Thermodynamic Performance of Adsorption Working Pairs for Low-Temperature Waste Heat Upgrading in Industrial Applications

The present work aims at the thermodynamic analysis of different working pairs in adsorption heat transformers (AdHT) for low-temperature waste heat upgrade in industrial processes. Two different AdHT configurations have been simulated, namely with and without heat recovery between the adsorbent beds. Ten working pairs, employing different adsorbent materials and four different refrigerants, have been compared at varying working boundary conditions. The effects of heat recovery and the presence of a temperature gradient for heat transfer between sinks/sources and the AdHT components have been analyzed. The achieved results demonstrate the possibility of increasing the overall performance when internal heat recovery is implemented. They also highlight the relevant role played by the existing temperature gradient between heat transfer fluids and components, that strongly affect the real operating cycle of the AdHT and thus its expected performance. Both extremely low, i.e., 40–50 °C, and low (i.e., 80 °C) waste heat source temperatures were investigated at variable ambient temperatures, evaluating the achievable COP and specific energy. The main results demonstrate that optimal performance can be achieved when 40–50 K of temperature difference between waste heat source and ambient temperature are guaranteed. Furthermore, composite sorbents demonstrated to be the most promising adsorbent materials for this application, given their high sorption capacity compared to pure adsorbents, which is reflected in much higher achievable specific energy.


Introduction
Energy conversion processes are associated with the release of waste energy, usually in the form of heat, which is commonly referred to as waste heat and is often dumped to the environment. The amount of waste heat produced at EU level was estimated to ca. 305 TWh/y, with a large portion of it in the temperature range 100-200 • C [1]. The proper exploitation of these waste energy streams represents a critical task to further increase the energy efficiency of industrial processes, which can have a huge impact from both economic and environmental points of view. Indeed, when the temperature level is sufficiently high (i.e., above 150 • C), there are several established technologies that can be employed to produce power, heating, and cooling, namely sorption heating and cooling technologies, organic Rankine cycles (ORC), steam, and Kalina cycles [2]. When the waste heat temperature is too low for being efficiently exploited, i.e., below 100 • C, the only way to make use of it is to upgrade the temperature level, thus re-using the energy in the same industrial process or providing external services, like feeding district heating networks (DHN). Recently, the development of high-temperature industrial heat pumps AdHT technology for industrial waste heat applications. Recently, the AdHT cycle was proposed to exploit extremely low ambient temperatures under specific climatic conditions, for instance in Siberia (Russia), to upgrade waste heat in residential applications for space heating purposes [16]. The authors performed a deep development activity, starting from thermodynamic analysis [16,17] up to the experimental characterization of small-scale dynamics of the process [18]. They were then able to design, realize, and test a lab-scale prototype, based on the working pair silica gel-LiCl/methanol, which was tested under controlled operating conditions [19]. The obtained results demonstrated the ability of the technology to achieve up to 25 K of temperature lift, using 20 to 30 • C of waste heat and −20 • C of ambient temperature. An even more attractive result is the achievable specific energy, which reached up to 620 kJ/kg at a specific power ranging between 6.0 and 10.8 kW/kg. Based on the above reported literature, it is evident how the AdHT technology could be considered as an interesting option for waste heat upgrade, able to overcome most of the limitations of other concurrent technologies. Nevertheless, the literature still lacks a detailed thermodynamic investigation of possible working pairs suitable for the expected working operating conditions. Accordingly, this paper focuses on the description of AdHT thermodynamics of two different AdHT architectures. Subsequently, a comparative analysis of the achievable performance, in terms of COP and specific energy, of several working pairs available in the literature is conducted. It can be considered as a screening tool for defining the most suitable working pairs to be used for the design and operation of AdHT for different industrial applications.

Thermodynamic Analysis
In this section, the basic architecture of the AdHT and the thermodynamic analysis to evaluate efficiency and energy density are described. Figure 1 represents the basic architecture of an AdHT. Four main components define the overall operation of an AdHT: 1.
An adsorbent bed, which acts either as adsorber or desorber depending on the working phase of the AdHT cycle. It usually consists of a heat exchanger (HEX) filled with the adsorbent material, to achieve high heat and mass transfer rates during the system operation.

2.
A condenser, represented by a HEX in which the refrigerant released by the desorber in the vapor phase is condensed to the liquid phase, releasing the heat to the low temperature sink.

3.
An evaporator, represented by a HEX in which the waste heat is supplied to evaporate the refrigerant, which is then adsorbed in the adsorber releasing the upgraded heat.

