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water chemical heat pump
Applied Thermal Engineering 66 (2014) 274e281
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The optimization of mixing ratio of expanded graphite mixed chemical heat storage material for magnesium oxide/water chemical heat pump Seon Tae Kim, Junichi Ryu, Yukitaka Kato* Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1-N1-22, Ookayama, Meguro-ku, Tokyo 152-8550, Japan
h i g h l i g h t s The expanded graphite (EG) mixture was developed for MgO/H2O chemical heat pump. Optimization of mixing molar ratio between Mg(OH)2 and CaCl2 was conducted. The hydration reactivity of mixture was decreased as the mixing molar ratio increased. Heat output rate and capacity of optimized EG mixture was estimated. Optimized EG mixture shows better heat output performance than pure Mg(OH)2.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 August 2013 Accepted 9 February 2014 Available online 18 February 2014
A chemical heat storage composite material (EMC), a mixture of expanded graphite (EG), magnesium hydroxide (Mg(OH)2), and calcium chloride (CaCl2), was developed as a magnesium oxide/water chemical heat pump reactant. The potential of the EMC was confirmed and optimized mixing weight ratio between EG and Mg(OH)2 was suggested in previous study. In this study, the optimization of mixing molar ratio between Mg(OH)2 and CaCl2 for practical application was conducted; total six kinds of EMC mixtures, which have different mixing molar ratio from 0, to 0.01 to 0.20 with optimized mixing weight ratio, were prepared then dehydration and hydration experiments were carried out. From experimental results, it was confirmed that hydration reacted conversion was increased as increasing amount of CaCl2 in an EMC and the optimized mixing molar ratio was suggested as mixing molar ratio, a, is 0.1 at mixing weight ratio, n, is 0.8 by considering chemical rate constant and reacted conversion. Hydration under various vapor pressures and temperatures of optimized EMC was also conducted and optimized EMC showed better performance than pure Mg(OH)2. Finally, the heat output performance of optimized EMC was estimated numerically. In conclusion, optimized EMC performed better on dehydration and hydration than pure Mg(OH)2 by adding EG, which has high thermal conductivity and large specific surface, and CaCl2, which has hydrophilic property. Ó 2014 Published by Elsevier Ltd.
Keywords: Chemical heat pump Magnesium hydroxide Expanded graphite Calcium chloride Hydration Heat output estimation
1. Introduction Thermal energy storage is considered as an advanced energy technology, and there has been an increasing interest in the use of this essential technique for the thermal applications such as heating, hot water, air conditioning, and so on [1]. Chemical heat pump (CHP) system utilize the reversible chemical reaction to store and change the temperature level of thermal energy by using chemical substance [2]. In particular, a CHP that uses the chemical reaction
* Corresponding author. E-mail address: [email protected] (Y. Kato). http://dx.doi.org/10.1016/j.applthermaleng.2014.02.024 1359-4311/Ó 2014 Published by Elsevier Ltd.
between water (H2O) and magnesium oxide (MgO), as shown in Eqs. (1) and (2), has been studied by the authors’ group [3,4].
MgOðsÞ þ H2 OðgÞ4MgðOHÞ2 ðsÞ DH+ ¼ 81:0 kJ$mol1 H2 OðgÞ4H2 OðlÞ
DH+ ¼ 40:0 kJ$mol1
(1) (2)
Fig. 1 shows the operation of a MgO/H2O CHP system that store the thermal energy via the dehydration of magnesium hydroxide (Mg(OH)2), endothermic reaction, as shown in Fig. 1(a), and release the stored energy on demand via the hydration of magnesium oxide, exothermic reaction, in Fig. 1(b). The heat pump would be
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The potential of material mixed with expanded graphite (EG), magnesium hydroxide (Mg(OH)2), and calcium chloride (CaCl2), referred to as EMC, was confirmed [11] and the optimization of mixing weight ratio of EMC between Mg(OH)2 and EG in EM, mixture of EG and Mg(OH)2, for practical application was discussed and optimized mixing weight ratio was suggested in previous studies [12]. As a series of above mentioned studies, optimization of mixing molar ratio of EMC, between Mg(OH)2 and CaCl2 in EMC, was discussed and the optimized mixing molar ratio for practical application was suggested in this study. Furthermore, hydration and heat output performance of optimized EMC was also examined and estimated. 2. Experimental 2.1. Expanded graphite
Fig. 1. Principles of the magnesium oxide/water chemical heat pump: (a) heat storage operation and (b) heat supply operation.
unique system that can store heat at around 300e400 C and release heat at around 100e200 C with the heat amplification under less than atmospheric pressure. The advantages of the chemical heat pump are that it can store exhaust or surplus heat generated from a cogeneration process, the reactant materials are safe, economical and environmentally friendly, and the heat can be stored for longer periods without heat losses than other conventional heat storage ways [5]. Due to the low thermal conductivity of magnesium oxide, the increasing or decreasing of bed temperature, as endothermic or exothermic reaction process, takes a long time, such as 3 h. This causes a decrease in the driving force for the reaction, since it may be expressed as a difference of pressure at the gas phase and the solid reactant for the equilibrium pressure [6]. Methods for enhancement of the thermal conductivity of reaction materials for a packed bed reactor in a chemical heat pump have been investigated. One promising method is the introduction of carbon based materials that is carbon nanofibers, carbon nanotubes, and expanded graphite into heat storage reactants [7]. In this study, expanded graphite (EG) was selected among the carbon based materials because EG has a high possibility of mass production and cost performance. EG is known as flexible and porous graphite and it was reported that the heat transfer and reactivity of reactants for solidegas chemical heat pumps was improved by the mixing EG and solid reactants [8]. EG is also durable at high temperatures and chemically inert. EG with special designed properties to satisfy different demands in industrial also has been widely used as a kind of functional carbon material in sealing, catalyzing, mechanical parts for space flight, military affairs, and environmental protection [9,10].
