# OSES 2018

I recently heard that the OSES (Offshore Energy and Storage Summit) conference series may still be considering abstracts for their conference on 4-6 July 2018 in Ningbo, China.

This is a great conference and a great place for ideas and discussion surrounding all aspects of offshore energy. Thermo-mechanical energy storage technologies in particular are a major theme due to their potential for use with large scale offshore renewable technologies, and the conference committee certainly contains some of leaders in this field; Seamus Garvey, Rupp Carriveau, Tonio Saint, Daniel Friedrich, Jonathan Shek and Andrew Pimm.

I was lucky enough to go to the inaugural OSES conference in 2014, where I presented a concept for isobaric CAES using carbon dioxide to maintain high pressure storage.  It was thoroughly enjoyable as well as introducing me to a lot of interesting people and ideas.

Unfortunately I won’t be able to attend this year, but I plan to return to the thermo-mechanical scene soon so perhaps in 2019…

Also – for anyone wondering – I never got around to publishing the “isobaric CAES using CO2” concept in a journal article, but last year another team from China had the same idea. I’m definitely annoyed that I didn’t get around to submitting it as I have had a very similar article ready to submit (the extension of my conference paper), but it will teach me to be more proactive and I guess it is good that other people are thinking hard about CAES too!

# Lightsail – another setback for thermo-mechanical energy storage

Recently there has been another blow for thermo-mechanical energy storage, and in particular adiabatic CAES, as Lightsail – the much hyped company bankrolled by Bill Gates – has entered “hibernation”. This appears to be due to running out of cash, with the company ceasing operations. This is can be added to list of failures in CAES, including SustainX and ApexCAES.

Lightsail’s concept – the $70 million idea Many have watched the company with interest given its hype, larger than life founder and large amounts of investor funding – sources indicate this exceeded$70 million. Their various claims of high thermodynamic efficiencies which had already been achieved were also interesting – although it is hard to tell from the little available information whether this was simply a result of including the compression heat in their calculations (if you are interested in compressor performance you typically only consider the difference in air enthalpy between compressor inlet and outlet). As such, a little skepticism regarding this is probably healthy, which is emphasized by the company’s switch from CAES system to high pressure storage container manufacturer. Their water-spray injected compressor was an interesting idea, but was probably difficult to manufacture in practice. Moisture in compressed air can cause many problems including corrosion, aiding the build up of sludge deposits by mixing with oil/dust and as a result increasing pipe pressure losses, and causing faults in sensor and control equipment to name just a few issues off the top of my head. Crucially, it must also have been very difficult to avoid freezing during their expansion process, and water droplets/icicles in fast moving machinery can also be incredibly damaging. I should also note that their patent does also refer to oil spray injection.

Lightsail’s move to high pressure container storage manufacturer smacks of desperation and suggests to me that the management realised that they had completely underestimated the scale of the ACAES challenge – indeed a review from a former employee on glassdoor quotes the Cons of working at Lightsail as “Large scale energy storage is NOT an easy problem to solve”! The high pressure storage tank is probably the only part of the ACAES system that actually exists off-the-shelf, which throws up questions of why this would be the component of choice to manufacture. I have discussed in previous posts my opinion that it is most certainly a misconception to think that a ACAES system can be constructed with “off-the-shelf” components. The primary reason would seem to be that they thought they could implement a marked reduction in container costs compared to leading manufacturers, and a recognition that building high pressure vessels was certainly possible, as these type of containers do exist and have a market. This would have potentially allowed them to make incremental scientific progress and make a better or cheaper version of a product that already exists rather than the more ambitious aim of a game-changing energy storage technology. The problem with this turned out to be that they couldn’t make a product that was enough of an improvement to ship many orders.

