Excess Isotherms Research Articles

Five definitions of adsorption and their relevance to the formulation of dynamic mass balances in gas adsorption columns

Numerous dynamic mass balances in the literature that describe the adsorption of gases in a column are written in terms of actual or absolute adsorption, while unwittingly and incorrectly utilizing excess adsorption isotherms. Perhaps this is because the actual and absolute adsorption isotherms cannot be experimentally measured nor predicted without making uncertain assumptions. The objective here was to derive unambiguous relationships between actual, absolute, excess, net and column amounts adsorbed that provide a straightforward understanding of the subtle differences between these quantities and that provide a simple means for incorporating them into dynamic mass balances. For this purpose, the actual, absolute, excess, net and column amounts adsorbed (loadings) were clearly defined, along with various volumes, porosities and densities that exist inside and outside an adsorbent contained in a column with a gaseous adsorbate. These adsorption definitions and quantities were used to derive four interconversion relationships for each type of adsorption in terms of the actual loading. The resulting expressions, based on intensive properties, can be used to relate any adsorption definition to any other adsorption definition. These relationships were also used to derive five dynamic mass balances, one for each type of adsorption. The similarities and differences in the terms between each of these five dynamic mass balances were discussed, along with their applicability to real world problems. In some cases at low pressure where the isotherms do not differ appreciably, it may be approximately correct to use excess or net adsorption isotherms in a dynamic mass balance written in terms of actual or absolute adsorption. However, the extent of the incorrectness is unknown due to mass transfer effects. So, it is recommended to use the dynamic mass balance with its specific type of adsorption, most likely excess adsorption. Then, when certain assumptions are made about the adsorbing and non-adsorbing void fractions, these expressions can be readily used in adsorption process simulation.

Non-destructive chromatographic determination of surface area in reverse phase chromatographic columns

One of the critical but underutilized parameters that affect chromatographic separation is an adsorbent surface area (S.A.). We introduce a concept of direct determination of the total surface area of chromatographic columns by utilizing a nondestructive measurement of eluent component excess adsorption isotherm measurement and the application of the Standard Excess Adsorption Isotherm from acetonitrile-water and methanol-water binary mixtures for direct determination of the S.A. in chromatographic columns. This nondestructive technique was used to determine the surface area of five commercial columns, including three core-shell particle type columns (Kinetex-C18, Ascentis C18, and Hallo C18) and in-housemade C18 columns. The traditional low-temperature nitrogen adsorption (LTNA) technique was compared to the novel chromatographic method of nondestructive surface area determination for adsorbents modified with octadecylsilanes. The chromatographically determined surface area was in good agreement with the conventional techniques for all columns used. The difference between the three techniques is less than 10%. Columns were characterized in terms of adsorbent geometry (e.g., pore volume, column void volume, interparticle volume), ligands bonding density, and the amount of the packing material in a chromatographic column.

Actual Amount Adsorbed as Estimated from the Surface Excess Isotherm.

The amount of adsorption at equilibrium is commonly used for reporting solid/solution isotherms, despite the admonishment by the International Union of Pure and Applied Chemistry (IUPAC) against equating the surface excess (i.e., the measurable quantity for sorption, signifying the competitive sorption of adsorbate and solvent) with the actual amount adsorbed. The consensus, more generally stated, is that the surface excess cannot be divided into individual isotherms for sorbate and solvent unless simplifying model assumptions are introduced. Here we show, contrary to the IUPAC report, that there exists a simple method for assigning the total isotherm to the sorbate's actual amount adsorbed and to the individual solute isotherm. This requires a combination of isotherm and volumetric measurements. For dilute sorbates, we establish criteria to show if the total isotherm is dominated by the amount of sorption at the interface, in agreement with the common assumption in the practical literature. In the absence of the volume data, we propose an approximate yet more versatile method based on the specific surface area to carry out order-of-magnitude analysis to examine whether the actual amount adsorbed dominates surface excess. Application of our methods to the adsorption of sodium decyl sulfate on polystyrene latex, malachite green on activated carbons, and thiophenes on a metal-organic framework all demonstrated the dominance of the actual amount adsorbed, significantly simplifying isotherm analysis in terms of the underlying interactions (i.e., surface-sorbate and net self-interactions at the interface), eliminating the need for excess surface quantities. Analysis of fully miscible solvent-sorbate isotherms (e.g., the mixtures of organic solvents adsorbed on mesoporous silica and carbonaceous adsorbents) indicates the contributions from both sorbate and solvent isotherms.

