Desorption-driven sorption cooling: a thermodynamic analysis of a variable-volume implementation

1 Introduction

Heating and cooling are essential for residential, transportation and industrial applications. However, the energy required for these processes contributes significantly to global energy consumption and related environmental impacts. For this reason, improving the efficiency and sustainability of heating and cooling technologies has become an important research focus. At present, vapor compression systems dominate the commercial market due to their relatively high thermodynamic performance. Absorption systems are also used in certain applications, particularly where thermal energy from waste heat or solar sources is available.

Adsorption-based heating and cooling systems represent an alternative technology that has attracted considerable attention in recent decades. Similar to absorption systems, they can be driven by thermal energy and typically utilize environmentally benign working fluids, such as water or methanol. In a conventional adsorption cooling cycle, an adsorbent bed is heated to induce desorption of the working liquid, while cooling of the adsorbent promotes adsorption during the subsequent stage of the cycle. The vapor released during desorption condenses in a condenser and the liquid refrigerant subsequently evaporates in an evaporator, producing the desired cooling effect.

Despite their potential advantages, adsorption cooling systems have not yet become a widely adopted commercial alternative to compression-based technologies. One important limitation is their relatively low thermodynamic performance compared with vapor compression systems. In addition, conventional adsorption cycles require periodic heating and cooling of the adsorbent bed to drive desorption and adsorption. This requirement introduces significant thermal losses and limits the achievable system performance.

Considerable efforts have therefore been directed toward improving adsorption cooling systems. These include the employment of more suitable adsorbent-adsorbate pairs and the optimization of adsorbent structures to enhance heat and mass transfer. Silica gel, activated carbon and zeolites are among the most widely studied adsorbents, while water and methanol are commonly used adsorbates due to their favorable thermophysical properties (Chauhan et al., 2022; Henninger et al., 2024; Cabeza et al., 2017). Strategies such as heat recovery between adsorption beds and the use of adsorbent coatings on metallic substrates have been investigated to reduce thermal resistance and improve system performance (Akisawa et al., 2022; Banos et al., 2022; Caprì et al., 2020; Tatlier et al., 2014). In particular, structured adsorbent coatings can significantly enhance heat transfer and adsorption kinetics by reducing contact resistance and optimizing adsorbent layer thickness (Calabrese et al., 2017; Schnabel et al., 2010; Maras et al., 2021). Zeolites such as types A, X, Y and SAPO-34 have been identified as promising materials due to their relatively high water adsorption capacities and suitable thermodynamic properties for adsorption cooling applications (Tatlier et al., 2022; Tatlier, 2021; Calabrese et al., 2019). Recent studies have further investigated several approaches to improving the performance and sustainability of thermally regenerated adsorption cooling systems, including the development of high-performance composite and biomass-derived adsorbents and the optimization of operating conditions (Chauhan and Tyagi, 2023a; Chauhan et al., 2025; Chauhan and Tyagi, 2024). The integration of adsorption cooling with alternative heat sources, including bioenergy, has also been investigated (Chauhan and Tyagi, 2023b).

However, even with these improvements, conventional adsorption cooling systems still rely on thermal regeneration of the adsorbent, which requires significant heat input and limits operation to applications where sufficiently high-temperature heat sources are available. Several pressure-swing sorption cooling concepts have previously been proposed, in which adsorption and desorption are driven by externally imposed pressure variations rather than thermal regeneration. These include compressor-driven adsorption cooling cycles (Sward and LeVan, 1999), pressure-swing adsorption refrigeration systems employing predominantly activated carbon/CO₂ working pairs (Anupam et al., 2011; Roy et al., 2021) and continuous pressure-swing adsorption cooling configurations utilizing externally supplied gas and valve arrangements, where the influence of different desorption routes on cooling performance has also been investigated (Koley and Ghosh, 2016). More recently, pressure-driven adsorption heating and cooling have been further developed using CO₂–MOF working pairs, including hybrid compression–adsorption cycles, continuous pressure-driven chillers with circulating adsorbent particles, and experimental demonstrations using MOF-coated heat exchangers (Shamim et al., 2022; Pasqualin et al., 2025; Hu et al., 2026). In these systems, cooling is associated with the endothermic heat of desorption, while the required pressure variation is generally produced by gas compression or other external pressure-control methods. Compression-driven adsorption cooling systems generally rely on gas compression to establish the required pressure swing and are therefore influenced by the efficiencies of conventional compression devices. Bellows structures have also been investigated in adsorption cooling systems to improve the heat and mass transfer characteristics of conventional thermally regenerated adsorption cycles (Boukhanouf and Riffat, 2007).

