*3.3. Key Indicators*

One of the most important indicators of an energy-storage system is the RTE. For the SAES system, the RTE is calculated by

$$\eta\_{\rm It} = \frac{W\_{\rm out}}{W\_{\rm in}} = \frac{W\_{\rm turb}^{\rm a} - W\_{\rm pump}^{\rm h}}{W\_{\rm comp}^{\rm a} + W\_{\rm pump}^{\rm w} + W\_{\rm rm}^{\rm a} + W\_{\rm rm}^{\rm w} + W\_{\rm rm}^{\rm h} + W\_{\rm hp}^{\rm latter}}.\tag{4}$$

This relates the net electricity *W*out, obtained upon discharging, to the electricity that had to be used for charging.

Another important parameter for characterizing stationary EES systems is the volumetric energy density which expresses the amount of energy stored per unit volume. Considering only the air stored in the SA, the volumetric (solidified) air-based energy density is given by

$$w\_{\rm v}^{\rm a} = \frac{W\_{\rm out}}{V\_{\rm storage}e^{\rm h}}.\tag{5}$$

To account for the size of the TES system, which is a crucial part of any energy-storage system in which a gas is compressed and expanded, the total energy density

$$w\_{\rm V}^{\rm tot} = \frac{W\_{\rm out}}{V\_{\rm storage^{h}} + V\_{\rm escrible^{a}} + V\_{\rm later^{h}} + V\_{\rm storage^{ow}}} \tag{6}$$

is defined in addition.

#### **4. Results and Discussion**

This section provides a thermodynamic analysis of the SAES reference plant, followed by the determination of optimal operating conditions and a sensitivity analysis.

#### *4.1. Thermodynamic Analysis*

The SAES plant outlined above is modeled using the reference parameters provided in Table 1. As the following analysis will show, these parameters optimize the RTE of the reference plant. An overview of the corresponding states of air, water, and SA is provided in Table 2 for all components of the plant. Key indicators are summarized and compared to a LAES plant in Table 3.

While the RTEs are fairly similar, there is a significant difference in the energy densities. That is mainly because of the more than three-fold density of air in the liquid state compared to SA. The total energy density of LAES including TES has not yet been reported, though, a similar reduction with respect to the air-based value seems reasonable. The big difference between *w*<sup>a</sup> <sup>v</sup> and *w*tot <sup>v</sup> already indicates the importance of TES in the SAES plant. This is highlighted even more by the following figures: To generate a net electricity *W*out of 1.000 kWh, roughly 1.754 kWh and 2.205 kWh of heat have to be stored in the sensible and latent heat storage unit, respectively. For comparison, the compressor (*W*<sup>a</sup> comp) and turbine work (*W*<sup>a</sup> turb) are 1.729 kWh and 1.107 kWh , respectively.

**Table 2.** States for the reference case.


**Table 3.** Key indicators for the reference case of SAES and for LAES.


To better illustrate these relations, Figure 3 shows a detailed analysis of the works during charging and discharging, again normalized to a net work output of 1.000 kWh.

While *W*<sup>a</sup> comp and *W*<sup>a</sup> turb dominate the picture, the works necessary for the compression of water (*W*<sup>w</sup> pump) and SA (*W*<sup>h</sup> pump) stand out as well. As together they sum up to about 25% of the net work output, potential improvements of the RTE are possible by either storing at high pressures instead of the two expansions in the system or by using a water turbine in the expansion process. The arrow in the storage stage termed "different losses" is used to close the enthalpy balance. It combines all heat and storage losses, but also all other losses associated with the various processes executed during charging.

**Figure 3.** Sankey diagram to illustrate the relation between works (normalized to *W*out) occurring in the SAES reference case.

#### *4.2. Optimum Operating Conditions*

A further analysis of the SAES plant aims at exploring the RTE of the plant while varying the main operational parameters. Figure 4a displays the RTE at different formation and dissociation temperatures.

**Figure 4.** (**a**) Heat map of the RTE as a function of the formation and dissociation temperature. Bright spots indicate a high efficiency, dark spots a low efficiency. (**b**) Sum of process works, normalized to a net work output of 1.000 kWh, as a function of formation temperature. The dissociation temperature is kept constant at 274 K. Note that *W*<sup>a</sup> rm and *W*<sup>w</sup> rm are negligible on the scale of the graph and omitted for better readability.