Understanding roles of moisture in CO2 adsorption and desorption hysteresis on deep gas-bearing shales under high temperature and pressure

To understand injectivity and storage stability of CO2 into gas-bearing shale reservoirs, CO2 adsorption and desorption on the dry and moist shales with diverse properties were conducted at 353.15 K and pressures up to 14 MPa. Multiple characterizations were combined to examine pore characteristics of the shales before and after CO2 adsorption/desorption. The resultant CO2 adsorption and desorption hysteresis on the shales was revealed ultimately. Results indicated that both the excess and absolute adsorption isotherms of CO2 witness slow increase stage, rapid increase stage, and decrease stage. The adsorption capability of the shales positively depends on the TOC content and pore abundance. Moreover, the clay minerals and oxygenic functional groups also benefit CO2 adsorption. The moisture significantly reduces the experimentally-determined maximum absolute adsorption capacity of the shales by 5.78–46.39 % due to pore space occupation. During the adsorption/desorption, the CO2 molecules could interact with the shales, thereby initiating extraction of partial organic matter, transformation of CO2 from supercritical state to gas state, and dissolution of inorganic minerals. Those effects consume CO2 and dominantly change the micropore structure of the dry shales and the mesopore structure of the moist shales, thus leading to CO2 adsorption and desorption hysteresis. Notably, the moisture dramatically raises the hysteresis degree on the shales by 8.42–59.45 % because of its solubility to CO2 and promotion to mineral dissolution. Overall, shale reservoir moisture could weaken injectivity but strengthen storage stability of CO2. Hence, the critical moisture content and occurrence pattern of organic matter and clay minerals are required for target shale reservoir selection.

In‐situ temperature‐depth profile evaluation of South African unmineable coal seams to determine CO2 sequestration potential

AbstractThis study aimed to investigate the sorption behaviour of South African coal seams with relation to the effect of temperature during CO2 sequestration. The excess adsorption isotherms of CO2 adsorption were undertaken using a high‐pressure volumetric system for four coals of different coal rank (denoted by Somkele [SK], anthracite KZN [AN], Tshikondeni [TD], and Syferfontein [SF]). The volumetric pressure step method was conducted at increments of system temperature of 35, 45, 55, and 65°C for pure CO2 adsorption at incremental pressures up to 93 bar. The results showed that high temperatures have a very significant negative effect on the amount of CO2 adsorbed on the coal samples. The high‐rank coal samples (SK and AN) demonstrated elevated CO2 adsorption capacity across all tested temperatures due to their high vitrinite content. The medium‐rank coals (TD and SF) exhibited comparatively lower CO2 adsorption capacity, attributed to the presence of adsorption hindrances such as higher ash content and volatile and mineral matter. The isosteric heat of adsorption revealed an increasing trend with coverage for all coal samples, with higher rank coals displaying greater slopes. The determined range of the isosteric heat of adsorption, spanning from 10 to 59 kJ/mol, indicated that the adsorption process is primarily of a physisorption nature. Three theoretical models (Langmuir, Freundlich, and Temkin) were evaluated and fitted to the sorption experimental data. The Temkin model exhibited superior fitting compared to the Langmuir and Freundlich isotherms. The Temkin isotherm parameters suggest that the adsorption of CO2 onto coal is a physisorption process.

Unary Adsorption Equilibria of Hydrogen, Nitrogen, and Carbon Dioxide on Y-Type Zeolites at Temperatures from 298 to 393 K and at Pressures up to 3 MPa.

The equilibrium adsorption of CO2, N2, and H2 on commercially available Zeolite H-Y, Na-Y, and cation-exchanged NaTMA-Y was measured up to 3 MPa at 298.15, 313.15, 333.15, 353.15, and 393.15 K gravimetrically using a magnetic suspension balance. The chemical and textural characterization of the materials was carried out by thermogravimetric analysis, helium gravimetry, and N2 (77 K) physisorption. We report the excess and net isotherms as measured and estimates of the absolute adsorption isotherms. The latter are modeled using the simplified statistical isotherm (SSI) model to evaluate adsorbate-adsorbent interactions and parametrize the data for process modeling. When reported per unit volume of zeolite supercage, the SSI model indicates that the saturation capacity for a given gas takes the same value for the three adsorbents. The Henry's constants predicted by the model show a strong effect of the cation on the affinity of each adsorbate.