For production of expandable graphite, it is possible to insert various atomic or molecular layers of a different chemical species, halogens, alkali metals, sulfate, nitrate, and various organic acids, as intercalation between graphite layers in a graphite host material due to the weakness of the van der Waals-type forces [13,14]. In this study, the expandable graphite flake (SS-3, Air Water INC.) was used as graphite intercalation compound [15]. The flake was heated at 700 C for 10 min in a furnace, and the intercalated reagent decomposed and changed into the gas product and the graphite layers were expanded by gas generation. The resulting expanded graphite material increased in volume of 180 mL/g that has over 100 times volume of its original flake [16]. The morphologies of EG were observed by SEM (SM-200, TOPCON Corp.) and it shows that small abundant honeycomb pores by expansion of raw EG flake in Fig. 2(a). The pores are used as a binder to improve heat and mass transfer in the bed, and, the furrows resulting from the parting of graphite layers in EG provide channels for retaining the Mg(OH)2 powder and facilitating the transport of gas phase materials [17]. There are two different ways to use EG to improve the overall thermal properties of materials: the one is blend method and the other is fin method. In this study, blend method, developed in institute des materiaux et procédés (IMP) in Perpignan, France at 1983, based on intimate mixing the EG powder with magnesium hydroxide to insert the magnesium hydroxide particles in the small pores of expanded graphite, was tried [18,19]. 2.2. Preparation procedure First of all, mixing weight ratio, n, and mixing molar ratio, a, of EMC was defined as follow equations, Eqs. (3) and (4).
Mixing weight ratioðnÞ ¼
Mixing molar ratioðaÞ ¼
wMgðOHÞ2 wEG þ wMgðOHÞ2
(3)
mole number of CaCl2 in EMC ½mole mole number of MgðOHÞ2 in EMC ½mole (4)
The synthesized material of expanded graphite, magnesium hydroxide (99.9%, primary particle diameter of 0.07 mm, Wako Pure Chemical Industries, Ltd.), and calcium chloride (99.9%, Wako Pure Chemical Industries, Ltd.) with optimized mixing weight ratio (n ¼ 0.8) and six different mixing molar ratios (a ¼ 0, 0.01, 0.05, 0.10, 0.15, and 0.20) were prepared by following procedure [20].
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Fig. 3. Effect of mixing molar ratio, a, on dehydration and hydration of EMCs.
assumed that the Mg(OH)2 is mixed with EG homogeneously and substitute calculated mass of Mg(OH)2 for wMgðOHÞ2 in Eq. (5).
2 6 y ½ ¼ 41 þ
Fig. 2. SEM photographs of exterior of (a) expanded graphite (b) EMC (n ¼ 0.8, a ¼ 0.05).
Fig. 2(b) shows EMC ( n ¼ 0.8, a ¼ 0.05) and it is confirmed that the salts, Mg(OH)2 and CaCl2, covered surface of EG well. (1) The mass of Mg(OH)2 and CaCl2 were measured using a digital balance. (2) The materials were charged into a flask with 100 mL of ethanol. (3) The Mg(OH)2 and CaCl2 were dispersed in ethanol by using an ultrasonic bath. (4) The measured EG was charged in a flask. The flask was set in a rotary evaporator and rotated at 303 K under a pressure lower than atmosphere, then, ethanol was removed from the flask. (5) The mixed material in paste state in the flask was dried in an oven at 120 C for over 10 h. Take out the final product, dried mixed material, from flask. 2.3. Evaluation method To know the influence of mixing molar ratio of EMC mixture on heat storage and discharge performance, the dehydration and hydration of EMCs were conducted by using thermobalance (TGD9600, Ulvac-Riko Inc.) system. The dehydration experiment was conducted at 300 C for 120 min and hydration was carried out at 110 C for 120 min with saturation point of 85 C corresponding to vapor pressure of 57.8 kPa. The reacted mole fraction, y, between MgO and Mg(OH)2 in EMC mixture was calculated by using the Eq. (5) [3]. First, it was
3
DwH2 O MH2 O MMgðOHÞ2
wMgðOHÞ2
7 5
(5)
where DwH2 O [g] is the weight change of the sample, MH2 O [g/mol] is the molecular weight of water, MMgðOHÞ2 [g/mol] is the molecular weight of Mg(OH)2, and wMgðOHÞ2 [g] is the calculated initial mass of Mg(OH)2 in the charged sample in the cell. The mixed materials were not perfectly homogeneous. Therefore, seven samples of each mixing molar ratio’s material were used for reacted fraction measurements under the same conditions, and averaged measured values of reacted mole fraction, y, were employed as a representative reacted fraction. 3. Results and discussion 3.1. Experimental results according to mixing molar ratio Six kinds of EMC mixtures which have different mixing molar ratio (a ¼ 0, 0.01, 0.05, 0.10, 0.15, and 0.20) with optimized mixing weight ratio (n ¼ 0.8) were prepared by according to mentioned process in Section 2.2 and one dehydration, heat storage process, and one hydration, heat output process, experiments for all materials were carried out. Fig. 3 shows the effect of mixing molar ratio, a, on reacted mole fraction in the dehydration and hydration of prepared EMC mixtures. In dehydration (t ¼ 70e220 min), all EMCs showed higher dehydration rate than pure Mg(OH)2 and EM, and there is no certain sequence according to mixing molar ratio but contained CaCl2 in mixture should be reduced as much as possible to secure the large heat storage capacity per unit mass of EMC. From Fig. 3, it is also confirmed that the mixing molar ratio, a, is important factor for hydration than dehydration, therefore, only hydration of EMCs were enlarged, Fig. 4, and it showed that the hydration reactivity of EMCs was enhanced by the increase of the mixing molar ratio.
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Fig. 4. Hydration of EMCs according to mixing molar ratio, a, and example of reacted conversions for pure Mg(OH)2 and EMC (n ¼ 0.8, a ¼ 0.1).
3.2. Kinetic analysis of experimental results The hydration process of the EMC was discussed kinetically based on experimental results. The hydration period of EMC can be divided into two parts: physical adsorption and chemical reaction, having tendency of diffusion control [3]. Physical adsorption and chemical reaction is occurred sequentially by difference of activation energy. The more important reaction part for chemical heat pump is chemical reaction part, because, chemical reaction has larger heat output capacity and last considerably longer than physical adsorption. 3.2.1. Physical adsorption period In physical adsorption period on Fig. 4, certain sequential trend was confirmed; as increasing the amount of CaCl2 in EMC, reacted conversion was increased. EMCs which have the low mixing mole ratio (a ¼ 0.01 and 0.05) show the poor physical adsorption amount than pure Mg(OH)2. That means that those materials have less heat output capacities than pure Mg(OH)2, even, the EMCs show higher chemical reaction rate than pure Mg(OH)2. In this study, the physical adsorption period was assumed that when decrease of hydration reacted fraction, dy/dt, was reached 0.0002 [s1], after vapor supply was started. Because every experimental result showed low and stable reacted fraction value after that point; that means chemical reaction is started from that time. 3.2.2. Chemical reaction period Chemical reaction control model was defined after finish the physical adsorption period on hydration. Film diffusion control model, which represent experimental results well among the three kinds of shrinking core models (film diffusion, ash diffusion, and reaction control model) [21], was selected to calculate the chemical rate constant, kr, and Eq. (6) shows the conversion-time expression for film diffusion control model.
