Equilibrium adsorption isotherm

The thermodynamics consistency for binary adsorption equilibria isotherm equations was studied by Myers and Sircar [26]. Franses et al. [27] used similar thermodynamics arguments and proposed the following differential criterion for testing the thermodynamics consistency of adsorption isotherm equations of binary systems ... 

The chromatographic resolution of bi-naphthol enantiomers was considered for simulation purposes [18]. The chiral stationary phase is 3,5-dinitrobenzoyl phenyl-glycine bonded to silica gel and a mixture of 72 28 (v/v) heptane/isopropanol was used as eluent. The adsorption equilibrium isotherms, measured at 25 °C, are of bi-Langmuir type and were proposed by the Separex group ... 

For nonlinear systems, however, the evaluation of the flow rates is not straightforward. Morbidelli and co-workers developed a complete design of the binary separation by SMB chromatography in the frame of Equilibrium Theory for various adsorption equilibrium isotherms the constant selectivity stoichiometric model [21, 22], the constant selectivity Langmuir adsorption isotherm [23], the variable selectivity modified Langmuir isotherm [24], and the bi-Langmuir isotherm [25]. The region for complete separation was defined in terms of the flow rate ratios in the four sections of the equivalent TMB unit ... 

The separation of bi-naphthol enantiomers can be performed using a Pirkle-type stationary phase, the 3,5-dinitrobenzoyl phenylglycine covalently bonded to silica gel. Eight columns (105 mm length) were packed with particle diameter of 25 0 fiva. The solvent is a 72 28 (v/v) heptane isopropanol mixture. The feed concentration is 2.9 g for each enantiomer. The adsorption equilibrium isotherms were determined by the Separex group and already reported in Equation (28) [33]. 

Figure 6.17. Effective double layer adsorption equilibrium isotherms for kj=l and various values of the parameter Ajll.

When a specific feed composition is given, the constraints on m1 and m4 as well as the complete separation region in the (m2, m3) plane can be determined,since these depend only on the parameters of the adsorption equilibrium isotherms and the feed composition itself. Based on these values an operating point can be selected, i. e. a set of four values of = 1,..., 4 fulfilling the complete separation requirements. Since the flow rate ratios are dimensionless groups combining column volumes, flow rates and switching intervals, the constraints on the flow rate ratios are independent of the size and productivity of the SMB unit. 

Fig. 3. Adsorption equilibrium. isotherms for moisture on three commercial adsorbents pelletized 4A zeolite (—), silica gel (-), and a typical activated...

Fig. 2. (a) comparison of CO2 gas adsorption equilibrium isotherm curve of a-AlaOs support and CMS at 2931 (b) equilibrium isotherm curve of MTES unssuport at 313K (b) CO2 stepwise uptake curve of top layer of membrane(TPABr sol) at 293K. 

Their analysis is based on the separation of a mixture of two components, A and B, whose single-component adsorption equilibrium isotherms are represented by the relationship = cia(Ca,Cb) and qe = b(C/i,Cb). The mixture is separated with a displacer D, of concentration Co and isotherm qo — qo Co), having an affinity for the sorbent that is greater than that of either component of the feed mixture considered. According to Antia and Horv4th [32], a necessary condition for the establishment of fully resolved bands in this process is expressed... 

In these inequalities, and Cg are the concentrations that the components A and B, respectively, woidd attain in an isotachic displacement train in which these two species would be fully resolved into two pure component bands. The values of C and C depend only on the two pure component adsorption equilibrium isotherms and on the displacer concentration. They are calculated from the Glueckauf relationship... 

For experimental verification of these models, Foplewska et al. [33] used binary mixtures of methanol-water and acetonitrile-water as the mobile phases and measured the adsorption equilibrium isotherms of cyclopentanone on two similar adsorbents having different degrees of sruface heterogeneity, a Cis non-endcapped and a Cig endcapped silica. Ehie to its structure, cyclopentanone exhibits affinity for adsorption on the bonded alkyl chains and for the polar, im-covered silica sruface of the adsorbent. Overloaded elution bands of cyclopentanone in piue water were recorded (Figrue 15.3) and the isotherms were derived using an inverse method (see Chapter 3). Five independent parameters (the excess coefficients and the eqiulibrirun constants for partition-adsorption and for... 

The nitrogen adsorption equilibrium isotherms for AlTUD-1 and [WL]-TUD are plotted in Figure 2. The micropore volumes (Vmioro) and mesopore surface areas (Smeso) (obtained by the r-method), the total pore volume (Vp) and the BET surface are presented in Table 1. The N2 adsorption isotherms for both samples... 

The process variables known to influence arsenic capacity and column performance of alumina, GFH, and other adsorbents are as follows adsorbent, adsorbent particle size, flow rate, EBCT, and water quality parameters including arsenic concentration, As(III)/(V) speciation, pH, silica, phosphate, fluoride, hardness, and sulfate concentrations. Even with a complete water analysis, it is prudent to perform pilot studies with competitive adsorbents on the water to be treated because of the numerous factors that influence arsenic adsorption. Equilibrium isotherms and rapid small-scale column tests (RSSCTs) are typically run prior to the pilot study (7). 

FIGURE 1.11. Comparison of adsorption equilibrium isotherms for water, oxygen, and n-hexane on NaX zeolite and silicalite. (From ref. 26, reprinted by permission from Nature, 271, 512. Copyright 1978 Macmillan Journals Limited.)... 

In the preceding analysis we considered the diffusivity as constant but if the uptake curve is measured over a large concentration step this may be a poor approximation. In many zeolitic systems the concentration dependence of the intracrystalline diffusivity is given approximately by Eq. (5.6), with Dq independent of concentration. If the adsorption equilibrium isotherm obeys the Langmuir equation this gives as the expression for the concentration dependence of the diffusivity... 

Equilibrium Isotherm for Glucose Adsorption. Equilibrium isotherm data for adsorption of glucose from an aqueous solution to activated alumina are as follows (H3) ... 

Figure 1 Adsorption equilibrium isotherms on pellets of 5A zeolite a) n-pentane b) n-hexane. Points are experimental data (Silva and Rodrigues. [19], [20]). Lines are model predictions. Absolute temperatures are quoted in each curve.

Whereas zeolites adsorb nitrogen preferentially and produce an 02-rich stream at the exit of the separation device, CMSs separate the components of air on a kinetic basis. Although the adsorption equilibrium isotherms for the two gases are nearly the same, oxygen is adsorbed faster than nitrogen. 

Note 2. Because in the desorption kinetics of physisorbed molecules one may reasonably assume that E coincides with the adsorption energy q and because (p q) can be determined from adsorption equilibrium isotherms, there is the possibility of comparing the distribution fimetion resulting from kinetic experiments with that resulting from equilibrium experiments. 

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