For designing a compact absorber with membrane contactor at liquid-vapor interface--influence of membrane properties on water vapor transfer.
The absorber is one of the major components in absorption chillers and has a direct effect on the chiller size. Introducing polymeric hydrophobic microporous membranes into the absorber design could provide one of the alternatives for achieving highly compact absorbers. For lithium bromide-water (LiBr-[H.sub.2]O) absorption chillers, the hydrophobic membranes can be used to form confined solution channels. In this case, the water vapor pressure difference across the membrane is the driving force for water vapor transfer (refrigerant). As the absorber is working under vacuum pressure, the membrane pores are filled with water vapor, while the hydrophobic nature of the membrane prevents penetration of the aqueous solution into the pores. Therefore, only water vapor is transported through the membrane into the solution. Consequently, using a narrowly confined solution flow channel formed with membrane sheets will significantly increase the mass transfer area per unit volume. The above technique as well as mass transfer enhanced at liquid/vapor interface by forced convection in the narrow confined flow channels lead to the reduced absorber unit size and weight. Drost et al. (2005) cited that the development of compact absorbers enables the deployment of small heat-actuated absorption heat pumps for distributed space heating and cooling applications, heat-actuated automotive air conditioning, and man-portable cooling devices. The present study is concerned with the factors that affect the water vapor transfer flux when using a membrane contactor at LiBr-[H.sub.2]O solution/water vapor interface in such an absorber design. Therefore, the literature review focuses on studies which utilized membranes in absorption chiller systems. Schaal et al. (2005) experimentally investigated and simulated an absorber with a single micropo-rous hollow fibre membrane in which ammonia/water is used. Chen et al. (2006) performed a simulation study of a proposed hybrid absorber-heat exchanger using microporous hollow fibre membrane modules for the ammonia-water absorption cycle. In their model, they considered the ammonia-water concentration across this microporous membrane as the refrigerant driving force. In contrast, Baker (2004) indicates that in the case of microporous membranes without a static pressure difference across the membrane the vapor partial pressure difference at the membrane sides is the driving force for mass transfer. For LiBr-[H.sub.2]O absorption chillers, Ali and Schwerdt (2008) specified the characteristics of the appropriate membrane for use in this absorber design. They indicated that this membrane should have a high permeability to water vapor and must be hydrophobic to the aqueous solution with a high liquid entry pressure to avoid penetration of the membrane pores. No capillary condensation of water vapor should occur to avoid blocking of the pores. They concluded that for practical use the membrane should have a thin hydro-phobic microporous active layer with a thickness up to 60 [micro]m on a support layer, with a mean pore size around 0.45 [micro]m and porosity of up to 80 %.
Throughout the literature, more research work have been performed on using membranes for vapor desorption inside the desorber/generator of absorption heat pumps considered than the absorber case. Drost et al. (2005) experimentally studied and also simulated the ultra-thin film channel in a LiBr-[H.sub.2]O desorption process using microporous membrane separation. Thorud et al. (2006) experimentally investigated the performance of vapor extraction from an aqueous lithium bromide solution as a function of the film thickness, the pressure difference across the microporous membrane and the inlet concentration to the microchannel. As the desorption process is close to a distillation process, Sudoh et al. (1997) investigated experimentally the permeation flux of water vapor in membrane distillation of an aqueous lithium bromide solution. Riffat et al. (2004) presented and investigated experimentally a novel vapor absorption refrigeration system in which a pervaporation membrane replaces the conventional generator for concentration of the working fluids.
To the authors' knowledge, few investigations are available in literature regarding the use of the membrane contactors in absorption heat pump applications. Despite the important need for compact and low cooling capacity absorption chillers with the potential use of microporous membranes for solution/ vapor contacting purposes in the absorber, there has been relatively little research so far concerning this topic. In addition, there is no literature available on water vapor transfer flux through membrane contactors into lithium bromide-water solution with both the vapor and the solution under equal vacuum static pressure, which is the case in the absorber of LiBr-[H.sub.2]O absorption chillers. However, since the membrane acts as a barrier to the mass transfer process, its properties affect the water vapor mass transfer flux. Therefore, investigations on the water vapor (refrigerant) mass transfer flux into the aqueous solution for commercially available microporous hydrophobic membranes, under realistic operating conditions inside the absorber, need to be performed. The common commercially available hydrophobic microporous membranes in capillary or flat sheet shape are made of polypropylene (PP), polyvinylidenefluoride (PVDF) and polytetrafluoroethylene (PTFE, Teflon).