t=s ¼ kr $t ¼ Dyr ;
s ¼
rB Rp 3bkg CAg
(6)
where s [s] is time for complete conversion of a reactant particle to product, Rp [m] is the radius of reactant particle, b [-] is the stoichiometry parameter for gas/solid reaction, kg [mol/(m2 Pa s)] is the
277
Fig. 5. Effect of mixing molar ratio, a, on chemical rate constants, kr, and physical adsorption amount, Dya.
mass transfer coefficient between fluid and particle, rB [kg/m3] is the density of magnesium oxide in solid, and CAg [mol/m3] is the concentration of gas in main fluid body. 3.3. Optimized mixing molar ratio The optimized mixing molar ratio for practical application was suggested by kinetic analysis of results of hydration part. Fig. 5 shows the physical adsorption amount, Dya, during initial part of hydration and chemical rate constant, kr, according to mixing molar ratio, a. All EMC showed higher value of kr than pure Mg(OH)2 and EM. The hydration rate constants, kr, of EMCs were decreased as increasing mixing molar ratio, a, in EMC. On the other hand, physical water adsorption, Dya, of EMC is increased monotonously as increasing mixing molar ratio in EMC. Pure Mg(OH)2 shows higher value than EM on chemical rate constant, kr, and physical adsorption amount, Dya, both aspect. To know the effect of mixing molar ratio, a, of EMC on hydration reacted conversion, corresponding to heat output capacity, evaluation function, h [-], was introduced and defined as following Eq. (7).
h ¼ hydration reacted conversion difference between EMC and pure MgðOHÞ2 at 120 min in hydration ¼
operation=mixing molar ration . a yiEMC yiMgðOHÞ2
(7)
¼ DyM =a The definitions of hydration reacted conversion of EMC, yi-EMC, and pure Mg(OH)2, yiMgðOHÞ2 , are shown in Fig. 4 and the results of h is shown in Fig. 6. From Fig. 6, it is confirmed that the value of evaluation function, h [-], is increased as increasing mixing molar ratio; however, EMCs which have low mixing molar ratio one (a ¼ 0.01 and 0.05) show lower values of h than pure Mg(OH)2, that means reacted conversion, corresponding to heat output capacity, of those materials are poor than pure Mg(OH)2. The value of h is superior to one of pure Mg(OH)2 at a is over 0.1. Especially, the result of a is 0.1 one, denoted by a circle with dot line, shows the highest value of h.
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Fig. 7. Effect of vapor pressure on hydration of optimized EMC. Fig. 6. Change of evaluation function, h, according to mixing molar ratio, a
In conclusion, around 0.1 of a was suggested as an optimized mixing molar ratio of EMC at n is 0.8 for practical application by considering physical adsorption amount, Dya, chemical rate constant, kr, and results of evaluation function, h, in Figs. 5 and 6. 4. Performance OF optimized EMC Hydration, heat output, performance of optimized EMC (n ¼ 0.8,
a ¼ 0.1) was evaluated by two ways; one is effect of vapor pressure
and the other is effect of hydration temperature. The standard experimental conditions were as follow: dehydration temperature, Td, is 300 C for 120 min and hydration temperature, Th, is 110 C for 120 min with saturation point of 85 C corresponding to vapor pressure of 57.8 kPa. Experimental condition was changed on purposes of each experiment.
reaction equations according to reaction temperature were also suggested by kinetic analysis of experimental results. Fig. 8 shows the experimental results of optimized EMC with various hydration temperatures (110,140,160,180, and 200 C) under vapor pressure of 57.8 kPa. The reacted conversion and chemical reaction rate became lower as hydration temperature changed higher. On the other hand, it was confirmed that optimized EMC had hydration reactivity up to 200 C. In case of pure Mg(OH)2 showed hydration reactivity only up to 150 C [3]. From this result, it was though that CaCl2 had positive effect on hydration reactivity of Mg(OH)2. 4.2.1. Kinetic analysis of experimental results Hydration process of the optimized EMC was investigated to propose a reaction equation according to reaction temperature.
4.1. Effect of vapor pressure on hydration The hydration with various vapor pressures was carried out to know the effect of hydration pressure on hydration of the optimized EMC. The supplied vapor pressures were controlled by controlling amount of supplied H2O and Ar into evaporator. Each experiment was conducted five times with different samples under same conditions to enhance the reliability of results and mean value was adopted as represent values as shown in Fig. 7. Optimized EMC shows that the both physical water adsorption amount, Dya, and chemical rate constant, kr, is decreased as decreasing vapor pressure. The chemical reaction is obviously observed at 57.8 and 38.6 kPa; however, the result at low pressure, Ph is 19.9 kPa, shows almost adsorption process and most amount of chemical reaction amount was removed after vapor supply was stopped around 350 min. From this result, it is found that over 25.0 kPa of vapor pressure is needed to operate the optimized EMC as a packed bed reactor of MgO/H2O chemical heat pump. 4.2. Effect of hydration temperature on hydration The effect of hydration temperature on hydration performance of optimized EMC was discussed experimentally. Furthermore, the
Fig. 8. Effect of hydration temperature on hydration of optimized EMC.
S.T. Kim et al. / Applied Thermal Engineering 66 (2014) 274e281
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Fig. 10. Comparison of calculated and measured reacted mole fraction for hydration of optimized EMC.
from experimental results and approximate line in Fig. 9(a). Finally, the adsorption constant (ka) was derived as Eq. (9) and activation energy for the adsorption of optimized EMC was e 34.3 kJ/mol.
Dya ¼ ka ¼ 1:49 105 exp
34:27 103 R$Th
(9)
4.2.1.2. Chemical reaction period. The chemical rate constant was derived by using film diffusion control model, Eq. (6), in the same way as chemical reaction period on section 3.2. The Arrhenius plot for chemical reaction was obtained and plotted in Fig. 9(b), and Eq. (10) was obtained by using the equation which was obtained from a least square method.
38:75 103 ¼ kr ¼ 1:63 1010 exp s R$Th
1
Fig. 9. Temperature dependency of ka and kr according to Arrhenius law during (a) physical adsorption period and (b) chemical reaction period.
