Single-Stage Differential Operation

A reduced solution to the problem can be obtained if we eliminate time as a variable and establish the instantaneous relation between the state variables, for example, W =f Xyf). This is still a highly useful result because it can tell us how much of a given initial charge must be distilled to obtain a desired enrichment Xg. It also provides us with other items of interest and falls short only by failing to establish the full time dependence of the variables. 

Mass Transfer and Separation Processes Principles and Applications 

We start the derivation of the model by composing the unsteady integral mass balances for the system  

To eliminate the time variable, we resort to a favorite trick of ours, one that is frequently used and should be part of the analyst s tool box. The two mass balances are divided, thereby eliminating not only time as a variable but also the unknown distillation rate D. Thus, 

Formal integration of this expression then leads to 

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A thermodynamic analysis of the energy requirements of desalting processes is presented, to clarify the conditions under which such calculations are valid. The effects of departure from isothermal operation, finite product recovery, differential as opposed to single-stage operation, and salt concentration in the feed are examined. A comparison shows that there is essentially no difference between the energy requirements for a distillation and a freezing process. The minimum heat consumption and maximum number of efFects for a multiple-effect evaporation plant are calculated. The above analysis leads to the conclusion that efficiencies in the range 10 to 20% will be very difficult to achieve. 

The most usual problem encountered is that of determining the degree of separation for a single-stage embodiment, which can certainly be complicated. The extension to multistage and differential permeation operations will only be alluded to, with referral made to Hoffman (2003). 

Successive flash vaporizations can be made on the residual liquids in a series of single-stage operations, whereupon the separation will be better than that obtained if the same amount of vapor were formed in a single operation. As the amount of vapor formed in each stage becbmes smaller and the total number of vaporizations larger, the operation approaches differential distillation in the limit. 

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. 

However, the conunercial lAMS apparatus is too cumbersome for use in field analysis of air samples. Unfortunately, the commercial apparatus is not practical for the study of atmospheric environments. Therefore, to develop a new, compact and fieldable lAMS system by eliminating the differential pumping stage is desirable. The primary objeetive for the development was to design a system that can be easily transported to the field and that can detect any chemical species at atmospheric pressirre on a real-time basis. A single turbomolecular pump is employed as the vacuirm system to fill the basic requirements for vacuum conditions this is simple and cost effective. The optimal operation parameters for its use, the details and operation of the capillary leak inlet, and the system s analytical power in some preliminary applications are described also in this section... 

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