Exergy
Background.
In our world the developed and developing worlds have a rapidly growing energy demand. There is increased pressure to restrict obtaining this energy from fossil-based sources, oil and gas. Renewables are a partial solution, provided the wind blows and the sun shines. Combine this with aggressive geopolitics, its not surprising that energy costs swing like a pendulum.
Perhaps it is timely to visit or revisit the concept ‘Exergy’. It is not Energy with a typing error, but it is closely related to Energy and has the same units J/g or J/kmol for the ‘specific exergy’ carried by each mass or molar unit in a flowing material stream or kW (unit of power) for the exergy ‘flow’ carried by a total stream. Electrical energy is the most versatile form of energy as it can be converted into most other forms with only a small loss.
So, what is Exergy?
Exergy is the ultimate common factor - a number which represents the true value of energy in all its forms – heat, shaft work, electricity, high pressure gas - on a ‘level playing field’. The term used as a specific property of a substance depends on its composition and temperature and pressure (i.e. its state), like its enthalpy (heat content).
Two key factors to remember are:
1) The value is affected by the environmental conditions, but not significantly on the planet’s surface,
2) The amount of exergy entering any (real) process is always greater than the amount leaving. Some is always lost. One job of the engineer is to minimise this loss to the extent that is economic. We explain this later.
Chemical Exergy and nuclear Exergy are slightly different forms as they actually alter the environment. Burning fuels to provide heat energy for an engine or for space heating rely on the chemical energy in a fuel which is reduced by combustion in return for producing heat energy. Where the fuel is of ‘fossil origin’, i.e. contains carbon – it clearly also affects the environment. Hydrogen is one of the few fuels whose combustion does not affect the environment in any significant way. Unfortunately, although it has a high chemical exergy, it cannot be mined, and its production and storage also require energy from another source – be it renewable or fossil origin such as natural gas.
Is there a conflict with the First Law - conservation of energy?
We learn at school that energy can be neither created nor destroyed, but it can be converted from one form to another with the total remaining constant. This is the so-called ‘First Law of Thermodynamics’. On the other hand, Exergy can be destroyed – for ever. This harsh reality is the essence of the ‘Second law of Thermodynamics’.
History.
The basic concept was identified almost 200 years ago by Nicolas Léonard Sadi Carnot, a French military engineer and physicist, often described as the "father of thermodynamics". His hypothetical power generation cycle – ‘the Carnot cycle’ established the maximum amount of shaft work (effectively the electrical energy) that can be extracted from a heat source at a higher temperature than the environment. This maximum amount is the Exergy of that heat source, and has the same units as energy (kJ) or for power, which means energy flow (kW). A corollary is that - as a fluid stream or a body’s conditions (eg its pressure and temperature) approach those of the environment, its Exergy approaches zero.
After Carnot, in 1889 two physicists, Gouy and Stodola independently produced a relationship which enables calculation of an ‘Exergy balance’ for a process. But as we stated, except for a perfect hypothetical process – such as Carnot’s cycle, Exergy does not balance. In any practical real process there is a certain amount destroyed irreversibly and this is generally as heat passing to the environment. The balancing term in Guoy-Stodola’s equation is To x ΔS-irr, where To is the environment temperature (in degrees absolute) and ΔS-irr is the entropy produced by irreversible actions – eg friction in a machine, high temperature differences in a heat exchanger, high pressure fluid streams wastefully throttled through a valve., etc. Entropy (symbol S) is an abstract term for the property of a fluid which reflects its degree of disorder, uncertainty and chaos. (Young children often have a high level of this).
More recently still Ilya Prigogine (1917-2003) looked at the application of the concept of locally low entropy (high exergy) in living creatures and other organised structures.
Application to a cryogenic process
To re-iterate, the exergy of a process stream is defined as the maximum amount of useful work (eg electric power) that can be extracted from that stream by bringing it reversibly to complete equilibrium with the local environment.
Mathematically for the purists: E = ΔH – To. ΔS
Where ΔH is the change in enthalpy (heat content) of the stream and ΔS is the entropy change of the stream when bringing the stream reversibly to equilibrium with the environment at To. (degrees Kelvin = ºC + 273.15).
‘Reversibly’ means frictionless equipment with negligibly small driving forces, so no overall Entropy production.
An ideal concept which could be effortlessly changed in direction to restore the stream back to its original condition.
Equilibrium
Equilibrium (Equi-librium) with the environment means in balance with the local conditions. The local environment – the air or sea constitutes an essentially infinite heat source or more often a heat sink. It has no exergy and is the ‘datum’ or zero point. We mention Local environment because for someone sweating in the tropics, the arctic environment would have some value and vice versa.
Renewable energy sources such as wind, wave, geothermal exploit the fact that our environment is not uniform but dynamic. Wind is ultimately a result of solar energy causing bulk disturbances to the earth’s oceans, the atmosphere and the spinning of the earth on its axis. The wind that spirals around isobars towards a region of low pressure is ‘attempting’ to even out or come to equilibrium or to a uniform pressure and temperature. Conversely, the air that rises and spirals gently outward from a region of higher pressure is part of dynamic unending dance in search of equilibrium.
