Entropy and Exergy Balances

The complete entropy and exergy balance would include the heat exchange with the fluid medium in the balance compartment. 

Entropy and exergy balances from Equafions 23.50 and 23.60 yield... 

Chapter 6 - Entropy and Exergy Balances with specific heat Cp. Consequently... 

The converged mass and heat balances and the exergy loss profiles produced by the Aspen Plus simulator can help in assessing the thermodynamic performance of distillation columns. The exergy values are estimated from the enthalpy and entropy of the streams generated by the simulator. In the following examples, the assessment studies illustrate the use of exergy in the separation sections of a methanol production plant, a 15-component two-column... 

Component, energy and entropy balances are developed in the GLRDVE. The entropy and, in particular, the entropy production rate are of paramount importance to determine exergy losses and the responsiveness of the process. The balances lead to the following set of DAEs,... 

Based on the combination of energy and entropy balances and according to the definition of availability an exergy balance can be obtained for a given phase (a) (appendix A in Luyben et al. (1999)),... 

Because heat loss to the environment is very small in comparison to the heat transferred within an open heat exchanger, the first law efficiency is close to unity. However, mixing streams is an irreversible process that generates entropy and thus destroys exergy. Assuming no heat loss to the environment, using Equation 23.42 yields the energy balance of the open feed heater. 

It is not always this easy to set up the whole exergy balance of a plant, and the less to draw inference from it. Generally, we can compute the entropy production (or loss of exergy) in individual nodes, but the final judgement will depend on how the node is included in the technological system. See also Sections 6.3 and 6.4. 

Finally, Example 8 is more complex in that it comprises entropy production due to chemical reaction in combination with heat transfer, and also diffusion the role of the latter appears as marginal. The example can also be regarded as an example of complex single-node balancing, a kind of thermodynamic analysis included. Concerning the entropy production (or loss of exergy), it turns out that the chemical portion, thus the term -(Gr / Tj ) Wr in (6.2.109) can represent an enormous item in the exergy balance it can be computed, but this is usually all that we can do in practice. In other terms, what kind of work has been actually lost, is a matter of theoretical speculations only. 

For deriving the exergy balance for heat and work streams, first we multiply the entropy balance by the temperature Jq 2nd then subtract it from the energy balance, and we obtain... 

Borel, L., "General Theory of Exergy and Practical Applications 1. Energy Balance, Coenergy and coenthalpy," Entropie, 15, No. 85, 3 (1979). 

Exergy is a unifying concept of many forms of energy, such as heat, mechanical work, and chemical energy. We can derive the exergy Ex relation from the energy and entropy balances for the composite system shown in Figure 4.15... 

In the case of a practical heat engine an energy balance and a flow balance are made up based on knowledge of turbine blade, heat exchanger and other characteristics. An exergy account, or entropy balance, then establishes the detail of the losses or irreversibilities. No such losses occur in the equilibrium of Figure A.I. See Figure 2.2 of Barclay (1998). 

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