Multilayer Adsorption Model Research Articles

An innovative guanidinium-based ionic covalent organic frameworks with abundant aromatic rings for high-efficiency naproxen removal: Adsorption behavior, mechanisms, and density functional theory calculations

In recent years, naproxen (NPX) has raised significant environmental concerns requiring urgent attention. This study presents an innovative guanidinium-based ionic covalent organic framework (TFPB-TgCl), containing abundant aromatic rings, which was successfully synthesized via Schiff base reaction for the efficient and selective removal of NPX. Remarkably, TFPB-TgCl manifested a maximal NPX adsorption capacity of 308 mg/g at pH = 5. The adsorption on the active site (AOAS) model highlighted the simultaneous occurrence of both physical and chemical adsorption during the NPX uptake. The coefficients of the physical adsorption rates (5.6479, 1.9224, and 1.9224 min−1 for NPX concentrations of 20, 50, and 100 mg/L, respectively) were significantly higher than those of the chemical adsorption rates (0.1759, 0.0681, and 0.0567 g·mg−1·min−1 for the same concentrations), indicating the predominance of physical adsorption. Furthermore, the multilayer adsorption (MLA) model suggested that an adsorption site can interact with more NPX molecules, benefiting from various electrostatic and π-π interactions. The negative values of enthalpy change (ΔH° = −11.956 kJ/mol) and Gibbs free energy (ΔG < 0) confirmed the exothermic and spontaneous nature of the adsorption process. Additionally, in the optimal adsorption configuration (−131.57 kcal/mol), the Independent Gradient Model based on Hirshfeld partition (IGMH) was utilized to identify interaction sites between the guanidinium group of TFPB-TgCl and the carboxyl group of NPX, with subsequent electrostatic potential (ESP) analysis emphasizing their crucial role in electrostatic adsorption. Overall, the adsorption mechanism of electrostatic and π-π interactions in TFPB-TgCl highlights the significant contribution of its guanidinium and aromatic rings in facilitating NPX adsorption.

Polyethyleneimine-functionalized magnetic sugarcane bagasse cellulose film for the efficient adsorption of ibuprofen

Polyethyleneimine-modified magnetic sugarcane bagasse cellulose film (P-SBC/Fe3O4 film) was simply fabricated for the removal of ibuprofen (IBP), a typical emerging organic contaminant. The P-SBC/Fe3O4 film exhibited an equilibrium adsorption amount of 370.52 mg/g for IBP and a corresponding removal efficiency of 92.63 % under following adsorption conditions: 318 K, pH 4, and 0.25 mg/mL dosage. Thermodynamic studies indicated that adsorption of IBP on the P-SBC/Fe3O4 film was spontaneous (∆G < 0) and endothermic (∆H > 0). The adsorption data conformed to the Freundlich isotherm model and multilayer adsorption model (two layers), and an average of 3–4 active sites on the P-SBC/Fe3O4 film share an IBP molecule. Both the EDR-IDR and AOAS models vividly described the dynamic characteristics of adsorption process. Model fitting results, theoretical calculations, and comprehensive characterization revealed that adsorption is driven by electrostatic interactions between the primary amine of P-SBC/Fe3O4 film and the carboxyl group of IBP molecule, while other weak interactions are also non-ignorable. Furthermore, quantitative calculations based on density functional theory (DFT) underscored the importance of PEI functionalization. In conclusion, P-SBC/Fe3O4 film is an environmentally friendly and cost-effective adsorbent with significant potential for effectively removing IBP, while maintaining its efficacy over multiple cycles.

