Performance characterizations and thermodynamic analysis of magnesium sulfate-impregnated zeolite 13X and activated alumina composite sorbents for thermal energy storage

The composite sorbents of MgSO 4 -impregnated zeolite 13X and activated alumina are developed for thermal energy storage (TES) with different temperature ranges. The sorption and desorption characteristics of raw and MgSO 4 -impregnated activated alumina are studied, and the performances of the selected sorbents are tested in a closed-system TES device. The results are compared with those of raw and MgSO 4 -impregnated zeolite 13X. It is shown that the impregnated MgSO 4 improves the overall TES performances of zeolite 13X and activated alumina. Compared to the raw host matrices, the impregnated MgSO 4 remarkably accelerates the temperature-rising rate of zeolite 13X to about three times and improves the temperature lift of activated alumina by 32.5%. The experimental energy storage densities of MgSO 4 -impregnated zeolite 13X and activated alumina are 123.4 kWh m −3 and 82.6 kWh m −3 , respectively. The sorption temperature region of activated alumina is more aligned with the preferred hydration temperature of MgSO 4 in comparison with zeolite 13X. The hydration characteristics of MgSO 4 can resolve the solution leakage issue of open systems. Thermodynamic analysis is conducted to evaluate the performances of the TES device with different sorbents. It is found that entransy can be used to assess thermally and electrically driven TES systems reasonably.

x water uptake, adsorption ratio [g g −1 ] Greek letters

Introduction
With the development and modernization of civilization, thermal comfort has become essential in daily life. The pervasiveness of heating, ventilation, and air-conditioning (HVAC) systems in residential and commercial buildings improves the indoor thermal environment that people experience and makes the thermal exposures closer to the ideal conditions [1]. Buildings consume 35% of the world energy use and account for around one-third of the global CO2 emissions [2]. In China, space and water heating is responsible for 71% of the final energy consumption in the residential sector and 68% of the final energy consumption in the commercial sector. In the European Union, 70% of the building final energy consumption is used for space and water heating, dominated by the residential space heating demand [2]. In the United Kingdom, direct gas use accounts for as high as 81% of the residential heat consumption for space and water heating, and electricity only delivers 8% [3]. Consequently, the transformation of heat sources from unsustainable fuels to renewable energy is crucial to mitigate the depletion of fossil fuels and solve energy crisis. Solar thermal energy and renewable electricity are the most promising low-carbon heat sources substituting for fossil fuels. Thermal energy storage (TES) systems can alleviate or eliminate the discordance in time and power between heat supply and demand [4]. Therefore, solar heating systems with seasonal TES can substantially fulfill the heat demand and effectively reduce the heating peak in winter. Besides, with the increasing trend in renewable energy, electricity will become a utility source of sustainable energy in the coming decades, and electricity-to-heat systems comprising resistive heating and heat pumps will also become low-carbon solutions for heating [5]. TES and electricity-to-heat are identified as effective measures to increase the flexibility of building energy systems [6]. Additionally, TES systems can also be charged by off-peak and excess electricity, which can improve the pattern and magnitude of electricity consumption [7].
Among all TES technologies, thermochemical heat storage, including sorption and chemical reaction, enjoys the highest energy storage density compared with sensible and latent heat storage [8]. Energy can be stored in the thermochemical TES medium at near ambient temperature without self-discharge. During the discharging process, the thermochemical TES medium experiences a noticeable temperature lift. These are essential features to realize long-term and seasonal TES [9]. Therefore, thermochemical TES systems allow more compact and longer-term storage of heat.
Magnesium sulfate (MgSO4) is considered a promising thermochemical TES medium due to its high theoretical TES capability. The theoretical specific energy storage capacity of MgSO4 is 3377 kJ kg −1 , and the theoretical energy storage density of its heptahydrate MgSO4·7H2O is 770 kWh m −3 [10]. However, it was reported that the real thermochemical performance of pure MgSO4 is not ideal. For example, Bales et al. [11] found that energy storage density of MgSO4·7H2O descends to 420 kWh m −3 under suitable conditions. Van Essen et al. [12] tested a reactor with 40 g MgSO4 under 150°C charging temperature, 25°C reactor temperature, and 25°C evaporating temperature. They reported that the temperature lift in the hydration process of MgSO4 is only about 6.5°C. During the hydration process, the salt crystals may clump together and form a hardly permeable layer that impedes the water uptake [12,13]. The kinetic hindrance prevents the material to display its full theoretical TES capability. The impregnation of the salt into host matrices and physical adsorbents is a measure to disperse the salt and solve the kinetic hindrance to the hydration reaction [13][14][15]. Meanwhile, the overall performance of the physical adsorbents also can be improved by the salt. Such a kind of materials is called composite salt in porous matrix (CSPM) [16].  [15] improved the temperature lift of MgSO4 by 11-18°C through impregnating the salt into activated carbon pellets. Brancato et al. [19] studied the MgSO4·7H2O-embedded polymeric foams with salt hydrate mass fractions from 40% to 70%. They found that the threshold mass fraction around 60% realizes a good compromise between the ability, flexibility, and hydration/dehydration capacity of the foam. Posern et al. [14] investigated the thermochemical characterizations of MgSO4-impregnated porous glasses with different pore sizes. They concluded that CSPM materials are promising for thermochemical heat storage with high storage density. However, there are also negative results published in the literature. Whiting et al. [20] reported that the overall released heat of the zeolite Na-X/MgSO4 composites with salt mass fractions of 5%, 10%, and 15% is significantly lower than that of zeolite Na-X. Mahon et al. [21] tested the characterizations of the zeolite 13X/MgSO4 composites prepared by wetness impregnation and pellet press methods, but the dehydration peak