Towards an accurate method for column void volume determination using liquid chromatography-mass spectrometry

Prediction of analyte retention times requires prior knowledge of the column void volume, the measurement of which is still highly contested within the literature and therefore experimental based prediction is often used. In this study, we investigated deuterated acetonitrile as an isotopically labelled mobile phase component to observe its elution behaviour in a binary mixture with water at 25 different mobile phase compositions (from 5 to 95 vol.% of acetonitrile), on two stationary phases (C8 and C18), and at two temperatures (30 and 40 °C) using LC-MS. The same experimental design was additionally used for three commonly used neutral void volume markers: uracil, phloroglucinol and N,N-dimethylformamide. Temperature was observed to influence the elution of acetonitrile in an inversely proportional manner with higher temperatures coinciding with lower elution times. By utilizing a three-way ANOVA, the composition of the mobile phase has been shown to have a significant effect on deuterated acetonitrile and other investigated void volume markers, demonstrating the fact that both void volume markers and acetonitrile itself exhibit retention-like behaviour. Excess adsorption isotherms for acetonitrile were calculated using deuterated acetonitrile elution data. The comparison of void volumes, obtained with conventional neutral void volume markers, revealed the former to be 24–36% lower than the void volume obtained using deuterated acetonitrile, as an isotopically labelled mobile phase component. For a water:acetonitrile mobile phase, the minor disturbance method using deuterated acetonitrile to obtain an integral average void volume (2.08 and 2.05 mL for C18 at 30 and 40 °C, respectively and 2.16 and 2.13 mL for C8 at 30 and 40 °C, respectively) was found to be the most appropriate method for determining the elusive column void volume.

Molecular simulation of adsorption and diffusion behavior of CO2 in pyrophyllite

Understanding the microscopic process of adsorption and diffusion of CO2 in clay minerals is important for geological storage of CO2. In this study, Grand Canonical Monte Carlo (GCMC) and Molecular Dynamics (MD) simulations are used to obtain the adsorption and diffusion behavior of CO2 in pyrophyllite slit pores. The influence of split pore size, temperature, pressure, and water content were analyzed in detail. The adsorption characteristics of CO2 in pyrophyllite were revealed by discussing the distribution of CO2 density profile, adsorption capacity, isosteric heat of adsorption, interaction energy, mean square displacement, self-diffusion coefficient, and molecular orientation distribution. It shows that the excess adsorption isotherm of CO2 in pyrophyllite slit pores demonstrate significant supercritical adsorption characteristics. Surface attractions originating from both pore walls overlap in the middle of pore, leading to an enhanced adsorption capacity of CO2 in pyrophyllite slit pores when pore aperture is lower than 3 nm. In pyrophyllite pores, the presence of water has an enhancing effect on CO2 adsorption when the water content is below 30 wt%. A maximum value of CO2 adsorption amount is reached at the water content of 10 wt%, while negative growth occurs at 35 wt%. At low water content, water molecules form a weak adsorption layer due to the weak attraction of pyrophyllite to water. As water content increases, the self-diffusion coefficient of the CO2 decreases, and the diffusion capacity decreases. The adsorption state of the CO2 molecule on the mineral surface is primarily a parallel configuration, while the water molecule has no clear orientation. Our calculated results can provide guidance for further study of clay-water-adsorbate interface reaction of hydrophobic minerals.

