3.3.2.1.1 Generator

The internal temperature T₂ in the generator is assumed to be uniform (Figure 3.7) even if it varies along the heat exchanger due to the variation of the concentration of the solution (Patnaik et al., 1993). As in most studies on absorption systems and supported by various experiments, the generator model is based on heat transfer (Banasiak and Koziol, 2009). The power exchanged by the generator internal (solution) and external flows is evaluated by using the logarithmic mean temperature difference approach. The modeling rests on the assumption that the values of the overall heat transfer coefficient of the generator heat exchanger (UA)₂ are constant. Actually, the values of UA vary somewhat with the temperature as well as with the mass flows, but this variation is relatively small in most cases (Patnaik et al., 1993; Grossman et al., 1995). The exchanged heat in the generator is therefore

$Q_2={\left(UA\right)}_2\cdot \frac{T_{\mathrm{g}\mathrm{i}}-T_{\mathrm{go}}}{ln\left(\frac{T_{\mathrm{g}\mathrm{i}}-T_2}{T_{\mathrm{g}\mathrm{i}}-T_2}\right)}=m_{\mathrm{g}}\cdot C{p}_{\mathrm{p}\mathrm{w}}\cdot \left(T_{\mathrm{g}\mathrm{i}}-T_{\mathrm{go}}\right)$

Equations (3.4) and (3.5) are solved to estimate the generator heat losses to the ambient, assuming that the generator shell is isothermal. Equation (3.4) expresses the generator shell internal energy variation, which is the difference between the internal heat received by convection and the external one.

${\left(MCp\right)}_{2\mathrm{s}\mathrm{h}}\cdot \frac{\mathrm{d}{T}_{2\mathrm{s}\mathrm{h}}}{\mathrm{d}t}={\left(UA\right)}_{2\mathrm{s}\mathrm{h}int}\cdot \left(T_2-T_{2\mathrm{s}\mathrm{h}}\right)-{\left(UA\right)}_{2\mathrm{shext}}\cdot \left(T_{2\mathrm{s}\mathrm{h}}-T_{\mathrm{r}\mathrm{e}\mathrm{f}}\right)$

$Q_{2\mathrm{loss}}={\left(UA\right)}_{2\mathrm{shint}}\cdot \left(T_2-T_{2\mathrm{s}\mathrm{h}}\right)$

In order to take into account the fact that the solution leaving the generator is not in equilibrium conditions, a mass transfer effectiveness α, also called absorption percentage or absorption equilibrium factor (Andberg and Vliet, 1983; Kaushik et al., 1985; George and Murthy, 1989; Patnaik et al., 1993), is introduced in Equation (3.9). The absorption percentage is the ratio of the actual change in concentration of the solution to the maximum possible change that could be obtained with an infinitely long plate. The maximum possible change is the difference between the generator inlet concentration and the equilibrium concentration.

Mass and energy balances in the generator yield Equations (3.6)–(3.15):

$m_{2\mathrm{i}}=m_{1\mathrm{o}}=v_{1\mathrm{o}}\cdot {\rho }_{\mathrm{sol}}\left(T_1,x_{1\mathrm{l}\mathrm{i}\mathrm{q}}\right)\mathrm{mass}\mathrm{continuity}\mathrm{equation}$

$m_{2\mathrm{i}}=m_{2\mathrm{o}}+m_{2\mathrm{v}}\mathrm{global}\mathrm{mass}\mathrm{balance}$

$m_{2\mathrm{i}}\cdot x_{2\mathrm{i}}=m_{2\mathrm{o}}\cdot x_{2\mathrm{o}}\mathrm{LiBr}\mathrm{mass}\mathrm{balance}$

$x_{2\mathrm{i}}-x_{2\mathrm{o}}=\alpha \cdot \left(x_{2\mathrm{i}}-x_{2\mathrm{o}\mathrm{e}\mathrm{q}}\right)$

$m_{2\mathrm{i}}\cdot h_{2\mathrm{i}}+Q_2=m_{2\mathrm{o}}\cdot h_{2\mathrm{o}}+m_{2\mathrm{v}}\cdot h_{2\mathrm{v}}+Q_{2\mathrm{loss}}\mathrm{energy}\mathrm{balance}$