It is very difficult to work out exactly what went on at Lightsail – I would love to talk to someone who worked there as I’m sure they were full of talented employees. There were also various reports about questionable spending habits on behalf of the senior management – again a look on glassdoor also suggests this. At least they were probably good to their employees, even offering pet insurance as a benefit…

In any case, it’s a huge shame for thermo-mechanical energy storage, and what’s most frustrating is that there is almost no ability for anyone to learn from the technical failures that undoubtedly sank the company. Picking through the Lightsail patents (now owned by the Silicon Valley Bank) is difficult, and they just seem to be full of quite generic ideas, with no indication of any ingenuity in the designs. This reinforces why these early stage companies are so frustrating, and can ultimately be bad for the technology development, as they simply put-off would be investors while no new scientific knowledge can be gained. Maybe I will email Bill Gates and see if he can push for any knowledge to be made public…

# CAES: A simple idea but a difficult practice

In the mainstream there are two main branches of Compressed Air Energy Storage (CAES) – conventional and adiabatic.

1. Conventional CAES

Conventional (also known as diabatic) CAES plants are essentially gas turbines in which air is pre-compressed using off-peak electricity, rather than running a turbine and compressor simultaneously. In these plants, off-peak grid electricity is used to compress air which is stored, and then mixed with natural gas and combusted during expansion. Compression is staged and the majority of the compression heat wasted (although some may be stored in a recuperator to pre-heat the air before combustion). Currently there are two commercial CAES plants worldwide; the Huntorf plant in Germany and the McIntosh plant in Alabama.

• Huntorf CAES plant: Data from [1]. 310,000m3 cavern at a depth of 600m, pressure tolerance between 50 – 70 bar, converted from a solution mined salt dome. Daily charging cycle of 8h, output of 290MW for 2 hours. 0.8kWh of electricity and 1.6kWh of gas required to produce 1kWh of electricity. Notably, built when the price of gas turbines was historically high.
• McIntosh CAES plant: Data from [2]. 538,000m3 salt cavern at a depth of 450m, pressure tolerance between 45-76 bar. Originally it provided an output of 110MW for 26 hours but in 1998 two extra generators were added and its total output capacity is now 226MW. 0.69kWh of electricity and 1.17kWh of gas to produce 1kWh of electricity.

Both plants are commercially viable and still running in their respective markets!

Figure 1: Schematic of diabatic CAES system.

As with Pumped Hydro Storage (PHS), CAES also requires favourable geography to provide the underground air storage caverns. However there are many more suitable sites worldwide than for PHS, although the costs are highly site specific. The costs of mining a suitable underground cavern where suitable geology doesn’t exist or creating an above-ground equivalent storage container are potentially prohibitive, whereas alternatively a naturally occurring cavern or somewhere easily minable may offer a very attractive price of storage in terms of $/kWh (or dollars per metre cubed of air storage). Caverns can be created in salt geology (typically using salt solution mining techniques) or existing caverns can be exploited provided that they are capable of housing the desired pressure. Geological formations such as aquifers and salt formations (bedded salt and domal salt) offer potential locations. Costs can also be reduced if existing well infrastructure is in place from previous underground drilling operations. While specific geology is required, this geology is relatively widespread. For example, the EPRI suggests that up to 80% of the US could have favourable geology [3] (see Figure 2). US CAES map with wind resources marked Figure 2: US geology for compressed air caverns. Regions with high wind resources are also indicated with the idea that CAES sites and wind turbines could be co-located [4]. Estimates for the costs of cavern mining can be as low as$1/kWh of storage capacity if solution mining techniques can be used [5]. In solution mining, fresh water is pumped in a salt deposit, becomes saturated with salt and is then removed. One problem however is that disposal of this brine can cause environmental issues.

1.1 CAES Performance Characteristics and Applications

CAES systems have traditionally been designed as centralised storage facilities which are intended to cycle on a daily basis and to operate efficiently during partial load conditions. This design approach allows CAES units to swing quickly from generation to compression modes and means that they are well suited to ancillary services markets, providing frequency regulation. Their ability to operate on a (intra) daily cycles means that they are also useful for load-following/peak shaving. The air storage caverns can also be very large, allowing for multiple days worth of electricity storage.

