Net, excess and absolute adsorption and adsorption of helium

Aspects of Gas Storage: Confined Geometry Effects on the High-Pressure Adsorption Behavior of Supercritical Fluids

During the last decades, major progress was made concerning the understanding of subcritical low-pressure adsorption of fluids like nitrogen and argon at their boiling temperatures in nanoporous materials. It was possible to understand how structural properties affect the shape of the adsorption isotherms. However, within the context of gas storage applications, supercritical high-pressure gas adsorption is important. A key feature here is that the experimentally determined surface excess adsorption isotherm may exhibit a characteristic maximum at a certain pressure. For a given temperature and adsorptive/adsorbent system, the surface excess maximum (and the corresponding adsorbed amount) is related to the storage capacity of the adsorbent. However, there is still a lack of understanding of how key textural properties such as surface area and pore size affect details of the shape of supercritical high-pressure adsorption isotherms. To address these open questions, we have performed a systematic experimental study assessing the effect of pore size/structure on the supercritical adsorption isotherms of pure fluids such as C2H4, CO2, and SF6 over a wider range of temperatures and pressures on a series of model materials exhibiting well-defined pore sizes, i.e., ordered micro- and mesoporous materials (e.g., NaY zeolite, KIT-6 silica, and MCM-48 silica). A fundamental result of our experiments is a unique fluid-independent correlation between the pressure of the surface excess maximum pmax (at a given temperature) and the pore size (by taking into account the kinetic diameter of the fluid and the underlying effective attractive fluid-wall interaction). Summarizing, our results suggest important structure-property relationships, allowing one to determine, for given thermodynamic conditions, important information related to the optimal operating conditions for supercritical adsorption applications. The insights may also serve as a basis for optimizing and tailoring the properties of nanoporous adsorbent materials for gas storage applications.

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.

High-Pressure Gravimetric Measurements for Binary Gas Adsorption Equilibria and Comparisons with Ideal Adsorbed Solution Theory (IAST)

Measurements of gas mixture adsorption equilibria at high pressures are important for assessing actual adsorbent selectivities but are often out of reach, given the challenging nature of the required experiments. Here, we report a high-pressure gravimetric binary gas adsorption equilibrium measurement system based on simultaneous gas density and mixture adsorption measurements in a single gas cell coupled to a magnetic-suspension balance. Compared to traditional techniques which rely on analytical measurements of gas composition, this approach does not require any sampling. Adsorption measurements of two gas mixtures (0.500 N2 + 0.500 CH4 and 0.400 N2 + 0.600 CO2, mole fraction) on a commercially available molecular sieve (NaY, sodium molecular sieve type Y) were carried out in the temperature range 282 to 325 K with a pressure up to 10 MPa. A prediction method for the gas mixture adsorption equilibria in a closed system using the ideal adsorbed solution theory (IAST) model was used to compare the experimental results. For binary mixtures of components with similar adsorption capacities (here N2 and CH4), the system can measure the adsorption equilibria at pressures higher than 1.0 MPa and the result agrees well with the IAST model prediction. For two gases with very different adsorption capacities, the uncertainty in the adsorption equilibrium measurement is much larger. The dominant uncertainty source is the gas density measurement, whose uncertainty could potentially be cut to half if the current titanium sinker is replaced with a sinker made of single-crystal silicon and with a larger volume.

The Rigid Adsorbent Lattice Fluid Model: Thermodynamic Consistency and Relationship to the Real Adsorbed Solution Theory

The Rigid Adsorbent Lattice Fluid model has been shown to comply with all the requirements for thermodynamic consistency in the case of an adsorbent that does not undergo structural changes. This is achieved by introducing a correction to the reduced density function that multiplies the combinatorial term. A procedure to calculate the predicted adsorbed mixture activity coefficients has been presented that allows the production of excess Gibbs energy plots at a constant reduced grand potential. The predicted nonideality is structurally consistent with the Non-Ideal Adsorbed Solution Theory of Myers in terms of both its dependence on concentration and reduced grand potential. The ability to generate excess Gibbs energy values allows linking the new Rigid Adsorbent Lattice Fluid model to the traditional Real Adsorbed Solution Theory providing an alternative approach to predicting multicomponent adsorption based solely on pure component data.