Finally thermal performance of chemical heat pump which uses optimized EMC was estimated from the proposed equation. 4.2.1.1. Physical adsorption period. The hydration part was divided into physical adsorption part and chemical reaction part by using same way in section 3.2. For physical adsorption period, instead of a rate equation, Freuntrich’s isotherm equation was adopted to express the initial physical adsorption [3].
Dya ¼ ka pbh
(8)
Since reaction pressure had little influence on the initial adsorption with the experimental condition, reaction order b in Eq. (8) is replaced by 0. The parameters in Eq. (8) could be obtained
(10)
The activation energy for chemical reaction is 38.8 kJ/mol. Those negative temperature dependencies of physical adsorption and chemical reaction imply that the equilibrium reaction of adsorbed water between MgO and the intermediate establishes according to hydration temperature. 4.2.1.3. Apparent reacted mole fraction of hydration. The apparent reacted mole fraction, y, of optimized EMC was defined as aggregation of structure water, Dys, physical adsorption amount, Dya, and chemical reaction amount, Dyr, as Eq. (11) from Eqs. (9) and (10).
y ¼ Dys þ Dya þ Dyr
(11)
Fig. 10 shows comparison between the measured and calculated reacted mole fraction, and calculated values represent well measured values. In conclusion, it was assumed that the assumptions in this study were appropriate for estimation of hydration rate of optimized EMC.
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Because physical adsorption process has lower enthalpy change value than chemical reaction process, optimized EMC showed gradually increasing heat output capacity, even, it showed suddenly increased reacted mole fraction on initial part of Fig. 10. In this figure, optimized EMC, 466.5 kJ/kg, also shows better performance than pure Mg(OH)2, 357.9 kJ/kg, at 110 C during first 30 min. 5. Conclusion
Fig. 11. Effect of hydration temperature on mean heat output rate per unit mass of Mg(OH)2 in optimized EMC.
4.3. Heat output performance of optimized EMC The heat output performance of the MgO/H2O chemical heat pump using optimized EMC as packed bed material was calculated numerically based on the hydration rate equations. The mean heat output rate, W, is defined as the averaged heat output rate per unit mass of Mg(OH)2 in optimized EMC during regular time interval after hydration was started.
W ¼
DHr $Dyr DHa $Dya th $MMgðOHÞ2
(12)
The DHr [kJ/mol] in first term on the numerator of the righthand side in Eq. (12) corresponds to enthalpy change of MgO hydration. The DHa in second term on the numerator is corresponding to enthalpy change of vapor condensation. MMgðOHÞ2 is the molecular weight of magnesium hydroxide and results, W, are described on Fig. 11. Fig. 11 shows the effect of reaction temperature on W per unit mass of Mg(OH)2 in EMC ðWMgðOHÞ2 Þ when the reaction pressure, ph, is 57.8 kPa. WMgðOHÞ2 shows values from 324.9 W/kg at 110 C to 54.2 W/kg at 200 C during the first 30 min. On the other hand, pure Mg(OH)2 shows 233.3 W/kg at 110 C. Fig. 12 shows the influence of hydration temperature on heat output capacities per unit mass of Mg(OH)2 in EMC (QMg(OH)2).
The optimization of mixing molar ratio of EMC mixture for practical application was conducted and hydration, heat output process, performance of CHP using optimized EMC was also estimated in this study. The amount of CaCl2 in EMC was important factor on hydration than dehydration; therefore, physical adsorption amount, Dya, chemical rate constant, kr, and the results of evaluation function, h, were considered to optimize the mixing molar ratio between Mg(OH)2 and CaCl2 in EMC. The physical adsorption period was defined up to dy/dt of 0.0002 and chemical rate constant, kr, for the hydration of optimized EMC was obtained from experimental results by using film diffusion control model among the shrinking core models. To know the effect of CaCl2’s amount in EMC on reacted conversion, evaluation function, h, was introduced and the optimized mixing molar ratio was suggested as a of 0.1 at n of 0.8, optimized mixing weight ratio. Hydration performance of optimized EMC was examined in two ways: hydration under various vapor pressures and reaction temperatures. Optimized EMC showed better performance than pure Mg(OH)2 and reaction rate equation was obtained from kinetic analysis of experimental results. The heat output performance of chemical heat pump, using optimized EMC as packed bed reactant, was estimated by using obtained reaction rate equation numerically. Unit mass of Mg(OH)2 in optimized EMC showed higher mean heat output rate and capacity than pure Mg(OH)2 at the same conditions. In conclusion, optimized EMC showed superior heat output performance than pure Mg(OH)2 and durability of optimized material should be assessed for practical application as a further study. Acknowledgments This study was executed with the support of the Grant-in-Aid for Scientific Research (B) # 20360404 from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. Nomenclature
Fig. 12. Effect of hydration temperature on heat output capacity per unit mass of Mg(OH)2 in optimized EMC.