The objective of designing a compact absorber for absorption chillers is investigated with experimental and analytical studies of hydrophobic microporous membranes. This study focuses on the influence of membrane properties on the water vapor transfer flux into a LiBr-water solution through membrane contactor at the liquid/vapor interface forming a confined narrow channel. In addition, the effect of the flow channel dimensions on the water vapor flux is also studied.
As shown in Figure 1, for the heat and mass transfer process in the absorber cell, a microporous hydrophobic membrane is the contactor between the aqueous lithium bromide-water solution and the water vapor (refrigerant). The refrigerant vapor pressure and the partial pressure of water vapor in the aqueous lithium bromide solution induce a vapor pressure difference across the membrane, which is the driving potential for the water vapor flux into the solution. Thus, the driving potential is based on the LiBr solution concentration, temperature and hydrodynamic conditions and the evaporator pressure (the saturation pressure corresponding to the evaporator temperature). In LiBr-[H.sub.2]O absorber application, due to the hydrophobicity of the membrane, the aqueous solution cannot enter the membrane pores, while at the vapor side, the vapor enters the pore and a liquid-vapor interface is formed at the pore mouths on the solution side. The passed water vapor condenses and dilutes the bulk solution. Due to the water vapor concentration gradient phenomena at the aqueous solution side, the water vapor pressure near the membrane is different from the bulk of the solution. Consequently, there are two resistances to the water vapor and heat fluxes. The first is the membrane resistance and the second is the boundary layer resistances at liquid/vapor interface in the solution side of the membrane. Modelling of the heat and mass transfer in an absorber cell is shown in Figure 1 based on a composite membrane, in which the membrane is constituted by a thin active layer laminated on a hydrophobic porous support material. The pore size of this support is considerably high (>10 ([micro]m). The support layer should not interfere with the mass transport and should only serve to increase the mechanical strength of the membrane. The porosity of the support net and the pore diameter should be as high as possible in order to avoid additional mass transfer resistance, Trifunovic and Tragardh (2005). A support layer at the solution side would be wetted by the aqueous solution. Then the active layer is the only part of the membrane where water transport occurs in the gas phase. In this case, the support resistance must be taken into account. On the other hand, Alves and Coelhoso (2004) show that no resistance exists if the support layer is at the water vapor side.
[FIGURE 1 OMITTED]
The mass transfer model is based on the following assumptions: the support layer resistance to mass transfer is neglected; steady state conditions; one-dimensional mass transfer; absorption occurs instantaneously; adiabatic process, heat losses to/or gain from the surroundings being negligible. Figure 1 illustrates the water vapor pressure and temperature profiles in the case of LiBr-[H.sub.2]O absorber application. The overall mass transfer resistance is expressed as a function of the individual resistances. The water vapor mass flux crossing the membrane is expressed as follows:
J = [k.sub.m]([P.sub.v] - [p.sub.[m,s]]) = [k.sub.m][DELTA]p [kg * [m.sup.-2] * [s.sup.-1]] (1)
where [k.sub.m] is the membrane equivalent mass transfer coefficient, [P.sub.v] and [p.sub.[m,s]] are water vapor (refrigerant) pressure and partial water vapor pressure of the aqueous lithium bromide solution at the membrane pores mouths in Pa, respectively. The value of water vapor partial pressure in the bulk solution, [p.sub.s], is a function of the solution concentration and temperature and is calculated from the correlation of ASHRAE (2005). According to the dusty-gas model for gas transport through porous media reported in Martmez and Rodriguez-Maroto (2007), the vapor transport through the membrane pores takes place via a combined Knudsen and molecular diffusion mechanism and is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the molecular weight of water, R the universal gas constant, [T.sub.m] is the membrane average temperature, [p.sub.air] is the partial pressure of the air entrapped in the pores, P is the total static pressure inside the pores and [D.sub.k] is the Knudsen diffusion