The reversible reactant salt–water vapor thermochemical reaction is generally expressed as follows: M ⋅ ( x + y ) H 2 O ( s ) + x Δ H r ⇔ Discharging Charging M ⋅ y H 2 O ( s ) + x H 2 O ( g ) , (1) where M·(x + y)H₂O is the reactant salt rich in water, M·yH₂O is the reactant salt poor in water, ΔH_r is the enthalpy of the reaction per mole of water, and x is the stoichiometric coefficient.

Figure 1 illustrates the P–T diagrams of the proposed and conventional modes by employing the SrBr₂·H₂O/H₂O pair, which is applied for a detailed description of the operating principle. During the charging (also known as dehydration) process of the conventional system, the reactant salt M·(x + y)H₂O packed in the reactor absorbs heat from low-grade thermal energy (at T₁′) and decomposes into its less-hydrous or anhydrous form M·yH₂O and water vapor at condensation pressure (P_con); meanwhile, the thermal energy is steadily stored in the bonds of chemical compounds. This procedure is an isobaric step, corresponding to the ①′→② process in Figure 1. The water vapor flows out of the reactor into the condenser and condenses into a liquid by transferring heat to the environment at T₂, as follows: H 2 O ( g ) ⇔ Condensation Evaporation H 2 O ( l ) + Δ H eva , (2) where ΔH_eva corresponds to the evaporation enthalpy of water.

For the proposed system, the MBP is located between the reactor and the condenser. With the aid of the MBP, the charging process is conducted at a lower pressure (P_low) than P_con, meaning it can operate at a lower temperature level (T₁) compared to the conventional system (T₁′), as shown in Figure 1. The desorbed water vapor is pressurized to P_con by the MBP and condensed at ambient temperature (T₂), corresponding to a non-isobaric step of ①→②. Consequently, the proposed system can effectively reduce the requirement of charging temperature (region shown in purple and denoted as ΔT₁ = T₁′−T₁), facilitating the utilization of low-grade thermal energy.

After the charging process, the reactors of the conventional and proposed systems follow the preheating process of ①′→④ and ①→④, respectively, by utilizing a portion of the hydration heat of Eq. 1 or the superheated water vapor produced by the MBP in the proposed system. Meanwhile, the condensers of the conventional and proposed systems are heated from T₂ to the evaporating temperature of T₁′ and T₃, ②→③′ and ②→③, respectively, when the charging and discharging processes operate discontinuously; e.g., the solar thermal energy is stored during daytime while released at night.

During the discharging (hydration) process of the conventional system, a low-grade thermal energy is used to provide the required heat (Q₃) for vapor generation, corresponding to the left-to-right process in Eq. 2 and displayed as ③′→④ in Figure 1. The water vapor from the evaporator at the saturation pressure of P_high corresponding to the low-grade heat temperature (T₁′) flows toward the reactor, where it reacts with M·yH₂O inside the reactor and releases the reaction heat in a higher temperature level (T₄). For the discharging process in the proposed system, the MBP is located between the evaporator and the reactor. The water vapor pressure is boosted from P_eva to P_high by the MBP when the heat source temperature (T₃) is inferior to the required operating temperature (T₁′). Hence, the evaporation can take place at a lower vapor pressure (P_eva) leading to a lower driving temperature (T₃) while maintaining the same discharging temperature (T₄) as the conventional one. The reduction in driving temperature is denoted as ΔT₂ = T₁′ − T₃ (region shown in yellow).

The operation principle mentioned above demonstrates that both the MBP-assisted charging and discharging processes of the TCES system can enlarge the operating temperature range.

In this study, three types of MBP-assisted modes according to the installation position of MBP are evaluated, i.e., the MBP-assisted charging mode (A mode, Figure 2A), MBP-assisted discharging mode (B mode, Figure 2B), and MBP-assisted charging and discharging mode (C mode, Figure 2C). In order to facilitate comparison, the conventional mode is also depicted in Figure 2D.

(1) For the A mode, the MBP is located between the reactor and the condenser in the charging process. The discharging process runs identically as in the conventional one. This mode is characterized by four temperature levels (T₂ < T₁ < T₁′ < T₄) and three pressure levels (P_low < P_con < P_high).

It is worth noting that T₁ and T₃ can be either the same or different, depending on the heat source temperature and the compression ratio of the MBP. The switch of the charging and discharging process can be realized by regulating Valve 1 (V1) and Valve 2 (V2); i.e., V1 is open, and V2 is closed in the charging process, while operating reversely in the discharging process. Table 1 describes the operating points depicted on the P–T diagrams and schematic diagrams for charging and discharging processes in the proposed and conventional modes.

