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| Fig. 1: Energy stored by different storage materials, using a temperature difference of 100 °C for the sensible heat calculation. For comparison, a typical reported specific energy density for a Li-ion battery is included. (Image Source: N. Lutz) |
Residential and commercial buildings accounted for 36.9% of total U.S. energy consumption in 2023. [1] Nearly half of global building energy consumption is used for heating, with building heating accounting for 10% of global emissions in 2021. Of this building heating, over 40% was generated through burning gas in on-site gas furnaces and around 10% through heat pumps in 2021. [2] Heat pumps use electricity to transfer heat from a cooler environment (outdoors) to a warmer environment (indoors). If the inputted electricity comes from renewable sources, heat pumps greatly reduce the carbon emissions of building heating. Therefore, to reduce global emissions, heat pumps are forecasted to contribute 25% of building heating by 2030 under the IEA's Announced Pledges Scenario. [2]
Thermal energy storage (TES) can help in this transition to heating buildings with renewable energy in several ways, a few of which are summarized in Table 1. First, TES can help shift electricity consumption from peak demand hours, or load shift. At the building scale, during an off-peak period, a heat pump can convert electricity to heat, and the heat can be transferred to a material and stored as thermal energy until the building needs heating. On the grid scale, when excess electricity is available from renewables, electricity can be converted into thermal energy. Alternatively, industrial waste heat can be converted to thermal energy. When needed, the thermal energy can then be used directly for heating in industrial processes or district heating or can be partially converted back to electricity by a heat engine for general use, including by buildings. Beyond load shifting, TES can allow for seasonal storage, reducing the amount of electricity used for heating and cooling each year. Seasonal storage has been used since ancient times, including before 300 BC in China, in the form of ice harvested in the winter and stored in insulated materials for use in the summer. [3]
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| Table 1: General thermal energy storage uses. |
There are three main types of TES: sensible, latent, and thermochemical. Sensible heat storage is the simplest and most common. Heat is added to a material, causing its temperature to rise, without the material undergoing a phase transformation. Energy can then later be extracted from the material in the form of heat or converted to electricity through a heat engine. A desirable sensible storage material has a high heat capacity, meaning it can absorb a lot of heat per increase in temperature, and is cheap and abundant. Water satisfies these conditions and is thus commonly used in low-temperature systems below its ambient boiling point of 100°C. Due to their higher boiling points, molten salts are common in high-temperature systems, including in concentrating solar power applications. [4] Sand is also used in some systems due to its abundance and high thermal stability. [5]
Alternatively, in latent heat storage, heat is stored and extracted via phase change of a storage material. During phase change, added heat goes into changing the material's phase rather than raising the temperature. Common latent heat storage materials include polymers, salts, waxes, and metal alloys. Materials are chosen that undergo phase change in the required temperature range of the given application. For on-site building use, a material that changes phase near room temperature is desired. Another less developed form of TES is thermochemical heat storage, in which energy is used to drive an endothermic (heat-absorbing) reaction to take place. To later extract heat from the material, the reaction is allowed to proceed in the opposite, exothermic (heat-releasing) direction. The released heat during the chemical reaction is the heat, or enthalpy, of reaction.
The heat transferred, and thus the thermal energy stored, by each of these forms of TES at a constant pressure can be calculated using the equations
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(1) | |||
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(2) | |||
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(3) |
where cp is specific heat at constant pressure, Δhphase change is the the phase transition latent heat, and Δhreaction is the enthalpy change per mass of a reaction taking place. The equations were written using the condition of constant pressure, the first law of thermodynamics, the definition of enthalpy, and the assumption that only expansion and compression work can be done. Eq. (1) assumes that cp is approximately constant within the temperature range used for sensible storage. For greater accuracy, an integral accounting for the temperature dependence of cp can be used or the H-H°(Tr) values from NIST Janaf can be directly used. [6] Values for typical storage materials are listed in Table 2.