coefficient of water vapor depending on the membrane mean pore diameter [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the diffusion coefficient of water in air, [epsilon] is the membrane porosity, [[delta].sub.m] is the membrane thickness and [tau] is the membrane pore tortuosity. The membrane tortuosity (x) reflects the length of the average pore compared to the membrane thickness. Usually pores take a more meandering path through the membrane; simple cylindrical pores at right angles to the membrane surface have a tortuosity of one. The manufacturers do not normally supply its values but it can be evaluated from the membrane porosity, Iversen et al. (1997). For a membrane structure that is more spongy, similar to the interstices between closely packed spheres such as the porous support layer, the tortuosity factor is calculated by [tau] = [(2 - [epsilon]).sup.2]/[epsilon]. For the case of polymer structures of random clusters membranes, however, which is a typical stretched membrane, it is calculated by [tau] = 1/[epsilon]. The value of [D.sub.K] is estimated using the exact solution of the kinetic theory of gases that is presented in Martmez and Rodriguez-Maroto (2006) and is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
For modelling water vapor transfer through membranes in various systems, which are mostly working under atmospheric pressure conditions, except vacuum membrane distillation systems, the term [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in equation (2), expressing the resistance due to air inside the membrane pores, is significant. In contrast, this term is very small in the case of absorption chillers, due to vacuum conditions inside the absorber. Therefore, it is assumed that its effect on the vapor flux is not significant. This assumption is checked in quantitative value by assuming a residual air fraction in the membrane pores with a partial pressure of 10 % of the absorber pressure corresponding to 4 [degrees]C. Then the term [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in Equation 2, is calculated using the equation presented in Martmez and Rodriguez-Maroto (2006). It is found that its ratio to the total value of terms in the brackets is 0.3 %. Therefore, Equation 2 can be rewritten as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
The value of [p.sub.[m,s]] as part of driving potential in the form represented by Equation 1 cannot be easily determined because it requires the knowledge of both temperature and solution composition (water activity) at the membrane solution interface. The interfacial conditions are not always accessible. Therefore, the water vapor transport in the cell referring to the bulk conditions of the liquid and vapor streams is given by:
J = [k.sub.ov]([P.sub.v] - [p.sub.s]) [kg * [m.sup.-2] * [s.sup.-1]] (5)
where [k.sub.ov] is the overall mass transfer coefficient. The overall mass transfer resistance between the bulk water vapor (refrigerant) and bulk aqueous solution can be divided into the following parts. Diffusion of the water vapor through the membrane support net layer, combined sorption and diffusion through the membrane active layer, desorption as vapor phase to the aqueous solution side of the membrane and diffusion through the solution boundary layers to the bulk of the solution. However, as the diffusion of the water vapor through the membrane support layer could be neglected, the overall mass transfer coefficient [k.sub.ov] is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where [k.sub.[int,m,s]] is the mass transfer coefficient between the water vapor and the bulk of the aqueous solution at the vapor/solution interface. In this study, since metal wire mesh was used as spacer the value of [k.sub.[int,m,s]] is calculated from the correlation of Martmez and Rodriguez-Maroto (2006). The value of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in Equation 6 is obtained following the steps outlined below. The mass transfer in the solution boundary layer can be calculated by the formula of Alves and Coelhoso (2007) given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
After replacing the values of the water activity, [a.sub.[m,s]] and [a.sub.s], in Equation 7 by their values that is the ratios between the vapor pressure at such location to the saturated water pressure, [P*.sub.s], corresponding to the location temperature, Equation 7 can be rewritten as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
From Equation 5 the value of the water vapor mass transfer is obtained.
