Appropriate volumes for adsorption isotherm studies: The absolute void volume, accessible pore volume and enclosing particle volume

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.

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.

Supercritical CO2 Exposure-Induced Surface Property, Pore Structure, and Adsorption Capacity Alterations in Various Rank Coals

Carbon dioxide (CO2) has been used to replace coal seam gas for recovery enhancement and carbon sequestration. To better understand the alternations of coal seam in response to CO2 sequestration, the properties of four different coals before and after supercritical CO2 (ScCO2) exposure at 40 °C and 16 MPa were analyzed with Fourier Transform infrared spectroscopy (FTIR), low-pressure nitrogen, and CO2 adsorption methods. Further, high-pressure CO2 adsorption isotherms were performed at 40 °C using a gravimetric method. The results indicate that the density of functional groups and mineral matters on coal surface decreased after ScCO2 exposure, especially for low-rank coal. With ScCO2 exposure, only minimal changes in pore shape were observed for various rank coals. However, the micropore specific surface area (SSA) and pore volume increased while the values for mesopore decreased as determined by low-pressure N2 and CO2 adsorption. The combined effects of surface property and pore structure alterations lead to a higher CO2 adsorption capacity at lower pressures but lower CO2 adsorption capacity at higher pressures. Langmuir model fitting shows a decreasing trend in monolayer capacity after ScCO2 exposure, indicating an elimination of the adsorption sites. The results provide new insights for the long-term safety for the evaluation of CO2-enhanced coal seam gas recovery.

Volumetric Measurements of Methane-Coal Adsorption and Desorption Isotherms—Effects of Equations of State and Implication for Initial Gas Reserves

This study presents the effects of equations of state (EOSs) on methane adsorption capacity, sorption hysteresis and initial gas reserves of a medium volatile bituminous coal. The sorption experiments were performed, at temperatures of 25 °C and 40 °C and up to 7MPa pressure, using a high-pressure volumetric analyzer (HPVA-II). The measured isotherms were parameterized with the modified (three-parameter) Langmuir model. Gas compressibility factors were calculated using six popular equations of state and the results were compared with those obtained using gas compressibility factors from NIST-Refprop® (which implies McCarty and Arp’s EOS for Z-factor of helium and Setzmann and Wagner’s EOS for that of methane). Significant variations were observed in the resulting isotherms and associated model parameters with EOS. Negligible hysteresis was observed with NIST-refprop at both experimental temperatures, with the desorption isotherm being slightly lower than the adsorption isotherm at 25 °C. Compared to NIST-refprop, it was observed that equations of state that gave lower values of Z-factor for methane resulted in “positive hysteresis”, (one in which the desorption isotherm is above the corresponding adsorption curve) and the more negatively deviated the Z-factors are, the bigger the observed hysteresis loop. Conversely, equations of state that gave positively deviated Z-factors of methane relatively produced “negative hysteresis” loops where the desorption isotherms are lower than the corresponding adsorption isotherms. Adsorbed gas accounted for over 90% of the calculated original gas in place (OGIP) and the larger the Langmuir volume, the larger the proportion of OGIP that was adsorbed.

Computational methodology for determining textural properties of simulated porous carbons

We have refined and improved the computational efficiency of the TriPOD technique, used to determine the accessible characteristics of porous solids with a known configuration of solid atoms. Instead of placing a probe molecule randomly, as described in the original version of the TriPOD method (Herrera et al., 2011), we implemented a scheme for dividing the porous solid into 3D-grids and computing the solid-fluid potential energies at these grid points. We illustrate the potential of this technique in determining the total pore volume, the surface area and the pore size distribution of various molecular models of porous carbons, ranging from simple pore models to a more complex simulated porous carbon model; the latter is constructed from a canonical Monte Carlo simulation of carbon microcrystallites of various sizes.

Adsorption in alumina pores open at one and at both ends

We have studied adsorption in regular, self-ordered alumina pores open at both ends or only at one end. The straight, non-connected pores have diameters ranging from 22 to 83 nm, with a relative dispersion below 1% in the pore size. Adsorption isotherms measured in open pores with a torsional microbalance show pronounced hysteresis loops characterized by nearly vertical and parallel adsorption and desorption branches. Blocking one end of the pores with glue has a strong influence on adsorption, as expected from classical macroscopic arguments. However, the experimental measurements show an unexpectedly rich phenomenology dependent on the pore size. For large pores (Dp ≥ 67 nm), the isotherms for closed end pores present much narrower hysteresis loops whose adsorption and desorption boundaries envelop the desorption branches of the isotherms for the corresponding open pores of the same size. The loop for small closed end pores (Dp = 22 nm) is slightly wider than that for open pores while the adsorption branches coincide. For large pores, in contrast, the desorption branches of pores with the same Dp overlap regardless of the pore opening. These observations are in agreement with our grand canonical Monte Carlo (GCMC) simulations for a cylindrical pore model with constrictions, suggesting that the alumina pores could be modeled using a constricted pore model whose adsorption isotherm depends on the ratio of the constriction size to the pore size (Dc/Dp).