Materials
In order to cover both mid-temperature and low-temperature TES, two kinds of physical adsorbents are selected as the host matrices for MgSO4.

Host matrices
Zeolite 13X is an excellent physical adsorbent for TES because of its high adsorption heat, water uptake, and energy storage density [23]. Zeolite 13X-water TES systems generally enjoy high temperature lifts and good performances for mid-temperature heat storage as well as space and water heating [24][25][26]. Besides, zeolite 13X has been used as the host matrix for MgSO4 to produce CSPM materials [10,17,18,20,21]. It was reported that MgSO4-impregnated zeolite 13X with the salt mass fraction of 15% improves the energy storage density of zeolite 13X by approximately 15%-27% [10,17]. The composite sorbent of zeolite 13X/MgSO4 is suitable for mid-temperature TES, as its maximum sorption temperature is as high as 92-110°C for long-term cycle [10]. Nonetheless, the high maximum sorption temperature of zeolite 13X does not match the preferred hydration condition of MgSO4. The TES capability of MgSO4 can be better utilized if it is impregnated into host matrices with relatively lower temperature lifts.
For low-temperature TES, silica gel, activated carbon, vermiculite, activated alumina, and expanded natural graphite are the promising host matrices [8]. Silica gel has been impregnated with LiCl [27], CaCl2 [28], and SrBr2 [29] to produce CSPM materials for low-temperature TES, and the energy storage densities range from 164 kWh m −3 to 203 kWh m −3 under the sorption temperatures of 30-35°C and the charging temperature of 80°C. Nonetheless, a pilot system with the silica gel-water working pair has the energy storage density of 50 kWh m −3 , which is only 25% of the theoretical value of silica gel, because of the limitations of the available heat source and sink [30]. Besides, silica gel loses its adsorption capability if the desorption temperature is higher than 120°C [31], so the charging temperature must be strictly controlled. The activated carbon/MgSO4 materials successfully improve the maximum hydration temperature of MgSO4 by 11-18°C in an open TES system, and the specific energy storage capacities are 1030-1270 kJ kg −1 [15]. However, carbon adsorbents do not have the preference for adsorption of water, which means that the impurities in the polluted air can displace water vapor from activated carbon in open systems [23]. The vermiculite composite sorbents impregnated with SrBr2 [32] and LiCl [33] have the predicted energy storage densities of 105 kWh m −3 and 224 kWh m −3 , respectively. The experimental study of an open TES system shows that vermiculite/CaCl2 is a promising material for low-temperature heat storage with the energy storage density of 120-160 kWh m −3 , but vermiculite/MgSO4 underperforms compared with the data on dehydration heat [34]. Activated alumina is a promising host matrix adsorbent for low-temperature TES because of its relatively high thermal conductivity and material strength. The LiCl-impregnated activated alumina has the predicted energy storage density of 318 kWh m −3 at 120°C charging temperature [35]. An open sorption TES system with the activated alumina/LiCl composite sorbent realizes the energy storage density of 191 kWh m −3 for space heating [36].
Expanded natural graphite treated with sulfuric acid (ENG-TSA) has the advantage of high thermal conductivity. The ENG-TSA/SrBr2 composite material significantly improves the heat transfer performance of SrBr2, and the host matrix of ENG-TSA does not influence the water uptake of the material [29]. ENG-TSA is used as the host matrix for MnCl2/CaCl2 multi-salt sorbent for ammonia sorption, which enhances the heat and mass transfer performance of the composite sorbent [37,38].