EXPERIMENTAL APPARATUS AND PROCEDURES
The experimental setup shown schematically in Figure 2 is used to carry out measurements on the absorption of water vapor mass flux into aqueous lithium bromide solution through different commercially available hydrophobic micro-spores membranes under vacuum static pressure conditions in a narrow flow channel. The apparatus consists mainly of an absorber membrane cell that is included in the solution flow loop, an evaporator, a vacuum pump, and the appropriate measuring instrumentation. The test cell was designed to create a thin film of the aqueous solution between the hydro-phobic microporous membrane and the back, made of acrylic glass, in which a gasket ring is used to control the channel depth. Water vapor out from the evaporator is fed to the test cell at the other side of the membrane. It passes the membrane and is completely absorbed by the aqueous solution. The test cell has a net contact membrane area to the solution ranging from 41.9 [cm.sup.2] to 50.3 [cm.sup.2] based on the diameter of the gasket ring used to form the channel depth. A wire mesh is inserted in the aqueous solution flow channel in order to provide a uniform solution flow as well as to enhance the mass transfer coefficient between the bulk solution and the solution-vapor interface layer near the membrane. Two different meshes are used, one having a mesh size of 0.5 mm and a total thickness of 0.7 mm, the second having a mesh size of 2 mm and a thickness of 4 mm, respectively. Thus, the corresponding solution flow channel depths were 0.7 mm and 4 mm, respectively. Three commercially available hydrophobic membranes with various mean pore diameters and thicknesses were tested in the cell; the membranes properties are presented in Table 1. The membrane is in direct contact with both the aqueous solution and the water vapor from the other side. The water vapor chamber has the same membrane area but with a depth of 5 mm. A gear pump is used to circulate the solution from a reservoir through the test cell. Flow-controlling valves were used to adjust the solution flow rate, which is measured by a turbine meter with measuring range from 0-14 1/h and accuracy of 1%. The solution flow loop and test cell were constructed to operate over a wide range of operating conditions. The evaporator was kept in a temperature-controlled water bath in order to keep the evaporation conditions constant. Before the experiments, the evaporator is free from the water. The average value of the water vapor flux is estimated from the time required for absorption of a vaporized mass of water filled in the evaporator at the beginning of each experiment through the membrane. The amount of water was weighted by digital scale with accuracy of 0.1 g and the time was recorded by digital stopwatch with accuracy of 0.01 s. An additional heat exchanger was used to control the aqueous solution temperature. All temperatures were measured at the locations as shown in Figure 2, by using type K thermocouples with a diameter of 1.5 mm. Pressure transducers with a measuring range from 0.0 to 0.4 bar absolute were used for pressure measurements. The electrical conductivity of the aqueous lithium bromide solution was measured by standard conductivity cell sensor with a measuring range of (0-500) x 10-3 (Siemens) S/cm and accuracy of 1 [micro]S/cm. The electrical conductivity of the aqueous solution is converted into weight ratio of the LiBr aqueous solution from the calibration correlation of the conductivity cell sensor. The error in weight % of LiBr (X) values with this correlation as well as in this study is within 0.3%. A data acquisition system was used for recording all measured signals. Before carrying out the experimental runs, flow visualization tests inside the cell were performed. To check the effects of size and orientation of the wire mesh on uniformity of the solution flow under the membrane, coloured ink was injected into the flow. Snapshots of the flow distribution under the membrane for the two cases of the mesh being parallel and diagonal to the flow, with angles of 0 and 45[degrees] respectively, are shown in Figure 3. It is clear from the pictures that the case of mesh wires diagonal 45[degrees] to the flow direction provides a better flow distribution under the membrane. Through the data reduction of the experimental measurements, the uncertainties were determined based on the measuring devices uncertainties reported by the manufactures and the deviations of the variables recorded by using the formula for computing overall errors of Doeblin (1990). The minimum and the maximum uncertainties are estimated in measured water vapor mass flux ranging between 6.8 % and 13.5 %, respectively.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
Table 1. Main Structural Properties of the Membranes Made from PTFE as Given by Manufacture and/or Measured in Literatures Properties Sartorius AG Millipore FGLP Pall TF200 Type 118 Dp, [mu]m 0.45 0.22 0.2 [[delta].sub.m][mu]m 65-100/ 80 Hong 175 (include 139 (include et al. (2003) PE-support) PP-support) [epsilon], % --/ 64 Hong et 70 75 al. (2003)
RESULTS AND DISCUSSION
In the experimental part of this study, the test cell was used to determine the permeability of water vapor transfer into the aqueous solution at various flow rates for three commercially available hydrophobic membranes with various pore diameters and thicknesses. Throughout all experimental results presented, due to the limitation of the experimental setup, the mass ratio of circulating solution to water vapor varied from 2.6 to 13.6 and the aqueous solution mass flow rate ranged from 2.8 to 19.4 kg/(h [m.sup.2]). The concentration of the inlet aqueous solution varied from 52 to 54 wt% LiBr, while its temperature varied between 22.4 and 25.1 [degrees]C. The evaporator temperature varied between 8.7 and 10 [degrees]C corresponding driving pressure differences across the membrane ranged from 0.56 to 0.78 kPa.