The present study considers pressure-induced desorption cooling from a broader thermodynamic perspective. Rather than focusing on a particular pressure-generation mechanism, it examines a broader desorption-driven sorption cooling framework in which cooling is generated by reducing the adsorbate partial pressure. The present work differs from previous pressure-driven adsorption cooling studies by investigating this framework for water–based adsorption cooling using zeolite as the adsorbent and by considering variable-volume adsorption cooling (VVAC) as a representative low-work implementation, in which the reduction and subsequent enhancement of the adsorbate partial pressure are directly generated through changes in the adsorber state. In the VVAC system, the vapor pressure decreases during mechanical expansion of the adsorber, initiating desorption and producing a cooling effect through the heat of desorption at temperatures close to ambient conditions. Consequently, the adsorber volume is reduced to its initial size to promote adsorption. In the VVAC implementation considered here, pressure-induced desorption provides an alternative to conventional high temperature thermal regeneration. In contrast to compression-based pressure-swing systems, the variable-volume concept investigated in the present study requires only the work associated with changing the adsorber volume. Although the practical work will depend on the mechanical implementation, the theoretical minimum work considered here is comparatively small, suggesting the potential for favorable thermodynamic performance. This theoretical minimum corresponds solely to the reversible work associated with changing the adsorber volume. In practical compressor-based pressure swing systems, the required work may be higher because pressure variation is generally achieved through compression of a larger gas inventory and operation of auxiliary flow components. The extent of this difference depends on the specific system configuration and is therefore beyond the scope of the present thermodynamic analysis.

Although a variable-volume adsorber is investigated in the present study, desorption-driven sorption cooling is intended as a broader thermodynamic concept and is not restricted to mechanical volume variation. Any process capable of reducing the adsorbate partial pressure while maintaining the adsorbent near ambient temperature could potentially utilize the endothermic heat of desorption for cooling.

The thermodynamic feasibility of the VVAC system was investigated by using a simplified theoretical framework. Calculations were performed for the zeolite-water working pair, employing adsorption data for zeolites NaX and NaY, to evaluate the influence of key operating parameters, including the initial adsorber pressure and the ratio of final to initial adsorber volumes. The results support the thermodynamic feasibility of desorption-driven sorption cooling within the variable-volume implementation considered and provide a foundation for investigating alternative low-work methods for reducing adsorbate partial pressure in future studies.

2 Concept and theoretical analysis of the proposed system

In conventional adsorption heat pump and cooling systems, an adsorbate circulates between the adsorber and the condenser-evaporator pair. The useful heating or cooling effects are generated by the condensation and evaporation of the adsorbate in these components. The adsorbent is located in the adsorber and may be used in different forms, such as pellets or coatings on metallic heat exchanger surfaces.

The operation of a conventional adsorption cooling cycle typically begins with heating the adsorber to initiate desorption. As the adsorbent temperature increases, the equilibrium loading decreases and the adsorbate vapor is released from the adsorbent bed. The resulting pressure increase drives the vapor toward the condenser, where it condenses and releases its latent heat. In the subsequent stage, the adsorber is cooled, which promotes adsorption of the vapor generated in the evaporator. The evaporation of the adsorbate in the evaporator produces the desired cooling effect, and the cycle is completed when the adsorbate is re-adsorbed by the adsorbent.

An important thermodynamic feature of adsorption systems is that adsorption and desorption are accompanied by heat effects. Desorption is an endothermic process and therefore requires heat input, while adsorption is exothermic and releases heat. In conventional adsorption cooling cycles, the heat absorbed during desorption occurs at relatively high temperatures because the adsorbent must be heated to initiate desorption. Consequently, this cooling effect cannot be utilized directly for refrigeration purposes. Conversely, the heat released during adsorption occurs while the adsorbent is being cooled, which limits its usefulness as a heating source within the cycle.

Thus, utilizing the endothermic heat of desorption directly for cooling may provide a fundamentally different thermodynamic pathway for adsorption-based refrigeration. In conventional adsorption cooling systems, useful cooling is generated by evaporation of the adsorbate, while thermal energy must be supplied to regenerate the adsorbent through desorption. In desorption cooling, pressure-induced desorption replaces thermal regeneration, allowing the endothermic heat of desorption itself to become the useful cooling effect. Consequently, the external thermal energy required for regeneration is replaced by the work needed to reduce the adsorbate partial pressure. The thermodynamic performance therefore depends primarily on how efficiently this pressure reduction can be achieved.

The system proposed in this study aims to utilize the intrinsic heat effects of adsorption and desorption more effectively. In particular, the concept focuses on generating a cooling effect directly from the heat of desorption under near-ambient temperature conditions. In the generalized desorption-driven sorption cooling concept, the essential requirement is the reduction of the adsorbate partial pressure while maintaining the adsorbent near ambient temperature. This pressure reduction may, in principle, be achieved by various methods, including mechanical volume variation, humidity swing, membrane-assisted vapor removal or other pressure control strategies. The present work considers variable-volume operation as one representative implementation because it provides a simple theoretical framework for investigating the thermodynamic performance of the concept.