It should be noted that the inlet pressure (45-76 bar) for the CAES high pressure turbine is much higher than the equivalent for a typical gas turbine (about 11 bar) so a typical gas turbine can only be used as the low pressure expander. The high pressure turbine at Huntorf is based on a small-intermediate steam turbine design.

1.2 Table of Cost Estimates

 Typical Capacity Typical Power Efficiency Storage Duration $/kWh$/kW Lifespan Cycling capacity 500MWh – 2.5GWh 50 – 300MW n/a Hours – days 4-7 [6], 2-50 [7], 60  – 120 [8] 300-600 [6], 400-800 [7], 1000-1250 [8] 20-40 years High

Table 1: CAES cost characteristics

Adiabatic CAES is an energy storage concept that removes the natural gas combustion from conventional diabatic CAES. In adiabatic CAES the heat generated by the compression of air (the charging process) is stored in a Thermal Energy Store (TES) which is separate from the ambient temperature high pressure air store. When the system is discharged the high pressure air is reheated using this stored heat and then expanded. Without the stored heat, the process has an unacceptably low efficiency – this is because significant exergy is stored in the heat as well as the cool high pressure air. When the heat is recovered, the expected practical efficiency of these systems is debated – though the second law of thermodynamics does not pose a ceiling on the efficiency as for  heat engine – it just means that the real process has to be less than 100% efficient. Pragmatic estimates of the real efficiencies of this type of system are debated; most of the academic literature estimates practical efficiencies in the range of 60-75% [9,10]. If a plant could be constructed with no inefficiencies in any process – the theoretical efficiency would approach 100%.

2.1 Status

As no demonstration plant has ever been successfully constructed, Adiabatic CAES must be considered as an unproven technology. It does however have significant promise for use with renewables integration, energy management, peak shaving and grid reserves. The largest planned demonstration ACAES facility is a 290 MW adiabatic CAES project based in Germany called project ADELE [11]. It is a consortium between German utilities RWE and GE, the German Aerospace Center DLR, construction company Zublin, the Fraunhofer IOSB and the Unversity of Magdeburg.

Figure 3: A simple schematic of an ACAES configuration. There is a thermal store for each compression stage.

A schematic diagram of an ACAES system is shown Figure 3. In this configuration, air is compressed and then cooled using counter-current heat exchangers that transfer the heat from the air into a thermal fluid. This thermal fluid could then be stored in an insulated tank and used to reheat the air prior to each expansion stage. Several people have also suggested the use of Packed Bed regenerators to store the compression heat in the air.

2.2 Underwater CAES

Underwater CAES is a sub-type of ACAES which exploits an underwater Compressed Air Store at a depth of typically around 400m. The ambient pressure at this depth is approximately 40 times the atmospheric pressure, and the air store is either a flexible bag or a dome structure open at the bottom. As air is pumped into the storage container it displaces water and thus the store can operate at a constant pressure. This idea was pioneered by Prof Seamus Garvey and Dr Andrew Pimm at the University of Nottingham, as well as by researchers at the University of Windsor Ontario and Canadian startup Hydrostor (whose work is ongoing at the time of writing).

2.3 Fuelless CAES

The usage of the term “adiabatic CAES” is also somewhat ambiguous, as the term “adiabatic” is sometimes used to refer to the compressions and sometimes to refer to the overall process – i.e. the energy storage process aims to be adiabatic in the sense that ideally, it would exchange negligible heat with the surroundings. Therefore some authors therefore prefer the use of the umbrella term Fuelless CAES. This then clearly encompasses all compressed air processes which aim to store and return energy without the use of fossil fuels. This includes systems which have typically been labelled as isothermal CAES.

