Minimum energy required for separation

Per mole of the mixture, the minimum energy required is given by 

King (1980, p. 661) has provided this expression with the appropriate earlier references/sources. For feed mixtures behaving as ideal mixtures at constant pressure and temperamre. 

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. 

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The minimum energy requirement for treating separated pig slurry to control odour was 110 Wh pig place-1 day-1, assuming an aerator efficiency of 1kg 02/kWh input. 

Bond dissociation energies may be determined by studies of the type just mentioned139. For a series of aliphatic hydrocarbons the voltage required to produce H+ ions was determined. By measurement of the kinetic energies of H+ and use of the laws of conservation of momentum and of energy it was possible to determine the minimum energy required to separate H atoms from the parent molecules. 

In practice, the energy requirement for separation will be many times greater than this minimum value W j. Different t) s of separation processes exist and each requires a different amount of energy. Thus, the production of fresh water from the sea, which is a very practical problem, can be performed by several commercially available separation... 

Minimum energy required for membrane gas permeation, distillation, extraction and other separation... 

In this section, we wiU illustrate the calculation of the minimum energy required for a variety of separation processes, e.g. membrane gas permeation, distillation, extraction and adsorption. 

Figure 1 shows the results obtained by Qian et al. [1 ] in a process when AFM probe approaches and then separates from a SiQ2 substrate. The normal force required for separating the probe-substrate contact reads 33 nN. From a thermodynamic point of view, adhesion is in fact a state of the system at the energy minimum when the contact pairs interact with each other through interface, and additional work has to be applied to change the state of the system. 

It is generally agreed that electrolysis of aqueous solutions offers the best prospect for the production of hydrogen from water, because of the easy separation of the H2 and O2 products and because of the relatively low energy consumption if catalytically active metal electrodes are used. Thus, the minimum energy requirements are those for which water, hydrogen and oxygen, each at 1 atmosphere pressure, are in equilibrium ... 

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... 

The separation cost is often related directly to the degree of dilution for the component of interest in the initial mixture. This cost includes the fact that most separations use 50 times the minimum energy requirement based on the ideal thermodynamic requirements. To put the energy consumption in perspective, the chemical and petroleum refining industries in the US consume approximately 2.9 million barrels per day of crude oil in feedstock conversion [1], One method to visualize this cost factor is with the Sherwood plot shown in Figure 1.2. 

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