Equilibrium-based processes

For phase partitioning (equilibrium), the variable of interest is the solute concentration in the first phase that would be in equilibrium with the solute concentration in a second phase. For example, in the distillation example above, each component is partitioned between the vapor and liquid phases. The mathematical description of the equilibrium relationship is usually given as the concentration in one phase as a function of the concentration in the second phase as well as other parameters. Some examples are the Henry s Law relation for the mole fraction of a solute in a liquid as a function of the mole fraction of the solute in the gas phase which contacts the liquid  

A second example would be the Langmuir isotherm characterizing adsorption (Chapter 7), which relates the equilibrium amount of a solute sorbed onto a solid to the concentration in the fluid phase in contact with the solid  

An important factor in the use of phase partitioning for separations is the degree of change in composition between the two phases. In the limit where the composition in each phase is identical, separation by this mechanism is futile. For vapor-liquid equilibrium, the condition is called an azeotrope. Irrespective of the phases, this condition corresponds to a partition coefticient of unity. 

S ome data and model equations will be provided in the appropriate chapters. Appendix E provides additional information and references for data and calculation methods. 

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Determine the target separation criteria. What purity and recovery are needed for the various components in the feed stream For a feasible separation process, what is the separation factor based on the property difference chosen For an equilibrium-based process, this would be the separation factor for one stage. 

Figure 3.6 A non-adiabatic two-phase equilibrium-based process.

Figure 3.6 shows a non-adiabatic (heat is either lost to or gained from the environment surrounding the control volume) two-phase equilibrium-based process. There are two feed streams and two exit streams. The exit streams are in thermodynamic equiUbrium. 

Referring to the generic separation schematic (Figure 3.28), assume that it represents a single stage of an equilibrium-based process for the separation of a binary feed mixture. 

Figure 3.28 Generic binary feed separation stage for an equilibrium-based process.

Traditionally, it was believed that RCMs were only suitable for equilibrium-based separations and could not be used for the representation of kinetically based processes [15]. However, the differential equations which describe a residue curve are simply a combination of mass balance equations. Because of this, the inherent nature of RCMs is such that they can be used for equilibrium- as well as non-equilibrium-based processes. This now allows one to consider kinetically based processes, such as reactive distillation (see Chapter 8) as well as membrane separation processes. 

Hydrolysis (Sections 20 10 and 20 11) Ester hydrolysis may be catalyzed either by acids or by bases Acid catalyzed hydrolysis is an equilibrium controlled process the reverse of the Fischer esterification Hydrolysis in base IS irreversible and is the method usual ly chosen for preparative purposes... 

Data on the gas-liquid or vapor-liquid equilibrium for the system at hand. If absorption, stripping, and distillation operations are considered equilibrium-limited processes, which is the usual approach, these data are critical for determining the maximum possible separation. In some cases, the operations are are considerea rate-based (see Sec. 13) but require knowledge of eqmlibrium at the phase interface. Other data required include physical properties such as viscosity and density and thermodynamic properties such as enthalpy. Section 2 deals with sources of such data. 

The discussion can be restricted to the first and second reduction processes that are of particular interest in this context. The shift of the bipyridinium-based process is in agreement with the catenane coconformation in which the bipyridinium unit is located inside the cavity of the macrocyclic polyether (Fig. 13.33a) because of the CT interactions established with both the electron donor units of the macrocycle, its reduction is more difficult than in the free tetracationic cyclophane. The shift of the trans-1,2-bis(4-pyridinium)ethylene-based reduction indicates that, once the bipyridinium unit is reduced, the CT interaction that stabilize the initial coconformation are destroyed and, thereby, the tetracationic cyclophane circumrotates through the cavity of the macrocyclic polyether moving the tra ,v-bis(pyridinium)ethylene unit inside, as shown by comparison of its reduction potential with that of a catenane model compound.19 The original equilibrium between the two coconformations associated with catenane 384+ is restored upon oxidation of both units back to their dicationic states. 

Equilibrium in an accumulation process is empirically defined as the point at which a partitioning coefficient becomes invariant (reaches steady state), and theoretically as the point at which the fugacity ratio equals 1 (21). With phytoplankton, most published reports indicated that equilibrium was reached in a matter of hours (6, 8, 22-26). As a result, predictions of HOC accumulation in phytoplankton have been expressed as equilibrium-based equations exclusively. 

These data demonstrate that equilibrium is not reached as rapidly as was previously assumed. In addition, they indicate that the time required to reach equilibrium can differ significantly between compounds. However, because the system had not reached equilibrium, they do not reveal the time required to reach equilibrium or the extent of partitioning at equilibrium. The primary ramification of slower partitioning is that measured BAFs may differ from predicted equilibrium values because the process has not reached equilibrium. In order to better predict accumulation in a system that is not at steady state, equilibrium-based equations need to be replaced with kinetic-based equations. 

Phytoplankton play an important role in the accumulation of HOCs in aquatic food webs, but equilibrium-based equations have not adequately modeled this process. In addition to presenting three additional factors that can influence accumulation, this chapter demonstrates the importance of considering the kinetics of accumulation. 

Selectivity. Selectivity in a physical adsorption system may depend on differences in either equilibrium or kinetics, but the great majority of adsorption separation processes depend on equilibrium-based selectivity. Significant kinetic selectivity is. in general, restricted to molecular sieve adsorbents—carbon molecular sieves, zeolites, or zeolite analogues. 

SEE in the gaseous phase. The process is often carried out as an equilibrium competition process with some other base B, the PA of which is known ... 

The branch of thermodynamics known as the thermodynamics of reversible processes is actually a study of thermodynamic systems at equilibrium, and it is this branch that is so important in the application of thermodynamics to chemical systems. Starting from the fundamental conditions of equilibrium based on the second law, more-practical conditions,... 

In these systems, the interface between two phases is located at the high-throughput membrane porous matrix level. Physicochemical, structural and geometrical properties of porous meso- and microporous membranes are exploited to facilitate mass transfer between two contacting immiscible phases, e.g., gas-liquid, vapor-liquid, liquid-liquid, liquid-supercritical fluid, etc., without dispersing one phase in the other (except for membrane emulsification, where two phases are contacted and then dispersed drop by drop one into another under precise controlled conditions). Separation depends primarily on phase equilibrium. Membrane-based absorbers and strippers, extractors and back extractors, supported gas membrane-based processes and osmotic distillation are examples of such processes that have already been in some cases commercialized. Membrane distillation, membrane... 

For an equilibrium-based separation process a convenient measure of the intrinsic selectivity of the adsorbent is the separation factor an, defined by analogy with relative volatility as ... 

Mass-transfer calculations, such as the analysis or design of separation units, can be solved by two distinctly different methods, based on either the concept of (1) Equilibrium stage processes or (2) Diffusional rate processes. 

In real reactive absorption processes, the thermodynamic equilibrium can seldom be reached. Therefore, some correlation parameters such as tray efficiencies or HETP-values (Height Equivalent to One Theoretical Plate) are introduced to adjust the equilibrium-based theoretical description to the reality. However, reactive absorption always occurs in multicomponent mixtures, for which this simplified concept often fails [16, 23, 24]. 

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