Modeling and Simulation of Combined Heat and Mass Transfer in Zeolite SAPO-34 Coating for an Adsorption Heat Pump

Heat and mass transfers inside an adsorbent bed of an adsorption heat pump (AHP) are considered poor; consequently, they can cause low system performance. They should be enhanced so as to increase the coeﬃcient of performance of the cooling machine. The aim of this work is to study an adsorbent bed coated with the zeolite SAPO-34. A simulation model based on governing equations for energy, mass, and momentum transfers is developed using COMSOL Multiphysics software. The system zeolite SAPO-34/water has been considered. Modeling results are validated by experimental database available at the Institute for Advanced Energy Technologies “Nicola Giordano,” Italy. It has been shown that the adsorption heat pump performance is aﬀected by both heat and mass transfer. The enhancement of heat transfer solely is not suﬃcient to attain high values of speciﬁc cooling power. In the case of water vapor/SAPO-34 pair, mass transfer has a signiﬁcant impact on the duration of the cooling step which should be shortened if one would want to increase the speciﬁc cooling power. The sole way to do it is to enhance mass transfer inside porous adsorbent.


Introduction
Refrigeration and air conditioning systems are major consumers of electricity for heating and cooling demands [1]. ese machines use CFCs for their operation which causes the depletion of the ozone layer [2]. In this context, the use of renewable energies as an alternative to fossil fuels is becoming increasingly essential [1,3]. Nowadays, adsorption heat pump (AHP) has received much attention as a sustainable energy solution using environmentally friendly refrigerants such as water, methanol, and ammonia [4,5].
e literature review showed that silica gel/water, activated carbon/methanol, activated carbon/ammonia, and zeolite (13X and 4A)/water are the most studied couples in the case of the adsorption heat pumps [6]. Wang et al. studied adsorption characteristics and the progress of the couple silica gel/water in adsorption refrigeration technologies [7,8]. Interestingly, they found that the pair silica gel/ water is considered ideal for solar energy applications due to its low regeneration temperature. It requires a low-quality heat source, typically below 85°C. In addition, water has the advantage of having higher latent heat than other conventional refrigerants. It is suitable for air conditioning applications with high chilled water flows, where high evaporating temperatures can be used [7,8]. Nevertheless, this pair has low adsorption capacity as well as low vapor pressure, which can limit mass transfer [9,10]. e activated carbon/methanol is one of the most common working pairs in refrigeration adsorption systems. It also operates at low regeneration temperatures (care must be taken because regeneration temperatures above 120°C promote methanol decomposition), while its evaporative adsorption lift temperature is limited to 40°C [10]. In turn, the activated carbon/ammonia pair requires regeneration temperatures which can exceed 150°C. Its heat of adsorption is similar to that of the activated carbon/ methanol pair, but it requires higher operating pressures. Activated carbon/methanol pair leads to improving heat and mass transfer performance and shortens cycle time. All of these factors help to increase the specific cooling capacity of the system and make it even more attractive to researchers. However, activated carbon has a lower adsorption capacity for ammonia than methanol. In addition, care should be taken due to the toxicity of ammonia. It is very dangerous, forming an explosive mixture with air, and can form a certain chemical reaction with materials of construction of the machine such as copper [10,11]. Cacciola and Restuccia compared the performances obtained from the regenerative cycles (heat pump or refrigeration system) for three pairs, zeolite 13X/water, zeolite 4A/water, and activated carbon AC35/methanol. ey found that zeolite-water is the most suitable couple for making machines for use in domestic applications in southern European countries, where the market demand for devices, able to generate heat during the winter and cold during the summer, has been increased considerably [12]. Nonetheless, the pairs zeolite 13X/water and zeolite 4A/ water have the disadvantage of requiring high regeneration temperature [6].
Considerable research activities on the development of new generations of porous materials for use in AHP were performed. In the last years, the silicophosphate SAPO-34 zeolite showed a high potential for cooling applications. e adsorbent material AQSOA-Z02, produced and developed by Mitsubishi Plastic Inc., is used as the commercial name for SAPO-34 [13].
Mitsubishi is a leading global manufacturer of highperformance thermoplastic materials. Heat conductivity, chemical resistance, and temperature resistance consist some of their specific topics in the focus of their current material development activities. e compound zeolite SAPO-34 showed a high potential for cooling applications. Indeed, this adsorbent shows very suitable adsorption characteristics such as a high capacity of adsorption of water and typical conditions for adsorption cooling machines [13]. e enhancement of heat and mass transfers in adsorbers is a key factor for the development of adsorption heat applications. So, several concepts are proposed in innovative research to contact the adsorbent material with a metallic heat exchanger (HEX) [14].  [17]. Lang et al. investigated the adsorption rates of different compact zeolite layers for an adsorption machine [18]. e comparison of a consolidated adsorber with an adsorber of grains, made by Guilleminot et al., demonstrates that the consolidated material has better heat transport characteristics than the granular adsorbent [17].
Publications about adsorber developments for AHP showed that the main problem encountered in the design of consolidated and granular configurations is due to the highest heat and mass transfer resistances [19]. In order to overcome this issue, a coated adsorbent concept has been developed. Freni et al. tested a SAPO-34 coated adsorbent heat exchanger (Ad-HEX) [20]. Waszkiewicz et al. studied the performance of a coated finned tube of zeolite CBV901 [21]. Van Hayden et al. evaluated the performance of ALPO-18 coated-aluminum bed [22]. Freni et al. verified hydrothermal and mechanical stabilities of adsorbent coatings for AHP applications [23]. Okamoto et al. developed AQSOA-Z01, Z02, and Z05 coated heat exchangers for AHP [24]. Despite many advantages of the adsorption cooling machine, heat and mass transfers inside the adsorbent bed are considered poor; consequently, they can cause low system performance [5,25,26]. In order to overcome these issues, the coated heat bed, for adsorption cooling systems, showed very promising properties and better performances in terms of specific cooling power (SCP) [27]. e most common parameters used to evaluate the performance of an adsorption heat system are the coefficient of performance (COP) and the specific cooling power (SCP).
Melkon Tatlier investigated the specific cooling power (SCP) for different zeolite coatings. e power values obtained for zeolite NaX and zeolite LiX, were 0.69 kW/kg and 1.13 kW/kg, respectively [28]. Restuccia et al. performed a detailed study, realizing a solid adsorption chiller based on a heat exchanger coated with the Y type zeolite. e experimental results showed a SCP of 30-60 W/kg and a COP varies between 0.1 and 0.12 [29]. Suxin Qian et al. studied the performance of an adsorption chiller using a synthetic zeolite/water pair. In their study, the SCP of the cycle ranged from 0.1 to 0.9 kW/kg [30]. e objective of the present work is to investigate the coupled heat and mass transfer inside a cylindrical zeolite SAPO-34 coated bed numerically and experimentally. e performance of the adsorption bed is assessed through the evaluation of the parameters COP and SCP.

