In practice neither of these perfect thermodynamic cycles are obtainable, as some heat losses are unavoidable.
A highly efficient arrangement, which fits neatly into none of the above categories, uses high, medium and low pressure pistons in series, with each stage followed by an airblast venturi that draws ambient air (or seawater as in early compressed air torpedo designs) over an air-to-air (or air-to-seawater) heat exchanger between each expansion stage. This warms the exhaust of the preceding stage and admits this preheated air to the following stage. This practice was widely practiced on various compressed air vehicles such as H. K. Porter, Inc in mining locomotives ( see CHARLES HODGES AND THE PORTER COMPOUND AIR LOCOMOTIVES ) and trams. .
Here the heat of compression is effectively stored in the atmosphere (or sea) and returned later on, but interestingly it is not not the "same" heat.
Air is stored in mass quantity in underground in a cavern created by solution mining (salt is dissolved away) or an abandoned mine. Plants are designed to operate on a daily cycle, charging at night and discharging during the day.
The ideal gas law, for an isothermal process is:
This amounts to about 2.271 kJ at 0 degrees Celsius (273.15 kelvin) or 2.478 kJ at 25 °C (298 K), per mole.
One mole of gas molecules at standard temperature and pressure (0 °C, 0.1 MPa), occupies 22.4 liters and there are 1000 liters in 1 m³. So there are about moles of gas molecules in 1 m³ and we get 101 kJ at 0 °C or 111 kJ at 25 °C per m³ of gas (at 0.1 MPa = aprox. atmospheric pressure):
An isothermal process is thermodynamically reversible, so to the extent the processes are isothermal, the efficiency of compressed air storage will approach 100%. The equation above represents the maximum energy that can be stored. In practice, the process will not be perfectly isothermal and the compressors and motors will have heat-related energy losses.
When gas is compressed adiabatically, some of the compression work goes into heating the gas. If this heat is then lost to the surroundings, and assuming the same quantity of heat is not added back to the gas upon expansion, the energy storage efficiency will be reduced. Energy storage systems often use large natural underground caverns. This is the preferred system design, due to the very large gas volume, and thus the large quantity of energy that can be stored with only a small change in pressure. The cavern space can be compressed adiabatically and the resulting temperature change and heat losses are small.
Compressing air heats it up and expanding it cools it down. Therefore practical air engines require heat exchangers in order to avoid excessively high or low temperatures and even so don't reach ideal constant temperature conditions. Nevertheless it is useful to describe the maximum energy storable using the isothermal case, which works out to about 110 kJ/m3-N at 24°Celsius. One m3-N is one cubic meter of gas volume at normal, i.e. atmospheric pressure, conditions. Thus if 1.0 m3 of ambient air is very slowly compressed into a 5-liter bottle at 200 bar, the potential energy stored is 583 kJ (or 0.16 kWh). A highly efficient air motor could transfer this into kinetic energy if it runs very slowly and manages to expand the air from its initial 200 bar pressure completely down to 1 bar (bottle completely "empty" at ambient pressure). Achieving high efficiency is a technical challenge both due to nonlinear energy storage and the thermodynamic considerations. If the bottle above is emptied down to 10 bar, the energy extractable is about 330 kJ at the motor shaft. The efficiency of isothermal compressed gas storage is theoretically 100% but in practice the process is not isothermal and the two engines (compressor and motor) have additional types of losses.
A standard 200 bar 5 liter steel bottle has a mass of 7.5 kg, a superior one, 5 kg. Bottles reinforced with, or built from, high-tensile fibers such as carbon-fiber or kevlar can be below 2 kg in this size, consistent with the legal safety codes. 1 m3 of air contained inside such a full bottle has a mass of 1.225 kg (at 0°C). Thus, theoretical energy densities are from roughly 70 kJ/kg at the motor shaft for a plain steel bottle to 180 kJ/kg at the motor shaft for an advanced fiber-wound one, whereas practical achievable energy densities for the same containers would be from 40 kJ/kg to 100 kJ/kg. Comparing to the data given for rechargeable batteries, this makes the advanced fiber-reinforced bottle example comparable to the lead-acid battery in terms of energy density and advanced battery systems are several times better. Batteries also provide nearly constant voltage over their entire charge level, whereas the pressure of compressed air storage varies greatly with charge level. It is technically challenging to design air engines to maintain high efficiency and sufficient power over such a wide range of pressures. Compressed air can transfer power at very high rates, which is a principal objective of transportation prime-movers, for acceleration and deceleration; particularly for hybrid vehicles.