The following assumptions have been made:

(1) The system works under steady-state conditions

The reversible chemical reaction of the three selected salts with water vapor can be formulated as follows: C a C l 2 ⋅ 2 H 2 O ( s ) + Δ H r ⇔ C a C l 2 ⋅ H 2 O ( s ) + H 2 O ( g ) , (3) SrBr 2 ⋅ 6 H 2 O ( s ) + 5 Δ H r ⇔ SrBr 2 ⋅ H 2 O ( s ) + 5 H 2 O ( g ) , (4) LiOH ⋅ H 2 O ( s ) + Δ H r ⇔ LiOH ( s ) + H 2 O ( g ) . (5)

The liquid–vapor equilibrium line of water and solid–vapor equilibrium line of the thermoplastic material are determined by the Clausius–Clapeyron relation (Goetz et al., 1993), as follows: P P 0 = exp ( − Δ H r R T + Δ S r R ) , (6) where P₀ is the reference pressure (100 kPa); P and T are the equilibrium pressure and temperature of the liquid–vapor or solid–vapor, respectively; R is the ideal gas molar constant [J/(molK)]; and ΔH_r and ΔS_r are, respectively, the standard enthalpy of reaction [J/mol] and standard entropy of reaction [J/(mol K)] per mole of water vapor and hypothesized to not change with temperature. The thermodynamic parameters of the water and reactant salts are tabulated in Table 2, while the P–T curves of pure water and selected reactant salts are illustrated in Figure 3.

The outlet vapor from the MBP is required to be heated up to the output temperature of the reactor (T₄) and is calculated as follows: Q v = c p , v η r Δ N H 2 O ( T 4 − T d ) , (7) where c_p,v is the specific heat of water vapor at MBP discharge; T_d is the temperature of vapor exiting the MBP; ΔN_H2O is the theoretical molar amount of water vapor which is released from M·(x + y)H₂O during the charging process or adsorbed by M·yH₂O within the discharging period; and η _r is reaction advancement representing the fraction of actual molar amount of released or adsorbed water vapor at any moment during the process relative to the theoretical molar amount of water vapor, which is employed to indicate the degree of completeness of the reaction. It is worth mentioning that the increasing T_d reduces the heat load requirement. When T_d > T₄, the surplus heat contained in water vapor is conducive to the heat output of the reactor.

The heat load required for the reactant salts to reach the operating conditions of the discharging process, i.e., T₄ and P_high, can be calculated as follows: Q s a l t = Δ N H 2 O ν H 2 O ( T 4 − T 2 ) [ c p , M ⋅ y H 2 O η r + c p , M ⋅ ( x + y ) H 2 O ( 1 − η r ) ] , (8) where c_p,MxH2O and c_{p,M·(x+y)H2O} are, respectively, the specific heat of M·(x + y)H₂O and M·xH₂O; v_H2O is the stoichiometric coefficient of H₂O in Eq. 1.

In the preheating process, a part of the hydration heat, which is given by Eq. 9, is employed to heat up the reactant salt. Q r = Δ H r η r . (9)

The output heat of the reactor can then be obtained by subtracting Q_v and Q_salt from Q_r, as follows: Q d i s = Δ H r η r − Δ N H 2 O ν H 2 O ( T 4 − T 2 ) [ c p , M ⋅ y H 2 O η r + c p , M ⋅ ( x + y ) H 2 O ( 1 − η r ) ] − c p , v η r Δ N H 2 O ( T 4 − T d ) . (10)

The actual power consumed by the MBP per mole of vapor in [kJ/mol] can be obtained by employing the following equation: W p = R T s η p k k − 1 [ ( P d P s ) k − 1 k − 1 ] , (11) where T and P represent the temperature and pressure of water vapor, respectively; subscripts s and d denote the suction and discharge port of the MBP, respectively; and isentropic efficiency, η _p , is defined as a ratio of power consumed by the MBP under isentropic conditions to the actual power consumed. Depending on design and size, typical compressor isentropic efficiency ranges from 65% to 100% (Cengel and Boles, 2015). The isentropic efficiency range of 70%∼90% has been considered in this study. R is the ideal gas constant [J/mol/K]. k is the ratio of specific heat at constant pressure (c_p,v) to specific heat at constant volume (c_v,v) [1.33 for water vapor (Engineering ToolBox, 2003)], expressed as follows: k = c p , v c v , v . (12)

Compression ratio is defined as the ratio of the MBP’s discharge pressure (P _d ) to suction pressure (P _s ) and can be calculated as follows: C r = P d P s . (13)

In the case of the MBP-assisted charging mode, P _s is the reactor pressure at heat source temperature and P _d is equal to the condensing pressure at ambient temperature, while in the case of the MBP-assisted discharging mode, P _s is the same as the evaporating pressure at heat source temperature and P _d is the reactor pressure that corresponds to the output temperature of the reactor.

