Computing the temperature dependence of adsorption selectivity in porous solids
Introduction
Advanced adsorption studies and porous materials characterization, are performed almost routinely in commercially available adsorption instruments and pore size analysers [[1], [2], [3]]. Nowadays, single component adsorption data can be obtained at any temperature of interest even at cryogenic conditions (<200 K) using specially designed thermostats and pressure controllers [4]. On the other hand, mixed gas adsorption experiments are less amenable to automation and far more complex than the single component experiments [5]. They require custom equipment and an elaborate data analysis [6]. More important is that equilibrium conditions for adsorbate mixtures may need several hours to be detected or ensured. Considering the time and the resources required for multicomponent experimental adsorption, it is intractable to perform such experiments at lengthy arrays of temperatures, pressures and feeding compositions. To minimize the conceivable effort for thorough experimental investigations, we propose a computational method that combines the ideal adsorbed solution theory and the Clausius Clapeyron equation to estimate gas mixture adsorption at a range of conditions.
The ideal adsorbed solution theory (IAST) is developed by Myers and Prausnitz in 1965 [7]. It is a thermodynamic framework that predicts multi-component adsorption using only data from single component adsorption at the temperature of interest. IAST describes the adsorbed phase as a two dimensional layer along the solid surface, where the adsorbed species exert a spreading pressure π. The spreading pressure is the analogy of the pressure in two dimensions. A key assumption of IAST is that, although the individual adsorbate components behave non-ideally (i.e., adsorbate species may obey nonlinear isotherms like Langmuir, Freundlich etc.), their mixture along the solid surface is ideal [8,9]. The surface area occupied per mole, by an adsorbate, is the same regardless if other adsorbates are also present in the layer and the capacities of single and multi component adsorption obey the Raoult's law of gas mixtures. These approximations are reasonable for adsorbate mixtures having particles with similar size, shape and molecular interactions of equivalent strength.
The capability of IAST to predict multicomponent competitive interactions has been confirmed decades ago [[8], [9], [10]]. M. Benjamin has introduced a new IAST solution approach, allowing the model equations to be solved using a simple spreadsheet analysis [11]. Simon et al., provided a python package that performs IAST calculations, where the pure component isotherms can be characterized using appropriate fitting models or linear interpolation [12]. Likewise IAST, the Flory-Huggins theory has been also proposed as a binary mixture predictive model and validated with experimental binary adsorption data [13,14]. Comparison studies between IAST predictions and direct mixture adsorption simulations, have been reported, for many pore structural models, like carbons, porous crystallines and metal organic frameworks and for different number and types of adsorbate components [[15], [16], [17]].
CO2 and CH4 are typical gases in industrial applications omnipresent in feed and post-combustion streams of relevant processes. The reduction of greenhouse gas emissions and the purification of biogas and natural gas, demanded the development of technologies for separating the specific components. Adsorption based technologies using porous solids have been identified as an attractive option. Existing and newly developed porous materials have been considered for CO2 capture or CO2/CH4 separation. Such materials include adsorbents like carbons, zeolites and metal-organic frameworks. A general overview of the advantages and limitations of such adsorbents can be found in the literature [18,19].
In this work we consider four representative solids, an activated carbon cloth an ordered mesoporous carbon, the alpha magnesium formate and ZIF69 (i.e, a zeolitic imidazolate framework). We use an initial dataset of CO2 and CH4 adsorption isotherms at three temperatures. We apply the Clausius Clapeyron equation to interpolate the available isotherms at an array of specified temperatures. We employ the ideal adsorbed solution theory to compute the mixture adsorption densities at the specified temperatures and for the full range of CO2-CH4 mixture compositions. The experimental CO2 and CH4 adsorption isotherms of the two carbons and the magnesium formate are taken from the literature [[20], [21], [22]]. Complementary, we perform grand canonical adsorption simulations to produce the relevant CO2 and CH4 isotherms of ZIF69. The IAST predictions for the adsorbate mixture capacities on ZIF69 are examined and validated after performing direct mixture component adsorption simulations at the same conditions.
Section snippets
Method
When the isotherms for a single component adsorption are available at three or more temperatures, the relation between the pressure p and the uptake q (or coverage) on an isotherm operating at temperature T, is given by the Clausius-Clapeyron equation [1] where (Qst)q is the isosteric heat of adsorption at a coverage q. The heat of adsorption depends on the coverage, therefore we compute for a range of coverages qi. We consider n equally spaced qi, in the
Single component experimental adsorption
We consider an activated carbon cloth (acc) for a first adsorbent. This material results from the carbonization of a viscose rayon cloth [26]. It is a non-fragile carbon that maintains the cloth-like texture of its precursor. We obtain the set of experimental CO2 and CH4 isotherms shown in Fig. 1 for a carbon cloth, from Kostoglou et al., who studied the particular sorbent for selective (CO2/CH4) gas separation [20].
Second, we consider an ordered mesoporous carbon sample (omc). The ordered
Isotherms interpolation
Fig. 2 shows the interpolated isotherms of the two adsorbate components for the three samples. We used the Clausius Clapeyron equation on the experimental isotherms of Fig. 1. We consider 20 temperatures in the range [274,312] K using the interval dT = 2 K. The isosteric heat (or enthalpy) of adsorption Qst, is shown in the inset plots of Fig. 2. The enthalpy varies with the uptake, due to the surface heterogeneity of the solid and the interactions of adsorbate molecules within the adsorbed
IAST calculations
IAST calculations for binary CO2-CH4 mixture adsorption on an activated carbon cloth are shown in Fig. 3. The calculations are based on the single component adsorption isotherms given in Fig. 2. The feeding pressure is Pfeed = 1000 mbar and the temperature range is T = [274…312] K. The adsorption loading of the two components increases with the respective mole fraction and decreases with temperature. The CH4 uptake curves for the different temperatures almost coincide at high CO2 feed
Simulations of CO2/CH4 adsorption on ZIF69
ZIF69 is a zinc based organic framework having imidazolate and chloro benzo-imidazolate (cbIm) ligands. The framework of ZIF69 is illustrated in Fig. 6. The crystal consists of distinct hexahedral and dodecahedral channels. A special feature of ZIF69 is a set of cbIm ligands which are normally projected from half of the edges of the dodecahedral pores having their chlorine atoms pointing to the center of the cavity. The pore size analysis of ZIF69 is given in Table 1. The pore metrics are
Conclusions
Clausius Clapeyron equation and the ideal adsorbed solution theory can play a key role in materials screening algorithms for gas separation performances. Such algorithms implement simple routines able to compute fast the adsorption capacities of mixture components for large databases of porous sorbents. These algorithms are used to suggest the most promising materials along with an optimal set of operating conditions. We employ a method that estimates fast the adsorption selectivity at a broad
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