Mathematical Modeling:
Governing Equations e model under consideration has a cylindrical geometry (see Figure 1). Indeed, the compounds considered are as follows: the heating/cooling fluid (water), the metal tube, and the adsorbent bed zeolite SAPO-34 (AQSOA-Z02) which are all placed in a vacuum chamber. e development of the mathematical model will be simplified by employing the following assumptions: (i) e adsorbent bed is composed of particles with identical properties and is uniformly distributed (ii) Densities, thermal conductivities, and specific heats for all materials are constant 2 Advances in Materials Science and Engineering (iii) Heating/cooling fluid flows at a constant velocity within the tube (iv) Adsorbate vapor phase behaves as an ideal gas (v) Dynamic viscosity, permeability, total porosity, and heat of adsorption are taken as constant (vi) No heat losses are considered

Energy Conservation Equations.
e energy balance for the circulating fluid (HTF) includes only energy transport by conduction and convection [31][32][33]: (1) e energy equation for the metal tube including heat conduction is given by [34][35][36] e energy equation for the adsorbent material has a complex form due to the three different phases: solid, adsorbate phases, and gas. e energy balance for the porous media is written as [19,32] ( Adsorbate vapor phase (water vapor) behaves as an ideal gas and its equation of state is written as [37] P � ρ v R v T s . (4)

Momentum Equations.
For the mass momentum equation in porous media, the velocity of adsorbate gas, U, is considered in the radial and axial directions by using Darcy's equation [38,39]: where κ is the bed permeability and evaluated by the following equation [38,39]:

Mass Conservation Equation.
e mass balance equation inside the adsorbent bed can be expressed as [19,37] ε e amount adsorbed, X, can be calculated using the Linear Driving Force (LDF) model [38,40]: where k m is the internal mass transfer coefficient given by [38] k m � 15 e equilibrium adsorption capacity, X e , of AQSOA-Z02 (SAPO-34)/water pair, is expressed by the Dubinin-Astakhov equation (see Table 1) [39,[41][42][43]: P sat defines the saturation pressure of water vapor inside the adsorbent bed [44]:

Initial and Boundary
Conditions. e temperature distribution for the HTF tube and the adsorbent bed are initially considered to be uniform as well as the adsorption capacity in the porous media:

Advances in Materials Science and Engineering
e boundary conditions for the heating/cooling fluid (HTF) and the tube are given as follows: e boundary conditions for the adsorbent bed are as follows: (i) Temperature boundary conditions: (ii) Pressure boundary conditions: � P c , when connected to the condenser, � P e , when connected to the evaporator.