The operating principle of the proposed variable-volume adsorption cooling (VVAC) system is illustrated in Figure 1. Initially, the adsorbent located in the adsorber is saturated with the adsorbate at the operating temperature, and the system pressure is adjusted to the initial pressure (P₁). The cycle begins with expansion of the adsorber volume from (V₁) to (V₂). This expansion decreases the vapor pressure inside the adsorber from (P₁) to (P₂), shifting the adsorption equilibrium toward lower equilibrium loadings and inducing desorption of the adsorbate from the adsorbent.

It should be emphasized that the mechanical expansion is only one possible means of reducing the adsorbate partial pressure and is considered here solely as a representative implementation of the desorption-driven sorption cooling concept.

Since desorption is an endothermic process, heat is absorbed from the surroundings or from the heat exchange fluid circulating in the adsorber. This heat absorption produces the cooling effect of the system. The cooling effect may be transferred to the heat-exchange fluid through heat exchanger tubes located inside the adsorber.

Following the desorption stage, the adsorber volume is reduced from (V₂) back to (V₁). This compression increases the pressure in the adsorber and promotes adsorption of the vapor by the adsorbent. During this stage, the heat of adsorption is released and is rejected to the surroundings or used as a heating effect if desired. The completion of this adsorption step returns the system to its initial state and completes one cycle of the proposed variable-volume adsorption cooling (VVAC) system.

The operating principle of the proposed VVAC cycle may be represented step by step as follows.

Stage 1: Expansion

• - Volume increases
• - Pressure decreases
• - Desorption occurs
• - Cooling effect is produced

Stage 2: Compression

• - Volume decreases
• - Pressure increases
• - Adsorption occurs
• - Heat is released

For continuous operation, two or more adsorbers may be operated out of phase, enabling simultaneous and continuous production of heating and cooling effects. An idealized pressure-volume diagram of the proposed system is illustrated in Figure 2. Expansion of the adsorber (1→2) decreases vapor pressure and induces desorption and cooling, while compression (2→1) promotes adsorption. The enclosed area represents the mechanical work required to drive the cycle.

2.1 Adsorption equilibrium model

Zeolite–water systems were selected because they exhibit steep adsorption isotherms and large adsorption enthalpies, which favor significant loading variations under relatively small pressure changes. Zeolites NaX and NaY, both having high water capacity, the latter being relatively more hydrophobic, were selected as the adsorbents. The adsorption data, fitted to the Langmuir isotherm equation (n_z = n_zs bP/(1+bP)), were expressed as follows to determine n_z (g/g zeolite), the amount of adsorbate in the adsorbent.

n z = 0.340 * 22.93 P / 1 + 22.93 P (1)

for zeolite NaX in Equation 1 (Zito et al., 2015)

n z = 0.364 * 14.4 P / 1 + 14.4 P (2)

for zeolite NaY in Equation 2 (Zito et al., 2015)

Figure 3 presents a representative equilibrium water adsorption isotherm, expressed as adsorbed water loading per unit mass of zeolite (g/g zeolite) and, generated by using Equation 2. The reduction in equilibrium pressure from P₁ to P₂ leads to a decrease in loading from n_z,1 to n_z,2, corresponding to the desorption of the adsorbate. The difference Δn_z determines the extent of cooling produced via the heat of desorption.

2.2 Cycle simulation method

Calculations were performed to investigate the feasibility of the proposed VVAC system. The simplifying assumptions used in the calculations were as follows.

• The adsorbent was initially saturated under the operating conditions.
• The system operated under isothermal conditions at 298 K. This assumption does not represent the actual transient temperature evolution during desorption. Rather, it provides an upper-bound estimate of the equilibrium desorption response at a fixed reference temperature. In an actual system, the endothermic heat of desorption would reduce the adsorbent temperature, thereby altering the equilibrium loading and the resulting desorption capacity.
• Adsorption kinetics and intraparticle diffusion were assumed to be sufficiently fast to enable distinct desorption and adsorption steps. The calculated desorption amounts therefore represent equilibrium capacities rather than experimentally achievable rates. In an actual system, diffusion and heat transfer resistances would reduce the sorption rates and may limit the extent to which equilibrium is reached during a finite cycle, resulting in lower practical cooling power.

The pressure in the adsorber (P), the amount of adsorbate in the adsorber environment (n) and the amount of adsorbate in the adsorbent (n_z) were determined using the ideal gas law.