The time average values of the measured water vapor flux transferred into the LiBr solution through three different membranes, at various solution flow rates and two solution flow channel heights are presented in Figure 4. As shown in the figure, the general trend for the presented conditions, the water vapor flux increases with the increase of the aqueous solution mass flow rate. This is due to the fact that, the membrane mass transfer resistance is higher and rather constant. Therefore, for the case of low solution flow rate, the membrane mass transfer resistance dominates the overall mass transfer resistance. While, as the solution flow rate increases, the mass transfer coefficient between the interface boundary layer and the bulk of the solution increased as a result of reduced hydrodynamic boundary layer resistance. The determined flow Reynolds number (without considering the wire mesh in the channel) for the case of a solution channel height [[delta].sub.s]=4 mm is ranging from 28 to 225, while the range for a solution channel height [[delta].sub.s] = 0.7 mm Reynolds number (without considering the wire mesh in the channel) is from 160 to 1280, respectively. In the present experiments, two of the membranes used have an active layer on a support layer, while the one with [d.sub.p] = 45 [micro]m is without support layer. Thus, it can be seen from Figure 4 at [[delta].sub.s] = 4 mm that the later membrane does not have the maximum water vapor flux while it has the larger mean pore diameter. For the case of [[delta].sub.s] = 0.7 mm, this membrane shows the higher water vapor transfer flux. This result can be attributed to a higher flow Reynolds number followed by higher mass transfer coefficient at the aqueous solution/vapor interface layer that has a more dominant effect on the water vapor transfer flux than the thin membrane effective layer thickness. Thus, it is evident from Figure 4 that under higher flow Reynolds numbers, the water vapor flux increases with the increase of the mean membrane pore diameter. Details clarifying these effects on the water vapor flux in quantitative values will be discussed in the analytical results. Detailed effects of the operating parameters on the water vapor transfer flux for the cases of the membrane with mean pore diameter of 45 [micro]m at [[delta].sub.s] = 4 mm and 0.7 mm are presented in Figure 5. As seen in the figure, despite precautions taken during the experimental runs to control the operating temperatures of the aqueous solution and the water vapor as well as the aqueous solution concentration, slight differences in their values are noticed as shown in Figure 5a. The corresponding driving vapor pressure difference across the membrane and the water vapor mass flux at this operating condition is shown in Figure 5b. The higher value of the water vapor flux for the case of [[delta].sub.s] = 0.7 mm is due to both the effect of the higher flow Reynolds number plus the slightly higher driving potential of the partial vapor pressure difference across the membrane. Thus, any increase in solution flow rate would have a significant effect on the increase of the water vapor flux. Therefore, improvement in the water vapor flux is evident at higher flow Reynolds numbers for higher membrane pore diameters.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
The results of membrane properties influencing the water vapor flux into the aqueous solution will be presented after validation of the model results with experimental results obtained in this study. In this section, the calculated water vapor flux passing the membrane into the LiBr solution are carried out at the operating conditions [X.sub.s] = 57.7%, [T.sub.s] = 36.6 [degrees]C, evaporator temperature 4 [degrees]C, being close to real working conditions in the absorber of an absorption chiller driven by hot water at 85 [degrees]C and cooled by water at 27 [degrees]C. Throughout the analytical results, the flow channels heights were kept constant for [[delta].sub.s] = 1.0 mm and [[delta].sub.v] = 2.0 mm, respectively.
