Diffuse Double Layer Theory Research Articles

On wettability of shale rocks

The low recovery of hydraulic fracturing fluid in unconventional shale reservoirs has been in the centre of attention from both technical and environmental perspectives in the last decade. One explanation for the loss of hydraulic fracturing fluid is fluid uptake by the shale matrix; where capillarity is the dominant process controlling this uptake. Detailed understanding of the rock wettability is thus an essential step in analysis of loss of the hydraulic fracturing fluid in shale reservoirs, especially at reservoir conditions. We therefore performed a suit of contact angle measurements on a shale sample with oil and aqueous ionic solutions, and tested the influence of different ion types (NaCl, KCl, MgCl2, CaCl2), concentrations (0.1, 0.5 and 1M), pressures (0.1, 10 and 20MPa) and temperatures (35 and 70°C). Furthermore, a physical model was developed based on the diffuse double layer theory to provide a framework for the observed experimental data.Our results show that the water contact angle for bivalent ions is larger than for monovalent ions; and that the contact angle (of both oil and different aqueous ionic solutions) increases with increase in pressure and/or temperature; these increases are more pronounced at higher ionic concentrations. Finally, the developed model correctly predicted the influence of each tested variable on contact angle. Knowing contact angle and therefore wettability, the contribution of the capillary process in terms of water uptake into shale rocks and the possible impairment of hydrocarbon production due to such uptake can be quantified.

Effect of thermal history on the properties of bentonite

The effect of thermal history on the properties of bentonite was studied through a number of experimental tests. The desired thermal history was created on samples of bentonite by keeping them at a fixed temperature (50, 100, 150, 200 and 250 °C) for a specific duration (3, 7, 14 and 30 days). Standard compaction, Atterberg limits, free swelling and swelling pressure tests were carried out on the samples on the dry side of optimum, optimum and wet side of optimum of the compaction curve with desired thermal history. In addition chemical tests were carried out on the flooding water at the end of the swelling test. The results showed that the changes in compaction characteristics were not considerable but the Atterberg limits, free swelling and swelling pressure of the soil were changed due to the thermal history in comparison with the soil without any thermal history. The magnitudes of free swelling and swelling pressure were dependent on the location of prepared sample on the compaction curve. In addition, the changes in Atteberg limits and swelling parameters (amount of free swelling and swelling pressure) were functions of magnitude of temperature and duration of time that the sample experienced the temperature in its temperature history. The effects of temperature and also duration of exposure of the soil to temperature was discussed with the aid of the Diffuse Double Layer (DDL) theory. It was found that the temperature may change the gradation of soil due to cementation of particles as a result of formation of some salts and oxides that help to paste the particles together and change the properties of the soil.

Compressibility and saturated hydraulic permeability of clay-polymer composites — experimental and theoretical analysis

In this study, the volumetric behaviour, hydraulic permeability and micro-fabric of clay-polymer composites fabricated by the use of polyacrylamide polymers were experimentally investigated and discussed by use of theoretical multiscale approaches. Composites were varied systematically in composition taking into account constitutive properties controlling clay-polymer interaction, i.e., clay mineralogy (kaolinite and montmorillonite dominated clays with predominantly mono- and divalent counterions, respectively) and polymer charge (nonionic, cationic, anionic). Composites were produced according to their individual maximum adsorbing capacity and prepared to slurry conditions. 1D compression and rebound tests were performed (2–800–25kPa) and the hydraulic permeability was calculated for each loading increment. Additionally, microscopic investigations in environmental scanning electron microscope were performed. It was found that cationic and anionic polymer adsorption promote aggregated and flocculated clay fabrics, respectively, whereas nonionic polymers promote dispersed clay fabrics. Macroscopically, this led to an increase in void ratio at the same stress level as well as to an increase (cationic polymers) or decrease (nonionic polymers) in hydraulic permeability. Micro- and macroscopic findings were theoretically analysed by use of diffuse double-layer (DDL) theory and cluster-model. A modified approach of DDL theory accounting for the effect of adsorbed nonionic polymers on the electric potential in the nearfield of clay mineral surfaces was derived. Theoretical results were found to be in good agreement with experimental results on volumetric behaviour. By use of cluster-model, hydraulic permeabilities were found to correlate to the microscopic findings on clay micro-fabric.

