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Optimization of the cycle durations of adsorption heat pumps employing zeolite coatings synthesized on metal supports
Microporous and Mesoporous Materials 34 (2000) 23–30 www.elsevier.nl/locate/micromeso
Optimization of the cycle durations of adsorption heat pumps employing zeolite coatings synthesized on metal supports Melkon Tatlıer, Ays¸e Erdem-S¸enatalar * Department of Chemical Engineering, Istanbul Technical University, Maslak, 80626 Istanbul, Turkey Received 2 June 1998; accepted for publication 22 July 1999
Abstract In order to remove the limitations originating from inefficient heat and mass transfer in adsorption heat pumps an arrangement involving zeolite 4A coatings synthesized on stainless steel heat exchanger tubes was recently proposed and a related mathematical model was presented. In this study, the same mathematical model is employed to optimize the cycle durations in order to obtain the maximum amount of power from the adsorption heat pumps. Accordingly, the temperature and concentration profiles across the adsorbent layer are computed for distinct cases employing various cycle durations. The optimum cycle durations that maximize the energy obtained during a specific period of time for a given adsorber volume, corresponding to the employment of various zeolite layer thicknesses as well as two distinct wall thicknesses of the heat exchanger tubes are determined. The ratios between the optimum cycle durations and those obtained previously by allowing the operation of a cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C, remain around 0.2–0.4 for the cases investigated. The employment of the optimum cycle durations results in an increase of almost twofold in the power obtained from the adsorption heat pumps while the optimum zeolite layer thickness value obtained in this case is observed to increase by about 50% and is found to be in the range 75–150 mm depending on the wall thickness of the heat exchanger tubes utilized in this study. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Adsorption heat pumps; Cycle duration; Zeolite coating thickness
1. Introduction Adsorption heat pumps have been proposed as alternatives to the traditionally employed compression machines in processes involving heating and cooling [1–5]. The former employ completely natural cycles and thus eliminate the necessity of utilizing electricity and CFC refrigerants and also
* Tel: +90 212 285 6896; fax: +90 212 285 2925. E-mail address: [email protected] (A. Erdem-S¸enatalar)
provide a reliable and silent operation. However, adsorption heat pumps have lower efficiencies in comparison with the compression types and this has promoted the development of internal heat recovery systems [6,7], as well as the efforts to eliminate the heat and mass transfer limitations present in the adsorber [8,9]. The heat and mass transfer limitations result in extended durations of the adsorption heat pump cycles. An arrangement involving zeolite 4A coatings synthesized on metal heat exchanger tubes has recently been proposed [10] to eliminate the limitations originating from inefficient heat transfer in adsorption heat pumps.
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Nomenclature C concentration of the adsorbate (mol per g zeolite) C specific heat capacity (J g−1 K−1) p d ratio between the durations determined by two distinct methods L latent heat of vaporization (J g−1) m mass (g) n number of cycles realized in 2 h (cycles per 2 h) Q amount of heat obtained per cycle (J cycle−1) Q amount of heat obtained in 2 h (J per 2 h) 2 r radius (mm) r wall thickness (mm) w t time (s) T temperature ( K ) W amount of the adsorbate (g per g dry zeolite) DW total amount of adsorbate circulating in the system (g per g dry zeolite) Subscripts a c dz e max min opt z
adsorbate condenser dry zeolite evaporator maximum minimum optimum zeolite
Such an arrangement, which allows a good contact between the metal and the adsorbent and within the adsorbent layer itself, provides the opportunity of shortening the cycles to a great extent. A mathematical model was developed for the proposed arrangement and the durations of adsorption heat pump cycles corresponding to various zeolite layer thicknesses were then calculated [10–12]. The durations of the adsorption heat pump cycles were determined to vary according to the zeolite layer thicknesses utilized and were found to be equal to about 2 min and 1 h for the cases employing zeolite layer thicknesses of 5 and 400 mm, respectively [10,11]. The period of time required to complete a single cycle was observed to be prolonged in significant amounts above a zeolite layer thickness of 100 mm. In order to obtain the maximum amount of power from the adsorption heat pumps utilizing zeolite coatings synthesized on metal heat exchanger tubes,
an appropriate thickness for the zeolite layer should be utilized. Thus an optimization was made in order to determine the most favorable thickness values pertaining to the distinct cases where heat exchanger tubes made of different metals were employed [11,12]. It was observed that the metal type of the heat exchanger tubes did not affect the cycle duration significantly and the mass diffusivity of the adsorbate in the adsorbent was the limiting parameter in the system [12]. The optimum value for the thickness of the zeolite layer synthesized on the heat exchanger tubes made of different metals was determined to be in the range 50– 100 mm depending on the wall thickness of the tubes for the cases investigated. In the case of the employment of stainless steel heat exchanger tubes with wall thicknesses of 0.75 and 2.4 mm, the optimum zeolite layer thickness values were determined to be equal to 55 and 90 mm, respectively [11]. The cycle durations in all these calculations
M. Tatlıer, A. Erdem-S¸enatalar / Microporous and Mesoporous Materials 34 (2000) 23–30
were determined by allowing a single adsorption heat pump cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C and the concentration of the adsorbate attains the corresponding equilibrium value. Such an operation, though, does not ensure the provision of the maximum amount of energy in a specific period of time. Thus a further optimization might be made with respect to the cycle duration to determine the most favorable conditions under which the adsorption heat pumps employing zeolite coatings synthesized on metal heat exchanger tubes operate in a manner supplying the maximum amount of power. In this study, the optimum values of the durations of adsorption heat pump cycles employing various zeolite layer thickness values are determined by considering the fact that a single cycle may be ended at any instant rather than when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C and the concentration of the adsorbate attains the corresponding equilibrium value. Such a mode of operation creates the opportunity of determining the most favorable conditions that will provide the maximum amount of power. The mathematical model recently developed [10] is employed to determine the maximum and minimum temperatures attained by zeolite 4A synthesized on stainless steel heat exchanger tubes as well as the concentration of water, employed as the adsorbate, across the zeolite layer. Thus the amount of energy that can be obtained in a specific period of time is calculated for various zeolite layer thicknesses and selected, distinct cycle durations. The optimum durations of the adsorption heat pump cycles, corresponding to the cases where the highest amount of energy for a given adsorber volume is obtained in a specific period of time, are determined. A further optimization is accomplished by taking into account the optimum durations obtained for each of the various zeolite layer thicknesses investigated and the most favorable zeolite layer thickness values are determined for the two distinct wall thicknesses of heat exchanger tubes utilized in this study.
