Exergy is a quantity used by process engineers in analyzing energy flows in industrial processes to improve designs and to minimize total energy usage.

The *First Law of Thermodynamics* states that in any process energy is conserved, and for a steady state flow process

A real process must comply with Equation (1), but compliance does not guarantee that the process is actually feasible.

The Second Law of Thermodynamics stipulates that energy transformations in which entropy is reduced are not possible. From the definition of entropy,

and by substitution in Equation (1),

The maximum work available from a process is therefore

The maximum available work defined by Equation (4) is the *stream availability*, more commonly termed *exergy*. This is the amount of work or energy that can be obtained from a reversible steady-state flow process. With real irreversible processes, driving forces (such as temperature differences between cooling and warming streams) result in a net increase in total entropy. Exergy is lost and the equivalent potential for doing work is lost.

For a steady-state process which has feed-and-product streams and exchanges energy with its surroundings, the work input to the process is given by the *Gouy-Stodola equation*:

The term T_{0}ΔS_{irr} is the ‘lost work’ and is the amount of potential work lost from the process. In a reversible process, this value is zero.

*Carnot* showed that if heat produces work by driving a reversible heat engine, then the maximum amount of work that can be delivered is:

Similarly,

as exergy is the maximum work that can be obtained via a reversible process, from a temperature T, when the cold sink is the surroundings at temperature T_{0}. The amount of work obtained is always less than the heat input and the ratio is termed the ‘Carnot efficiency.’

If T is less than T_{0}, Equation (7) gives the minimum (reversible) work input to ‘pump’ heat from a low to high temperature, such as in a refrigeration cycle.

A difference in pressure or chemical concentration can produce work. In general, any system not in equilibrium with its environment can produce work via some sort of engine and the maximum quantity of work equals the initial exergy value of the system.

The concept of reversible process, upon which exergy is based, is useful because it gives a yardstick for comparing the actual performance of real processes. Clearly, ‘lost work’ should be minimized to improve overall process energy efficiency because it represents wastage—either of work input to the process or work that could have been usefully extracted from the process. Recognition of this is crucial for good process plant design.

Lost work is reduced and energy is saved by operating processes more closely to thermodynamic reversibility. An evaluation of process irreversibility and inefficiency is termed exergy analysis. Exergy analysis plays a key role in providing an understanding of how to minimize overall energy consumption [Kotas (1985), Sussmann (1980)].

Exergy analysis, as typically applied to a large-scale process plant, involves evaluation of lost work for each part of the process and examination of where the largest losses lie. It identifies areas of the overall process where further design work and optimization will be of most value and the scope for improvement of energy utilization. Results of exergy analyses have often led to the adoption of energy-efficient technology, especially in processes with high-energy consumption such as cryogenics and distillation [Gaggioli (1980)].

A conventional exergy analysis can be a painstaking exercise and recently, short-cut techniques have been developed to help designers examine process inefficiency via simple equations and checklists [Linnhoff (1983), Tomlinson et al. (1990), Steinmeyer (1992)]. These techniques can generate ideas to aid in process selection prior to fixing details of the process and can even enable process energy requirements to be estimated prior to the selection of process technology.

Exergy is useful as it gives both ideal and practical targets for energy conversion processes. However, exergy is only one aspect of energy, and there is no direct relation between exergy and the economic value of energy. It is up to the engineer to decide how to interpret the results of an exergy analysis, but used correctly it can be a very powerful tool for optimizing process flowsheets and individual process equipment.

#### REFERENCES

Gaggioli, R. A. Ed. (1980) Thermodynamics Second Law Analysis. American Chemical Society. Washington, D. C.

Kotas, T. J. (1985) *The Exergy Method of Thermal Plant Analysis*, Butterworth. London. DOI: 10.1016/0009-2509(87)80094-5

Linnhoff, B. (1983) New concepts in thermodynamics for better chemical process design, *Chem. Eng. Res. Dev*. 61(4)207.

Steinmeyer, D. (1992) Save energy, without entropy. *Hyd. Proc.* 71(10): 55.

Sussmann, M. V. (1980) *Availability (Exergy) Analysis*. Mulliken House. Lexington, MA.

Tomlinson, T. R., Finn, A. J., and Limb, D. I. (1990) Exergy analysis in process development. *The Chemical Engineer*. No. 483 & 484.