Exergy destruction

A continuation of this application of the second-law analyses is an examination of the various irreversibilities in the reformer process for potential improvements. The chief sources of thermodynamic irreversibilities (with the associated exergy destruction) are (1) frictional losses, (2) heat transfer with a finite temperature difference, (3) chemical reaction far from equilibrium, and (4) diffusion. 

The first two effects are calculated directly from the overall process design. The frictional losses are obtained from the compressor power requirements. They amount to a total exergy destruction of 10 MW. Heat exchanger losses due to heat transfer in Units 1-6 (excluding the reformer) can be evaluated from the exergy exchange calculations they amount to 49 MW for a 20K temperature difference. 

Thermodynamic properties of the flow streams at various locations as well as the thermal and mechanical energy flows for the cycle are shown in Figure 2 using 1 g-mole of liquid methanol as the basis. Also shown in the figure are the magnitudes of entropy production and exergy destruction in each of the process steps. 

In order to clarify these ideas, we need to compare the irreversible entropy productions (or the exergy destruction) in cycles that utilize regenerative heating of compressed air, thermal recuperation in the form of evaporation and superheating of the methanol fuel, and chemical recuperation through either reforming or cracking reaction with methanol. The next section presents such a comparison in a simplified form to illustrate the utility of thermodynamic analyses. 

From these two equations, the exergy destruction in the system is obtained as... 

From these equations it is concluded that the summation of all process vectors gives rise to a vertical vector of which the magnitude corresponds to the exergy destruction, as shown in Fig. 13 (b). 

Singular system. It is found from Eqs. (16) and (17) that only a process with AH = 0 and AS 0 is able to constitute a process system by itself. Then it can proceed spontaneously without tranformation of exergy with other processes, as schematically shown in Fig. 17 (b). Of couse its vector appears vertically on the thermodynamic compass, as shown in Fig. 17 (a) and its length corresponds to the magnitude of the exergy destruction in the system. 

The temperature [K] and pressure [atm] of the input and output streams are specified following the mark . The adiabatic nature of this process is disclosed by the value of AH. The exergy destruction ToEASi is, therefore, given by changing sign of the exergy increase of this adiabatic process. Adiabatic compression and expansion are other examples of the singular system. 

When a target is decomposed into several subtargets, each subtarget and its coupled processes compose a process system of smaller scale, i.e., a subsystem, as shown by the broken lines in Fig. 24. For each subsystem, Eqs. (16) and (17) hold and we can obtain the exergy destruction in it, as shown in Fig. 26. Since the subtarget has the same characteristics as the target, the quotation mark is used also for subtargets in the SPEED. 

Exergy of objective outputs + Exergy of wastes + Exergy destruction... 

Then the exergy destruction for any process system may be obtained as the shaded area on the energy - direction factor diagram shown in Fig. A2. When the number of subprocesses is increased, the width of each AHha is decreased, resulting in continuous change in Dha 1" and Dhd ", Of course the exergy destruction obtained in this method is the same as that in the text (jL), hut Eq. (29) becomes now the sufficient condition for a process system to hold. 

If we assume that the reaction proceeds in an isothermal reactor at 740 K, the heat of reaction is obtained as 22.254 kJ, as shown in Figure 7. When this heat is absorbed by a heat sink at the same temperature, the exergy destruction caused by the reaction itself is given as 12.038 kj. 

The use of an augmentation device results in an improved heat transfer coefficient, thus reducing exergy destruction due to convective heat transfer however, exergy destruction due to frictional effects may increase. The exergy destruction number Nx is the ratio of the nondimensional exergy destruction number of the augmented system to that of the... 

Here, exm is the flow-exergy destruction, or irreversibility, and T0 the reference temperature. The system will be thermodynamically advantageous only if the Nx is less than unity. The exergy destruction number is widely used in second-law-based thermoeconomic analysis of thermal processes such as heat exchangers. 

Let us now explore in more detail the factors that determine the number of steady-state solutions. First, we notice from Eq. (5.11) that the slope of the line is steep for small heat exchangers (e<heat exchanger at all (e = 0). This is completely opposite to what we observed for a jacketed CSTR in Chap. 4. In a jacketed CSTR the slope of the heat removal line increases with the size of the heat transfer area. The difference is that, in the case of a CSTR, a large heat transfer area increases the rate of heat removal (exergy destruction), driving the system toward stable operation at a single steady state, whereas in the case of an FEHE system,... 

From a control standpoint we seek strategies and designs that allow us to alter quickly the exergy destruction rate To Act. The total rate of entropy production is... 

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