Impact of organic pollutants on the macro and microstructure responses of Na-bentonite

Bentonite (Bent) is a favorable buffer material for waste containment barriers, although its properties may be affected by the pore fluid chemistry. Hence, this study investigates the role of different organic pollutants including methanol, acetone, acetic acid, and citric acid on the macro and microstructure responses of Na+-Bent. The chemicals at various concentrations (0 to 80% by the volume of distilled water) were separately added to the soil samples which were then subjected to a set of tests. The results indicate that an increase in the concentration of organic permeants by decreasing the dielectric constant (ε) reduces the plasticity index, compressibility and swelling potential of soil; whereas, the permeability increases. Such changes are ascribed to a tighter packing of the clay particles, as clearly confirmed by the SEM micrographs and XRD patterns. The decrease in the absolute value of soil zeta potential also supports the development of coagulated structure in the artificially contaminated samples upon reducing the ε of solution. However, the results reveal that the sensitivity of soil properties to the variations in the ε value is pronounced at the intermediate stages of concentration (i.e. the organic fluid/water ratio<60%) when the ε is higher than 50. In addition, at relatively low concentration, the acidic permeants dramatically alter the soil fabric due to having lower pH, causing remarkable effects on the hydro-mechanical parameters as compared to the other chemicals. Overall, the organic pollutants, depending on their type and concentration, exert negative impact on the barrier performance of Na+-Bent which are not precisely comparable only with reference to the changes in the dielectric constant of pore fluid, and thereby may not be completely explained by the diffuse double layer (DDL) theory.

Consolidation behaviour of bentonites in the presence of salt solutions

Due to its high swelling capacity and lower value of hydraulic conductivity, compacted bentonite is used as a liner material at the waste disposal site. Salts presents in landfill leachates may cause the diffuse double layer of bentonite to shrink which in turn affects its swelling and compressibility behaviour. Consolidation is among important properties of the liner material which need to be studied for settlement analysis. This study was carried out to investigate the effect of NaCl and CaCl2 solutions of varying concentrations, on the consolidation behaviour of two compacted bentonites having different mineralogical composition. The bentonites were studied in terms of changes in the mechanical parameters including the coefficient of volume change (mv), coefficient of consolidation (cv), compression index (Cc) and time taken to complete 90% of consolidation (t90) in the presence of the salt solutions. The results showed that the Cc, mv and t90 of the bentonites decreased, whereas, cv increased with the increase in salt concentration. Bentonite of higher quality defined by having a higher cation exchange capacity, exchangeable sodium percentage and swelling capacity, exhibited higher values for Cc, mv and t90 in comparison to lower quality bentonite. Results also showed that irrespective of the salt solution present cv decreased, whereas, t90 increased with increase in the consolidation pressure. However, with increasing in the pressure, mv increased initially and after reaching a peak value it decreased. A higher value of theoretical void ratio was obtained from diffuse double layer theory for both the bentonites at lower overburden pressure and water as pore fluid. However, with increase in the consolidation pressure the theoretically obtained void ratio–pressure curve converged towards the experimentally obtained curve and crossed it at certain pressure and diverged again. However, with salt as a pore fluid a higher value of experimentally obtained void ratio was observed.

Prediction of Compressibility Data for Highly Plastic Clays Using Diffuse Double-Layer Theory

AbstractMontmorillonite-rich clays are important in many engineering applications. The compressibility of such plastic clays at high consolidation pressures is important for predicting routine settlement and for applications in nuclear-waste repositories. Laboratory measurement of compressibility data at high consolidation pressures is not only time consuming but very expensive also. Theoretical predictions can help to determine the compressibility of plastic clays at high consolidation pressures. A linear relationship between e/eNvs. 1/√P (eN is the normalization void ratio at normalization pressure N and P is the consolidation pressure) was derived using diffuse double-layer theory. The compressibility data of several plastic clays in published studies were found to support the derived relationship. A generalized theoretical equation was proposed to predict the compressibility data over a wide range of consolidation pressures using an experimentally measured void ratio at low consolidation pressure. The compressibility data for different plastic clays were predicted accurately up to maximum consolidation pressures that ranged from 0.7 to 30 MPa using an experimentally measured void ratio near the pre-consolidation pressure. The preconsolidation pressures for different clays considered here ranged from 25 to 133 kPa. The proposed predictive model is supported by experimental data, is simple, and does not require knowledge of clay-surface and pore-fluid parameters.