Zeolite 13X is suitable for mid-temperature TES with the maximum adsorption temperature higher than 90°C, and activated alumina adapts to low-temperature TES below 60°C. Both of these two host matrices have good water uptake performances and display potential for CSPM materials impregnated with MgSO4.
Besides, ENG-TSA is selected as the packing material to fill the gaps between the host matrix pellets. All the chosen materials can tolerate the high temperature of 300°C, which simplifies the control of the sorbent temperature when the TES device is charged by the electric heater. As a result, in this study, zeolite 13X and activated alumina are selected as the host matrices of MgSO4, and ENG-TSA is used as the packing material to increase the thermal conductivity when the sorbents are filled in the adsorber. Figure 1 illustrates the preparation procedure of the composite sorbents [10]. First, the spherical host matrix pellets are dried in the oven (1). Then an appropriate amount of MgSO4 aqueous solution is added to the host matrix pellets (2). The mixture is stirred and let stand for a long time to impregnate the salt into the host matrix (3). The impregnated salt content primarily depends on the concentration of the solution. Afterward, the pellets are taken out from the solution and dried again to remove water (4). The MgSO4-impregnated host matrix is thus prepared. For the sorbents tested in the TES device, ENG-TSA is added as the packing material (5). The mixture is stirred until the constituents are uniformly distributed (6). The host matrix/MgSO4/ENG-TSA composite is filled into the adsorber with the help of a mold (7). Finally, the material is compressed to let the pellets stack closely with ENG-TSA filling the clearance (8). For the host matrix/ENG-TSA sorbents without MgSO4, the preparation follows steps (1) and (5)-(8) in Figure 1.

Composite sorbents
According to Reference [17], the recommended mass fraction of magnesium sulfate for zeolite 13X/MgSO4 is 15%, so the MgSO4-impregnated zeolite 13X with the salt mass fraction of 15% (denoted as XM15) is prepared. The optimum salt mass fraction for activated alumina/MgSO4 needs to be determined by material characterizations. Too high salt content can cause severer pore-blocking effect of the porous matrix, and too low salt content cannot provide adequate performance improvement of the composite sorbent.
Therefore, MgSO4-impregnated activated alumina sorbents with different salt contents are prepared for investigation.

Experimental methods
The performance characterizations of the sorbents are acquired from the material test and system experiments. The sorption and desorption characteristics of the sorbent samples are tested, and a TES device is applied to study the actual performances of the sorbents.

Material test
The sorption characteristics are described by the water uptake kinetic characteristics, i.e., the water uptake it is generally not feasible to heat the sorbent in the adsorber at a meager rate in practical application, the heating rate for STA is set to 5°C min −1 that accords with the practical condition of the heating and desorption process in the TES device. The sorbent samples are placed in the constant temperature and humidity chamber to take in water thoroughly before the test. Figure 2 shows the photo and schematic diagram of the TES device [10].