Synthesis of conjugated microporous polymers rich in sulfonic acid groups for the highly efficient adsorption of Cs+

Conjugated microporous polymers (CMPs) with extended π-conjugated systems and permanent microporous scaffolders have broad application prospects in the treatment of radionuclides in nuclear wastewater. Herein, the Sonogashira–Hagihara coupling process was employed to generate three CMPs, called CMP1–3. CMP1S–3S with different degrees of sulfonation were produced and employed for Cs+ ion adsorption by adjusting the sulfonation time using chlorosulfonic acid as the sulfonating agent. This is the first attempt to apply CMPs containing sulfonic acid groups to Cs+ ion adsorption, which show excellent adsorption properties. CMP1S-48 with the highest surface sulfonic acid group density exhibited the fastest adsorption rate, and it reached adsorption equilibrium on Cs+ ion in an aqueous solution under 1 min. The adsorption process corresponded to the Freundlich isotherm model of multilayer adsorption, with an adsorption capacity of up to 288.1 mg g−1. Compare with CMP2S-48 and CMP3S-48, CMP1S-48 with more sulfonic acid groups shows the highest adsorption capacity. Moreover, the selectivity of CMP1S-48 adsorbing Cs+ ion was exceeded high. Notably, the adsorption mechanism of Cs+ ion by CMP1S–3S involved ion exchange with H+ in the sulfonic acid groups, as well as its complexation and electrostatic attraction with the sulfonic acid groups. This work opens up a new way for CMPs rich in sulfonic acid groups to treat Cs+ ion-contaminated water sources.

High capacity and selective adsorption of Congo red by cellulose-based aerogel with mesoporous structure: Adsorption properties and statistical data simulation

Large quantities of organic dyes are discharged into the environment, causing serious damage to the ecosystem. Therefore, it is urgent to develop inexpensive adsorbents to remove organic dyes. A novel cellulose-based aerogel (MPPA) with 3D porous structure was prepared by using cassava residue (cellulose) as basic construction blocks, doping ferroferric oxide (Fe3O4) for magnetic separation, and applying polyethyleneimine (PEI) as functional material for highly efficient and selective capture of Congo red (CR). MPPA exhibited porous network structure, numerous active capture sites, nontoxicity, high hydrophilicity, and excellent thermal stability. MPPA showed superior adsorption property for CR, with an equilibrium adsorption capacity of 2018.14 mg/g, and still had an adsorption property of 1189.31 mg/g after five recycling procedures. In addition, MPPA has excellent selectivity for CR in four binary dye systems. The adsorption behavior of MPPA on CR was further explored using a multilayer adsorption model, EDR-IDR hybrid model and AOAS model. Electrostatic potential and independent gradient models were used to further verify the possible interaction between MPPA and CR molecules. In conclusion, MPPA is a promising adsorbent in the field of treating anionic dyes.

Fabrication of Iron-Containing Biochar by One-Step Ball Milling for Cr(VI) and Tetracycline Removal from Wastewater.

Simple ball milling technology can simultaneously improve the adsorption performance of adsorbents for heavy metals and organic pollutants and has attracted increasing attention. Iron-modified biochar (Fe@MBC) was prepared by one-step ball milling, and the characterization results proved that FeCl3 was successfully loaded on biochar. The removal rates of Cr(VI) and tetracycline hydrochloride (TC) by Fe@MBC were increased by 88.27% and 82.64% compared with BC. The average pore size, oxygen-containing functional groups and graphitization degree of Fe@MBC are higher than those of BC, which is more conducive to promoting adsorption. The adsorption isotherms show that the adsorption of Cr(VI) and TC on the Fe@MBC surface conforms to the Langmuir type of single-layer adsorption and the Freundlich model of multilayer adsorption, respectively. The maximum adsorption capacities of Cr(VI) and TC are 25.46 and 66.91 mg·g-1, respectively. Kinetic experiments show that the adsorption process is more consistent with the pseudo-second-order model of chemical adsorption. The adsorption process of Cr(VI) and TC on the Fe@MBC surface is a spontaneous endothermic process that becomes more obvious as the temperature increases. The increase in solution pH has a significant impact on the removal rate of Fe@MBC. When the pH value increased from 3 to 11, the adsorption rates decreased by 53.74% and 17.16%, respectively. The presence of PO43-, CO32-, K+, and Cu2+ significantly affects the adsorption of TC by Fe@MBC, and PO43- and CO32- also affect the adsorption of Cr(VI). Mechanistic studies show that ion exchange, electrostatic interaction, pore filling, and hydrogen bonding contribute to the removal of Cr(VI) and TC by Fe@MBC. The removal mechanism of Cr(VI) also involves complexation and redox reactions, and the removal mechanism of TC involves π-π bonds and van der Waals forces. The results show that Fe@MBC is a green and efficient adsorbent.