b CAg g ka kg kr l M n ph Q R Rp s th T W y
stoichiometry factor concentration of gas, [mol/m3] gas physical adsorption constant, [s1] mass transfer coefficient, [mol/m2 Pa s] chemical rate constant, [s1] liquid molecular weight, [g/mol] mixing weight ratio, [-] hydration pressure, [kPa] heat output capacity, [kJ/kg] gas constant, 8.314 [J/Kmol] radius of reactant particle, [m] solid hydration time, [s] reaction temperature mean heat output rate, [W/kg] reacted mole fraction, [-]
S.T. Kim et al. / Applied Thermal Engineering 66 (2014) 274e281
ys ya yr yi yM
structural water, [-] physical water adsorption, [-] chemical reaction, [-] hydration reacted conversion, [-] reacted conversion difference between EMC and pure Mg(OH)2, [-]
Greeks
a h H
rB s w
mixing molar ratio, [-] evaluation function, [-] reaction enthalpy change, [kJ mol1] density of magnesium oxide, [kg/m3] time for complete conversion, [s] weight of the sample, [g]
Superscript and subscripts a physical adsorption b reaction order c condensation d dehydration EG expanded graphite h hydration H2O water r chemical reaction v vapor Mg(OH)2 magnesium hydroxide References [1] I. Dincer, M.A. Rosen, Thermal Energy Storage: Systems and Applications, Wiley&Sons, Chichester, 2002. [2] H. Kawasaki, T. Watanabe, A. Kanzawa, Proposal of a chemical heat pump with paraldehyde depolymerization for cooling system, Appl. Therm. Eng. 19 (2) (1999) 133e143. [3] Y. Kato, N. Yamashita, K. Kobayashi, Y. Yoshizawa, Kinetic study of the hydration of magnesium oxide for a chemical heat pump, Appl. Therm. Eng. 16 (11) (1996) 853e862.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
The optimization of mixing ratio of expanded graphite mixed chemical heat storage material for magnesium oxide/water chemical heat pump Seon Tae Kim, Junichi Ryu, Yukitaka Kato* Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1-N1-22, Ookayama, Meguro-ku, Tokyo 152-8550, Japan
h i g h l i g h t s The expanded graphite (EG) mixture was developed for MgO/H2O chemical heat pump. Optimization of mixing molar ratio between Mg(OH)2 and CaCl2 was conducted. The hydration reactivity of mixture was decreased as the mixing molar ratio increased. Heat output rate and capacity of optimized EG mixture was estimated. Optimized EG mixture shows better heat output performance than pure Mg(OH)2.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 August 2013 Accepted 9 February 2014 Available online 18 February 2014
A chemical heat storage composite material (EMC), a mixture of expanded graphite (EG), magnesium hydroxide (Mg(OH)2), and calcium chloride (CaCl2), was developed as a magnesium oxide/water chemical heat pump reactant. The potential of the EMC was confirmed and optimized mixing weight ratio between EG and Mg(OH)2 was suggested in previous study. In this study, the optimization of mixing molar ratio between Mg(OH)2 and CaCl2 for practical application was conducted; total six kinds of EMC mixtures, which have different mixing molar ratio from 0, to 0.01 to 0.20 with optimized mixing weight ratio, were prepared then dehydration and hydration experiments were carried out. From experimental results, it was confirmed that hydration reacted conversion was increased as increasing amount of CaCl2 in an EMC and the optimized mixing molar ratio was suggested as mixing molar ratio, a, is 0.1 at mixing weight ratio, n, is 0.8 by considering chemical rate constant and reacted conversion. Hydration under various vapor pressures and temperatures of optimized EMC was also conducted and optimized EMC showed better performance than pure Mg(OH)2. Finally, the heat output performance of optimized EMC was estimated numerically. In conclusion, optimized EMC performed better on dehydration and hydration than pure Mg(OH)2 by adding EG, which has high thermal conductivity and large specific surface, and CaCl2, which has hydrophilic property. Ó 2014 Published by Elsevier Ltd.
Keywords: Chemical heat pump Magnesium hydroxide Expanded graphite Calcium chloride Hydration Heat output estimation
1. Introduction Thermal energy storage is considered as an advanced energy technology, and there has been an increasing interest in the use of this essential technique for the thermal applications such as heating, hot water, air conditioning, and so on [1]. Chemical heat pump (CHP) system utilize the reversible chemical reaction to store and change the temperature level of thermal energy by using chemical substance [2]. In particular, a CHP that uses the chemical reaction
* Corresponding author. E-mail address: [email protected] (Y. Kato). http://dx.doi.org/10.1016/j.applthermaleng.2014.02.024 1359-4311/Ó 2014 Published by Elsevier Ltd.
between water (H2O) and magnesium oxide (MgO), as shown in Eqs. (1) and (2), has been studied by the authors’ group [3,4].
MgOðsÞ þ H2 OðgÞ4MgðOHÞ2 ðsÞ DH+ ¼ 81:0 kJ$mol1 H2 OðgÞ4H2 OðlÞ
DH+ ¼ 40:0 kJ$mol1
(1) (2)
Fig. 1 shows the operation of a MgO/H2O CHP system that store the thermal energy via the dehydration of magnesium hydroxide (Mg(OH)2), endothermic reaction, as shown in Fig. 1(a), and release the stored energy on demand via the hydration of magnesium oxide, exothermic reaction, in Fig. 1(b). The heat pump would be
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The potential of material mixed with expanded graphite (EG), magnesium hydroxide (Mg(OH)2), and calcium chloride (CaCl2), referred to as EMC, was confirmed [11] and the optimization of mixing weight ratio of EMC between Mg(OH)2 and EG in EM, mixture of EG and Mg(OH)2, for practical application was discussed and optimized mixing weight ratio was suggested in previous studies [12]. As a series of above mentioned studies, optimization of mixing molar ratio of EMC, between Mg(OH)2 and CaCl2 in EMC, was discussed and the optimized mixing molar ratio for practical application was suggested in this study. Furthermore, hydration and heat output performance of optimized EMC was also examined and estimated. 2. Experimental 2.1. Expanded graphite
Fig. 1. Principles of the magnesium oxide/water chemical heat pump: (a) heat storage operation and (b) heat supply operation.
unique system that can store heat at around 300e400 C and release heat at around 100e200 C with the heat amplification under less than atmospheric pressure. The advantages of the chemical heat pump are that it can store exhaust or surplus heat generated from a cogeneration process, the reactant materials are safe, economical and environmentally friendly, and the heat can be stored for longer periods without heat losses than other conventional heat storage ways [5]. Due to the low thermal conductivity of magnesium oxide, the increasing or decreasing of bed temperature, as endothermic or exothermic reaction process, takes a long time, such as 3 h. This causes a decrease in the driving force for the reaction, since it may be expressed as a difference of pressure at the gas phase and the solid reactant for the equilibrium pressure [6]. Methods for enhancement of the thermal conductivity of reaction materials for a packed bed reactor in a chemical heat pump have been investigated. One promising method is the introduction of carbon based materials that is carbon nanofibers, carbon nanotubes, and expanded graphite into heat storage reactants [7]. In this study, expanded graphite (EG) was selected among the carbon based materials because EG has a high possibility of mass production and cost performance. EG is known as flexible and porous graphite and it was reported that the heat transfer and reactivity of reactants for solidegas chemical heat pumps was improved by the mixing EG and solid reactants [8]. EG is also durable at high temperatures and chemically inert. EG with special designed properties to satisfy different demands in industrial also has been widely used as a kind of functional carbon material in sealing, catalyzing, mechanical parts for space flight, military affairs, and environmental protection [9,10].