PV = nRT (3)

For the desorption stage, first, n₁ was calculated from Equation 3 and n_z,1 was calculated from the water adsorption isotherm using the initial pressure (P₁) and initial volume (V₁). The adsorber was then expanded to the specified final volume (V₂) and P₂ was calculated from Equation 3 using V₂ and the initial gas phase amount n₁. Subsequently, n_z,2 was determined from the adsorption isotherm using P₂, representing the equilibrium amount of water adsorbed in the zeolite at the expanded volume. The gas phase amount n₂ was then calculated from the change in the amount of adsorbed water using Equation 4:where m_z represents the zeolite mass and 18 is the molar mass of water in g/mol. Thus, the total amount of water in the closed adsorber is conserved throughout the calculation procedure, as shown in Equation 5.

n i + 1 = n i + m z n z , i – n z , i + 1 / 18 (4)

n total = n i + m z n z , i / 18 = constant (5)

Using the updated n₂, the vapor pressure P₃ and the corresponding equilibrium loading n_z,3 were recalculated at the same volume V₂. These re-equilibration calculations were continued for a prescribed number of desorption/adsorption steps. The desorption stage was then followed by compression to the initial volume, and the same calculation procedure was applied to the adsorption stage. A computer program was written and used to perform these calculations. The main steps are summarized as follows:

• Initial conditions: Specify the initial volume V₁, pressure P₁, and temperature T₁.
• Initial refrigerant amounts: Calculate the initial gas-phase water amount n₁ from the ideal gas equation and the initial adsorbed water loading n_z,1 from the adsorption isotherm.
• Expansion: Change the adsorber volume from V₁ to V₂.
• Pressure calculation: Calculate the corresponding vapor pressure P₂ from the ideal gas equation using the gas-phase water amount.
• Re-equilibration after expansion (desorption): Calculate the equilibrium adsorbed water loading n_z,2 from the adsorption isotherm at P₂, and calculate the corresponding gas-phase water amount n₂ from the conserved total water inventory.
• Successive re-equilibration steps: Recalculate P_i, n_z,i and n_i at the expanded volume V₂ for a prescribed number of desorption/adsorption steps.
• Compression: Return the adsorber volume from V₂ to V₁.
• Adsorption: During compression, the pressure, equilibrium adsorbed water loading and gas-phase water amount are recalculated using the ideal gas equation, adsorption isotherm, and conserved total water inventory.

An initial water vapor pressure of 3 kPa at 25 °C was selected so that the working fluid remained in the vapor phase under the assumed isothermal conditions, while operating close to the saturation pressure of water. The initial pressure was also varied to investigate its effect on the performance of the VVAC system.

2.3 Performance evaluation

Although the amount of adsorbate in the gas phase is small compared with the adsorbed phase, the equilibrium loading of the adsorbent is determined by the vapor pressure. Therefore, even a moderate pressure reduction can significantly shift the adsorption equilibrium and induce desorption, particularly for highly microporous adsorbents, such as zeolites. Δn_z represents the total amount of adsorbate desorbed from or adsorbed in the adsorbent during the desorption and adsorption stages, respectively, as obtained from adsorption isotherm equations.

The thermodynamic performance of the proposed VVAC system was evaluated in terms of an ideal coefficient of performance (COP), defined in Equation 6 as follows.

COP ideal = Q u / W the (6)

Q u = m z Δ n z Δ H ads / des (7)

ΔH_ads/des indicates the heat of adsorption or desorption, which was taken to be equal to 59.2 kJ/mol and 60.5 kJ/mol for zeolites NaX (Tatlier, 2017) and NaY (Tatlier, 2021), respectively. In Equation 7, Q_u is the useful effect obtained from the heat of desorption/adsorption in the adsorber. Assuming reversible isothermal expansion/compression of the vapor phase inside the adsorber (i.e., heat exchange occurs at nearly constant temperature), the minimum reversible theoretical mechanical work required to change the adsorber volume is given by the following.n₁ represents the initial amount of water vapor present in the adsorber prior to desorption. In Equation 8, when pressure and volume are expressed in units of Pa and m³, W_the has the unit of J.

W the = n 1 RT ln V 2 / V 1 (8)

The minimum reversible work associated with the volume change is relatively small compared with the heat of adsorption/desorption of water on zeolites. Consequently, the ideal thermodynamic performance of the proposed VVAC system may be relatively high, provided that the heat generated during adsorption and absorbed during desorption can be effectively exchanged with the working fluid. On the other hand, the ideal COP defined in the present study represents the ratio of the useful heat of desorption to the minimum reversible work required to generate the pressure reduction. It therefore represents an ideal thermodynamic upper limit and does not account for mechanical losses, finite adsorption kinetics, intraparticle diffusion, heat transfer resistance, temperature gradients within the adsorbent, finite heat-transfer-fluid response, leakage, actuator losses, or auxiliary energy consumption. Similar to the Carnot COP, the present COP represents an ideal thermodynamic limit rather than the performance of a practical device. Consequently, the reported values should not be interpreted as practical system COPs. The ideal COP is therefore intended to assess the thermodynamic feasibility and theoretical potential of the proposed system rather than the expected performance of a practical device.