Physical properties of a generalized model of multilayer adsorption of dimers.

We investigate the transport properties of a complex porous structure with branched fractal architectures formed due to the gradual deposition of dimers in a model of multilayer adsorption. We thoroughly study the interplay between the orientational anisotropy parameter p_{0} of deposited dimers and the formation of porous structures, as well as its impact on the conductivity of the system, through extensive numerical simulations. By systematically varying the value of p_{0}, several critical and off-critical scaling relations characterizing the behavior of the system are examined. The results demonstrate that the degree of orientational anisotropy of dimers plays a significant role in determining the structural and physical characteristics of the system. We find that the Einstein relation relating to the size scaling of the electrical conductance holds true only in the limiting case of p_{0}→1. Monitoring the fractal dimension of the interface of the multilayer formation for various p_{0} values, we reveal that in a wide range of p_{0}>0.2 interface shows the characteristic of a self-avoiding random walk, compared to the limiting case of p_{0}→0 where it is characterized by the fractal dimension of the backbone of ordinary percolation cluster at criticality. Our results thus can provide useful information about the fundamental mechanisms underlying the formation and behavior of wide varieties of amorphous and disordered systems that are of paramount importance both in science and technology as well as in environmental studies.

Vector characteristics of microscale gas transport in coalbed methane reservoirs

Elucidating the microscale geological control mechanism of gas transport in coalbed methane (CBM) reservoirs is the basis for efficient development of CBM reservoirs. At present, there is a lack of systematic research on the gas transport vector properties under the influence of microscale gravitational field. In this paper, firstly, a coupling model of multi-layer adsorption and surface jump is established, and the gas adsorption/desorption equilibrium mechanism under the condition of multi-layer adsorption is revealed. Secondly, a coupled model of gas transport in bulk gas field and weak adsorption field is established by an area weight method, and the coupling control mechanism of “coal rank-pressure” on gas transport in the direction parallel to wall is clarified. Thirdly, considering the strength distribution characteristics of microscale gravitational field in the direction perpendicular to wall, the “coal rank-pressure” coupling influence mechanism on gas transport mechanism conversion in weak adsorption field is revealed. It is found that (a) microscale gas transport is vectorial, and surface jump is not contradictory to multilayer adsorption; (b) under low pressure, the influence of residual pressure on surface jump rate can reach more than 10 times; (c) coal rank has a significant impact on microscale gas transport by controlling residual pressure, microscale gravitational field thickness and pore radius; (d) under low pressure, the flow perpendicular to wall in weak adsorption field has an obvious transition phenomenon of transport mechanism, and the influence of residual pressure is significant.

Onion skin–derived sorbent for the sequestration of methylparaben in contaminated aqueous medium