$P_2=P_{2\mathrm{v}}=P_{3\mathrm{v}}=P_3$

$P_2=P_{\mathrm{sol}}\left(T_2,x_{2\mathrm{o}}\right)\mathrm{state}\mathrm{balance}$

$T_2=T_{2\mathrm{o}}=T_{2\mathrm{v}}=T_{3\mathrm{v}}$

$m_{1\mathrm{o}}\cdot h_{1\mathrm{o}}+w_1=m_{2\mathrm{i}}\cdot h_{2\mathrm{i}}+Q_{1\to 2\mathrm{loss}}\mathrm{energy}\mathrm{balance}\mathrm{on}1\to 2$

$h_{2\mathrm{o}}=h_{\mathrm{sol}}\left(T_2,x_{2\mathrm{o}}\right)\mathrm{state}\mathrm{equation}$

3.3.2.1.2 Condenser/Evaporator

The modeling of the condenser is similar to that of the generator. It is added to the previous assumptions that the amount of water vapor desorbed in the generator is completely condensed in the condenser. Conversely, all the water vapor produced in the evaporator is absorbed by the solution in the absorber.

$m_{3\mathrm{i}}=m_{4\mathrm{o}}=v_{4\mathrm{o}}\cdot {\rho }_{\mathrm{wliq}}\left(T_4\right)$

$m_{3\mathrm{i}}+m_{3\mathrm{v}}=m_{3\mathrm{o}}\mathrm{global}\mathrm{mass}\mathrm{balance}$

$m_{3\mathrm{i}}\cdot h_{3\mathrm{i}}+m_{3\mathrm{v}}\cdot h_{3\mathrm{v}}=m_{3\mathrm{o}}\cdot h_{3\mathrm{o}}+Q_{3\mathrm{loss}}+Q_3\mathrm{energy}\mathrm{balance}$

$P_3=P_{\mathrm{w}}\left(T_3\right)$

$T_3=T_{3\mathrm{o}}$

$m_{4\mathrm{o}}\cdot h_{4\mathrm{o}}+w_4=m_{3\mathrm{i}}\cdot h_{3\mathrm{i}}+Q_{4\to 3\mathrm{loss}}\mathrm{energy}\mathrm{balance}\mathrm{on}\mathrm{tube}4\to 3$

$h_{3\mathrm{o}}=h_{\mathrm{w}\mathrm{liq}}\left(T_3\right)\mathrm{state}\mathrm{equation}\left(\mathrm{saturation}\right)$

$h_{3\mathrm{v}}=h_{\mathrm{w}\mathrm{v}}\left(T_2,P_2\right)\mathrm{state}\mathrm{equation}$

3.3.2.1.3 Solution Tank

The tank model is based on global mass and energy balances. The solution tank is then assumed to be well mixed (temperature and concentration), and the mass of solution accumulated in the other components of the process is neglected in comparison to the mass of solution in the storage tank. Crystals are considered to be in equilibrium with the saturated solution when they appear. The following equations apply:

$M_1=M_1^{\prime }+\left(m_{1\mathrm{i}}-m_{1\mathrm{o}}\right)\cdot \mathrm{d}t\mathrm{global}\mathrm{mass}\mathrm{balance}$

$M_1\cdot x_1=M_{1\mathrm{l}\mathrm{i}\mathrm{q}}\cdot x_{1\mathrm{l}\mathrm{i}\mathrm{q}}+M_{\mathrm{c}\mathrm{r}}\cdot k=M_{\mathrm{LiBr}}\mathrm{LiBr}\mathrm{mass}\mathrm{balance}$

$M_{1\mathrm{l}\mathrm{i}\mathrm{q}}\cdot h_{1\mathrm{l}\mathrm{i}\mathrm{q}}+M_{\mathrm{c}\mathrm{r}}\cdot h_{\mathrm{c}\mathrm{r}}=M_{1\mathrm{l}\mathrm{i}\mathrm{q}}^{\prime }\cdot h_{1\mathrm{l}\mathrm{i}\mathrm{q}}^{\prime }+M_{\mathrm{c}\mathrm{r}}^{\prime }\cdot h_{\mathrm{c}\mathrm{r}}^{\prime }+\left(m_{1\mathrm{i}}\cdot h_{1\mathrm{i}}-Q_{1\mathrm{loss}}-m_{1\mathrm{o}}\cdot h_{1\mathrm{o}}\right)\cdot \mathrm{d}t\mathrm{energy}\mathrm{balance}$

