The Physics of Energy, page 165
Example 37.1 Dinorwig Pumped Hydro Facility in Wales, UK
When Great Britain anticipated deploying large amounts of nuclear electric power generation in the 1970s, several pumped hydro facilities were constructed to provide rapidly dispatchable peak power, which nuclear plants are unable to supply. The Dinorwig Power Station in North Wales, completed in 1983, combined Llyn Peris, a natural lake with its surface at approximately 100 m, with a reservoir created by damming the outlet of an abandoned quarry above the lake. The surface of the resulting Marchlyn Mawr Reservoir is at roughly 635 m. Its capacity is m3. Each of the six turbines at Dinorwig is capable of generating up to 288 MWe or pumping at 275 MW. The turbines can go from standstill to full load in less than two minutes. The round-trip efficiency of the pumped hydro storage is 75%.
What is the flow rate from the reservoir at maximum power? The total storage capacity is stated to be 9 GWh (32 TJ). To what fraction of the reservoir volume does this capacity correspond?
Assuming that the efficiency of generation and production are equal, electricity is generated at efficiency. The required flow rate of water would be
Ignoring the drop in the level of the reservoir, we estimate the volume of water required to produce a total energy of 9 GWhe to be
which is 77% of the reservoir’s capacity.
The discovery of the North Sea gas fields and concerns about nuclear safety derailed the UK’s anticipated switch to nuclear power. Nevertheless, the Dinorwig plant is still used to meet sudden surges in electricity demand. According to Wikipedia, one such scenario occurs during advertising breaks in popular television shows when British consumers make tea and demand surges by as much as 2.8 GW. Assuming 2–3 kW per kettle, one can estimate the number of viewing households to be of order .
(Image credit: RWE Power AG)
Consider first the isothermal idealization, in the approximation that air is an ideal gas, so . The work done to isothermally compress air initially at pressure and volume to a pressure and a volume is, from eq. (10.4),
(37.1)
In a CAES storage facility, typically the air is kept at a minimum pressure after discharge. Additional air that is originally at pressure is pumped in from the outside until finally the storage facility volume V is filled with air at a maximum pressure . The total work done is the difference between the work required to pressurize all the gas from to and the work that would have already been done pressurizing the initial volume of gas to ,
(37.2)
The third term in this expression comes from the work supplied by the outside pressure in the compression process, . Thermal energy equal to is expelled into the surrounding environment during compression, and this is the maximum work available via subsequent isothermal expansion of the stored air. A particular CAES facility is analyzed in Example 37.2. For the parameters of that facility ( atm, atm), the isothermal work is ~130 kJ/kg, but due to inefficiencies only a fraction of this energy can be extracted in the re-expansion process.
For an idealized adiabatic system, a similar analysis (Problem 37.5) can be used to compute the total energy stored. The energy stored as internal energy of the gas in the adiabatic case is less than the energy stored in the idealized isothermal case for an equal storage volume and maximum pressure . This can be seen from the fact that at each stage in the compression, as the pressure increases by a given amount, the change in the volume dV is smaller in the adiabatic case (since the temperature increases, increasing the pressure more rapidly with the change in volume). Thus, compression to a final pressure gives a smaller integral in the adiabatic case. Furthermore, adiabatic compression of air to high pressure gives rise to high temperatures. Compressing a volume of air from pressure to raises the temperature by a factor of , where is the adiabatic index of air (eq. (10.9)). For and K, this gives K; this rise in temperature makes pure adiabatic CAES impractical in most storage environments (Problem 37.6).
Existing compressed air energy storage facilities use mechanical devices known as intercoolers to expel thermal energy from the gas as it is compressed. The net result is that the compressed air is stored close to the ambient temperature. For a given V, , and , the stored energy is the same as the isothermal case (37.2). The energy used by the intercoolers, however, must be taken into account when determining the complete efficiency of round-trip storage. Sometimes this form of irreversible isothermal compression is referred to as diabatic compression, to contrast with adiabatic compression in which no heat transfer takes place.
Because it was computed assuming reversible isothermal compression, (37.2) expresses the exergy (§36.4) of a volume V of gas at temperature and pressure minus the exergy of the same volume of gas at the same temperature and pressure (Problem 37.7). Note that there is no extra internal energy stored in the compressed air in the chamber. By virtue of its exergy, however, the compressed air can still be used to produce useful work. If the gas were expanded reversibly and isothermally back to the initial conditions, energy equal to would be available for conversion to mechanical or electrical energy. Unfortunately, it is impractical to extract all the available work by allowing the gas to expand isothermally and reversibly, while absorbing heat from the surrounding rock. If, instead, the gas were allowed to expand adiabatically from back to a certain amount of work could be extracted (see Example 37.2 and Problem 37.5), but the gas would cool far below . Further work could, in principle, be extracted by running a heat engine between the ambient temperature and the temperature of the adiabatically expanded gas. Indeed, if both the adiabatic expansion and the heat engine were run reversibly, the full amount of available work could be extracted from the compressed gas. Such a complicated reversible process is also impractical. In practice, the compressed gas is used as input to a natural gas powered turbine, thereby increasing the efficiency of the turbine (see Example 37.2), but capturing only a fraction of the exergy stored in the compressed gas.
