Adsorbate concentration

There are interactions between the adsorbates themselves, which greatly affect the structure of the adsorbates [32]. If surface difhision is sufficiently facile during or following the adsorption step, attractive interactions can induce the adsorbates to fomi islands in which the local adsorbate concentration is quite high. Other adsorbates may repel each other at low coverages fomiing structures in which the distance between adsorbates... 

K, A, and S are as defined in Figure 10. Adsorbent concentration of component 2 less than... 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

This expression can be used to describe both pore and solid diffusion so long as the driving force is expressed in terms of the appropriate concentrations. Although the driving force should be more correctly expressed in terms of chemical potentials, Eq. (16-63) provides a qualitatively and quantitatively correct representation of adsorption systems so long as the diffusivity is allowed to be a function of the adsorbate concentration. The diffusivity will be constant only for a thermodynamically ideal system, which is only an adequate approximation for a limited number of adsorption systems. 

The diffusion coefficient in these phases D,j is usually considerably smaller than that in fluid-filled pores however, the adsorbate concentration is often much larger. Thus, the diffusion rate can be smaller or larger than can be expected for pore diffusion, depending on the magnitude of the flmd/solid partition coefficient. 

Zeohte ciyst lite diffusivities for sorbed gases range from 10" to lO" " cmVs. These diffusivities generally show a strong increase with the adsorbate concentration that is accounted for by the Darken thermodynamic correction factor... 

In this section, we consider the transient adsorption of a solute from a dilute solution in a constant-volume, well-mixed batch system or, equivalently, adsorption of a pure gas. The solutions provided can approximate the response of a stirred vessel containing suspended adsorbent particles, or that of a very short adsorption bed. Uniform, spherical particles of radius are assumed. These particles, initially of uniform adsorbate concentration, are assumed to be exposed to a step change in concentration of the external fluid. 

A numerical solution of this equation for a constant surface concentration (infinite fluid volume) is given by Garg and Ruthven [Chem. Eng. ScL, 27, 417 (1972)]. The solution depends on the value of A. = n i — n )/ n — n ). Because of the effect of adsorbate concentration on the effective diffusivity, for large concentration steps adsorption is faster than desorption, while for small concentration steps, when D, can be taken to he essentially constant, adsorption and desorption curves are mirror images of each other as predicted by Eq. (16-96) see Ruthven, gen. refs., p. 175. 

The repressurization step that returns the adsorber to feed pressure and completes the steps of a PSA cycle should be completed with pressure equalization steps to conserve gas and compression energy. Portions of the effluent gas during depressurization, blowdown, and enrichment purge can be used for repressurization to reduce the quantity of feed or product gas needed to pressurize the beds. The most efficient cycle is one that most closely matches available pressures and adsorbate concentration to the appropriate portion of the bed at the proper point in the cycle. 

Adsorbate concentration in the feed is less than about 3 wt %. 

If adsorbate concentration in the feed is very low, it may he practical to discard the loaded adsorbent or reprocess off-site. 

In the first step, in which the molecules of the fluid come in contact with the adsorbent, an equihbrium is established between the adsorbed fluid and the fluid remaining in the fluid phase. Figures 25-7 through 25-9 show several experimental equihbrium adsorption isotherms for a number of components adsorbed on various adsorbents. Consider Fig. 25-7, in which the concentration of adsorbed gas on the solid is plotted against the equilibrium partial pressure p of the vapor or gas at constant temperature. At 40° C, for example, pure propane vapor at a pressure of 550 mm Hg is in equilibrium with an adsorbate concentration at point P of 0.04 lb adsorbed propane per pound of silica gel. Increasing the pressure of the propane will cause... 

SEXAFS can be measured from adsorbate concentrations as low as "0.05 mono-layers in favorable circumstances, although the detection limits for routine use are several times higher. By using appropriate standards, bond lengths can be determined as precisely as 0.01 A in some cases. Systematic errors often make the accu-... 

The cycle consists of two phases. In the first, suppose pumping to be anticlockwise, and initially that bed 1 is cold (maximum adsorbent concentration) and bed 2 is hot (minimum adsorbent concentration). The oil recovers heat from bed 2, has a further heat addition from the gas heat exchanger and then proceeds to heat bed 1 via the special heat exchanger within it. Bed 1 desorbs refrigerant which passes to the condenser (giving a useful heat output in the case of a heat pump) and bed 2 adsorbs gas from the evaporator which... 

Despite very high adsorbed concentrations, R32 would appear to have a much lower adsorbed refrigeration capacity than ammonia. Butane has even less merit than R32. 