In order to account for mechanical losses, an overall mechanical efficiency, η_m, may be introduced to relate the actual work requirement to the theoretical minimum work, as shown in Equation 9:

W act = W the / η m (9)

The corresponding actual COP given in Equation 10 is therefore

COP act = η m COP ideal (10)

For example, assuming an overall mechanical efficiency of 50%, the actual COP would be approximately half of the ideal value.

In the proposed VVAC system, heat exchangers coated with zeolites may be used to enhance contact between the adsorbent and the heat exchanger surface, thereby improving heat transfer and enabling faster thermal response of the heat-transfer fluid. The zeolite coating thickness can be optimized according to the selected operating conditions to balance adsorbent capacity, heat transfer and mass transfer kinetics (Tatlier and Erdem-Senatalar, 2000). The current model determines the thermodynamic potential of the system, whereas prediction of practical cooling power requires a coupled heat and mass transfer analysis.

The present study does not attempt to optimize a specific mechanical architecture. The large adsorber volume ratios investigated are parametric thermodynamic conditions used to examine the potential operating range of the proposed concept and should not be interpreted as requirements for a practical device. Such large volume ratios may imply substantial piston displacement and/or deformation of a flexible-volume structure. The practical mechanical implementation, including the achievable volume ratio, actuator requirements, dead volume, and mechanical durability, will depend on the selected architecture and is beyond the scope of the present equilibrium analysis.

3 Results and discussion

Calculations were performed to evaluate the feasibility of the proposed variable-volume adsorption cooling (VVAC) system. The results for the desorption stage, during which the cooling effect is generated, are presented first. Figure 4 shows the variations in adsorbate partial pressure and gas-phase water amount during successive desorption/adsorption steps following expansion of the adsorber volume, while Figure 5 presents the corresponding variations in adsorbate partial pressure and water loading in zeolite NaX.

In these calculations, the mass of zeolite was 100 g and the initial pressure (P₁) was 3 kPa. The adsorber volume was varied between 20 L (V₁) and 1000 L (V₂), corresponding to a V₂/V₁ ratio of 50. The first points in Figures 4, 5 represent the initial desorption response following expansion of the adsorber volume from V₁ to V₂, while the subsequent points represent successive desorption/adsorption re-equilibration states at the expanded volume. Following the initial desorption, the redistribution of water between the gas and adsorbed phases produced alternating changes in vapor pressure and adsorbent loading. Under these operating conditions, the amplitude of these changes progressively decreased as the system approached a periodic steady state. Under these operating conditions, the amount of water desorbed from zeolite NaX during the first desorption step was approximately 0.14 g/g zeolite. When the periodic steady-state was approached, however, the net amount of water desorbed from the adsorbent decreased to about 0.035 g/g zeolite. The maximum amount of water present in the adsorber environment during the process was approximately 0.8 mol. The difference between the maximum vapor inventory and the net change in adsorbent loading reflects the redistribution of water between the gas and adsorbed phases during the successive desorption/adsorption re-equilibration steps. As the periodic steady-state is approached, progressively smaller amounts of water are transferred between the two phases at each step.

Additional calculations were performed to investigate the influence of the operating conditions on the dynamic behavior of the proposed system. In the first case, the initial pressure (P₁ = 3 kPa) and the zeolite mass (100 g) were kept constant, while the adsorber volume ratio (V₂/V₁) was reduced to 10. The adsorber volume was varied between 20 L (V₁) and 200 L (V₂). Figure 6 shows the resulting variations in adsorbate partial pressure and amount of water in the zeolite NaX adsorbent during successive desorption/adsorption steps following expansion of the adsorber volume. Under these conditions, corresponding to a considerably smaller expansion ratio, both the initial and net amounts of water desorbed from zeolite NaX decreased to approximately 0.04 g/g zeolite and 0.03 g/g zeolite, respectively. Reducing the expansion ratio substantially decreased the pressure swing produced during each cycle, thereby reducing the change in equilibrium loading and the amount of water transferred during each desorption/adsorption step. The oscillations again decreased progressively in amplitude as the system approached steady-state; however, this approach was considerably slower than for the larger expansion ratio (V₂/V₁ = 50).

In another case, the initial pressure was reduced to P₁ = 1 kPa, while the zeolite mass and the adsorber volume ratio were maintained at 100 g and V₂/V₁ = 50, respectively. The adsorber volume was varied between 20 L (V₁) and 1000 L (V₂). The results are presented in Figure 7. Under these conditions, the adsorbate partial pressure exhibited regular fluctuations between two values during successive desorption and adsorption steps following expansion of the adsorber volume. At the same time, the amount of water desorbed from zeolite NaX increased to approximately 0.22 g/g zeolite during the initial desorption stage, due to the enhanced change in equilibrium loading with the increase in the pressure swing.

