Net work consumption

In the two examples considered in Sections 10.1.1 and 10.1.2, the minimum energy required for separation in 

If Qh = Qt and no other energy sources are involved, then the net amount of work required for separation is 

Both expressions (10.1.21) and (10.1.22) represent what is called the net work consumption for the separation process driven by heat 

Suppose the separation device is using heat working between 120 °C and 25 °C, Qf, = Qt and To = (25 + 273) K. Then the fraction of the heat actually used for separation is 

In Sections 10.1.1 and 10.1.2, we obtained the minimum energy required for separating 1 m of water as -0.71 kW-hr/m. If the energy supplied for separation is thermal energy between 120 °C and 25 °C, then the minimum amount of heat energy required for separation is (0.71/0.24) = 2.95kW-hr/m of water. 

---

For a reversible separation process, LW = 0 and (- lV et) = AB. For an actual separation process, LW >0, (— IVne,) > AB, and a thermodynamic efficiency can be defined as the ratio of the change in availability function to the net work consumption for the actual process, provided that AB is positive. 

Processes that involve operations other than separation steps may result in a AB that is negative, thus indicating that it would be possible to obtain useful work from a reversible process. In that case, for the actual process it will still be true that LW>0 and -W a)> B. However, the thermodynamic efficiency should now be defined as a ratio of the net work consumption for the actual process to the change in availability function... 

A rigorous expression for the relationship between the net work consumption and the minimum (or maximum) rate of work required for a given process was derived by Denbigh for the general case of streams entering and leaving the process at different temperatures and pressures and with any number of heat reservoirs at different temperatures, including the infinite medium at T . From the first law of thermodynamics for a continuous steady-state process ... 

The term involving Q/ is identical to (17-17) and corresponds to the equivalent work that could be produced by supplying Q, from a heat reservoir at T) to a reversible heat engine that exhausts to the infinite medium at T . It is convenient to combine this equivalent work with the shaft work to obtain a net work consumption... 

Calculate the net work consumption, the thermodynamic efficiency, and the lost work. Discuss possible means of improving the thermodynamic efficiency. 

Solution. Because the feed and product conditions are those of Example 17.1, AB = (- 1Vmi ) in that example. The net work consumption in British thermal units per hour is computed from (17-23) by summing the shaft work and the equivalent work. For example, the shaft work for the first-stage compressor is... 

Table 17.2 Net work consumption for double-effect process of Fig. 17.7... 

For more information, tire reader is referred to the works of Linnhoff, De Neveis, Sussman, and De Nevers and Seader. Also, the texts of Kin and Henl and Seader contain some discussion of thermodynamic analysis based on minimum work of separation and net work consumption. 

First we will illustrate the minimum energy required to separate a small amount of mixture for the following processes evaporation of water from a saline solution recovery of water by reverse osmosis separation of an ideal binary gas mixture by membrane permeation. Then we will consider the definition of net work consumption for thermally driven processes. Next we will consider a variety of separation processes vis-k-vis their minimum energy requirement for separation. 

For close-boiling mixtures, where fn ai2 may be approximated by (ai2—1), and all other conditions of distillation identified in the previous analysis are valid, Hou-gen et al. (1959) and King (1980, p. 666) have provided a compact expression for the net work consumption in... 

The expressions for minimum energy required and the net work consumption per unit time are obtained as foUows ... 

---