Performance analysis of adsorption refrigeration system using silicagel/methanol pair: experimental & analytical approaches

An adsorption refrigeration system (ARS) working on silica-gel/methanol pair has been investigated analytically and experimentally. By applying the mass balance in the adsorber bed the mechanism of adsorption in the thermal compressor with respect to time and bed length was determined. An experimental analysis was performed using a thermal gravimetric analyzer(TGA) to evaluate the mass transfer coefficient and optimum cycle time for silica-gel/ methanol pair at different working temperatures. The Diffusion coefficient Ds and Activation energy Ea for silica-gel/methanol pair were found 2.55 × 10 –4 m2/s and 83.08 KJ/mol. Further, the results of variation of regeneration temperature on the performance of the system in terms of COP (Coefficient of Performance) and SCP (Specific Cooling Power) was evaluated; the maximum average theoretical COP and SCP achieved by the system was 0.5 and 102 W/kg near about 127°C regeneration temperature. Cite this article as: Soni P, Gaba VK. Performance analysis of adsorption refrigeration system using silicagel/methanol pair: experimental & analytical approaches. J Ther Eng 2021;7(5):1079–1089. Journal of Thermal Engineering Web page info: https://jten.yildiz.edu.tr DOI: 10.18186/thermal.977913


INTRODUCTION
The adsorption refrigeration technology uses a low grade of energy (Heat) instead of a high grade of energy (Work) for refrigeration purposes. Since the refrigerant used in the system is eco-friendly and natural refrigerants like water, ammonia, and methanol can be used for refrigeration, it makes this system suitable for the future era.
Another advantage is that these systems do not require electricity, which solves the problem for those areas where electricity is either not available or not reliable. The disadvantage associated with ARS is that this system comprises more components as compared to vapour compression system (VCS). In addition, debris resulting from the corrosion fouls narrow down the openings in the system.
In a conventional VCS, the compressor is a major part of the system, which is used to compress the refrigerant from evaporator pressure to condenser pressure and also continue to circulate the refrigerant through the refrigerating system. In a similar manner, a unit thatperforms the same function as a conventional compressor but utilizes heat energy in the sorption system is known as a thermal compressor.
The researcher found that the heat transfer rate in thermal adsorber bed is very poor; this is because of low thermal conductivity of adsorbent, inefficient design of adsorber bed, and low heat transfer coefficient between the heat transfer fluid and adsorber bed walls. There are few ways to enhance heat transfer.
• By mixing the metal powder and metal foam. • By making the composite of adsorbent using expanded natural graphite, activated carbon fibre, CaCl 2 , etc. • Improving the design of adsorber bed, which provides more surface area for heat transfer like spiral plate, fined tube type adsorber bed. • Reducing the thermal contact resistance between wall and adsorbent (using coated adsorber bed) • By using the heat pipes in the adsorber bed to improve the heat transfer.
At the beginning of the 2000s, Chua et al. [1] experimentally analysed the adsorption characteristics of pure water vapour with two different types of silica-gel in the range of temperature 25°C to 65°C and at different equilibrium pressure range between 500 to 7000 Pa using a volumetric technique. Freni et al. [2] presented an ARS for cold storage using solar energy for regeneration. They used ethanol as a working fluid instead of methanol due to it's less toxic and corrosive nature and obtained a COP of 0.1. Skoda and Suzuki [3] presented some fundamental experimental and theoretical studies which were carried out for silica-gel/water working pair. Berdja et al. [4] represented an experimental model that adopted an adsorption tube collector for refrigeration. The thermal COP obtained is 0.49 and the solar COP obtained is 0.081. Liu et al. [5] built up an ARS working on silica-gel/water pair without using any refrigerant valves. This component decreased the expense of the system and made it progressively solid as there arefewermovable parts that could permit air invasion.