Advantages of compressed air over electric storage are the longer lifetime of pressure vessels compared to batteries and the lower toxicity of the materials used. Costs are thus potentially lower, however advanced pressure vessels are costly to develop and safety-test and at present are more expensive than mass-produced batteries.
As with electric technology, it must be stressed that compressed air energy storage depends on external energy sources and overall consumption can only be as "clean" as these.
Many people have been working on the idea of compressed air vehicles with renewed interest since the 1990s energy crisis.
A compressed air engine uses the expansion of compressed air to drive the pistons of an engine, an axle, or to drive a turbine.
Sometimes efficiency is increased by the following methods:
A highly efficient arrangement uses high, medium and low pressure pistons in series, with each stage followed by an airblast venturi that draws ambient air over an air-to-air heat exchanger between each expansion stage. This warms the exhaust of the preceding stage and admits this preheated air to the following stage..
The only exhaust gas from each stage is cold air which can be as cold as (−15 °C), this may also be used for air conditioning in a car.
Additional heat can be supplied by burning fuel as in 1904 for Whitehead's torpedoes. This improves the range and speed available for a given tank volume at the cost of the additional fuel.
As an alternative to pistons or turbines, the Quasiturbine is also capable of running on compressed air, and is thus also a compressed air engine.
Several companies claim to have been developing compressed air cars for public use, since about 1990, but none are available yet. Typically the main advantages are claimed to be: no roadside emissions, low cost technology, engine uses food oil for lubrication, and integrated air conditioning.
The tanks may be refilled at a service station (using volume transfer), or in a few hours at home or in parking lots plugging the car into the electric grid via an on-board compressor. The cost of driving such car is typically projected to be around €0.75 per 100 km, with a complete refill at the "tank-station" at about US$3.
In addition, Compressed air engines can be used in conjunction with an electric battery. The compressed air engine, drawing its energy from compressed air tanks, recharge the electric battery. This system (called a Pne-PHEV or Pneumatic Plug-in Hybrid Electric Vehicle-system) and was being promoted by the apparently defunct Energine.
The operating duration of the McIntosh plant is 24 hours, with the extended operation being achieved through the combined burning of a natural gas/compressed air mix.
Additional facilities are under development in Norton, Ohio and Iowa Stored Energy Park (ISEP). This 2700 MW Norton project has been started in 2001, but in early 2007 construction had not actually begun.
Increased efficiency is expected at ISEP, due to the use of aquifer storage rather than cavern storage. The displacement of water in the aquifer results in regulation of the air pressure by the constant hydrostatic pressure of the water. A spokesperson for ISEP claims "you can optimize your equipment for better efficiency if you have a constant pressure." It is planned to have 75 - 150 MW of capacity.
One of the biggest problems with a large penetration of Wind power in power generation applications, according to Paul – Frederik Bach who ran the Western Denmark Power grid for a number of years is the sudden curtailment of wind farm output over a wide area as storms sweep over.
Hence a means of prolonging the wind turbine output whilst fossil stations on warming ramp up output or load is shed is needed. One possibility is sunken caissons, which could be integrated with the floating support structure for the wind turbine which the Norwegians are already developing. Whilst perfectly feasible, using existing technology, whether or not this is worthwhile is another matter.
Energy storage in sunken caissons
One possibility is to sink the type of caisson used in the Normandy Mulberry Harbours of which - about 115 of these huge structures were built in about 9 months during WW 2 http://www.everything2.org/index.pl?node_id=1306625
They were initially sunk off Folkestone to hide them from enemy observation, and then re floated prior to D Day using compressed air then towed into position and sunk.
In theory similar structures could be constructed and floated into much deeper water, sunk and anchored to the bottom using rock anchors. A flexible air pipe could be brought to the surface, to say a wind turbine base, housing an air compressor and an air turbine generator set. By simply pumping compressed air down to the caisson, water would be ejected lowering the internal water surface to the bottom of the caissons. To recover the stored energy the air valve would be opened and the energy recovered via the air turbine as the water re enters and air is forced out. Note that because the container is open bottomed, there is no internal or external pressure force - both inside and outside the caisson will be at near identical pressures at all times. However there will be massive floatation forces to be restrained but these present no real engineering difficulty. The flexible pipe would simply be a solid steel pipe which over 100 m can cope with significant bending - the Pluto pipelines, to bring fuel to allied troops after D Day were basically a 3 inch dia steel pipe unreeled from a gigantic 10 m diameter cotton real - 17 were laid in a few days across the Channel after D Day just by being unreeled (These Pluto pipes are the basis for modern submerged cables ). The deeper the water, the more energy can be stored per caisson. Since the compressed air will be at high pressure (10 bar at 100m depth) a lower cost air turbine can be used (compared to a low pressure one). The air pressure will be fairly constant as well, meaning an efficient air motor configuration can be chosen.