The dynamic behavior of the VVAC system depended strongly on the selected operating conditions. Under some combinations of initial pressure, adsorber volume and expansion ratio, the amplitudes of the pressure and loading oscillations decreased progressively, indicating an approach toward a periodic steady state. Under other conditions, however, nearly constant oscillations were maintained throughout the calculations, indicating that repeated desorption and adsorption continued to produce comparable pressure and loading changes during successive cycles. This behavior arises from the coupling between the adsorber volume and the amount of water vapor present in the gas phase. Expansion of the adsorber decreases the vapor pressure, whereas desorption increases the amount of vapor in the gas phase and partially compensates for this pressure reduction. The relative magnitudes of these opposing effects determine whether the oscillations decay progressively or remain nearly constant during repeated cycling.

The calculations further indicate that increasing the expansion ratio (V₂/V₁) or increasing the initial adsorber volume shifts the system toward the decaying-oscillation regime, whereas lower initial pressures tend to promote approximately persistent oscillations. The observed alternating pressure and loading changes represent the successive redistribution states predicted by the model following the volume change. However, because the present model assumes instantaneous adsorption equilibrium and does not include explicit time-dependent mass- and heat-transfer kinetics, the calculations do not establish the actual transient rate or time scale of the predicted oscillations. Experimental validation and a coupled transient heat and mass transfer model will be required to determine the exact transient behavior and time scale of these processes in a practical system.

Another significant operating parameter was the amount of adsorbent contained in the adsorber. Increasing the zeolite mass increases the total adsorption capacity of the system and therefore influences the pressure evolution, the amount of water transferred during each cycle and ultimately the cooling performance of the proposed VVAC system.

Figure 8 illustrates the variations in adsorbate partial pressure and the water loading of zeolite NaX during successive desorption/adsorption steps following expansion of the adsorber volume when the zeolite mass was increased to 500 g. The initial pressure and the adsorber volume ratio were maintained at 3 kPa and V₂/V₁ = 50, respectively. However, the adsorber volume was increased to 70 L (V₁) and 3500 L (V₂) to prevent the vapor pressure from exceeding the saturation pressure of water during the cycle. The minimum initial adsorber volume required to avoid condensation was found to depend on both the adsorbent mass and the expansion ratio. For example, at an expansion ratio of 10 and the same zeolite mass, the minimum initial volume was approximately 100 L, corresponding to a final adsorber volume of 1000 L.

As shown in Figure 8, increasing the adsorbent mass preserved the decaying oscillatory behavior observed previously, although the approach toward the periodic operating regime became somewhat slower. The initial amount of water desorbed from the zeolite remained approximately 0.14 g/g zeolite. These results indicate that the practical use of larger adsorbent inventories is primarily constrained by the minimum adsorber volume required to avoid condensation. When this condition is satisfied, increasing the adsorbent mass provides greater total water transfer and therefore offers the potential for increased cooling capacity without fundamentally altering the operating principle of the VVAC system.

Investigations were also conducted by systematically varying the initial pressure (P₁) and the adsorber volume ratio (V₂/V₁). Figure 9 shows the variation in the amount of water desorbed from zeolite NaX (Δn_z) as a function of the initial pressure for V₂/V₁ ratios of 10, 25 and 50. The calculations considered the amount of water released during the initial desorption stage following volume expansion, irrespective of whether the subsequent system response exhibited decaying or persistent periodic oscillations.

The results indicate that lower initial pressures lead to significantly greater water desorption for all investigated V₂/V₁ ratios. Increasing the V₂/V₁ ratio also substantially enhances the amount of desorbed water. For example, at an initial pressure of 0.5 kPa, Δn_z increased from about 0.13 g/g zeolite to 0.25 g/g zeolite as the V₂/V₁ ratio increased from 10 to 50. At an initial pressure of 3 kPa, the same increase in V₂/V₁ ratio raised Δn_z from about 0.040 g/g zeolite to 0.14 g/g zeolite. The benefit of increasing the expansion ratio became more pronounced as the initial vapor pressure decreased. The results clearly demonstrate that the cyclic water uptake and the cooling capacity of the proposed VVAC system can be controlled over a wide range through appropriate selection of the initial pressure and the expansion ratio.

Figure 10 presents the variation of Δn_z with the V₂/V₁ ratio for initial pressures of 1 kPa, 2 kPa and 3 kPa. The same general trend is observed: higher V₂/V₁ ratios and lower initial pressures both promote greater desorption. For instance, at V₂/V₁ = 10, reducing the initial pressure from 3 kPa to 1 kPa, increased Δn_z from about 0.039 g/g zeolite to 0.089 g/g zeolite. When the V₂/V₁ ratio was increased to 50, the same reduction in initial pressure increased Δn_z from approximately 0.14 g/g zeolite to 0.22 g/g zeolite. At sufficiently large expansion ratios, the increase in Δn_z became progressively smaller, indicating diminishing returns as the equilibrium loading approached its minimum value under the selected operating conditions.