Using Table 2 and Eq. (1), the thermal energy stored by heating water, molten salt, and sand solely composed of quartz (SiO2) from 0 to 100 °C are around 418, 742, and 156 kJ/kg, respectively. These results are shown in Fig. 1, in which a typical reported practical energy density for a Li-ion battery is also included for comparison. Battery literature varies in which components of the battery are considered active mass in specific energy density calculations, but 200 Wh/kg, or 720 kJ/kg, is within the range of values commonly reported. The energy stored in a Li-ion battery is higher quality energy than in TES, though, due to the limitation imposed by the second law of thermodynamics on converting heat to work. That is, converting thermal energy to electricity results in much more waste heat than converting chemical energy to electricity. As a result, thermal energy storage options are often better suited for heating applications than electricity generation.
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| Table 2: Thermodynamic data to calculate the energy stored by several materials using Eqs. (1)-(3). The energy stored in the Fe(OH)2 system is calculated as described below, the specific heats of water, SiO2, and Fe(OH)2 are extracted from NIST Janaf at 298.15°K, and the remaining data is taken from Alva et al.. [4,6] |
To get an estimate of the energy stored in a system utilizing the reaction Fe(OH) 2 → FeO + H2O, let's consider a closed system that follows the cycle depicted in Fig. 2. In state 1, we begin with iron hydroxide in air at an ambient temperature of 298.15°K. If the air were completely dry, water would escape from the iron hydroxide to become water vapor at any temperature. Therefore, we assume that the air has enough water such that iron hydroxide is stable and decomposes a negligible amount at 298.15°K. In this system, for Fe(OH)2(cr) → FeO(cr) + H2O(g) to be thermodynamically favorable, the Gibbs of reaction, as given by
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(4) |
must be negative. Using NIST Janaf values, the Gibbs free energy of reaction is 11.96 kJ per mol of iron hydroxide at 298.15°K and -4.289 kJ/mol at 400°K. [6] By interpolation, the reaction begins to be favorable around 373°K. The heat of reaction is 670 kJ/kg iron hydroxide at 298.15°K and 653 kJ/kg at 400°K, using
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(5) |
By interpolation, 643 kJ/kg is the heat of reaction at the thermodynamically favorable temperature, 373°K. Therefore, to get the iron hydroxide to fully decompose to FeO and H2O, we must raise the temperature of the system to 373°K. During the process of slowly increasing the temperature of the system, water gradually leaves iron hydroxide in the form of vapor, until all water has left at 373°K. We then have FeO + H2O at 373°K in state 2. Because enthalpy is a state function, the heat absorbed during this process can be calculated following the gray path in Fig. 2. For step 1a, Equation 1 is used with an average cp for Fe(OH)2 taken from NIST Janaf. The sensible heat of the air is not calculated. For step 1b, Eq. 5 is used as explained above to get 643 kJ/kg. The change in Gibbs due to the mixing of water vapor and dry air components is neglected here for simplicity.
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| Fig. 2: Thermodynamic cycle considered for the Fe(OH)2 thermochemical system. The gray box shown is an intermediate state used during calculations. Arrows are labeled with the calculated heats absorbed (positive) or released (negative) per kg of iron hydroxide in the system. (Image Source: N. Lutz) |
The components are then separated in a process which is assumed to involve no energy transfer with the environment. Next, the separated components are allowed to equilibrate to ambient temperature. The heat released from cooling FeO is calculated with Eq. 1 and an average cp value from NIST Janaf. In the container with water vapor and air, as the temperature decreases at ambient pressure, more and more water vapor condenses. At ambient temperature, it is assumed that all the water vapor has become liquid; the water in the vapor phase is assumed to be negligible. This process releases over 500 kJ/kg of heat. The air also cools during this process, releasing the same amount of heat absorbed by the air in step 1a. The components are then put into contact and spontaneously react, due to Δgreaction being negative. The iron oxide is thus hydrated and again reaches state 1, releasing 176 kJ/kg by Eq. 5. We can now check the validity of the cycle and calculations using the first law of thermodynamics. The change in energy of any cycle must be zero. Assuming that the cycle has no work transfer, the change in energy is the sum of the heat transfer terms. Summing the numbers in Fig. 2 yields 2 kJ/kg iron hydroxide, very close to zero, confirming the calculations. The value is presumably not exactly zero due to rounding errors.