For production of expandable graphite, it is possible to insert various atomic or molecular layers of a different chemical species, halogens, alkali metals, sulfate, nitrate, and various organic acids, as intercalation between graphite layers in a graphite host material due to the weakness of the van der Waals-type forces [13,14]. In this study, the expandable graphite flake (SS-3, Air Water INC.) was used as graphite intercalation compound [15]. The flake was heated at 700 C for 10 min in a furnace, and the intercalated reagent decomposed and changed into the gas product and the graphite layers were expanded by gas generation. The resulting expanded graphite material increased in volume of 180 mL/g that has over 100 times volume of its original flake [16]. The morphologies of EG were observed by SEM (SM-200, TOPCON Corp.) and it shows that small abundant honeycomb pores by expansion of raw EG flake in Fig. 2(a). The pores are used as a binder to improve heat and mass transfer in the bed, and, the furrows resulting from the parting of graphite layers in EG provide channels for retaining the Mg(OH)2 powder and facilitating the transport of gas phase materials [17]. There are two different ways to use EG to improve the overall thermal properties of materials: the one is blend method and the other is fin method. In this study, blend method, developed in institute des materiaux et procédés (IMP) in Perpignan, France at 1983, based on intimate mixing the EG powder with magnesium hydroxide to insert the magnesium hydroxide particles in the small pores of expanded graphite, was tried [18,19]. 2.2. Preparation procedure First of all, mixing weight ratio, n, and mixing molar ratio, a, of EMC was defined as follow equations, Eqs. (3) and (4).
Mixing weight ratioðnÞ ¼
Mixing molar ratioðaÞ ¼
wMgðOHÞ2 wEG þ wMgðOHÞ2
(3)
mole number of CaCl2 in EMC ½mole mole number of MgðOHÞ2 in EMC ½mole (4)
The synthesized material of expanded graphite, magnesium hydroxide (99.9%, primary particle diameter of 0.07 mm, Wako Pure Chemical Industries, Ltd.), and calcium chloride (99.9%, Wako Pure Chemical Industries, Ltd.) with optimized mixing weight ratio (n ¼ 0.8) and six different mixing molar ratios (a ¼ 0, 0.01, 0.05, 0.10, 0.15, and 0.20) were prepared by following procedure [20].
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Fig. 3. Effect of mixing molar ratio, a, on dehydration and hydration of EMCs.
assumed that the Mg(OH)2 is mixed with EG homogeneously and substitute calculated mass of Mg(OH)2 for wMgðOHÞ2 in Eq. (5).
2 6 y ½ ¼ 41 þ
Fig. 2. SEM photographs of exterior of (a) expanded graphite (b) EMC (n ¼ 0.8, a ¼ 0.05).
Fig. 2(b) shows EMC ( n ¼ 0.8, a ¼ 0.05) and it is confirmed that the salts, Mg(OH)2 and CaCl2, covered surface of EG well. (1) The mass of Mg(OH)2 and CaCl2 were measured using a digital balance. (2) The materials were charged into a flask with 100 mL of ethanol. (3) The Mg(OH)2 and CaCl2 were dispersed in ethanol by using an ultrasonic bath. (4) The measured EG was charged in a flask. The flask was set in a rotary evaporator and rotated at 303 K under a pressure lower than atmosphere, then, ethanol was removed from the flask. (5) The mixed material in paste state in the flask was dried in an oven at 120 C for over 10 h. Take out the final product, dried mixed material, from flask. 2.3. Evaluation method To know the influence of mixing molar ratio of EMC mixture on heat storage and discharge performance, the dehydration and hydration of EMCs were conducted by using thermobalance (TGD9600, Ulvac-Riko Inc.) system. The dehydration experiment was conducted at 300 C for 120 min and hydration was carried out at 110 C for 120 min with saturation point of 85 C corresponding to vapor pressure of 57.8 kPa. The reacted mole fraction, y, between MgO and Mg(OH)2 in EMC mixture was calculated by using the Eq. (5) [3]. First, it was
3
DwH2 O MH2 O MMgðOHÞ2
wMgðOHÞ2
7 5
(5)
where DwH2 O [g] is the weight change of the sample, MH2 O [g/mol] is the molecular weight of water, MMgðOHÞ2 [g/mol] is the molecular weight of Mg(OH)2, and wMgðOHÞ2 [g] is the calculated initial mass of Mg(OH)2 in the charged sample in the cell. The mixed materials were not perfectly homogeneous. Therefore, seven samples of each mixing molar ratio’s material were used for reacted fraction measurements under the same conditions, and averaged measured values of reacted mole fraction, y, were employed as a representative reacted fraction. 3. Results and discussion 3.1. Experimental results according to mixing molar ratio Six kinds of EMC mixtures which have different mixing molar ratio (a ¼ 0, 0.01, 0.05, 0.10, 0.15, and 0.20) with optimized mixing weight ratio (n ¼ 0.8) were prepared by according to mentioned process in Section 2.2 and one dehydration, heat storage process, and one hydration, heat output process, experiments for all materials were carried out. Fig. 3 shows the effect of mixing molar ratio, a, on reacted mole fraction in the dehydration and hydration of prepared EMC mixtures. In dehydration (t ¼ 70e220 min), all EMCs showed higher dehydration rate than pure Mg(OH)2 and EM, and there is no certain sequence according to mixing molar ratio but contained CaCl2 in mixture should be reduced as much as possible to secure the large heat storage capacity per unit mass of EMC. From Fig. 3, it is also confirmed that the mixing molar ratio, a, is important factor for hydration than dehydration, therefore, only hydration of EMCs were enlarged, Fig. 4, and it showed that the hydration reactivity of EMCs was enhanced by the increase of the mixing molar ratio.
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Fig. 4. Hydration of EMCs according to mixing molar ratio, a, and example of reacted conversions for pure Mg(OH)2 and EMC (n ¼ 0.8, a ¼ 0.1).
3.2. Kinetic analysis of experimental results The hydration process of the EMC was discussed kinetically based on experimental results. The hydration period of EMC can be divided into two parts: physical adsorption and chemical reaction, having tendency of diffusion control [3]. Physical adsorption and chemical reaction is occurred sequentially by difference of activation energy. The more important reaction part for chemical heat pump is chemical reaction part, because, chemical reaction has larger heat output capacity and last considerably longer than physical adsorption. 3.2.1. Physical adsorption period In physical adsorption period on Fig. 4, certain sequential trend was confirmed; as increasing the amount of CaCl2 in EMC, reacted conversion was increased. EMCs which have the low mixing mole ratio (a ¼ 0.01 and 0.05) show the poor physical adsorption amount than pure Mg(OH)2. That means that those materials have less heat output capacities than pure Mg(OH)2, even, the EMCs show higher chemical reaction rate than pure Mg(OH)2. In this study, the physical adsorption period was assumed that when decrease of hydration reacted fraction, dy/dt, was reached 0.0002 [s1], after vapor supply was started. Because every experimental result showed low and stable reacted fraction value after that point; that means chemical reaction is started from that time. 3.2.2. Chemical reaction period Chemical reaction control model was defined after finish the physical adsorption period on hydration. Film diffusion control model, which represent experimental results well among the three kinds of shrinking core models (film diffusion, ash diffusion, and reaction control model) [21], was selected to calculate the chemical rate constant, kr, and Eq. (6) shows the conversion-time expression for film diffusion control model.
