Analysis of adiabatic heat and mass transfer of microporous hydrophobic hollow fiber membrane-based generator in vapor absorption refrigeration system

Journal of Membrane Science 564 (2018) 415–427

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Analysis of adiabatic heat and mass transfer of microporous hydrophobic hollow fiber membrane-based generator in vapor absorption refrigeration system Sung Joo Hong, Eiji Hihara, Chaobin Dang

T

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Department of Human and Engineered Environmental Studies, Graduate School of Frontier Science, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 2778563, Japan

A R T I C LE I N FO

A B S T R A C T

Keywords: Absorption refrigeration system Car air conditioner Desorber Generator Hollow fiber membrane Vacuum membrane distillation

A microporous hydrophobic hollow fiber membrane-based generator (HFM-G) is expected to be an alternative type of generator in vapor absorption refrigeration system, which can be compact and lightweight with the enhanced heat and mass transfer. This paper pursues a comprehensive understanding of a detailed desorption mechanism of the proposed HFM-G, and suggests the feasible configuration for the practical use. A theoretical HFM-G mechanism is first introduced to gain an understanding of the adiabatic heat and mass transfer. A gas permeation test determines the nominal pore size of the membrane, which characterizes the mass transfer across the membrane. Transient experiments demonstrate the characteristics of the adiabatic desorption process on the HFM-G for wide range of feed solution concentrations under various practical operating conditions. A comparison shows that the experimental heat and mass transfer results are consistent with the theoretical values of adiabatic desorption heat and mass transfer on the HFM-G.

1. Introduction Vapor absorption refrigeration systems (VARs) are capable of utilizing low-grade thermal energy directly for the purpose of air conditioning. This heat-actuated absorption system is able to run without additional energy consumption by using waste heat obtained from the exhaust gas of an internal combustion engine. The absorbent and refrigerant in VARs, a lithium bromide (LiBr) and water pair, are ecofriendly, and therefore, VARs do not contribute to environmental problems, such as the greenhouse effect or ozone depletion. Certain challenges, however, must be overcome so that VARs can become more attractive for portable applications. VARs have a much more complex thermodynamic cycle compared to conventional automotive compression refrigeration systems, which allows them to achieve a high theoretical system performance. However, this higher performance demands a number of heat and mass exchangers and complex control systems. VARs are too heavy to be used in vehicle applications, as the major heat and mass exchangers are stainless steel-based structures due to the high corrosiveness of the LiBr solution [24]. The system's large heat and mass exchangers are responsible for the high cost and volume required to attain the required cooling capacity. A LiBr-water absorption system runs at a static vacuum pressure associated with the large

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specific volume of water vapor, causing the large bulk and weight of the system. The generator and absorber are both major components that determine the system performance. The heat and mass transfer to volume ratio in a conventional generator is quite poor. In general, a heating tube bundle is installed in a conventional generator and is immersed in the LiBr solution, where the heat transfer occurs by boiling the solution. The inefficient use of space against the heat transfer surface leads to the inefficient desorption of water vapor. Desorption takes place only at the liquid-vapor interface, which also impedes mass transfer. Additionally, the liquid phase of the LiBr solution has a considerably large mass resistance. The absorption of water vapor takes place in a conventional falling film absorber, but the gravity-driven hydrodynamic formation of the LiBr falling film resists the water vapor absorption through the formation of a thick falling film produced over the cooling tube [7]. Mal-distribution of the sprayed LiBr solution also leads to a low heat and mass transfer to volume ratio [19]. VARs have not been an attractive alternative for portable air conditioning systems as the unconstrained LiBr solution (i.e. liquid-vapor interface) exists in both the absorber and generator. For example, the LiBr solution is likely to overflow into the condenser when the vehicle drives on hills and is then intermixed with the liquid refrigerant, causing the system to malfunction. While the vehicle is in motion, the slope and vibration also

Corresponding author at: E-mail address: [email protected] (C. Dang).

https://doi.org/10.1016/j.memsci.2018.07.048 Received 17 January 2018; Received in revised form 18 July 2018; Accepted 19 July 2018 Available online 20 July 2018 0376-7388/ © 2018 Elsevier B.V. All rights reserved.