The discharge temperature of the MBP is given by T d = T s + T s C r k − 1 k − T s η p . (14)

Similarly, the heat required to heat up the reactant salt from ambient temperature to the charging temperature in the charging process is given by the following equation: Q 0 = Δ N H 2 O ν H 2 O ( T 1 − T 2 ) [ c p , M ⋅ y H 2 O ( 1 − η r ) + c p , M ⋅ ( x + y ) H 2 O η r ] . (15)

Consequently, the total heat supplied to the reactor during the charging process can be obtained by summing up Q₀ and the dehydration reaction heat which is assumed to be identical to the hydration heat as Eq. 9. Q 1 = Δ H r η r + Δ N H 2 O ν H 2 O ( T 1 − T 2 ) [ c p , M ⋅ y H 2 O ( 1 − η r ) + c p , M ⋅ ( x + y ) H 2 O η r ] . (16)

In the preheating process ②→③, the heat needed to raise the liquid water in the condenser from ambient temperature to the evaporating temperature is expressed as follows: Q 2 = c p , l Δ N H 2 O ( T 3 − T 2 ) . (17)

In the evaporating process, the heat supplied to the evaporator can be written as follows: Q 3 = Δ H v a p Δ N H 2 O η r , (18) where ΔH_r is the enthalpy of vaporization of water at T₃.

In the precooling step, the heat exchange between the reactor/condenser and the environment is not considered in evaluating the performance indicators because the environment plays the role of a heat sink. Consequently, this topic will not be discussed further here.

In order to quantify the enhancements achieved by the MBP-assisted TCES modes over the conventional system, several key performance indicators have been considered as follows.

Two distinct coefficients of performance, i.e., the total coefficient of performance (COP_total) and the electrical coefficient of performance (COP_elec), are defined to investigate system performance from the first law of thermodynamics perspective. COP_total is the ratio of the useful heat output from the reactor during the discharging process to the total energy consumption of the system, illustrated as follows: C O P t o t a l = Q 4 Q 1 + Q 2 + Q 3 + Q 5 + W p , t , (19) where W _p,t is the total power consumption of the MBP in the charging and discharging process, in [kJ].

COP _elec is the ratio of the useful heat output from the reactor during the discharging process to the power consumed by the MBP. It can be used to compare with the heat pump system and is represented as follows: C O P e l e c = Q 4 W p , t . (20)

The investigation based on the first law does not account for the energy quality. In order to obtain a more comprehensive thermodynamical performance assessment for the proposed system, the exergy analysis that relies on the second law of thermodynamics has also been studied. Exergy analysis provides an accurate indication of the available exergy that can be utilized from a system when it reaches the thermodynamic equilibrium with the reference environment. Exergy efficiency is a ratio of output flow of exergy to input flow of exergy, defined as follows: η e x = O u t p u t   e x e r g y I n p u t   e x e r g y = Q 4 ( 1 − T 2 T 4 ) Q 1 ( 1 − T 2 T 1 ) + ( Q 2 + Q 3 ) ( 1 − T 2 T 3 ) + W p , t , (21) where the output exergy corresponds to exergy of the heat discharged from the reactor at T ₄ to the environment; the input exergy is the sum of the exergies associated with heat transfer from T ₂ to T ₁ in the reactant salt during the charging process, the heat required to warm up the liquid water from T ₂ to T ₃, the vaporization heat required for the evaporation, and the work input to the MBP. The first and second terms in the denominator are defined as the input exergy caused by heat transfer, while the last term represents the input exergy induced by the electric power consumed.

Figure 4 illustrates the heat source temperature as a function of the compression ratio at different condensing temperatures. Solid lines and dotted lines indicate the discharging process and charging process, respectively. Cr = 1.0 represents the conventional mode without the MBP, while Cr > 1.0 indicates the proposed modes with the MBP. During the simulation, the heat output temperatures of the reactor in the discharging process at the condensing temperature of 7, 16, and 24°C are set as 72, 78, and 83°C for SrBr₂·H₂O/H₂O; 87, 94, and 100°C for LiOH/H₂O; and 122, 135, and 146°C for CaCl₂·H₂O/H₂O, respectively. According to Figure 4, the heat source temperature is lower for a higher compression ratio. This is because the discharge pressure of the MBP set at a fixed value results in the decrease in suction pressure with the increased compression ratio, and therefore, lower heat source temperature is required. Taking the CaCl₂·H₂O/H₂O working pair as an instance (Figure 4C), the discharging process can work when the driving temperature is higher than 38°C under Cr = 3.0 and T_con = 24°C; however, the lowest driving temperature is about 60°C for the conventional mode (i.e., Cr = 1.0). As the condensing temperature decreases, the heat source temperature reduces due to the lower condensing temperature corresponding to lower vapor pressure, as can be predicted from Figure 1. In addition, it can be observed that heat source temperatures required for the charging process are higher than those of the discharging process under the same operating conditions. This is mainly because the condenser pressure in the charging process is much lower than that of the reactor in the discharging process, leading to a smaller change in pressure during the charging process under the same compression ratio and, thus, a smaller temperature change. It should be mentioned again that heat source temperatures in both processes are equal at the compression ratio of 1 (i.e., the conventional thermochemical cycle), thus giving rise to the abovementioned results.