$Q_{1\mathrm{loss}}=U{A}_1\cdot \left(T_1,T_{tank}\right)\mathrm{heat}\mathrm{loss}\mathrm{t}\mathrm{o}\mathrm{the}\mathrm{ambient}$

$h_{1\mathrm{o}}=h_{1\mathrm{l}\mathrm{i}\mathrm{q}}=h_{\mathrm{sol}}\left(T_1,x_{1\mathrm{l}\mathrm{i}\mathrm{q}}\right)\mathrm{state}\mathrm{equation}$

$P_1=P_{\mathrm{sol}}\left(T_1,x_{1\mathrm{l}\mathrm{i}\mathrm{q}}\right)\mathrm{state}\mathrm{equation}$

$m_{1\mathrm{i}}\cdot h_{1\mathrm{i}}+Q_{2\to 1\mathrm{loss}}=m_{2\mathrm{o}}\cdot h_{2\mathrm{o}}\mathrm{energy}\mathrm{balance}\mathrm{on}\mathrm{tube}2\to 1$

$h_{\mathrm{c}\mathrm{r}}=h_{1\mathrm{l}\mathrm{i}\mathrm{q}}+\mathrm{\Delta }{h}_{\mathrm{c}\mathrm{r}}\mathrm{\Delta }{h}_{\mathrm{c}\mathrm{r}}\approx 64.5\mathrm{kJ}{\mathrm{kg}}^{-1}\left(\mathrm{Apelblat}\mathrm{and}\mathrm{Tamir},1986\right)$

3.3.2.1.4 Water Tank

Assumptions in the water tank modeling are the same as in the case of the solution tank, except that there is no crystal:

$M_4=M_4^{\prime }+\left(m_{4\mathrm{i}}-m_{4\mathrm{o}}\right)\cdot \mathrm{d}t\mathrm{global}\mathrm{mass}\mathrm{balance}$

$M_4\cdot h_4=M_4^{\prime }\cdot h_4^{\prime }+\left(m_{4\mathrm{i}}\cdot h_{4\mathrm{i}}-Q_{4\mathrm{loss}}-m_{4\mathrm{o}}\cdot h_{4\mathrm{o}}\right)\cdot \mathrm{d}t\mathrm{energy}\mathrm{balance}$

$Q_{4\mathrm{loss}}=U{A}_4\cdot \left(T_4-T_{tank}\right)\mathrm{heat}\mathrm{loss}\mathrm{t}\mathrm{o}\mathrm{the}\mathrm{ambient}$

$h_{4\mathrm{o}}=h_4=h_{\mathrm{w}\mathrm{liq}}\left(T_4\right)\mathrm{state}\mathrm{equation}\left(\mathrm{saturation}\right)$

$P_4=P_{\mathrm{w}}\left(T_4\right)\mathrm{state}\mathrm{equation}$

$m_{4\mathrm{i}}\cdot h_{4\mathrm{i}}+Q_{3\to 4\mathrm{loss}}=m_{3\mathrm{o}}\cdot h_{3\mathrm{o}}\mathrm{energy}\mathrm{balance}\mathrm{on}\mathrm{tube}3\to 4$

3.3.2.1.5 Connection Tubes

The evaluation of the heat losses of tubes that connect the process components is made, granted that the specific heat of the fluid in the tube is constant along the tube. Equations (3.37) and (3.38), for example, give the heat losses to the ambient for the connection tube between the generator 2 and the solution tank 1.

