrane behavior are discussed from the viewpoints of the diffuse-double layer and the interparticle pore size with the assistance of SEM.

Calcium-Resistant Membrane Behavior of Polymerized Bentonite

Traditional (unmodified) sodium bentonite (Na-bentonite) has been shown to exhibit semipermeable membrane behavior, which is beneficial in terms of the use of Na-bentonites as barriers or components of barriers for hydraulic containment applications. However, degradation of such membrane behavior due to the diffusion of cations into the bentonite also is known to occur, and this degradation increases with increasing salt concentration and increasing valence (charge) of the principle salt cation (e.g., Ca2+ versus K+). In this study, the membrane behavior of a polymerized bentonite referred to as a bentonite-polymer nanocomposite (BPN) was determined during multistage membrane tests using solutions of CaCl2. The BPN illustrated improved membrane behavior relative to that previously reported for both traditional and other chemically modified bentonites. However, complete degradation of the membrane behavior was ultimately observed for specimens of the BPN exposed to 10 mM CaCl2 for a test conducted in a rigid-wall cell and 20 mM CaCl2 for a test conducted in a flexible-wall cell. The destruction of membrane behavior for the specimen in the rigid-wall cell was attributed to short-circuiting along the side walls of the rigid-wall cell after shrinkage of the BPN, whereas destruction of the membrane behavior in the flexible-wall cell correlated with the time required to reach steady-state diffusion of calcium (Ca2+). Thus, the enhanced calcium-resistant behavior of the BPN was limited and was affected by the type of cell (rigid-wall versus flexible-wall) in which the membrane behavior was measured.

Improving membrane performance via bentonite polymer nanocomposite

Traditional (non-treated) sodium bentonite has been shown to exhibit substantial semipermeable membrane behavior, or the ability to restrict the migration of solutes. However, partial or complete degradation of the membrane behavior due to diffusion of invading salt cations into the sodium bentonite also has been observed. In this study, a polyacrylate modified bentonite, referred to as a bentonite polymer nanocomposite, or BPN, was evaluated as a potential substitute for sodium bentonite for the purpose of providing increased resistance to salt degradation of membrane behavior. The membrane behavior of the BPN was measured in the laboratory by establishing differences in salt concentrations ranging from 4.7 to 54mM KCl across specimens contained in either rigid-wall or flexible-wall cells under closed-system boundary conditions. The measured membrane efficiency coefficients, ω, for the BPN specimens were greater than those previously reported for specimens containing sodium bentonite under similar testing conditions. For example, the measured ω values for the BPN specimens ranged from 109% to 433% of those previously reported for the specimens containing traditional sodium bentonite, depending on the initial porosity or initial effective stress of the specimen, the concentration of KCl, and the type of test cell (rigid vs. flexible), and despite the BPN specimens not being flushed of soluble salts prior to membrane testing as in the case of the specimens containing sodium bentonite. Thus, the BPN exhibited substantially improved membrane behavior under conditions that presumably were more adverse with respect to soluble salts than those previously reported for specimens containing a sodium bentonite. However, the potential role that any excess low molecular weight polymer in the BPN may have played in affecting the results is uncertain, such that additional testing of the BPN is warranted to better understand the long-term behavior of the BPN.

Consolidation enhanced membrane behavior of a geosynthetic clay liner

Semipermeable membrane behavior in clays refers to the ability of clays to restrict the migration of solutes. Thus, membrane behavior represents a potential benefit to the containment function of clay barriers used for hydraulic containment applications. In this regard, the potential influence of consolidation effective stress, σ′, on the membrane behavior of a geosynthetic clay liner (GCL) containing sodium bentonite was evaluated in the laboratory by establishing differences in salt (KCl) concentrations ranging from 3.9 to 47 mM across specimens of the GCL in a flexible-wall cell under closed-system boundary conditions. The membrane behavior exhibited by the GCL was enhanced via consolidation such that an increase in σ′ from 34.5 kPa (5 psi) to 241 kPa (35 psi) correlated with an increase in membrane efficiency from 0.015 (1.5%) to 0.784 (78.4%), respectively. The membrane efficiencies measured in this study at σ′ of 172 kPa (25 psi) and 241 kPa (35 psi) were similar to those previously reported for the same GCL using a rigid-wall cell but at unknown states of stress. The practical significance of the results is illustrated in the form of an analysis showing a reduction in liquid flux across the GCL with increasing membrane efficiency.

Osmotic efficiency in Callovo-Oxfordian argillites: Experimental vs. theoretical models

Argillaceous media are known for their possible semi-permeable membrane behaviour which is represented by the osmotic efficiency ε. The identification of this parameter allows a characterization of the possible coupled fluxes through such media. Osmotic experiments conducted by Andra in the Callovo-Oxfordian argillite at Meuse/Haute-Marne URL have been interpreted using a numerical model. These interpretations provide values for the osmotic efficiency in this formation. These experimental data are then compared with estimates obtained using theoretical models for the osmotic efficiency. These models are the “average frictional” model by Marine and Fritz (Marine, I.W., Fritz, S.J., 1981. Osmotic model to explain anomalous hydraulic heads. Water Resources Research 17 (1), 73–82; Fritz, S.J., Marine, I.W., 1983. Experimental support for a predictive osmotic model of clay membranes. Geochimica and Cosmochimica Acta 47, 1515–1522), the “integrated frictional” model by Bresler (Bresler, E., 1973. Anion exclusion and coupling effects in nonsteady transport unsaturated soils: I. Theory. Soil Science Society of America Proceedings 37 (5), 663–669) and the “mechanical” model by Revil and Leroy (Leroy, P., Revil, A., 2004. A triple-layer of the surface electrochemical properties of clay minerals. Journal of Colloid and Interfacial Science 270, 371–380). The values for the physical and petrophysical parameters which must be introduced in such theoretical models to match the measured osmotic efficiency are compared to the available data in the literature. The “average frictional” model does not reproduce the data with realistic parameters. Despite the satisfactory results obtained with the Bresler’s model (Bresler, E., 1973. Anion exclusion and coupling effects in nonsteady transport unsaturated soils: I. Theory. Soil Science Society of America Proceedings 37 (5), 663–669), in its current form, this model is questionable since the electrical model which is implemented is not accurate known theory. The “mechanical” model gives promising results, despite a limitation for high concentrations. We show that the pore size is a crucial petrophysical parameter for the theoretical models. The pore size required in the “mechanical” model is ∼5 nm. This value is representative of the pore size where the osmotic process can exist. This value would thus suggest a throat effect.