Using the proposed modes, the heat source temperature can be adjusted in a wider range when necessary. For example, in the case of SrBr₂·H₂O/H₂O, when the compression ratio increases from 1.0 to 3.0, heat source temperatures of the evaporator (discharging process) and reactor (charging process) decrease from 57°C to 36°C and 43°C at the condensing temperature of 24°C, from 50°C to 30°C and 37°C at the condensing temperature of 16°C, and from 43°C to 23°C and 30°C at the condensing temperature of 7°C, respectively.

Figure 5 shows the variation of MBP discharge temperature for different condensing temperatures at different compression ratios. As can be seen from Figure 5, the discharge temperature of the MBP has a rising trend with the increase of compression ratio that shows the opposite tendency to that of the heat source temperature. Additionally, it can be noticed that the improvement of MBP isentropic efficiency is associated with a reduction in the MBP discharge temperature, and the magnitude of this reduction becomes more obvious with an increase in compression ratio. For example, when using SrBr₂·H₂O/H₂O, the temperature reduction achieved between the isentropic efficiency of 70% and 90% at the condensing temperature of 24°C rises from 11°C to 31°C as the compression ratio increases from 1.5 to 3.0. This is attributed to MBP discharge temperature that is proportional to the compression ratio but inversely correlated with MBP isentropic efficiency for a given heat source temperature, according to Eq. 11. The discharge temperature of the MBP in the charging process is higher than that of the discharging process caused by the higher T_s, as revealed in Figure 5. In addition, due to the higher heat source temperature requirement, CaCl₂·H₂O/H₂O has a greater MBP discharge temperature than the other two pairs. The highest MBP discharge temperature is noticed under the operating conditions of T_con = 24°C, Cr = 3.0, and η_p = 70% in the charging process, which is 207°C for CaCl₂·H₂O/H₂O, followed by 193°C for LiOH/H₂O and 184°C for SrBr₂·H₂O/H₂O. To ensure that the discharge temperature of the MBP is not exceeding the maximum permissible value of 180°C, the compression ratio must be lower (or the heat source temperature must be higher than) than a specific value, which is determined by the operating modes, conditions, and working pairs. Under the selected conditions, systems with η_p of 90% can satisfy the requirement of temperature limit. However, systems with a low η_p value cannot function normally under certain operating conditions, especially at high-condensing temperature and high-compression ratio regions. Therefore, it demonstrates that the maximum allowable operating Cr and condensing temperature can be increased by improving the isentropic efficiency of the MBP.

Figure 6 illustrates the variations of electricity consumption of the MBP and COP_elec in the A mode and B mode with compression ratios for different MBP isentropic efficiencies. The condensing temperature and reaction advancement are kept constant as 7°C and 1, respectively. With the increase of compression ratio, the electricity consumptions increase while COP_elecs decrease. It can be noticed that the COP_elecs obtained with the A mode are slightly lower than those obtained with the B mode, but the difference is marginal. There are two reasons accountable for this difference. The first is that the electricity consumption in the A mode is higher than that in the B mode, as can be observed from Figure 6. The second is that the amount of heat released from the reactor during the discharging process in the B mode increases with the compression ratio and is larger than that in the A mode which remains constant, as illustrated in Supplementary Figure S1. The reason behind the increase in the amount of heat released in the B mode is that the rise in the MBP discharge temperature, as discussed above and shown in Figure 5, contributes to the reduction of heat load requirement for the preheating process of ①→④, while the high-temperature discharge vapor from the MBP in the charging process is condensed in the condenser, releasing directly its sensible and latent heat to the ambient environment. Furthermore, as the compressor efficiency increases, the electricity consumption reduces. The magnitude of this reduction becomes more evident with the increase in compression ratio, representing the same trend as the MBP discharge temperature mentioned above.