System and procedure
As depicted in Figure 2a, the sorption TES device mainly consists of an adsorber, a condenser/evaporator, and a reservoir. Pipes with valves link the condenser/evaporator and the reservoir. Figure  The sorption TES device experiences two working phases in one cycle, i.e., the charging phase and the discharging phase [10]. During the charging phase, the adsorber electric heater is turned on to heat the sorbent, and water vapor is desorbed from the sorbent and condensed in the water tray of the condenser/evaporator. The fluid in the condenser/evaporator coil pipe is turned on which takes away the condensation heat. The adsorber electric heater is turned off when the sorbent temperature reaches the charging temperature, and the charging phase finishes. Afterward, V2 is opened to drain the water in the condenser/evaporator to the reservoir, and the fluid in the condenser/evaporator coil pipe is turned off. Then V2 is closed to separate the water in the reservoir from the sorbent in the adsorber, and thus self-discharging is avoided. During the discharging phase, the fluid in the adsorber coil pipe recovers the sensible heat from the sorbent. Before the sorption process starts, the fluid in the adsorber coil pipe is turned off. The reservoir electric heater is switched on to increase the temperature and pressure in the reservoir. When the vapor pressure in the reservoir is high enough to pump the water in the reservoir to the condenser/evaporator, the reservoir electric heater is switched off, and V1 is opened.
After a sufficient amount of water is pumped, V1 is closed. The water evaporates from the water tray, and the water vapor is adsorbed by or reacts with the sorbent in the adsorber. The fluid in the condenser/evaporator coil pipe is turned on to provide the evaporation heat. Sorption heat is released during the sorption process and elevates the temperature of the sorbent. When the sorbent temperature does not rise anymore, the fluid in the adsorber coil pipe is turned on to retrieve the sorption heat. The fluid in both coil pipes is turned off at the end of the discharging phase.
If the evaporating temperature is elevated, the TES device will operate as a sorption heat pump. In this case, a thermostatic bath is used to control the evaporating temperature of the system. When the evaporating temperature is above the room temperature, the fluid leaving the evaporator coil pipe is led to the adsorber coil pipe during the discharging phase so that the heat below the evaporating temperature will not be discharged.

Data processing
The specific desorption heat of the sorbent in STA is obtained by The heat measured in each process of the TES device is calculated by The temperature lift of the TES device during the sorption process is The specific energy storage capacity of the TES device is The energy storage density of the TES device is The statistical (type-A) uncertainty of the quantity z measured for n times is The systematic (type-B) uncertainty of the quantity z directly measured by the instrument with a continuous uniform (rectangular) probability distribution is The combined uncertainty (type-A and type-B) of the quantity y is The relative uncertainty of the indirectly-measured quantity y is calculated by The calculated relative uncertainties of the discharging heat in the long-term TES cycles are approximately 11.4% for 13X/ENG-TSA, 9.1% for XM15/ENG-TSA, 8.7% for AA/ENG-TSA, and 6.3% for AM16.5/ENG-TSA. As shown in Figure 3, most of the MgSO4-impregnated composite sorbents display higher water uptake rates or amounts than those of the raw host matrixes. Raising the saturation temperature from 25°C to 40°C leads to significant improvement of the water uptake rates for all the tested sorbents. The water uptake amounts and rates of zeolite 13X sorbents (13X and XM15) are much higher than those of activated alumina sorbents (AA, AM8.4, AM11.1, AM13.9, AM16.5, and AM20.9). For example, under the saturation temperature of 25°C, it requires approximately 1.2 hours for XM15 to reach the water uptake of 0.08 g g −1 , while AM16.5 needs more than 5 hours to get to the same water uptake.