$T_{1\mathrm{i}}=T_{\mathrm{r}\mathrm{e}\mathrm{f}}+\left(T_{2\mathrm{o}}-T_{\mathrm{r}\mathrm{e}\mathrm{f}}\right)\cdot exp\left(\frac{-{\left(UA\right)}_{2\to 1}}{m_{1\mathrm{i}}\cdot C{p}_{\mathrm{sol}}}\right)$

$Q_{2\to 1\mathrm{loss}}=m_{2\mathrm{o}}\cdot \left(h_{2\mathrm{o}}-h_{1\mathrm{i}}\right)$

3.3.2.1.6 Circulating Pumps

The energy transferred to the solution and water by the circulating pumps (W₁ and W₂) is estimated by considering an isentropic efficiency η_is for each pump, and the fact that the density of the liquid is constant between the tank outlet and the heat exchanger inlet. Thus, Equation (3.39) gives the work w₁ provided by circulating pump W₁ to the solution.

$w_1=v_{1\mathrm{o}}\cdot \frac{\left(P_2-P_1\right)}{{\eta }_{\mathrm{is}{W}_1}}$

A value of 0.8, which is relatively low, is used as the isentropic efficiency of the pumps, as its influence is low on the system performances.

3.3.2.1.7 Environment: Heat Sink/Low-Temperature Heat Source

Simplified models for the condenser heat sink (charging period) and the evaporator low-temperature heat source (discharging period) are introduced. The temperature of the cooling fluid at the entrance of the condenser T_ci is set to 3 °C below the outdoor air temperature when the latter is higher than 10 °C; otherwise, T_ci is set to 5 °C. The HTF temperature entering the evaporator is constant and equal to 10 °C.

3.3.2.3.1 Effects of the Heat Exchanger Sizes

The generator and condenser overall heat transfer coefficients UA_g and UA_c respectively were varied from 0.2 to 0.8 kW K^− 1, and results are reported in Figure 3.8. This UA range is chosen based on the power (< 2 kW) necessary to cover the passive house needs. The storage density can be improved by about 60% when increasing the heat exchanger performance within the considered UA range. This is due to a lower minimum concentration of the cycle (points 1 and 2 in Figure 3.6). Indeed, the smaller temperature difference between the heat exchanger sides for high UA values for a given power has two consequences on the cycle. One is that the evaporator temperature increases (point E in Figure 3.6). The other is that the required absorber temperature is lower (points 6-7 in Figure 3.6).

The required solar thermal collector area also decreases when the UA value increases (Figure 3.8) because desorption is more efficient. This is due to a higher generator temperature and lower condenser temperature on average. For very low UA values (for both UA_g = UA_c = 0.2 kW K^− 1 in the present case), the system performance drops sharply.

Further simulations with a solution heat exchanger (SHX) between the solution tank and the generator (Figure 3.9) show that it strongly improves the process thermal efficiency and its storage density. However, this SHX could lead to technical issues (crystal formation and tube clogging), as will be discussed in Section 3.3.3.

3.3.2.3.2 Effects of the Absorption Percentage

The effect of the absorption percentage on the storage density is also studied. The requirements to reach a mean heat supply temperature of 30 °C and a maximum crystallization ratio of 67% are summarized in Table 3.2. The storage density decreases with a low absorption percentage. Indeed, the solution temperature in the absorber is lower than the equilibrium temperature. Thus, a higher minimum concentration of the cycle is needed. Similarly, during desorption, with low absorption percentage, the generator outlet bulk concentration is lower than the interface concentration, so that the actual amount of generated water is lower than in equilibrium conditions. There are then greater sensible heat losses and greater heat needs for desorption, which result in a larger solar collector area.

Special attention should thus be paid to the generator design, because the absorption percentage depends on the exchanger design and the solution flow rate.

3.3.2.3.3 Effects of the Maximum Crystallization Ratio

Figure 3.10 shows the storage density as a function of the maximum crystallization ratio at average heat supply temperatures of 30 °C and 33 °C. Crystallization can increase the storage density more than three times. However, above a maximum crystallization ratio of 70%, savings become less and less significant, while the technical complexity of the process increases. Thus, a compromise has to be made for the choice of the optimal crystallization ratio.

