**1. Introduction**

With the increasing expansion of renewable energy sources for power generation, the integration of their volatile production capacity into the electrical grid infrastructure is becoming an ever greater challenge. To address this challenge, a variety of flexibility measures and electrical energy storage (EES) have been discussed in the literature. See, e.g., the review of Zehrran et al. [1], the discussions about storage demands by Sterner and Stadler [2], as well as recent simulation results from Child et al. [3] and Schill et al. [4]. In general, for low-to-medium (up to 70%) penetration of renewable energy into the electricity supply mix, flexibility measures such as demand-side management and flexible power plants appear most cost effective. However, in a 100% renewable energy system, EES with storage periods of some hours up to a day play a major role.

In this respect, a plethora of solutions for EES have been developed, deployed, or are at the demonstration stage (see the reviews by Chen et al. [5], Gür [6], and Hameer and van Niekerk [7]). All of them aim to meet one or more of the following requirements: high (volumetric) storage density, low storage losses, fast charge and discharge rates, cheap to build, cheap to operate, and cheap to scale. While there are a few solutions that can meet several of these requirements, none of them perform well in all of these aspects. The requirement of scalability is particularly hard to meet, as it demands the

**Citation:** Hiller, S.; Hartmann, C.; Hebenstreit, B.; Arzbacher, S. Solidified-Air Energy Storage: Conceptualization and Thermodynamic Analysis. *Energies* **2022**, *15*, 2159. https://doi.org/ 10.3390/en15062159

Academic Editors: Alon Kuperman and Alessandro Lampasi

Received: 22 February 2022 Accepted: 14 March 2022 Published: 16 March 2022

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utilization of materials which are both cheap and sufficiently abundant on Earth. Next to an increasing number of materials which are discussed as solutions, particularly for thermo- and electrochemical energy storage systems (see the comprehensive review by Gür [6]), these two criteria are also prominently met by (1) water and (2) air.

(1) Water is predominantly used as an easy-to-transport carrier of potential energy in pumped-storage hydroelectricity (PSH) plants which exhibit superior cost-effectiveness and the highest round-trip efficiency (RTE), between roughly 70% and 80% [8]. As the technology for PSH is now over a hundred years old, mature, and well-tested, PSH provides the largest capacity for grid-scale energy storage to date [8]. However, the expansion of PSH capacity is becoming ever more challenging as the number of sites which are technically and economically feasible for PSH is reducing, as Rehman et al. [8], Kucukali et al. [9], and Lu et al. [10] report independently.

(2) Air, on the other hand, is a ubiquitous gas which serves as the storage medium for internal energy in compressed air energy storage (CAES) systems (see the reviews by Budt et al. [11] and Chen et al. [12]). Excess electricity is used to compress the air and raise its internal energy which can be converted back to electricity by expanding the air in a gas turbine. Due to the low volumetric energy density of CAES (0.5 kWh to 25 kWh per m3 of compressed air storage [11]), storage is done most cost-effectively underground in large salt caverns. This implies that here, too, suitable geological structures are required for large scale EES, hence limiting the deployment of the technology to a small number of sites, such as the Huntdorf and the McIntosh plant, both described in detail by Budt et al. [11] and Chen et al. [12].

One way to get around the geographic dependence while still benefiting from the advantages of the ubiquity of air is liquid-air energy storage (LAES), a cryogenic energy storage (CES) technology, which has recently been implemented for the first time in a pilot-scale demonstration plant [13]. The idea is to simply liquefy the air and store it in the liquid instead of the compressed state. The 600 volumes of air at standard temperature and pressure (STP) which are contained within one volume of liquid can eventually be used to drive a gas turbine when the liquid is evaporated using low temperature heat. As the liquid air can be readily stored in well-insulated cryogenic containers which minimize the boil-off losses, LAES is free from geological constraints. Moreover, almost all processes and components in an LAES plant are well-known from cryotechnology (e.g., the liquefaction of air), making the design and operation of the plant calculable and low-risk for the operators. Yet, the liquefaction of air is a heat-intensive process which results in only mediocre RTEs of less than about 50%, even when the heat is stored and recycled. This follows from independent thermodynamic analyses of idealized and simplified plants [13–16]. In practice, though, RTEs can also be significantly lower. For instance, Ameel et al. [14] and Borri et al. [17] report RTEs of only 20% and 10%, respectively. This is in part because of the extremely low temperature of the liquid air (<77 K) which makes the storage and recovery of cold energy prone to large losses, particularly for extended periods of storage (e.g., many hours to several days).