Carbon-based adsorbents were produced from onion skin waste for the adsorption of methylparaben from contaminated water. The biomass-derived carbon was characterized using various established analytical techniques. The microscopic examinations revealed micro- and mesoporous structures with a partially disordered network of the graphenic carbon-like multilayer structure, confirmed by XPS and Raman spectra. XRD analysis revealed that the biomass-derived carbon is largely amorphous with the graphitic phase also confirmed. Aside from the prominence of sp2 hybridized carbon, FTIR analysis shows the existence of moieties and functional groups that may facilitate the sorption of methylparaben or other organic pollutants if explored. The adsorption isotherm revealed that the multilayer adsorption model (Freundlich) best fits experimental data with an SSE value of 0.454. A complex adsorption process is suspected between methylparaben and OSDC, and the physicochemical properties of the sorbate and sorbent played a huge role in the sorption process. The plausible interactions include van der Waals, hydrophobic bonding, hydrogen bonding, π-π stacking, and pore-filling mechanisms, leading to a hysteretic sorption process. The optimal removal efficiency and adsorption maxima of ~ 100% and ~ 8200 mg/g are obtainable at optimum process conditions. Therefore, waste valorization and adsorption performance achieved in this study suggest a sustainable and cost-effective pathway for pollution remediation.

Partition Constant of Binary Mixtures for the Equilibrium between a Bulk and a Confined Phase.

It is well-known that the thermodynamic, kinetic and structural properties of fluids, and in particular of water and its solutions, can be drastically affected in nanospaces. A possible consequence of nanoscale confinement of a solution is the partial segregation of its components. Thereby, confinement in nanoporous materials (NPM) has been proposed as a means for the separation of mixtures. In fact, separation science can take great advantage of NPM due to the tunability of their properties as a function of nanostructure, morphology, pore size, and surface chemistry. Alcohol-water mixtures are in this context among the most relevant systems. However, a quantitative thermodynamic description allowing for the prediction of the segregation capabilities as a function of the material-solution characteristics is missing. In the present study we attempt to fill this vacancy, by contributing a thermodynamic treatment for the calculation of the partition coefficient in confinement. Combining the multilayer adsorption model for binary mixtures with the Young equation, we conclude that the liquid-vapor surface tension and the contact angle of the pure substances can be used to predict the separation ability of a particular material for a given mixture to a semiquantitative extent. Moreover, we develop a Kelvin-type equation that relates the partition coefficient to the radius of the pore, the contact angle, and the liquid-vapor surface tensions of the constituents. To assess the validity of our thermodynamic formulation, coarse grained molecular dynamics simulations were performed on models of alcohol-water mixtures confined in cylindrical pores. To this end, a coarse-grained amphiphilic molecule was parametrized to be used in conjunction with the mW potential for water. This amphiphilic model reproduces some of the properties of methanol such as enthalpy of vaporization and liquid-vapor surface tension, and the minimum of the excess enthalpy for the aqueous solution. The partition coefficient turns out to be highly dependent on the molar fraction, on the interaction between the components and the confining matrix, and on the radius of the pore. A remarkable agreement between the theory and the simulations is found for pores of radius larger than 15 Å.

Enhancing arsenic (III) removal by integrated electrocatalytic oxidation and electrosorption reactions on nano-textured bimetal composite of iron oxyhydroxide and manganese dioxide polymorphs (α-, γ-, β-, and ε-MnxFe1−xO)

A composite electrode of manganese oxide (MnO2) incorporated with iron oxide (α-FeOOH) was synthesized for arsenite (As(III)) oxidation and subsequent arsenate (As(V)) electrosorption. The crystal structure and chemical state of MnO2 polymorphs were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), X-ray photoelectron spectroscopy (XPS), and BET surface area. The redox couple of Mn(III)/Mn(IV) mediated the catalytic electron transfer with respect to As(III)/As(V) redox equilibrium. The Mn site contributed a high diffusive current to the redox capacitance, meanwhile the Fe site better provided the double-layer capacitive deionization for arsenic species. Electrolysis of arsenite under constant anodic potential mode (+1.0 V vs. Ag/AgCl) enabled assess the performance of the electrodes. Among the polymorphs, γ-Mn0.2Fe0.8O exhibited the best arsenic adsorption capacity of 48 mg-As g−1, compared to that of α-FeOOH NPs (15 mg-As g−1) and γ-MnO2 (7 mg-As g−1), based on multilayer Langmuir adsorption model.

