A thermodynamic modeling of 2-bed adsorption desalination to promote main equipment performance

Adsorption desalination utilizes the discrete adsorption of the water vapor from the evaporator, and is capable of being discharged to the condenser. This study illuminated an advanced cycle of mass and heat recovery among beds, condensers, and evaporators. Morover, the thermodynamic modeling of adsorption desalination systems (ADS) under different operating conditions was investigated. Furthermore, its effect on the evaporator vapor production and the water vapor adsorption and desorption in the adsorption beds were accounted for. Parenthetically, the mathematical model of ADS thermodynamics was validated with the experimental data. Besides, the advanced ADS modeling was conducted via mass and heat recovery among beds, condensers, and evaporators. In addition to the amount of desalinated water, the time history chart of the equipment applied in the process with and without the thermal and mass recovery is also illustrated. Finally, under such operating conditions, the specific daily water production (SDWP) advanced ADS is 153% higher than conventional ADS.


INTRODUCTION
Lack of water is due to the lack of freshwater resources to meet water needs. This problem affects all continents, and in 2019 it was cited by the World Economic Forum as one of the largest global threats in terms of its potential impact over the next decade. The lack of water is exacerbated by economic competition for the water quantity or quality, consumer disparities, irreversible depletion of groundwater, and adverse environmental (1) it requires low temperature heat so it can use the waste heat in industries as a heat source; (2) maintenance costs are very low because there are only a few moving parts; (3) due to low operating temperature and pressure, it causes low scaling and corrosion; (4) the produced water is of very high quality; (5) it is capable of producing cooling simultaneously with the production of desalinated water. Recently, a large number of studies have been conducted in the realm of adsorption desalination. Recent adsorption desalination systems (ADS) improvements are listed in Table 1. Thu et al. (, a, b) and Ng et al. () studied the performance of the adsorption desalination system with silica gel adsorbent to produce desalinated water and cooling power. Also, they investigated the effect of cooling water and hot water temperature, condenser and evaporator temperature and cycle time with respect to the cycle performance parameters. Besides, they investigated the two-and four-bed absorption desalination system. In the two-bed system, the amount of water produced is 7.4 m 3 /ton of silica gel/day, and in the four-bed system, the amount of water produced is 8.9 m 3 /ton of silica gel/day. Ali & Chakraborty () investigated the adsorption desalination system via zeolite and silica gels as adsorbents. The system consists of two stages as well as two evaporators, which transfer the heat from the condenser to the evaporator. The amount of water produced in this system was 5% higher than the con- They studied the heat recovery of the condenser to the Also, its effect on the evaporator vapor production and the water vapor adsorption and desorption in the adsorption beds were examined. The mathematical model of ADS thermodynamics was then validated with the experimental data.
The advanced ADS modeling was also conducted via mass and heat recovery among beds, condensers and evaporators, and in addition to the amount of the desalinated water, the time history chart of the equipment applied in the process with and without the thermal recovery and mass was revealed. The cycle performance was evaluated in terms of daily specific water production (SDWP), specific cooling capacity (SCC), and coefficient of performance (COP). The recovery mode was new to this plan. This configuration could improve the ADS performance to a great extent.
The ADS cycle's configuration Figure 1 shows the ADS design of the two beds with the mass and heat recovery designs in different modes. The system consists of an evaporator, two adsorption beds, and a condenser. In the first mode, bed 2 is in the adsorption mode and bed 1 is in the desorption mode. In this mode, thermal recovery operates between bed 2 and the condenser to evaporator. In the second mode, mass recovery, the two beds are connected to each other and the mass and pressure are transferred from the high temperature bed to the low temperature bed. In the third mode, the final thermal recovery is performed between the high temperature bed, the low temperature bed, and the condenser to the evaporator.

Mass and energy balances equations
The equation of mass balance for each cycle is obtained by: Two-bed adsorption desalination works in three modes of the absorption/desorption, the mass and heat recovery.
The energy balance during the adsorption/desorption mode can be written as follows: (M sg cp sg þ M cu cp cu þ M al cp al þ M sg w cp g(T bed ) ) bed dT bed dt ¼ The energy balance during the mass and heat recovery mode is given as below respectively: (M sg cp sg þ M cu cp cu þ M al cp al þ M sg w cp g þ M w,ads cp w(T bed ) ) bed dT bed dt ¼ 0 (4) (M sg cp sg þ M cu cp cu þ M al cp al þ M sg w cp g(T bed) ) bed dT bed dt ¼ À _ m cw cp cw(T bed ) (T cw,out À T cw,in ) bed The evaporator and condenser energy balance is given as below respectively: À _ m cw,cond cp w(T cond ) (T cw,out À T cw,in ) cond The desorption, condensation and evaporation heat are derived by: Finally, the system performance is evaluated by the Specific Daily Water Production (SDWP) and the performance ratio (PR).

RESULTS AND DISCUSSION
In this study, to validate the present ADS mathematical  Table 2.
In Figure 3, the amount of water adsorbed in the adsorption beds with and without recovery state is shown in the adsorption cycles. Recovery mode includes heat recovery between the adsorption beds and the condenser    to the evaporator, as well as mass recovery between the two beds. As shown in Figure 3, the first and third half cycles correspond to bed 1 and the second and fourth half cycles correspond to bed 2. In the recovery mode, the slope of the absorbed water diagram is greater than the one in the non-recovery mode, indicating that the adsorption rate is higher in the recovery mode. Figure 4 shows the time history of the bed-1 water uptake and offtake with and without mass and heat recovery. As can be seen in the diagram, the slope of the recovery mode is higher than the non-recovery mode. Figure 5 illustrates the amount of water excreted in the adsorbed beds in the desorption state. As shown in the figure, the first and third half cycles are related to bed 2, and the second and fourth half cycles pertain to bed 1. In the first half cycle of bed 2, since the system has not produced the vapor yet, almost no vapor is excreted in the desorption mode. The slope of the recovery mode diagram   is higher than the one without the recovery mode, indicating that the amount of the water adsorbed, and ultimately the amount of the water produced, would be higher. Figure 6 shows the time history of the bed-2 water uptake and offtake with and without mass and heat recovery. Figure 7 shows the reduction of seawater mass inside the evaporator versus the time without and with the mass and heat recovery. As the figure reveals, the amount of water reduction in the evaporator in the recovery mode is higher than in the non-recovery mode, and this issue indicates that, in this case, the amount of water produced would also be higher. As shown in the recovery mode, the evaporation rate decreases with an increase in seawater concentration. In the first two cycles, the mass of seawater decreases from 3 to 1.8 kg, while, in the next three cycles, its mass only decreases from 1.8 to 1.45 kg. Figures 8 and 9 illustrate the temperature variations for the evaporator, condenser, and adsorption beds. As shown  Therefore, the amount of fresh water produced would be much higher than that of the conventional adsorption desalination.  gel at the hot water temperature of 92.5 C. This increased rate of desalinated water production is due to the mass and heat recovery of the ADS process. It is worth noting that the fin pitch in the bed heat exchanger was assumed to be 4 mm. Figure 11 elucidates the time history of the cooling water temperatures with and without the mass and heat recovery.
As shown in the figure, the cold water temperature output from the system in the recovery mode is higher than in the non-recovery mode. This issue can be due to the transfer of the internal heat from the beds and the condenser to the evaporator.

CONCLUSIONS
In this study, a conventional ADS with heat and mass recovery cycles was modeled. The results indicated that the