Survey on Adsorption of Low Molecular Weight Compounds in Cu-BTC Metal-Organic Framework: Experimental Results and Thermodynamic Modeling

This contribution aims at providing a critical overview of experimental results for the sorption of low molecular weight compounds in the Cu-BTC Metal-Organic Framework (MOF) and of their interpretation using available and new, specifically developed, theoretical approaches. First, a literature review of experimental results for the sorption of gases and vapors is presented, with particular focus on the results obtained from vibrational spectroscopy techniques. Then, an overview of theoretical models available in the literature is presented starting from semiempirical theoretical approaches suitable to interpret the adsorption thermodynamics of gases and vapors in Cu-BTC. A more detailed description is provided of a recently proposed Lattice Fluid approach, the Rigid Adsorbent Lattice Fluid (RALF) model. In addition, to deal with the cases where specific self- and cross-interactions (e.g., H-bonding, Lewis acid/Lewis base interactions) play a role, a modification of the RALF model, i.e., the RALFHB model, is introduced here for the first time. An extension of both RALF and RALFHB is also presented to cope with the cases in which the heterogeneity of the rigid adsorbent displaying a different kind of adsorbent cages is of relevance, as it occurs for the adsorption of some low molecular weight substances in Cu-BTC MOF.

Simultaneous Estimation of Gas Adsorption Equilibria and Kinetics of Individual Shaped Adsorbents

Shaped adsorbents (e.g., pellets, extrudates) are typically employed in several gas separation and sensing applications. The performance of these adsorbents is dictated by two key factors, their adsorption equilibrium capacity and kinetics. Often, adsorption equilibrium and textural properties are reported for materials. Adsorption kinetics are seldom presented due to the challenges associated with measuring them. The overarching goal of this work is to develop an approach to characterize the adsorption properties of individual shaped adsorbents with less than 100 mg of material. To this aim, we have developed an experimental dynamic sorption setup and complemented it with mathematical models, to describe the mass transport in the system. We embed these models into a derivative-free optimizer to predict model parameters for adsorption equilibrium and kinetics. We evaluate and independently validate the performance of our approach on three adsorbents that exhibit differences in their chemistry, synthesis, formulation, and textural properties. Further, we test the robustness of our mathematical framework using a digital twin. We show that the framework can rapidly (i.e., in a few hours) and quantitatively characterize adsorption properties at a milligram scale, making it suitable for the screening of novel porous materials.

Absolute adsorption and adsorbed volume modeling for supercritical methane adsorption on shale

Adsorbed methane significantly affects shale gas reservoir estimates and shale gas transport in shale formations. Hence, a practical model for accurately representing methane adsorption behavior at high-pressure and high-temperature in shale is imperative. In this study, a reliable mathematical framework that estimates the absolute adsorption directly from low-pressure excess adsorption data is applied to describe the excess methane adsorption data in literature. This method provides detailed information on the volume and density of adsorbed methane. The obtained results indicate that the extensively used supercritical Dubinin-Radushkevich model with constant adsorbed phase density underestimates absolute adsorption at high pressure. The adsorbed methane volume increases both the pressure and expands with the temperature. The adsorbed methane density reduces above 10 MPa, and approaches a steady value at high pressure. This study provides a novel method for estimating adsorbed shale gas, which is expected improve the prediction of shale gas in place and gas production.

Application of Raman Spectroscopy for Sorption Analysis of Functionalized Porous Materials

Functionalized porous materials could play a key role in improving the efficiency of gas separation processes as required by applications such as carbon capture and storage (CCS) and across the hydrogen value chain. Due to the large number of different functionalizations, new experimental approaches are needed to determine if an adsorbent is suitable for a specific separation task. Here, it is shown for the first time that Raman spectroscopy is an efficient tool to characterize the adsorption capacity and selectivity of translucent functionalized porous materials at high pressures, whereby translucence is the precondition to study mass transport inside of a material. As a proof of function, the performance of three silica ionogels to separate an equimolar (hydrogen + carbon dioxide) gas mixture is determined by both accurate gravimetric sorption measurements and Raman spectroscopy, with the observed consistency establishing the latter as a novel measurement technique for the determination of adsorption capacity. These results encourage the use of the spectroscopic approach as a rapid screening method for translucent porous materials, particularly since only very small amounts of sample are required.

