Here, we propose a chemical heat pump chiller with a SrBr 2 hydration reaction system for utilization of waste heat. The SrBr 2 hydration reaction could recover waste heat in low temperatures ranging from 373 K to 353 K, and the system showed good potential in terms of the high cooling thermal-storage density. Previous studies have given little information on the reaction characteristics of the SrBr 2 hydration reaction. In this paper, we developed a measuring method for the hydration reaction equilibrium and reaction rate based on the volumetric method. We analyzed the hydration reaction rate with an unreacted-core shell model. In the experiments, the SrBr 2 equilibrium temperature observed was equal to the theoretical equilibrium temperature obtained from thermodynamic databases. In addition, the hysteresis gap between the hydration and dehydration values was 2.0 K. Thus, the hysteresis effect was negligible for the chemical heat pump cooling operation. The reaction fraction of the SrBr 2 hydration reached 0.7 within 20 s. By analyzing the hydration reaction rate with the unreacted-core shell model, the activation energy value was calculated to be56.6 kJ/mol. The calculation results showed good agreement with those of the experiment as the reaction fraction reached 0.7.
In correspondence with increasing energy consumption since the Industrial Revolution, the amount of industrial waste heat has been rising. Energy-cascading technologies have been developed to save on energy consumption, and recently, chemical heat pumps (CHPs) have been receiving much attention. The CHPs can store waste heat and supply energy at various temperature levels on demand [
A previous study by Lahmidi et al. (2006) has revealed that CHPs employing the SrBr2 hydration reaction can be used to provide heating and cooling storage functions with solar thermal systems [
We have developed a measuring method for the hydration reaction rate based on the volumetric method. We can analyze the hydration reaction rate with this method on the condition that the effects of thermal and mass transfer resistance are minimized.
During the reactions for CHPs, it is well known that the hydration/dehydration reactions display hysteresis between the theoretical and ideal equilibrium (Matsuda et al., 1985; Kubota et al., 2000; Ogura et al., 2007) [
In this work, we have examined the SrBr2 hydration reaction characteristics for CHP cooling modes. We discuss both 1) the equilibrium vapor temperature of the SrBr2 hydration reaction―during which we identify ideal equilibrium relations of the SrBr2 hydration reaction―and 2) the reaction rate of hydration―whereby we evaluate the reaction rate correlations with anunreacted-core model.
Solid-gas reaction models have been suggested for use as mathematical models. From such models, we selected an unreacted-core model. This model was utilized in the analysis of the hydration/dehydration reaction system [
So, the overall hydration reaction rate is composed of three steps. These steps include the interface reaction rate-determining step,the intra particle diffusion rate-determining step, and the gas film rate-determining step. Overall, the reaction rate can be written as follows:
where krf, De, and kr are expressions for the gas film coefficient, intra particle diffusion coefficient, and rate coefficient of the reaction, respectively. Rs is the particle radius. Pe and P represent the SrBr2 hydration equilibrium pressure and the system pressure, respectively. In general, the gas film rate is much faster than the interface reaction rate and intra particle diffusion rate under measuring rate conditions. It may be assumed that the gas film rate is not affected by the overall reaction rate. Here, the overall reaction rate r was rewritten by shortening the gas film rate step. The overall reaction rate γ is as follows:
Equation (2) was expanded in order to determine the steps that affect the overall reaction rate. If each step influences the overall reaction rate, Equations ((5) and (7)) can be obtained on the supposition of the effect step.
In this case, the reaction rate is defined as follows (
The following Equation (5) was obtained by integrating Equation (4):
In this case, the reaction rate is defined as follows (
The following Equation (7) was obtained by integrating Equation (6):
and
By use of Equations ((4) and (6)), the f(X) plot with time can be obtained for the reaction rate-determining step.
The experimental apparatus used for the volumetric measurements is shown in
A sample of SrBr2∙6H2O was obtained from KANTO CHEMICAL Co., Inc., in Japan. We heated the SrBr2∙ 6H2O at 353 K to obtain non-hydrated SrBr2 for the initial experiments. Thereafter, the sample particle diameter was adjusted for the experimental conditions.