Thermodynamic and Kinetic Binding Behaviors of Human Serum Albumin to Silver Nanoparticles

A nanoparticle, under biological milieu, is inclined to be combined with various biomolecules, particularly protein, generating an interfacial corona which provides a new biological identity. Herein, the binding interaction between silver nanoparticles (AgNPs) and human serum albumin (HSA) was studied with transmission electron microscopy (TEM), circular dichroism (CD), and multiple spectroscopic techniques. Due to the ground state complex formed mainly through hydrophobic interactions, the fluorescence titration method proved that intrinsic fluorescence for HSA was probably statically quenched by AgNPs. The complete thermodynamic parameters were derived, indicating that the interaction between HSA and AgNPs is an entropy-driven process. Additionally, synchronous fluorescence and CD spectrum results suggested the conformational variation it has upon binding to AgNPs and the α-helix content has HSA visibly decreased. The kinetic experiments proved the double hysteresis effect has in HSA’s binding to the AgNPs surface. Moreover, the binding has between HSA and AgNPs follows the pseudo-second-order kinetic characteristic and fits the Freundlich model for multilayer adsorption. These results facilitate the comprehension about NPs’ underlying biological effects under a physiological environment and promote the secure applications of NPs biologically and medically.

Improved mathematical model of apparent permeability: A focused study on free and multilayer adsorptive phase flow

Apparent permeability is the quantification of gas transport in confined pore, which includes the pressure gradient-driven continuous flow (slip flow), the concentration gradient-driven molecular diffusion (Fick's diffusion, Knudsen diffusion) and the chemical gradient-driven surface diffusion. Molecular diffusion of free/adsorbed gas plays an important role in gas transfer, especially in nanopores. Most existing apparent permeability models simply define free gas diffusion as Knudsen diffusion, and surface diffusion as the diffusion of monolayer adsorbed molecules. However, the pore scale-dependent Knudsen diffusion, the molecular diffusion of free gas also includes the pore scale-independent Fick's diffusion. In addition, the empirical formula of surface diffusion coefficient derived from plug core diffusion experiment should be used cautiously, because there are other diffusion regimes involved in the diffusion process in multi-scale pores. In this work, the diffusion mechanisms of adsorbed/free gas were classified. A supercritical multilayer adsorption (SC-DA) model was obtained by fitting the adsorption data of homogeneous nano activated carbon, and the adsorption effect was applied to pore aperture change and surface diffusion, which is suitable for single/multilayer adsorption. Applying the improved surface diffusion flow and free gas diffusion flow into gas transport, a unified mathematical transport model was presented, from which the apparent permeability model was derived. Later, the improved model was verified using the experimental data from the micro-flow permeability of the nanofilms with regular size. Furthermore, the influence of each flow mechanism in nanopores was calculated and compared. The results showed that the gas transport in nanopores is dominated by molecular diffusion, but the contribution of surface diffusion in gas transfer is exaggerated if its diffusion coefficient is not chosen properly.

Pristine and activated bentonite for toxic metal removal from wastewater

AbstractNatural bentonite clay (NBC) was activated using nitric acid (HNO3). Characterization techniques including FTIR, SEM, XRD and BET were employed to examine the morphology of NBC and ABC (activated bentonite clay) sorbents. Comparative application of ABC and NBC to remove heavy metals (Fe2+, Zn2+, Ni2+) from pharmaceutical effluents was investigated under various experimental conditions. The maximum proportional removal by ABC was 88.90, 81.80 and 75.50% at pH 8, and 63.90, 59.60, 58.70% at pH 10 for NBC, both for Zn2+, Fe2+ and Ni2+ respectively. The Freundlich multilayer adsorption model and pseudo-second-order kinetics best fit the experimental data, suggesting the formation of multiple adsorption layers via strong ionic and electrostatic interactions. Heavy metals adsorption is more favorable with ABC than NBC, due to the availability of more sorption sites and a larger specific surface. The thermodynamic parameters (ΔH°, ΔS°, and ΔG°) revealed that the adsorption is endothermic and spontaneous in nature for both ABC and NBC.