Improving Reproducibility in Hydrogen Storage Material Research

Research into new reversible hydrogen storage materials has the potential to help accelerate the transition to a hydrogen economy. The discovery of an efficient and cost-effective method of safely storing hydrogen would revolutionise its use as a sustainable energy carrier. Accurately measuring storage capacities - particularly of novel nanomaterials - has however proved challenging, and progress is being hindered by ongoing problems with reproducibility. Various metal and complex hydrides are being investigated, together with nanoporous adsorbents such as carbons, metal-organic frameworks and microporous organic polymers. The hydrogen storage properties of these materials are commonly determined using either the manometric (or Sieverts) technique or gravimetric methods, but both approaches are prone to significant error, if not performed with great care. Although commercial manometric and gravimetric instruments are widely available, they must be operated with an awareness of the limits of their applicability and the error sources inherent to the measurement techniques. This article therefore describes the measurement of hydrogen sorption and covers the required experimental procedures, aspects of troubleshooting and recommended reporting guidelines, with a view of helping improve reproducibility in experimental hydrogen storage material research.

Performance-Based Screening of Porous Materials for Carbon Capture

Computational screening methods have changed the way new materials and processes are discovered and designed. For adsorption-based gas separations and carbon capture, recent efforts have been directed toward the development of multiscale and performance-based screening workflows where we can go from the atomistic structure of an adsorbent to its equilibrium and transport properties at different scales, and eventually to its separation performance at the process level. The objective of this work is to review the current status of this new approach, discuss its potential and impact on the field of materials screening, and highlight the challenges that limit its application. We compile and introduce all the elements required for the development, implementation, and operation of multiscale workflows, hence providing a useful practical guide and a comprehensive source of reference to the scientific communities who work in this area. Our review includes information about available materials databases, state-of-the-art molecular simulation and process modeling tools, and a complete catalogue of data and parameters that are required at each stage of the multiscale screening. We thoroughly discuss the challenges associated with data availability, consistency of the models, and reproducibility of the data and, finally, propose new directions for the future of the field.

Measurement and interpretation of unary supercritical gas adsorption isotherms in micro-mesoporous solids

Gas adsorption at high pressures in porous solids is commonly quantified in terms of the excess amount adsorbed. Despite the wide spectrum of adsorbent morphologies available, the analysis of excess adsorption isotherms has mostly focused on microporous materials and the role of mesoporosity remains largely unexplored. Here, we present supercritical CO2 adsorption isotherms measured at $$T=308$$ T = 308  K in the pressure range $$p=0.02{-}21$$ p = 0.02 - 21  MPa on three adsorbents with distinct fractions of microporosity, $$\phi_2$$ ϕ 2 , namely a microporous metal-organic framework ($$\phi_2=70$$ ϕ 2 = 70 %), a micro-mesoporous zeolite ($$\phi_2=38$$ ϕ 2 = 38 %) and a mesoporous carbon ($$\phi_2<0.1$$ ϕ 2 < 0.1 %). The results are compared systematically in terms of excess and net adsorption relative to two distinct reference states–the space filled with gas in the presence/absence of adsorbent–that are defined from two separate experiments using helium as the probing gas. We discuss the inherent difficulties in extracting from the supercritical adsorption isotherms quantitative information on the properties of the adsorbed phase (its density or volume), because of the nonuniform distribution of the latter within and across the different classes of pore sizes. Yet, the data clearly reveal pore-size dependent adsorption behaviour, which can be used to identify characteristic types of isotherm and to complement the information obtained using the more traditional textural analysis by physisorption.

A review of common practices in gravimetric and volumetric adsorption kinetic experiments

The availability of commercial gravimetric and volumetric systems for the measurement of adsorption equilibrium has seen also a growth of the use of these instruments to measure adsorption kinetics. A review of publications from the past 20 years has been used to assess common practice in 180 cases. There are worrying trends observed, such as lack of information on the actual conditions used in the experiment and the fact that the analysis of the data is often based on models that do not apply to the experimental systems used. To provide guidance to users of these techniques this contribution is divided into two parts: a discussion of the appropriate models to describe diffusion in porous materials is presented for different gravimetric and volumetric systems, followed by a structured discussion of the main trends in common practice uncovered reviewing a large number of recent publications. We conclude with recommendations for best practice to avoid incorrect interpretation of these experiments.