In renewables, man obtains power for his needs by harnessing Nature’s blind quest for even-ness. In general, it is in Nature’s nature to proceed irreversibly. Man can interrupt this entropy production and, in the process, get some useful work for his/her own ends.
Chemical exergy of a substance (in particular fuel) is one of the most concentrated forms of exergy, but in using (converting) it we gradually change the environment itself, particularly for some fuels. (Global warming).
What is the use for an exergy analysis?
Exergy provides a steer towards process improvements and a deeper understanding of process features that may have arisen by accident, trial and error or intuition, or even application of common practice. Without Exergy analysis, the full appreciation of the reason for a particular feature’s benefits are lost and the opportunities to transfer the insights to other situations may be overlooked. A sister methodology is ‘Entropy Minimisation’. Application of this to heat exchanger networks led Bodo Linnhoff to develop ‘Pinch Technology’ in 1978-80.
Exergy is commonly applied to low temperature (cryogenic) processes such as LNG, LPG recovery or air separation or in refrigeration cycles or conversely in heat engines for generating power, simply because these processes are energy intensive and the rewards are greater. However, it is universally applicable. The analysis tells us the minimum energy that we will need to make a process work. It can also tell us where the exergy is being used and how much is being lost in irreversible entropy generating steps. We can then decide to what extent it is cost beneficial to reduce that irreversibility. (It can sometimes be worth allowing it to increase in order to reduce capital investments. This is the familiar capital cost versus energy trade-off.)
The exergy value of Heat - or its antithesis ‘Cold’
The Exergy (real) value of a unit of heat energy vs. the temperature available - or required.
The graph shows that as the temperature of a quantity of heat energy increases (to the right) the ‘value’ of that heat i.e. its exergy approaches unity, but never actually gets there. At room temperature around 300K (27C), heat has zero exergy. It cannot be used to generate power in an engine.
Going to the left, at lower temperatures the lower the temperature the greater is the exergy of the unit of ‘cold’. In other words the higher is the amount of work needed to provide a unit of ‘cold’ (refrigeration) at low temperatures, even with a perfect (ie. a reverse Carnot) refrigeration cycle. In fact the Carnot relation says it approaches infinity as absolute zero is approached. Although absolute zero cannot be achieved, thanks to clever physics and a techniques known as adiabatic demagnetisation, what we call absolute zero has actually been approached to within a few thousandths of a degree (milli -Kelvins).
A Case Study.
The Exergy method was recently applied to a small project to extract 100 metric tons per day of LPG (C3/C4) from a condensate stream by distillation. After screening several process options a single column process with a pasteurising section to remove light ends and excess propane was selected based on lowest capex. In developing the design and evaluating what butane recovery to adopt (with a fixed production rate) an unexpected phenomenon came to light. Namely, as the feed flow was increased (for fixed production) the reboil duty reduced - up to a point - but then began to increase again. One could simply select the conditions with the lowest reboil duty as the optimum and forget about it. However, not quite understanding the reason for this minimum was a serious irritant to an inquisitive process engineer.
Enter exergy analysis as a possible tool for investigation.
The first step was to see whether a prefect reversible separation process would also show a minimum in energy demand as the feed rate was increased. Indeed, it did so but at a lower feed rate. The exergy flows in the various product streams and in the reboil and condenser duties were assessed as the feed rate increased. This showed that the irreversibility steadily reduced as the feed was increased but flattened out near the optimum. The findings provided some insights but also prompted further questions – such as what the irreversibility on each distillation tray is where the rising vapour and the descending liquid reflux mix? This is an ongoing R&D topic.
In numerous other instances exergy analysis has been used to assess the ‘goodness’ of a design and to highlight where it might be improved.
Other applications of Exergy Analysis
Just one application is comparison of the work (Exergy) of liquefaction of a gas - say Natural gas to produce LNG or nitrogen gas to produce LIN. The process is conveniently shown on a Temperature-Entropy (T-S) diagram.
The examples below show the effect of Pressure on the Exergy (minimum theoretical work) needed for liquefaction.
The area shown in pale blue in this diagram is the work required at low pressure.
Similarly in the next diagram for liquefaction at high pressure the pale blue area is much smaller.
In each case the required exergy (minimum reversible work) is given by Exergy at final condition - Exergy at initial feed condition at ambient To.
Interestingly, the minimum Exergy needed to supply the feed gas at higher pressure in order to reduce the exergy needed from the refrigeration cycle is the isothermal work of compression of the feed, and this exactly balances the exergy save by the liquefaction cycle. On reflection, this has to be the case, as it’s not possible to improve on a reversible process. The potential benefit of pre-compression depends on the relative irreversibility (entropy generated) in the compressor or the cooling equipment.
Any actual real world process requires signifcantly more energy to compensate for irreversible losses. A task of the Cryogenic Process engineer is to identify these losses and use ingenuity to eliminate or minimise them to the extent possible - within economic constraints,