Journal of Membrane Science 564 (2018) 415–427

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Nomenclature Amem Bm Cm D Dh Dk Dk-v Dv d dp dp dwv dx ΔHv Δpbt fD G h hf HFM Jv kB k Kn l M ṁ n Nu p Pr pv Q̇ b R Re rp Sc

Sh T u x

contact area of hollow fiber membranes [m2] membrane distillation coefficient [kg m−2 s−1 Pa−1] permeability coefficient of membrane [kg m−1 s−1 Pa−1] mass diffusivity [m2 s−1] hydraulic diameter [m] Knudsen diffusion coefficient [m2 s−1] Knudsen-Viscous diffusion coefficient [m2 s−1] Viscous diffusion coefficient [m2 s−1] diameter of hollow fiber membrane [m] pressure drop [Pa] membrane pore size [m] molecular size of water vapor single element of HFM latent heat of vaporization [J kg−1] breakthrough pressure [Pa] Darcy friction factor mass flux [kg m−2 s−1] specific enthalpy [J kg−1] convective heat transfer coefficient [W m−2] hollow fiber membrane mass flux across the membrane [kg m−2 s−1] Boltzmann constant [J K−1] thermal conductivity [W m−1] Knudsen number length of hollow fiber membrane [m] molecular weight [kg mol−1] mass flow rate [kg s−1] number of hollow fiber membranes Nusselt number pressure [Pa] Prandtl number vapor pressure at membrane surface [Pa] heat flux [W m−2] gas constant [m3 Pa K−1 mol−1] Reynolds number radius of membrane pore [m] Schmidt number

Sherwood number Temperature [°C] velocity [m/s] concentration of LiBr solution [%]

Greek symbols α τ δ ρ ε μ σ θ λ

convective mass transfer coefficient [m s−1] membrane tortuosity membrane thickness [m] Density [kg m−3] membrane porosity dynamic viscosity [kg m−1 s−1] surface tension [N m−1] contact angle [°] mean free path

Subscript ass b cal cond feed flux LiBr i in m mem ms mt N2 o out p sol v wv

assumed bulk calculated condenser feed flux lithium bromide solution inner inlet mean membrane membrane surface material nitrogen gas outer outlet pore solution vapor water vapor

2. Application

hinder the uniform distribution of the sprayed solution over the cooling tube in the absorber, leading to unstable system performance. Thus, VARs promise a bright future for vehicle air conditioning system due to the use of waste heat and an eco-friendly refrigerant; however, low heat and mass transfer has prohibited VARs from compact and lightweight scaled system applications, and the existence of the free surface of the working fluids remains as another challenge before portable applications can be attained.

2.1. Hydrophobic membrane Hydrophobic membranes have been widely used in the separation of water from an aqueous solution, which can be driven by low-grade waste heat or solar energy. Khayet [18]. A microporous membrane is a thin film made of polymers having sub-microscale interconnected pores that characterize the mass transfer. A microporous hydrophobic

Table 1 Summary of hydrophobic membrane-based heat and mass exchangers in LiBr-water VARs. Reference

Membrane

Configuration

Membrane material

Pore size [µm]

Porosity [%]

Thickness [µm]

Dimensiona [µm]

Study

Thorud et al. [30] Kim et al. [20] Isfahani et al. [16] Ali et al. [1] Yu et al. [35] Isfahani et al. [15,17] Asfand et al. [5] Venegas et al. [36] Wang et al. [32] Hong et al. [14]

Flat sheet Flat sheet Flat sheet Flat sheet Flat sheet Flat sheet Flat sheet Flat sheet Hollow fiber Hollow fiber

Generator Generator Generator Absorber Absorber Absorber Absorber Absorber Generator Generator

PTFE N/A PTFE PTFE N/A PTFE N/A N/A PVDF N/A

N/A N/A 0.45 0.2–0.45 6.0 1.0 1.0 1.0 0.16 0.16

N/A N/A N/A N/A 60 80 75 80 85 85

N/A N/A 50 60–175 20 N/A 40 60 150 150

170 × 745 300 N/A 4000 × N/A 50 × N/A 100, 160 N/A 150 × 1500 800 800

Experimental Numerical Experimental Experimental Numerical Experimental Numerical Numerical Experimental Numerical

a

Dimension: inner diameter for the HFM and height × width of a micro-channel for the flat sheet membrane. 416