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2. Theoretical The details of a mathematical model describing an arrangement involving zeolite 4A coatings synthesized on stainless steel heat exchanger tubes were presented recently [10]. An arrangement consisting of heat exchanger tubes and the zeolite layers covering each of them was envisioned to be placed in the adsorber of an adsorption heat pump. The system was divided into two separate regions, namely the wall of the heat exchanger tube and the zeolite layer, and the differential equations pertaining to both of these regions during the periods of heating, desorption, cooling and adsorption were obtained by using the shell balance method. The energy and mass balances as well as the initial and boundary conditions employed to determine the temperature profiles in the adsorbent layer and the wall of the heat exchanger tube, as well as the concentration profile of the adsorbate across the adsorbent layer in the radial direction during the course of operation, were detailed in the same study [10]. The durations of each of the distinct stages found in an adsorption heat pump cycle could also be computed by employing the related equations. The heating and cooling of the wall of the heat exchanger tube and the zeolite layer were provided by a heat exchange fluid, the temperature of which was assumed to be kept at 151 and 19°C during the heating+desorption periods and the cooling+adsorption periods, respectively. The operation of a single cycle of the adsorption heat pump was allowed to be completed only when the temperature difference between the surface temperature of the adsorbent layer and the heat exchange fluid decreased to 1°C and the concentration of the adsorbate attained the corresponding equilibrium value. In this study, the referred mathematical model [10] is employed to determine the optimum cycle durations maximizing the power obtained from the adsorption heat pumps utilizing zeolite coatings synthesized on metal heat exchanger tubes. For this purpose, specific cycle durations are selected and employed for the heating+desorption and cooling+adsorption periods and the corresponding temperature and concentration values are computed. As a first step, an initial temperature
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for the adsorbent+metal is assumed while the concentration of the adsorbate is taken to be equal to the equilibrium value corresponding to the related temperature. The operation of the adsorption heat pump starts with the periods of heating and desorption at the end of which the temperature and concentration profiles across the adsorbent layer are obtained for the selected duration. The maximum temperature and the respective concentration values computed at each point represent the initial conditions of the system at the same point for the stages of cooling and adsorption which are again simulated to last for a selected, specific period of time. As a result, the minimum temperature of the adsorbent and the concentration of the adsorbate across the coating could be determined. A two-dimensional discretization of the system is accomplished in accordance with the finite difference scheme employed such that T and C represent the temperature and conceni,j i,j tration values at each node, respectively. i denotes the increments in the radial direction whereas j represents the time increments. T and C values i,m i,m corresponding to the end of the heating+ desorption periods at a selected time also represent the initial conditions for the cooling+adsorption periods at the node denoted by i and may be expressed as T and C , respectively, for the i,0 i,0 cooling+adsorption periods. m is equal to the total number of time increments employed until the maximum temperature and the respective concentration values are attained. This operation is repeated at all of the nodes ik where k represents the total number of nodes employed in the radial direction. k is taken to be equal to 5 in this study. In a similar fashion, the T and C values i,m i,m corresponding to any stage are assumed to be equal to the initial conditions of the following stage in the following order which is in accordance with the operating principles of the adsorption heat pumps: heating+desorptioncooling+ adsorption. The selected cycle durations for the heating+ desorption and the cooling+adsorption periods are taken to be equal throughout this study. The exact temperature and concentration values are determined only when a periodic regime is reached and the temperature of the adsorbent and the
concentration of the adsorbate start to remain constant. In order to find the optimum durations of the adsorption heat pump cycles, the conditions providing the highest amount of energy in a specific period of time for a given adsorber volume should be determined. A parameter representing the amount of heat extracted from the environment by the evaporator during an arbitrarily determined period of time has been defined previously [11]: Q =Q n. 2 e
(1)
In Eq. (1) n represents the number of cycles that can be realized in an arbitrarily selected period of time while Q signifies the useful effect obtained e from the evaporator during a single cycle. Q may e be expressed as: Q =DWm L−C m DW(T −T ). e dz pa dz c e
(2)
In Eq. (2) L denotes the latent heat of vaporization of the adsorbate while C represents its specific pa heat capacity. DW signifies the amount of adsorbate circulating in the system and m is equal to dz the mass of the dry adsorbent. m values corredz sponding to various zeolite layer thicknesses could be determined by designing an adsorber with a fixed volume [11] of 100 cm×100 cm×20 cm. The length of the heat exchanger tubes is chosen to be equal to 20 cm and two different sizes of standard stainless steel heat exchanger tubes with wall thicknesses of 0.75 and 2.4 mm are used in the calculations, as in the previous studies [10–12]. The zeolite 4A–water pair is employed throughout the calculations as the adsorbent–adsorbate pair of the adsorption heat pump. The specific heat capacity of zeolite 4A [13] is expressed in terms of its water content (W ) and temperature by using the following relationship: C = pz
0.2+0.0119(T−273)+4.2W 1+W
.
