1. Introduction
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A considerable amount of industrial energy consumption is discharged to the environment as waste heat. Part of this waste energy can be recovered by upgrading the waste heat, which would improve the overall thermal efficiency of the process [1]. Heat pumps, then, have emerged as a useful method for waste heat recovery. On the other hand, the presence of a compressor and the use of hazardous refrigerants are the two shortcomings of conventional heat pumps. Chemical Heat Pumps (CHP) has emerged as an environmentally friendly alternative since upgrading and recovery of waste heat is achieved by a reversible solid-gas chemical reaction instead of the compression and decompression cycles in conventional heat pumps. In CHPs, environmentally benign refrigerants, e.g., water, ethanol, ammonia, and sorbents, e.g. zeolites, activated carbon, silica gel, and earth metal salts, are used. Furthermore, CHPs enable heat recovery or refrigeration over a wide range of temperatures based on the thermicity of the reversible reaction [2, 3]. Due to the high sorption capacities, the earth metal salts-ammonia have been a promising pair to employ in CHPs. For example, NH3 sorption capacity of 1 mole of MgCl2 is 6 moles. Low material cost, fast reaction rate, and convenient adsorption/desorption temperature ranges are other important advantages of using MgCl2-NH3 pair in CHP applications. However, very low thermal conductivities of the salts (0.1-0.5 W m−1 K−1) are the major problems during the heating and cooling cycles of the heat pumps [4, 5]. Although studies show that using a suitable binder (such as ENG, carbon fiber, etc.) increases the heat and mass transfer properties, the addition of binders is not preferable because of decreasing the sorption capacity of the salt. Another drawback of this system stems from the irreversible volume increase of the salt crystals after the first adsorption-desorption cycle since the molar volume of MgCl2.6NH3 is approximately two times higher than that of MgCl2.2NH3 [6]. This irreversible swell of the salt grains damages the structural integrity of the bed [7-10].
In order to overcome the specified major problems, metal salt-NH3 reactions have been investigated in many earlier theoretical and experimental studies. The “shrinking core model” and “particle/pellet model” are widely employed in the literature to capture the salt-NH3 reactions. Goetz and Marty [5] modeled the MnCl2-NH3 reactive system by using the grain-pellet model, in which the reaction in each grain was assumed to follow the shrinking core model. They kept the pellet porosity and size of the grains constant while allowing the pellet volume to change due to the reaction. They reported that the progress of the reaction zone was controlled by the conductive heat transfer. In the theoretical study of Lu et al. [11], both heat and mass transfer were considered at the pellet level, and it was assumed that there was no structural change. They reported that at low pressure (<1 bar), permeability was an important factor for the reaction of global advancement. Han et al. [12], also reported the importance of permeability for the MgCl2-NH3- graphite reactive system. Graphite was added to the reactive medium to enhance the system’s thermal conductivity and permeability. According to their results, heat transfer was not a limiting factor, while the system became mass transfer limited, especially at low pressures and high graphite amounts. Mofidi and Udell [6] also enhanced the thermal conductivity of the reactive system by adding graphite. They observed a heat transfer-limited system when the permeability was high. All these studies have shown that, as an alternative to time-consuming and costly experiments, mathematical modeling and simulation of metal salt-NH3 reactions can be instrumental in adopting them to some crucial applications such as NH3 storage or chemical heat pumps. In the earlier modeling studies, the metal salt-NH3 reaction kinetics was incorporated into the calculations by switching between adsorption and desorption expressions based on the reaction conditions. One of the first suggested kinetic model was reported by Mazet et al. [13]. They expressed reaction rate as the combination of reaction progression term and rate constant term for adsorption and desorption, individually. The reaction rate constant term was defined as the multiplication of Arrhenius term and pressure equilibrium drop term. The reaction conditions were set based on this pressure equilibrium drop term. For example, when the pressure was higher than the equilibrium pressure at the specified temperature, they used only the adsorption reaction rate expression while the pressure was lower than the equilibrium pressure then they switched to the desorption rate expression. Many studies were conducted on this topic and researchers mainly focused on the equilibrium drop term in terms of pressure drop term [4, 14], temperature drop terms [15], or the combination [16]. Still, the common point of all these studies is that reaction rates are given separately for adsorption and desorption reactions. On the other hand, the observed reaction is the outcome of these two simultaneously competing reactions, i.e. adsorption and desorption. Therefore, a reversible reaction kinetics model that includes both adsorption and desorption terms is potentially more accurate than those used in earlier studies in predicting net reaction rate at a given condition. In the presented study, theoretical reversible reaction rate expression for the MgCl2-NH3 reactive system is obtained by using literature values in the relevant thermodynamic relations. Also, the MgCl2-NH3 reactive system is modeled and simulated considering both heat and mass transfer and the reversible reaction. The operating parameters are selected to ensure net adsorption reaction. The particle-pellet model is used to investigate heat and mass transport at the pellet level. In addition, the volume change in the salt pellet during the reaction is considered and modeled to investigate its impact on the process. The effect of gas NH3 pressure change on the heat and mass transfer characteristics, conversion, and pellet volume change are simulated. The results are presented in the following sections.
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