Validity of the model results
Experimental results for water vapor transfer flux through the microporous hydrophobic membrane contactor at the aqueous solution-water vapor interface are used to compare and validate the model. For validation stage of the model, the operating conditions and the used membrane dimensions and properties are the inputs to the model. The membrane properties are net area of 46.57c[m.sup.2], 0.45 [micro]m mean pore diameter, active microporous layer thickness of 65 [micro]m and porosity of 75%. The calculated results of the water vapor mass transfer flux from the model as a function of the mass transfer driving potential are compared with the experimental results as shown in Figure 6. During experiments, the mass transfer driving potential varies with time as the solution concentration, temperature and evaporator pressure are slightly varying with time. It is clear from the figure that both calculated and measured values are in total agreement. In addition, the model results are comparable to experimental data of Albrecht (2005) for absorption of water vapor into aqueous Lithium Chloride solution. The properties of the lithium chloride solution presented in Conde (2004) and the unit parameters of Albrecht et al. (2005) are input to the model. The obtained results are shown in Figure 7. It is clear from Figure 7 that, both the predicted and the measured water vapor mass flux values are quite congruent. Therefore, it can be stated that the absorber model is capable of describing the mass transfer processes in the absorber membrane cell within the level of accuracy of the measurement method. Consequently, the proposed model can be quite confidently used for investigating the effect of membrane properties on the water vapor mass flux when utilizing membrane contactors at aqueous solution/water vapor interface in the absorber of absorption chillers.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
Influence of the Mean Membrane Pore Diameter on the Water Vapor Flux
The effect of the mean membrane pore diameter ranged from 0.2 [micro]m to 1.0 [micro]m on water vapor transfer through the membrane, is shown in Figure 8 for an active membrane layer thickness of 60 [micro]m and different values of the membrane porosity. The value of the membrane active layer thickness is chosen based on the results that reported by Khayet et al. (2006). For PTFE membranes the measured thickness of the active layers responsible for vapor transport was found to have similar sizes (54.8 [+ or -] 6.2 [micro]m for [d.sub.pm] = 0.2 [micro]m and 60.0 [+ or -] 6.7 [micro]m for [d.sub.pm] = 0.54 [micro]m). As seen from the figure a general trend observed is that the water vapor flux at different membrane porosities has a linear relationship with membrane pore diameter. As the membrane porosity varied from 0.5 to 0.8, it can be seen from Figure 8 that a large pore diameter combined with a higher porosity value of 0.8 leads to an almost doubled water vapor flux through the membrane compared to 0.5 porosity value. To avoid the penetration of membrane pores by the liquid phase the membrane pores should be limited to a certain size around 0.45 as reported by Ali and Schwerdt (2008).
[FIGURE 8 OMITTED]
Influence of the Membrane Porosity on the Water Vapor Flux
The membrane porosity, also referred to as void volume, is an important parameter affecting water vapor flux into the solution. Membranes with higher porosity exhibit more surface area for water vapor transfer. The calculated water vapor flux passing the membrane into the LiBr solution as a function of membrane porosity ranging from 0.5 to 0.85 is shown in Figure 9 for different mean membrane pore diameters. The figure shows that membrane porosity greater than 0.7 results in higher water fluxes regardless of the membrane pore diameters. It must be pointed out that, in practice, the membrane must be able to withstand all the operating conditions such as mechanical stress, pressure, temperature and a highly aggressive working fluid. However, the desired membrane to be used in the absorber of an absorption chiller should have porosity ranged 0.7 to 0.8 in order to have the sufficient strength needed by a secure fixation inside the absorber. In the case of porosity higher than 0.8, it is expected that the membrane strength would be decreased significantly.
[FIGURE 9 OMITTED]
Influence of the Membrane Active Layer Thickness on the Water Vapor Flux
As shown in Equation 4 for the membrane resistance to mass transfer, the water vapor flux is inversely proportional to the membrane active layer thickness. The effect of the membrane thickness on the water vapor flux crossing the membrane ranged from 10 [micro]m to 200 [micro]m at membrane porosity value of 0.75 is shown in Figure 10 for different mean membrane pore diameters. As shown in the figure, for the case of membrane pore diameter of 0.45 [micro]m, the water vapor flux values at membrane thicknesses of 10, 60,100 and 200 [micro]m are 9.14, 1.87, 1.14 and 0.58 kg/(h.[m.sup.2]), respectively.