Sorbent characterizations
In Figure 3a, the water uptake amounts of 13X under 25°C and 40°C saturation temperatures after 7 hours are 0.148 g g −1 and 0.160 g g −1 , respectively. The water uptake amounts of XM15 under 25°C and 40°C saturation temperatures after 7 hours are 0.156 g g −1 and 0.165 g g −1 , respectively. The impregnation of MgSO4 in zeolite 13X improves the 7-hour water uptake amount and the water uptake rate slightly.  at 30°C and 60% RH (relative humidity) before the test, which is a typical sorption condition for long-term closed-system TES.
As demonstrated in Figure 4, MgSO4-impregnated zeolite 13X and activated alumina have higher maximum water uptake compared to the raw host matrixes. The maximum water uptake of XM15 is 0.01 g g −1 higher than that of 13X, and the maximum water uptakes of the MgSO4-impregnated activated alumina sorbents are around 0.019 g g −1 higher than that of the raw activated alumina. The characteristics of the DSC curves for zeolite 13X and activated alumina sorbents are different. In Figure 4a, the DSC curve of 13X has only one endothermic peak during the heating and desorption process, whereas XM15 displays two endothermic peaks. The peak heat flow of XM15 is higher than that of 13X. In Figure 4b, with the increase of the salt mass fraction for MgSO4-impregnated activated alumina, the endothermic peak has the general trend to descend towards the lower peak heat flow and to move right towards the higher temperature. All the activated alumina sorbents display only one endothermic peak individually. For XM15, the second endothermic peak mainly originates from the host matrix of zeolite 13X, and the first peak primarily results from the dehydration of MgSO4 hydrates [10]. As for activated alumina, since the endothermic peak of MgSO4 hydrates almost coincides with that of activated alumina, the MgSO4-impregnated activated alumina sorbents each displays only one combined endothermic peak. Moreover, it can be seen that the poreblocking effect in MgSO4-impregnated activated alumina is severer than that in XM15, so the peak heat flow rises for zeolite 13X and descends for activated alumina after the impregnation of MgSO4. It can be found from Table 2 that the impregnated MgSO4 improves the maximum water uptake and the specific desorption heat of zeolite 13X and activated alumina. The maximum water uptake and the specific desorption heat of XM15 are 5.1% and 6.3% higher than those of 13X, respectively. Although AM20.9 has the highest maximum water uptake after thorough sorption among all the MgSO4-impregnated activated alumina sorbents, AM20.9 still contains the most amount of water uptake at the temperature of 200°C. Thus AM20.9 has the lowest water uptake difference under the charging temperature of 200°C. Among all the MgSO4-impregnated activated alumina sorbents, AM16.5 enjoys the highest specific desorption heat. The maximum water uptake and the specific desorption heat of AM16.5 are 15.7% and 35.7% higher than those of AA, respectively. In summary, both the water uptake kinetic characteristics and the STA results indicate the better performances of the MgSO4-impregnated zeolite 13X and activated alumina than raw host matrices. The recommended salt mass fraction for MgSO4-impregnated zeolite 13X is 15% according to the literature [17], and the optimum salt content of MgSO4-impregnated activated alumina is 16.5% based on the water uptake kinetic characteristics and STA results. Thus, XM15 and AM16.5 are adopted as the sorbents to be tested in the TES device, and 13X and AA are also tested for comparison.