To overcome the drawbacks of site restrictions and low round-trip efficiencies attributed to CAES and LAES, respectively, this work introduces a novel concept for the large-scale storage of electrical energy using solidified air as the storage medium. Solidified air, i.e., the clathrate hydrate of air, or air hydrate for short (see Koh et al. [18] for a general overview on clathrate hydrates and Miller [19], Pauer et al. [20], and Shoji et al. [21] for details on naturally occurring air hydrate), is an inclusion compound of water and air in which around 170 volumes of air at STP can be stored in one volume of the solid. This makes up a molecular storage tank for compressed air with an achievable air-based volumetric storage density of about one-quarter that of LAES systems. While the utilization of hydrogen-bonded water cavities as the high-pressure containment for air allows for cheap and scalable storage, the disadvantage of a slightly lower storage density could be set off by milder storage conditions. Together this could yield a CES system which alleviates the heat storage-loss problem of LAES but retains and extends its advantages.

Although clathrate hydrates of natural gas, also termed solidified natural gas (SNG) by Linga and coworkers [22–24], are widely discussed as alternative solutions for the storage of chemical energy in the form of natural gas, the usage of air hydrates or solidified air (here used in analogy to SNG) in a CES system has not been considered so far. Based on equilibrium thermodynamics and a well justified assumption, the utilization of solidified air (SA) for EES seems feasible on first thought. Yet, due to the complexity of the phase diagram and a few unknowns with respect to the kinetics and thermodynamics of SA, careful evaluation of the new approach to CES is needed.

Therefore, in this paper, the concept for a SAES system is laid out for the first time, examined, and compared with the state of the art of LAES using a thermodynamic analysis. While the main goal of our analysis is to clarify whether the concept of SAES is technically feasible at all, it is additionally used to provide an initial recommendation as to whether the concept is worth developing further and—if so—where future research must be directed at.

#### **2. Conception**

The principle idea behind SAES is to use excess electricity, water, and air, to form SA and store it in heaps or skips on or in ground, respectively. In periods of high electricity demand, the SA is dissociated to recover the water and air, which, similar to LAES, is used to drive a turbine and generate electricity.

The term SA refers to air hydrate [19], an inclusion compound in which the molecules of the air (predominantly N2 and O2) occupy cavities formed by a hydrogen-bonded network of water molecules (see Figure 1a for an illustration). The composition of SA is nonstoiciometric, i.e., not all cavities of the structure need to be occupied. However, the maximum occupancy is 5.75 mol of water per mole of air. That relates to approximately 170 volumes of air at STP per volume of hydrate, which is about one-quarter the air storage capacity of liquefied air (600 vol/vol), but relates to approximately 17 MPa, a pressure much larger than that applied in CAES (typically <10 MPa [11,12]).

**Figure 1.** (**a**) Artistic illustration of the molecular structure of SA, i.e., air hydrate. The large grey balls denote air molecules (N2 and O2), the red balls denote the oxygen atoms of water molecules which form a hydrogen-bonded network of cavities around the air molecules. (**b**) Hydrate–liquid–vapor equilibrium data for pure air hydrate (data from Mohammadi et al. [25]) and for hydrates of air with the growth-promoting substances Tetrahydrofuran (THF), Cyclopentane (CP), Tetrabutylammonium bromide (TBAB) (data from Yang et al. [26]). The solid grey lines fit the data and denote the phase boundary above which the hydrate is thermodynamically stable (also see Lipenkov and Istomin [27] and Mohammadi and Richon [28] for a discussion of the phase diagram).

Due to its water-rich composition, many of the SA's properties, such as its appearance or density (approx. 1 g/cm<sup>3</sup> [29]), resemble those of ice. Likewise, the heat of their dissociation is comparable to the heat of fusion of ice (334 kJ/kg [30]). While due to their large heat of fusion, both ice and gas hydrates can be utilized for thermal energy storage (see the reviews by Saito [31] for ice and Wang et al. [32] for gas hydrate thermal energy storage), gas hydrates can additionally be used to store electrical energy if their ability to act as molecular storage vessel for gases is exploited. SA can be formed by bringing together liquid water and air at conditions above the hydrate–liquid–vapor equilibrium curve (the solid gray lines in Figure 1b), which means at moderately low temperatures but high pressures. It can be dissociated by exposing it to conditions below that curve, that is, by superheating or underpressurizing with respect to stability conditions. The equilibrium curve and its variation with temperature is very important in the context of this paper, because, by varying the temperature, the SA formation and dissociation pressure can be modified drastically. For instance, one could form SA at low temperature/pressure and dissociate it at higher temperature/pressure to minimize the work of compression while maximizing that of turbine expansion. Furthermore, as shown in Figure 1b, the addition of small amounts of stability-promoting substances such as THF, CP, and TBAB, can have a dramatic effect on the equilibrium curve and thus on both formation and dissociation conditions [26]. Although promoters and their effects must be addressed because of their potential to improve the RTE of a future SAES plant, for ease of understanding, stabilitypromoting substances are left out in our analysis of a very first reference case.