2.4 Isothermal CAES

In isothermal CAES the compressions aim to be isothermal and reversible. This is theoretically achieved by minimising the temperature differences which drive heat flow from the compressors to the environment (which is at a lower temperature). A huge challenge here is to make an isothermal compression process which operates sufficiently quickly to be of practical industrial importance but which is still slow enough to maintain the small temperature differences required for high reversibility. One idea for near-isothermal compression which has been suggested by LightSail (a start-up company in California) involves a water spray into the compression chamber of a specially designed reciprocating compressor/expander unit (see Figure 4). The water droplets absorb the heat of compression and their high specific heat capacity causes the temperature increase in the compression chamber to be much smaller. This warm water is then stored and on discharge is re-injected as a mist into the reciprocating machine which now acts as an expander.

Figure 4: Illustrating a near-isothermal CAES concept [12]

Isothermal CAES was also being pioneered by SustainX, however this company has ceased operations citing spiralling system costs. Lightsail Energy and SustainX had a similar goal of an efficiency above 60% for their first generation of machines and believe that 75% is achievable in the long term. The SustainX prototype was a 1.5 MW machine.

2.5 ACAES Challenges

There are several challenges which must be overcome before adiabatic CAES can become a viable energy storage technology option.

• Specialised compressor equipment must be developed, in which the heat generated during the compression procedure is stored in a highly reversible manner. This process seems most likely to consist of a series of adiabatic compressions in which heat losses from the compressor to the surroundings are minimised. The compressors must also operate with much higher compression ratios than current compressors which do not involve cooling during the compression. Each of the compressions is then followed by a cooling stage which aims to reversibly extract the compression heat. Possible options for heat extraction include packed bed regenerators or counter-current indirect contact air-to-fluid heat exchangers. This type of compression equipment is fundamentally different to industrial many industrial compressors. Why? Because the vast majority of compressors are designed to minimise the work required to achieve air at a given pressure. Most industrial compressions then typically involve trying to shed as much heat as possible from the compression process – as hot air takes more work to compress. The ACAES process is fundamentally different as reversibility should be maximised rather than work minimised. In fact, the greater the reversible work is per cubic metre of compressed air the higher the energy density of the storage system.
• Specialised expansion equipment must also be developed. Air turbines which provide highly isentropic expansions and operate within the desired pressure ratios are required. The expansion process of an Adiabatic CAES system should aim to mirror as closely as possible the reverse compression process. Therefore it should include the same number of expansion stages and heating stages, and expansion stages must aim to minimise heat gain and return all heat reversibly during the heating stages. While these turbines do not currently exist on the industrial market, it is anticipated that their design can learn much from the current generation of gas turbines for power generation. The pressure ratios will likely be smaller than most current gas turbines. One specific advantage is that the material demands will be much less (in terms of temperature tolerance) than current gas turbines which operate with inlet temperatures up to 2200K.
• Sliding pressures. Unless the system can be operated between constant operational pressures, both the compression and expansion machinery must operate at maximum efficiency over a range of pressure ratios. A single constant high pressure air storage is a primary advantage of UnderWater CAES.
• High pressure air storage. Depending on the chosen method of storage high pressure, air storage tanks must be developed which have minimum cost. This has apparently been a problem area both for SustainX and LightSail, however LightSail have released statements which hint that they may have found a method of lowering the costs.
• highly reversible heat exchangers will also be required which can minimise the temperature difference between the working fluid and the thermal storage medium while introducing minimal pressure drops.

2.6 Notable experimental ACAES development

Lightsail (California) – startup. http://www.lightsail.com/

Hydrostor (Ontario) – startup. https://hydrostor.ca/

SustainX (Massachusetts) – startup (liquidated)

University of Windsor – Prof. Rupp Carriveau and Dr. David Ting

University of Nottingham – Prof Seamus Garvey and Dr Andrew Pimm

References

[1] BBC Brown Boveri. Huntorf Air Storage Gas turbine Power Plant. https://www.eon.com/content/dam/eon-content-pool/eon/company-asset-finder/asset-profiles/shared-ekk/BBC_Huntorf_engl.pdf