On the irreversibility of the adsorption isotherm in a closed-end pore

We present a simulation study of argon adsorption in a closed-end mesopore of uniform diameter in order to investigate the occurrence of hysteresis and propose two principal reasons for its existence: the variation in the shape and radius of curvature of the meniscus and the change in the packing of adsorbate during adsorption and desorption. This interpretation differs from classical theories that neglect both of these factors, and therefore find that adsorption-desorption in a closed-end pore is reversible. A detailed simulation study of the effects of temperature on the microscopic behavior of the adsorbate supports the interpretation proposed here.

Monte Carlo simulation of cavitation in pores with nonwetting defects

We investigate the onset of cavitation in a metastable fluid confined to nanoscale pores with nonwetting defects present. Using grand canonical and gauge cell mesocanonical Monte Carlo simulations, we study the degree of metastability (relative vapor pressure), at which the critical bubble forms in a spherical pore with a circular nonwetting defect. It is shown that an increase of the defect size leads to a transition from homogeneous to heterogeneous nucleation of critical bubbles formed at the defect site. In this case, the desorption process may be initiated at larger relative vapor pressures than those predicted by the theories of homogeneous cavitation.

Monte Carlo optimization scheme to determine the physical properties of porous and nonporous solids

A new method, based on a Monte Carlo scheme, is developed to determine physical properties of nonporous and porous solids. In the case of nonporous solids, we calculate the surface area. This surface area is found as the sum of areas of patches of different surface energy on the solid, which is assumed to take a patchwise topology (i.e., adsorption sites of the same energy are grouped together in one patch). As a result of this assumption, we derive not only the surface area, but also the accessible volume and the surface energy distribution. In the case of porous solids, the optimization method is used to derive the surface area and the pore size distribution simultaneously. The derivation of these physical properties is based on adsorption data from a volumetric apparatus. We test this novel idea with the inversion problem of deriving surface areas of patches of different energies for a number of nonporous solids. The method is also tested with the derivation of the pore size distribution of some porous solid models. The results are very encouraging and demonstrate the great potential of this method as an alternative to the usual deterministic optimization algorithms which are known to be sensitive to the choice of the initial guess of the parameters. Since the geometrical parameters are physical quantities (i.e., only positive values are accepted), we also propose a scheme to enforce the positivity constraint of the solution.

On the existence of negative excess isotherms for argon adsorption on graphite surfaces and in graphitic pores under supercritical conditions at pressures up to 10,000 atm

In this paper, we consider in detail the computer simulation of argon adsorption on a graphite surface and inside graphitic slit pores under supercritical conditions. Experimental results in the literature for graphitic adsorbents show that excess isotherms pass through a maximum and then become negative at high pressures (even for adsorption on open surfaces) when a helium void volume is used in the calculation of the excess amount. Here we show that, by using the appropriate accessible volume (which is smaller than the helium void volume), the excess isotherms still have a maximum but are always positive. The existence and the magnitude of this maximum is because the rate of change of the adsorbed density is equal to that of the bulk gas, which has a large change in bulk gas density for a small variation in pressure for temperatures not far above the critical point. However for temperatures far above T(c), this change in the bulk gas density is no longer significant and the maximum in the surface excess density becomes less pronounced and even disappears at high enough temperatures. The positivity of the adsorption excess persists for all pressures up to 10,000 atm for adsorption on surfaces and in slit pores of all sizes. For adsorption on a surface, the surface excess density eventually reaches a plateau at high pressures as expected, because the change in the adsorbed phase is comparable to that of the bulk gas. Positive excess lends support to our physical argument that the adsorbed phase is denser than the bulk gas, and this is logical as the forces exerted by the pore walls should aid to the compression of the adsorbed phase.

On the Henry constant and isosteric heat at zero loading in gas phase adsorption

The Henry constant and the isosteric heat of adsorption at zero loading are commonly used as indicators of the strength of the affinity of an adsorbate for a solid adsorbent. It is assumed that (i) they are observable in practice, (ii) the Van Hoff's plot of the logarithm of the Henry constant versus the inverse of temperature is always linear and the slope is equal to the heat of adsorption, and (iii) the isosteric heat of adsorption at zero loading is either constant or weakly dependent on temperature. We show in this paper that none of these three points is necessarily correct, first because these variables might not be observable since they are outside the range of measurability; second that the linearity of the Van Hoff plot breaks down at very high temperature, and third that the isosteric heat versus loading is a strong function of temperature. We demonstrate these points using Monte Carlo integration and Monte Carlo simulation of adsorption of various gases on a graphite surface. Another issue concerning the Henry constant is related to the way the adsorption excess is defined. The most commonly used equation is the one that assumes that the void volume is the volume extended all the way to a boundary passing through the centres of the outermost solid atoms. With this definition the Henry constant can become negative at high temperatures. Although adsorption at these temperatures may not be practical because of the very low value of the Henry constant, it is more useful to define the Henry constant in such a way that it is always positive at all temperatures. Here we propose the use of the accessible volume; the volume probed by the adsorbate when it is in nonpositive regions of the potential, to calculate the Henry constant.