Analysis of gas storage and transport in Eagle Ford shale using pressure pulse decay measurements with He, Kr and CO2

Detailed characterization of gas transport and storage in low-permeability and organic-rich shales is associated with an array of challenges due to the complex morphology of the pore space, representing a broad range of pore sizes, combined with the heterogeneous fabric of the shale matrix. These factors, and their interplay during gas transport and sorption, complicate a) the analysis of shale samples at the laboratory scale (∼ up to a ft. In length), and b) the prediction of natural gas production and carbon sequestration potential at larger scales.In this work, tandem experiments with inert (helium – He) and adsorbing (krypton - Kr and carbon dioxide - CO2) gases were performed and analyzed to develop an efficient workflow for characterizing and modeling transport and sorption at the laboratory scale. In particular, pressure pulse-decay (PPD) measurements were conducted on an Eagle Ford shale core sample at room temperature using He, Kr, and CO2. PPD measurements with He (a non-sorbing gas) were employed to probe the overall porosity, including natural fractures, microcracks, mesopores, and micropores. A triple-porosity model (TPM) was adopted to interpret the gas transport in the shale sample: The pore space is represented by three interacting continua, including macropores (larger fractures), mesopores (including microcracks), and micropores. To facilitate the application of the TPM, a modified analytical approach is introduced to extract effective transport parameters (in terms of the characteristic time for transport at relevant porosity levels) directly from the PPD measurements with He. To validate the modeling approach, model parameters extracted from two He PPD measurements are demonstrated to provide excellent agreement with a 3rd He PPD measurement performed at a higher pressure.The effective transport parameters, extracted from the He experiments, were subsequently converted for application to the Kr and CO2 PPD experiments, by accounting for relevant transport modes and differences in fluid properties. Excess adsorption isotherms were extracted from the equilibrium pressures of the Kr and CO2 PPD experiments using the He pore volume as a baseline. These adsorption isotherms were then integrated into the TPM to predict combined gas transport and sorption for Kr and CO2, with transport coefficients translated from the He measurements. The predictions for Kr and CO2 are demonstrated to be in excellent agreement with the experimental observations. This, in turn, demonstrates that the proposed analytical approach provides for an effective characterization of mass transfer rates in shales, that can be applied directly in a TPM representation of mass transfer and sorption.

Predicting the Concentration Dependence of the Surface Tension of Ternary Systems

A comparative analysis of semi-empirical methods based on the Kohler, Bonnier, and Toop models for predicting the surface tension (ST) of ternary systems has been performed. Surface tension–concentration dependence calculations have been carried out in the indium–tin–lead and indium–tin–gallium systems. The ternary indium–tin–lead system is characterized by the fact that the excess surface tension isotherms of all the side binary melts are symmetrically shaped with respect to the equimolar composition, and such systems are called symmetric. In the ternary indium–tin–gallium system, the excessive surface tension isotherms of side binary indium–gallium and tin–gallium systems have pronounced asymmetry with respectto the equimolar composition, and such systems are called asymmetric. It has been shown that a method based on the Kohler model rather precisely describes the concentration dependence of the surface tension ofsymmetric ternary systems. However, this method does not predict the concentration dependence of the surface tension of asymmetric systems. It has been revealed that the Bonnier and Toop models can predict thesurface tension–concentration dependence for asymmetric ternary systems with strong asymmetry in the excess surface tension isotherms of two side binary systems independently of the degree of complexity in these isotherms within overall error of experiment.

Factors affecting mixed-mode retention properties of cation-exchange stationary phases

Cation-exchange stationary phases were characterized in different chromatographic modes (HILIC, RPLC, IC) and applied to the separation of non-charged hydrophobic and hydrophilic analytes. The set of columns under investigation included both commercially available cation-exchangers and self-prepared PS/DVB-based columns, the latter consisting of adjustable amounts of carboxylic and sulfonic acid functional groups. The influence of cation-exchange site and polymer substrate on the multimodal properties of cation-exchangers was identified using selectivity parameters, polymer imaging and excess adsorption isotherms. Introducing weakly acidic cation-exchange functional groups to the unmodified PS/DVB-substrate effectively reduced hydrophobic interactions, whilst a low degree of sulfonation (0.09 to 0.27% w/w sulphur) mainly influenced electrostatic interactions. Silica substrate was found to be another important factor for inducing hydrophilic interactions. The presented results demonstrate that cation-exchange resins are suitable for mixed-mode applications and offer versatile selectivity.