Model evaluation of geochemically induced swelling/shrinkage in argillaceous formations for nuclear waste disposal

Argillaceous formations are being considered as host rocks for geologic disposal of nuclear waste in a number of countries. One advantage of emplacing nuclear waste in such formations is the potential self-sealing capability of clay due to swelling, which is of particular importance for the sealing and healing of disturbed rock zones (DRZ). It is therefore necessary to understand and be able to predict the changes in swelling properties within clay rock near the waste-emplacement tunnel. In this paper, considering that the clay rock formation is mostly under saturated conditions and the swelling property changes are mostly due to geochemical changes, we propose a modeling method that links a THC simulator with a swelling module that is based on diffuse double layer theory. Simulations were conducted to evaluate the geochemically induced changes in the swelling properties of the clay rock. Our findings are as follows: (1) geochemically induced swelling/shrinkage occurs exclusively in the EBS–clay formation interface, within a few meters from the waste-emplacement tunnels; (2) swelling/shrinkage-induced porosity changes are generally much smaller than those caused by mineral precipitation/dissolution processes; (3) geochemically induced swelling/shrinkage of the host clay rock is affected by variations in the pore water chemistry, exchangeable cations, and smectite abundance. Neglecting any of these three factors might lead to a miscalculation of the geochemically induced swelling pressure.

Influence of phosphate sorption on dispersion of a Ferralsol

Soil dispersion induces soil erosion and colloidal leaching. Nutrients are lost at the same time and this causes water contamination. Phosphate is an essential element for living organisms. Because phosphate influences soil dispersion and it is an important limited resource, this influence must be evaluated well in order to diminish negative effects on soil structure. In this paper, we firstly evaluated the influence of phosphate sorption on soil dispersion by calculating repulsive potential energy between soil particles. Ferralsol, which is a typical soil in rainy tropical regions, was used as the material. The dispersion-flocculation phenomena were investigated with absorbance of soil suspension under different pH, phosphate adsorption and electrolyte concentration in an Na-NO3-PO4 system. The repulsive potential energy was calculated based on the diffuse double layer theory and the measured zeta potential. We indicated that the measured absorbance increased with the increase of the repulsive potential energy. The repulsive potential energy increased with increasing phosphate sorption up to about 5 to 20 mmol kg−1 at all pH, and it induced the soil dispersion, because phosphate sorption increased the negative charge of the soil. After its peak, it decreased with increasing phosphate sorption because the electrolyte concentration increased and the electrolyte screened the electric field near the soil surface. The repulsive potential energy also increased with increasing pH because of the increase of the negative charge of the soil. Even at low pH, after a certain amount of phosphate sorption, the soil dispersed due to the increase of repulsive potential energy, although the soil flocculated before phosphate application. Because the soil dispersion causes soil and phosphorus loss, the influence of soil pH and phosphate sorption on the soil dispersion should be considered for good soil management.

Effects of pore water chemical composition on the hydro-mechanical behavior of natural stiff clays

Boom Clay and Ypresian Clays have been considered as potential geological host formations for radioactive waste disposal in Belgium. Considering the significant differences in pore water chemical composition between several sites involving these two formations as well as the possible evolution of the chemical composition during the large lifespan of a radioactive waste disposal, it appeared important to investigate the effects of pore water chemical composition on the hydro-mechanical behaviors of these two potential host formations. In this study, these effects were investigated by carrying out specific œdometer tests. Different compositions were considered for this purpose: distilled water, synthetic site water, and Sodium Chloride solutions at concentrations of 15 and 30g/L. Clear effects of pore water chemical composition on the hydro-mechanical behavior were observed: increasing pore water salt concentration gave rise to (i) increase of œdometric modulus Eœd, permeability K and consolidation coefficient Cv; and (ii) decrease of compression slope c′c, swelling slope c′s and secondary compression coefficient Cαe, which is in agreement with the diffuse double layer theory and the clay particle aggregation as identified by microstructural analyses. Furthermore, the pore water chemical composition effects were found to be mineralogy, stress state and salt concentration dependent: (i) Ypresian Clays with higher smectite content showed clearer chemical effect on the coefficient of consolidation Cv; (ii) the chemical effects on compressibility and swelling capacity parameters were found to be attenuated with increasing vertical stress; and (iii) the increase of chemical effect with increasing pore water salinity was limited to a certain salt concentration. The competition between the physico-chemical and mechanical effects was identified: the pore water chemical composition effect is clear only in the low-stress range where the hydro-mechanical behavior is dominated by the physico-chemical effect.

