Pure Gas Adsorption Equilibria

The standard method to measure pure gas adsorption equilibria most often used today is the volumetric or manometric method. Chap. 2. Basically it is the mass balance of a certain amount of gas partly adsorbed on the sorbent material. This method can be realized in either open or closed systems, the former ones often using a carrier gas, the adsorption of which normally being neglected. Complemented by a gas analyzer (chromatograph, mass spectrometer) this method also can be used to measure multicomponent or coadsorption equilibria. 

Impedance Spectroscopic Measurements of Pure Gas Adsorption Equilibria on Zeolites,... 

Figure 2.1. Experimental setup for (static) volumetric measurements of pure gas adsorption equilibria.

Instrument for gravimetric measurements of pure gas adsorption equilibria using a two beam balance (Sartorius Th. Gast, 4104 S). 

One may argue that combined volumetric - gravimetric measurements of pure gas adsorption equilibria could provide a means to measure the mass adsorbed (m ) and the void volume of the sorbent and the sorbate phase (V ) simultaneously. Unfortunately this does not hold true. Instead, specializing equations (4.1. 6) to the case of pure gases (mi—>m, m2 = 0) and combining them one gets... 

MEASUREMENT OF PURE GAS ADSORPTION EQUILIBRIA (N=l) BY SLOW OSCILLATIONS OF A ROTATIONAL PENDULUM... 

DIELECTRIC-GRAVIMETRIC MEASUREMENTS OF PURE GAS ADSORPTION EQUILIBRIA... 

The prediction of mixed-gas adsorption equilibria by ideal-adsorbed-solution theorf is based onEqs. (14.124) and (14.128). The following is a brief outline of the procedure. Since there are N "r 1 degrees of freedom, both T and P, as well as the gas-phase composition, must be specified. Solution is for the adsorbate compositionand the specific amount adsorbed. Adsorption isotherms for eachpure species must be known over the pressure range from zero to the value that produces the spreading pressure of the mixed-gas adsorbate. For purposes of illustration we assume Eq. (14.107), the Langmuir isotherm, to apply for each pure species, writing it ... 

A common practice is to develop a specific model for the adsorptive process of interest and use simplistic descriptions (models or empirical) of pure and multicomponent gas adsorption equilibria and kinetics in order to describe the effects of various operating variables to obtain an optimum design. The effort is always closely tied to experimental verification and empirical fine-tuning using actual process data from pilot plants. A comprehensive set of data on pure and multicomponent adsorption equilibria of the components of SMROG on an activated carbon and a 5A zeolite is available in published literature.73... 

Adsorption equilibria determine the thermodynamic limits of the specific amounts of adsorption (mol/g) of a pure gas or the components of a fluid mixture (gas or liquid) under a given set of conditions [pressure (P), temperature (T), and mole function (y or Xi) of component /] of the bulk fluid phase. The simplest way to describe adsorption equilibria of pure gas i is in the form of adsorption isotherms where the amount adsorbed (n ) is plotted as a function of gas pressure (P) at a constant temperature (P). The pure gas adsorption isotherms can have various shapes (Types I-V) by Brunauer classification depending on the porosity of the adsorbent (microporous, mesoporous, or nonpo-rous) and the system temperature (below or above the critical temperature of the adsorbate). However, the most common isotherm shape is Type I, which is depicted by most microporous adsorbents of practical use. These isotherms exhibit a linear section in the very low-pressure region (Henry s law region) where the amount adsorbed is proportional to the gas pressure [ n ) = KiP]. The proportionality constant is called... 

Among the theories of predicting mixed-gas adsorption equilibria from pure component adsorption isotherms, the ideal adsorbed solution theory (IAST) [14] has become the standard and often serves as a benchmark for the purpose of comparison by other models. IA ST is a thermodynamically rigorous theory based on the mixing of individual components at constant spreading pressure to form an ideal solution. It has the advantages that (1) no mixture data are required and (2) the theory is independent of the actual model of physical adsorption. 

Traditionally, a variety of heats of adsorption and desorption for pure and multicomponent gas-solid systems have been defined by using thermodynamic models [3-6]. Experimental techniques have also been developed to measure these heats [4,7]. These models generally use the actual amounts adsorbed as the primary variables for representing the extents of adsorption of the adsorbates. Unfortunately, the Gibbsian surface excesses (GSE), and not the actual amounts adsorbed, are the only true experimental variables for measuring the extent of adsorption [8-10]. In view of this fact, a detailed thermodynamic model for multi-component gas adsorption equilibria using GSE as base variables has already been developed [9]. 

The three pure gas adsorption models described by Table 3 have been extended to cover multicomponent adsorption equilibria. Table 4 gives the multicomponent... 

Gravimetric adsorption measurements are used today to characterize porous media [3.10, 3.12, 3.19], to measure gas adsorption equilibria [3.13, 3.14, 3.18, 3.55], and to investigate adsorption kinetics [3.14-3.18], [4.21-4.23]. We here will mainly discuss methods to measure pure gas and mixture gas adsorption equilibria gravimetrically. Other aspects can only be taken into account by presenting few complementary examples. 

This chapter is organized as follows In Sect. 2 we consider pure gas adsorption measurements by both two beam and single beam balances. Section 3 is devoted to thermogravimetry. In Section 4 multicomponent gas adsorption equilibria are discussed. Finally in Sect. 5 pros and cons of gravimetry especially compared to volumetry/manometry are elucidated. A list of symbols and abbreviations used is given followed by references dted. 

Combining the dielectric measurements with either manometric, gravimetric or oscillometric measurements of gas adsorption equilibria states, one gets calibration curves allowing one the determination of Gibbs excess adsorbed masses by purely electric measurements which normally can be performed fairly quickly and on site in industrial situations. 

