Isotherms Henry coefficient

In the limit of low pressure the front end of the adsorption isotherm is approximated by the Henry regime which states that the number of adsorbed molecules per unit volume is proportional to the pressure and to the Henry coefficient, Kh. ... 

For propane, n-pentane and n-hexane the differential heats of adsorption over FER dropped more rapidly, right after 1 molecule was adsorbed per Bronsted acid site. Similar results were obtained with TON. In contrast, with MOR and FAU the drop in the differential heats of adsorption for n-alkanes occurred at lower coverages, indicating that only a certain fraction of the Bronsted acid sites were accessible to the adsorbing alkane probe molecules. With MFI the drop did not occur until 2 molecules of n-alkane were adsorbed per Bronsted acid site, suggesting perhaps a higher stoichiometry of about two n-alkanes per Bronsted acid site. In the cases of i-butane and i-pentane the drop occurred around one alkane per Bronsted acid site. Finally, n-butane adsorption isotherms measured over TON framework type catalysts having three different A1 contents (Si/Al2 = 90, 104, 128) showed Henry coefficients to increase with increase in the A1 content [5], Based... 

Here a is the equilibrium or Henry constant at infinite dilution, a is also equal to the initial slope of the adsorption isotherm. The coefficient b is the equilibrium constant per unit of surface area, and hence this coefficient is related to the adsorption energy. C is the mobile phase concentration of the analyte in equilibrium with q, the concentration of the analyte in the stationary phase. The monolayer capacity, qs (qs = alb) is the upper limit of concentration in the stationary phase (sometimes called specific saturation capacity of the stationary phase). The Langmuir equation can also be written as ... 

Figure 2.16 shows the relationship between the isotherms of two different components and their Henry coefficients. 

The goal is to obtain the unknown parameters for a selected isotherm equation. Special parameters of nearly all types of isotherms are the Henry coefficient as well as the saturation capacities for large concentrations. It is advisable to check the validity of the single-component isotherm equation before determining the component interaction parameters. In general the decision on a certain isotherm equation should be made on the basis of the ability to predict the experimental overloaded concentration profiles rather than fitting the experimental isotherm data. In any case, consistency with the Henry coefficient determined from initial pulse experiments with very low sample amounts must be fulfilled. 

Henry coefficients are generally determined independently from other isotherm parameters, by pulse injections with very low amounts of solutes to ensure linear iso-... 

As an example, Fig. 6.25a gives the results of the isotherm determination for Troger s base enantiomer on Chiralpak AD (dp = 20 xm) from perturbation measurements (Mihlbachler et al., 2001). Theoretical retention times for the pure components and racemic mixtures (lines) were fitted to the measured data (symbols) by means of Eq. 6.185 to determine the unknown parameter in Eq. 6.186. Total differentials for the mixture (Eq. 6.53) were evaluated using the coherence condition Eq. 6.54, resulting in the isotherm equation Eq. 6.186. Note that the Henry coefficients were independently determined by pulse experiments and were fixed during the fitting procedure. 

For the linear part of the isotherm, the Henry coefficient may be determined separately by pulse experiments (Section 6.5.7.2). If a significant deviation from the value obtained with the isotherm equation is encountered, additional experiments in the low concentration range should be carried out. These can be used to clarify whether the isotherm equation (e.g. adding an extra linear term as in Eq. 2.47) or the method of isotherm determination must be changed. 

For linear isotherms the ratio between fluid concentration and loading of the adsorbent is constant and a function of the Henry coefficient H . 

The retention time for a concentration c of the disperse desorption front can be described as a function of the isotherms derivative (Chapter 6.2). This implies that the maximum time for desorption or the minimum migration velocity is given by the derivative of the isotherms at lowest concentration (c —>0), which is equal to the Henry coefficient. 

In section I the more strongly retained component A has to desorb while no B is present. The minimum m, is therefore the initial slope or the Henry coefficient of the isotherm. 

The direction of propagation of a component within the TMBR depends on the dimensionless flow rates in each section of the process. Assuming a linear isotherm a component propagates with the fluid if the dimensionless flow rate is higher than the Henry coefficient. If the flow rate is smaller than the Henry coefficient a component is transported in the direction of the solid flow. Therefore, Lode et al. (2001) subdivided the separation region into the three regions shown in Fig. 8.10. 

To examine the effect of reaction kinetics on the reaction region the derived design criteria are applied for the reversible solid-phase reaction A B + C. A linear adsorption isotherm of the components is assumed, with Henry coefficients of 0.4 (reactant), 0.2 and 0.6 (products) respectively. A process with an equal number of columns in sections II and III is considered. The conversion that has to be reached is set to 99.99%. 

Figure 17.17 Evaluation of the separation area of the Troger s base enantiomers. Solid line Anal5Ttical Solution with the Henry coefficients derived from the analytical chromatograms. Dashed line Analytical Solution with the Best Fit Langmuir Isotherm Data. Symbols +, calculated Umits of the separation area based on the correct isotherm and the true porosity of each column o calculated limits of the separation area based on the average column porosity experimental conditions of the experiments performed. K. Mihlbachler, A. Seidel-Morgenstem, G. Guiochon, AlChE J., 50 (2004) 611 (Fig. 6). Reproduced by permission of the American Institute of Chemical Engineers. 1997 AlChE. All rights reserved.

Equilibrium of adsorption on a solid is characterized by an adsorption isotherm, which shows the concentration on the solid as a function of the concentration in the contacting fluid. A quantitative measure of uptake of a gaseous species by a liquid is the distribution coefficient, defined as the ratio of the concentration on the solid to that in the contacting fluid. If concentration-independent, the coefficient is also called Henry coefficient. Diffusion of a species in a porous solid is expressed in terms of an effective diffusion coefficient, whose value accounts for the retardation by the solid matrix. Mass transfer to or from a solid is expressed in terms of a mass-transfer coefficient, the flux being the product of that coefficient and a concentration difference as "driving force."... 