Overall, the calculations indicate that the initial adsorbate pressure and the expansion ratio constitute the two principal operating parameters governing the amount of water transferred during each desorption cycle and therefore the attainable cooling effect of the proposed VVAC system.

Zeolite NaY is more hydrophobic than NaX zeolite, which may lead to different amounts of water desorption/adsorption under similar operating conditions in the VVAC system investigated. Similar trends were observed in the relationships between initial pressure, V₂/V₁ ratio and the amount of water desorbed for zeolite NaY. However, the amount of water desorbed from zeolite NaY was generally higher. This behavior is consistent with the more hydrophobic character of NaY, which results in lower equilibrium water loadings at a given vapor pressure and consequently larger changes in equilibrium loading during pressure reduction. Figure 11 shows the variation of Δn_z with the initial pressure for V₂/V₁ ratios of 10, 25 and 50, when zeolite NaY was used. At an initial pressure of 0.5 kPa, Δn_z increased from approximately 0.16 g/g zeolite to 0.27 g/g zeolite, as the V₂/V₁ ratio increased from 10 to 50. At an initial pressure of 3 kPa, with the same increase in the V₂/V₁ ratio, Δn_z increased from about 0.060 g/g zeolite to 0.19 g/g zeolite. Overall, replacing NaX by NaY increased the desorbed water loading by approximately 9%–36%, depending on the operating conditions.

Figure 12 presents the variation of Δn_z with the V₂/V₁ ratio for initial pressures of 1 kPa, 2 kPa and 3 kPa when zeolite NaY was used. For a V₂/V₁ ratio of 10, when the initial pressure decreased from 3 kPa to 1 kPa, Δn_z increased from about 0.06 g/g zeolite to 0.13 g/g zeolite. At a V₂/V₁ ratio of 50, the same reduction in initial pressure led Δn_z to increase from about 0.19 g/g zeolite to 0.26 g/g zeolite. For these cases, the enhancement in Δn_z when NaY was used instead of NaX, ranged from approximately 15%–36%. These results indicate that adsorbents exhibiting relatively lower water affinity at the operating pressure may provide larger desorption capacities and therefore greater cooling potential within the proposed VVAC concept.

To assess the sensitivity of the predicted cyclic performance to the equilibrium parameters, a representative ±10% variation in the saturation capacity (n_zs) and affinity parameter (b) in the Langmuir equation was performed for both zeolite NaX and zeolite NaY. The resulting changes in the cyclic water uptake, calculated from the difference between the equilibrium loadings at the adsorption and desorption states shown in Figures 9, 11, are summarized in Table 1. The analysis shows that the saturation capacity parameter produces approximately proportional changes in cyclic water uptake, whereas the influence of the affinity parameter varies with the initial pressure and V₂/V₁ ratio. Nevertheless, the overall trends and conclusions remain unchanged.

TABLE 1. Sensitivity of the cyclic water uptake to ±10% variations in the Langmuir parameters for the conditions shown in Figures 9, 11.

When the adsorber volume was reduced from V₂ back to V₁, adsorption generally occurred within the first desorption/adsorption step under the operating conditions investigated, with little or no subsequent variation in adsorber pressure. The amount of water adsorbed during this stage was estimated as the difference between the saturation loading and the loading remaining after the final desorption step of the preceding desorption stage. Under all operating conditions considered, the amount of water adsorbed during the first adsorption step was approximately equal to the amount desorbed during the initial desorption step, thereby completing the adsorption-desorption cycle. The absence of significant pressure fluctuations during the adsorption stage is attributed to the relatively high vapor pressure generated immediately after volume reduction, which rapidly restores the adsorbent loading toward its equilibrium value. Consequently, the driving force for further adsorption becomes very small after the initial adsorption step.

To evaluate the thermodynamic performance of the proposed VVAC system, some estimates of the coefficient of performance (COP_ideal) were calculated, based on the simplified assumptions of the model. It should be reminded that the work calculated by Equation 8 represents the minimum reversible mechanical work required to produce the initial expansion of the adsorber from V₁ to V₂, assuming the initial vapor content prior to desorption. Subsequent desorption occurs spontaneously as the adsorption equilibrium shifts following the pressure reduction. Therefore, the calculated COP represents an ideal thermodynamic upper limit estimate, based on the idealized work required for the specified volume change. In practice, the required work will depend on the particular mechanism used to generate the pressure reduction and will also include mechanical inefficiencies, heat and mass transfer limitations, leakage and auxiliary energy consumption. Additionally, a complete practical work assessment would require consideration of the actual pressure-volume path during simultaneous volume change and sorption. Nevertheless, the calculations indicated that the idealized work associated with the specified volume change may be substantially smaller than the heat of desorption released by the adsorbent, indicating significant thermodynamic potential for the proposed system.