New insights into the selective adsorption mechanism of cationic and anionic dyes using MIL-101(Fe) metal-organic framework: Modeling and interpretation of physicochemical parameters

In the current study, iron-based metal organic framework (MOF) MIL-101(Fe) was successfully prepared via a facile solvothermal method. The as–synthesized MIL-101(Fe) was characterized by XRD, FE-SEM, FTIR, TGA and zeta potential techniques, and then employed as an adsorbent for methyl orange (MO) and methylene blue (MB) dyes. The adsorbed quantities of MO (1067 to 831 mg/g) were higher than those of MB (402 to 353 mg/g) indicating the high selectivity of MIL-101(Fe) towards the anionic dye at all temperatures (20–60 °C). Adsorption processes of MO and MB followed the pseudo-second order kinetics and the Langmuir equilibrium model. The interaction mechanism at a molecular level was analyzed and deeply interpreted via the advanced multilayer adsorption model. Steric parameters indicated that MO molecular aggregation (n) was 0.95–1.33 thus signifying the presence of multi–docking and multi–interactions mechanisms. The aggregated number of MB was superior to unity (i.e., n = 1.17–1.78) suggesting a vertical adsorption position and a multi-interactions mechanism at all operating temperatures. The density of MIL-101(Fe) active sites (DM = 77.33–52.38 mg/g for MB and 149.91–107.07 for MO) and the total adsorbed dye layers (Nt = 3.12–2.49 for MB and 5.36–3.67 for MO) resulted in improving the adsorption capacities of MO dye. The adsorption energies ranged from 8.89 to 33.73 kJ/mol and they displayed that MO and MB uptake processes were exothermic controlled by physical interactions at all temperatures. Regeneration results indicated that this adsorbent can be reutilized without a significant loss in its removal efficiency after five adsorption-desorption cycles. Overall, the adsorption capacity, chemical stability, and regeneration performance of MIL-101(Fe) support its application as a very promising adsorbent for the removal of organic hazardous pollutants from water.

Effective adsorption of crystal violet dye on sugarcane bagasse–bentonite/sodium alginate composite aerogel: Characterisation, experiments, and advanced modelling

A novel sugarcane bagasse–bentonite/sodium alginate (SCB–Ben/SA) composite aerogel was prepared as an effective green adsorbent via blending–cross-linking for the removal of crystal violet (CV) dye from aqueous solution. The equilibrium adsorption capacity of SCB–Ben/SA for CV was 839.9 mg/g at 0.8 mg/mL adsorbent dosage, temperature 303 K, pH 4, and 800 mg/L initial CV concentration, and presented a removal rate of 85%. Adsorption kinetics studied using the novel pseudo-first-order and pseudo-second-order (PFO–PSO) combined model showed that CV adsorption by SCB–Ben/SA was a complex process and did not include a single mechanism, but involved both chemical and physical adsorption reactions; however, chemisorption was the dominant kinetic mechanism. The dynamic characteristics of CV adsorption process achieved through the liquid film around SCB–Ben/SA and the pores inside SCB–Ben/SA was described satisfactorily and conveniently using the novel film–pore mass transfer (FPMT) model. A multilayer adsorption model was applied to further understand the CV adsorption behaviour of SCB–Ben/SA. The number of linked CV molecules per functional group varied from 0.53 to 0.63 for SCB–Ben/SA. The CV molecules were adsorbed on SCB–Ben/SA via mixed orientation. The adsorption isotherms and thermodynamics revealed that the multilayer adsorption process was endothermic and spontaneous. Overall, SCB–Ben/SA was found to be an efficient, low-cost, green, and recyclable adsorbent for organic dye removal.