Investigations on Supercritical Methane Adsorption and Storage in the Lower Longmaxi Shale of Nanchuan Area, Southeast Sichuan Basin

A series of high-pressure methane adsorption measurements were performed at various temperatures on whole shale and kerogen samples collected from the Lower Longmaxi shale in the Nanchuan area, southeast Sichuan Basin, to investigate supercritical methane adsorption properties and evaluate in-place methane storage capacity as a function of burial depth. The results show that the supercritical Dubinin–Radushkevich (SDR) model fits the excess adsorption isotherms marginally better than the supercritical Langmuir model. However, the fitted adsorbed methane density of kerogens obtained from the SDR model may be greater than the liquid methane density at the atmospheric boiling point (0.423 g/cm3). The proposed multiple regression fitting carried out in this work illustrates that approximately 57.59% (34.51–85.45%) and 37.60% (10.74–59.52%) of the methane adsorption capacity at 333.15 K can be attributed to organic matter (OM) and clay minerals (CMs), respectively, for whole shales investigated. According to thermodynamic analyses, the significant contribution of OM to the methane adsorption capacity can be attributed to the stronger affinity between kerogens and methane molecules in contrast to that between CMs and whole shales. The methane storage capacity estimated as a function of burial depth showed that the adsorbed gas storage capacity declines with increasing burial depth between 2000 and 5000 m, while the free gas storage capacity shows the opposite trends. Gas accumulation pressure primarily exerts a significant effect on the free gas storage capacity rather than adsorbed gas storage capacity, and adsorbed gas storage capacity begins to exceed free gas storage capacity at shallow burial depths for normally pressured gas accumulations. Normally pressured shale gas accumulations at shallow burial depths, which are widely distributed in the residual syncline of the study area, should be given more attention due to their relatively low development costs and relatively high storage capacity for adsorbed gas.

Quantitative Studies on the Characterization and Evaluation of Adsorbed Gas and Free Gas in Deep Shale Reservoirs

The quantitative characterization of adsorbed gas and free gas in shale reservoirs is a key issue in exploration and development of shale gas. Thus, the aforementioned topic is of great significance to the evaluation of reserves, the screening of favorable target areas, and the formulation of development plans. However, research on our current understanding of the quantities of adsorbed gas and free gas in deep shale gas reservoirs is still lacking. To address this problem, deep shales from the Longmaxi Formation in southern China were collected to conduct high-pressure isothermal adsorption experiments. The high-pressure isothermal adsorption model was used to describe the adsorption behavior of methane in deep shales, and the adsorbed gas and free gas in the deep shales were characterized quantitatively. The effects of temperature, pressure, and moisture on the adsorbed gas and the density of the free gas were analyzed. The results indicated that the excess adsorption isotherm curve for methane in deep shales increased and then decreased with the increase of pressure, and the modified Langmuir adsorption model may be used to describe the high-pressure adsorption behaviors. The adsorbed gas in shales decreases gradually with the increase of pressure, and the proportion of adsorbed gas and free gas is between 23 and 74% when the pressure reaches 50 MPa. The adsorbed gas in deep shales decreases with an increase of temperature, and the presence of water greatly reduces the adsorption capacity of the deep shale. The pore space occupied by the free gas in shale increased with the increase in the density of the free phase, and the ratio of the adsorbed gas to the free gas decreased. This research provides a useful reference for explaining how to best evaluate shale gas reservoirs, estimate the reserves in deep shales, and evaluate the adsorption and flow capacity of deep shale gas.

Examining Supercritical Methane Adsorption on Nanoporous Shales Using Constant and Varying Adsorbed Phase Density Approaches

Supercritical adsorption studies are crucial, as adsorbed methane has a significant contribution to the total gas-in-place along with the free gas-in-shale reservoirs. Due to the low specific adsorption of shales, Gibbs excess isotherms that decrease after a certain pressure are being reported. Corrections to the excess adsorption amount can be made using models that predict absolute adsorption through empirically estimated adsorbed phase density. However, due to the inherent heterogeneity of shale and uncertainties in the adsorbed phase density estimated from different models, the quantitative characterization of adsorption is becoming increasingly challenging. The assumption of constant adsorbed phase density is being challenged with varying adsorbed phase density approaches, which are theoretically correct; however, their applicability has not been analyzed distinctively. In this work, supercritical adsorption models like supercritical BET (SBET), supercritical Dubinin–Radushkevich (SDR), Ono–Kondo mono- and multilayer, fixed volume Ono–Kondo (FV-OK1), and variable density Langmuir (VD-Langmuir) are revisited, analyzed, and compared for their applicability in shale reservoirs. For this, methane adsorption isotherms at two different temperatures (45 and 90 °C) are generated for four samples with varying geochemical and petrophysical properties selected from the Cambay and Krishna–Godavari (KG) basins of India. Through this analysis, it has been found that fixed-density approaches better explain the isotherms in comparison to varying density approaches. The average adsorbed phase density estimated using SBET and SDR models was closer to 0.2 g/cm3, which is very low in comparison to the theoretical limit. The SBET and Ono–Kondo theories have displayed that the probability of adsorption after the third layer is low. The VD-Langmuir and FV-OK1 could fit perfectly to highly specific adsorbing solids; however, they failed to explain adsorption in low-adsorbing solids. The mathematical drawbacks of variable density approaches have not been analyzed previously and are explained in this work.