3.3.3.3.1 The Water Desorption Rate in the Desorber

An average value of the water desorption rate is calculated for each test by dividing the total mass of the desorbed water during the test by the test duration (Table 3.4). The mean water desorption rate is 1.3 kg h^− 1. This visibly low rate implies a small concentration change in the desorber (1-2 m%).

The tests suggest that the main variables affecting the water desorption rate are

– The solution flow rate: its increase results in a better heat transfer in the desorber, and thus, a higher water flow release

– The inlet temperature of the HTF in the condenser, which increases the water desorption rate when decreasing

These behaviors can be derived from simple mass and heat transfer analysis and are as foreseen in the process simulation (N'Tsoukpoe et al., 2012).

3.3.3.3.2 Heat Transfer in the Desorber

The observed power is acceptable, according to the process design for a real plant (2-5 kW; Table 3.4).

Average values of two indicators are evaluated and used for the heat transfer analysis: the overall heat transfer coefficient UA and the Reynolds number. For a test, $\overline{UA}$ (Equation (3.42)) is the average value of the calculated UA values at each measurement step during the test:

$Q_2=UA\cdot \left(\frac{T_{\mathrm{g}\mathrm{i}}-T_{\mathrm{go}}}{ln\left(\frac{T_{\mathrm{g}\mathrm{i}}-T_2}{T_{\mathrm{go}}-T_2}\right)}\right)=m_{\mathrm{g}}\cdot C{p}_{\mathrm{g}}\cdot \left(T_{\mathrm{g}\mathrm{i}}-T_{\mathrm{go}}\right)$

$\overline{UA}=\mathrm{average}\left(m_{\mathrm{g}}\cdot C{p}_{\mathrm{g}}\cdot ln\left(\frac{T_{\mathrm{g}\mathrm{i}}-T_2}{T_{\mathrm{go}}-T_2}\right)\right)$

Similarly, the average Reynolds number $\overline{Re}$ is defined as follows (Equation (3.43)):

$\overline{Re}=\mathrm{average}\left(\frac{4{\Gamma }_{2\mathrm{i}}}{\mu }\right)=\mathrm{average}\left(\frac{4m_{2\mathrm{i}}}{\pi \cdot d\cdot n\cdot \mu }\right)$

The solution properties are calculated at the desorber inlet.

The solution flow rate appears to be the variable that mostly affects the heat transfer rate in the explored experimental range (Figure 3.14): $\overline{UA}$ roughly doubles when the solution flow rate doubles. This significant change is not in accordance with the process simulation hypotheses, which assume that the solution side thermal resistance does not change significantly with the solution flow rate (N'Tsoukpoe et al., 2012). Anyway, the solution side remains the heat transfer controlling side.

The plot of $\overline{UA}$ with respect to $\overline{Re}$ allows further analysis: there is a significant change in the trend for $\overline{Re}$ above 30-35 (Figure 3.15). The observed $\overline{Re}$ range is from 10 to 40. According to studies on absorption falling film heat exchangers operating with LiBr aqueous solution, this yields two different flow regimes: the smooth laminar flow and the wavy laminar flow. Indeed, the smooth-wavy transition occurs between Re = 20 and 30 (Morioka and Kiyota, 1991; Kim et al., 1995; Medrano et al., 2002). The significant $\overline{UA}$ increase can then be explained by the change in the flow pattern. The low values observed during tests no. 1 and 2 (Figure 3.15) can be explained by the fact that they are quite in the transition zone.

The occurrence of the wavy laminar regime, which is the most common in absorption falling film heat exchangers (Morioka and Kiyota, 1991) because it promotes the mixing of the film, has enhanced somewhat the heat transfer, but the design overall heat transfer coefficient (UA = 0.4 kW °C^− 1, that is U = 1.2 kW m^− 2 °C^− 1) was not reached. The low heat transfer yields a large temperature difference between the solution and the HTF in the desorber (25-30 °C), when considering the corresponding power range (2-5 kW).

The main reason for this low performance is probably the maldistribution of the solution in the tubes due to the overflow weir distribution at the top of the tubes (see Section 3.3.3.1). A possible lack of verticality of the heat exchanger in the reactor could be another cause of poor distribution.