[FIGURE 10 OMITTED]
For example, increasing the membrane thickness from 60 [micro]m to 100 [micro]m results in a decrease in the vapor flux by about 39%. Therefore, it is clearly shown in the figure that the membrane thickness plays a significant role in dictating the resistance to the membrane mass transfer. Some commercially available membranes with thickness of up to 200 [micro]m have no additional support. However, if membranes are used as a contactor at aqueous solution/water vapor interface in the absorber of absorption chillers to take advantage of a high specific area per unit volume, the active layer should be as thin as possible to keep the additional resistance to mass transfer as low as possible. An active layer thickness around 60 [micro]m is recommended as a compromise between mechanical stability and resistance to mass transfer. Additionally, the membrane should have the active layer laminated on a support structure.
For designing a compact absorber for lithium bromide-water absorption chillers, this study aims at investigating experimentally and analytically, at various operating parameters, the influence of commercially available microporous hydrophobic membrane properties as well as the flow channel dimensions on the water vapor transfer flux through a hydrophobic microporous membrane contactor at liquid-vapor interface into the aqueous solution under vacuum pressure conditions. The following can be concluded:
* The experimental results show that improvement in the transferred water vapor flux is evident at higher aqueous lithium bromide solution flow Reynolds numbers for larger pore diameters. The effect of the flow Reynolds number has a more dominant effect on the water vapor transfer flux than the membrane effective layer thickness.
* The predicted and the measured water vapor mass flux values are quite congruent
* The analytical results show that:
1. A large pore diameter combined with a higher porosity value of 0.8 leads to an almost doubled water vapor flux through the membrane compared to 0.5 porosity value.
2. Membrane porosity greater than 0.7 results in higher water vapor fluxes regardless of the membrane pore diameters. However, in order to achieve higher water vapor fluxes and considering a sufficient strength needed to secure fixation of the membrane inside the absorber, the appropriate membrane should have a porosity ranging from 0.7 to 0.8.
3. The membrane active layer thickness plays a significant role in dictating the resistance to the membrane mass transfer. Therefore, the membrane active layer thickness should be up to 60 [micro]m as a compromise between required mechanical stability and low resistance to water vapor transfer. An additional highly porous support layer on the vapor side of the membrane would significantly increase the mechanical stability without degrading the vapor flux.
The author Ahmed Hamza H. Ali would like to acknowledge the Alexander von Humboldt Foundation, Germany for the fellowship grant during this work at the Fraunhofer Institute for Environmental, Safety, and Energy Technology, UMSICHT, Oberhausen, Germany.
m = mass flow rate, kg [s.sup.-1]
A = surface area, [m.sup.2]
d = diameter, m
D = mass diffusivity, [m.sup.2] [s.sup.-1]
[D.sub.k] = Knudsen mass diffusivity, [m.sup.2] [s.sup.-1]
J = water vapor mass flux, kg [m.sup.-2] [s.sup.-1]
k = mass transfer coefficient, m [s.sup.-1]
M = molecular weight of water, kg * [mol*.sup.1]
P = total pressure, Pa
p= partial or vapor pressure, Pa
PE = Polyethylene
PP = Polypropylene
PTFE = polytetrafluoroethylene, --
R = the universal gas constant, 8314 J [kg*.sup.1] [mol*.sup.1] [K*.sup.1]
T = temperature, [degrees]C or K
X = LiBr mass fraction, %
[delta] = thickness, m
[epsilon] = membrane porosity, --
[rho] = density (kg [m.sup.-3])
[tau] = membrane pore tortuosity
air = air
[H.sub.2]O = water
in = inlet
int = aqueous solution-vapor interface
m = membrane
out = outlet
ov = overall
p = pore
s = aqueous lithium bromide solution
v = water vapor
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Ahmed Hamza H. Ali is a professor in the Department of Mechanical Engineering at Assiut University, Assiut, Egypt. Peter Schwerdt is a researcher with the Fraunhofer Institute for Environmental, Safety, and Energy Technology, UMSICHT, Oberhausen, Germany.
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|Author:||Ali, Ahmed Hamza H.; Schwerdt, Peter|
|Date:||Jan 1, 2010|
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