Note 90% the energy will be in the displaced water only 10% in the compressed air itself.
The calculation is as follows:
Assume the top of the caisson is 100 m below the surface.
A 1 m sq surface will have a water pressure of 100 m3 above it = 100 x 1000kg = 10e5 kg = 10e6 newtons.
Force this surface up by 1 m and you perform 10e6 Newton metres of work = 1.0 M Joules = 1.0 MJ
There are 3.6 MJ / kWh, so 1.0 MJ = 10MJ/3.6MJ = 0.277 kWh.
Scale that up by the volume and you get 0.277 x 20 x 20 x 70 = 7777 kWh = 7.7 MWh
Assuming an in out efficiency of say 50%,
Then the energy available as electricity is probably say 3.5 MWh = 3.5 MW for 1.0 hours.
However, since he average output of a 3.5 MW turbine is only about 1.2 MW, the caisson wold give the average output for 3 hours, or if tailed off linearly, 6 hours, which is enough time to start a coal station from warm.
On the face of it, it would work to have one of these per 3 MW floating wind turbine, and this would store sufficient energy to allow the wind turbine output to be prolonged sufficiently for thermal plants to start up, and or loads to be shed. Whether it is an economically worthwhile proposition is another matter. However considering that the Norwegians are planning constructing floating wind turbines for the North Sea, it would seem to be a logical place to put them, ie as integrated into part of the floatation structure.
An alternative to compressed air to force water from the caisson could be a water pump and turbine, but this would have to be located 100m down which may pose maintenance problems - This would be more efficient than the compressed air system and probably cheaper.
Sea bed anchored energy bags are being researched as solutions to the problem of storing energy generated by renewable sources at The University of Nottingham.
Academics have received €1.4m (£1.1m) in funding from E.ON, one of Europe's leading power and gas companies, to develop a new generation of and undersea storage bags that will collect energy in the form of compressed air.
Phoenix: The primary breakwater was to be provided by concrete caissons. These were to be from 25 to 60 feet high and 174 to 204 feet long. The displacement was up to 6,000 tons. http://www.hksw.org/despatches_107_1_a.htm
115 of these were built in about 9 months:
Pluto – pipeline under the ocean
http://en.wikipedia.org/wiki/Operation_Pluto After full-scale testing of a 45 nautical mile (83 km) HAIS pipe between Swansea in Wales and Watermouth in North Devon, the first line to France was laid on August 12, 1944, over the 70 nautical miles (130 km) from the Isle of Wight through the English Channel to Cherbourg. A further HAIS pipe and two HAMELs followed. As the fighting moved closer to Germany, 17 other lines (11 HAIS and 6 HAMEL) were laid from Dungeness to Ambleteuse in the Pas-de-Calais.
Note the 3 inch pipe bent around the 10 m dia drum Pluto //http://news.bbc.co.uk/1/shared/spl/hi/picture_gallery/04/uk_d_day_inventions/html/6.stm//
Pluto was Pipeline Under The Ocean, vital arteries that pumped millions of gallons of fuel from Britain to Allied forces in France. Two lines were built, codenamed Dumbo and Bambi. Pumping stations were disguised as ice cream shops, garages and bungalows. The sea bed cables were laid by 30ft diameter Conun drums pulled by tugs. This is one of more than 1,000 secret photographs of the pipeline operation newly released and available to be viewed free at The National Archives in Kew.
Concrete is about £300 per tonne in place. http://www.hksw.org/despatches_107_1_a.htm says the displacement was 6000 tonnes so that means to make them would cost about £1.8m. (But most of that cost could be paid for as part of the flotation structure of an off shore mill).
A fully installed gas turbine generator set of 3.5 MW is probably say £400/kw but that includes the combustor and compressor bit, so assume say £300/kW ie the air turbine generator might be about £1m. The compressor say the same again. So probably do each one costs £5m, but a lot of that cost would be born anyway by the floating turbine.
The going rate estimate for an offshore turbine is £3000 per kW so you would expect to pay £10m for the whole turbine anyway.
Of course the Mulberry caisson is an arbitrary choice simply because we know we can build them in a hurry. Obviously you would use a more economical shape - probably spherical. That would bring costs down.
Only detailed modelling can reveal if this sort of thing is worth while. Fun idea though.