Experimental and modelling studies of carbon dioxide capture onto pristine, nitrogen-doped, and activated ordered mesoporous carbons.

The search for suitable materials for carbon dioxide capture and storage has attracted the attention of the scientific community in view of the increased global CO2 levels and its after-effects. Among the different materials under research, porous carbons and their doped analogues are extensively debated for their ability to store carbon dioxide at high pressures. The present paper examined high-pressure carbon dioxide storage studies of 1-D hexagonal and 3-D cubic ordered mesoporous pristine and N-doped carbons prepared using the nano-casting method. Excess carbon dioxide sorption isotherms were obtained using the volumetric technique and were fitted using the Toth model. Various parameters that influence CO2 storage on metal-free ordered mesoporous carbons, such as the effect of pore size, pore dimension, pyrolysis temperature, the impact of nitrogen substitution, and the effect of ammonia activation are discussed. It was observed that the carbon dioxide storage capacity has an inverse relation to the total nitrogen doped, the amount of pyridinic nitrogen functionality, and the pyrolysis temperature, whereas the pore size seems to have a linear relationship. On the other hand, the presence of oxygen has a positive effect on the sorption capacity. Among the prepared ordered mesoporous carbons, the ammonia-treated one has shown the highest adsorption capacity of 37.8 mmol g-1 at 34 bar and 0 °C.

Mobile-Phase Contributions to Organic-Solvent Excess Adsorption and Surface Diffusion in Reversed-Phase Liquid Chromatography.

Fast transport of retained analytes in reversed-phase liquid chromatography occurs through surface diffusion in the organic-solvent (OS)-enriched interfacial "ditch" region between the hydrophobic stationary phase and the water (W)-OS mobile phase. Through molecular dynamics simulations that recover the OS excess adsorption isotherms of a typical C18-stationary phase for methanol and acetonitrile, we explore the relation between OS properties, OS excess adsorption, and surface diffusion. The emerging molecular-level picture attributes the mobile-phase contribution to surface diffusion to the hydrogen-bond capability and the eluting power of the OS. The higher affinity of methanol for the formation of W-OS hydrogen bonds at the soft, hydrophobic surface presented by the bonded-phase (C18) chains reduces the OS excess and the related viscosity drop in the ditch. The lower eluting power of methanol, however, translates to increased bonded-phase contacts for analytes, which can increase their mobility gain from surface diffusion above the gain observed with acetonitrile.

Structure and thermodynamics of a 2D Lennard-Jones hexagonal fluid

ABSTRACT The thermodynamic and structural properties of the 2D hexagonal soft-sites fluid are examined by integral equation theory benchmarked against extensive Monte Carlo simulations. Hexamers are built of six equal Lennard-Jones segments. Site-site integral equation theory is used to compute site–site correlation functions, excess internal energies and isotherms over a wide range of conditions and compared with results obtained from Monte Carlo simulations. Various approaches for computing the pressure are discussed as well. Satisfactory qualitative agreement between theory and simulations is found with details depending on the applied closure relation.