In summary, chromatographic batch separation depends, besides the feed concentrations, on the following dimensionless parameters Peclet and Stanton numbers, dimensionless injection time, Henry coefficients, and dimensionless isotherm (e.g. Langmuir) parameters. 

Henry coefficients are generally determined independently from other isotherm parameters analyzing the response to pulse injections performed with very low amounts of solutes to ensure linear isotherm behavior (Section 6.5.3.1). The linearity can be tested by comparing two or three pulse responses belonging to different concentrations. If the results for the determined Henry coefficients are identical, the system is linear. H is calculated by moment analysis using the measured Pt c+inj+piant and Equations 6.134 and 6.137 ... 

Sometimes the adsorption isotherm has been experimentally determined only for a certain temperature, for instance for the room temperature. The equation of Dubinin-Astakov can be used as a basis to extrapolate loadings to other temperatures when the relative pore filling v/v x is plotted against the adsorption potential e = RT %) since the characteristic energy e is constant for a certain adsorptive-adsorbent combination, see Fig. 2.4-5. The Henry coefficient of a certain component / depends on the temperature according to the equation of van t Hoff ... 

In comparison to low-molecular systems, the amount of data for copolymer solutions is still rather small. About 300 literature sources were perused for the purpose of this handbook, including some dissertations and diploma papers. Several hundred vapor-pressure isotherms, Henry s constants, LLE and HPPE data sets, a number of PVT data and some second osmotic virial coefficients are reported. 

In this work we have used NVT Monte Ccirlo simulations in combination with the CBMC technique (see chapter 2) to determine the heat of adsorption and the Henry coefficient [69,107]. The adsorption isotherms have been determined using grcmd-Ccmonical Monte Ccirlo simulations, cdso in combination with the CBMC technique. The technical details of these methods cire described in refs. [107,145] and in chapter 2 below a short description is given. 

In figure 4.6 the experimental isotherms for hexane of Stach et al. [124], Richard and Rees [128], and Sun etal. [131] are compared with the simulation results using the model of June etal. and the model developed in this work. From the comparison with the Henry coefficients (see figure 4.3) it was already clear that the model of June et al. would overestimate the adsorption significantly. Our model gives a better agreement with experiments. 

The fitted parameter k is practically identical for linear and branched alkcines. The S parameter, on the other hand, is about two to three orders of magnitude lower for the branched alkanes as compared to the linear ones. This causes the inflection behavior for branched alkcines to be much more prominent. The information presented in figure 4.22 could be extrapolated to estimate the isotherms for alkanes with higher carbon numbers. We note in passing that the constant k X 0max presented in figure 4.22 corresponds remarkably well with the Henry coefficients shown in figure 4.3. 

Adsorption isotherms of methane in Silicalite have been determined by several groups [149,151, 182,184, 186, 200, 201]. At low pressures the data from Hufton and Danner [182], Yamazaki et al. [184], Otteta/. [201], Rees etal. [151], and Golden and Sirccir [186] are in very good agreement. From these adsorption isotherms we have determined the Henry coefficients and we have used H = 7.5 X 10 [mmol/g/Pa] as experimental value for the Henry coefficient. 

Adsorption isotherms of pentane in Silicalite have been measured by Rakhmatkariev et al. [126] and Dubinin et al. [127]. Dubinin et al. [127] report data at low pressures yielding a Henry coefficient of 0.187 [mmol/g/Pa]. 

For hexane adsorption isotherms have been measured by Stach et al. [124] and Richard and Rees [128]. We have used the average of the two Henry coefficients, namely 3.05 [mmol/g/Pa]. For the longer alkanes we could not find sufficiently reliable isotherms at low pressures to compute a Henry coefficient at room temperature. 

In the previous chapter, we have focussed on adsorption of pure linear and branched cdkcines on Silicalite and found that our model is able to reproduce experimental data very well. Here, we will use the same model and simulation technique to study mixtures. In figures 5.1-5.4, the mixture isotherms of C4, C5, Cg, and C7 isomers are presented. We focus on a mixture of a linear alkane and the 2-methyl isomer with a 50%-50% mixture in the gas phase. Details about these simulations can be found in chapter 4. For all mixtures we see the following trends. At low pressure the linear and branched alkanes adsorb independently. The adsorption of the two components is proportional to the Henry coefficients of the pure components. At a total mixture loading of 4 molecules per unit cell the adsorption of the branched alkanes reaches a maximum and decreases with increasing pressure. For C5, Cg and C7 mixtures, the branched alkane is completely removed from the zeolite. The adsorption of the linear alkanes however increases with increasing pressure till saturation is reached. 

In chapter 4, we discuss the adsorption of linear and branched alkanes in the zeolite Silicalite. We have used the simulation techniques described in the previous chapters for this. Silicalite has a three dimensional channel structure which consists of straight and zigzag channels that cross at the intersections (see figures 1.1 en 4.1). To compute the adsorption behavior, we have fitted a force field which is able to reproduce the Henry coefficient (adsorption isotherm at low pressure) and the heat of adsorption. From CBMC simulations it turns out that linear alkanes can occupy all channels of Silicalite. For u-Cg en u-C/, the length of the molecule is almost identical to the length of the zigzag channel. In literature, this process is called commensurate freezing and causes an inflection in the adsorption isotherm of these molecules. This effect has also been observed experimentally. 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

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