4.
A circulating pump needed to move the liquid refrigerant from the condenser to the evaporator. Figure 2 represents the working cycle of the AdHT on a pressure-temperature chart, plotted over an isosteric diagram of a reference working pair. Specifically, the two limiting isosters, namely the rich isoster (w 1 ) and the weak isoster (w 2 ), which define the operating range of the AdHT, are reported.
The main difference between the AdHT technology and standard cycle (i.e., heat pump or chiller), as already detailed in [20], is that the adsorption (SP) and desorption (QR) processes are pressure-driven isothermal processes, instead of the typical isobaric temperature-driven ad-desorption stages of adsorption heat pumps and similarly to the discharge stage of a sorption seasonal storage [21]. Furthermore, the working fluid is evaporated by exploiting the heat of evaporation supplied by waste heat at a temperature level, T L in Figures 1 and 2, which is higher than the temperature, T 0 , at which the condensation heat is dumped to the environment. Accordingly, the pressure inside the condenser is lower than the pressure inside the evaporator, thus making the use of a pump necessary to increase the pressure level of the liquid refrigerant and guarantee the correct operation and refrigerant transfer from the condenser to the evaporator. Schematic architecture of an adsorption heat transformers (AdHT) reporting the main components, the energy fluxes, and the temperature levels. TL, TA, and T0 represent the waste heat temperature, upgraded temperature, and ambient temperature, respectively. The same temperatures marked with the apex considers a possible temperature gradient to drive the heat transfer process. QL and Q'L represent the heat flux of the waste heat to the evaporator and to the adsorbent bed, respectively, while QA and Q0 represent the heat flux of the upgraded heat and discharged at the condenser, respectively. Figure 2 represents the working cycle of the AdHT on a pressure-temperature chart, plotted over an isosteric diagram of a reference working pair. Specifically, the two limiting isosters, namely the rich isoster (w1) and the weak isoster (w2), which define the operating range of the AdHT, are reported. Figure 2. Thermodynamic cycle of an AdHT plotted over a reference isosteric chart, showing the typical pressure-driven working cycle, highlighting the rich isoster (w1) and the weak isoster (w2). p0 and pL represent the pressure corresponding to the ambient temperature and waste heat temperature levels respectively. TL, TA, and T0 represent the waste heat temperature, upgraded temperature, and ambient temperature, respectively. QL and Q'L represent the heat flux of the waste heat to the evaporator and to the adsorbent bed, respectively, while QA and Q0 represent the heat Schematic architecture of an adsorption heat transformers (AdHT) reporting the main components, the energy fluxes, and the temperature levels. T L , T A , and T 0 represent the waste heat temperature, upgraded temperature, and ambient temperature, respectively. The same temperatures marked with the apex considers a possible temperature gradient to drive the heat transfer process. Q L and Q' L represent the heat flux of the waste heat to the evaporator and to the adsorbent bed, respectively, while Q A and Q 0 represent the heat flux of the upgraded heat and discharged at the condenser, respectively. Figure 1. Schematic architecture of an adsorption heat transformers (AdHT) reporting the main components, the energy fluxes, and the temperature levels. TL, TA, and T0 represent the waste heat temperature, upgraded temperature, and ambient temperature, respectively. The same temperatures marked with the apex considers a possible temperature gradient to drive the heat transfer process. QL and Q'L represent the heat flux of the waste heat to the evaporator and to the adsorbent bed, respectively, while QA and Q0 represent the heat flux of the upgraded heat and discharged at the condenser, respectively. Figure 2 represents the working cycle of the AdHT on a pressure-temperature chart, plotted over an isosteric diagram of a reference working pair. Specifically, the two limiting isosters, namely the rich isoster (w1) and the weak isoster (w2), which define the operating range of the AdHT, are reported. Thermodynamic cycle of an AdHT plotted over a reference isosteric chart, showing the typical pressure-driven working cycle, highlighting the rich isoster (w1) and the weak isoster (w2). p0 and pL represent the pressure corresponding to the ambient temperature and waste heat temperature levels respectively. TL, TA, and T0 represent the waste heat temperature, upgraded temperature, and ambient temperature, respectively. QL and Q'L represent the heat flux of the waste heat to the evaporator and to the adsorbent bed, respectively, while QA and Q0 represent the heat flux of the upgraded heat and discharged at the condenser, respectively.
Thermodynamic cycle of an AdHT plotted over a reference isosteric chart, showing the typical pressure-driven working cycle, highlighting the rich isoster (w 1 ) and the weak isoster (w 2 ). p 0 and p L represent the pressure corresponding to the ambient temperature and waste heat temperature levels respectively. T L , T A , and T 0 represent the waste heat temperature, upgraded temperature, and ambient temperature, respectively. Q L and Q' L represent the heat flux of the waste heat to the evaporator and to the adsorbent bed, respectively, while Q A and Q 0 represent the heat flux of the upgraded heat and discharged at the condenser, respectively. The AdHT cycle can be described following the representation reported in Figure 2. It mainly consists of two phases: A pre-cooling and desorption phase (P-Q-R) and a pre-heating and adsorption phase (R-S-P).

•
During the desorption phase, the adsorbent bed (operating as desorber in this phase) is regenerated, releasing the adsorbed refrigerant, exploiting the waste heat, Q L ', at temperature level, T L , as shown in Figure 1 The desorbed refrigerant is then condensed at the pressure p0, imposed by the sink temperature, T 0 , to which the condenser is connected. The first stage of the desorption process occurs under isosteric conditions (P-Q). Once the waste heat temperature level, T L , is attained, the refrigerant is isothermally desorbed down to the condenser pressure (Q-R).