An electrification mechanism of sand grains based on the diffuse double layer and Hertz contact theory

The electrification of sand grains lifting off from sand bed is investigated experimentally. It was found that sand grains were able to carry charges, which is comparable in magnitude with the experimental results and is related to grain sizes, pH of soil, relative humidity, and electric field. Based on the theory of diffuse double layer (DDL) and Hertz contact theory, an electrification mechanism due to the break of DDLs of sand grains is presented and a formula which takes environmental conditions and grain parameters into consideration is obtained to calculate the charge-mass ratio of lift-off sand grains.

An alternative approach for the use of DDL theory to estimate the swelling pressure of bentonites

An approach to estimate the swelling pressure of compacted bentonite (Bent) using Gouy–Chapman diffuse double layer theory is presented. Several laboratory swelling pressure tests on compacted Bent (MX80 and Calcigel) under constant volume conditions were performed and compared with the calculated swelling pressure using the original theory. The study revealed that at low dry density the as prepared total void ratios are less than theoretical void ratios using diffuse double layer theory, however, reverse behavior has been noticed for high compaction dry densities. Based on the experimental results of Bent with different valences, the relationship between the theoretical void ratio from diffuse double layer theory and as prepared total void ratio were determined. New equations were derived on the basis of diffuse double layer theory and experimental swelling pressure data. The method categorizes the different Bents into two groups depending upon the weighted average valency. A good agreement was observed in all the cases between experimental and estimated swelling pressure using derived equations. The applicability of the proposed method was investigated by comparing the estimated swelling pressure results with the additional reported in literature laboratory results on swelling pressure of compacted Bent.

Effect of Stern-layer on the compressibility behaviour of bentonites

The Stern theory as applicable to interacting parallel clay platelet systems was used to study the compressibility behaviour of bentonites. For a constant surface electrical potential, the distribution of the total electrical charge among the Stern-layer and the Gouy-layer was found to have significant influence on the electrical potential at the midplane between clay platelets. Consideration of the Stern-layer was found to reduce the repulsive pressure or the swelling pressure between clay platelets at large platelet spacing, whereas the repulsive pressure increased significantly when the interacting Gouy-layers were pushed aside. A far greater repulsive pressure was noted for Ca-bentonite than that occurred for Na-bentonite at a platelet distance close to 1.0 nm. Similarly, strong interaction between clay platelets was noted due to suppressed Gouy-layers when the bulk fluid concentration was increased. The repulsive pressure generated due to the overlapping of the Stern-layers was found to be sensitive to changes in the specific adsorption potential, the dielectric constant of the pore fluid in the Stern-layer, and the surface electrical potential. Comparisons of the calculated pressure–void ratio relationships from the Stern theory and the Gouy-Chapman diffuse double layer theory with the experimental consolidation test results of Na- and divalent-rich bentonites showed that, in general, the Stern theory improved the predictions of pressure–void ratio relationships, particularly for pressures greater than 100 kPa; however, strong agreements were lacking in all the cases studied.

A coupled mechanical and chemical damage model for concrete affected by alkali–silica reaction

To model the complex degradation phenomena occurring in concrete affected by alkali–silica reaction (ASR), we formulate a poro-mechanical model with two isotropic internal variables: the chemical and the mechanical damage. The chemical damage, related to the evolution of the reaction, is caused by the pressure generated by the expanding ASR gel on the solid concrete skeleton. The mechanical damage describes the strength and stiffness degradation induced by the external loads. As suggested by experimental results, degradation due to ASR is considered to be localized around reactive sites. The effect of the degree of saturation and of the temperature on the reaction development is also modeled. The chemical damage evolution is calibrated using the value of the gel pressure estimated by applying the electrical diffuse double-layer theory to experimental values of the surface charge density in ASR gel specimens reported in the literature. The chemo-damage model is first validated by simulating expansion tests on reactive specimens and beams; the coupled chemo-mechanical damage model is then employed to simulate compression and flexure tests results also taken from the literature.

