Exergy of mixing

In the last chapter, the concepts of exergy and physical exergy, in particular, were introduced. This chapter deals with three other important concepts, namely, exergy of mixing, chemical exergy, and cumulative exergy consumption, and their numerical evaluation. 

Recall that exergy values reflect the extent to which a compound or mixture is out of equilibrium with our environment. Examples are differences in pressure and temperature with the environment. Differences in temperature lead to heat transfer, while differences in pressure lead to mass flow. Chapter 6 shows that the physical exergy represents the maximum amount of work that can be obtained from a system by converting a system s pressure and temperature to those of our environment. 

To clarify the concept of the exergy of mixing, we give the example of pure oxygen at ambient conditions P0 and T0. Consider a system, for convenience 

For the calculation of the exergy value at P, T of a mixture, of a given composition, with respect to the exergy values of the pure components at P and T, the exergy difference is defined as 

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The chemical exergy of a molecule in a mixture is smaller than in its pure state, as it will require work to separate the mixture in its pure constituents, the exergy of separation. This exergy will be lost as the exergy of mixing when the pure constituents spontaneously form the mixture. The total exergy of a... 

Fig. 10.5. Exergy of mixing for one mole of a binary ideal gas mixture at our environmental temperature T0 and pressure pn...

This is the definition of the physical exergy of the effluent stream The computation of the terms will yield the physical component of the stream, and the combination with the chemical and mixing components will allow for the computation of the efficiency. The question now remains Why did the computation of the efficiency based on the Carnot factor give the correct number The answer is that since the temperature of the effluent gases is fixed, it mimics an infinite heat reservoir, and therefore n[AH - TqAS] simplifies to nAH[ 1 - T0(AS/AH)] = nAH[ 1 - (T0/T)], since AG = AH - TAS = 0 at equilibrium. 

The losses in the reactor are chemical exergy losses, whereas the cooler losses can be attributed to physical exergy losses. Mixing constitutes physical losses as do the losses in the extruder due to the dissipation of mechanical energy to heat. The losses in the purge vessel (V3) are due to the fact that the gas is incinerated. The sum of all losses equals 4.73MJ/kg PE, or US 0.0465 per kg PE. 

As some intermediate thermodynamic data are missing or not well known (enthalpy of mixing of CuCl and CuCl2 in HC1/H20 mixtures for example) and some heat exchanges or separation are not linear (for instance, HC1/H20 mixture has an azeotrope which cannot be crossed), we decided to proceed to a global exergy analysis instead of a flow sheet analysis. 

Total exergy Ex of a multicomponent material stream consists of physical, chemical, and mixing parts. Disregarding kinetic and potential exergy contributions, the rate of exergy of a stream is Ex // T0S, Ex = hEx, where h is the molar flow rate of a stream and Ex the molar exergy. Similarly, H and W, are the stream enthalpy and entropy rates, respectively, and are based on reference conditions. T0 is the environmental temperature usually assumed as 298.15 K. 

The recovery and purification of the desired product demands a further breakdown of exergy in the sense of mixing the aqueous feed with (pure) solvents (precipitation and extraction), salts (ion exchange), heat (evaporation and solvent recovery), electrical power (electrodialysis), pressure (filtration and membrane separations), or just extra water (gel filtration). This is shown schematically in Fig. 5. 

We would now like to illustrate essentials of such an analysis and the role of the exergy concept with a simple example. We borrow this example from Sussman [2] because we can hardly think of a nicer and clearer illustration. Figure 6.5 illustrates how a stream of 1 kg/s of liquid water at 0°C is adia-batically mixed with a second stream of 1 kg/s of liquid water at 100°C to produce a stream of 2 kg/s of liquid water. The task at hand is to provide a thermodynamic analysis or exergy analysis of this process. The temperature of the environment is 25°C. 

In general, a flow-sheeting program can give the total entropy and enthalpy of the stream, in which case the physical and mixing exergies can be computed as... 

Separation of remaining reactants and products are one of the main issues in many thermochemical cycles or high temperature electrolysis. Usually reversible chemical reactions are used. Here the term reversible is used in terms in chemical reversibility, but in terms of exergy the chemical reaction usually has to be handled in a very irreversible manner to ensure that reactants and products do not mix together. 

In the case of non-ideal mixtures (e.g. liquid and solid solutions), the activity ai = y has to be used instead of the molar fraction xi of substance i after the logarithmic sign in Eq. 10.23 to express the mixing term of the exergy at the exergy reference temperature T0 and pressure ft as shown in Eq. 10.27 ... 

We notice in Fig. 11.9 that no vector of thermal processes can occupy the separating and mixing regimes in the exergy vector diagram. 

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