Equilibria relative separation

Before leaving this section we consider a slightly different optimization problem that may also be expensive to solve. In flowsheet optimization, the process simulator is based almost entirely on equilibrium concepts. Separation units are described by equilibrium stage models, and reactors are frequently represented by fixed conversion or equilibrium models. More complex reactor models usually need to be developed and added to the simulator by the engineer. Here the modular nature of the simulator requires the reactor model to be solved for every flowsheet pass, a potentially expensive calculation. For simulation, if the reactor is relatively insensitive to the flowsheet, a simpler model can often be substituted. For process optimization, a simpler, insensitive model will necessarily lead to suboptimal (or even infeasible) results. The reactor and flowsheet models must therefore be considered simultaneously in the optimization. 

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 ... 

The V-B coupling Hamiltonian to first order in the three HOD dimensionless normal coordinates is Hv b = —2, c], l , where F, is the inter-molecular force due to the solvent exerted on the harmonic normal coordinate, evaluated at the equilibrium position of the latter. This force obviously depends on the relative separations of all molecules, and on their relative orientations. In the most rigorous quantum description of rotations, this term would depend on the excited molecule rotational eigenstates and of the solvent molecules. Instead rotation was treated classically, a reasonable approximation for water at room temperature. With this form for the coupling, the formal conversion of the Golden Rule formula into a rate expression follows along the lines developed by Oxtoby (2,53), with a slight variation to maintain the explicit time dependence of the vibrational coordinates (57),... 

The TEA-Chlorex azeotrope consists of approximately 1 part of TEA and 1 part of Chlorex. The presence of Chlorex increases the relative volatility between dodecene and TEA from 1.4 to 11.0 as measured in a Colburn equilibrium still. Separation of dodecene from TEA thus becomes a relatively simple matter. Most of the dodecene can be removed with little TEA contamination in a column with five to ten theoretical plates operating at a reflux ratio of 1 to 1. 

All other variables being equal, a partitioned equilibrium for the analyte between the sample matrix and the extraction solvent is reached more quickly at higher temperature and pressure because the analyte solubilization kinetics are improved. Therefore, cycle time can be much shorter for ASE extractions relative to room-temperature/pressure-solvent extractions. If certain sample variables such as pore size or structure make rapid equilibrium questionable, it is simple to design a recovery versus extraction time experiment (the results of which are shown in Figure 9) so that variability and lower recovery due to a pre-equilibrium phase separation can be avoided. The desirable extraction duration is a trade-off between the recovery and the time required to achieve it and generally runs from 10 to 17 min. 

The equilibrium flash separator is the simplest equilibrium-stage process with which the designer must deal. Despite the fact that only one stage is involved, the calculation of the compositions and the relative amounts of the vapor and liquid phases at any given pressure and temperature usually involves a tedious trial-and-error solution. 

Sinple distillation columns are not able to conpletely separate mixtures when azeotropes occur, and the columns are very e5q>ensive when the relative volatility is close to 1. Distillation columns can be coupled with other separation methods to break the azeotrope. This is discussed in the first section. Extractive distillation, azeotropic distillation, and two-pressure distillation are methods for modifying the equilibrium to separate these conplex mixtures. These three methods are described in Sections 8.2 to E2 of this chapter, hi Section 8.8 we discuss the use of a distillation column as a chemical reactor, to simultaneously react and separate a mixture. 

The separation power in a distillation column comes from the thermodynamic vapor-liquid equilibrium relative volatility, the number of theoretical stages achieved by the column, and the... 

Figure 1.22 Transient equilibrium - relative activities of parent and daughter nuclides after separation...

Fig. 8.19. Plots of normalized contact zones size d and normalized contact force P versus normalized relative separation distance 6 between centers of the spheres as given in (8.114) and (8.113), respectively. The points corresponding to equilibrium under zero applied force or under zero relative displacement are identified. The point on the P versus 6 curve with horizontal tangent locates a state of instability during separation of the spheres under applied force. Likewise, the point on the same curve with vertical tangent locates a state of instability during separation under imposed relative displacement.

PSA gas purification and separation operations can be categorized as equilibrium-based or diffusion-rate-based. Equilibrium-based separations, which are the most common, depend on the ability of the adsorbent to adsorb a greater quantity of heavy species than of light species at equilibrium. Diffusion-rate-based operations separate components because one species diffuses more rapidly than the other components. The performance of equilibrium-based systems can be predicted by relatively simple models, while the diffusion-rate-based systems require more complicated models to account for the effects of mass transfer within the individual adsorbent particles. 

In equilibrium processes, separation is based on differences in the relative amounts of the adsorbates within the adsorbent once equilibrium has been established. The process is dictated by the differences in the isotectic heats of adsorption (gg() between the different adsorbate molecules and the adsorbent. In the case of steric... 

The interatomic distances in ionic lattices containing 3d transition metal ions, which have a nonspherically symmetric electronic ground state, are shortened by the crystal field relative to that of a similar structure in which the interionic potential is purely of the Madelung type. This is illustrated in Figure 1. If the binding between ions is of the latter type, a nearly monotonic (dotted line) change is expected in the equilibrium interionic separation with atomic number of the cation in isostructural salts with the same anion. The... 

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