Accurate blank corrections for zero length column experiments

In this study we present a new methodology for correcting experimental Zero Length Column data, to account for contributions to the measured signal arising from extra-column volumes and the detector. The methodology considers the experimental setup as a series of mixing volumes with diffusive pockets whose contributions to the overall measured signal can be accurately described by simple model functions. The composite effect of the individual contributions is subsequently described through the method of convolution. It is shown that the model parameters are closely related to the physical characteristics of the setup components and as such they remain valid over a range of process conditions. The methodology is firstly validated through fitting to experimental experiments without adsorbent present. The inverse procedure of deconvolution can in turn be applied to experimental data with adsorbent, to yield corrected data which can readily be modelled using standard tools for equilibrium and kinetic analysis. A number of case studies is finally presented exemplifying the effect of applying accurate blank corrections, demonstrating also the application to a nonlinear adsorption system.

Uncertainty analysis of adsorption measurements using commercial gravimetric sorption analyzers with simultaneous density measurement based on a magnetic-suspension balance

A commercial gravimetric sorption analyzer, which is based on a magnetic-suspension balance, was significantly improved to reduce the uncertainty in adsorption measurements. In a previous paper, we investigated the force-transmission error (FTE) of the instrument’s magnetic-suspension coupling, and we analysed the uncertainty of the density measurement. In the present paper, equations for the determination of the adsorption on porous and quasi non-porous materials are provided, where the FTE is taken into account, and a detailed uncertainty analysis is presented. The uncertainty analysis was applied to both the improved measurement system and a typical commercial gravimetric sorption analyzer. Adsorption test measurements were conducted with carbon dioxide along the T = 283 K isotherm at pressures up to the dew-point pressure using both a porous material (zeolite 13X) and a quasi non-porous material (solid metallic sinkers). The major uncertainty contributions for adsorption on the porous material were the mass and volume of the adsorbent sample and the assumption of the density of the adsorbed fluid; for the quasi non-porous material, the main contributions were the weighing values of the balance, the density of the investigated fluid in the gas phase, and the volume of the non-porous material. The influence of the FTE on the adsorption on the porous material was approximately 0.002 mmol⋅g−1, which was negligibly small; but the influence of the FTE was significant in the case of the quasi non-porous material, i.e., approximately 0.7 mmol⋅m−2 or about 22% of the adsorption capacity with the highest adsorption observed in this work (near the dew-point pressure). This indicates that the influence of the FTE increases significantly with decreasing adsorption capacity of the adsorbent sample.

Computational Investigation of Correlations in Adsorbate Entropy for Pure-Silica Zeolite Adsorbents

Vast numbers of unstudied hypothetical porous frameworks continue to spark interest in optimizing adsorption and catalytic processes. Evaluating the use of such materials depends on the accessibility of thermodynamic metrics such as the free energy, which, in turn, depend on the satisfactory estimation or calculation of the adsorption entropy, which often remains elusive. Previous works using simulations and experimental data have demonstrated relationships between the entropy and system descriptors, allowing for sensible predictions based on more-easily obtained physical parameters. However, the resultant conclusions were either based on experimental data for industrially relevant alkanes or lacked a significant sample size. In this paper, we evaluate correlations between gas-phase and adsorbed-phase entropies for a larger and more chemically diverse set of adsorbate molecules by using force fields and statistical mechanical expressions to calculate those entropies. In total, we perform calculations for 37 molecules across 10 chemical categories available in the TraPPE force field set, as adsorbed in five siliceous zeolites. Our results show that linear correlations between the gas- and adsorbed-phase entropies persist for the larger and diverse set of adsorbate molecules studied here, proving a broader applicability and justifying the use of simple correlations for many adsorbates and, presumably, adsorbent materials.

Effects of Moisture and Salinity on Methane Adsorption in Kerogen: A Molecular Simulation Study