(3)
Other parameter values employed in the calculations also are in accordance with the previous studies [10–12].
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Table 1 The maximum and minimum temperatures of the surface of the adsorbent layer corresponding to the optimum cycle durations and the ratios between the durations of cycles pertaining to two distinct operation types, namely those employing the optimum cycle durations and the durations obtained by allowing a single cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C Thickness (mm)
15 50 100
r =0.75 mm w
r =2.4 mm w
d
T (°C ) max
T
0.26 0.38 0.25
117 134 139
37 27 24
3. Results and discussion The results obtained are given in Table 1 and Figs. 1–5. The condenser and evaporator temperatures employed in this study are taken to be equal to 20 and 2°C, respectively. The initial temperature of the system is assumed to be equal to 20°C while the initial water concentration in the zeolite corresponds to the amount present under equilibrium conditions at 20°C. Specific cycle durations are selected in a sufficiently narrow range to allow for an optimization for the stages of heating+ desorption and cooling+adsorption while the temperature and concentration values obtained for the previous stage become the initial conditions for the following one. This mode of operation makes it necessary for a periodic regime to be attained so that the temperature and concentration ranges of operation might be determined. However,
Fig. 1. The concentration profile of water in the radial direction in a 400 mm thick zeolite layer during the period of adsorption, for the ideal case after (×) 5 s, (#) 20 s and (&) 50 s of operation and for the actual case after (%) 5 s, ($) 20 s and (+) 50 s of operation.
min
(°C )
d
T (°C ) max
T (°C ) min
0.21 0.34 0.35
109 126 135
42 32 26
especially for fairly thick zeolite layers, the time required to reach a periodic regime is quite long and until then the concentration distribution of the adsorbate within the adsorbent exhibits an irregular pattern. Although the same behavior may be observed for thinner zeolite layers, this transient effect is more pronounced for layers thicker than 200 mm. Fig. 1 shows the variation of the concentration of water in a 400 mm thick zeolite layer with respect to the distance of the layer from the metal surface, during the period of adsorption. The periods of heating+desorption and cooling+adsorption are each selected to be of 50 s duration and two distinct cases are depicted in Fig. 1. The first one represents an ideal case which assumes that the whole of the zeolite layer is at adsorption equilibrium at the temperature values attained after 50 s of heating+desorption and employs the equilibrium values corresponding to those temperatures as the initial conditions for the cooling+adsorption periods. In contrast, the second case utilizes the computed concentration values obtained after 50 s of heating+desorption as the initial conditions for the periods of cooling+adsorption. In Fig. 1, the first run for adsorption is depicted at three different time values. It may be easily observed that for the actual case the concentration distribution of water within the zeolite layer exhibits an irregular pattern which tends to become more regular with increasing time. With each additional run made, the significance of the irregular behavior will become less pronounced. Although the process of adsorption ideally fills the adsorbent beginning from the outer surface, the concentration of the adsorbate
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Fig. 2. The relationship between the total amount of energy obtained after 2 h of operation from a fixed adsorber volume and the duration of a single adsorption heat pump cycle for zeolite layer thicknesses of ($) 15 mm, (+) 50 mm and (×) 100 mm when the wall thickness of the heat exchanger tubes is equal to 0.75 mm.
Fig. 3. The relationship between the total amount of energy obtained after 2 h of operation from a fixed adsorber volume and the duration of a single adsorption heat pump cycle for zeolite layer thicknesses of ($) 15 mm, (+) 50 mm and (×) 100 mm when the wall thickness of the heat exchanger tubes is equal to 2.4 mm.
is higher at the inner surface in the actual case during the period that the irregular behavior is observed and actually for most of the adsorbent layer it is above the value determined by the equilibrium conditions. This irregular behavior observed for the cases utilizing thick zeolite layers may lead to transient losses in the amount of the adsorbate circulating in the system until a periodic regime is attained since at least one part of the zeolite layer will not be able to participate in adsorption. Depending on the initial amount of the water content of the adsorbent at the beginning of operation, this type of irregular behavior may be mainly expected to be observed for either the period of adsorption or desorption in a single heat pump cycle. Fig. 2 depicts the relationship between the total amount of energy obtained after 2 h of operation from the selected adsorber volume and the duration of a single adsorption heat pump cycle for three different thickness values of the zeolite layer. The wall thickness of the heat exchanger tubes is taken to be equal to 0.75 mm. It may be easily observed that for every zeolite layer thickness an optimum cycle duration exists and these values increase as the zeolite layer gets thicker. It may also be easily seen [11,12] that the optimum cycle durations do not correspond to the cycle durations obtained by allowing a single cycle to be completed
only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C. Fig. 3 represents the same relationship, i.e. the variation of the total amount of energy obtained after 2 h of operation from the same adsorber volume, with respect to the cycle duration for three different thickness values of the zeolite layer, in this case for a wall thickness of 2.4 mm. An optimum cycle duration for each zeolite layer thickness employed may be observed to exist here, too. However, the amount of energy to be obtained is much lower and the optimum cycle durations are higher than those calculated for the cases employing heat exchanger tubes with thinner walls. The temperature ranges of operation corresponding to the optimum cycle durations and the values of d are given in Table 1 for the two distinct wall thicknesses employed. d represents the ratio between the optimum duration of an adsorption heat pump cycle and the duration determined by allowing a single cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C. The d values obtained for the cases investigated in this study generally remain between 0.2 and 0.4 and attain their highest levels when a zeolite layer thickness of about 50 mm and a range of values between 50–100 mm are employed
M. Tatlıer, A. Erdem-S¸enatalar / Microporous and Mesoporous Materials 34 (2000) 23–30
Fig. 4. The variation of the optimum cycle durations with respect to the thickness of the zeolite layer when heat exchanger tubes with wall thicknesses of (+) 0.75 mm and (×) 2.4 mm are employed.
