Minimum work of separation

Concentration and purity can both be traced to the minimum work of separation, W, where Tq is the sink temperature Ai is the number of moles of a species present in the feed x = and y is an activity coefficient. The value of Wprovides a target that is easily calculated and approachable in... 

We have seen several examples of a technique for separation of gas mixtures which, in contrast with most commercial processes, requires no physical transfer of solvent, handling of solids, or cycling of temperature or pressure. The energy requirements can also be far lower The thermodynamic minimum work of separation is, under isothermal conditions, the free energy difference between the process stream and byproduct, or permeate, stream. When this difference is due only to the partial pressure difference of component 1, it becomes ... 

So far only the energy requirement for a process in the form of work has been considered. Freezing, vapor compression, and reverse osmosis processes are examples of processes that require a work input. There are, however, other important processes, such as multiple-effect evaporation and flash evaporation, for which the energy input is in the form of heat. How does one relate the energy requirement of these processes to the minimum work of separation One method is to convert the heat requirement to a work equivalent by means of the Carnot cycle. If T is the absolute temperature of the heat source and T0 the heat-sink temperature, then one can use the familiar relation... 

Calculations showed that the thermal contribution to AAfeed- product is only of the total. It is also interesting to note that the value of AA eecalculated value for the isothermal minimum work of separation, 0.36(10 ) Btu/hr, (2). Therefore this column qualifies as one in which the mass transfer process dominates over the heat transfer processes. 

From a thermodynamic viewpoint, a typical thermodynamic efficiency of a distillation system is about 10 percent (4). This can be enhanced if intercondensers and interreboilers are used, In fact, it has been shown that conceptually, a distillation system can be devised which requires only the minimum work of separation. Although a thermodynamic efficiency of 10 percent appears low, not many other processes are more efficient (4). 

For more information, the render is referred to the works of Linnhoff, 9 De Nevers,16 Suss man.17 and De Nevers and Seader.18 Also, the texts of King2 and Henley and Sender contain some discussion of chermodyanmic analysis bssed on minimum work of separation and net woth consumption. 

Reverse osmosis will have a lower energy requirement than most competing methods of separation, since its woik requirement differs from the minimum work of separation only by the ratio Plr. However, it is limited to modest concentration of veiy dilute solutions because the osmotic pressure becomes quite large... 

Several cases will be examined. Thus, for an ideal mixture at low pressure the minimum work of separation is ... 

For more information, die reader is lefened to the woiks of Linnhoff, De Nevers, Sussman, and De Neveis and Seader." Also, the texts of King and Henl and Seader contain some discusaon of theimodynamic analysis based on minimum work of separation and net woik consumptkm. 

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