Compressed Air Energy Storage (CAES)
Compressed air energy storage is often discussed as a potential mechanism for grid-scale energy storage. Although energy densities achieved in principle can be greater than 100 kJ/kg, this energy is difficult to extract with high efficiency due to the need for rapid and efficient heat exchange. Existing systems use the exergy of compressed air to augment the output of gas turbines, providing only a modest fraction of the stored energy as net output energy.
As of 2016, two utility-scale diabatic CAES plants were in operation: a 290 MW plant in Huntorf, Germany built in 1978, and a 110 MW plant in McIntosh, Alabama built in 1991 (see Example 37.2). Some smaller (1–2 MW) systems are also operating using dedicated manufactured storage vessels. A number of other plants are currently in various stages of design and development.
Example 37.2 McIntosh Compressed Air Energy Storage Plant
In McIntosh, Alabama, a solution-mined salt cavern with volume 270 000 m3 is used for compressed air energy storage. Initially the cavern is filled with air at 45 atm. Additional air is pumped in until the pressurereaches a maximum of 75 atm.
In the McIntosh plant, the heat from compression is jettisoned to the external environment. After compression, eq. (37.2) tells us that approximately 3.4 TJ (130 kJ/kg) is stored in the compressed gas. Because the compression is diabatic rather than truly isothermal, however, a substantially larger amount of energy is actually needed to compress the gas into the cavern and expel excess heat to the environment.
The total exergy of 3.4 TJ could only be extracted if the gas were expanded isothermally, which is not practical. Simply allowing the air to expand adiabatically, leaving the original volume of air in the cavernat 45 atm, and allowing the remaining air to expand to 1 atm would do 1.4 TJ of work (Problem 37.8),recapturing about 41% of the energy available in the stored gas. This would not use all the exergy originally stored in the reservoir, since the expanded air would be very cold. (The air expelled to the environment would beat 87 K and the air left in the mine would be at 260 K.) One could, for example, operate a heat engine between the ambient temperature and the cold air and thereby extract more work. In fact if the adiabatic expansion were performed reversibly and a reversible Carnot engine were used to extract further work, all of the 3.4 TJ could be extracted from the stored gas. This is not feasible in practice, however.
To extract useful energy from the compressed air at the McIntosh facility, rather than directly using the workdone by expansion, the compressed air is used as input to a natural gas powered turbine. As explained in §13.5.1,in a standard natural gas power plant, much of the combustion energy is used to compress the gas–air mixture.Thus, using the compressed air from CAES increases the efficiency of a natural gas plant. According to [287], at the McIntosh plant, 0.82 MJ of energy used for compression combine with 1.2 MJ of energy from natural gasto provide 1 MJ of output energy. The same amount of natural gas used to fuel a state-of-the-art CCGT power plant at 60% efficiency would produce 0.72 MJ of electric energy. The McIntosh plant can thus use 0.82 MJof excess wind or solar energy to enhance the energy available from natural gas by 0.28 MJ. This represents a round-trip storage efficiency. A more detailed exergy-based efficiency analysis quotes 36% cycle efficiency for the McIntosh plant, 29% cycle efficiency for the Hundorf plant, and estimates over 40% for a more modern diabatic design proposal [285].
In order to increase the efficiency of CAES beyond what is possible in existing diabatic plants, in recent years there has been increased interest in advanced-adiabatic CAES (AA-CAES) systems, which are designed to remove and store the thermal energy produced when air is compressed adiabatically and then release this energy when the air is expanded. Several systems of this type are currently in design/development phases. In Germany, a project known as ADELE plans to store the thermal energy of the compressed gas in a large heat storage facility containing stone or ceramic bricks with a high heat capacity. Another possibility is to use water – actually a fine, dense mist – to absorb the heat of compression, forming steam which is then stored and later extracted when it is needed to reheat the air during expansion. An exergy-based analysis of AA-CAES [286] suggests that a cycle efficiency of 50% or more may be possible with AA-CAES, though such systems will be somewhat complicated and may be more expensive than underground pumped hydro facilities of comparable size, which are capable of reaching cycle efficiencies of 75% or more.
37.2.3 Thermal Storage
Thermal energy is much easier to store than mechanical or electromagnetic energy. It may be impractical, however, to store electrical energy by converting it to thermal energy, since the 2nd law penalty that must be paid when converting back to electrical energy would make the storage quite inefficient. Thus thermal energy storage is not a good option for storing the output of solar PV arrays or wind farms. On the other hand, as discussed in §24, solar thermal energy (STE) collected for conversion to electrical power can be stored in thermal form for hours or days before conversion.