for wall thicknesses of 0.75 and 2.4 mm, respectively. The highest d values seem to correspond to the optimum zeolite layer thickness values determined previously [11] by allowing a single cycle to be completed only when a DT=1°C is obtained between the heat exchange fluid and the surface temperature of the adsorbent layer. Fig. 4 depicts the relationship between the thickness of the zeolite layer and the corresponding optimum cycle duration for the two distinct wall thickness values employed. It may be observed that for the case utilizing heat exchanger tubes with thicker walls, the optimum cycle durations increase more rapidly as the zeolite layer gets thicker when compared with the case employing heat exchanger tubes with thinner walls. An optimization is also made among the optimum cycle durations obtained for various zeolite layer thicknesses in order to determine the thickness value that will provide the highest amount of power. The optimum values for the zeolite layer thicknesses synthesized on metal heat exchanger tubes determined by using the optimum cycle durations are given in Fig. 5 for the two distinct wall thicknesses of heat exchanger tubes. When the heat exchanger tubes with thicker walls are employed, the amount of energy obtained in a specific period of time does not vary to a great extent for the zeolite layer thickness values between 100 and 200 mm. For the case where a wall thickness of 0.75 mm is employed, an optimum cycle duration of 50 s, an optimum zeolite layer thick-
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Fig. 5. The variation of the total amount of energy obtained after 2 h of operation from a fixed adsorber volume with respect to the thickness of the zeolite layer when heat exchanger tubes with wall thicknesses of (+) 0.75 mm and (×) 2.4 mm are employed.
ness of 75 mm and a Q value of 171 MJ per 2 h 2 are obtained. On the other hand, for the case utilizing a wall thickness of 2.4 mm, an optimum cycle duration of 175 s, an optimum zeolite layer thickness of 150 mm and a Q value of 87 MJ per 2 2 h are obtained. The durations of the heating+ desorption and the cooling+adsorption stages corresponding to the optimum cases are both equal to 25 and 87.5 s for the cases employing thinner and thicker walls of heat exchanger tubes, respectively. The maximum amount of energy that can be obtained in a specific period of time from a fixed adsorber volume increases almost twofold with respect to the case [11] where the operation of a cycle is allowed to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent decreases to 1°C. It is apparent that heat exchanger tubes with thinner walls are more favorable in terms of increasing the power, and there exists a possibility of increasing the power of the system further, by decreasing the wall thickness values of the heat exchanger tubes. A decrease made in the wall thickness value may also reduce the amount of metal mass used in the adsorber resulting in an enhancement of the coefficient of performance (COP) values of the adsorption heat pumps. The COP value is an indicator of the efficiency of the conversion of heat received to the useful effect obtained from the system. Independent of the operational mode employed,
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utilizing thinner heat exchanger walls should also be expected to lead to a decrease in the optimum zeolite layer thickness value that provides the maximum amount of power obtained from the adsorption heat pumps. It seems that the actual power and COP values in such systems will be limited by the minimum wall thickness of heat exchanger tubes and the minimum cycle durations achievable economically by the available technology.
obtained previously [11]. The operation of an adsorption heat pump in a manner involving the selection of specific cycle durations beforehand leads to an irregular pattern concerning the distribution of water across the zeolite layer for fairly thick layers. This may lead to adverse effects on the performance of the system until a periodic regime is reached whenever zeolite layers thicker than 200 mm are employed.
Acknowledgement 4. Conclusions Adsorption heat pumps employing zeolite 4A coatings synthesized on metal heat exchanger tubes might remove the limitations originating from inefficient heat and mass transfer to a great extent whenever an optimum zeolite layer thickness value is utilized. In this study, in order to provide additional improvements in the power obtained from the adsorption heat pumps, an optimization concerning the cycle durations is made. The optimum cycle durations determined are different from the durations obtained previously [11] by allowing the operation of a cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent decreases to 1°C. The ratios between the optimum cycle durations and the durations obtained by the method utilized previously remain around 0.2–0.4 for the zeolite layer and heat exchanger wall thicknesses investigated in this study. As a result of the employment of the optimum cycle durations, the amount of energy that can be obtained in a specific period of time from a fixed adsorber volume increases almost twofold. Depending on the wall thickness values utilized in this study, the optimum zeolite layer thickness range that provides the maximum amount of power is determined to be around 75– 150 mm, slightly higher than the range (50–100 mm)
The Ph.D. scholarship provided by TUBITAK Mu¨nir Birsel Foundation to M.T. is gratefully acknowledged.
References [1] D.I. Tchernev, in: L.B. Sand, F.A. Mumpton ( Eds.), Natural Zeolites: Occurrence Properties and Use, Pergamon, London, 1978, p. 479. [2] J.J. Guilleminot, F. Meunier, Rev. Gen. Therm. 20 (1981) 825. [3] J.J. Guilleminot, F. Meunier, B. Mischler, Rev. Phys. Appl. 15 (1980) 441. [4] S.C. Chang, J.A. Roux, J. Solar Energy Eng. 107 (1985) 189. [5] G. Restuccia, G. Cacciola, R. Quagliata, Int. J. Energy Res. 12 (1988) 101. [6 ] N. Douss, F. Meunier, L.M. Sun, Ind. Eng. Chem. Res. 27 (1988) 310. [7] G.H.W. Van Benthem, G. Cacciola, G. Restuccia, Heat Recovery Syst. CHP 15 (1995) 531. [8] J.J. Guilleminot, A. Choisier, J.B. Chalfen, S. Nicolas, J.L. Reymoney, Heat Recovery Syst. CHP 13 (1993) 297. [9] G. Cacciola, G. Restuccia, Heat Recovery Syst. CHP 14 (1994) 409. [10] M. Tatlıer, B. Tantekin-Ersolmaz, A. Erdem-S¸enatalar, Microporous Mesoporous Mater. 27 (1999) 1. [11] M. Tatlıer, A. Erdem-S¸enatalar, in: Proceedings 12th International Zeolite Conference, Materials Research Society, Pittsburgh, PA, 1999, p. 583. [12] M. Tatlıer, A. Erdem-S¸enatalar, Microporous Mesoporous Mater. 28 (1999) 195. [13] Grange, F.B. Hannouni, O.B. Bouillot, Thermochim. Acta 101 (1986) 217.
