Thermal Energy Storage

Ben Reinhardt October 24, 2010

Submitted as coursework for Physics 240, Stanford University, Fall 2010

The technology of thermal energy storage is governed by two principles:

1. Sensible Heat Storage
2. Latent heat storage

Sensible heat results in a change in temperature. An identifying characteristic of sensible heat is the flow of heat from hot to cold by means of conduction, convection, or radiation. The governing equation for sensible heat is q = m Cp(T2-T1), where m is mass, Cp is specific heat at constant pressure, and T1 and T2 are the two temperatures before and after heating. [1] This type of heat storage is dependent on the temperature gradient and requires insulation to maintain the temperature gradient. [2]

Latent heat works by a different law. As heat is pumped into a material, the temperature does not change. Latent heat accumulates in a material before a phase change and can be defined as the energy necessary for a phase change. The equation for latent heat is q = m CpdT (s) + m L + m Cp dT, where L is the enthalpy of fusion and dT is the temperature difference. [1] The first term is the sensible heat of the solid phase, the second the latent heat of fusion, and the third the sensible heat of the liquid phase. Because of the latent heat, there is an advantage in thermal storage when using phase-change materials (PCMs).

The use of PCMs is a promising technology because it provides a way of storing heat from renewable sources such as the sun and waste heat from industrial processes (4). A PCM can handle much more heat at the same temperature than a constant state material. This is because of the latent heat term. As examined by Akiyama et al., a 53/40/7 wt% mixture of inorganic salts KNO3/NaNO2/NaNO3 exhibited a 239 kJ/kg difference between LHS and SHS heat storage at the composite's melting point. [1] In addition to the higher heat storage capacity, a PCM can also act as a constant temperature heat source; this is because it can gain and release heat while remaining in its phase change state. For this reason, a PCM can work permanently and experiences little degradation over time. [1]

Materials that are usually used as PCMs include organic paraffins and non-paraffins and inorganic salts and metals. [1] The most popular PCMs as of 2009 are organic paraffins, fatty acids, and hydrates. [1] They have been used to collect solar and industrial waste heat, however they all have melting temperatures under 200°C and are used for small scale heating rather than on the order of electricity generation. [1] At high temperatures (above 200°C), the PCMs used are inorganic salts, which have much lower thermal conductivities, making them less effective, constant heat sources. [1]

The reason PCMs are effective for storage of low temperature industrial waste and solar heat can be demonstrated with simple calculations. A paraffin-wax used by Khin et al. has a melting point of 62°C and an enthalpy of fusion of 145-240 kJ/kg. [3] Because water has a boiling point of 100°C, it will not undergo any change at 62°C. Therefore, water will be used as a low temperature non-PCM counterexample. With a Cp of 4.186 kJ/kg/K and an assumed starting temperature of 25C, the sensible heat storage for water at 62C, assuming constant specific heat, is 154.9 kJ/kg (6). The calculation is seen below:

q = (4.186 kJ/kg/K) (335K-298K) = 154.9 kJ/kg

This is comparable to the paraffin's latent heat value of 145-240 kJ/kg alone, so with the additional paraffin sensible heat, the paraffin PCM is advantageous at lower temperatures.

However, at higher temperatures, PCMs begin to lose their advantage. The molten salts and metals that are primarily used for the higher temperature thermal storage have latent heat values as high as 1754.4 kJ/kg. [1] Water, since operating temperatures for these materials will be well over 200°C, will be turned to superheated steam with a heat of vaporization assumed to be around the 100°C value of 2257 kJ/kg. [4] This value, along with the relatively high heat capacity of water, will be much larger than the energy stored per kilogram of PCM, demonstrating that high temperature thermal storage with PCMs is impractical.

Though impractical as of today, the development of a more efficient inorganic PCM will have many applications, such as the storage of geothermal energy. The geothermal capacity of the United States in 2004 was 2,564 MWe with total electricity production at 17,917 GWh. [5] Geothermal energy is advantageous because the earth's internal processes create a nearly infinite amount of energy, and is therefore considered a renewable energy source. [6] Geothermal energy can be described, like PCM usage, in two categories: low and high temperature use. [6] However, high temperature geothermal electricity production is inefficient. The efficiency ranges between 10-17%, roughly three times less than fossil fuel. [6] Much of the inefficiency is due to the composition of geothermal gases. The gases typically contain non-condensable gases such as carbon dioxide and hydrogen sulfide, which must be removed in order to condense. [6] This requires more energy input and a reduced efficiency. The energy of this super heated steam, with heat content as high as 2800 kJ/kg, could instead potentially be stored in an improved PCM, where it can be transported for other uses or more efficient processing. [6]

© Benjamin Reinhardt. 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.

References

[1] T. Nomura, N. Okinaka and T. Akiyama, "Technology of Latent Heat Storage for High Temperature Application: A Review," Inst. Iron Steel Jpn. International, 50, 1229 (2010).

[2] R. A. Huggins, Thermal Energy Storage, 1st Edition (Springer, 2010), pp. 21-27.

[3] M. N. A. Hawlader, M. S. Uddin, M. M. Khin, "Microencapsulated PCM Thermal-Energy Storage System," Appl. Energy 74, 195 (2003).

[4] J. M. Smith, H. C. Van Ness and M. M. Abbott, Introduction to Chemical Engineering Thermodynamics. 7th ed. (McGraw-Hill, 2006), pp. 134-35, 685.

[5] R. Bertani, "World Geothermal Power Generation in the Period 2001 - 2005," Geothermics 34, 651 (2005).

[6] E. Barbier, "Geothermal Energy Technology and Current Status: an Overview," Renewable and Sustainable Energy Reviews 6, 6 (2002).