1. Introduction
There is a global aim to decrease energy consumption from fossil fuels considering their limited resources and environmental issues. To achieve this, the increasing use of renewable energy sources is necessary. Solar energy, basically known for its infinite and renewable nature, is one of the most widely used today. However, considering its variability and seasonal availability, the major challenge continues to be the need of storing this free source of energy for time periods with little solar radiation. The technology of thermochemical energy storage has been proposed as a promising approach for minimizing the temporal mismatch between heating demand and solar energy supply. In comparison to other thermal energy storage methods, the remarkable advantage of this technology is long-term energy preservation with negligible heat loss and high energy density. In these systems, the reversible process of desorption and adsorption makes it possible to store solar heat from summer to winter, so that the heat can be supplied to residential buildings with a very high proportion of solar energy.
Adsorption is the adhesion of an atom, ion, or molecule (adsorbate) to a surface of commonly a porous solid (adsorbent). A film of the adsorbate is created on the adsorbent surface in this process. The reverse process is called desorption. This phenomenon is a surface phenomenon since it occurs just on the solid surface and does not include the bulk of the solid material, like what is observed in the absorption process [
1].
Different adsorption materials have been studied by researchers. Activated carbon, zeolite sieves, silica gel, and natural rocks are traditional physical sorbents [
2,
3]. Among them, zeolite sieves, which are aluminosilicate minerals of alkaline or alkali earth metals (calcium, sodium, and potassium) with a microporous structure for moisture adsorption, are one of the most used. They have regeneration temperatures in the range of 150–300 °C and high storage density. Until now there are more than 40 types of natural zeolites and more than 150 synthesized zeolites [
4]. Zeolites 4A, 5A, 10X, and 13X are among the most used zeolites for sorption energy storage [
5]. Among them, zeolite 13X with a maximum water adsorption capacity of 12–36% by mass [
6,
7] is known as the one with the most potential considering its large sorption capacity and high sorption rate. Compared with silica gel, which is another traditional sorbent, zeolite has a higher energy storage density; however, a higher regeneration temperature is required. A regeneration temperature of about 180–300 °C and adsorption enthalpy of about 3300–4200 kJ/kg have been reported for the zeolite–water pair by Wang et al. [
8]. Zeolite 13X has various applications such as thermal storage [
9] and sorption cooling [
10,
11]. High adsorption enthalpy of the zeolite/water pair in comparison with other adsorption pairs such as activated carbon/ammonia or silica gel/water make it a promising candidate for thermal storage applications.
The main objective of research in the area of sorption storage systems for buildings is to develop a reactor with the ability to provide adsorption heat at temperature levels suitable for space heating. A thermochemical (sorption) energy storage prototype for space heating was developed by [
12] in the MonoSorp project framework. In this system, zeolite 4A honeycomb structures (70 kg) were utilized. During the experiments, a sorption temperature of about 20 °C and a regeneration temperature of 180 °C was used. Based on the experiments, in the system with an inlet air temperature of 19 °C and an inlet water vapor pressure of 8.7 mbar, they measured 22 °C as maximum temperature increase and discharging powers of 1–1.5 kW. Another prototype was developed by Jähnig et al. [
13] with about 200 kg of silica gel. The experiments showed an energy density of about 50 kWh/m
3 for the materials and a temperature lift of only 5 K, revealing that silica gel has a very poor thermal conductivity and also that a very limited temperature increase can be achieved. The main conclusion claimed by the authors is that silica gel is not suitable for heat storage purposes. In an experimental study conducted by Hongois et al. [
14], sorption experiments in a reactor filled with 200 g zeolite-MgSO
4 composites were carried out. They considered different relative humidities of air and mass flow rates. Their results demonstrated a high influence of relative humidity of air on the system operation.
The most investigated reactors are fixed-bed reactors. In these reactors, the sorbent is kept within the reactor, and both adsorption and desorption occur in the reactor. A reaction zone with relatively high temperatures is formed, which moves from the area of the steam inlet to the steam outlet [
5]. In the COMTES project [
9,
15], zeolite 13XBF was used for seasonal heat storage purposes in buildings. They developed a fixed bed reactor with about 300 L and 164 kg of zeolite. Based on their results, an energy density of about 177 kWh/m
3 can be provided by this system.