A key aspect of our concept for SAES is the storage of the synthesized SA at the most cost-efficient conditions, i.e., preferably at ambient conditions. Yet, as can be seen from the phase diagram in Figure 1b, SA is far from thermodynamic stability at ambient conditions. Therefore, storage in the stable form is unsuitable for our purposes. However, a kinetic anomaly termed "self-preservation" (SP) [33], which results in very low rates of dissociation at conditions far outside the stability region, is likely to allow for a mediumterm (days to weeks) storage of SA at ambient pressure and temperatures just below 273 K with minute amounts of "boil-off" losses. While SP has been reported numerous times for hydrates of CH4 [34,35] and CO2 [36,37], little is known for hydrates of air, probably because it seemed not relevant enough to this date. However, several reports [38–40] of SP for O2 and N2—the major constituents of air—render the occurrence of SP in SA plausible. In case SP in SA is similarly effective as in hydrates of CH4, SA could be stored at subzero temperatures and ambient pressure for months with losses of only a few percent [41]. Additionally, due to the strongly endothermic transition, every dissociation of SA cools down the environment. Therefore, when the stored SA is thermally well insulated, it does not have to be actively cooled.

For the rest of this work we build on the assumption of pronounced SP with the full knowledge that its refutation will render the whole concept purely theoretical. Even then, though, this work can still be regarded a long-missing potential application needed to stimulate research on SP in hydrates of air.

#### **3. Materials and Methods**

In this section, a theoretical process for SAES is outlined before a thermodynamic model for the steady-state operation of a reference plant is developed. Besides, performance parameters are defined to allow for comparisons with competing EES technologies.

#### *3.1. Plant Description*

The SAES plant is conceptualized in the process scheme in Figure 2.

**Figure 2.** Simplified process scheme of a reference plant for SAES. Solid black lines denote pathways for media transport. Dashed red lines are used to indicate heat transport. Short green arrows are used to label energy flows. In the state labeling, consecutive numbers are used according to a "energy charging → energy storage → energy discharging" order. Superscripts "a", "w", and "h" denote air, water and hydrate (i.e., SA), respectively.

Similar to CAES and LAES, electrical energy is used to compress air (1a to 2a). However, instead of storing the pressurized air directly, like in CAES, or liquefying the air, as in LAES, SA is formed from the pressurized air and water (3 to 4). Before entering the reactor, air and water are brought to formation conditions (1 to 3.2). After its formation in the reactor, the SA is extracted and pelletized (as described by, e.g., Rehder et al. [42]) for ease of transport. Note that this step is neither shown in the process scheme nor taken into account in the calculation. Other options for SA processing, such as in a slurry or via "dry water" [43], complicate the process scheme and are therefore not considered for now. The pelletized SA is cooled below 0 ◦C and the pressure is released (4<sup>h</sup> to 6h). At this state, i.e., at ambient pressure and moderately below 0 ◦C, the SA reaches SP conditions and can be stored in the SA storage. During discharge, the process is reversed. To this end, the SA is first pressurized by a high-density solids pump, e.g., a single or two-cylinder piston pump (6 to 7). The dissociation of the SA to air and water takes place in the dissociation reactor (7 to 8). Eventually, the air is heated (8<sup>a</sup> to 9a) and expanded in a turbine (9a to 10a) to recover electricity.

Both processes, the compression/expansion of air, as well as the formation/dissociation of SA, are heat intensive. Therefore, three thermal energy storage (TES) units are integrated: a sensible heat storage, which is charged by the hot air after the compressor (2a to 3.1a) and discharged by the cool air before the turbine (8a to 9a); a latent heat storage, which is charged during the exothermic SA formation (3 to 4) and discharged during the endothermic SA dissociation (7 to 8); and a water tank, to reuse the cold water exiting the dissociation reactor (8w) in the next cycle. Water losses are compensated by mixing with water at ambient conditions (1w to 2w). Where no heat integration is possible, refrigeration machines and heat pumps are used. To account for minimum temperature difference constraints as well as heat losses in the storage units, two refrigeration machines are

integrated for air and water, to ensure the attainability of the formation conditions (3.1 to 3.2). Another refrigeration machine is used to cool the SA after formation (4 to 5) to the storage temperature. A heat pump, integrated between the formation reactor and the latent heat storage unit, is operated only in case the minimum temperature difference constraint cannot be met for charging the latent heat storage unit. During discharge, no further refrigeration machines or heat pumps are used. When the heat stored in the latent heat storage unit is not sufficient to completely dissociate the SA, low-temperature ambient heat can be used in addition. The sensible heat storage unit enables the reuse of the heat of compression and determines the inlet temperature at the turbine.

In this very first analysis of SAES, one-stage compression and expansion are assumed for the air. This leads to unrealistically high temperatures and compression rates. It is believed, though, that this approach still allows for valuable insights into the SAES concept. Clearly, upon further developing the idea, multistep compression and expansion have to be considered.
