Equilibrium stages, applicability

The application of a 50 percent Murphree vapor-phase efficiency on a y-x magram is illustrated in Fig. 13-40. A pseudo-equilibrium cui ve is drawn halfway (on a vertical line) between the operating hnes and the true-equilibrium cui ve. The true-equilibrium cui ve is used for the first stage (the partial reboiler is assumed to be an equilibrium stage), but for 1 other stages the vapor leaving each stage is assumed to approach the equilibrium value only 50 percent of me way Consequently, the steps in Fig. 13-40 represent actual trays. 

Thermodynamic control (Figure 1, right) is based on adsorption of substances until quasi-equilibrium stage. In this case, the surface ratio of the adsorbed species is defined by the ratio of products of their concentration and binding constant. This deposition is much less influenced by poorly controllable fluctuations of external conditions and provides much better reproducibility. The total coverage can be almost 100%. Because of these reasons, the thermodynamic control is advantageous for preparation of mixed nanostructured monolayers for electrochemical applications including a formation of spreader-bar structures for their application as molecular templates for synthesis of nanoparticles. 

Binary systems of course can be handled by the computer programs devised for multicomponent mixtures that are mentioned later. Constant molal overflow cases are handled by binary computer programs such as the one used in Example 13.4 for the enriching section which employ repeated alternate application of material balance and equilibrium stage-by-stage. Methods also are available that employ closed form equations that can give desired results quickly for the special case of constant or suitable average relative volatility. 

Use of HETP Data for Absorber Design Distillation design methods (see Sec. 13) normally involve determination of the number of theoretical equilibrium stages N. Thus, when packed towers are employed in distillation applications, it is common practice to rate the efficiency of tower packings in terms of the height of packing equivalent to one theoretical stage (HETP). 

The structural differences between the various sulfur-containing molecules make it impractical to have a single rate expression applicable to all reactions in hydrodesulfurization. Each sulfur-containing molecule has its own hydrogenolysis kinetics that is usually complex because several successive equilibrium stages are involved and these are often controlled by internal diffusion limitations during refining. 

All results demonstrate a good agreement between the simulations and experiments. The simulation studies warn of equilibrium stage model application, which appears to be completely inappropriate for the case of finite rate reactions. The film reaction consideration is found to be crucial. 

Discuss the applicability of sieve trays. The sieve tray is probably the most versatile contacting device. It should be considered first for the design of a tray column. It has the lowest installed cost of any equilibrium-stage-type device, its fouling tendencies are low, and it offers good efficiency when properly designed. 

In general, application of a constant efficiency to each stage as in Fig. 13-31 will not give the same answer as obtained when the number of equilibrium stages (obtained by using the true equilibrium curve) is divided by the same efficiency factor. 

Example 1 Application of FUG Method A large butane-pentane splitter is to be shut down for repairs. Some of its feed will be diverted temporarily to an available smaller column, which has only 11 trays plus a partial reboiler. The feed enters on the middle tray. Past experience with similar feeds indicates that the 11 trays plus the reboiler are roughly equivalent to 10 equilibrium stages and that the column has a maximum top vapor capacity of 1.75 times the feed rate on a mole basis. The column will operate at a condenser pressure of 827.4 kPa (120 psia). The feed will be at its bubble point (q = 1.0) at the feed tray conditions and has the following composition on the basis of 0.0126 kg-mol/s (100 Ib-mol/h) ... 

The disadvantage is that volumetric efficiency is usually much less than conventional trays or packed contactors. Applications are usually limited to cases when only a few transfer units or a single equilibrium stage is required. Since many of these applications tend to be in heat-transfer service, the following discussion will be in terms of thermal properties and thermal measures of performance. 

In contrast to the investigations with calcium where Ca, which is not the preferable calcium isotope for application purposes, is enriched in the chloroform phase (see Chap. 4.2.2), Li which is of importance for the production of tritium is enriched in that phase. Certainly, corresponding to the disadvantageous distribution coefficient (see Table 10) a small amount of enriched Li is only obtainable within one equilibrium stage. Therefore, a cascade experiment as described in Chap. 2.5.2 must be applied. 

Two different approaches have evolved for the simulation and design of multicomponent distillation columns. The conventional approach is through the use of an equilibrium stage model together with methods for estimating the tray efficiency. This approach is discussed in Chapter 13. An alternative approach based on direct use of matrix models of multicomponent mass transfer is developed in Chapter 14. This nonequilibrium stage model is also applicable, with only minor modification, to gas absorption and liquid-liquid extraction and to operations in trayed or packed columns. 

Although real-life processes may not actually reach equilibrium, the assumption of an equilibrium stage is essential for a rigorous solution of a problem and for providing a sound basis for column design and performance evaluation. The application of equilibrium stage calculation results to actual performance information which is usually accomplished by utilizing tray efficiencies, a concept that is discussed in Chapter 14. 

With a single equilibrium stage and no reflux, the separation power in differential distillation is obviously limited. It is the equivalent of a batch flash operation. Consequently, practical applications would include the separation of wide-boiling mixtures, with low expectations on the purity of the products. 

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