•
During the adsorption phase, the waste heat, Q L , is supplied to the evaporator at the temperature T L . The evaporated refrigerant is adsorbed in the adsorber and, due to the exothermic adsorption reaction, it is heated up until the upgraded heat temperature level, T A , is reached and the related energy Q A is released as shown in Figure 1. Furthermore, in this process, a first isosteric stage takes place (R-S), which is prolonged until the upgraded temperature level, T A , is reached. At this stage, the sorption process continues isothermally (S-P), releasing the heat until the evaporator pressure is reached.
To comparatively evaluate different operating conditions, the useful effect is defined as gross temperature lift (GTL) representing the temperature difference between the upgraded heat (T A ) and the waste heat (T L ).
The main parameter to evaluate the AdHT efficiency, according to the first-law of thermodynamic, is the coefficient of performance (COP), defined as follows: Beside the overall AdHT efficiency, another relevant parameter needed to estimate the amount of sorbent material needed to upgrade the waste heat source, is represented by the specific energy, Q A [J/g], whose definition is given by Equation (5) in Section 2.2.

Main Scope and Field of Application
In the present paper, the achievable performance by two AdHT configurations will be comparatively analyzed; namely, one bed connected to one condenser/evaporator ( Figure 3a) and two separated beds connected to one condenser and one evaporator ( Figure 3b). Configuration II has the merits of:

•
Offering a quasi-continuous delivery of upgraded heat (with configuration I only during the adsorption phase); • The possibility of implementing a heat recovery between the adsorber and the desorber beds allowing higher COP. Similarly to the case of adsorption heat pumps, this solution can be implemented without excessive technical complication to the system [22,23].
It has to be pointed out that the thermodynamic analysis can be conducted either considering the ideal case, in which no temperature gradient exists between external sources/sinks and the component, or considering a suitable temperature gradient. Accordingly, temperature inside each component will be evaluated as: where ∆T = 0 K in the ideal case and ∆T > 0 K in real conditions. In the following, the thermodynamic model derived for both Configuration I and Configuration II is reported, which consists of heat and mass balance for each component. It is worth pointing out that the analysis presented here is intended as a first screening of different working pairs to identify the most suitable ones for different applications, mainly District Heating Networks (DHN) of recent construction (fourth generation) and low-grade industrial heat upgrade. Such a screening is a necessary step for the design of an AdHT, which needs to take into account also the dynamic aspects [8].

T = T + ∆T
(2) where ΔT = 0 K in the ideal case and ΔT > 0 K in real conditions. In the following, the thermodynamic model derived for both Configuration I and Configuration II is reported, which consists of heat and mass balance for each component. It is worth pointing out that the analysis presented here is intended as a first screening of different working pairs to identify the most suitable ones for different applications, mainly District Heating Networks (DHN) of recent construction (fourth generation) and low-grade industrial heat upgrade. Such a screening is a necessary step for the design of an AdHT, which needs to take into account also the dynamic aspects [8].

Configuration I
As already pointed out, for Configuration I, no heat recovery process can be implemented. The specific thermal energy that can be released during the adsorption phase, QA, is: where ΔHAd [J/g] represents the integral heat of adsorption, which can be usually evaluated starting from the equilibrium data of the selected working pair [24,25]; cps, cpv, and cpL [J/gK] are the specific heat capacities of solid adsorbent, vapor, and liquid refrigerant, respectively, Δw [g/g] is the refrigerant uptake variation between adsorption and desorption phases and w2 [g/g] the uptake corresponding to the weak isoster of the cycle. The thermal energy provided to the evaporator by the low-grade heat source, QL, is:

Configuration I
As already pointed out, for Configuration I, no heat recovery process can be implemented. The specific thermal energy that can be released during the adsorption phase, Q A , is: where ∆H Ad [J/g] represents the integral heat of adsorption, which can be usually evaluated starting from the equilibrium data of the selected working pair [24,25]; cp s , cp v , and cp L [J/gK] are the specific heat capacities of solid adsorbent, vapor, and liquid refrigerant, respectively, ∆w [g/g] is the refrigerant uptake variation between adsorption and desorption phases and w 2 [g/g] the uptake corresponding to the weak isoster of the cycle. The thermal energy provided to the evaporator by the low-grade heat source, Q L , is: where ∆H ev [J/g] represents the latent heat of evaporation evaluated at the waste heat temperature. Finally, the thermal energy provided during desorption phase, Q' L , can be calculated as: where w 1 [g/g] is the uptake corresponding to the rich isoster of the cycle.