Although experiments are required for the investigation of processes in sorption reactors, it is usually time-consuming and expensive to conduct several experiments to study the different involved parameters. Here, numerical studies can provide a more effective and cheaper way to investigate adsorption and desorption processes. Therefore, some numerical studies have been conducted to understand the process properly. Jänchen et al. [
16] performed a CFD simulation to compare the performance of zeolite 4A pellet beds zeolite and 4A honeycombs with and without binder in the adsorption process. The results have shown the better performance of binder-free zeolite honeycombs, which might be due to the optimum secondary pore size distribution, leading to enhanced performance during the adsorption process.
The aim of the present work is to develop a one-dimensional code using computational fluid dynamics (CFD) to model the adsorption process of zeolite 13X and water in a fixed-bed reactor utilizing past experimental results to study this process in detail and under various boundary conditions. A parametric study is conducted to investigate different effective parameters during this process and the influence of each parameter is discussed and compared, so that an efficient discharging process can be estimated.
4. Results and Discussion
In the current investigation, a CFD code was developed to model the adsorption process between zeolite and water for seasonal storage purposes. The effect of desorption temperature, humidity, and mass flow rate of the incoming air on the reaction is studied. The following section discusses the results considering different ranges for input parameters. The influence of desorption temperature and partial pressure on the outlet temperature is discussed and also a parametric study is presented to investigate the influence of input parameters on the discharging time and adsorption enthalpy. In this study, the discharging time is considered as the time from the beginning of the adsorption process until there is no longer any change in the humidity of the outlet air which indicates that the zeolite is completely saturated.
The reaction rate between zeolite and water can be defined using the following equation:
where
is the bulk density of zeolite.
The value of the reaction rate during the adsorption process is plotted in
Figure 3 for the case of
of 15 mbar and adsorption temperature of 30 °C as shown in
Figure 3. As can be observed, the reaction occurs in short time periods, shaping the reaction zone with narrow intervals, due to the high reaction rate of zeolite, and when the zeolite in the reaction zone is saturated, this reaction zone moves forward. Moreover, as time passes, the amplitude of the reaction rate decreases slightly, which is due to the fact that the upstream points have absorbed a small amount of water vapor, which causes the maximum amount of reaction rate for these points to be slightly lower.
The temperature provided during desorption, , has a great influence on the stored energy in the sorbent, and consequently the released energy in the adsorption process. This is especially important for heating applications where hot air above some specific temperatures should be provided for the desired time period. Having knowledge about the parameters influencing the outlet temperature and discharging time can be extremely helpful to adjust them in the most efficient way.
To study the influence of this temperature, simulations are conducted at four different charging temperatures of 100, 140, 180, and 220 °C, and the results are presented in
Figure 4.
To compare the results from different cases better, assume that an outlet temperature of 60 °C (the temperate provided by a conventional heating system for buildings) is needed at the outlet of the system. Based on the simulation results, in the same adsorption temperature of 30 °C and partial pressure of 15 mbar, a maximum achieved outlet temperature, is equal to 59.14 °C in the case with a of 100 °C. For of 140 °C, the highest temperature of 65 °C can be provided at the outlet with the possibility of supplying a temperature higher than 60 °C for 117 min. For the case of 180 °C, the maximum achieved temperature is equal to 68 °C and the system can provide the outlet temperature, , higher than 60 °C for a time period of about 174 min. A maximum outlet temperature of 69 °C, and a duration of 221 min above 60 °C can be achieved for cases with of 220 °C.
As predicted, when a higher temperature is provided during the desorption process, a higher outlet temperature for a longer time period can be achieved, showing the importance of the desorption temperature; however, there is no linear relationship between the desorption temperature and the maximum achieved temperature in the adsorption process.
The comparison of the released adsorption enthalpy also shows that the system is highly sensitive to the desorption temperature, which is because of the fact that at higher
Tdes, less water exists in the zeolite at the end of the desorption process, so more capacity is available during discharging. Another important parameter that influences the reaction between zeolite and water is the partial pressure of water vapor,
, which is an indicator of the incoming air humidity. As can be clearly observed in
Figure 5, the released energy from zeolite increases significantly with increasing the partial pressure. The reason is increasing available water vapor that can react with zeolite, leading to higher outlet temperature. However, the discharge time decreases because the zeolite becomes saturated sooner.
To study the influence of the mass flow rate (MFR) of the incoming air on the discharging process, three different values—1, 1.5, and 2 —are considered for mass flow rate and the variations of discharging time, outlet temperature, and released adsorption enthalpy are calculated.