Performance Coefficients Equations.
e performance of an adsorption heat pump can be measured by two coefficients: the coefficient of performance (COP) and the specific cooling power (SCP) [45]: e cooling energy production in the evaporator, Q e , can be calculated by the following expression: where For the water vapor as adsorbate, L o � 3171.2 kJ/kg and α L � − 2.4425 kJ/kg. K [33].
e energy supplied to the adsorber during the heating period can be calculated from

Model Validation.
e model relative to a coated bed of SAPO-34/water adsorption heat pump previously described in detail will be validated by comparing simulation results to ones from the experimental database available at the Institute for Advanced Energy Technologies "Nicola Giordano," ITAE (CNR ITAE). An aluminum cylindrical tube is coated by the adsorbent material. e coating was prepared by dip-coating method starting from a water suspension of SAPO-34 zeolite and a silane-based binder. e coating's preparation and characterization were investigated according to the experimental testing method developed in [20]. Mechanical characterizations of the coatings were performed by a number of experimental protocols, conforming to [23].
Simulations have been achieved using the input data provided in Tables 2 and 3. A two-dimensional axisymmetric geometry is considered. A time-dependent analysis of the coupled heat and mass transfer models has been performed using COMSOL Multiphysics software. In the simulation program, the heat transfer module for energy balances, chemical engineering module for mass balances, and partial differential equation (PDE) for the LDF module are chosen for the adaptation of governing equations. e convection and conduction physics mode was selected to be the application module that describes heat transfer, respectively, in the HTF, metal tube, and the  (1)-(3). While convection and diffusion (equation (7)) were added to simulate the adsorption/desorption processes in micropores of sorbent particles via mass transport. Equation (8) was written as a differential equation and it can be introduced to COMSOL using a PDE form under COMSOL Multiphysics modules. Simulated configuration is meshed in COMSOL by using an extremely fine mesh to produce over 301846 triangular elements.
In order to enable high accuracy and convergence, solver settings of the COMSOL have the following properties: (i) Transient analysis type with ten seconds of step setting (ii) Direct impact method (iii) Relative tolerance: 0.1 (iv) Absolute tolerance: 0.001 (v) Stability of solution been set to automatic Simulations are performed for adsorption and desorption processes.
Simulations are obtained for the following operating conditions: T i � 28.65°C, T h � 89.28°C, T ev � 8°C, T c � 28°C, and cycle time t cyc � 320 s; they correspond to those used to get experimental database available at the Institute for Advanced Energy Technologies "Nicola Giordano," ITAE (CNR ITAE) previously indicated. e adsorbed amount variation with time, during the whole cycles (adsorption/desorption cycles), is shown in Figure 2. At the time t � 0 s, the adsorbed amount being at its maximum value, Xo � 0.31 kg w /kg s , begins to decrease when heating starts. For this heat transfer fluid temperature (T h � 89.28°C), it can be seen that SAPO-34 is nearly totally desorbed just after 50 s of heating during the desorption process. e bed becomes uniformly loaded without being completely desorbed. One has to increase the temperature of the heat transfer fluid to further reduce the amount adsorbed at the end of the heating step. e notable reduction of the duration of the heating step shows that the heat transfer between the adsorbent layer and the metal surface has been enormously enhanced by using the coating technique resulting in the obtention of a very reduced thickness (r b � 0.1 mm). Figure 3 shows a comparison between experimental and simulated average temperature evolutions of SAPO-34 coated bed during the adsorption/desorption process. It can be seen that the difference between the numerical results and experimental measurements in the adsorber is quite small. erefore, the simulation results could be considered satisfactory insofar as the deviation between the two results does not exceed ± 2%. e simulation model could be used safely to predict system performance with high accuracy. One can note that, at t � 60 s and during the desorption cycle, the bed is totally heated and reaches almost the cycle maximum temperature of 362.43 K. Due to heat transfer enhancement induced by the coating reduced thickness, a heating duration of 60 s is sufficient and there is no need to extend the heating time beyond 60 seconds especially as the bed becomes uniformly desorbed as previously noted. e cooling duration should not be reduced because the bed takes more time to be totally saturated due to the reduction of the mass transfer rate in comparison to the one during heating (see Figure 2). e mass transfer rate is modeled herein by the Linear Driving Force (LDF) model. In fact, the values of diffusivities (D s � D so . exp (− E a /R × T)) of water vapor are 7.80 × 10 − 17 and 0.4 × 10 − 17 m 2 /s during heating (T h � 89.28°C) and cooling (T c � 28°C), respectively. e diffusivity is multiplied by nearly a factor of 20 when there is a 61°C temperature increase.
For adsorption heat pump applications, the coefficient of performance and the specific cooling power represent two important parameters to evaluate their performances.
Employing equations (16) and (17), the SCP and COP of the adsorbent material SAPO-34 (AQSOA-Z02) and water of an AHP are calculated and are summarized in Table 4.
For cycle time t cyc � 320 s (160 s for heating and 160 s for cooling), COP and SCP values obtained by simulation are   Advances in Materials Science and Engineering 0.58 and 1.7 kW/kg, respectively. If the cooling time is taken equal to 60 s (t cyc � 220 s) for the reasons given previously, the value of SCP obtained is 2.49, and COP remains unchanged (see Table 4). It can be noted that the coated adsorber shows a good performance in terms of COP. On the other hand, it presents a high specific cooling power. For granular and consolidated beds, the values of COP are around 0.4 and 0.24, respectively [47], and the COP improvement is significant. us, the coated adsorbent bed seems to be a promising configuration for adsorption heat pumps technologies. Table 5 illustrates a comparison of SCP values obtained in this study with those of some SAPO-34 coatings for adsorption heat pump reported in the literature.
In the following, after being validated, the simulation model will be used to assess the effect of the temperature of the heat transfer fluid and the evaporator pressure on the performance of the adsorption heat pump.