A sample in the reaction cell is shown in
recorded on a PC. When the tank pressure change reached an equilibrium state, we calculated the amount of H2O used in the hydration/dehydration reaction from the quantity of the pressure change. In this method, the tanks and the sample weight of SrBr2 were adjusted in order to keep the quantity of tank pressure change under 5%.
A previous study revealed that a decline in the reaction rate will occur during hydration reaction repetition (Kato et al., 1998). The hydration/dehydration reaction involves the expansion and contraction of reactant particles and particle condensation. We confirmed that the effect of SrBr2 hydration reaction repetition was negligible on the reaction rate over 10 repetitions.
The thermodynamic equilibrium of the SrBr2 1 - 6 hydration reaction was expressed by the Clausiu-Clapeyron equation as follows:
where Pe and Te are the equilibrium pressure and temperature, respectively. P0 is the atmospheric pressure. ∆H and ∆S represent the enthalpy and entropy changes in the reaction, respectively.
In this experiment, 50 mg of non-hydrated SrBr2 (particle diameter 100 - 106 μm) was placed in the reaction cell. Then, the tank was pressurized to the experimental pressure and the sample was allowed to react to 0 - 1 hydration at equilibrium temperature. During the hydration step, the thermostat bath temperature for the reaction cell was lowered at a rate of 1 (K/h). The temperature of the reaction cell then achieved the SrBr2 1 - 6 equilibrium temperatures, and the tank pressure dropped along with the hydration reaction. When the pressure dropped quickly, it was recorded as the hydration equilibrium temperature at the set pressure. When SrBr2 was hydrated at the equilibrium temperature, the temperature of the reaction cell was kept stable until the sample was completely hydrated.
After the hydration reaction was complete, the temperature of the reaction cell was raised and we measured the dehydration equilibrium temperature. During this experiment, the quantity of the pressure change with the hydration reaction was sufficiently small relative to the set pressure, which means that the reaction occurred under isobaric conditions.
An experimental demonstration is shown in
In this experiment, we evaluated the effect of sample weight on the hydration reaction rate. The sample weights used were 10, 32, 60, 140, and 670 mg. As the sample weight increased, the thickness of the sample packed beds increased. Heat and mass transfer resistance depended on the sample packed bed thickness.
Tank Pressure | 1.23 (kPa) | 1.56 (kPa) | 4.23 (kPa) |
---|---|---|---|
Hydration | 1.2 (K) | 1.5 (K) | 0.4 (K) |
Dehydration | 2.0 (K) | 0.9 (K) | 1.2 (K) |
We also evaluated the effect of sample particle diameter on the hydration reaction rate. For this, we prepared samples of SrBr2 whose particle diameters were 5 μm, 42 - 52 μm, 100 - 106 μm, and >200 μm.
The activation energy was calculated to be 56.6 kJ/mol. This value was lower than that obtained for some different hydration reactions (Kato et al., 1998; Abliz et al., 2002). Thus, SrBr2 hydration reactions could be valuable in many applications.
In this study, SrBr2 hydration reaction characteristics for chemical heat pump cooling modes were evaluated.
From the experimental study and analytic calculations, we obtained the following results.
1) An equilibrium temperature gap existed between the experimental and theoretical data, but the maximum value of the temperature gap was only 2.0 K. Hysteresis was also detected between the hydration and dehydration values in the experiment. Overall, the SrBr2 hydration reaction equilibrium temperature showed good agreement with the theoretical equilibrium temperature.
2) The SrBr2 hydration reaction rate can be measured effectively with the proposed method on the condition that effects of thermal and mass transfer resistance are minimized. In the experiment, the duration time to reach Xreact = 0.7 was within 20 s. By analyzing the hydration reaction rate with the unreacted-core shell model, the active energy value was calculated to be 56.6 kJ/mol. Additionally, the calculation results showed good agreement with the experimental ones at the initial reaction fraction.
TakehiroEsaki,NoriyukiKobayashi, (2016) Reaction Rate Characteristics of SrBr2 Hydration System for Chemical Heat Pump Cooling Mode. Journal of Materials Science and Chemical Engineering,04,106-115. doi: 10.4236/msce.2016.42012