Exergy, chemical

For the determination of a compound s chemical exergy value we need to define a reference environment. This reference environment is a reflection of our natural environment, the earth, and consists of components of the atmosphere, the oceans, and the earth s crust. If, at P0 and T0, the substances present in the atmosphere, the oceans, and the upper part of the crust of our earth are allowed to react with each other to the most stable state, the Gibbs energy of this whole system will have decreased to a minimum value. We can then define the value of the Gibbs energy for a subsystem, the reference environment —at sea level, at rest, and without other force fields present than the gravity field—to be zero as well as for each of the phases present under these conditions. It is a logical extension of these assumptions to 

Disregarding the kinetic and potential energy effects, the energy balance over the control volume for a steady-state operation is 

We need enthalpy of formation data, since some fuels are normally composed of several chemical species. The heating value of a fuel is the enthalpy of combustion a lower heating value occurs when all the water is in vapor state. The entropy balance for the combustion cell is 

The entropies of the mixture components can be calculated using the appropriate partial pressures 

We can determine the specific enthalpies and the specific entropies from the temperature, pressure, and composition of the environment. Once we specify the environmental conditions, all enthalpy and entropy terms are fully defined regardless of the process within the control volume. The term 7 0 b depends on the nature of the process and the irreversibility. Chemical exergy, Exch, is 

Chemical exergy leads to maximum theoretical work when there is no irreversibility. A similar equation in terms of the Gibbs function g h Ts of respective substances becomes 

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Kotas [3] has drawn a distinction between the environmental state, called the dead state by Haywood [1], in which reactants and products (each at po. To) are in restricted thermal and mechanical equilibrium with the environment and the truly or completely dead state , in which they are also in chemical equilibrium, with partial pressures (/)j) the same as those of the atmosphere. Kotas defines the chemical exergy as the sum of the maximum work obtained from the reaction with components atpo. To, [—AGo], and work extraction and delivery terms. The delivery work term is Yk k kJo ln(fo/pt), where Pii is a partial pressure, and is positive. The extraction work is also Yk kRkTo n(po/Pk) but is negative. 

Chemical exergy out of equilibrium with the environment in composition. 

This work is called the chemical exergy of methane and is the maximum amount of work that this compound has available for performing work in the environment (Figure 6.3). Indeed, natural gas is an important fuel for a power station. Table 6.1 gives the chemical exergy or available work of a number of compounds energy carriers, raw materials, and pure products. 

The first term on the right-hand side of this equation expresses the amount of work available due to differences in pressure and temperature with the environment. The second term, the chemical exergy, expresses the amount of work available due to the differences in composition with respect to the environment. The superscript in Ex, expresses that the chemical exergy is considered at ambient conditions. 

Table 6.2 lists exergy values for methane. It is clear from this table that methane carries an impressive amount of exergy as chemical exergy. Further, the table shows (1) the influence of increased pressure and temperature on the physical exergy and (2) that this latter contribution of exergy is nearly two orders smaller than the chemical contribution. Chemical exergy is the exclusive subject of Chapter 7. 

Exergy is a convenient concept if one wishes to assign a quantitative quality mark to a stream or a product. This quality mark expresses the maximum available work or potential to perform work because of its possible differences in pressure, temperature, and composition with the prevailing environment. The physical exergy, Exphys, only accounts for the differences in pressure and temperature the standard chemical exergy, Ex/hf.rn, accounts for the difference in composition with the environment at the environment s pressure and temperature. Thus... 

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. 

From these data, we can calculate the chemical, exergy values of these components in the pure state at P0 and T0. Air at these conditions can, to a good approximation, be considered as an ideal gas therefore, separation... 

From this equation, we can show [2] that the standard chemical exergy at P0 and T0 of a pure component can be calculated from its partial pressure Pt in air with Equation 7.6 ... 

The standard chemical exergy values for the main constituents of air as listed in Table 7.1 are given in Table 7.2. 

Exergy values for the elements in their stable modification at T0 = 298.15 K and P0 = 101.325 kPa are called standard chemical exergy values Ex. For the calculation of the chemical exergy value of all kinds of substances, the standard chemical exergy values of all elements are required. 

The following example for graphite illustrates how the chemical exergy value for all other elements can now be calculated (Table 7.3). For the calculation of... 

Standard Chemical Exergy Values at P0/ T0 of Various Components Present in Air... 

For the remaining elements, reference compounds have been chosen, as they occur in seawater or in the lithosphere, the earth s crust. An important aspect of this choice has been that the calculated exergy values of most compounds should be positive. Table 7.3 lists the standard chemical exergy values of the elements as presented in Szargut s well-known standard work [1]. Chapter 8 gives an example, the adiabatic combustion of H2, to illustrate the use of these exergy values in an interesting application. 

Table 7.3 is useful for the calculation of the standard chemical exergy values of compounds. We illustrate this for methane and start from its hypothetical formation reaction at standard conditions ... 

In general, we can calculate the standard chemical exergy of a component from the standard chemical exergy of its elements with the equation... 

Standard Chemical Exergy Values of Selected Compounds... 

Suppose we deal with a process in which iron, Fe, has to be used as a reactant, for example, in a reduction reaction. The standard chemical exergy of Fe is 376.4 kj/mol. If we wish to carry out a thermodynamic or exergy analysis of this process, this value is not appropriate. After all, to put the exergy cost of the product, for which Fe was needed as a reactant, in proper perspective, we need to consider all the exergetic costs incurred in order to produce this product all the way from the original natural resources— iron ore and fossil fuel in this example. The production of iron from, for example, the iron ore hematite and coal has a thermodynamic efficiency of about 30% [1], and therefore it is not 376.4 kj/mol Fe that we need to consider... 

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... 

The concept of cumulative chemical exergy consumption is very useful and accounts for the fact that when a compound (e.g., ammonia) is introduced into a process, its chemical exergy has to be corrected for the exergy consumption accumulated since this compound was manufactured from its natural constituents (air and natural gas in the case of ammonia). 

If the thermodynamic efficiency of a process step is calculated, the chemical exergies should be excluded from the calculation if the process step does not include chemical conversions. If it does, it may be appropriate to distinguish between the physical and the chemical efficiency, itphys and T chem, °f the process step. 

The conditions of a natural gas reservoir are 30 MPa and 100°C. The gas, assumed to be pure methane, is spontaneously expanded to a pressure of 7MPa (Figure 8.1). Assuming that this expansion is adiabatic, calculate the amount of work that is lost in the process, and express it as a fraction of the originally available amount of work per mole of gas in the reservoir. Carry out this calculation while making a distinction between the physical and chemical exergy of the gas. 

Next, we wish to calculate which fraction this lost work is of the work originally available in the gas. The chemical exergy of the gas, assumed to be methane, is significant, 831.65 kj/mol, but it should be excluded from the calculation because no chemistry is involved in the expansion step. The work available in the gas at initial and final conditions can be calculated from Equation 6.11 ... 

The fraction of nonchemical work available in the gas that has been lost in the expansion process can now be calculated from W /Exj = 3.325/13.501 = 0.246. If we had included the chemical exergy of the gas, this number would have been reduced to 0.00393, but as the expansion step is strictly nonchemical, this result is meaningless. Of course, the calculation of Wlost itself would not be affected as the chemical exergy would have to be included in both Exj and Ex2 and would drop out. 

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