The Simple Cascade

The relation between recovery, overall enrichment, and number of stages then is 

The line for is also shown in Fig. 12.14. This is the highest recovery that can be 

Such a simple cascade, with an infinite number of stages each performing an infinitesimal amount of separation, is equivalent to type A differential st e separation. Equation (12.51) is equivalent to the form of the Rayleigh equation (12.35), when one recognizes that w in the simple cascade is equivalent to the heads separation factor 0 in differential stage enrichment, and a in the simple cascade is equivalent to the local separation factor a.  

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In the simple cascade of Fig. 12.12, whose performance was illustrated in Fig. 12.14, it is impossible to obtain high recovery of desired component because of losses in the tails streams leaving every stage. Desired component in these streams can be recovered by recycling these... 

Although the recovery of heavy water is better than in the simple cascade without recycle. 

In the flow sheet of Fig. 13.16, the recovery of deuterium from the three stages of the simple cascade is... 

The optimal network increases total residence time by 48 per cent when compared with an equivalent MSMPR of the same volume and throughput. This increase would translate into a similar increase in mean crystal size and a 78 per cent increase in yield. Exactly the same residence time as for the single crystallizer have been reported from simple cascade configurations previously designed for stage-wise crystallization processes for slight improvements in... 

Figure 10.2a. Block diagram of a simple cascade control system with reference to the furnace problem.

Example 10.1 Consider a simple cascade system as shown in Fig. 10.2a with a PI controller in the primary loop, and a proportional controller in the slave loop. For simplicity,... 

Rather than use the simple cycle shown in Figure 24.44 for the liquefaction of natural gas, much more complex arrangements using multiple cycles (with both pure and mixed refrigerants) and cascade systems can be used. 

The angular dependence of the secondary ion intensity is expected to follow a simple cosine law, in particular for randomly oriented polycrystalline surfaces. The explanation for this is that upon impact the collision cascade takes care of an isotropic distribution of the energy through the sample. Hence the intensity of collision... 

Grigg has utilized the Heck reaction in several ways, from the simple cyclization of N-(2-iodobenzoyl)pyrrole (139) to afford tricyclic lactam (140) [100] to the complex cascade... 

Oxidation (usually by means of a simple cascade open to the atmosphere), which helps to convert soluble Fe to far less soluble Fe3+, as well as allowing pH to rise by venting excess C02 (where present), until equilibrium with the atmospheric CO2 content is attained. 

Computer simulations as well as studies of experimental models have led to the following conclusions.343 311 Even simple cascade mechanisms, such as the one shown in Fig. 11-10, can provide a more flexible response... 

In heat exchanger applications, cascade loops are configured so that the master detects the process temperature and the slave detects a variable, such as steam pressure, that may upset the process temperature. The cascade loop, responds immediately and corrects for the effect of the upset before it can influence the process temperature. The cascade master adjusts the set point of the slave controller to assist in achieving this. Therefore, the slave must be much faster than the master. A rule of thumb is that the time constant of the primary controller should be ten times that of the secondary, or the period of oscillation of the primary should be three times that of the secondary. One of the quickest (and therefore best) cascade slaves is the simple and inexpensive pressure regulator. 

To further expand the scope of this new silver(I)-mediated reaction sequence, interrupted Nazarov cyclizations were explored using the halocyclopropane chemistry, an investigation that was prompted by the discovery of an intriguing result. It was found that treatment of the phenethyl-substituted compound 76 with 1.5 equiv of silver tetrafluoroborate in dichloromethane provided benzohydrindenone 77 as the sole product, with no apparent formation of the simple a-chlorocyclopentenone (Scheme 4.24). This prompted an examination of appropriately substituted gem-dichlorocyclopropane substrates in analogous interrupted Nazarov processes to ascertain the scope of this new cascade reaction sequence. 

Cascade Control. The response of the simple feedback control to changes in the cooling water temperature can be improved by measuring the cooling water temperature and taking control action before its effect has been felt by the reacting mixture as shown... 

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