t=s ¼ kr $t ¼ Dyr ;
s ¼
rB Rp 3bkg CAg
(6)
where s [s] is time for complete conversion of a reactant particle to product, Rp [m] is the radius of reactant particle, b [-] is the stoichiometry parameter for gas/solid reaction, kg [mol/(m2 Pa s)] is the
277
Fig. 5. Effect of mixing molar ratio, a, on chemical rate constants, kr, and physical adsorption amount, Dya.
mass transfer coefficient between fluid and particle, rB [kg/m3] is the density of magnesium oxide in solid, and CAg [mol/m3] is the concentration of gas in main fluid body. 3.3. Optimized mixing molar ratio The optimized mixing molar ratio for practical application was suggested by kinetic analysis of results of hydration part. Fig. 5 shows the physical adsorption amount, Dya, during initial part of hydration and chemical rate constant, kr, according to mixing molar ratio, a. All EMC showed higher value of kr than pure Mg(OH)2 and EM. The hydration rate constants, kr, of EMCs were decreased as increasing mixing molar ratio, a, in EMC. On the other hand, physical water adsorption, Dya, of EMC is increased monotonously as increasing mixing molar ratio in EMC. Pure Mg(OH)2 shows higher value than EM on chemical rate constant, kr, and physical adsorption amount, Dya, both aspect. To know the effect of mixing molar ratio, a, of EMC on hydration reacted conversion, corresponding to heat output capacity, evaluation function, h [-], was introduced and defined as following Eq. (7).
h ¼ hydration reacted conversion difference between EMC and pure MgðOHÞ2 at 120 min in hydration ¼
operation=mixing molar ration . a yiEMC yiMgðOHÞ2
(7)
¼ DyM =a The definitions of hydration reacted conversion of EMC, yi-EMC, and pure Mg(OH)2, yiMgðOHÞ2 , are shown in Fig. 4 and the results of h is shown in Fig. 6. From Fig. 6, it is confirmed that the value of evaluation function, h [-], is increased as increasing mixing molar ratio; however, EMCs which have low mixing molar ratio one (a ¼ 0.01 and 0.05) show lower values of h than pure Mg(OH)2, that means reacted conversion, corresponding to heat output capacity, of those materials are poor than pure Mg(OH)2. The value of h is superior to one of pure Mg(OH)2 at a is over 0.1. Especially, the result of a is 0.1 one, denoted by a circle with dot line, shows the highest value of h.
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Fig. 7. Effect of vapor pressure on hydration of optimized EMC. Fig. 6. Change of evaluation function, h, according to mixing molar ratio, a
In conclusion, around 0.1 of a was suggested as an optimized mixing molar ratio of EMC at n is 0.8 for practical application by considering physical adsorption amount, Dya, chemical rate constant, kr, and results of evaluation function, h, in Figs. 5 and 6. 4. Performance OF optimized EMC Hydration, heat output, performance of optimized EMC (n ¼ 0.8,
a ¼ 0.1) was evaluated by two ways; one is effect of vapor pressure
and the other is effect of hydration temperature. The standard experimental conditions were as follow: dehydration temperature, Td, is 300 C for 120 min and hydration temperature, Th, is 110 C for 120 min with saturation point of 85 C corresponding to vapor pressure of 57.8 kPa. Experimental condition was changed on purposes of each experiment.
reaction equations according to reaction temperature were also suggested by kinetic analysis of experimental results. Fig. 8 shows the experimental results of optimized EMC with various hydration temperatures (110,140,160,180, and 200 C) under vapor pressure of 57.8 kPa. The reacted conversion and chemical reaction rate became lower as hydration temperature changed higher. On the other hand, it was confirmed that optimized EMC had hydration reactivity up to 200 C. In case of pure Mg(OH)2 showed hydration reactivity only up to 150 C [3]. From this result, it was though that CaCl2 had positive effect on hydration reactivity of Mg(OH)2. 4.2.1. Kinetic analysis of experimental results Hydration process of the optimized EMC was investigated to propose a reaction equation according to reaction temperature.
4.1. Effect of vapor pressure on hydration The hydration with various vapor pressures was carried out to know the effect of hydration pressure on hydration of the optimized EMC. The supplied vapor pressures were controlled by controlling amount of supplied H2O and Ar into evaporator. Each experiment was conducted five times with different samples under same conditions to enhance the reliability of results and mean value was adopted as represent values as shown in Fig. 7. Optimized EMC shows that the both physical water adsorption amount, Dya, and chemical rate constant, kr, is decreased as decreasing vapor pressure. The chemical reaction is obviously observed at 57.8 and 38.6 kPa; however, the result at low pressure, Ph is 19.9 kPa, shows almost adsorption process and most amount of chemical reaction amount was removed after vapor supply was stopped around 350 min. From this result, it is found that over 25.0 kPa of vapor pressure is needed to operate the optimized EMC as a packed bed reactor of MgO/H2O chemical heat pump. 4.2. Effect of hydration temperature on hydration The effect of hydration temperature on hydration performance of optimized EMC was discussed experimentally. Furthermore, the
Fig. 8. Effect of hydration temperature on hydration of optimized EMC.
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Fig. 10. Comparison of calculated and measured reacted mole fraction for hydration of optimized EMC.
from experimental results and approximate line in Fig. 9(a). Finally, the adsorption constant (ka) was derived as Eq. (9) and activation energy for the adsorption of optimized EMC was e 34.3 kJ/mol.
Dya ¼ ka ¼ 1:49 105 exp
34:27 103 R$Th
(9)
4.2.1.2. Chemical reaction period. The chemical rate constant was derived by using film diffusion control model, Eq. (6), in the same way as chemical reaction period on section 3.2. The Arrhenius plot for chemical reaction was obtained and plotted in Fig. 9(b), and Eq. (10) was obtained by using the equation which was obtained from a least square method.
38:75 103 ¼ kr ¼ 1:63 1010 exp s R$Th
1
Fig. 9. Temperature dependency of ka and kr according to Arrhenius law during (a) physical adsorption period and (b) chemical reaction period.