Optimization of the cycle durations of adsorption heat pumps employing zeolite coatings synthesized on metal supports Melkon Tatlıer, Ays¸e Erdem-S¸enatalar * Department of Chemical Engineering, Istanbul Technical University, Maslak, 80626 Istanbul, Turkey Received 2 June 1998; accepted for publication 22 July 1999
Abstract In order to remove the limitations originating from inefficient heat and mass transfer in adsorption heat pumps an arrangement involving zeolite 4A coatings synthesized on stainless steel heat exchanger tubes was recently proposed and a related mathematical model was presented. In this study, the same mathematical model is employed to optimize the cycle durations in order to obtain the maximum amount of power from the adsorption heat pumps. Accordingly, the temperature and concentration profiles across the adsorbent layer are computed for distinct cases employing various cycle durations. The optimum cycle durations that maximize the energy obtained during a specific period of time for a given adsorber volume, corresponding to the employment of various zeolite layer thicknesses as well as two distinct wall thicknesses of the heat exchanger tubes are determined. The ratios between the optimum cycle durations and those obtained previously by allowing the operation of a cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C, remain around 0.2–0.4 for the cases investigated. The employment of the optimum cycle durations results in an increase of almost twofold in the power obtained from the adsorption heat pumps while the optimum zeolite layer thickness value obtained in this case is observed to increase by about 50% and is found to be in the range 75–150 mm depending on the wall thickness of the heat exchanger tubes utilized in this study. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Adsorption heat pumps; Cycle duration; Zeolite coating thickness
1. Introduction Adsorption heat pumps have been proposed as alternatives to the traditionally employed compression machines in processes involving heating and cooling [1–5]. The former employ completely natural cycles and thus eliminate the necessity of utilizing electricity and CFC refrigerants and also
* Tel: +90 212 285 6896; fax: +90 212 285 2925. E-mail address: [email protected] (A. Erdem-S¸enatalar)
provide a reliable and silent operation. However, adsorption heat pumps have lower efficiencies in comparison with the compression types and this has promoted the development of internal heat recovery systems [6,7], as well as the efforts to eliminate the heat and mass transfer limitations present in the adsorber [8,9]. The heat and mass transfer limitations result in extended durations of the adsorption heat pump cycles. An arrangement involving zeolite 4A coatings synthesized on metal heat exchanger tubes has recently been proposed [10] to eliminate the limitations originating from inefficient heat transfer in adsorption heat pumps.
1387-1811/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S1 3 8 7 -1 8 1 1 ( 9 9 ) 0 0 15 2 - 3
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M. Tatlıer, A. Erdem-S¸enatalar / Microporous and Mesoporous Materials 34 (2000) 23–30
Nomenclature C concentration of the adsorbate (mol per g zeolite) C specific heat capacity (J g−1 K−1) p d ratio between the durations determined by two distinct methods L latent heat of vaporization (J g−1) m mass (g) n number of cycles realized in 2 h (cycles per 2 h) Q amount of heat obtained per cycle (J cycle−1) Q amount of heat obtained in 2 h (J per 2 h) 2 r radius (mm) r wall thickness (mm) w t time (s) T temperature ( K ) W amount of the adsorbate (g per g dry zeolite) DW total amount of adsorbate circulating in the system (g per g dry zeolite) Subscripts a c dz e max min opt z
adsorbate condenser dry zeolite evaporator maximum minimum optimum zeolite
Such an arrangement, which allows a good contact between the metal and the adsorbent and within the adsorbent layer itself, provides the opportunity of shortening the cycles to a great extent. A mathematical model was developed for the proposed arrangement and the durations of adsorption heat pump cycles corresponding to various zeolite layer thicknesses were then calculated [10–12]. The durations of the adsorption heat pump cycles were determined to vary according to the zeolite layer thicknesses utilized and were found to be equal to about 2 min and 1 h for the cases employing zeolite layer thicknesses of 5 and 400 mm, respectively [10,11]. The period of time required to complete a single cycle was observed to be prolonged in significant amounts above a zeolite layer thickness of 100 mm. In order to obtain the maximum amount of power from the adsorption heat pumps utilizing zeolite coatings synthesized on metal heat exchanger tubes,
an appropriate thickness for the zeolite layer should be utilized. Thus an optimization was made in order to determine the most favorable thickness values pertaining to the distinct cases where heat exchanger tubes made of different metals were employed [11,12]. It was observed that the metal type of the heat exchanger tubes did not affect the cycle duration significantly and the mass diffusivity of the adsorbate in the adsorbent was the limiting parameter in the system [12]. The optimum value for the thickness of the zeolite layer synthesized on the heat exchanger tubes made of different metals was determined to be in the range 50– 100 mm depending on the wall thickness of the tubes for the cases investigated. In the case of the employment of stainless steel heat exchanger tubes with wall thicknesses of 0.75 and 2.4 mm, the optimum zeolite layer thickness values were determined to be equal to 55 and 90 mm, respectively [11]. The cycle durations in all these calculations
M. Tatlıer, A. Erdem-S¸enatalar / Microporous and Mesoporous Materials 34 (2000) 23–30
were determined by allowing a single adsorption heat pump cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C and the concentration of the adsorbate attains the corresponding equilibrium value. Such an operation, though, does not ensure the provision of the maximum amount of energy in a specific period of time. Thus a further optimization might be made with respect to the cycle duration to determine the most favorable conditions under which the adsorption heat pumps employing zeolite coatings synthesized on metal heat exchanger tubes operate in a manner supplying the maximum amount of power. In this study, the optimum values of the durations of adsorption heat pump cycles employing various zeolite layer thickness values are determined by considering the fact that a single cycle may be ended at any instant rather than when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C and the concentration of the adsorbate attains the corresponding equilibrium value. Such a mode of operation creates the opportunity of determining the most favorable conditions that will provide the maximum amount of power. The mathematical model recently developed [10] is employed to determine the maximum and minimum temperatures attained by zeolite 4A synthesized on stainless steel heat exchanger tubes as well as the concentration of water, employed as the adsorbate, across the zeolite layer. Thus the amount of energy that can be obtained in a specific period of time is calculated for various zeolite layer thicknesses and selected, distinct cycle durations. The optimum durations of the adsorption heat pump cycles, corresponding to the cases where the highest amount of energy for a given adsorber volume is obtained in a specific period of time, are determined. A further optimization is accomplished by taking into account the optimum durations obtained for each of the various zeolite layer thicknesses investigated and the most favorable zeolite layer thickness values are determined for the two distinct wall thicknesses of heat exchanger tubes utilized in this study.
