6.2 Ef fi cient Equipment for Liquid Desiccant
6.2.2 Modeling and Performance Simulation of a Internally
6.2.2.1 Mathematical Model and Verification
In order to simulate the heat and mass transfer process for internally heated regenerator under different operation conditions, a simple mathematical model was set up.
Fig. 6.20 Effect of solution temperature on the humidity ratio difference for regeneration [16]
The internally heated regenerator in Fig.6.21 had two types of channels including one type of hot water channels (channel I) and the other type of air and desiccant channels (channel II). If the hot water was not inactivated, the regenerator was an adiabatic regenerator. Fins were equipped between two plates in the air and desiccant channels to expend the heat and mass transfer area for air and liquid desiccant. The internally heated regenerator was 300 mm in length (L), 1000 mm in height (H). Besides, the channel II was 24 mm in width, and the extended coeffi- cient of the area of thefin in the regenerator (b) was 4.
The finite difference model is used, and the control volume is also shown in Fig.6.21. In the control volume, heat and mass transfer happens between three types offluids. Firstly, heat and mass transfer happens between the air and desic- cant. According to Refs. [11,17], the change of air temperature and humidity ratio can be expressed as follows:
dtaẳ2hcðtstaịLb MaCpa
dz ð6:31ị
dwaẳ2hdðwewaịLb Ma
dz ð6:32ị
Secondly, heat transfer also happens between liquid desiccant and air.
Temperature of the desiccant solution changes due to heat transfer with the air and hot water, which can be expressed by:
dtsẳ MadhaỵMwCpwdtwỵMaCpstsdwa
CpsMs ð6:33ị Due to the evaporation of the water in the solution, the massflow rate and the concentration of the desiccant also change, which can be determined by following equations:
Fig. 6.21 Regenerator structure and control volume
dXsẳ Madwa
MsþMadwa
Xs ð6:34ị
dMsẳ Madwa ð6:35ị
According to the energy balance, temperature change of the hot water can be calculated as follows:
dtwẳhcwðtstwịL CpwMw
dz ð6:36ị
In addition, the dimensionless correlation of mass transfer coefficient is derived based on the experiments aforementioned. It is written as:
Shaẳ25:8154ts3:36Re1a:55Sc0a:33 ð6:37ị Based on the mathematical model and the dimensionless correlation, the outlet air temperature, humidity ratio and desiccant temperature were predicted. The deviation between predicted values and experimental data was within 5%, which has been validated in Ref. [17]. This indicated that the model could give reasonable prediction for heat and mass transfer between air and liquid desiccant. Therefore, the model could be used to investigate the effects of inlet parameters.
6.2.2.2 Performance Indexes and Performance Comparison
The regenerator is desired to vaporize water from the desiccant solution as much as possible, so the moisture evaporation rate is taken as a performance index and it is defined as:
MrẳMaðwaowaiị ð6:38ị Since the internally heated regenerator consumes extra energy to provide latent heat, it is necessary to evaluate how much energy actually contributed to the phase transition of water. Thus, regeneration thermal efficiency (ηr) is also taken as per- formance index and is defined as:
gr ẳMaðwaowaiịr
Qh ð6:39ị
whereQhis the total heat input to the regeneration.
In addition, lithium chloride aqueous solution is used as desiccant and both air and liquid desiccant enter the regenerator from the top. The inlet conditions are listed in Table6.7.
Figure6.22 presents moisture evaporation rate and regeneration thermal effi- ciency under different solution massflow rates. It seems that in the internally heated regenerator, both moisture evaporation rate and regeneration thermal efficiency show weak sensitivity to the solution mass flow rate. However, in the adiabatic regenerator, both moisture evaporation rate and regeneration thermal efficiency firstly increase notably with the solution massflow rate and afterward keep nearly unchanged. It must be pointed out that when the solution massflow rate is very low, the moisture evaporation rate is less than zero, which means dehumidification occurs in the adiabatic regenerator. This is because in the adiabatic regenerator, the available heat for regeneration is mainly provided by the liquid desiccant. When the solution massflow rate is very low, the available heat for regeneration is very little and the solution temperature drops dramatically during regeneration. As a result, the vapor pressure at the solution surface is less than the vapor pressure of the air and dehumidification occurs accordingly. In this case, the heating water helping to maintain the solution temperature can promote the regeneration performance effectively. Thus, the moisture evaporation rate of the internally heated regenerator is much higher than that of the adiabatic regenerator when the solution massflow rate is low. It can be concluded that the internally heated regenerator shows great superiority in the case of low solution flow rate while the adiabatic regenerator works well only when the solution flow rate is relatively high. Since the low solution flow rate can relieve the problem of carryover, the internally heated regenerator is a potential alternative to the zero-carryover application.