This book is the result of a fruitful collaboration of a theoretician (JUK) and an experimentalist (RS) over more than twelve years in the field of gas adsorption systems at the Institute of Fluid- and Thermodynamics (IFT) at the University of Siegen, Siegen, Germany. This collaboration resulted in the development of several new methods to measure not only pure gas adsorption, but gas mixture or coadsorption equilibria on inert porous solids. Also several new theoretical results could be achieved leading to new types of so-called adsorption isotherms based on the concepts of molecular association and -phenomenologically speaking - on that of thermodynamic phases of fractal dimension. Naturally, results of international collaboration of the authors over the years (1980-2000) also are included. 

Figure Bl.26.3. The lUPAC classification of adsorption isothemis for gas-solid equilibria (Sing K S W, Everett D H, Haul RAW, Mosoul L, Pierotti R A, Rouguerol J and Siemieiiiewska T 1985 Pure. Appl. Chem. 57 603-19).

The first systematic attempt to interpret adsorption isotherms for gas/solid equilibria was by Braunauer, Deming, Deming, and Teller (BDDT) in 1940.78 They classified the adsorption isotherms into five types, and the BDDT classification became the core of the modem International Union of Pure and Applied Chemistry... 

There are several reports in the literature that measure binary adsorption equilibria using gas chromatography [4,S,6]. In GC techniques the adsorbent is equilibrated with a continuous flow of carrier gas (gas 1). Then a pulse of gas 2 is injected at the column inlet. A peak of the gas 2 is eluted at the exit of the column after some time. Net retention time (or volume) is calculated from the first moment of the peak after correcting for void volume (by measuring the retention time of a non-adsorbing species). If the carrier gas is inert (i.e. helium) the net retention time is related to the pure component Henry s constant. Typical binary measurements reported so r use a mixture of the two gases as carrier and introduce a small perturbation in composition. The net retention volume is related to the thermodynamic properties by [4]... 

Equation (5) is an equation-of-state for the adsorption of a pure gas as a function of temperature and pressure. The constants of this equation are the Henry constant, the saturation capacity, and the virial coefficients at a reference temperature. The temperature variable is incorporated in Equation (5) by the virial coefficients for the differential enthalpy. This equation-of-state for adsorption of single gases provides an accurate basis for predicting the thermodynamic properties and phase equilibria for adsorption from gaseous mixtures. 

The fundamental adsorptive properties governing the performance of the separation processes are the multicomponent equilibria, kinetics, and heat. A large volume of data, as well as models to describe them, exist in the published literature only for adsorption of pure gases and binary liquid mixtures. Binary gas adsorption data are sporadic. Multicomponent data are rare. Existence of adsorbent heterogeneity can introduce severe complexity in the multicomponent adsorption behavior. 

Generally, wastewaters are complex mixtures of solutes, which require theoretical approaches to predict multicomponent adsorption equilibria flxtm pure component adsorption data. The Ideal Adsorbed Solution model (IAS) was first established for a mixed gas adsorption by Myers and Prausnitz [9], and then extended to a multi-solute adsorption from dilute liquid solution by Radke and Prausnitz [10]. The model is based on the fundamental hypothesis that the multicomponent solution has the same spreading pressure s as that of the ideal single solution of the i component, the spreading pressure being the difference between the interfacial tension of the pure solvent and that of the solution containing the solute. This hypothesis is described by the Gibbs equation ... 

Adsorption measurement for multicomponent systems is a function of the composition, temperature, pressure, and properties of adsorbate and adsorbent. As the number of components increases, the number of measurements needed to define the adsorption equilibrium increases rapidly and eventually becomes infeasible. Adsorption equilibrium models are therefore needed to correlate and predict the multicomponent adsorption equilibria. These models should be able to predict the mixture equilibria using the information available on pure component equilibria, as the latter are relatively easy to measure and furthermore there is an abundance of pure component isotherm data available in the literature. As a result, predictive models for gas mixture adsorption are necessary in the design and modeling of adsorption processes. 

The basic assumption in the potential theory approach to predicting the adsorption equilibria of a gas mixture is that the adsorption data for all pure components on the same adsorbent will fall on the same line when plotted on some appropriate coordinate (coalescing) [39,631. This principle is reflected in the Lewis method [64] and in the Grant-Manes (G-M) method [65] and its modification by Metha and Danner [66]. 

The HEL model is a noniterative model and has a reasonable prediction capability. With the pure component isotherm parameters derived from the LUD equation, the model can be employed to predict the adsorption equilibria of gas mixtures at any other temperature. Since the LUD equation is flexible in correlating the pure component data, the HEL model prediction for a gas mixture is generally good. Kapoor et al. [79] demonstrated in their study that the HEL model gave satisfactory results for a number of systems, which were comparable in many cases to the results from the lAST or even HIAST model. 

The MPSD model can be conveniently extended to describe the adsorption equilibria of a gas mixture with N components. The generalized MPSD model simply takes the extended Langmuir equation as the local isotherm while using the MPSD information obtained from pure component data ... 

Abstract This introductory chapter provides some background information of the material to be presented experimental methods to measure adsorption equilibria of pure and mixed gases on inert porous solids. Applications of gas adsorption processes in science and technology are outlined. An overview of the contents of the book is given. Remarks on subjects, measurement methods and other fields of adsorption science which could not be considered within this monography are mentioned. Hints to respective literature and references are given. 

Figure 3.5. Magnetic suspension balance (Rubotherm GmbH) for automated gravimetric measurements of adsorption equilibria of pure corrosive gases. On the r. h. side of the balance 6 electro-pneumatic valves (Hoke, Frankfurt) for controlling the gas supply and evacuation of the installation clearly can be recognized.

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