System performances
The sorbents of 13X/ENG-TSA, XM15/ENG-TSA, AA/ENG-TSA, and AM16.5/ENG-TSA are filled into the adsorber of the TES device separately, and the system performances under different conditions are tested. The sorbents are heated to the discharging temperature and kept for hours when the TES device is evacuated in the vacuum condition for thorough desorption. According to the STA results in Figure 4, the discharging temperatures of 13X/ENG-TSA, XM15/ENG-TSA, AA/ENG-TSA, and AM16.5/ENG-TSA are set to 250°C, 250°C, 150°C, and 200°C, respectively. Figure 5a shows the evolution of sorbent temperatures of different types of well-regenerated sorbents during the sorption processes in the TES device, and Figure 5b presents the division of the discharging heat. The performances of XM15/ENG-TSA and AM16.5/ENG-TSA are further tested in the TES device. If the evaporating temperature is raised, the maximum sorption temperature also can be elevated, and the TES device will operate as a sorption heat pump. Figure 6a shows the evolution of sorbent temperatures of XM15/ENG-TSA and AM16.5/ENG-TSA during the sorption processes in the TES device under 25°C, 30°C, and 40°C evaporating temperatures, and Figure 6b illustrates the division of the discharging heat.
From Figure 6a it can be found that the maximum sorption temperatures and the temperature lifts of XM15/ENG-TSA and AM16.5/ENG-TSA rise with the increase of the evaporating temperature when the sorption temperature does not change. The variation of the maximum sorption temperature of XM15/ENG-TSA with the evaporating temperature is much more significant than that of AM16.5/ENG-TSA. According to Figure 6b, the discharging heat of XM15/ENG-TSA and AM16.5/ENG-TSA at the evaporating temperature of 30°C is higher compared to the other conditions. There are only minor differences among the discharging heat of XM15/ENG-TSA at different evaporating temperatures, but for AM16.5/ENG-TSA, the discharging heat at the evaporating temperature of 30°C is noticeably higher than the other conditions. Although the high evaporating temperature can increase the pressure of water vapor and thus promote the water uptake rate, it affects the maximum water uptake and hinders the hydration of MgSO4, as the sorbent temperature in the sorption process is also elevated. The evaporating temperature of 30°C realizes the balance between the two effects. For XM15/ENG-TSA, since the temperature lift and the maximum sorption temperature are high enough, the evaporating temperature from 25°C to 40°C seemingly does not have much influence on the discharging heat. As for AM16.5/ENG-TSA, the maximum sorption temperature is in the range of 48-54°C, which is much closer to the evaporating temperature range of 25-40°C, so the influence of the evaporating temperature on the discharging heat is more noticeable compared with XM15/ENG-TSA.
If the sorption process is initiated before the sensible heat is completely retrieved, the sorption temperature will be higher than the ambient temperature, and the remaining sensible heat will be recovered along with the released sorption heat. This circumstance is for short-term TES. Figure 7a shows the variation of sorbent temperatures in the sorption processes with the composite sorbents of XM15/ENG-TSA and AM16.5/ENG-TSA under the sorption temperatures of 30°C, 60°C, and 80°C, and Figure 7b shows the division of the discharging heat. From Figure 7b, the discharging heat of XM15/ENG-TSA is similar under different sorption temperatures, whereas for AM16.5/ENG-TSA, the discharging heat at 30°C evaporating temperature is markedly higher in comparison with the other conditions. The reason is that the sorption temperatures of 60°C and 100°C are beyond the preferred temperature range of activated alumina, and the high sorption temperature affects the discharging heat of AM16.5/ENG-TSA more severely than XM15/ENG-TSA. Compared with AM16.5/ENG-TSA, the higher temperature lift of XM15/ENG-TSA mainly benefits from the higher specific adsorption heat of zeolite 13X. Nevertheless, the sorption heat of XM15/ENG-TSA decreases a bit after several cycles, whereas AM16.5/ENG-TSA seemingly does not suffer from such detectable performance attenuation. This is because zeolite 13X can adsorb air as well and thus is more sensitive to the slight vacuum loss of the device compared to activated alumina. This problem can be solved by regenerating the sorbents in the vacuum condition or further decreasing the leak rate of the device. Table 3 outlines the performance parameters of the TES device with different sorbents.

Discussion
Thermodynamic analysis is conducted to evaluate the performances of the TES device with different sorbents. The effect of the impregnated MgSO4 in the composite sorbents, the relevant influencing factors of the sorbent performances, and the applications of the sorbents are discussed.