Quantitative Interpretation of Anomalous Coagulation Behavior of Colloidal Silica Using a Swellable Polyelectrolyte Gel Model of Electrical Double Layer

Electrolyte-induced coagulation of colloidal dispersions of silica has remained a puzzle for many decades, and it is widely considered anomalous from the viewpoint of traditional Gouy-Chapman theory of diffuse double layer and ζ-potential at ideal surfaces and of their electrostatic interaction (Derjaguin-Landau-Verwey-Overbeek, DLVO theory). It is suggested that this anomaly is caused by the fact that silica particles are covered with swellable gel layers. Theoretical stability ratios are calculated combining the attractive van der Waals and repulsive electrosteric interactions between core-shell (soft) model spheres with homogeneously distributed fixed charges in the shells and matched with the experimental ones measured for nonporous silica microspheres of different diameters (50, 150, and 320 nm) in an univalent electrolyte (KCl) of increasing concentration and pH (2.6, 4, 6, and 8). The variation in the shell thickness with the KCl concentration (mimicking the charged gel layer swelling) as the only adjustable parameter, deduced in such a way from data at pH 6 and 8, not only can explain the parallel experimental electrophoretic mobilities but also conforms itself to a scaling law derived from the thermodynamic theory of polyelectrolyte hydrogels. A resulting inapplicability of the DLVO theory and the ζ-potential concept for a quantitative predicting the coagulation kinetics of gel layer-covered colloids is discussed.

Modification of clay adhesion to improve tunnelling excavation

Mechanical tunnel driving by means of tunnel boring machines through clayey soils often leads to clogging problems which cause delays in tunnel construction and economic issues. Taking into account the diffuse double-layer theory, two very well-known clay formations, namely the Ypresian and Boom clays were investigated. Several geotechnical tests and a new adhesion test (cone pull-out test) were performed using water and solutions with different sodium chloride concentration as pore fluids. The results showed a reduction of the liquid limit for both clays when salt solutions were used instead of water. Undrained shear strength of the Ypresian clay progressively increased as the sodium chloride concentration of the pore fluid increased, whereas that of the Boom clay, which contains less smectite, was less sensitive to the chemical composition of the pore fluids. Cone pull-out tests, developed to detect the adhesive properties of clays, showed a drastic drop of clogging for the Ypresian clay when mixed with sodium chloride solutions within the entire consistency range studied, whereas in the case of Boom clay the variation was less evident and a clear effect was only observed at low consistencies. The results are promising for improving tunnelling excavation performance by adding sodium chloride solutions to avoid problems derived from adhesion of clayey soils.

Novel procedure for the estimation of swelling pressures of compacted bentonites based on diffuse double layer theory

Bentonite clays are proven to be attractive as buffer and backfill material in high-level nuclear waste repositories around the world. A quick estimation of swelling pressures of the compacted bentonites for different clay–water–electrolyte interactions is essential in the design of buffer and backfill materials. The theoretical studies on the swelling behavior of bentonites are based on diffuse double layer (DDL) theory. To establish theoretical relationship between void ratio and swelling pressure (e versus P), evaluation of elliptic integral and inverse analysis are unavoidable. In this paper, a novel procedure is presented to establish theoretical relationship of e versus P based on the Gouy–Chapman method. The proposed procedure establishes a unique relationship between electric potentials of interacting and non-interacting diffuse clay–water–electrolyte systems. A procedure is, thus, proposed to deduce the relation between swelling pressures and void ratio from the established relation between electric potentials. This approach is simple and alleviates the need for elliptic integral evaluation and also the inverse analysis. Further, application of the proposed approach to estimate swelling pressures of four compacted bentonites, for example, MX 80, Febex, Montigel and Kunigel V1, at different dry densities, shows that the method is very simple and predicts solutions with very good accuracy. Moreover, the proposed procedure provides continuous distributions of e versus P and thus it is computationally efficient when compared with the existing techniques.