Zhong et al. [6] proposed an air conditioning system based on adsorption technology for a heavy-duty truck. The system works on Zeolite/water pair using the exhaust heat of the diesel engine as a prime heat source. It is observed that the COP varies in the range of 0.23 to 0.498 and SCP in the range of 40 W/kg to 125 W/kg. Saha et al. [7] performed an experimental analysis on a double-stage, fourbed, non-regenerative ARS usingsolar/waste heat sources in the range of 50°C and 70°C. Nunez et al. [8] prepared and examined a silica-gel/water ARS with apurported cooling power of 3.5 kW. Saha et al. [9] studied adsorption capacity of ethanol into a pitch-based activated carbon fibre (ACF) of type (A-20). Direct adsorption capacity, as well as the adsorbent temperature, is observed with the help ofa thermal gravimetric analyzer (TGA) unit. Chin Ni et al. [10] played out an estimation of the clear solid-side mass diffusivity of water fume adsorbed in a normal thickness silica gel by utilizing a constant-pressure TGA. Hamdeh et al. [11] performed an experimental analysis to optimize the design parameter of the solar ARS. The minimum temperature of 9°C was observed in the evaporator corresponding to the atmospheric temperature of 26°C. Deshmukh et al. [12] presented a new design of ARS in which three adsorber bed (two identical small and one big) was used this system attain an average COP and SCP of 0.63 and 337.5 kJ/kg respectively.Sur et al. [13] developed simple equilibrium and dynamic models which can be used for generating simulation resultsof different combinations of adsorbate and adsorbent. Sheikholeslami et al. [14] [15] investigates the impact of using fins and nano-sized materials on the performance of the discharging system. Dixitetal. [16] presented the waste heat driven triple effect refrigeration cycle from the viewpoint of both energy and exergy concepts of thermodynamics. Javadi et al. [17] reproduced an ordinary consolidated cycle power age unit in Iran by a numerical strategy to perform an affectability examination on climate discharge and power cost. Sheikholeslami et al. [18] [19] explained various ways of heat transfer enhancement in a heat exchangers using nanofluids. Kurtulmus et al. [20] modelled and analyseda Vapour Absorption coolingsystem;this system utilised the waste heat from the exhaust gases of the I.C. engine of a passenger bus. This system is used for the air conditioning of the driver cabin with different working conditions. Kalla et al. [21] performed a comparative analysis between different refrigerants such as R22, R407C, R432A, R438A and NM1 (R32/R125/R600a) to obtain a perfect replacement of HCFC 22 for refrigeration purposes. Javadi et al. [22] introduced a joined cycle power plant with an ostensible limit of 500 MW, the examination is done to enhance three target elements of exergy efficiency, CO 2 emanation and created power costs. Anand et al. [23] performed the energy and exergy analysis on an absorption refrigeration system which is used for the air conditioning purpose of a residential building. In this system, the solar energy is used for regeneration purpose. Bhargav et al. [24] developed an ARS system working on activated carbon/ methanol pair using the solar energy for regeneration. This system is used forfood preservation and they produced a cooling effect of 554 kJ in 6 hours in 10 kg of water.
Only a few people work on the design of an adsorber bed using the mass transfer analysis, in this article many concepts have been covered. The main aim is to promote quick, reasonably, reliable design by taking into account the most important properties of adsorbent: capacity, kinetics, bed dynamics, and adsorption dynamics, etc. because of the simplification and idealisation there are many factors that could not be addressed. Moreover, there are only a few researchers found that sheds light on that type of adsorption system which is operated using the waste heat of the I.C. engine.
As water cannot be used as a refrigerant for those applications where the sub-zero temperature is required to attend, so a silica-gel/methanol pair has gained importance. Due to the lower freezing temperature of methanol as compared to water, it can be used as a working fluid for thermally driven refrigeration system therefore, it was decided to investigate the ideal performance of an engine exhaustdriven silica-gel/methanol-based ARS, using the approach of Skoda et al. [3] and the result is presented in this paper.