As can be clearly seen in
Figure 6, this parameter has a significant effect on the discharging time; with increasing MFR, the reaction between water and zeolite occurs faster. However, there is no significant influence on
.
The cases with MFRs of 1, 1.5, and 2 have the maximum achievable temperatures of 67.7 °C, 68 °C, and 68.1 °C, respectively, but the duration with a temperature above 60 °C is equal to 174 min, 170 min, and 131 min, respectively, showing that with increasing mass flow rate, outlet temperature higher than 60 °C can be achieved for a shorter period of time.
To interpret the influence of different factors on the process of adsorption of zeolite/water pairs, three decisive parameters of desorption temperature (Tdes), partial pressure of water vapor (Pw,ads), and air mass flow rate (MFR) are considered, and changing of mean adsorption enthalpy, discharging time, and amount of adsorbed water in adsorption process are also considered. Desorption temperature is the temperature provided during the charging process. To involve this parameter in the study, the amount of water loading of zeolite after the desorption process under the charging temperature is read from the zeolite isotherms based on the Dubinin equation and imported as the initial loading of zeolite at the beginning of the adsorption process. To have the same condition for all simulations, the partial pressure during the desorption process is considered equal to 10 mbar for all cases. A range between 120–180 °C is taken into account for desorption temperatures and the impact of this parameter on the adsorption process of zeolite/water is studied. The other parameter of interest is the partial pressure of water vapor in the inlet during the adsorption process. For numerical study, values between 5–25 mbar are considered for this parameter. The other studied parameter is the mass flow rate of air valued between 0.5–2 . Considering these ranges, several simulations are conducted to study the influence of these parameters on adsorption mean specific enthalpy, amount of adsorbed water during adsorption, and time to complete the adsorption process.
The released enthalpy during the adsorption process is represented by mean specific adsorption enthalpy
hads,m. The influence of
,
, and MFR on
hads,m are studied, and the results of simulations are illustrated in
Figure 7.
As can be seen, higher mean specific adsorption enthalpy hads,m can be achieved by proving higher desorption temperatures or higher partial pressures, while the mass flow rate has little influence on the amount of the adsorption enthalpy.
Figure 7b shows the changes of
hads,m under different partial pressures and mass flow rates at a desorption temperature of 150 °C, and
Figure 7d shows the variation of
hads,m with
for the case with an MFR of 1
and partial pressure of 15 mbar. At lower desorption temperatures, more water remains inside the zeolite, and due to higher loading, the interaction between the adsorptive decreases, and the bonding forces also decrease, leading to a reduction in adsorption enthalpy.
For the considered parameters, an equation in terms of coded factors can be utilized to make predictions about the response. The relative influence of each parameter can be identified using the code by comparing the factor coefficients. Changes of
hads,m according to relevant parameters can present the following mathematical relationship.
This relationship also emphasizes the great importance of desorption temperature on the released energy during adsorption. However, it can be seen that partial pressure also has a somehow important effect on the adsorption enthalpy, which means that if, for example, a very high temperature cannot be provided during desorption, this can be compensated to some extent by providing higher moisture.
The variation of discharging time with changing desorption temperature, partial pressure, and incoming mass flow rate is investigated and presented in
Figure 8. It appears that the mass flow rate of the incoming air has a great potential to influence the discharging time. This time also increases with increasing charging temperatures because in higher
there is less loading inside the zeolite, and under constant partial pressure more time is required for saturation. By augmenting the partial pressure of water vapor, the amount of water entering the reactor increases, so the reaction rate rises, and the reaction occurs faster and causes the reactor to discharge faster.
The changes of discharging time according to relevant parameters are presented in
Figure 8, and Equation (18) can present the following associations.
The influence of the partial pressure and temperature during the desorption on the adsorbed amount of water was investigated. Based on the results, presented in
Figure 9, a much higher temperature is provided in the desorption process, and the higher the partial pressure of the water vapor, the greater the capacity of the zeolite to absorb water, which means more sorption storage density and released energy. However, the mass flow rate has a negligible influence on the amount of adsorbed water.
Variations of adsorbed water amount in terms of the coded factors can be represented using the following mathematical relationship.
Based on the above equation, the desorption temperature has the highest influence on the amount of adsorbed water, which also leads to higher amounts of released energy.