Configuration II
Regarding Configuration II, it is possible to recover a certain amount of energy, by circulating the heat transfer fluid between adsorber and desorber during the switching phase, thus transferring part of the sensible heat from the bed starting to act as a desorber (along the path (P-Q) to heat up the bed starting to work as an adsorber (along the path Appl. Sci. 2021, 11, 3389 7 of 18 R-S). Therefore, the first step is to evaluate the theoretical equilibrium temperature T eq , which can be obtained when the temperatures of adsorber and desorber are equalized and thus no heat recovery can be performed anymore: This equilibrium temperature is evaluated by equalizing the energy recovered by the desorber and provided to the adsorber. Clearly, also in this case, in real application in order to guarantee a proper heat transfer efficiency between the two components, a given temperature gradient, ∆T, must be considered. Accordingly, the ending temperatures of the heat recovery phase will be: where T P * [ • C] represents the end desorber temperature during the recovery phase, while T R * [ • C] is the end adsorber temperature. For Configuration II, the specific upgraded heat can be calculated according to Equation (11) for the ideal case and to Equation (12) considering the real case.
Similarly, to calculate Q' L , Equation (13) can be used for the ideal case and Equation (14) for the real case scenario.

Investigated Working Pairs
The main aim of the investigation is to analyze the achievable thermodynamic performance of possible sorption working pairs, whose equilibrium data are available in the literature. The term working pair refers to the pair constituted by a solid sorbent material and a refrigerant (working fluid) that allow to perform the expected AdHT cycle.
To this aim, some of the main refrigerants typically employed in adsorption cycles were selected, and are listed in Table 1 along with their most relevant thermophysical properties. Different adsorbent materials, whose equilibrium data are available in the literature, were selected. As reported in Table 2, they were selected trying to cover both the standard physical adsorbents (e.g., zeolites, activated carbons, silica gels) as well as the composite sorbents, based on the impregnation of a hygroscopic salt (e.g., LiCl, LiBr) inside a porous structure (e.g., silica gel, MWCNT), to enhance the sorption properties. This wide selection of materials will also allow to identify possible critical issues as well as future perspectives in the further development of working pairs for AdHT application. In future Appl. Sci. 2021, 11, 3389 8 of 18 activities, this first investigation can be enlarged to cover new sorbent materials (e.g., Metal-Organic Frameworks). The Dubinin-Astakhov [25] approach to describe the equilibrium data of all the investigated working pairs was used. Table 2 reports the investigated working pairs in this paper along with the reference from which the equilibrium data were taken.

Simulation Results
The aim of the performed simulations is the evaluation of thermodynamic efficiency of adsorbent working pairs for AdHT operation under different boundary conditions. For this reason, firstly, the investigated boundary conditions are described, and subsequently, the main results and the comparison of the achievable performance are detailed.

Operating Conditions
To investigate the AdHT performance, the operating conditions under which the technology is working must be defined. These refer to the waste heat temperature, which is recovered from the process as well as to the ambient heat temperature, which is exploited as heat sink for the process. Table 3 summarizes the range of operating conditions that are investigated in this paper. The main application field of the present analysis is the exploitation of extremely lowgrade temperature source, which is usually dumped into the environment. The investigated ambient heat temperature ranges from extremely low values, typical of operation in cold climates during winter, up to temperature levels commonly encountered in warm climates during summer season. It has to be pointed out that, for the working pairs using water as the refrigerant, the minimum ambient heat temperature that can be considered for the calculation is 5 • C, if freezing issues inside the system are to be avoided.

Comparison between One-Bed and Two-Beds Configurations
In order to comparatively evaluate the different achievable performance of the Configuration I (one adsorbent bed) against the Configuration II (two adsorbent beds), the expected COP and specific energies were calculated. The selected working pair was the AQSOA Z02/water, while, for the sake of simplicity, the compared conditions were the ones exploiting ambient heat at 10 • C, both in the case of 40 • C and 80 • C of waste heat. In this case, ∆T = 0 K, which stays for ideal heat transfer, was considered. Figure 4 summarizes the obtained results. The evolutions are plotted against the gross temperature lift, GTL, as defined before.