Finally thermal performance of chemical heat pump which uses optimized EMC was estimated from the proposed equation. 4.2.1.1. Physical adsorption period. The hydration part was divided into physical adsorption part and chemical reaction part by using same way in section 3.2. For physical adsorption period, instead of a rate equation, Freuntrich’s isotherm equation was adopted to express the initial physical adsorption [3].
Dya ¼ ka pbh
(8)
Since reaction pressure had little influence on the initial adsorption with the experimental condition, reaction order b in Eq. (8) is replaced by 0. The parameters in Eq. (8) could be obtained
(10)
The activation energy for chemical reaction is 38.8 kJ/mol. Those negative temperature dependencies of physical adsorption and chemical reaction imply that the equilibrium reaction of adsorbed water between MgO and the intermediate establishes according to hydration temperature. 4.2.1.3. Apparent reacted mole fraction of hydration. The apparent reacted mole fraction, y, of optimized EMC was defined as aggregation of structure water, Dys, physical adsorption amount, Dya, and chemical reaction amount, Dyr, as Eq. (11) from Eqs. (9) and (10).
y ¼ Dys þ Dya þ Dyr
(11)
Fig. 10 shows comparison between the measured and calculated reacted mole fraction, and calculated values represent well measured values. In conclusion, it was assumed that the assumptions in this study were appropriate for estimation of hydration rate of optimized EMC.
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Because physical adsorption process has lower enthalpy change value than chemical reaction process, optimized EMC showed gradually increasing heat output capacity, even, it showed suddenly increased reacted mole fraction on initial part of Fig. 10. In this figure, optimized EMC, 466.5 kJ/kg, also shows better performance than pure Mg(OH)2, 357.9 kJ/kg, at 110 C during first 30 min. 5. Conclusion
Fig. 11. Effect of hydration temperature on mean heat output rate per unit mass of Mg(OH)2 in optimized EMC.
4.3. Heat output performance of optimized EMC The heat output performance of the MgO/H2O chemical heat pump using optimized EMC as packed bed material was calculated numerically based on the hydration rate equations. The mean heat output rate, W, is defined as the averaged heat output rate per unit mass of Mg(OH)2 in optimized EMC during regular time interval after hydration was started.
W ¼
DHr $Dyr DHa $Dya th $MMgðOHÞ2
(12)
The DHr [kJ/mol] in first term on the numerator of the righthand side in Eq. (12) corresponds to enthalpy change of MgO hydration. The DHa in second term on the numerator is corresponding to enthalpy change of vapor condensation. MMgðOHÞ2 is the molecular weight of magnesium hydroxide and results, W, are described on Fig. 11. Fig. 11 shows the effect of reaction temperature on W per unit mass of Mg(OH)2 in EMC ðWMgðOHÞ2 Þ when the reaction pressure, ph, is 57.8 kPa. WMgðOHÞ2 shows values from 324.9 W/kg at 110 C to 54.2 W/kg at 200 C during the first 30 min. On the other hand, pure Mg(OH)2 shows 233.3 W/kg at 110 C. Fig. 12 shows the influence of hydration temperature on heat output capacities per unit mass of Mg(OH)2 in EMC (QMg(OH)2).
The optimization of mixing molar ratio of EMC mixture for practical application was conducted and hydration, heat output process, performance of CHP using optimized EMC was also estimated in this study. The amount of CaCl2 in EMC was important factor on hydration than dehydration; therefore, physical adsorption amount, Dya, chemical rate constant, kr, and the results of evaluation function, h, were considered to optimize the mixing molar ratio between Mg(OH)2 and CaCl2 in EMC. The physical adsorption period was defined up to dy/dt of 0.0002 and chemical rate constant, kr, for the hydration of optimized EMC was obtained from experimental results by using film diffusion control model among the shrinking core models. To know the effect of CaCl2’s amount in EMC on reacted conversion, evaluation function, h, was introduced and the optimized mixing molar ratio was suggested as a of 0.1 at n of 0.8, optimized mixing weight ratio. Hydration performance of optimized EMC was examined in two ways: hydration under various vapor pressures and reaction temperatures. Optimized EMC showed better performance than pure Mg(OH)2 and reaction rate equation was obtained from kinetic analysis of experimental results. The heat output performance of chemical heat pump, using optimized EMC as packed bed reactant, was estimated by using obtained reaction rate equation numerically. Unit mass of Mg(OH)2 in optimized EMC showed higher mean heat output rate and capacity than pure Mg(OH)2 at the same conditions. In conclusion, optimized EMC showed superior heat output performance than pure Mg(OH)2 and durability of optimized material should be assessed for practical application as a further study. Acknowledgments This study was executed with the support of the Grant-in-Aid for Scientific Research (B) # 20360404 from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. Nomenclature
Fig. 12. Effect of hydration temperature on heat output capacity per unit mass of Mg(OH)2 in optimized EMC.
b CAg g ka kg kr l M n ph Q R Rp s th T W y
stoichiometry factor concentration of gas, [mol/m3] gas physical adsorption constant, [s1] mass transfer coefficient, [mol/m2 Pa s] chemical rate constant, [s1] liquid molecular weight, [g/mol] mixing weight ratio, [-] hydration pressure, [kPa] heat output capacity, [kJ/kg] gas constant, 8.314 [J/Kmol] radius of reactant particle, [m] solid hydration time, [s] reaction temperature mean heat output rate, [W/kg] reacted mole fraction, [-]
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ys ya yr yi yM
structural water, [-] physical water adsorption, [-] chemical reaction, [-] hydration reacted conversion, [-] reacted conversion difference between EMC and pure Mg(OH)2, [-]
Greeks
a h H
rB s w
mixing molar ratio, [-] evaluation function, [-] reaction enthalpy change, [kJ mol1] density of magnesium oxide, [kg/m3] time for complete conversion, [s] weight of the sample, [g]
Superscript and subscripts a physical adsorption b reaction order c condensation d dehydration EG expanded graphite h hydration H2O water r chemical reaction v vapor Mg(OH)2 magnesium hydroxide References [1] I. Dincer, M.A. Rosen, Thermal Energy Storage: Systems and Applications, Wiley&Sons, Chichester, 2002. [2] H. Kawasaki, T. Watanabe, A. Kanzawa, Proposal of a chemical heat pump with paraldehyde depolymerization for cooling system, Appl. Therm. Eng. 19 (2) (1999) 133e143. [3] Y. Kato, N. Yamashita, K. Kobayashi, Y. Yoshizawa, Kinetic study of the hydration of magnesium oxide for a chemical heat pump, Appl. Therm. Eng. 16 (11) (1996) 853e862.
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