[2] M. Nakhamkin, L. Andersson, E. Swensen, J. Howard, R. Meyer, R. Schainker, R. Pollak, and B. Mehta, J. Eng. Gas Turbines Power 114, 695 (1992). https://doi.org/10.1115/1.2906644

[3] Compressed Air Energy Storage: Renewable Energy (2010, March 17) retrieved 22 April 2017 from https://phys.org/news/2010-03-compressed-air-energy-storage-renewable.html

[4] Succar, S & Williams, R.H.. Compressed Air Energy Storage: Theory, Resources, and Applications for Wind Power, Princeton University (published April 8, 2008)

[5] De Samaniego Steta, F. Modeling of an Advanced Adiabatic Compressed Air Energy Storage (AA-CAES) Unit and an Optimal Model-based Operation Strategy for its Integration into Power Markets. EEH – Power Systems Laboratory. Swiss Federal Institute of Technology (ETH) Zurich

[6] Kaldellis, J. K. & Zafirakis, D., 2007. Optimum energy storage techniques for the improvement of renewable energy sources-based electricity generation economic efficiency.. Energy, Volume 32, p. 2295–2305.

[7] Chen, H. et al., 2009. Progress in electrical energy storage system: A critical review. Progress in Natural Science, Volume 19, pp. 291-312.

[8] EPRI, 2010. Electricity Energy Storage Technology Options. http://large.stanford.edu/courses/2012/ph240/doshay1/docs/EPRI.pdf

[9] G. Grazzini, A. Milazzo. A Thermodynamic Analysis of Multistage Adiabatic CAES. Proc IEEE, 100 (2) (2012), pp. 461–472

[10] Barbour, E, Mignard, D, Ding, Y,  Li, Y. Adiabatic Compressed Air Energy Storage with packed bed thermal energy storage, Applied Energy, Volume 155, 1 October 2015

[12] Fong, D. Insights by Danielle Fong. https://daniellefong.com/

# My article published in Applied Energy

I have finally managed to get an article about Adiabatic Compressed Air Energy Storage (A-CAES) published in Applied Energy, after starting to think about A-CAES in 2010. Granted, that makes for a disappointing ratio of years-to-articles but whatever, it’s progress!

The link to the article “Adiabatic Compressed Air Energy Storage with packed bed thermal energy storage“, is here.

Anyway, the article deals with an A-CAES systems that uses packed bed regenerators to store the heat of compression and return it again, rather than indirect-contact exchangers and a thermal fluid. As far as I know it is the first article out there to rigorously analyse a system with packed beds, so hopefully it will be a useful contribution. Other articles have considered packed beds for use in Pumped Thermal Energy Storage. I think that an A-CAES system based around packed beds is a better preliminary design than a system which uses indirect-contact heat exchangers (i.e. shell and tube, plate-fin etc) and stores the compression heat in some kind of thermal fluid.

The packed beds allow the stratification of heat at different temperatures to be preserved during the storage process. And we all know that allowing heat at different temperatures to mix involves exergy destruction, so by keeping the heat stratified, a higher efficiency may be achieved. In the system I analyse, most of the exergy is destroyed by the compressors and expanders, with roughly 7% lost as heat escape from the packed beds. The article also explains that due to leftover heat in the beds, during continuous cycling the temperatures of the beds is significantly increased and results in a slightly lower efficiency – reduced from 71.1% to 70.8% in a system with 3 stages. The article develops and validates a numerical model which is available to download. I also made an animation of the simulation which shows how the temperature profile in the packed beds evolves as the system is charged, left in storage, and discharged again (shown below).

The appendix also derives a set of analytical equations for the work available from tank of compressed air in which the pressure in the tank depends on the volume of air contained.