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2. Theoretical The details of a mathematical model describing an arrangement involving zeolite 4A coatings synthesized on stainless steel heat exchanger tubes were presented recently [10]. An arrangement consisting of heat exchanger tubes and the zeolite layers covering each of them was envisioned to be placed in the adsorber of an adsorption heat pump. The system was divided into two separate regions, namely the wall of the heat exchanger tube and the zeolite layer, and the differential equations pertaining to both of these regions during the periods of heating, desorption, cooling and adsorption were obtained by using the shell balance method. The energy and mass balances as well as the initial and boundary conditions employed to determine the temperature profiles in the adsorbent layer and the wall of the heat exchanger tube, as well as the concentration profile of the adsorbate across the adsorbent layer in the radial direction during the course of operation, were detailed in the same study [10]. The durations of each of the distinct stages found in an adsorption heat pump cycle could also be computed by employing the related equations. The heating and cooling of the wall of the heat exchanger tube and the zeolite layer were provided by a heat exchange fluid, the temperature of which was assumed to be kept at 151 and 19°C during the heating+desorption periods and the cooling+adsorption periods, respectively. The operation of a single cycle of the adsorption heat pump was allowed to be completed only when the temperature difference between the surface temperature of the adsorbent layer and the heat exchange fluid decreased to 1°C and the concentration of the adsorbate attained the corresponding equilibrium value. In this study, the referred mathematical model [10] is employed to determine the optimum cycle durations maximizing the power obtained from the adsorption heat pumps utilizing zeolite coatings synthesized on metal heat exchanger tubes. For this purpose, specific cycle durations are selected and employed for the heating+desorption and cooling+adsorption periods and the corresponding temperature and concentration values are computed. As a first step, an initial temperature
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for the adsorbent+metal is assumed while the concentration of the adsorbate is taken to be equal to the equilibrium value corresponding to the related temperature. The operation of the adsorption heat pump starts with the periods of heating and desorption at the end of which the temperature and concentration profiles across the adsorbent layer are obtained for the selected duration. The maximum temperature and the respective concentration values computed at each point represent the initial conditions of the system at the same point for the stages of cooling and adsorption which are again simulated to last for a selected, specific period of time. As a result, the minimum temperature of the adsorbent and the concentration of the adsorbate across the coating could be determined. A two-dimensional discretization of the system is accomplished in accordance with the finite difference scheme employed such that T and C represent the temperature and conceni,j i,j tration values at each node, respectively. i denotes the increments in the radial direction whereas j represents the time increments. T and C values i,m i,m corresponding to the end of the heating+ desorption periods at a selected time also represent the initial conditions for the cooling+adsorption periods at the node denoted by i and may be expressed as T and C , respectively, for the i,0 i,0 cooling+adsorption periods. m is equal to the total number of time increments employed until the maximum temperature and the respective concentration values are attained. This operation is repeated at all of the nodes ik where k represents the total number of nodes employed in the radial direction. k is taken to be equal to 5 in this study. In a similar fashion, the T and C values i,m i,m corresponding to any stage are assumed to be equal to the initial conditions of the following stage in the following order which is in accordance with the operating principles of the adsorption heat pumps: heating+desorptioncooling+ adsorption. The selected cycle durations for the heating+ desorption and the cooling+adsorption periods are taken to be equal throughout this study. The exact temperature and concentration values are determined only when a periodic regime is reached and the temperature of the adsorbent and the
concentration of the adsorbate start to remain constant. In order to find the optimum durations of the adsorption heat pump cycles, the conditions providing the highest amount of energy in a specific period of time for a given adsorber volume should be determined. A parameter representing the amount of heat extracted from the environment by the evaporator during an arbitrarily determined period of time has been defined previously [11]: Q =Q n. 2 e
(1)
In Eq. (1) n represents the number of cycles that can be realized in an arbitrarily selected period of time while Q signifies the useful effect obtained e from the evaporator during a single cycle. Q may e be expressed as: Q =DWm L−C m DW(T −T ). e dz pa dz c e
(2)
In Eq. (2) L denotes the latent heat of vaporization of the adsorbate while C represents its specific pa heat capacity. DW signifies the amount of adsorbate circulating in the system and m is equal to dz the mass of the dry adsorbent. m values corredz sponding to various zeolite layer thicknesses could be determined by designing an adsorber with a fixed volume [11] of 100 cm×100 cm×20 cm. The length of the heat exchanger tubes is chosen to be equal to 20 cm and two different sizes of standard stainless steel heat exchanger tubes with wall thicknesses of 0.75 and 2.4 mm are used in the calculations, as in the previous studies [10–12]. The zeolite 4A–water pair is employed throughout the calculations as the adsorbent–adsorbate pair of the adsorption heat pump. The specific heat capacity of zeolite 4A [13] is expressed in terms of its water content (W ) and temperature by using the following relationship: C = pz
0.2+0.0119(T−273)+4.2W 1+W
.