Effect of Heating Fluid Temperature.
Variations with time of average temperature and adsorbed amount of water inside an adsorbent bed given by COMSOL simulations for the specified initial and boundary conditions are presented in Figures 4 and 5. All the results are obtained for the following operating conditions: T i � 28.65°C, T ev � 8°C, T c � 28°C, and cycle time (t cyc ) � 220 s. ree values of hot fluid inlet temperature were tested: T h � 89.28, 120, and 150°C.
It is shown in Figure 4 that the adsorber gets completely heated more rapidly when the temperature of the heat transfer fluid increases, and the bed temperature becomes uniform in a shorter time. For the lower temperature of heat transfer fluid (T h � 89.28°C), the adsorbent bed reaches a uniform temperature after t � 60 s, whereas for the higher one (T h � 150°C), the heating is completed in 30 s. In other words, the cycle time of the system decreases with increasing the temperature of the heat source. us, this permits increasing COP and SCP of the system. It is worth noting that the choice of the temperature of heat transfer fluid is often imposed by some constraints related to the availability of the heat source. For example, if the adsorption heat pump is intended to be powered by solar energy, a temperature of 89°C seems to be suitable given the efficiency of solar collectors.
In Figure 5, it can be seen that the temperature of the heat transfer fluid has a significant influence on the desorption mass transfer rate during heating. As mentioned previously, when T h increases, the diffusion coefficient of water vapor in the zeolite porous particles increases given its dependency with temperature resulting in a notable shortening of the desorption step. For T h � 150°C, the coated bed is completely desorbed in 20 s. For T h � 89.28°C, the coated bed could not be totally desorbed, nearly 15% of water vapor remains adsorbed in the bed at the end of the heating step regardless of the heating step time.
is diminishes notably the system performance. In fact, the cooling energy production in the evaporator (Q e ) of the system, is directly related to the difference of water vapor adsorbed amounts at the end of cooling and heating steps.
is difference in water vapor is cycled inside the adsorption heat pump flowing from the evaporator to the condenser and vice versa. One has to increase this difference for obtaining higher values of COP and SCP.