Figure 7 depicts the electricity consumption and COP_elec of B and C modes under various operating conditions. The electricity consumption of the C mode is the sum of A and B modes, approximately two times higher than that of the B mode (Figure 7A), leading to a degradation in COP_elec of about 50%, as shown in Figure 7B. Taking T_con = 7°C, η_p = 70%, and Cr = 2 as an example, the electricity consumption in the B mode and C mode is 103 and 207 kJ, with the corresponding COP_elec of 24.6 and 12.2, respectively.

The dependence of COP_elec and electricity consumption of MBP on the compression ratio for different working pairs at different condensing temperatures in the B mode is shown in Figure 8. According to Figure 8A, the electricity consumption follows the order of LiOH/H₂O > SrBr₂·H₂O/H₂O > CaCl₂·H₂O/H₂O under the same operating condition. This is because, as stated above, the mass of the three types of reactive salt is assumed to be 2 kg, resulting in the molar amount of water vapor (ΔN_H2O) reacted at the reaction advancement of 1 to be 37.7, 47.7, and 15.5 mol for SrBr₂·H₂O, LiOH/H₂O, and CaCl₂·H₂O, respectively. The higher the ΔN_H2O, the larger the electricity consumption. Although the higher suction temperature of the MBP, i.e., the evaporating temperature/heat source temperature (CaCl₂·H₂O/H₂O > LiOH/H₂O > SrBr₂·H₂O/H₂O as presented in Figure 4), also contributes to the increase of electricity consumption, ΔN_H2O has a more significant influence, according to Eq. 11. In addition, for the same working pair, a higher condensing temperature leads to larger electricity consumption at the same compression ratio due to the requirement of a higher evaporating temperature.

For each case, an increase in the compression ratio leads to a decrease in COP_elec due to the increase of electricity consumption of the MBP, as illustrated in Figure 8B. Unlike variation tendencies in electricity consumption, SrBr₂·H₂O/H₂O exhibits the highest COP_elec value, while CaCl₂·H₂O/H₂O shows the smallest value, although it consumes the lowest electric power. The reason is that, as discussed above, the amount of heat output of CaCl₂·H₂O/H₂O is much smaller than that of the other two working pairs at the given operating conditions. Furthermore, the condensing temperature has a negligible effect on COP_elec, especially under the large compression ratio, due to the much higher amount of heat output compared to electricity consumption. This further demonstrates that the proposed system can achieve satisfactory performance by sacrificing a small amount of electric energy.

In conclusion, values of COP_elec in A and B modes maintain a comparatively higher level, ranging from 7.04 (CaCl₂·H₂O/H₂O) to 13.72 (SrBr₂·H₂O/H₂O) for the A mode and from 8.01 (CaCl₂·H₂O/H₂O) to 14.92 (SrBr₂·H₂O/H₂O) for the B mode under the operating conditions of Cr = 3, T_con = 24°C, and η_r = 3. Concerning the C mode, the COP_elec values are smaller than those of the other two modes, varying from 3.98 (CaCl₂·H₂O/H₂O) to 7.37 (SrBr₂·H₂O/H₂O), which are still comparable to the conventional heat pump system.

Figure 9 plots the variation tendencies of COP_total for three different working pairs in different operating modes. By comparing Figures 9A–C, it can be observed that, for the A mode, a slight decline in COP_total with the compression ratio can be observed in the three working pairs. In contrast, COP_totals improve as the compression ratio increases in the B mode due to the positive contribution of high-temperature discharge vapor of the MBP to the heat output, as described in Figure 5. Under the combined influence of two MBPs (one in the charging process and the other in the discharging process), a slight increase of COP_total in the C mode is detected. Furthermore, the variation tendencies of COP_total with the change in condensing temperature when using SrBr₂·H₂O/H₂O or LiOH/H₂O as the working pair are similar, i.e., increases with an increase in condensing temperature, while CaCl₂·H₂O/H₂O exhibits an opposite trend. The primary cause is that the temperature differences between the heat output and the ambient temperature in the discharging process (ΔT₃ = T₄−T₂) and between the heat source and the condenser in the charging process (ΔT₄ = T₁−T₂) decline with the increase in condensing temperature for SrBr₂·H₂O/H₂O and LiOH/H₂O. Taking the SrBr₂·H₂O/H₂O pair employed in the B mode as an instance, ΔT₃ and ΔT₄ decrease from 65 to 59°C and from 36 to 33°C as the condensing temperature changes from 7 to 24°C, respectively, resulting in the reduction of Q_salt and Q₁ according to Eqs 8–16. Despite the electricity consumption of the MBP rising with the condensing temperature, as shown in Figure 8A, the total energy input (the denominator of Eq. 19) decreases, leading to the increase of COP_total. As for the CaCl₂·H₂O/H₂O pair, however, ΔT₃ and ΔT₄ increase from 115 to 122°C and from 52 to 56°C as the condensing temperature rises from 7 to 24°C, respectively, leading to the increment of Q_salt and Q₁ and, thus, the decrease of COP_total corresponding to Eq. 19.