(3)
Other parameter values employed in the calculations also are in accordance with the previous studies [10–12].
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Table 1 The maximum and minimum temperatures of the surface of the adsorbent layer corresponding to the optimum cycle durations and the ratios between the durations of cycles pertaining to two distinct operation types, namely those employing the optimum cycle durations and the durations obtained by allowing a single cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C Thickness (mm)
15 50 100
r =0.75 mm w
r =2.4 mm w
d
T (°C ) max
T
0.26 0.38 0.25
117 134 139
37 27 24
3. Results and discussion The results obtained are given in Table 1 and Figs. 1–5. The condenser and evaporator temperatures employed in this study are taken to be equal to 20 and 2°C, respectively. The initial temperature of the system is assumed to be equal to 20°C while the initial water concentration in the zeolite corresponds to the amount present under equilibrium conditions at 20°C. Specific cycle durations are selected in a sufficiently narrow range to allow for an optimization for the stages of heating+ desorption and cooling+adsorption while the temperature and concentration values obtained for the previous stage become the initial conditions for the following one. This mode of operation makes it necessary for a periodic regime to be attained so that the temperature and concentration ranges of operation might be determined. However,
Fig. 1. The concentration profile of water in the radial direction in a 400 mm thick zeolite layer during the period of adsorption, for the ideal case after (×) 5 s, (#) 20 s and (&) 50 s of operation and for the actual case after (%) 5 s, ($) 20 s and (+) 50 s of operation.
min
(°C )
d
T (°C ) max
T (°C ) min
0.21 0.34 0.35
109 126 135
42 32 26
especially for fairly thick zeolite layers, the time required to reach a periodic regime is quite long and until then the concentration distribution of the adsorbate within the adsorbent exhibits an irregular pattern. Although the same behavior may be observed for thinner zeolite layers, this transient effect is more pronounced for layers thicker than 200 mm. Fig. 1 shows the variation of the concentration of water in a 400 mm thick zeolite layer with respect to the distance of the layer from the metal surface, during the period of adsorption. The periods of heating+desorption and cooling+adsorption are each selected to be of 50 s duration and two distinct cases are depicted in Fig. 1. The first one represents an ideal case which assumes that the whole of the zeolite layer is at adsorption equilibrium at the temperature values attained after 50 s of heating+desorption and employs the equilibrium values corresponding to those temperatures as the initial conditions for the cooling+adsorption periods. In contrast, the second case utilizes the computed concentration values obtained after 50 s of heating+desorption as the initial conditions for the periods of cooling+adsorption. In Fig. 1, the first run for adsorption is depicted at three different time values. It may be easily observed that for the actual case the concentration distribution of water within the zeolite layer exhibits an irregular pattern which tends to become more regular with increasing time. With each additional run made, the significance of the irregular behavior will become less pronounced. Although the process of adsorption ideally fills the adsorbent beginning from the outer surface, the concentration of the adsorbate
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Fig. 2. The relationship between the total amount of energy obtained after 2 h of operation from a fixed adsorber volume and the duration of a single adsorption heat pump cycle for zeolite layer thicknesses of ($) 15 mm, (+) 50 mm and (×) 100 mm when the wall thickness of the heat exchanger tubes is equal to 0.75 mm.
Fig. 3. The relationship between the total amount of energy obtained after 2 h of operation from a fixed adsorber volume and the duration of a single adsorption heat pump cycle for zeolite layer thicknesses of ($) 15 mm, (+) 50 mm and (×) 100 mm when the wall thickness of the heat exchanger tubes is equal to 2.4 mm.
is higher at the inner surface in the actual case during the period that the irregular behavior is observed and actually for most of the adsorbent layer it is above the value determined by the equilibrium conditions. This irregular behavior observed for the cases utilizing thick zeolite layers may lead to transient losses in the amount of the adsorbate circulating in the system until a periodic regime is attained since at least one part of the zeolite layer will not be able to participate in adsorption. Depending on the initial amount of the water content of the adsorbent at the beginning of operation, this type of irregular behavior may be mainly expected to be observed for either the period of adsorption or desorption in a single heat pump cycle. Fig. 2 depicts the relationship between the total amount of energy obtained after 2 h of operation from the selected adsorber volume and the duration of a single adsorption heat pump cycle for three different thickness values of the zeolite layer. The wall thickness of the heat exchanger tubes is taken to be equal to 0.75 mm. It may be easily observed that for every zeolite layer thickness an optimum cycle duration exists and these values increase as the zeolite layer gets thicker. It may also be easily seen [11,12] that the optimum cycle durations do not correspond to the cycle durations obtained by allowing a single cycle to be completed
only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C. Fig. 3 represents the same relationship, i.e. the variation of the total amount of energy obtained after 2 h of operation from the same adsorber volume, with respect to the cycle duration for three different thickness values of the zeolite layer, in this case for a wall thickness of 2.4 mm. An optimum cycle duration for each zeolite layer thickness employed may be observed to exist here, too. However, the amount of energy to be obtained is much lower and the optimum cycle durations are higher than those calculated for the cases employing heat exchanger tubes with thinner walls. The temperature ranges of operation corresponding to the optimum cycle durations and the values of d are given in Table 1 for the two distinct wall thicknesses employed. d represents the ratio between the optimum duration of an adsorption heat pump cycle and the duration determined by allowing a single cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent layer decreases to 1°C. The d values obtained for the cases investigated in this study generally remain between 0.2 and 0.4 and attain their highest levels when a zeolite layer thickness of about 50 mm and a range of values between 50–100 mm are employed
M. Tatlıer, A. Erdem-S¸enatalar / Microporous and Mesoporous Materials 34 (2000) 23–30
Fig. 4. The variation of the optimum cycle durations with respect to the thickness of the zeolite layer when heat exchanger tubes with wall thicknesses of (+) 0.75 mm and (×) 2.4 mm are employed.