The adsorption characteristics of methane in shales play a critical role in the assessment of shale gas resources. The microscopic adsorption mechanism of methane considering the effect of moisture and especially salinity remains to be explored. In this work, combined molecular dynamics and grand canonical Monte Carlo simulations are conducted to investigate the adsorption behaviors of methane in the realistic kerogen matrixes containing different moisture contents (0-6 wt %) and various salinities (0-6 mol/L NaCl). Adsorption processes are simulated under realistic reservoir conditions at four temperatures in the range from 298.15 to 358.15 K and pressures up to 40 MPa. Effects of the moisture content on methane adsorption capacities are analyzed in detail. Simulation results show that the methane adsorption capacity declines as the moisture content increases. In comparison to the dry kerogen matrix, the reduction in the maximum CH4 adsorption capacity is as high as 42.5% in moist kerogen, with a moisture content of 6.0 wt % at 338.15 K. The overlap observed in the density distributions of water molecules and decrease in adsorbed methane indicates that the water molecules occupy the adsorption sites and, thus, lead to the reduction in methane adsorption capacity. Besides, the effects of salinity on CH4 adsorption isotherms are discussed. The salinity is found to have a negative influence on the methane adsorption capacity. The maximum CH4 adsorption capacity reduces around 6.0% under the salinity of 6 mol/L at 338.15 K. Adsorption of methane in kerogens of constant salinity but different moisture contents are further discussed. Results from the present study show that the moisture content has a greater impact on the adsorption of methane compared to that of salinity. The findings of this study have important implications for more accurate estimation of shale gas in place.

The role of molecular modelling and simulation in the discovery and deployment of metal-organic frameworks for gas storage and separation

Metal-organic frameworks (MOFs) are highly tuneable, extended-network, crystalline, nanoporous materials with applications in gas storage, separations, and sensing. We review how molecular models and simulations of gas adsorption in MOFs have informed the discovery of performant MOFs for methane, hydrogen, and oxygen storage, xenon, carbon dioxide, and chemical warfare agent capture, and xylene enrichment. Particularly, we highlight how large, open databases of MOF crystal structures, post-processed to enable molecular simulations, are a platform for computational materials discovery. We discuss how to orient research efforts to routinise the computational discovery of MOFs for adsorption-based engineering applications.

A reference high-pressure CO2 adsorption isotherm for ammonium ZSM-5 zeolite: results of an interlaboratory study

This paper reports the results of an international interlaboratory study led by the National Institute of Standards and Technology (NIST) on the measurement of high-pressure surface excess carbon dioxide adsorption isotherms on NIST Reference Material RM 8852 (ammonium ZSM-5 zeolite), at 293.15 K (20 °C) from 1 kPa up to 4.5 MPa. Eleven laboratories participated in this exercise and, for the first time, high-pressure adsorption reference data are reported using a reference material. An empirical reference equationn e x = d ( 1 + exp [ - ln ( P ) + a / b ] ) c , [n ex -surface excess uptake (mmol/g), P-equilibrium pressure (MPa), a = -6.22, b = 1.97, c = 4.73, and d = 3.87] along with the 95% uncertainty interval (U k = 2 = 0.075 mmol/g) were determined for the reference isotherm using a Bayesian, Markov Chain Monte Carlo method. Together, this zeolitic reference material and the associated adsorption data provide a means for laboratories to test and validate high-pressure adsorption equipment and measurements. Recommendations are provided for measuring reliable high-pressure adsorption isotherms using this material, including activation procedures, data processing methods to determine surface excess uptake, and the appropriate equation of state to be used.

Net, excess and absolute adsorption in mixed gas adsorption

The formulation of a thermodynamic framework for mixtures based on absolute, excess or net adsorption is discussed and the qualitative dependence with pressure and fugacity is used to highlight a practical issue that arises when extending the formulations to mixtures and to the Ideal Adsorbed Solution Theory (IAST). Two important conclusions are derived: the correct fundamental thermodynamic variable is the absolute adsorbed amount; there is only one possible definition of the ideal adsorbed solution and whichever starting point is used the same final IAST equations are obtained, contrary to what has been reported in the literature.

Review of Membranes for Helium Separation and Purification

Membrane gas separation has potential for the recovery and purification of helium, because the majority of membranes have selectivity for helium. This review reports on the current state of the research and patent literature for membranes undertaking helium separation. This includes direct recovery from natural gas, as an ancillary stage in natural gas processing, as well as niche applications where helium recycling has potential. A review of the available polymeric and inorganic membranes for helium separation is provided. Commercial gas separation membranes in comparable gas industries are discussed in terms of their potential in helium separation. Also presented are the various membrane process designs patented for the recovery and purification of helium from various sources, as these demonstrate that it is viable to separate helium through currently available polymeric membranes. This review places a particular focus on those processes where membranes are combined in series with another separation technology, commonly pressure swing adsorption. These combined processes have the most potential for membranes to produce a high purity helium product. The review demonstrates that membrane gas separation is technically feasible for helium recovery and purification, though membranes are currently only applied in niche applications focused on reusing helium rather than separation from natural sources.