Liquid limit of mixtures of smectite, kaolinite and quartz powder with water and NaCl solution

Clay mineralogy plays an important role in determining the mechanical properties of clayey materials. Several liquid limit and water uptake tests were performed on kaolinite-smectite mixtures for different quartz powder content and water and / or NaCl content as pore fluids. To interpret the results, the diffuse double layer theory is used. The experimental results show the effect of quartz powder in reducing the liquid limit of smectite with water and 1 M NaCl as fluid. A linear relationship is obtained from the tests. The quartz powder acts only to dilute the liquid limit values. To better understand the behavior of the clays regarding the liquid limit, predicted values for the liquid limit of all the mixtures with water and NaCl as pore fluid have been developed assuming the linear law to be valid. The prediction is very good for water, but it becomes less good with lower liquid limit values/higher quartz contents. The correlation with NaCl as fluid is not that good when the quartz content is high. A correlation of water uptake and liquid limit is also presented. The data fit is good. The overall results confirm that the effect of the pore fluid type is significant when the smectite content in the mixture is high.

Swelling Pressures of some initially Saturated and Compacted Saturated Bentonites

The swelling pressures of several bentonites (Bentonite S-2, Febex, Calcigel, Montigel, Kunigel, Kunigel V1, Na-Kunigel, Alaska, Ca-Fourges, MX80, Na-Ca MX80, Ca-Wyoming, and Na- Wyoming) were determined from the Gouy-Chapman diffuse double layer theory. Many of these bentonites have been considered as barrier and backfilling materials for the underground storage of nuclear waste in various countries. The theoretical swelling pressures were then compared with the reported experimental swelling pressures for both initially saturated and compacted saturated samples. Qualitative agreements between the theoretical predictions and the experimental results were noted for all the bentonites studied. However, it was noted that at low dry densities or high void ratios, the theory generally predicted higher swelling pressures with the reverse trend at high dry densities or low void ratios. The lesser magnitude of experimental swelling pressures at higher void ratios can possibly be attributed to the formation of clay domains. Such behaviour also supports the fact that the effects of counterion crowding near the surfaces of the clay platelets are to reduce the surface charge and the electric potential at the Gouy-Stern plane. At smaller void ratios, the overlapping of the Stern layers of adjacent clay platelets influenced the swelling pressures. In this case, much stronger swelling pressures were exhibited by the bentonites.

Influence of ethanol/water mixture on the undrained shear strength of pure clays

The mechanical properties of clays are highly dependent not only on the stress/strain ratio to which the material is subjected but also on the chemistry of the pore fluids which in turn affects the intergranular or the effective stresses. Atterberg limits and vane shear tests were performed with different pore fluids in order to observe how the fine-grained material mechanically responded. The diffuse double layer theory has been used to interpret the data of vane shear tests in order to explain the variation of geotechnical responses with the different clays. Van der Waals forces and double layer forces were obtained and capillary forces calculated. The results show that while for kaolinite and illite the chemistry of the pore fluids has no influence on the water content and hence on the mechanical behaviour of the material, Na-smectite shows a strong correlation between the dielectric constant of the pore fluids and an increase in undrained shear strength. The data obtained extends an understanding of the influence of the dielectric constant (e) of the pore fluids on the geotechnical properties of fine-grained materials.

Prediction of the compressibility behavior of highly plastic clays under high stresses

A simple method is proposed to predict the compressibility behavior of highly plastic clays (bentonites/montmorillonites) under high pressures using data describing their behavior under low pressures. It was shown that the void ratio of the compressible layer at 100kPa is an effective normalizing factor to predict the void ratio at higher pressures. Experimental results from the published literature on highly plastic clays were used to verify the proposed procedure. The different normalized equations, that are, i) e/e100 vs. log pressure p and ii) e/e100 with 1/p, were studied. Both of the equations yielded very good results in predicting the compressibility behavior under high pressures. Extremely high correlation was found out to exist between the proposed equation and the equation obtained using the diffuse double layer theory. Given the need to obtain the compressibility behavior and the difficulties involved in the experimental work to obtain reliable results at high pressures, the proposed method was found out to be very effective.