Effect of Evaporator Pressure.
e transient variation of average temperature and average adsorbed amount inside the adsorbent bed for different values of P e (P e � 0.8, 1.053, and 1.228 kPa) for the specified initial conditions are shown in Figures 6 and 7, with T i � 28.65°C, T h � 89.28°C, T c � 28°C, and cycle time (t cyc ) � 220 s. e three curves relative to the temperature variation with time for the different values of the evaporator pressure nearly coincide ( Figure 6). It is clear that temperature inside the adsorbent bed is not affected by varying P e as shown in Figure 6, despite the increase of the adsorbed amount as can be seen in Figure 7.
In fact, from Figure 7, it is found that increasing the evaporator pressure has a noticeable effect on the SAPO-34 uptakes. e highest value for adsorbed amount is obtained for the highest value of P e as can be predicted by the Dubinin-Astakhov equation.
Due to the variation of the adsorbed amount, the coefficient of performance (COP) and the specific cooling power (SCP) of the couple SAPO-34/water are affected by varying P e , as shown in Figure 8. e COP values vary from 0.521 for P e � 0.8 kPa to 0.622 for P e � 1.228 kPa. e corresponding values of SCP are 2.24 kW/kg and 2.68 kW/kg. Hence, as the evaporator pressure increases, the COP and SCP of the system increase. However, there is no significant    Advances in Materials Science and Engineering difference in the cycle time when the evaporator pressure increases. e duration of the cooling step is totally controlled by the mass transfer rate due to the slow diffusion of water vapor in porous zeolite particles as indicated previously. Enhancement of heat transfer would not have an impact on the cooling step time, the sole way to shorten it is to enhance mass transfer inside porous adsorbent. It has to be noted that the value of COP given by simulation for a SAPO-34 coated bed (0.622) is close to those of absorption heat pumps (around 0.7); this constitutes a great scientific advancement for adsorption heat pumps which could place them as serious competing technologies for cooling.
Furthermore, the values of COP and SCP are obtained for an adsorbent heat conductivity of 0.3 W/m K. Higher values are expected to be obtained for higher values of conductivity. In fact, much research and development work is being carried out to enhance heat transfer; one way to achieve that goal is to incorporate within the raw adsorbent additives possessing high conductivities. However, the increase of thermal conductivity could cause the decrease of adsorption capacity and mass transfer rate, so much  attention is needed when optimizing the preparation of the new adsorbent for heat transfer enhancement. is issue will be addressed in the forthcoming paper.

Conclusion
A 2D axisymmetric coupled heat and mass transfer model with initial and boundary conditions was proposed to study a SAPO-34 coated bed. us, mathematical modeling using COMSOL can provide a useful predictive tool for understanding, design, and optimization of AQSOA-Z02 adsorption/desorption process as an adsorbent material for AHP.
is enables us to make significant modifications to avoid damage and failure of the whole designed system.
(iii) e adsorption heat pump performance is affected by both heat and mass transfer. e enhancement of heat transfer solely is not sufficient to attain high values of COP and SCP. In the case of water vapor/ SAPO-34 pair, the mass transfer has a significant impact on the duration of the cooling step which should be shortened if one would want to increase the specific cooling power. e sole way to do it is to enhance mass transfer inside porous adsorbent. e most cited constraints for adsorption heat systems are the huge volume, heavyweight, and high cost. In order to decrease the system's overall volume and weight, several bed configurations can be employed such as finned tube heat exchangers. erefore, further works on the AHP's is needed to optimize the design of the bed and reduce the model's cost and weight of this study.

A:
HTF tube surface area, m 2 C p : Specific heat, J/kg. K C pl : Specific heat of liquid water, J/kg K C pv : Specific heat of vapor water, J/kg K COP: Coefficient of performance D so : Reference diffusivity, m 2 /s E: Characteristics energy, J/mol E a : Activation energy, J/mol h i : Convective heat transfer coefficient between tube and fluid, W/m 2 K h o : Wall heat transfer coefficient between tube and adsorbent, W/m 2 K k: ermal conductivity, W/m K L v : Latent heat of vaporization, J/kg m s : Mass of sorbent, kg P: Pressure, Pa R: Universal gas constant, kJ/kmol K R v : Ideal gas constant for vapor, J/kg K r: Radial coordinate, m SCP: Specific cooling power, kW/kg T: Temperature, K t: Time, s T i : Initial temperature, K T co : Cold fluid inlet temperature, K T h : Hot fluid inlet temperature, K U: Vapor velocity vector, m/s V: Volume, m 3 X: Amount of water adsorbed by adsorbent per unit, kg w /kg s z: Axial coordinate, m ε: Total porosity μ: Dynamic viscosity, kg/m. s ϑ: Velocity, m/s κ: Permeability, m 2 ρ: Density, kg/m 3 ΔH: Heat of adsorption, kJ/kg. Tube.

Data Availability
e data used to support the findings of this study are included within the article. More supported data can be obtained from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.