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each 170 and 745 µm in height. They reported the desorption rate in terms of the microchannel height, solution inlet concentration, and the pressure difference across the membrane. It was observed that the heat transfer resistance was reduced with thinner microchannels, and consequently, the desorption rate of the water vapor increased. Note that internal channel boiling does not impede the desorption rate as long as the solution does not reach critical heat flux. The maximum heat flux attained was 12.7 kW/m2, which was higher than the values achieved by the conventional falling film generator. Isfahani et al. [15,17] built a flat sheet membrane-based VARs and examined both the desorption and absorption characteristics in terms of the height of the microchannel. They found that thinner microchannels enhanced the heat transfer in the solution thermal boundary layer, causing an increase in absorption across the membrane. They also noted two modes of desorption: a direct diffusion mode where desorption occurs from the single phase of the LiBr solution and a boiling diffusion mode where the vapor phase exists in the LiBr solution. The boiling diffusion mode significantly intensified the desorption rate compared to the direct diffusion mode, and the increase in the velocity of the solution also improved the desorption rate. Compared to the conventional components in VARs, they asserted that the proposed flat sheet membrane-based heat and mass exchangers have several strong points, such as the ease of adjusting and optimizing the solution film thickness, solution flow rate, and heating area.

membrane is promising, particularly when introduced for portable applications, due to its reliability, compactness, light weight, low energy cost, high separation performance, large interfacial area to volume ratio, and fewer mechanical part demand [26]. The membrane surface properties determine the wettability when a liquid comes in direct contact. Due to an imbalance in the molecular forces, the hydrophobic membrane repels liquid and, thus, has the tendency to prohibit the liquid phase of the LiBr solution from seeping into the membrane pores. The separation process of the hydrophobic membrane is in general thermally driven, in which the water is evaporated and passes through the membrane pores. Only a low-grade energy source is necessary for the distillation of water. This process has high distillation efficiency due to the principle of liquid-vapor equilibrium at the vacuum condition. 2.2. Hydrophobic membrane-based absorber and generator in VARs In recent years, microporous hydrophobic membranes, including both hollow fiber and flat sheet membranes, have been applied to compact and lightweight heat and mass exchangers in VARs (Table 1). The hydrophobicity of the membrane prevents the passage of the liquid LiBr solution across the membrane layer by a large capillary action, while water vapor is allowed to pass through the membrane pores. The hollow fiber membranes (HFMs), which have submillimeter scale diameters, or flat sheet membranes with an array of microchannels considerably reduce the film thickness of a given stream of the LiBr solution, and thus, the heat and mass transfer is highly enhanced by the enlarged liquid-vapor mass transfer interfacial area. As listed in Table 1, both the HFM and flat sheet membrane are deliberated as either the generator or absorber; all of the related studies have asserted that the hydrophobic membrane-based heat and mass exchangers achieve a highly enhanced heat and mass transfer per volume ratio, leading an overall reduction in size [4]. In addition, the flow of the LiBr solution is confined, and therefore, it is expected that the system will have no deleterious effects from the slope or unexpected vibration while driving. The demand of fewer mechanical parts by introducing a nonmetallic hydrophobic membrane and plastic housing also gives rise to a notable reduction in the weight of VARs. Chen et al. [10] proposed an HFM-based absorber designed for the ammonia-water pair. They designed a non-adiabatic HFM-based absorber, which is composed of both microporous and non-porous HFMs for the flow of water vapor and cooling fluid, respectively. The proposed HFM-based absorber had a liquid-vapor mass transfer interfacial area that was 4.3 times larger than the traditional falling film-type absorber. They noted that a coefficient of performance (COP) of VARs combined with the proposed absorber increased by 14.8%, and the overall system exergy loss was reduced by 26.7%. Schaal et al. [27] also conducted an experimental study on an HFM-based absorber for the ammonia-water pair. They found a linear relationship between an increase in the absorption and an increase in the change of the ammonia mole fraction. From their observation, the size of the HFM-based absorber became 10 times smaller than that of the conventional plate absorber. Riffat et al. [25] investigated a prototype VARs in which a pervaporation membrane replaced the conventional generator. They successfully completed the absorption cycle with an evaporation temperature of 10 °C, generating temperature of 80 °C, and condensation temperature of 30 °C. However, the COP of the proposed cycle was lower than the conventional VARs and was further reduced as the circulation ratio increased (i.e. the ratio of the amount of desorbed water vapor to the feed flow rate of the solution increased). They used two types of membranes, a porous silicon membrane and a non-porous dense membrane. The distillation performance of the silicon membrane was much higher, approximately four to six times that of the dense membrane. However, the permeation rate of the silicon membrane decreased with running time due to the blockage of pores. Thorud et al. [30] reported the experimental results of the water vapor desorption rate from the LiBr solution flowing through two kinds of microchannels,