Catalytic oxidation and deionization of nitrite and nitrate ions using mesoporous carbon-supported nano-flaky cobalt and nickel oxyhydroxides

The composite electrode of NiCo oxide supported by porous carbon was synthesized for nitrite oxidation and nitrate electro-sorption. The crystal structure and chemical state of the Co and Ni oxyhydroxides which were precipitated on loofah-derived activated carbon (AC) using hypochlorite were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), X-ray photoelectron spectroscopy (XPS), and BET surface area. The voltammetry showed that the redox couple of Co(II)/Co(III) and Ni(II)/Ni(III) as the mediator catalytically transferred the electrons of NO2–/NO3–; the Ni site had a relatively high transfer coefficient and diffusive current, while the Co site was better in the capacitive removal of the nitrite and nitrate compounds. A batch electrolysis of nitrite ions was operated under constant anodic potential mode (0 to + 1.5 V vs. Ag/AgCl) to assess the performance of the composite electrodes. The adsorption capacity of NiCo/AC (Ni = 5% and Co = 5% on AC by weight) was 23.5 mg-N g−1, which was twice that of AC substrate (7.5 mg-N g−1), based on a multilayer adsorption model. The steady-state kinetics of the consecutive reaction were derived to determine the rate steps of the electrochemical oxidation of NO2– and adsorption of NO3–.

Rarefied gas transport in heterogeneous shale matrix using a practical apparent permeability model and fuzzy statistical method

A new shale gas transport model is derived to characterize the matrix structural heterogeneity impact on the gas apparent permeability (AP). The developed analytical model is built upon two steps: first, the homogeneous AP model is formulated by assigning the Knudsen-number-parameterized weight coefficients to flow mechanisms based on the analyses of representative rarefied gas transport models; then, the homogeneous model is improved to the heterogeneous model with the help of fuzzy statistical method to assess the structural heterogeneity influences. More specifically, the homogeneous AP model incorporates the multilayer adsorption, surface diffusion, real gas effect, and pore confinement effect. The physical terms in the apparent permeability including the rarefaction coefficient and multilayer adsorption model are simplified to facilitate the large-scale simulation. Meanwhile, the heterogeneous AP model is quantified by the distribution of porosity, tortuosity, and pore size. It is demonstrated that the developed AP model can reproduce the experimental and numerical experiments for five types of gases. It is concluded that the rarefaction in nanopores could be reasonably characterized by the weighted Knudsen diffusion and viscous flow mechanisms. Moreover, it is noticed that the surface diffusion and Knudsen diffusion cannot be ignored in nanopores with radius smaller than 3 nm at low reservoir pressures. In contrast, the viscous flow plays a significant role in shale gas transport in nanopores with radius larger than 75 nm. In addition, the fuzzy statistical method in the proposed heterogenous model provides the indicators to evaluate the impact of structural heterogeneity on the AP. It is observed that the heterogeneous model can accurately predict the realistic apparent permeability as the heterogeneity increases to σ = 0.15. However, the accuracy decreases when the matrix heterogeneity increases.

Lattice Model of Multilayer Adsorption of Particles with Orientation Dependent Interactions at Solid Surfaces.

A simple lattice model has been used to study the formation of multilayer films by fluids with orientation-dependent interactions on solid surfaces. The particles, composed of two halves (A and B) were allowed to take on one of six different orientations. The interaction between a pair of differently oriented neighboring particles was assumed to depend on the degrees to which their A and B parts overlap. Here, we have assumed that the AA interaction was strongly attractive, the AB interaction was set to zero, while the BB interaction was varied between 0 and . The ground state properties of the model have been determined for the systems being in contact with non-selective and selective walls over the entire range of BB interaction energies between 0 and . It has been demonstrated that the structure of multilayer films depends on the strengths of surface potential felt by differently oriented particles and the interaction between the B halves of fluid particles. Finite temperature behavior has been studied by Monte Carlo simulation methods. It has been shown that the bulk phase phase diagram is qualitatively independent of the BB interaction energy, and has the swan neck shape, since the high stability of the dense ordered phase suppresses the possibility of the formation of disordered liquid-like phase. Only one class of non-uniform systems with the BB interaction set to zero has been considered. The results have been found to be consistent with the predictions stemming form the ground state considerations. In particular, we have found that a complete wetting occurs at any temperature, down to zero. Furthermore, the sequences of layering transitions, and the structure of multilayer films, have been found to be the same as observed in the ground state.