Moreover, it can be found that COP_totals decrease as a function of increasing isentropic efficiency of MBP in B and C modes, while the opposite holds for A mode. In addition, the difference induced by MBP isentropic efficiency increases with the growth of compression ratio. This phenomenon can be attributed to the recovery of heat contained in the discharge vapor of the MBP, as discussed in Figure 5. The variation ranges of COP_total and COP_elec values at Cr = 3 and η_p = 70% are 0.53∼0.59 and 7.4∼19.6 for SrBr₂·H₂O/H₂O, 0.48∼0.53 and 6.6∼17.5 for LiOH/H₂O, and 0.28∼0.33 and 4.0∼8.6 for CaCl₂·H₂O/H₂O, respectively. On the whole, under the conditions that the conventional mode cannot work, the three proposed modes can acquire satisfied and relatively stable COP_total by sacrificing a small amount of electric energy. Moreover, the COP_elec value is comparable to that of the heat pump system.

The exergy efficiencies of different modes using different working pairs at varying compression ratios are presented in Figure 10. Reaction advancement is set as 1. It can be seen that lower MBP isentropic efficiency contributes to lower exergy efficiency because of higher electric power consumed. For instance, when using SrBr₂·H₂O/H₂O as the working pair, the decline in exergy efficiency is 7.5%, 5.9%, and 11.7% for A, B, and C modes, respectively, whereas isentropic efficiency suffers a decrease from 90% to 70% at T_con = 24°C and Cr = 3.

By comparing Figures 10A∼C, it can be observed that the exergy efficiency of SrBr₂·H₂O/H₂O and LiOH/H₂O working pairs tend to deteriorate with an increase in compression ratio in both A and B modes, thus resulting in the decrease in the C mode which is even more pronounced. Taking T_con = 24°C and η_p = 70% as an example, the exergy efficiencies of A, B, and C modes using SrBr₂·H₂O/H₂O decrease from 0.95 to 0.82, 0.88, and 0.78 (corresponding to the drop rates of 15.3%, 7.9%, and 22.3%), respectively, with the increase in compression ratio from 1.0 to 3.0. Compared to the A mode, a relatively slight reduction of exergy efficiency can be observed in the B mode for SrBr₂·H₂O/H₂O and LiOH/H₂O, primarily due to the lower electricity consumption and higher heat output.

It can be found that reversal points exist in all three modes when employing SrBr₂·H₂O/H₂O or LiOH/H₂O as working pairs. On the left side of the reversal point, the exergy efficiency slightly increases with the condensing temperature. In contrast, on the right side, higher condensing temperature causes lower exergy efficiency. It suggests that the higher the condensing temperature is, the more significant the reduction in exergy efficiency is with an increase in compression ratio due to greater electric power consumed, as depicted in Figure 8A. Also, the reversal point appears in a lower compression ratio region when the MBP isentropic efficiency is low. As an illustration, the reversal points are located in the compression ratio range of 1.25∼1.5 and 2.0∼2.5 for the C mode with an MBP isentropic efficiency of 70% and 90% when using SrBr₂·H₂O/H₂O as the working pair, respectively, as indicated in Figure 10C. This could be attributed to the following aspects. On the one hand, the higher condensing temperature leads to lower exergy output due to T₂/T₄ (i.e., the temperature ratio of the condenser to heat output) getting larger. On the other hand, the increase of condensing temperature will also result in the decline of exergy input caused by the heat transfer (i.e., the first and the second term of the denominator in Eq. 21), owing to the increase in T₂/T₁ and T₂/T₃ and the increase in electricity consumption. Although the exergy input by heat transfer plays the principal role in the variation of exergy input, i.e., the total exergy input decreases with condensing temperature, the electricity consumption is accounted for an increase in the proportion of total exergy input with the increase in condensing temperature and compression ratio. The increase in electricity consumption leads to a lower reducing rate of total exergy input than the exergy output at the high-compression ratio region and, therefore, the decrease in exergy efficiency. On the contrary, in the low-compression ratio region, the reduction in the total exergy input is more significant than that in the exergy output due to the effect of increasing electricity consumption on the reducing rate of total exergy input being less marked. This effect, however, will be enhanced with the descent of MBP isentropic efficiency. A similar behavior can be observed for LiOH/H₂O.