# CAES, thermodynamics, efficiency and exergy (part 2)

This is continued from CAES, thermodynamics, efficiency and exergy (part 1)

### A couple of notes on Fuel-less CAES

So now I’ll move on to Fuelless CAES…

Fuelless CAES (see the fuelless CAES variants) is a promising new energy storage technology that stores mechanical work in both compressed air and heat and returns it as mechanical work at a later stage (the mechanical work is usually converted from electricity by a motor and back to electricity by a generator). Fuel-less CAES systems are usually classed as either “Isothermal” vs “Adiabatic” CAES.

Figure 2: The general principle for the Fuelless CAES concept.

In most designs the compression and expansion can be near-isothermal or close to adiabatic – both involve a temperature rise during compression and require separate heat storage. True isothermal compression would be the ideal case it wouldn’t require a separate thermal store, as heat would essentially be stored at ambient temperature in the surrounding environment, however any compression approaching this would be too slow to be practical. It is a little confusing that near-isothermal compression is often dubbed as “isothermal”. Isothermal CAES designs typically propose the use of a near-isothermal compression in which a thermal fluid spray is injected into the compression chamber and which reduces the temperature rise experienced by the air during the compression. This warm thermal fluid must be stored in a separate heat store. Adiabatic CAES designs propose that the compression produces a temperature rise close to the adiabatic temperature rise. The compression heat must then be stored at a much higher temperature than the near isothermal case. This heat is usually removed and stored separately from the compressed air. It is important to note that the energy is stored both mechanically and as heat, and it is only the effective recombination of these two parts that can lead to an efficient system.

Thermodynamic work is path dependent. This has quite a profound consequence on the design of a fuelless CAES system: to maximise the work output of a CAES system the discharging process should follow the exact and opposite path of the compression process. Designs in which this is not the case are intrinsically inefficient and analyses of their efficiency are not reflective of a fundamental limit of the fuelless CAES concept (though this does not mean that they could not ever make economic sense). I have however read a number of academic articles that anaylse systems in which the expansion process is not the same as the compression and then seem to imply general conclusions about the system efficiency, which is misleading. Another common misconception is that the second law of thermodynamics imposes some fundamental limit less than 100% on the efficiency of the system. I think that this comes from a misapplication of the Carnot efficiency for a heat engine, as there is a re-heating element associated with the expansion part of the fuelless CAES process. What the second law of thermodynamics actually states is that even in the limiting case that a reversible system is designed with perfect lossless components, the round trip efficiency cannot be greater than 100%. In a perfect well designed system, the compression takes mechanical work and converts it into potential energy AND takes in heat at ambient temperature and moves it to a high temperature heat store. For perfect intercooling and an ideal gas the heat moved is equal to the work in, discounting the energy stored in the cold compressed air. Of course, this is not a violation of the first law as heat is also taken in with the ambient air. If one were to expand this cold air you would get some work out and you would have moved more heat than the net work put in. This is of course the principle of a heat pump and it is commonly known that these can have COP’s greater than 1. The expansion part then involves recombining the stored heat and the cold compressed air. With no heat losses and perfect inter-heating the compressed air is re-heated to exactly the same temperature as it was after the compression. And finally if the expansion is exactly the reverse of the compression the work out will be the same as the work in for the compression. Heat will be rejected at the ambient temperature with the compressed air. This perfect system does not solely convert heat into work, does not result in a net movement of heat from a lower temperature to a higher temperature without the addition of work and does not result in a net decrease of the entropy of the universe. Hence it is not disallowed by the second law. Of course in practice the second law means that no process is perfect and each real component will introduce losses, and so practically the second law means that the limiting efficiency value of the perfect fuelless CAES process is 100%.