Thermodynamic analysis
In addition to the performance parameters listed in Table 3, the thermodynamic evaluation indices of energy efficiency, exergy destruction, exergy efficiency, entransy loss, and entransy efficiency are studied.
The energy efficiency of the TES device depends on the useful heat output of the system. Typically, the useful heat includes sensible heat and sorption heat. For low-temperature TES, when the condensing temperature is high enough to provide heat output, condensation heat can be regarded as useful heat as well.
For seasonal TES, sensible heat is dissipated to the ambient after prolonged storage time, and only sorption heat can be recovered to provide useful heat output. Therefore, considering the different usage scenario, three types of energy efficiency are analyzed.
The (typical) energy efficiency of the TES device is The energy efficiency including condensation heat of the TES device is calculated by The seasonal energy efficiency of the TES device is obtained by The ideal seasonal energy efficiency of the TES device with compensation for heat loss of the electric heaters and the metal heat capacity can be calculated by The exergy destruction of the TES device is obtained by The exergy efficiency of the TES device is calculated by The entransy loss of the TES device is defined as The entransy efficiency of the TES device is defined as The aforementioned thermodynamic evaluation indices of the TES device with different sorbents are summarized in Table 4.
According to Table 4, the energy efficiency of activated alumina sorbents (AA/ENG-TSA and AM16.5/ENG-TSA) is lower than that of zeolite 13X sorbents (13X/ENG-TSA and XM15/ENG-TSA) because activated alumina sorbents have the slower water uptake kinetic characteristics and experience longer cycles. Nevertheless, the energy efficiency including condensation heat of AM16.5/ENG-TSA is as high as 0.712. Although the ideal seasonal energy efficiency of AA/ENG-TSA is the highest among the tested sorbents, the real seasonal energy efficiency of AA/ENG-TSA decreases significantly. The reason is that the charging heat of AA/ENG-TSA is the lowest among the tested sorbents, but meanwhile, the proportion of the electricity input of the reservoir electric heater used to pump water is the highest, and the long cycle time of activated alumina sorbents causes more heat dissipation. The actual energy efficiency can be raised if the thermal insulation is improved, the heat and mass transfer is enhanced, and the energy storage capacity of the system is increased. Besides, the ideal energy efficiency of MgSO4-impregnated sorbents tends to be lower than that of raw host matrices, as the additional desorption heat of MgSO4 hydrates cannot provide enough increase of the hydration heat. Consequently, in practical application, if the water uptake rate during the later period of the sorption process becomes too slow to provide effective discharging heat power, the further water uptake can be excess and should be avoided to reduce the required charging heat and improve the energy efficiency, especially for MgSO4-impregnated sorbents. Entropy, exergy, and entransy have been used to analyze the adsorption system [39], cascaded latent heat storage system [40], and thermochemical heat storage reactor [41], but the essential distinctions, applicable occasions, and optimization objectives of these thermodynamic evaluation indicators still seem vague in the previous studies. It is known that entransy dissipation and entropy production are both irreversibility-directing concepts, so they both can be used to analyze heat exchange processes without heat-work interaction and give the same direction of optimization, i.e., to decrease the irreversibility [42]. Nevertheless, since the definitions and physical meanings of entropy and entransy are different, the detailed optimum results with respect to them can be different.
As electrically driven TES systems charged by off-peak and excess electricity can deliver high flexibility and improve the electricity consumption profile, thermodynamic assessment should cover both thermally and electrically driven TES systems and exhibit enough comparability between the two kinds of TES systems.
However, it is evident that exergy destruction of electrically driven TES systems is distinctively higher than that of thermally driven TES systems because of the severe exergy loss in the electricity-to-heat conversion.
On the contrary, based on the theory of entransy, the entransy transfer accompanied with work transfer has the same form with heat transfer, as indicated in Equation (18). As a result, entransy provides the possibility of assessing thermally and electrically driven TES systems reasonably with the identical thermodynamic evaluation index.
From Table 4, it can be found that the exergy efficiency of the TES device with the tested sorbents is only 0.026-0.089, which is much lower than the energy efficiency. Given that the electrically driven TES system is generally charged by off-peak and excess electricity, the useful thermal energy discharged by the TES system can be more valuable than the excess electricity used to charge the system. Consequently, it is not appropriate to assess electrically driven TES systems by exergy in some circumstances. The entransy efficiency of the TES device is in the range of 0.326-0.456, which is slightly lower than the energy efficiency due to the temperature degradation of the TES device. As a result, entransy can be used to assess thermally and electrically driven TES systems reasonably. Entransy loss and entransy efficiency are useful to assess the TES system especially when the exergy difference between charging heat and excess electricity is of marginal importance. For example, as utilization of excess renewable electricity is almost as environmentally friendly as recovery of waste heat, both of them will be considerable heating sources to charge the TES system.   In order to achieve sufficient discharging heat in the sorption process, the advantaged sorption condition region of MgSO4 lies above equilibria c, e, and f in Figure 9, where the temperature and relative humidity enable the hydration reaction of MgSO4·7H2O or MgSO4·6H2O. According to the experimental results, the preferred evaporating temperatures of XM15 and AM16.5 are around 30°C. The sorption condition regions of XM15 and AM16.5 are marked by the shaded area with diagonal lines in Figure 9. and activated alumina is higher than that of raw host matrices, the entransy efficiency of MgSO4-impregnated zeolite 13X and activated alumina is noticeably higher than that of raw host matrices, which implies that the impregnated MgSO4 improves the mean discharging temperatures of the sorbents.