Table 6.7 Inlet parameters for internally heated regenerator
Variable Ma(kg/s) Ms(kg/s) Mw(kg/s) ta(°C) ts(°C) tw(°C) wa(g/kg) Xs
Ms 0.015 0.001–0.031 0.02 30.0 65.0 65.0 16.5 0.370
ts 0.015 0.004 0.02 30.0 50.0–100.0 65.0 16.5 0.370
Ma 0.001–0.021 0.004 0.02 30.0 65.0 65.0 16.5 0.370
ta 0.015 0.004 0.02 20.0–40.0 65.0 65.0 16.5 0.370
Mw 0.015 0.004 0.003–0.063 30.0 65.0 65.0 16.5 0.370
Fig. 6.22 Effects of solution flow rate for internally heated regenerator [11]: a moisture evaporation rateMr;bregeneration thermal efficiencyηr
Figure6.23 presents moisture evaporation rate and regeneration thermal effi- ciency under different solution temperatures. The moisture evaporation rate increases linearly for two types of regenerators due to higher mass transfer potential. The moisture evaporation rate of the internally heated regenerator is higher than that of the adiabatic regenerator on account of the existence of hot water. The regeneration thermal efficiency also increases with an increase in the solution temperature for two types of regenerators. This is because the moisture evaporation rate increases significantly with the temperature.
Figure6.24shows the effects of the air massflow rate. For the internally heated regenerator, the moisture evaporation rate shows an upward trend while for the adiabatic regenerator, the moisture evaporation rate increases when the airflow rate is less than 0.011 kg/s and further increase in the air flow rate will result in reversing this trend. This can be explained as follows. The higher air velocity improves the mass transfer coefficient when the air flow rate is low. Thus, the moisture evaporation rate becomes larger. But further increase in the air velocity causes strong heat transfer between air and liquid desiccant. The solution temper- ature decreases sharply in the adiabatic regenerator and dehumidification may occur, leading to the reduction of the moisture evaporation rate. In addition, the Fig. 6.23 Effects of solution temperature for internally heated regenerator [11]: a moisture evaporation rateMr;bregeneration thermal efficiencyηr
Fig. 6.24 Effects of airflow rate for internally heated regenerator [11]:amoisture evaporation rateMr;bregeneration thermal efficiencyηr
massflow rate has an adverse effect on the regeneration thermal efficiency for both regenerators. In the internally heated regenerator, the regeneration thermal effi- ciency decreases slightly while in the adiabatic regenerator, the regeneration ther- mal rate decreases sharply. This is because air with higher velocity carries away considerable heat from the liquid desiccant. So, more heat is wasted without con- verting into the useful latent heat. Hence, the regeneration thermal efficiency declines. In the adiabatic regenerator, no source is used to compensate the wasted heat, resulting in more rapid decrease of the regeneration thermal efficiency than the internally heated regenerator. This indicates the air flow rate must be selected carefully and has an optimal value in adiabatic regenerator.
In Fig.6.25, the moisture evaporation rate and the regeneration thermal efficiency are depicted under different air temperatures. As the air temperature rises, almost no change happens to the moisture evaporation rate in the internally heated regenerator.
But in the adiabatic regenerator, the moisture evaporation rate increases. For the adiabatic regenerator, the increase in the air temperature can effectively depress the decrease in the solution temperature during regeneration process. However, for the internally heated regenerator, the increase in the air temperature has little effect on the solution temperature due to large heat derived from the heating water. The variations of regeneration thermal efficiency in two types of regenerators are opposite. The decrease of the regeneration thermal efficiency in the internally heated regenerator is because extra heat is used to increase air temperature but little improvement in the evaporation rate is derived. The increase of the regeneration thermal efficiency in the adiabatic regenerator is because more moisture evaporation rate is obtained by increasing the air temperature.
In Fig.6.26, the effect of the heating water flow rate is illustrated. Since no heating water is used in the adiabatic regenerator, the regeneration performance stays unchanged with the increase in the heating waterflow rate. For the internally heated regenerator, the larger heating waterflow rate helps to enhance the moisture evaporation rate and the regeneration thermal efficiency. When the heating water flow rate is more than 0.025 kg/s, the moisture evaporation rate as well as the regeneration thermal efficiency almost keeps constant.
Fig. 6.25 Effects of air temperature for internally heated regenerator [11]:amoisture evaporation rateMr;bregeneration thermal efficiencyηr
From analysis above, the internally heated regenerator has a great advantage over the adiabatic regenerator. Different from the adiabatic regenerator, the inter- nally heated regenerator still shows prominent regeneration performance when the solution flow rate is very low. This helps to develop zero-carryover gas–liquid contactor. In addition, the internally heated regenerator also helps to reduce energy consumption during regeneration because of the high regeneration thermal effi- ciency. Great importance should be attached to the development of internally heated regenerators.