Adsorption for gas purification comes under the category of dynamic adsorption. Where a high separation efficiency is required, the adsorption would be stopped when the breakthrough point is reached. The relationship between adsorbate concentration in the gas stream and the solid may be determined experimentally and plotted in the form of isotherms. These are usually determined under static equilibrium conditions but dynamic adsorption conditions operating in gas purification bear little relationship to these results. Isotherms indicate the affinity of the adsorbent for the adsorbate but do not relate the contact time or the amount of adsorbent required to reduce the adsorbate from one concentration to another. Factors which influence the service time of an adsorbent bed include the grain size of the adsorbent depth of adsorbent bed gas velocity temperature of gas and adsorbent pressure of the gas stream concentration of the adsorbates concentration of other gas constituents which may be adsorbed at the same time moisture content of the gas and adsorbent concentration of substances which may polymerize or react with the adsorbent adsorptive capacity of the adsorbent for the adsorbate over the concentration range applicable over the filter or carbon bed efficiency of adsorbate removal required. 

Adsorbate Concentration The adsorption capacity of adsorbents is directly... 

The MTZ is that length of the adsorbent bed where the adsorbate concentration in the liquid varies from the influent concentration to zero or the specification value. At the same contact time, the single fixed-bed system at the higher LV stays onstream about 15 percent longer. 

The adsorption process generally is of an exothermal nature. With increasing temperature and decreasing adsorbate concentration the adsorption capacity decreases. For the design of adsorption processes it is important to know the adsorption capacity at constant temperature in relation to the adsorbate concentration. Figure 11 shows the adsorption isotherms for several common solvents. 

Although MIL-47, and especially MIL-53(A1), had been found on many occasions to dynamically respond to adsorption of particular compounds, referred to as breathing [35] in the literature, in these liquid phase conditions, only minor changes of the lattice parameters have been observed. A study of xylene separations in vapor phase on MIL-5 3(A1) shows that breathing profoundly influences the shape of the obtained breakthrough profiles as a function of adsorbate concentration [97]. 

With the adsorbate concentration low enough, the Langmuir isotherm transforms into the linear equation and becomes the simplest isotherm of adsorption, as described by Henry s law. 

As for equilibrium values of as and P they are mainly dependent on relations between such parameters of the systems as initial electric conductivity of adsorbent, concentration of chemisorbed particles, reciprocal position of the energy levels of absorbate and adsorbent. Thus, during acceptor adsorption in case of small concentration of adsorption particles one can use (1.82) and (1.84) to arrive to expressions for equilibrium values of ohmic electric conductivity and the tangent of inclination angle of VAC ... 

One of the distinct advantages of XPS is that, through analysis of the corelevel intensities, it can provide quantitative data on adsorbate concentrations. The following equation relates the surface concentration a to the intensities of... 

Recently, nonliving biomass of S. cucullata has been described as a low-cost absorbent of Cr(VI).106 Optimum conditions for the Cr(VI) adsorption by acid-treated S. cucullata were found out using a full factorial design. The Cr(VI) removal efficiency of the adsorbent was found to increase with the increase in time, temperature, adsorbate concentration, and stirring speed, and to decrease with increase in pH and adsorbent dose. The Fourier transform infrared spectroscopy (FT-IR) analysis revealed that in addition to electrostatic force, the adsorption may be due to... 

In the presence of NAPL, the concentration of contaminants in the soil moisture (Cw) can be calculated simply from the solubility of the compounds (equation 3 in Table 14.3). Adsorption of contaminants to the soil particles is a much more complex phenomenon, which depends both on contaminant properties and on soil characteristics. The simplest model for describing adsorption is based on the observation that organic compounds are preferentially bound to the organic matter of soil, and the following linear equation is proposed for calculating the adsorbed concentration (Cs) ... 

Cs Adsorbed concentration of contaminant in the soil particle (mg/kg) Ct Total quantity of contaminant per unit soil volume (mg/L)... 

The Langmuir equation has a strong theoretical basis, whereas the Freundlich equation is an almost purely empirical formulation because the coefficient N has embedded in it a number of thermodynamic parameters that cannot easily be measured independently.120 These two nonlinear isotherm equations have most of the same problems discussed earlier in relation to the distribution-coefficient equation. All parameters except adsorbent concentration C must be held constant when measuring Freundlich isotherms, and significant changes in environmental parameters, which would be expected at different times and locations in the deep-well environment, are very likely to result in large changes in the empirical constants. 

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