The highest RTE is attained at the lowest possible dissociation temperature of 274 K and a formation temperature of 278 K, i.e., conditions also used in the reference case. This indicates that lower formation/dissociation temperatures and thus lower pressures are, in general, favorable. The sudden increase in RTE along a diagonal step can be explained with the help of Figure 4b. Therein, all energies to be expended are displayed as a function of formation temperature while the dissociation temperature is kept constant at 274 K. This can be interpreted as a line plot from the leftmost lower corner in Figure 4a to the top. Following this line, the RTE jumps abruptly as soon as a formation temperature of 278 K is reached. This is because at 278 K the latent heat pump (*W*latent hp ) is no longer needed to ensure heat flow from the formation to the dissociation reactor. Consequently, the expended energy drops and the RTE increases. According to this observation, the dissociation pressure is best kept below the formation pressure to obtain high RTE. This is in contrast to the naive idea to use higher pressures at the turbine inlet than at the compressor outlet to both decrease compressor work and increase turbine work for maximal efficiency, an idea that the authors of this paper also initially fell for. According to the phase diagram in Figure 1, this would imply a higher dissociation than formation temperature. When a latent heat pump is to be

avoided for enhanced efficiency, this is only possible with an external heat supply for the dissociation, an option not further followed in this paper.

### *4.3. Sensitivity Analysis*

In addition to the effect of different temperatures, the sensitivity of the RTE to heat storage and other parameters is investigated in Figure 5a,b, respectively.

**Figure 5.** Sensitivity of the RTE to (**a**) heat storage and (**b**) other parameters with respect to a deviation from the reference case. The reference case (red cross) corresponds to the parameters of Table 1.

The parameters are varied by reducing/increasing them by fractions in the range of −20 % to 20 % with respect to the reference case values of Table 1 (indicated by a red cross). Note that to avoid unphysical values, some parameters do not extend over the full *x*-axis range. For example, all efficiency parameter lines were plotted only up to an efficiency of 100 %. From Figure 5a it becomes apparent that an efficient sensible heat storage system is crucial for the attainment of high RTE. As this holds in general for any storage system which includes the compression and expansion of gases, this observation is to be expected. Conversely, as can be seen from the influence of Δ*T*sensible, the heat transfer in the sensible storage unit is of only minor importance. Similarly, *η*latent, the efficiency of latent heat storage, exhibits hardly any effect on the RTE. That is because in the simulations, ambient heat (at *T*env *T*diss) is used to provide the missing heat of dissociation.

Regarding the performance parameters in Figure 5b, special attention has to be paid to the insentropic turbine efficiency *η*turb. Its reduction impairs the RTE significantly. Not as dramatic as the effect of *η*turb, but still important for an efficient plant operation, are the parameters *η*hn and *η*hs. These imply the importance of the degree of SP as well as of the air capacity of the SA structure. Remarkably, the slope of *η*hs changes distinctly at around −17 %. Naturally, a decrease in *η*hs results in a decrease in RTE, because the mass flow through the turbine decreases. At the same time, though, the sensible heat storage can heat the air to a higher temperature resulting in a higher *W*<sup>a</sup> turb. Yet, beyond a certain point (at around −17 % in Figure 5b), the temperature of the air cannot be increased any further (even though the required amount of heat would be available) because at this point, the minimum temperature difference Δ*T*sensible becomes the limiting factor. As the effect of *η*vs is negligible, the additional work because of the void space in and between the SA pellets is of no particular interest. The influence of *η*comp, though minor, is more interesting because its variation affects the RTE in two opposite directions. On the one hand, with a poorer isentropic efficiency, more work is needed for compression. On the other hand, a poorer efficiency also leads to more heat being released. This additional heat can be used to heat the air to higher temperatures before expansion, which in turn results in a larger turbine work. Ultimately, this can almost compensate the additional work needed for compression. Yet, from a technical point of view, it is to be doubted if this additional heat can be fully utilized. Hence, in a more realistic scenario, the influence of *η*comp on the RTE will most likely be larger than here.