SYSTEM DESCRIPTION
An ARS utilizes heat energy instead of mechanical work, so conventional compressor has to be replaced by a thermal compressor. A proposed thermal system for silica-gel/methanol pair is shown in Figure (1).
In this system silica-gel is used as an adsorbent and methanol is used as an adsorber. This system consists of two cylindrical vessels completely filled with silica-gel and methanol. Inside the cylindrical vessel, a concentric copper tube is placed for circulating hot and cold water throughout the adsorber bed respectively for heating and cooling the silica-gel. The silica-gel, when cooled, adsorb the methanol and when heated, desorbs it. The two adsorber bed is used for the continuous cooing operation.
In this system, the adsorber bed utilizes the heat energy of hot water, which is taking the heat of exhaust of the I.C. engine by passing through a heat exchanger. In the first phase of operation,the hot water is circulated through adsorber bed I and cooling water is circulated through bed II. Also in this phase, valves V 1 and V 4 are kept closed and V 2 and V 3 are kept open. Similarly, during the second phase hot water is circulated through adsorber bed II and cold water is circulated through adsorbed bed I, to achieve desorption in adsorber bed II and adsorption bed I. During the second phase valves, V 1 and V 4 are kept opened and V 2 and V 3 are kept closed.
With the help of two adsorber beds, this system is able to produce a continuous cooling effect. The cycle rehashes the same thing in a manner like the VCS by alternating the circulation of hot water and cold water in the adsorber bed I and adsorber bed II respectively. During desorption superheated methanol is released at the pressure of the condenser i.e. P cond in the same manner as in VCS. After that, the methanol is condensate at a temperature T cond in the condenser by rejecting the heat to the ambient at a temperature T a . Subsequently, it goes through an expansion valve, thus lowering the pressure to P ev . This methanol at low pressure and low temperature is evaporated at T evp by taking the heat from the evaporator.

Analysis of Adsorber Bed
The mechanism of adsorption in the adsorber bed is shown in Figure (2). Adsorber bed is packed with silica-gel, low-pressure methanol from the evaporator enters it and the maximum mass is adsorbed by silica-gel, a few of it is in pores and dead volume. The dead volume is the small zones within the adsorber bed where some methanol molecules are trapped without any participation in the refrigeration process. So applying the mass balance in the bed, Where Ṁ z represents the mass flow rate per unit area in the Z direction The mass of methanol adsorbed in the element volume is given by The mass of methanol accumulated in the pore volume is given by Where v is the interstitial velocity Substituting all these values in Equation (1) At the break through point, For a small change in amount adsorbed i.e. ∆n, equation can be rearranged as The step velocity V is defined as Hence Equation (4) yields From Henry's law n = HC, hence equation may be written as If L be the length of cylinder and t* be the equilibrium time for the adsorption, then the step velocity V is V=L/t* therefore t* is expressed as Further if Q is the flow rate of methanol and V ads be the volume of the adsorber bed, and then Equation (5) , ( ) * Using separation of variables, solution of Equation (6) By solving and taking λ = -1 for without any loss of generality, one gets And f z C e C e The equilibrium amount of adsorption, is proposed by Skoda et al. [3] as Where k is given by Where, ρ* for methanol is 800 kg/m 3 , ε p for silica-gel is 0.44 and ρ p for silica-gel is 1300 kg/m 3 . Hence the value of k for silica-gel/methanol pair is 0.27.
Using Equation (8), methanol per kg of silica-gel desorbed from bed i.e. ∆n is evaluated as [3]