for wall thicknesses of 0.75 and 2.4 mm, respectively. The highest d values seem to correspond to the optimum zeolite layer thickness values determined previously [11] by allowing a single cycle to be completed only when a DT=1°C is obtained between the heat exchange fluid and the surface temperature of the adsorbent layer. Fig. 4 depicts the relationship between the thickness of the zeolite layer and the corresponding optimum cycle duration for the two distinct wall thickness values employed. It may be observed that for the case utilizing heat exchanger tubes with thicker walls, the optimum cycle durations increase more rapidly as the zeolite layer gets thicker when compared with the case employing heat exchanger tubes with thinner walls. An optimization is also made among the optimum cycle durations obtained for various zeolite layer thicknesses in order to determine the thickness value that will provide the highest amount of power. The optimum values for the zeolite layer thicknesses synthesized on metal heat exchanger tubes determined by using the optimum cycle durations are given in Fig. 5 for the two distinct wall thicknesses of heat exchanger tubes. When the heat exchanger tubes with thicker walls are employed, the amount of energy obtained in a specific period of time does not vary to a great extent for the zeolite layer thickness values between 100 and 200 mm. For the case where a wall thickness of 0.75 mm is employed, an optimum cycle duration of 50 s, an optimum zeolite layer thick-
29
Fig. 5. The variation of the total amount of energy obtained after 2 h of operation from a fixed adsorber volume with respect to the thickness of the zeolite layer when heat exchanger tubes with wall thicknesses of (+) 0.75 mm and (×) 2.4 mm are employed.
ness of 75 mm and a Q value of 171 MJ per 2 h 2 are obtained. On the other hand, for the case utilizing a wall thickness of 2.4 mm, an optimum cycle duration of 175 s, an optimum zeolite layer thickness of 150 mm and a Q value of 87 MJ per 2 2 h are obtained. The durations of the heating+ desorption and the cooling+adsorption stages corresponding to the optimum cases are both equal to 25 and 87.5 s for the cases employing thinner and thicker walls of heat exchanger tubes, respectively. The maximum amount of energy that can be obtained in a specific period of time from a fixed adsorber volume increases almost twofold with respect to the case [11] where the operation of a cycle is allowed to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent decreases to 1°C. It is apparent that heat exchanger tubes with thinner walls are more favorable in terms of increasing the power, and there exists a possibility of increasing the power of the system further, by decreasing the wall thickness values of the heat exchanger tubes. A decrease made in the wall thickness value may also reduce the amount of metal mass used in the adsorber resulting in an enhancement of the coefficient of performance (COP) values of the adsorption heat pumps. The COP value is an indicator of the efficiency of the conversion of heat received to the useful effect obtained from the system. Independent of the operational mode employed,
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utilizing thinner heat exchanger walls should also be expected to lead to a decrease in the optimum zeolite layer thickness value that provides the maximum amount of power obtained from the adsorption heat pumps. It seems that the actual power and COP values in such systems will be limited by the minimum wall thickness of heat exchanger tubes and the minimum cycle durations achievable economically by the available technology.
obtained previously [11]. The operation of an adsorption heat pump in a manner involving the selection of specific cycle durations beforehand leads to an irregular pattern concerning the distribution of water across the zeolite layer for fairly thick layers. This may lead to adverse effects on the performance of the system until a periodic regime is reached whenever zeolite layers thicker than 200 mm are employed.
Acknowledgement 4. Conclusions Adsorption heat pumps employing zeolite 4A coatings synthesized on metal heat exchanger tubes might remove the limitations originating from inefficient heat and mass transfer to a great extent whenever an optimum zeolite layer thickness value is utilized. In this study, in order to provide additional improvements in the power obtained from the adsorption heat pumps, an optimization concerning the cycle durations is made. The optimum cycle durations determined are different from the durations obtained previously [11] by allowing the operation of a cycle to be completed only when the temperature difference between the heat exchange fluid and the surface temperature of the adsorbent decreases to 1°C. The ratios between the optimum cycle durations and the durations obtained by the method utilized previously remain around 0.2–0.4 for the zeolite layer and heat exchanger wall thicknesses investigated in this study. As a result of the employment of the optimum cycle durations, the amount of energy that can be obtained in a specific period of time from a fixed adsorber volume increases almost twofold. Depending on the wall thickness values utilized in this study, the optimum zeolite layer thickness range that provides the maximum amount of power is determined to be around 75– 150 mm, slightly higher than the range (50–100 mm)
The Ph.D. scholarship provided by TUBITAK Mu¨nir Birsel Foundation to M.T. is gratefully acknowledged.
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