#### **5. Conclusions**

Aiming for the development of a novel CES system which overcomes the drawbacks of low RTE and extremely low temperatures in LAES, the most popular CES system to date, a concept for EES in SA, i.e., the clathrate hydrate of air, has been developed and thermodynamically analyzed. Here, the SA acts as a water-based molecular storage vessel for compressed air, which, when released upon dissociation of the SA, drives a gas turbine.

Similar to LAES plants and due to the large heat of SA formation/dissociation and the heat generated during compression, the storage and recovery of heat is crucial for an efficient operation of an SAES plant. Assuming high rates of heat recovery but no utilization of waste heat from external processes, an RTE of 52% is calculated. While this reference case value is already comparable to the maximum RTE envisaged for mature large-scale LAES plants [13], the achievable energy density (47 kWh per m<sup>3</sup> of solidified air) is only half of that of the LAES plants. This is mainly due to a more than three-fold density of air in the liquid, when compared to that in SA.

Nevertheless, as the only components of SA are water and air, the concept of SAES is very friendly to the environment. Moreover, as practically all water can be recycled, water usage is negligible. Additionally, SAES offers some advantages which have the potential to become decisive in a comparison between SAES and LAES. Due to the possible reuse of the water, the addition of thermodynamic promoters is harmless but allows for the careful design of operating conditions. This means that conditions can be adapted to the environmental conditions at the site of the plant or to the conditions needed for the integration of SAES in a larger process. Both options are likely to enable the achievement of significantly higher RTE. Moreover, under the assumption of a pronounced degree of SP, the SA can be readily stored in huge heaps or skips. Therefore, storage tanks are unnecessary and capital expenditures can be reduced.

Though the concept for SAES is well substantiated, for now, the whole concept is purely theoretical. Before proofing the concept in a pilot plant, several questions have to be answered. With respect to the fundamentals, the phenomenon of SP in air hydrates has to be investigated and thoroughly ascertained. The practical goal is to find a route of SA processing which results in the most effective inhibition of SA dissociation at the conditions of storage. Similarly, fast routes for SA formation and dissociation have to be established for typical conditions in an SAES plant. With respect to process engineering, methods for the efficient transport, compression, and expansion of SA have to be studied. These analyses must include the options of processing in a slurry, in pellets, or in dry water hydrate. To better represent a real SAES plant, future models will also need to include multistage compression and expansion of the air, as well as more detailed heat transfer analyses.

In summary, SAES has the potential to compete with its closest competitor LAES, at least in terms of RTEs. This follows from our thermodynamic analysis and potentially milder storage conditions in the case of SAES, of course, given a pronounced degree of SP can be established for hydrates of air. The option to optimize RTEs by adjusting process parameters to the conditions at the plant's site further adds to the appeal of the concept. One particularly interesting option is the idea of combining subsea SAES with offshore wind power generation. There, water and air are abundant. Additionally, hydrostatic pressure aids in compression and allows for storage at thermodynamically stable conditions. Moreover, SA can be readily stored at the seafloor because the buoyancy of SA in water is close to zero.

However, since at the moment the concept is purely theoretical, technical difficulties associated with the processing and storage of SA are hard to foresee. Even if the assumption of a pronounced degree of SP holds, it will be technically very challenging to implement SAES on a large scale. In terms of economics, it will be similarly challenging to even compete with LAES, which has yet to prove itself. Nevertheless, as engineering developments favoring LAES will likely also favor SAES, it seems to early to ultimately decide on the future of SAES. To enable the decision-making on solid grounds, at least the most pressing open question, namely, that regarding the existence of a pronounced degree of SP in air hydrate, must be clarified first.

**Author Contributions:** Conceptualization, C.H., B.H. and S.A.; methodology, C.H., B.H., S.H. and S.A.; software, S.H. and S.A.; validation, S.H., B.H. and S.A.; formal analysis, S.H. and S.A.; investigation, S.A.; resources, S.A.; data curation, S.H.; writing—original draft preparation, S.H. and S.A.; writing—review and editing, S.H., B.H. and S.A.; visualization, S.H. and S.A.; supervision, S.A.; project administration, S.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** The funding from the illwerke vkw Endowed Professorship for Energy Efficiency as well as the Open Access Funding by the Vorarlberg University of Applied Sciences are greatly acknowledged.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