In contrast, for CaCl₂·H₂O/H₂O, the decline in condensing temperature gives rise to the enhancement of exergy efficiency, and no reversal point exists, which is consistent with that of the COP_total, as shown in Figure 10. This is because when the condensing temperature increases, the output exergy decreases, while the input exergy increases in all conditions. In addition, it can be found from Figure 10B that the increase in the compression ratio has a negligible influence on the exergy efficiency of CaCl₂·H₂O/H₂O in the B mode, owing to the output and input exergy sharing a close increasing rate with the compression ratio (as depicted in Supplementary Figure S2). This variation tendency differs from that observed in the A mode, whose output exergy remains constant (A mode) while the input exergy increases with the compression ratio due to the increase in electricity consumption.

It can be observed that the exergy efficiencies of the working pairs follow the same order as COPs under the same operating condition, i.e., SrBr₂·H₂O/H₂O (0.78∼0.95) > LiOH/H₂O (0.75∼0.89) > CaCl₂·H₂O/H₂O (0.56∼0.60). The explanation for the poor exergy efficiency value of CaCl₂·H₂O/H₂O is two-fold. One aspect is its small amount of heat output leads to smaller output exergy. The other aspect is the relatively higher heat input needed during the charging process and the higher temperature difference between the heat source and the condenser, bringing about larger input exergy.

In this section, the influence of the reaction advancement on performance indicators is investigated, taking the B mode using SrBr₂·H₂O/H₂O as the working pair as a representative.

Figure 11 exhibits the influence of reaction advancement on COP_elec and COP_total of the B mode employing SrBr₂·H₂O/H₂O as the working pair under various operating conditions. As shown in Figure 11A, the COP_elec indicates a rapid increase at first and then gradually increases with the reaction advancement. This is because the fractional change in the heat output with reaction advancement, which is expressed as α = (Q_out,2-Q_out,1)/Q_out,1 (where Q_out,2 and Q_out,1 are the amount of heat output at the reaction advancement of η_r,2 and η_r,1, respectively, e.g., η_r,2 = 0.15 and η_r,1 = 0.10), is much higher than that of the electricity consumption, which is expressed as β = (W_p,2−W_p,1)/W_p,1 (where W_p,2 and W_p,1 denote the amount of electricity consumption at the reaction advancement of η_r,2 and η_r,1, respectively), at the lower reaction advancement range (η_r < 0.2), as illustrated in Supplementary Figure S3. However, the difference between these two fractional changes becomes smaller when the reaction advancement is larger than 0.2.

The higher condensing temperature leads to a higher COP_elec when the reaction advancement is lower than 0.2; otherwise, the higher condensing temperature gives rise to a lower COP_elec. The main reason for this trend is that the ratio of heat output at different condensing temperatures is inferior to that of electricity consumption when the reaction advancement is under 0.2. For instance, as shown in Supplementary Figure S4, the ratio of heat output at 7°C (Q_out,7°C) to heat output at 24°C (Q_out,24°C) is smaller than the ratio of electricity consumption at 7°C (W_p,7°C) to electricity consumption at 24°C (W_p,24°C) when η_r < 0.2, resulting in higher COP_elec value at higher condensing temperature. Nevertheless, the situation is reversed when the reaction advancement exceeds 0.2, i.e., Q_out,7°C`/Q_out,24°C is greater than W_p,7°C/W_p,24°C, implying that the amount of heat output plays a more critical role in COP_elec rather than the electricity consumption of MBP.

It is observed from Supplementary Figure S5A that the LiOH/H₂O working pair has the same tendency as that in SrBr₂·H₂O/H₂O. However, this variation trend does not appear when using CaCl₂·H₂O/H₂O as the working pair as a lower condensing temperature contributes to a higher COP_elec within the whole range of reaction advancement, as illustrated in Supplementary Figure S5B. This is due to the higher amount of heat output and minor electricity consumption under the lower-condensing temperature condition than the higher one (Supplementary Figure S6C).

Similarly, COP_total increases with the reaction advancement, as illustrated in Figure 11B. The COP_total slightly increases with the higher condensing temperature, resulting from a minor temperature difference between the heat source and the condenser that reduces the heat load needed to preheat the working pairs. Compared to COP_elec, COP_total is little affected by the isentropic efficiency of the MBP due to the amount of heat output being higher at lower isentropic efficiency that counteracts the adverse effect of increased electricity consumption. Furthermore, it can be seen from Supplementary Figure S7 that, under the same operating conditions, the heat outputs in mode B with different compression ratios are high when compared with the conventional mode over the whole range of reaction advancement. As a consequence, the COP_totals are larger, as illustrated in Figure 12A.