Comparison between One-Bed and Two-Beds Configurations
In order to comparatively evaluate the different achievable performance of the Configuration I (one adsorbent bed) against the Configuration II (two adsorbent beds), the expected COP and specific energies were calculated. The selected working pair was the AQSOA Z02/water, while, for the sake of simplicity, the compared conditions were the ones exploiting ambient heat at 10 °C, both in the case of 40 °C and 80 °C of waste heat. In this case, ΔT = 0 K, which stays for ideal heat transfer, was considered. Figure 4 summarizes the obtained results. The evolutions are plotted against the gross temperature lift, GTL, as defined before. As expected, when the GTL increases, both COP and specific energy decrease, since the exchanged refrigerant per kg of the adsorbent in each cycle is reduced. Comparing Configurations I and II, it is evident that the efficiency for the two adsorbent beds configuration is always higher than the one adsorbent bed configuration, since the former one allows to recover part of the sensible energy during the switching phase, thus reducing the energy requested to drive the process. Additionally, in this case, being the process considered ideal, the maximum achievable heat recovery is considered, which is obtained when the ΔT between desorber and adsorber reaches 0 K. Differently, the curves for the specific energy obtained for the two configurations are almost overlapped, since the main benefit of Configuration II, from the thermodynamic point of view, lies in the reduction of the needed driving energy. Indeed, the increased waste heat temperature is associated with a higher COP for the same GTL or much higher GTL for the same COP. Same is valid for the specific energy upgraded. Both trends can be attributed to the much wider uptake difference ( − ) at the higher waste heat temperature. Considering the higher efficiency of Configuration II as well as the possibility of obtaining a quasi-continuous thermal energy production, this configuration will be considered in the following analysis. Nevertheless, it has to be pointed out that in some specific cases, like waste heat recovery from batch processes, the configuration with a single adsorbent bed can represent an attractive solution, thanks to the possibility of reducing the system complexity and thus the related capital expenditures (CAPEX). As expected, when the GTL increases, both COP and specific energy decrease, since the exchanged refrigerant per kg of the adsorbent in each cycle is reduced. Comparing Configurations I and II, it is evident that the efficiency for the two adsorbent beds configuration is always higher than the one adsorbent bed configuration, since the former one allows to recover part of the sensible energy during the switching phase, thus reducing the energy requested to drive the process. Additionally, in this case, being the process considered ideal, the maximum achievable heat recovery is considered, which is obtained when the ∆T between desorber and adsorber reaches 0 K. Differently, the curves for the specific energy obtained for the two configurations are almost overlapped, since the main benefit of Configuration II, from the thermodynamic point of view, lies in the reduction of the needed driving energy. Indeed, the increased waste heat temperature is associated with a higher COP for the same GTL or much higher GTL for the same COP. Same is valid for the specific energy upgraded. Both trends can be attributed to the much wider uptake difference (w 1 − w 2 ) at the higher waste heat temperature. Considering the higher efficiency of Configuration II as well as the possibility of obtaining a quasi-continuous thermal energy production, this configuration will be considered in the following analysis. Nevertheless, it has to be pointed out that in some specific cases, like waste heat recovery from batch processes, the configuration with a single adsorbent bed can represent an attractive solution, thanks to the possibility of reducing the system complexity and thus the related capital expenditures (CAPEX).

Effect of the Temperature Gradient for Heat Transfer
In thermodynamic performance analyses, the temperature gradient between heat sources/sinks and components, needed to realize the heat transfer process, is often neglected. Nevertheless, this can play a crucial role in the final selection of the most effective materials and components. For this reason, the achievable performance of the investigated working pairs when a reasonable ∆T = 5 K was compared against the reference condition where ∆T = 0 K. Figure 5 summarizes the results, both in terms of COP and specific energy, varying the waste heat and ambient temperature, using, AQSOA Z02/water as the reference working pair again for the sake of simplicity.
As shown by Figure 5a,c, the effect induced by accounting for a ∆T = 5 K for heat transfer in all AdHT components is extremely relevant for systems exploiting 40 • C of waste heat source temperature. Indeed, in this case, a heat upgrading effect, albeit limited, can be achieved only when the ambient temperature to which the process heat is dumped is below 10 • C. Only 10 K of GTL can be achieved at the minimum acceptable COP (i.e., 0.3) and quite low specific energy (i.e., 20 kJ/kg), when the ambient temperature is 5 • C. It has to be pointed out that the temperature gradient of 5 K is also considered in the heat recovery process between desorber and adsorber.
has to be pointed out that the temperature gradient of 5 K is also considered in the heat recovery process between desorber and adsorber.
Similar considerations are obtained when 80 °C of waste heat temperature are available, Figure 5b,d. Clearly, in this case, since the temperature difference between waste heat source and ambient heat is higher, the amount of refrigerant processed per each cycle is higher as well (see Figure 2), thus up to 52 K of GTL can be achieved at a COP of 0.3, even though with a very limited specific energy (i.e., below 50 kJ/kg). This demonstrates that, in practical applications, the right compromise must be sought between the needed GTL and the specific energy that can be extracted at the required temperature level, which cannot preclude from technological and economic aspects, which have to be taken into account to make the technology attractive for practical applications. Given the relevant role played by the temperature gradient to make the thermodynamic calculations reliable, a temperature gradient of ΔT = 5 K will be always considered Similar considerations are obtained when 80 • C of waste heat temperature are available, Figure 5b,d. Clearly, in this case, since the temperature difference between waste heat source and ambient heat is higher, the amount of refrigerant processed per each cycle is higher as well (see Figure 2), thus up to 52 K of GTL can be achieved at a COP of 0.3, even though with a very limited specific energy (i.e., below 50 kJ/kg). This demonstrates that, in practical applications, the right compromise must be sought between the needed GTL and the specific energy that can be extracted at the required temperature level, which cannot preclude from technological and economic aspects, which have to be taken into account to make the technology attractive for practical applications.
Given the relevant role played by the temperature gradient to make the thermodynamic calculations reliable, a temperature gradient of ∆T = 5 K will be always considered in the following analysis, focusing on the comparison among different working pairs. This can be assumed as a quite conservative approach, since good heat exchangers design can lead to smaller ∆T in real applications. Nevertheless, it guarantees that the reported results have practical relevance for the selection of the most attractive working pairs for different operating conditions.