Heterofullerene C48B12-impregnated MOF-5 and IRMOF-10 for hydrogen storage: A combined DFT and GCMC simulations study

The H2 storage properties of isoreticular metal-organic framework materials (IRMOFs), MOF-5 and IRMOF-10, impregnated with different numbers and types of heterogeneous C48B12 molecules were investigated using density functional theory and grand canonical Monte Carlo (GCMC) calculations. The excess hydrogen adsorption isotherms of IRMOFs at 77 K within 20 bar indicate that suitable number and type of C48B12 molecules play a crucial role in improving the H2 storage properties of IRMOFs. Among the studied pure and nC48B12 (n = 1, 2, 4, 8) in Ci symmetry impregnating into MOF-5, at 77 K under 6 bar, MOF-5-4C48B12 with a 3.5 wt% and 29.9 g/L hydrogen storage density, and at 77 K under 12 bar, the pure MOF-5 with a 4.9 wt% and 31.0 g/L hydrogen storage density has the best hydrogen storage properties. Whereas, among the studied pure and nC48B12 (n = 1, 2, 4, 8) in S6 symmetry impregnating into IRMOF-10, IRMOF-10-8C48B12 always shows the best hydrogen storage properties among the pure and C48B12-impregnated IRMOF-10 at 77 K within 20 bar. IRMOF-10-8C48B12 has a 6.0 wt% and 34.6 g/L hydrogen storage density at 77 K under 6 bar, and has a 7.1 wt% and 41.4 g/L hydrogen storage density at 77 K under 12 bar. The confinement effect of IRMOFs on C48B12 molecules, and steric hindrance effect of C48B12 molecules on IRMOFs mainly affects the H2 uptake capacity by comparing the absolute H2 molecules in individual IRMOFs units, C48B12 molecules, and IRMOFs-nC48B12 compounds. The absolute hydrogen adsorption profiles show that eight C48B12 molecules impregnating into MOF-5 can exert obvious steric effects for H2 adsorption. The saturated gravimetric and volumetric H2 densities of IRMOF-10-8C48B12 higher than those of MOF-5-8C48B12 due to with larger free volume.

A dilemma in calculating ethane absolute adsorption in shale gas reservoirs: A theoretical approach

Shale gas plays are composed of different constituent components (mineral and organics) and a mixture of fluids. To accurately estimate the gas in place (GIP) in such reservoirs, calculating the absolute adsorption quantity would be critical, particularly for ethane fluid as the second major component in the gas composition. In this study, for the first time, by employing hybrid grand canonical Monte Carlo/Molecular Dynamics (GCMC/MD) simulations, the behavior of ethane in graphene layers at various pore sizes (1, 2, and 4 nm), temperature (303.15, 363.15, and 363.15 K), and pressure ranges (0–50 MPa) is observed. Moreover, ethane and helium probes were employed to calculate the accessible volume followed by the absolute adsorption isotherm analysis based on Langmuir, Toth, and supercritical Dubinin–Radushkevich (SDR) adsorption models. Finally, the impacts of calculating the adsorbed density via the ethane density profile to convert the excess adsorption to the absolute adsorption isotherm was investigated. The results showed that despite a good fit of adsorption models with the excess adsorption isotherm, neither of the adsorption models can predict the absolute adsorption precisely. Thus, the better fit of the adsorption model with the excess adsorption isotherm alone cannot be a good criterion for calculating the absolute adsorption isotherm. Collectively, we proposed that adsorbed volume should be favored instead of adsorbed density to estimate the absolute adsorption.

Molecular simulation of methane adsorption in nanoscale rough slits

There are large amounts of nanoscale rough pores in shale, which provides the sites for methane adsorption. Proper understanding of the mechanisms of methane adsorption in nanoscale rough slits is important for estimating the shale gas reserves. In this study, graphene was used instead of shale to construct nanoscale slits with different widths and roughness, and the effects of roughness, slit width and pressure on the methane adsorption characteristics are investigated by using the GCMC and molecular dynamics methods. The results showed that the methane adsorption configurations are influenced by the slit width and surface roughness. The adsorption layers in rough slits are discontinuous and weak second adsorption layers are formed in large slits at high pressures. The inaccessible volume increases with the roughness resulting in the reduction of accessible volume. Therefore, both the excess adsorption and absolute adsorption decrease with the roughness, and they increase with the slit width in the microscopic scale due to the increased adsorption. While decrease slightly with the slit width in the mesoscopic scale due to the reduction of adsorbed phase density. The excess adsorption isotherms are well fitted by the Langmuir-Freundlich model. The adsorption is found more stable in smaller and rougher slits due to the superposition of adsorption potentials through the analysis of adsorbate potential energy and adsorption heat.