The maximum amount of heat that is charged during the different tests is 13 kWh. Thermal losses from the reactor are huge, as they can reach 25% of the total heat transferred. A better insulation of the reactor would reduce these losses.

3.3.3.3.3 Equilibrium Factor

The observed equilibrium factor values range from 0.2 to 0.9. This equilibrium factor decreases with the solution flow rate increase (Figure 3.16). The film thickness increase, due to the solution flow rate increase, results in a slower water diffusion within the film to the interface, which is theoretically in equilibrium conditions. The waves induced by the Reynolds number increase have not improved the equilibrium factor.

The observed results are summarized in Table 3.5.

The solution entering the absorber at 10-20 °C leaves it with a temperature of about 30-40 °C. Absorption occurs in the absorber and the produced temperature is sufficient for heating purposes (32-40 °C).

Generally, by disregarding the thermal loss to the ambient and assuming that there is no heat exchange between the solution and the HTF (balance of the overall heat exchange is zero), the absorption power is about 0.5 kW only (calculated with the solution flow temperature increase, that is, sensible heat).

3.3.3.4.2 Use of a Heat and Mass Transfer Enhancement Additive

It is an established fact that adding 2-ethyl-1-hexanol (2EH) in a LiBr aqueous solution improves its absorption heat and mass transfer characteristics (Ziegler and Grossman, 1996). Some tests were carried out after adding 2EH in the solution storage tank (100-200 ppm). The results show a slight improvement in the water absorption rate (≈+ 20%, see in Table 3.5: test no. 11 vs. test no. 23; test no. 12 vs. test no. 24). An increase in the equilibrium factor (Equation (3.9)) from 0.23 (tests without additive) up to 0.85 was also observed. However, no improvement in the overall heat transferred to the HTF was noticed.

3.3.3.4.3 Rise of the Absorber Inlet Solution Temperature

Two tests (no. 22 and no. 27) have been performed in order to know if the increase of the entering solution into the absorber had a major impact on the system performance. The temperature of the water bath around the solution tank was increased to 20 °C in order to feed the absorber with a higher temperature solution (basically, the storage tanks' surrounding temperature was maintained around 10 °C for the basic tests). This would be comparable, for instance, to the use of a SHX, as stated previously (see Figure 3.9), which would recover heat from the absorber outlet solution to increase the temperature of the absorber inlet solution. The corresponding tests have not yielded more satisfactory heat transfer to the HTF (power < 0.1 kW).

3.3.3.4.4 Possible Improvement Paths for the Absorber

Improving the performance of the absorber means improving its heat transfer coefficient.

The poor heat transfer coefficient seems mostly due to the hydraulic problems mentioned in Section 3.3.3.4.1. The size or the number of the orifices should be adjusted.

To address this issue, a SHX can also be used between the absorber and the solution tank for heat recovery (Figure 3.9). In absorption chiller and heat pump processes, this heat recovery unit is generally put between the absorber and the desorber in order to recover heat from the desorber outlet solution and preheat its inlet solution. This increases significantly the process thermal efficiency. The SHX would increase the absorber inlet solution temperature. Simulations (N'Tsoukpoe, 2012) show that the storage density is improved by about 30% when a SHX with an effectiveness ɛ = 0.8 is added to the process. The required solar collector area is also reduced significantly (50%). However, during desorption periods, there is a risk of crystallization in the SHX on the desorber outlet side. Indeed, the solution LiBr mass fraction is high and its temperature decreases in the SHX. To avoid such an eventuality, the SHX could be used only in discharging periods. The effect of this prevention measure on the storage density would be marginal, but the benefit of the required solar collector surface reduction would be lost.

Generally speaking, although the falling film type absorbers are the most commonly encountered absorber type in absorption machines (Kim et al., 1999), they feature several problems: low mass and heat transfer and large volume. An adiabatic absorber appears to be a solution to overcome these points and could be a better solution for this storage process. In an adiabatic absorber, an adiabatic part is introduced prior to the heat transfer part: the mass and heat transfer phenomena are separated (Grossman, 1982). The adiabatic and the heat exchange parts can be designed as two separate chambers in series or as one chamber. A specific constraint is the reversibility of the absorber unit so that it could be used in desorption mode, too.