Comparison of the Different Working Pairs
As already highlighted in Table 3, the waste heat source temperatures considered in this study ranged between 40 • C and 80 • C, thus representing temperature levels usually dumped into the ambient. In the following, the selected working pairs (see Table 2) were investigated considering two possible final applications, namely upgrading waste heat to be used as primary source for low-temperature district heating network (DHN) applications and upgrading waste heat to be re-used in the industrial process above 100 • C. For the former application, waste heat sources ranging between 40 • C and 50 • C were considered, with the injection of 50-60 • C in the DHN as the target, according to the fourth-generation DHN temperature levels [33]. For the latter application, waste heat source at 80 • C was considered, in order to guarantee the provision of heat at temperatures above 100 • C, which can be efficiently exploited in several industrial processes (e.g., pasteurization, sterilization, concentration, drying, distillation etc.) [34]. Figure 6 report both thermal COP and specific energy achievable by the different working pairs in case of 40 • C waste heat source temperatures. In this case, a minimum of 10 K of GTL was considered. Furthermore, the COP and specific energy were calculated every 10 K of GTL. As represented in Figure 6, when the waste heat source is available at 40 • C, only 10 K of GTL can be provided by most of the investigated working pairs with an appreciable efficiency and energy density. Furthermore, it is possible to obtain the GTL only when the ambient temperature, at which the process heat is dumped, is equal or below 10 • C. This restricts the exploitability of this waste heat stream to winter period and in cold climates. Another option is represented by the availability of other ambient heat sinks, characterized by a stable and low temperature throughout the year (e.g., lakes, rivers, etc.).
this study ranged between 40 °C and 80 °C, thus representing temperature levels usually dumped into the ambient. In the following, the selected working pairs (see Table 2) were investigated considering two possible final applications, namely upgrading waste heat to be used as primary source for low-temperature district heating network (DHN) applications and upgrading waste heat to be re-used in the industrial process above 100 °C. For the former application, waste heat sources ranging between 40 °C and 50 °C were considered, with the injection of 50-60 °C in the DHN as the target, according to the fourthgeneration DHN temperature levels [33]. For the latter application, waste heat source at 80 °C was considered, in order to guarantee the provision of heat at temperatures above 100 °C, which can be efficiently exploited in several industrial processes (e.g., pasteurization, sterilization, concentration, drying, distillation etc.) [34]. Figure 6 report both thermal COP and specific energy achievable by the different working pairs in case of 40 °C waste heat source temperatures. In this case, a minimum of 10 K of GTL was considered. Furthermore, the COP and specific energy were calculated every 10 K of GTL. As represented in Figure 6, when the waste heat source is available at 40 °C, only 10 K of GTL can be provided by most of the investigated working pairs with an appreciable efficiency and energy density. Furthermore, it is possible to obtain the GTL only when the ambient temperature, at which the process heat is dumped, is equal or below 10 °C. This restricts the exploitability of this waste heat stream to winter period and in cold climates. Another option is represented by the availability of other ambient heat sinks, characterized by a stable and low temperature throughout the year (e.g., lakes, rivers, etc.). In particular, two main working pairs showed promising performance, namely SGST-LiCl/water and MWCNT-LiCl/methanol. The former is able to achieve quite high COP, higher than 0.45 at 5 and 10 °C ambient temperature (Figure 6a), with specific energy ranging from 200 kJ/kg to 400 kJ/kg. The latter can achieve extremely high specific energy (Figure 6b), around 1500 kJ/kg for ambient temperature below 0 °C and above 400 kJ/kg at ambient temperature of 5 °C. In particular, two main working pairs showed promising performance, namely SGST-LiCl/water and MWCNT-LiCl/methanol. The former is able to achieve quite high COP, higher than 0.45 at 5 and 10 • C ambient temperature (Figure 6a), with specific energy ranging from 200 kJ/kg to 400 kJ/kg. The latter can achieve extremely high specific energy (Figure 6b), around 1500 kJ/kg for ambient temperature below 0 • C and above 400 kJ/kg at ambient temperature of 5 • C.
These evolutions are guaranteed by the favorable equilibrium conditions of the embedded salt, LiCl, under these operating conditions. Differently, most of the pure adsorbents cannot be considered suitable under these conditions, since the achievable COP and specific energy are too low, especially at ambient conditions above 0 • C. It has to be pointed out that the working pair MWCNT-LiCl/methanol can also efficiently provide 20 K of GTL when the ambient temperature is below 0 • C. Specifically, it can achieve 0.5 of COP both at −10 • C and 0 • C, with 1040 kJ/kg and 940 kJ/kg of specific energy, respectively.