By using an initial pressure of 3 kPa and a zeolite mass of 100 g, COP_ideal values of approximately 45.5 and 96.5 were obtained for V₂/V₁ ratios of 10 and 50, respectively. In these calculations performed for zeolite NaX, the useful cooling effect was determined from the amount of water desorbed during the first desorption step, while the input energy corresponded to the reversible minimum mechanical work required for both of the volume change operations of the idealized cycle.

Practical COP values of 0.75–1.4 have been reported for a continuous pressure-driven CO₂/MIL-101 system, while corresponding idealized values of 1.2–2.2 were obtained when component efficiencies were set to unity (Pasqualin et al., 2025). However, these COP values are not directly equivalent to those calculated in the present study. The pressure-driven system reported by Pasqualin et al. employs a compressor and auxiliary components for pressure generation, whereas the present study evaluates the reversible minimum work associated solely with changing the volume of the adsorber. The COP values reported here therefore represent an ideal thermodynamic upper limit rather than an estimate of achievable system-level COP. Direct numerical comparison between the two systems should consequently be made with caution.

Rather than focusing on the absolute COP values, it is more meaningful to note that a relatively small mechanical perturbation of the adsorber may trigger the release of a much larger amount of thermal energy stored in the adsorption equilibrium. Therefore, the COP values reported here should be interpreted as indicators of the thermodynamic potential of the VVAC system rather than as predictions of the performance of a practical cooling device.

Although a variable-volume adsorber was considered in this study, the required reduction in adsorbate partial pressure could potentially be achieved by various low-work mechanisms. Examples include piston-driven chambers, bellows-type structures, flexible volume systems, or other approaches capable of producing cyclic pressure variation. Investigation of such alternative implementations constitutes an important topic for future research.

4 Conclusion

Desorption-driven sorption cooling was investigated in this study as an alternative thermodynamic approach to conventionally thermally regenerated adsorption cooling systems. In this concept, cooling is produced directly by endothermic heat of desorption by reducing the adsorbate partial pressure, while operation near ambient temperature is possible without the need for external regeneration heat. A variable-volume adsorption cooling (VVAC) system was investigated as a representative implementation, in which desorption is induced by expansion of the adsorber volume. During the subsequent compression stage, adsorption is restored and the heat of adsorption may be utilized for heating purposes.

The theoretical analysis revealed that pressure-induced desorption in the VVAC system may proceed through different operating regimes depending on the selected operating conditions. Following expansion of the adsorber volume, after the first desorption, the system exhibited either decaying or approximately persistent cyclic pressure and loading variations under different operating conditions. Consequently, useful cooling may be obtained during the initial desorption stage, or through successive desorption waves. During the compression stage, adsorption generally occurred in a single step because of the relatively high vapor pressure established in the adsorber.

The initial adsorber pressure and the adsorber volume ratio were identified as the principal parameters governing system performance. Lower initial pressures and higher volume ratios produced greater water desorption from both NaX and NaY zeolites, with NaY exhibiting somewhat higher desorption capacities under investigated conditions. The analysis further demonstrated that a relatively small mechanical perturbation of the adsorber may initiate the release of a substantially larger amount of thermal energy stored in the adsorption equilibrium. Under the simplified assumptions adopted in the present study, the calculated ideal thermodynamic performances were correspondingly high, although these values represent upper thermodynamic limits based on the minimum reversible work required to initiate the pressure reduction.

The present analysis was intentionally limited to a simplified theoretical treatment intended to establish the thermodynamic feasibility of the proposed VVAC system. The pressure reduction was represented as a single idealized expansion step, and the actual mechanical work associated with simultaneous expansion and desorption was not considered. Future studies should therefore investigate gradual or continuous pressure variation, allowing simultaneous desorption and volume change, together with detailed heat and mass transfer analyses, to determine the actual work requirements and optimize practical implementations. Experimental validation of representative systems will also be required to evaluate mechanical design, heat transfer, adsorption kinetics and overall system performance.

The results support the thermodynamic feasibility of the VVAC system and demonstrate its potential as an alternative approach to sorption cooling based on pressure-induced desorption. Although the VVAC system served as a representative implementation, the proposed concept is not restricted to variable-volume operation and may be extended to other low-work methods capable of reducing the adsorbate partial pressure. The findings therefore provide a foundation for the future development and optimization of a broader class of desorption-driven sorption cooling technologies.

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Footnotes

Edited by: Shunmin Zhu, Chinese Academy of Sciences (CAS), China

Reviewed by: Marcin Sosnowski, Jan Długosz University, Poland

Prathvi Raj Chauhan, Thapar Institute of Engineering and Technology, India