Because of the limited heat and mass transfer performance, the reaction advancement is commonly regulated in the range from 0.7 to 0.9 under practical operating conditions (Jiang et al., 2020). Within this range, COP_totals of the B mode could be enhanced by 2%–7% when the compression ratio varies from 1.5 to 3.0, compared with those of the conventional mode, as indicated in Figure 12A. It can be observed that the values of COP_elec and COP_total are less than 0 when the reaction advancement is smaller than about 0.1. This phenomenon is because the sum of the heat required to preheat the reactant salt and the discharge vapor of the MBP, i.e., the second and third terms on the right-hand side of Eq. 10, is greater than the reaction heat (the first term on the right-hand side). A similar phenomenon is observed in the other two working pairs, as shown in Supplementary Figures S8, S9. Still, in the case of CaCl₂·H₂O/H₂O, the reaction advancement needs to be larger than 0.35 to make the reactor release heat properly, mainly because the heat required to warm the reactant salt is significantly higher than the heat output when the reaction advancement is lower than 0.35. The main reason for the higher heat demand on the CaCl₂·H₂O/H₂O pair is that the heat output temperature is much larger than that of the other two working pairs (e.g., 72, 87, and 122°C for SrBr₂·H₂O/H₂O, LiOH/H₂O, and CaCl₂·H₂O/H₂O, respectively, at the condensing temperature of 7°C, as shown in Supplementary Figure S10), contributing to a greater temperature difference (T₄ − T₂) as indicated in Eq. 8.

With the extension of reaction advancement, COP_elec increases significantly when the reaction advancement is less than 0.2, followed by a gradual increase, as illustrated in Figure 12B. Due to relatively low electricity consumption, the lower compression ratio and better MBP isentropic efficiency result in higher COP_elec. Under this scenario, the maximum and minimum values of COP_elec at the reaction advancement of 0.8 and the MBP isentropic efficiency of 70% are 41.3 (Cr = 1.5) and 15.2 (Cr = 3.0), respectively, and they remain at relatively high levels.

As demonstrated in Figure 12C, a higher compression ratio favors larger exergy efficiency when the reaction advancement is below 0.35; however, a higher compression ratio reduces exergy efficiency as the reaction advancement is before 0.35. In addition, the exergy efficiency differences between the B mode and the conventional mode increase with the increment of reaction advancement. The primary reason is that, for the B mode, although both the values of input and output exergies increase with reaction advancement, the increase is more pronounced in the former for reaction advancement greater than 0.35, as shown in Supplementary Figure S11A. Instead, the conventional mode shows the opposite pattern, i.e., the rise in the exergy output is more marked. The reason for the different behaviors of these two modes is that the electricity consumption of the MBP in the B mode utilizing SrBr₂·H₂O/H₂O as the working pair a growing share of the input exergy with the increasing reaction advancement and compression ratio. Furthermore, it becomes increasingly prominent when the MBP isentropic efficiency declines. Supplementary Figure S12 presents the exergy efficiency of the B mode (SrBr₂·H₂O/H₂O) with a higher MBP isentropic efficiency of 90%. It can be seen that the exergy efficiencies are enhanced, and the reversal point is elevated to about 0.75. In addition, the difference in exergy efficiency between the B mode and conventional mode becomes less noticeable when the reaction advancement exceeds the reversal point. The same behavior is also observed in the LiOH/H₂O working pair (data not shown).

However, no reversal point is observed for CaCl₂·H₂O/H₂O due to both operating modes’ input and output exergy change at a relatively stable rate, as displayed in Supplementary Figure S5B. In addition, it can be found that CaCl₂·H₂O/H₂O has the lowest output exergy, while LiOH/H₂O has the highest among the three working pairs. This is mainly because LiOH/H₂O has the largest amount of heat output (2886 kJ), followed by SrBr₂·H₂O/H₂O (2503 kJ) and CaCl₂·H₂O/H₂O (587 kJ) under the operating conditions of T_con = 7°C, η_p = 90%, Cr = 2, and η _r = 1, as shown in Supplementary Figure S6, even though CaCl₂·H₂O/H₂O has the highest heat output temperature (122°C, Supplementary Figure S10).

For the A mode using the SrBr₂·H₂O/H₂O working pair, as shown in Supplementary Figure S13A, the exergy efficiencies are all inferior to that of the conventional one. The decline observed in the exergy efficiency is attributed to the electricity consumption of the MBP in the charging process that made no contribution to the output exergy, unlike the B mode, as demonstrated in Figure 12C, although there is an effect on the reduction in the charging temperature and, thus, a lower input exergy; however, electricity consumption has an increasing impact on the input exergy with exergy efficiency and compression ratio, finally resulting in a higher input exergy (Supplementary Figure S13B). It can be seen from Supplementary Figure S14 that there is little difference between the A mode and conventional mode when employing CaCl₂·H₂O/H₂O at the MBP isentropic efficiency of 90% owing to the fact that the positive and negative effects of the MBP on the input exergy counteract each other.