Evaluation of sorbents
The pore sizes of zeolite 13X [17] and activated alumina [35] are around 0.8-0.9 nm and 1.7-31 nm in diameter, respectively. In accord with Reference [14], the pore size significantly affects the sorbent characteristics. According to the STA results in Figure 4, the heat flow tends to increase for zeolite 13X and decrease for activated alumina after the impregnation of MgSO4, which indicates that the pore-blocking effect in host matrices with larger pores is severer than that with smaller pores. The reason is that more MgSO4 molecules can be impregnated to the host matrix with larger pores, which obstructs the water adsorption on the pore surfaces to a greater extent. The kinetic hindrance of the hydration of MgSO4 can be solved when the pore sizes are small enough to offer effective dispersion of the salt molecules. However, if the pores are too small, the maximum sorption temperature of the host matrix will be too high for the hydration of MgSO4.
Consequently, neither too big or too small pore sizes are recommended. The overall sorption heat diminishes with the increasing pore size of the host matrix due to the decreasing adsorption heat of the host matrix, and meanwhile, the proportion of the hydration heat of MgSO4 rises with the increment of the pore size of the host matrix. There is a trade-off between these influencing factors. Therefore, determination of the optimum host matrix based on the impregnation and reaction mechanism is one of the critical problems in development of and it can discharge thermal energy to either air or water. According to the experimental results, XM15 is a useful material for closed-system mid-temperature TES due to the high and rapid temperature lift as well as the maximum discharging temperature above 90°C, which covers the temperature range of both space and water heating. AM16.5 realizes the extended sorption heat release for closed-system low-temperature TES, as the discharging temperature of AM16.5 can be in the range of 40-50°C for a very long period. For example, at the evaporating temperature of 40°C, the discharging temperature of AM16.5 is above 47°C for more than 10 hours. MgSO4 does not radically improve the water uptake capability of the impregnated host matrices.
Nevertheless, the high deliquescence relative humidity of MgSO4 can solve the issue of solution leakage for open systems. In consequence, both XM15 and AM16.5 are also useful materials for open-system TES.

Conclusions
In this article, the TES performances of the MgSO4-impregnated zeolite 13X and activated alumina are investigated. The following conclusions are made from this study: ( (2) Compared to the raw host matrices, the impregnated MgSO4 remarkably accelerates the temperaturerising rate of zeolite 13X to about three times and improves the temperature lift of activated alumina by 32.5%. The sorption temperature region of activated alumina is more aligned with the preferred hydration temperature of MgSO4 in comparison with zeolite 13X.
(3) XM15 is a useful material for closed-system mid-temperature TES with the maximum discharging temperature above 90°C. AM16.5 realizes the extended sorption heat release for closed-system low-