Interestingly, when the waste heat source temperature is increased to 50 • C, different working pairs can be considered suitable for the application, as represented in Figure 7 and Table 4, guaranteeing the possibility of providing up to 20 K of GTL, meaning 70 • C available, which can be used for feeding the DHN at higher operating temperature. As highlighted in Figure 7a and Table 4, all the investigated working pairs can be operated up to 10 • C of ambient temperature to achieve a GTL of 10 K, while some specific ones can also exploit higher ambient temperature, i.e., 20 • C. In particular, this is the case for the two composite sorbents using water as a refrigerant and the MWCNT-LiCl with methanol. Furthermore, the pure silica gel Siogel can also be operated up to 20 • C of ambient temperature, even if very limited COP and specific energy is expected. The MWCNT-LiCl/methanol working pair shows both GTLs of 10 K and 20 K, to be able to achieve COP almost constant at 0.5, with a decrease down to 0.35 at 20 • C ambient temperature (Figure 7a). The expected specific energy looks even more attractive, always being above 1000 kJ/kg when the ambient temperature is below or equal to 10 • C, both for 10 K and 20 K GTL (Table 4). This is mainly due to the feature of the composite sorbent which, under these operating conditions, is almost always able to exchange a constant amount of methanol, thus guaranteeing a flat evolution of these performance parameters, according to the equilibrium data reported in [28]. Other working pairs that show appreciable performance are the ones based on ammonia as a working fluid, especially when 10 K of GTL is requested. Nevertheless, both activated carbons using ammonia never overcome 380 kJ/kg as specific energy, thus making them less attractive than the MWCNT-LiCl/methanol working pair. As pointed out before, the two investigated composite sorbents using water as working fluid can also achieve appreciable performance under these conditions, and the SGST-LiCl especially shows quite high COP even at high ambient temperature and specific energy slightly lower that the MWCNT-LiCl/methanol, thus also making this working pair a valuable option.
perature, even if very limited COP and specific energy is expected. The MWCNT-LiCl/methanol working pair shows both GTLs of 10 K and 20 K, to be able to achieve COP almost constant at 0.5, with a decrease down to 0.35 at 20 °C ambient temperature (Figure 7a). The expected specific energy looks even more attractive, always being above 1000 kJ/kg when the ambient temperature is below or equal to 10 °C, both for 10 K and 20 K GTL (Table 4). This is mainly due to the feature of the composite sorbent which, under these operating conditions, is almost always able to exchange a constant amount of methanol, thus guaranteeing a flat evolution of these performance parameters, according to the equilibrium data reported in [28]. Other working pairs that show appreciable performance are the ones based on ammonia as a working fluid, especially when 10 K of GTL is requested. Nevertheless, both activated carbons using ammonia never overcome 380 kJ/kg as specific energy, thus making them less attractive than the MWCNT-LiCl/methanol working pair. As pointed out before, the two investigated composite sorbents using water as working fluid can also achieve appreciable performance under these conditions, and the SGST-LiCl especially shows quite high COP even at high ambient temperature and specific energy slightly lower that the MWCNT-LiCl/methanol, thus also making this working pair a valuable option.
Furthermore, in this case, there are some working pairs able to achieve GTLs up to 30 K, specifically AC SRD 1352-2/ammonia and AC Carbotech A35/methanol, which, when the ambient temperature is −10 °C, can achieve COP higher than 0.4 with specific energy higher than 100 kJ/kg. Even if these conditions can be considered useful only under some specific cases, they still represent an interesting option to enlarge the operation of the AdHT at higher delivering temperatures.   Furthermore, in this case, there are some working pairs able to achieve GTLs up to 30 K, specifically AC SRD 1352-2/ammonia and AC Carbotech A35/methanol, which, when the ambient temperature is −10 • C, can achieve COP higher than 0.4 with specific energy higher than 100 kJ/kg. Even if these conditions can be considered useful only under some specific cases, they still represent an interesting option to enlarge the operation of the AdHT at higher delivering temperatures.
The last investigated operating condition is the one exploiting 80 • C of waste heat source to upgrade heat that can be re-used in industrial processes. Figure 8 represents the COP and Table 5 specific energy calculated for the different working pairs for three different GTLs, namely, 20 K, 40 K, and 50 K. As can be seen in Figure 8a and in Table 5, in the case of GTL = 20 K, all the selected working pairs can achieve the expected target even exploiting 30 • C of ambient temperature. The three composite sorbents based on LiCl, using water and methanol as working fluids, are the ones showing the highest specific energy, above 1000 kJ/kg, irrespective of the ambient temperature at which they are operating. Differently, regarding the COP, the most effective working pairs are the ones using ammonia as a working fluid. Indeed, for these working pairs, the COP remains above 0.5. Interestingly, as highlighted in Figure 8b,c and in Table 5, for the other two investigated GTLs, namely 40 K and 50 K, the composite MWCNT-LiCl/methanol cannot be operated, since under these conditions, it is not able to produce sufficient heat upgrading effect. This of course represents a critical factor to consider for the working pair selection, indeed if higher temperature is requested by the industrial process, other pairs must be considered. In particular, the one showing the highest COP and specific energy is the SGST-LiCl-35/water. It has to be highlighted that, under these GTLs, the AdHT can be operated only up to 20 • C of ambient temperature, specifically at GTL = 50 K, only the above-mentioned working pair can be operated up to 20 • C.  As expected, for these operating conditions, the pure adsorbents are also characterized by lower performance, since the overall working fluid exchange per cycle is much lower than that of the composites, thus causing a reduction of the achievable specific energy.