2.3. Hollow fiber membrane-based generator (HFM-G) The microporous hydrophobic HFM module is shaped like a shell and tube heat exchanger and is primarily composed of a bundle of HFMs, two bonded sections for fixing the ends of the HFM bundle, and a housing to enclose and support the HFM bundle (Fig. 1). The lumen and shell side of the HFM module are ideally separated by placing the bonded sections together with the ends of housing. In the HFM-G, the feed LiBr solution enters the HFM capillaries, the number of which ranges in the several hundreds or thousands. The streams of the aqueous LiBr solution are in direct contact with the inner surface of the HFM and are mechanically constrained by the hydrophobic surface. The shell side is filled with water vapor at saturation conditions (i.e. connected with a condenser). The desorption of water vapor takes place across the HFMs when the hot LiBr solution enters the HFMs, where the vapor pressure of the solution is higher than the static equilibrium pressure at the shell side. Wang et al. [32] tested a polyvinylidene fluoride (PVDF) HFM module to investigate the desorption characteristics under several operating conditions, including feed solution temperature, feed solution flow rate, and pressure at the shell side. They found that the feed

Fig. 1. Schematic of the hydrophobic HFM-based generator. 417

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solution temperature was a major requirement to exponentially enhance the desorption rate; a higher feed solution flux and lower pressure at the shell side also brought about higher desorption mass flux performance. In our preliminary study, we presented a detailed theoretical heat and mass transfer mechanism on the HFM-G and also analyzed the HFM-G-based single-effect VARs to characterize the system performance under practical operating conditions [14]. It was concluded that the exhaust gas contained the available heat required to increase the generating temperature, and it effectively reduced the circulation ratio, which is responsible for the size and weight of the system. An increase in the number of HFMs per unit volume increases the system performance by extracting larger amounts of water vapor and also decreases the circulation ratio and pressure drop of the solution. Further, the HFM-G-based VARs theoretically has a lower COP than the conventional system due to the lower heat recovery performance associated with the temperature drop via the adiabatic desorption process. However, it was noteworthy that a recirculation process of the solution on the HFM-G gave rise to both a reduction in the temperature drop and an increase in the desorption mass transfer, resulting in a similar COP to that of a conventional system. In this paper, we firstly address the theoretical heat and mass transfer mechanism of the adiabatic desorption process via the HFM-G. The nominal membrane pore size is evaluated by a nitrogen gas permeable test to characterize the mass transfer characteristics. The transient experimental procedure for the evaluation of heat and mass transfer of the HFM-G is then proposed; experimental heat and mass transfer results are analyzed under various expected operation conditions. The theoretical simulation model of the desorption heat and mass transfer of the HFM-G is compared and verified with the experimental data. The effects of simultaneous variations in the feed temperature and solution flow rate or in dimensions of the HFM-G on the characteristics of the desorption mass transfer are theoretically evaluated. This paper aims to provide a comprehensive understanding of the detailed heat and mass transfer mechanism and aims to suggest a feasible application for the practical use of the proposed HFM-G.