Experimental and theoretical investigation of high- concentration elution bands in ion-pair chromatography

The effective separation of many solutes, including pharmaceuticals, can be performed using an ion-pair reagent (IPR) in the mobile phase. However, chromatographic separation and mathematical modelling are a challenge in ionpair chromatography (IPC), especially in preparative mode, due to the complicated chromatographic process. In this study, we present a retention mechanism and a mathematical model that predict overloaded concentration profiles in IPC using a system with X-Bridge C18 as stationary phase and tetrabutylammonium bromide in the 0 - 15 mM concentration range as the IPR. Two different mobile phases were used: (i) 15/85 [v/v] acetonitrile/water, (ii) 25/75 methanol/water. The model compounds were sodium salts of organic compounds with sulfonic acid functions. The analytical and preparative elution profiles were obtained for specified conditions. The analytical data were utilized to calculate the difference in electrical potential between the surface and bulk solution using firm electrostatic theory. In the preparative mode in a certain range of IPR concentrations, complicated U-shaped overloaded profiles were observed. In the other considered cases, Langmuir overloaded elution profiles were recorded. A multilayer adsorption model was derived, which is consistent with the dynamic ion exchange models. The model assumes that lipophilic IPR adsorbs on the stationary phase, creating charged active sites that serve as exchange sites for the solutes. The molecules of the solute can adsorb on the already formed IPR layer. It was also assumed that a subsequent layer of solute can form on the formed layer of complexes due to interactions between the solute molecules. The model takes into account the electrostatic attraction and repulsion of the molecules, depending on the considered situation. The proposed model allowed prediction of the overloaded concentration profiles with very good agreement for the model solute and followed the progression from Langmuirian, through U-shaped, to again Langmuirian profiles.

A novel model to determine gas content in naturally fractured shale

A shale reservoir’s gas content is an indispensable, crucial parameter used in exploration, formation evaluation, block selection and exploitation. Canister gas desorption measurements are used to quantify lost gas volumes that are key to determine the gas content of the reservoir Usually, a lost gas volume is evaluated using the United States Bureau of Mines (USBM) direct method and/or a polynomial curve-fitting method. These methods extrapolate desorption data to time zero in the curve of a cumulative desorption volume versus the square root of time. Lost gas time is the time spent lifting the core out of a hole, handling and placing it inside a canister for evaluation., For cores with densely developed natural fractures, neither the USBM method nor the polynomial curve-fitting method can accurately estimate the lost gas volume if the lifting, handling and canister storage takes a long time. The lost gas period is a non-isothermal gas desorption process; the surrounding temperature keeps declining. Experiments were conducted to determine the methane desorption volumes of a Duvernay shale sample under various pressures and temperatures. Using Boyle’s law and the multilayer adsorption model, a novel mathematical model was built to calculate lost gas volume, including free gas and desorption gas. Because gas desorption is an endothermic procedure, equations for the inhaled energy were developed to overcome the van der Waals force between the molecules, deorbit the vibration equilibrium and the migration of molecules into the air. Finally, a shale sample with dense natural fractures from the Duvernay formation of Alberta, Canada, was used to validate the mathematical model. For comparison, the results from the USBM method, polynomial curve-fitting method and model’s calculations are illustrated in tables and figures. The outcomes exposed the results from the USBM method and polynomial curve-fitting method as deviating from the real gas content in the Duvernay formation without the consideration of the free gas loss. The model is reliable for performing gas content evaluations because it considers dual-pore structure, PVT behaviour and free gas escape simultaneously.