Equilibria separation factor

If the absorption is multicomponent, the average equilibrium constant mave is determined for each of the solute components at the average temperature and pressure of the absorber, and a separate absorption factor Aave is defined for each component. These absorption factors can be used in Eq. (28) to define the absorbed fraction of the component. 

There are two types of separation factors commonly used the ideal and the actual separation factors. The ideal separation factor is based on the equilibrium concentrations or transport rates due to the fundamental physical and/or chemical phenomena that dictate the separation. This is the separation factor that would be obtained without regard to the effects of the configuration, flow characteristics, or efficiency of the separation device. This value can be calculated from basic thermodynamic or transport data, if available, or obtained from small-scale laboratory experiments. For an equilibrium-based separation, the ideal separation factor would be calculated based on composition values for complete equilibrium between phases. For a rate-based separation, this factor is calculated as the ratio of transport coefficients, such as diffusion coefficients, without accounting for competing or interactive effects. Each component is assumed to move independently through the separation device. 

The Fine Porous Model as presented by Xu and Spencer (1997), describes equilibrium and non-equilibrium factors of rejection. Only coupling between solvent and solute is taken into account, and no solute-solute coupling is permitted. Equilibrium parameters dominated separation, and these are described by the reflection coefficient (J in equation (3.28), where kii is the solute mass transfer coefficient in the membrane. 

One may define an equilibrium factor (/3) for the transition in a manner analogous to relative volatility or separation factor ... 

In Chapter 8 the equilibrium factor for a single adsorbed species was defined by analogy with the relative volatility. This definition is easily extended to a binary or multicomponent system. For competitive sorption the binary separation factor is defined by... 

The equilibrium factor measures the affinity of the adsorbent for a particular component relative to the same component in the fluid phase whereas the binary separation factor measures the relative preference of the adsorbent for two different competing adsorbates. If the equilibrium obeys the multicomponent Langmuir model ... 

In distillation towers, entrainment lowers the tray efficiency, and 1 pound of entrainment per 10 pounds of liquid is sometimes taken as the hmit for acceptable performance. However, the impact of entrainment on distiUation efficiency depends on the relative volatility of the component being considered. Entrainment has a minor impact on close separations when the difference between vapor and liquid concentration is smaU, but this factor can be dominant for systems where the liquid concentration is much higher than the vapor in equilibrium with it (i.e., when a component of the liquid has a very lowvolatiUty, as in an absorber). 

It is always important to keep in mind the relative nature of substituent effects. Thus, the effect of the chlorine atoms in the case of trichloroacetic acid is primarily to stabilize the dissociated anion. The acid is more highly dissociated than in the unsubstituted case because there is a more favorable energy difference between the parent acid and the anion. It is the energy differences, not the absolute energies, that determine the equilibrium constant for ionization. As we will discuss more fully in Chapter 4, there are other mechanisms by which substituents affect the energy of reactants and products. The detailed understanding of substituent effects will require that we separate polar effects fiom these other factors. 

In addition to constitution and configuration, there is a third important level of structure, that of conformation. Conformations are discrete molecular arrangements that differ in spatial arrangement as a result of facile rotations about single bonds. Usually, conformers are in thermal equilibrium and cannot be separated. The subject of conformational interconversion will be discussed in detail in Chapter 3. A special case of stereoisomerism arises when rotation about single bonds is sufficiently restricted by steric or other factors that- the different conformations can be separated. The term atropisomer is applied to stereoisomers that result fk m restricted bond rotation. ... 

The standard methods of drying can be classified as deposition of the moisture as either water or ice decomposition of the water chemical precipitation absorption adsorption mechanical separation and vaporization. The completeness with which dryness can be accomplished by any process depends upon the factors controlling the equilibrium conditions achieved in the operation. A brief discussion of each method is first given. 

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. 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

One chemical will be a solvent for another if the molecules are able to co-exist on a molecular scale, i.e. the molecules show no tendency to separate. In these circumstances we say that the two species are compatible. The definition concerns equilibrium properties and gives no indication of the rate of solution which will depend on other factors such as temperature, the molecular size of the solvent and the size of voids in the solute. 

The distribution coefficient can be determined by batch experiments in which a small known quantity of resin is shaken with a solution containing a known concentration of the solute, followed by analysis of the two phases after equilibrium has been attained. The separation factor, a, is used as a measure of the chromatographic separation possible and is given by the equation,... 

In processing, it is frequently necessary to separate a mixture into its components and, in a physical process, differences in a particular property are exploited as the basis for the separation process. Thus, fractional distillation depends on differences in volatility. gas absorption on differences in solubility of the gases in a selective absorbent and, similarly, liquid-liquid extraction is based on on the selectivity of an immiscible liquid solvent for one of the constituents. The rate at which the process takes place is dependent both on the driving force (concentration difference) and on the mass transfer resistance. In most of these applications, mass transfer takes place across a phase boundary where the concentrations on either side of the interface are related by the phase equilibrium relationship. Where a chemical reaction takes place during the course of the mass transfer process, the overall transfer rate depends on both the chemical kinetics of the reaction and on the mass transfer resistance, and it is important to understand the relative significance of these two factors in any practical application. 

We cover each of these types of examples in separate chapters of this book, but there is a clear connection as well. In all of these examples, the main factor that maintains thermodynamic disequilibrium is the living biosphere. Without the biosphere, some abiotic photochemical reactions would proceed, as would reactions associated with volcanism. But without the continuous production of oxygen in photosynthesis, various oxidation processes (e.g., with reduced organic matter at the Earth s surface, reduced sulfur or iron compounds in rocks and sediments) would consume free O2 and move the atmosphere towards thermodynamic equilibrium. The present-day chemical functioning of the planet is thus intimately tied to the biosphere. 

Furthermore, the application of the SOD membrane in a FT reaction has been investigated. The advantages of water removal in a FT reaction are threefold (i) reduction of H20-promoted catalyst deactivation, (ii) increased reactor productivity, and (iii) displaced water gas shift (WGS) equilibrium to enhance the conversion of CO2 to hydrocarbons [53]. Khajavi etal. report a mixture of H2O/H2 separation factors 10000 and water fluxes of 2.3 kg m h under... 

One of the most crucial influencing factors in planar chromatography is the vapor space and the interactions involved. The fact that the gas phase is present, in addition to stationary and mobile phases, makes planar chromatography different from other chromatographic techniques. Owing to the characteristic of an open system the stationary, mobile, and vapor phases interact with each other until they all are in equihbrium. This equilibrium is much faster obtained if chamber saturation is employed. This is the reason for differences in separation quality when saturated and unsaturated chambers are used. However, the humidity of the ambient air can also influence the activity of the layer and, thus, separation. Especially during sample application, the equihbrium between layer activity and relative humidity of the... 

Both liquid and vapor phases are totally miscible. Conventional vapor/liquid equilibrium. Neither phase is pure. Separation factors are moderate and decrease as purity increases. Ultrahigh purity is difficult to achieve. No theoretical limit on recovery. Liquid phases are totally miscible solid phases are not. Eutectic system. Solid phase is pure, except at eutectic point. Partition coefficients are very high (theoretically, they can be infinite). Ultrahigh purity is easy to achieve. Recovery is limited by eutectic composition. 

---