Experiment Analysis for Determination of Mass Transfer Coefficient k s a p for Silica-gel/Methanol Pair
For the performance enhancementof an ARS.The observation of the kinetics of the adsorbent/adsorbate (refrigerant) pair is necessary. However, design and modelling of adsorption processes require the numerical solution of a set of partial differential equations involving time and special variables. The computations can be greatly simplified by using the linear driving force (LDF) method [27]. Customarily, the calculations season of the code could be improved utilizing the notable linear driving force (LDF) relationship. In the LDF technique, the key boundary is the assurance of the overall particle mass transfer coefficient which is can be evaluated by tracking the experimental vapour-uptake behaviour.
Adsorption rate for every adsorbent/adsorbate upon the mass transfer coefficient (k s a p ) of the pair and adsorption rate is given by [3] dn dt k a n s p where mass transfer coefficient k s a p for adsorbent/adsorbate pairs depends upon the physical and chemical properties of the pair and also depends upon the temperature. For evaluating the k s a p value for silica-gel/methanol pair Thermal Gravimetric Analyzer (TGA) was used. To make a sample of silica-gel/methanol pair, first of all, methanol was added to silica-gel and left for sufficient time until adsorption had taken place uniformly in the silica-gel. Now a sample of 12.967 mg was taken and placed in a crucible of platinum. Now this crucible was placed inside the DTG-60 Thermal Gravimetric Analyzer (TGA) in an atmosphere of N 2 .The heating rate was adjusted 5°C/min ranging from room temperature to 200°C.
Let W = Equilibrium desorption capacity (kg/kg) w = Instantaneous desorption capacity (kg/kg) Then from Equation (10 Similarly, w can also be found out with the help of Equation (12) and Figure (8). So dw dt value can also be obtained at any time and at any temperature. Different k s a p value at any time and temperature can be evaluated by using Equation (11). k s a p is also given by [12] k a C C T s p

&
Hence Equation (13) can also be expressed as

Calculation for SCP and COP of the System
The thermophysical properties of the working fluid methanol are as follows [28]: Methanol gas characteristic constant given as: In all the equations, temperature T is in kelvin, K. Refrigeration effect per kg of adsorbent is known as specific cooling power (SCP) of the system now applying energy balance in bed [

RESULTS AND DISCUSSION
Using Equation (7), the adsorption in the adsorber bed with respect to time as well as the length of the bed was visualised as shown in Figures (3) and (4). In Figure (4) as the adsorption time is increasing more mass of methanol adsorbed but the time required to attend the maximum adsorption i.e. n* is practically not possible or in other words, it will take infinite time. Figure (4) shows the variation in adsorption with bed length (z), the adsorption (n) is higher at the entering side of methanol and lowers at the end of the adsorber bed which is due to the layer by layer phenomenon of adsorption. These graphs are important for the design of the adsorber bed.  For optimising the value of m, a graph between ∆n and mis plotted with different regeneration temperatures T reg , taking evaporator temperature T evp as 7°C, ambient temperature 37°C during peak summer and condenser temperature as 27°C respectively as shown in Figure (5). It is observed that there exists an optimum value of m for each regeneration temperature at which the capacity of adsorption of methanol reaches the maximum. The plot of Δn against m yields an optimum m value for silica-gel/methanol. It is also found that as regeneration temperature is enhanced, ∆n also increases due to the increase in saturation pressure corresponding to each regeneration temperature. All curves show maxima at m = 2 and thereforemis taken as 2.
Evaporator pressure and condenser pressure are two ranges of pressure between which a thermal compressor is operated. With the help of equation (9)  TGA was connected to a computer, having the facility of drawing plots between weight vs temperature and weight vs time. The curves obtained are shown in Figure (7) and Figure (8) respectively. It is clear from the Figure 7 and 8 that most of the amount of methanol desorbed up to 120ºC near about 16.6 minutes, after that the curves become constant it means that there are no significant outcomes of further increasing the temperature so here we can consider that the optimum desorption time is 16.6 minutes and from literature, we know that the adsorption time is slightly more than desorption time. So the total cycle time (adsorption time + desorption time) for silica-gel/methanol pair can be considered as 35 minutes and the optimum regeneration temperature can be considered as 120 ºC.
It is clear from Equation (14) that if a curve is plotted between In(k s a p )vs 1/T then both C 1 and C 2 can easily be found, so from Figure (9), the value of C 1 and C 2 are 4.332 sec -1 and 3197.9 K/sec, respectively. So Equation (14)  becomes In(k s a p ) = 4.332 -(3197.9/T) Figure 6. Adsorption cycle between two pressure limit.   Diffusion coefficient D s and activation energy E a for silica-gel/methanol pair are calculated as 2.55 × 10 -4 m 2 /s and 83.08 kJ/mol, respectively. Here the size of packed particles of silica-gel is between 8 and 20 meshes and the average radius, R p is 7.1 × 10 -3 m.
A comparison between the experimental value of mass transfer coefficient k s a p and the analytical value of k s a p identified by using Equation (13) corresponding to different regeneration temperatures is shown in Table 1. From the table, it is observed that the analytical results show a good validation with the experimental research data using the regression dependences. Using Equation (10) & (16), for producing a cooling effect at different evaporator temperatures i.e. 2°C, 7°C and 12°C both SCP and COP of the system were calculated by varying the regeneration temperature from 60°C to 120°C and assuming that ambient and condenser temperature is 37°C and 27°C, as shown in Figure (10) and Figure (11), respectively.
Both SCP, as well as COP, is the function of regeneration temperature, after minimum regeneration temperature (i.e. the minimum temperature required to run the cycle) both are increasing with regeneration temperature and attending a maximum value. This is due to the fact that more methanol is desorbed at a higher temperature and passing through the evaporator coil. But after certain regeneration temperature curves become constant because more losses are involved at the elevated temperature.