Comparison of Results for AdHT and Heat Pumping Applications
It is interesting to compare the achieved results, in terms of optimal working pairs, with similar analyses done for adsorption air conditioning and heat pumping applications. A quite extensive comparison of different materials and refrigerants for a wide variety of operating boundaries is reported in [35]. The LiBr-silica/water and LiCl-silica/methanol working pairs showed a superiority over the other ones also for air conditioning and refrigeration applications, as already discussed for the case of AdHT, thus stressing the attractive features of these composites in real applications. At the same time, for heat pumping applications analyzed in [35], the use of methanol was disregarded since heat source temperatures of 150 • C were evaluated, at which decomposition and stability problems of these refrigerants can occur. This stresses that, for applications with extremely low waste heat, new possibilities open up thanks to the higher specific energy density achievable by the composite sorbents. Indeed, whereas a heat source temperature of 150 • C is needed to reach a maximum energy density of 1000 kJ/kg for heat pumping applications (for LiBr-silica/water and FAM Z02/water) at 45 • C of supply temperature to the user, the AdHT cycle with composite sorbents employing LiCl allows reaching the same energy density but at a much lower temperature.

Conclusions
In the present paper, a thermodynamic analysis is carried out for AdHT systems, focused on the investigation of several working pairs that can be suitable for low-temperature industrial waste heat valorization. The investigation comprised 10 working pairs, using 4 working fluids, to represent a wide class of adsorbents that can be considered useful for the application. Different parameters were analyzed by evaluating thermodynamic efficiencies and specific energies of the AdHT. The main outcomes of the analysis are summarized below: - The implementation of an AdHT system using two separated adsorbent beds represents the most efficient solution, thanks to the possibility of implementing internal heat recovery between the operating phases. Furthermore, the double-adsorbers configuration allows the continuous provision of heat upgrading effect, thanks to the operation of the adsorbers in counter-phase. On the other hand, the specific energy that characterizes each working pair is only slightly affected by the AdHT architecture, thus representing a viable solution when a discontinuous process is expected, due to the much simpler architecture. - The effect of a temperature difference to be considered in each heat exchanger to guarantee a proper heat transfer was considered as well. Particularly, the comparison between ideal conditions and real conditions, in which 5 K of temperature difference between sinks/sources and components, were investigated. As expected, considering a real driving temperature in each circuit strongly affects the achievable performance, by lowering the achievable specific capacity and COP and thus reducing the operating conditions under which the AdHT can be effectively implemented. -Following the obtained results, the performance analysis of AdHT under different boundary conditions was performed for a double-adsorbers configuration and considering the reported temperature difference between external sinks/sources and the components. The investigated conditions considered a variable ambient temperature from −10 • C up to 30 • C and two main applications, extremely low waste heat temperature, i.e., 40-50 • C, to be upgraded for DHN applications and waste heat temperature at 80 • C to be upgraded and re-used in the industrial process. The results confirm that, for both cases, the most promising adsorbent materials are the composites, in which a hygroscopic salt is embedded in a porous matrix, thus enhancing the achievable sorption capacity. This is valid both with methanol and water as working fluids. In particular, a composite based on MWCNT and LiCl, with methanol, looks to be the most efficient one for upgrading waste heat at 40-50 • C, able to provide a GTL of 20 K up to the ambient temperature of 10 • C with an appreciable efficiency (i.e., COP = 0.5) and specific energy (i.e., higher than 1000 kJ/kg). Differently, for the higher waste heat temperature of 80 • C, the most promising solution is represented by a composite using a silica gel and LiCl with water as working fluid. In this case, a GTL up to 50 K can be achieved, with a maximum ambient temperature of 20 • C, still guaranteeing high COP (i.e., 0.48) and specific energy (i.e., higher than 220 kJ/kg).
These results demonstrate that, in general, to achieve a sufficient efficiency of the process, at least 40 to 50 K of temperature difference between waste heat source and ambient temperature should be available, thus confirming the fact that the AdHT technology is more suitable for industrial rather than residential applications. Furthermore, since the effect of temperature difference in each component is extremely relevant, careful design should be performed to maximize the achievable performance.
This preliminary study can be considered as a useful tool for the selection of working pairs for AdHT systems development. Further investigations will be performed to include the effect of inert masses (e.g., heat exchangers, working fluids) over the achievable performance as well as to investigate the kinetics of this process under the identified operating conditions.