So now on to exergy and CAES. As a physicist I had never come across exergy before I thought as an engineering PhD student that I’d better look at an engineering thermodynamics textbook. It is a very powerful concept. The exergy of a system is a measure of the available work extractable between that system and the “dead state”, which is just the ambient environment. It can be formulated by considering the energy and entropy changes in a general process that involves changes in the enthalpy of a flow through a system, internal energy changes, work in/out and heat flow in/out to the ambient. By simultaneously accounting for both energy and entropy, exergy accounts for the quality of different forms of energy. A good introduction to the concept can be found in most Engineering Thermodynamic textbooks (i.e. Fundamentals of Engineering Thermodynamics by Moran and Shapiro) and there are some good online resources like this. It is an incredibly useful concept in system analysis that accounts for the both the first and second laws simultaneously. In the analysis of engineering systems it allows the irreversibility of different system components to be analysed. In the design of a CAES system this is invaluable as it allows the “exergy destruction” in each component (heat exchangers, compressors, expanders etc) to be estimated. It also allows the maximum extractable work from the system to be easily calculated, which gives an indication of the reversibility of a perfect design.

As an example let’s do an exergy analysis of a CAES system with perfect lossless components with two compression stages and one expansion stage. This will illustrate that the maximum work out of the single expansion stage is less than the compression work put in, and crucially it illustrates where the remaining work is lost. The high pressure air store is considered isobaric so there is no increase in pressure as air is added to the store. The gas is an ideal gas with a constant specific heat capacity. With an isochoric store the equations just become a little more complicated and require more integration.

Consider a system with a 2-stage compression and single stage expansion as illustrated below.

Figure 3: Example asymmetric fuelless CAES system

Each compression increases the pressure ratio by a factor of r, so the total work input in the compression is given by Equation 1.

$\frac{W_{comp}}{m} = c_p T_0 ((\frac{P_2}{p_1})^{\frac{\gamma-1}{\gamma}} - 1) + c_p T_0 ((\frac{P_3}{p_3})^{\frac{\gamma-1}{\gamma}} - 1) = 2 c_p T_0 (r^x-1)$ (1)

$T_{max} = T_0 r^x$ (2)

where $r=\frac{P_2}{P_1}=\frac{P_3}{P_2}$ and $x=\frac{\gamma-1}{\gamma}$. The heat removed in each inter-cooling stage is:

$\frac{Q}{m} = c_p(T_{max}-T_0) = c_p T_0 (r^x-1)$ (3)

The maximum temperature to which the air can be heated without extra heat or work in before the expansion is the same as the temperature from the compression, so the work out of the single stage expansion is:

$\frac{W_{exp}}{m} = c_p T_{max} ((\frac{P_1}{P_3})^{\frac{\gamma-1}{\gamma}}-1) =c_pT_{max}(r^{-2x}-1)=c_pT_0(r^{-x}-r^{x})$ (4)

It has a negative value for r>1 which means work is done by the system. The outlet temperature of the turbine is colder than the ambient as the pressure ratio for the expansion stage is r2 rather than r for each expansion. It is given by:

$T_{out} = T_{max}r^{-2x}=T_0 r^{-x}$ (5)

The work that could be extracted from this cold ambient pressure air can be calculated by considering its exergy. The exergy associated from a flow of heat from some temperature to the ambient T0 is given by:

$B_{heatflow} = Q(1-\frac{T_0}{T})$ (6)

However as the heat is flowing from the body of air it is cooling down so we write:

$\delta B_{airout} = \delta Q (1-\frac{T_0}{T})=mc_p\delta T (1-\frac{T_0}{T})$ (7)

Integrating this from T = Ti to T = T0 gives

$B_{airout}=mc_p(T_i-T_0-T_0 \mbox{ln}\frac{T_i}{T_0}) = mc_pT_0(\frac{T_i}{T_0}-1-\mbox{ln}\frac{T_i}{T_0})$ (8)

Putting in the value for Ti gives:

$B_{airout} = mc_pT_0(\frac{T_{out}}{T_0}-1-\mbox{ln}\frac{T_{out}}{T_0})=mc_pT_0(r^{-x}-1-\mbox{ln}r^{-x})$ (9)

There is also heat left over from the compression, as only the heat from one intercooling stage could be used before the expansion (because no net heat will flow between two identical temperatures). The exergy associated with this leftover heat can also be calculated in the same manner as:

$B_{heatleft}=mc_pT_0(\frac{T_{max}}{T_0}-1-\mbox{ln}\frac{T_{max}}{T_0})=mc_pT_0(r^{x}-1-\mbox{ln}r^x)$ (10)

So now we have accounted for all the work in that went into the compression. With a single expansion stage extracting the work out the efficiency is limited to:

$\frac{r^{-x}-r^{x}}{2(r^x-1)}$

To check we have accounted for all the work into the system we sum the work out and the exergy associated with the cold outlet air and the leftover compression heat.

$\frac{W_{exp}}{m}+\frac{B_{heatleft}}{m}+\frac{B_{airout}}{m} = -c_pT_0(r^{-x}-r^x)+c_pT_0(r^{-x}-1-\mbox{ln}r^{-x})+c_pT_0(r^x-1-\mbox{ln}r^x)=c_pT_0(2r^x-2)=\frac{W_{comp}}{m}$ (12)

Low and behold the total is the compression work! Therefore we can see where all the work into the system has gone. Even with perfect isentropic lossless components it is not possible to extract all of the 2-stage compression work through a single expansion. The missing work has been accounted for as leftover stored heat and the exit loss from the turbine.

The point of this example is to give a small insight into the power of exergy and encourage its use in both CAES analyses and for informing designs.

# CAES, thermodynamics, efficiency and exergy (part 1)

I thought that I would write a post about CAES and a couple of issues that I feel are commonly misunderstood. This post has been inspired by things that I have heard at academic conferences and things that I have read in both academic and non-academic literature. I also thought that I would share a couple of insights about conventional CAES which have been passed down to me.

### A couple of notes about conventional CAES

Conventional CAES is an energy storage technology that has been around for several decades. It is interesting because although there are two plants currently functional and in existence, no new plant has been built in the last 20 years, despite the fact that both of the existing plants remain open and continue to function economically. This can probably be attributed to high CAPEX costs for CAES and other cheaper generation technologies which represent similar or better investments, added with an uncertainty of how to class CAES and view its efficiency.

Figure 1: The convential diabatic CAES system with a  recuperator. Natural gas is mixed with the compressed air in the generation unit.

Calculating the efficiency of CAES facilities is perhaps not as straightforward as it first seems. The McIntosh CAES plant uses 1 kWh of natural gas and 0.69 kWh of electricity to produce 1 kWh of peak electricity. The energy efficiency in terms of energy-output/energy-input is then around 59%, i.e. quite low for an energy storage technology. However, if instead you consider that the efficiency of a conventional thermal gas generator is around 40%, you would only ever get 0.4 kWh of electricity out of the 1 kWh of gas used in the CAES plant. This makes the efficiency look much better, as now it effectively appears as though you put 0.69 kWh + 0.4 kWh = 1.09 kWh of electricity in and you get 1 kWh of electricity out, giving an efficiency of 92%. Conversely, another argument would be that the 1 kWh of electricity required 2.5 kWh of gas to generate, and hence the energy input is 3.5 kWh of gas to produce 1 kWh of electricity, giving a much poorer efficiency of 29%.

The point of all this is that the “efficiency” values often quoted for CAES must be treated with caution and are generally not comparable with other storage technologies which input and output electricity only, as CAES plants are NEITHER purely energy storage NOR thermal generation, but in reality they represent a mix of both. I haven’t quite decided how to interpret this myself except that when considering CAES as an energy storage option, it is more important to consider from what source the electricity used in charging comes from than other energy storage technologies. For example, using CAES in the context where it would mainly have an electricity-from-renewable input could be regarded as boosting the efficiency of gas generation and hence a good thing under these circumstances, whereas using CAES as a way to store fossil fuel generated electricity would seem like a bad idea. I don’t fully endorse this last statement, rather I’m just using it as an illustration…

Keep an eye on the blog for part 2.