If just the heat released during mixing and hydration is utilized, only 24% of the energy stored is utilized, with 76% released as waste heat. If the sensible heat of the air is included, even less of the energy stored is utilized. Therefore, this system likely only makes practical sense if the energy released during equilibration of the separated components, particularly the water, is utilized. In Table 1 and Fig. 1, the energy storage value listed is thus considered to be the energy absorbed during dehydration (and later extracted during equilibration and hydration). However, the process discussed is not a very good energy storage system since equilibration occurs immediately after the charging process and releases over 76% of the energy stored. If practical, it would be advantageous to instead design the system and cycle such that the water vapor does not condense, through temperature and pressure control and insulation. The system would then release 655 kJ/kg during mixing and hydration at 298°K and ambient pressure.
Kinetics must also be considered when determining the reactor temperature and pressure. If the system is mass transfer limited, not all of the material will react, and the actual energy stored per mass will be lower than the theoretical thermodynamic value. [7] Nevertheless, the simplified thermodynamics analysis above gives us an idea of the theoretical amount of energy stored in a typical thermochemical storage material.
We saw in the calculations above that common sensible storage materials need relatively large temperature differences to store as much specific energy as thermochemical materials. However, sensible storage is particularly advantageous in that it can use extremely abundant and safe materials like water and sand, in contrast to latent and thermochemical storage which are more limited by available materials. One major disadvantage of sensible heat storage is that heat is lost to the environment over time during storage, due to insulation not being perfect. Heat can also be lost in latent heat systems in storage conditions that are thermodynamically favorable for phase change. In contrast, in thermochemical storage, if the reacting chemical components are kept separate during storage, the molecules will not react to release heat, no matter the storage conditions. However, we saw in the example case above that allowing water vapor to condense during storage releases a lot of energy. Nonetheless, thermochemical heat storage is often thought to be promising for long-term storage, including seasonal storage.
But thermochemical heat storage still suffers from degradation of storage material over cycling and from kinetic limitations. To increase the rate of the dehydration reaction used with materials such as iron oxide, particles with higher surface area, doping with other components, and molecular sieves are being researched. [4,8] While laboratory-scale demos in universities, national laboratories, and startups have proven successful, thermochemical heat storage requires more research and innovation for large-scale commercialization to be feasible.
© Naomi Lutz. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] "Monthly Energy Review October 2024," U.S. Energy Information Administration, DOE/EIA-0025(2024/10), October 2024.
[2] "The Future of Heat Pumps," International Energy Agency, December 2022.
[3] H. Li, "Study on the Ice Cellar Ruins in Early Ancient China," Athena Trans. Soc. Sci. Humanit. 2, 81 (2022).
[4] G. Alva, Y. Lin, and G. Fang, "An Overview of Thermal Energy Storage Systems," Energy 144, 341 (2018).
[5] O. A. Radwan and J. D. Humphrey, "Uses of Sands in Solar Thermal Technologies," Sol. Energy Mater. Sol. Cells 261, 112533 (2023).
[6] M. Chase, Jr. "NIST-JANAF Thermochemical Tables, 4th Ed.," J. Phys. Chem. Ref. Data, Monograph 9 (American Institute of Physics, 1998).
[7] D. Aydin, S. Casey, and S. Riffat, "The Latest Advancements on Thermochemical Heat Storage Systems," Renew. Sustain. Energy Rev. 41, 356 (2015).
[8] X. Zhang et al., "Heat Storage Performance Analysis of ZMS-Porous Media/CaCl2/MgSO4 Composite Thermochemical Heat Storage Materials," Sol. Energy Mater. Sol. Cells 230, 111246 (2021).