Uncertainty Analysis
There are a few wellsprings of uncertainty in any TGA analysis. Among these are vacillations in the balance, estimation of temperature by the thermocouple, and test readiness.
Where δW represent the uncertainty in the methanol adsorption/desorption uptake measurement, δd present the uncertainty of the evaporator diameter and δm is the uncertainty of sample mass measurement whilst δh is the uncertainty in methanol level height measurement using the digital microscope in the TGA experimental test rig. Using Equation (1) the uncertainty of the methanol adsorption/ desorption uptake measurement has been found to varying from 4.7% to 5.8%.

Validation of Model
A complete thermodynamic and experimental analysis of ARS working on silica-gel/methanol pair for cold storage was done by Oertel et al. [26]. They developed a laboratory test facility to predict the performance of the system under different working conditions. Table 2 shows a comparison between the COP obtained by Oertel and COP obtained by our numerical equilibrium model with the variation of regeneration temperature. From the table, it was observed that at 75ºC regeneration temperature the present numerical model show 4.76% lower COP whereas at 90ºC regeneration temperature it shows 3.33% higher COP as compare to Oertel experimental analysis. The variation was found because they used a fined tube type heat exchanger as an adsorber bed and here calculation was done by using a simple cylindrical adsorber bed.

CONCLUSION
A continuous vapour ARS with two adsorber beds powered by the exhaust gases of the I.C. engine has been described. An analytical approach has been used to describe the adsorption phenomenon of methanol into the adsorber bed. The system operates between the lower pressure limit of 0.006 bar and upper pressure of 0.304 bar where the difference in the adsorption uptake ∆n could be reached to 0.12 kg/kg of silica-gel. The optimum cycle time for silica-gel/methanol pair was found 35 minutes and the optimum regeneration temperature was found 120°C. It was found that the COP and SCP are the functions of regeneration temperature and as the regeneration temperature increases the COP and SCP also increases, the maximum theoretical COP and SCP achieved by the system at 7°C evaporator temperature was 0.5 and 102 W/kg near about 127°C regeneration temperature. The current work presented research efforts towards the enhancement of silica-gel/methanol adsorption cooling system and it can be considered as a strong foundation for future work. In the future, we can work on the different new composite adsorbents and can work on the development of a new design of adsorber beds to improve the heat and mass transfer performance and the overall efficiency of ARS.

DATA AVAILABILITY STATEMENT
No new data were created in this study. The published publication includes all graphics collected or developed during the study.

CONFLICT OF INTEREST
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

ETHICS
There are no ethical issues with the publication of this manuscript.