Thermal Energy Storage
Storing energy in thermal form makes most sense when the energy originates as thermal energy. For solar thermal power plants, thermal storage is an effective and efficient way of storing energy for days or weeks to match the intermittent supply to variations in demand. Molten salt mixtures have been developed with high heat capacity, low cost, and minimal toxicity, that can store solar energy for days with small losses before it is used to power generators.
A variety of materials have been proposed for storage of solar thermal energy at STE plants. Some existing plants use a molten salt composed of a binary mixture of sodium nitrate (NaNO3) and potassium nitrate (KNO3) that can be used effectively both for absorption of solar thermal energy and storage (Figure 37.4). This material is relatively inexpensive and non-toxic. Its heat capacity is roughly 1500 J/kg K. The binary nitrate salt has a melting point in the range 130–230, depending upon the precise ratio of nitrate salts used. It can be heated by solar energy to a temperature in the range of 400–550, and can be stored in insulated tanks at this temperature for several days with limited degradation. Thermal energy from the salt can then be transferred to a working fluid that drives a turbine, leaving the salt molten at a temperature around 250–300. The energy density of molten salt storage between these temperatures is thus on the order of 300–400 kJ/kg. Research at Sandia National Laboratory [288] and elsewhere on a variety of materials suggests that a ternary mixture of nitrate salts may provide an even better solar thermal medium, with a lower melting point closer to 100, and potentially accessible higher temperatures approaching 600. This would improve the efficiency and storage potential of concentrated solar power systems.
Figure 37.3 Sketch of the proposed ADELE AA-CAES facility. Thermal energy generated when air is compressed is held in a heat storage facility and used to reheat the air when it is expanded and used to drive the turbine. (Credit: RWE Power AG)
Figure 37.4 Molten salt storage tanks at the Andasol 1 power plant in Spain store thermal energy acquired during the day for power generation at night. (Credit: Solar Millenium)
Other options that have been suggested for solar thermal energy storage include solid materials such as graphite. Graphite has a specific heat capacity that is about 700 J/kg K at room temperature, and increases at higher temperatures (see Problem 5.9). Graphite can be heated safely to temperatures of 1800 or higher, providing an energy storage capacity per unit mass of 1–2 MJ/kg. At least one prototype solar thermal plant that uses graphite blocks as a storage medium is under construction, and other storage media are also being investigated.
A variant of thermal energy storage known as pumped heat electricity storage (PHES) uses a heat pump to convert electricity into thermal energy that is stored at high temperature and then used to generate electricity when required [289]. If both the heat pump and the generator ran at their Carnot efficiency, the round-trip efficiency of PHES would be 100%. Temperature differences within the system, along with other irreversibilities, reduce the efficiency, but recent analyses suggest round-trip efficiencies as high as 65–70% could be obtained, making PHES systems potentially competitive with pumped hydro and exceeding existing CAES systems. A further variant known as pumped cryogenic electricity storage (PCES) uses a refrigeration cycle to create a store of exergy in a cold reservoir.
37.3Mobile Energy Storage
For mobile systems that use substantial amounts of energy, such as automobiles, airplanes, and laptop computers, energy density is a principal consideration. In particular, the energy stored per unit mass combined with functional mass limits provides a basic bound on the range of an electric automobile or use time of a laptop computer and limits air transport to the use of fossil fuels for the forseeable future.
Petroleum-derived fuels including gasoline, kerosene, and diesel fuel dominate vehicle applications because of their extremely high specific energy of 40–44 MJ/kg. Even at 25% engine efficiency, this gives an effective storage density of over 10 MJ/kg. For comparison, bulk energy storage, described in the previous section, based on physical properties such as air pressure or thermal energy storage provides energy storage densities on the order of 1 MJ/kg or less. Furthermore, energy stored in such systems is not easily converted to electrical or mechanical energy in vehicles or small mobile devices. Most portable energy storage systems use chemical energy sources, which have energy densities ranging from below 1 MJ/kg for batteries to above 100 MJ/kg for hydrogen. Nuclear and mass energy, of course, have higher energy density than chemical storage systems, and nuclear-powered submarines and ships are in regular use. Nuclear-powered automobiles and spaceships have also been designed but never put into use. For common applications, the complexity of nuclear power systems is too great for small-scale implementation. Thus, we focus in this chapter on chemical means of energy storage – batteries (§37.3.1), fuel cells, and hydrogen energy storage (§37.3.2, 37.3.3), and combustible materials (§37.3.4). One other possible approach to energy storage that may yield high enough energy densities for vehicular use is flywheel technology; this is discussed in the following section (§37.4.1).
Example 37.3 Molten Salt Energy Storage
A nitrate salt mixture with a density of kg/m3 and heat capacity of 1500 J/kg K, is raised to a storage temperature of 500, and used in a power cycle through which it is cooled to a temperature of 250. Assuming an average conversion efficiency of 33%, what volume of salt must be stored to produce 100 MW of power for 12 hours? The volumetric energy density is
The total thermal energy required is