Fig. 2. Simplified schematic depicting the principle of heat and mass transfer across the solution boundary layer in a micro-porous hydrophobic HFM-G.

adhesion to the solid surface and the cohesive surface tension of the liquid that functions to diminish the liquid-vapor interface. When the LiBr solution flows in direct contact with the hydrophobic membrane surface, a curvature of the liquid-vapor interface is formed at the entrance of the pores due to the large capillary actions (Fig. 2). The liquid phase of the LiBr solution, therefore, cannot seep into the pores as long as the pressure difference across the membrane is kept lower than the breakthrough pressure, which is expressed by the Laplace equation shown in Eq. (2) [21]:

Δpbt =

3.1. Characterization of the hydrophobic HFM

3.2. Mass transfer

A hydrophobic HFM has pores across the membrane layers through which the vapor phase of a substance is transported. Pore size is an important factor to approximate the mass flux across the membrane layers. The nominal pore size is typically evaluated by several techniques: visual examination using scanning electron microscopy (SEM) [9], gas permeation testing [34], or bubble-point testing [13]. Porosity is the ratio of the volume of pores to the total volume of the HFM. A higher porosity leads to less mass transfer resistance, but the mechanical strength of membrane becomes weaker with this increase in porosity [28]. Tortuosity is defined as the ratio of the shortest pathway of the transport medium through the pores to the membrane thickness (i.e., the deviation of the pore structure from the cylindrical formation) [6]. This factor describes the mass transfer resistance across the membrane by estimating the travel length across the pores for the transport medium, and thus, a larger value of tortuosity has a lower mass transport performance. Several empirical and analytical works proposed the tortuosity evaluation as inversely proportional to the membrane porosity, as shown in Eq. (1) [12,2]:

1 ε

(2)

where Δpbt is the breakthrough pressure; σ is the surface tension of liquid phase of substance; θ the contact angle between the hydrophobic membrane surface and the liquid; dp,max is the maximum pore size.

3. Theory

τ=

4 σ cos θ dp, max

The volatile component, i.e., water, evaporates at the liquid-vapor interface and permeates through the pores as long as the pressure at the shell side that is occupied with water vapor is maintained below the equilibrium vapor pressure at the membrane surface (i.e., liquid-vapor interface at the entrance in pores), as shown in Fig. 2. Thus, the driving force of the water vapor mass flux across the HFMs is the vapor pressure difference between the membrane surface and the shell side. Fig. 2 also illustrates the profiles of temperature, concentration, and vapor pressure in the normal direction of the thermal boundary layer when the hot LiBr solution enters a given HFM capillary. Temperature and concentration polarizations between the bulk phase and the membrane surface occur due to simultaneous heat and mass transfer. The hydraulic characteristics in the boundary layer determine the temperature and concentration profiles. The non-volatile component, LiBr salt, is accumulated near the entrance of pores, which obstructs the movement of the volatile component to the liquid-vapor interface [3]. The mass flux of the water vapor across the HFM is evaluated according to Darcy's law as:

Jv = Bm (pv, ms − pwv, p )

(1)

where τ is the tortuosity of membrane; ε is the porosity of membrane. A critical requirement of the membrane is to confine and control the flow of the LiBr solution. A hydrophobic membrane has a repulsive response to the LiBr solution, which has a large surface tension. The capillary action in the pores depends on two contrary forces: the liquid

(3)

where Jv is the desorption mass flux of the water vapor across the membrane; Bm is the membrane distillation coefficient related to the membrane properties, such as pore size, porosity, tortuosity, and thickness of the membrane; pv,ms and pwv,p are the vapor pressure at membrane surface (i.e. liquid-vapor interface at the entrance of pore) 418

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and water vapor pressure at the permeate side, respectively. The one-dimensional diffusion of gas molecules in the porous media implies the existence of a frictional mass transfer resistance with the pore walls and collisions among molecules. The membrane distillation coefficient across the membrane, Bm, is estimated according to a dominant flow regime. The flow regimes involve the viscous, transitional, and Knudsen flow, depending on the Knudsen (Kn) number described in Eq. (4):

Kn =

λ dp

(4)

kB T 2 2 pπd wv

(5)

Sc =

3.3. Heat transfer The water desorption process through the HFMs essentially undergoes an adiabatic process. During the adiabatic water vapor desorption process, no available heat is transferred to the HFM-G. Thus, the LiBr solution temperature decreases along the flowing direction.

Qḃ = G (hb, in − hb, out )

where Kn is the Knudsen number; λ is the mean free path of water vapor in the pore; dp is the pore size; kB is the Boltzmann constant (1.3807 × 10–23 J/K); T and p are the temperature and pressure, respectively; dwv is the molecular size of water vapor. In the working conditions of the HFM-G considered herein, the range of the Knudsen number is plotted in Fig. 3 by taking into account of the submicron pore size, temperature, and equilibrium pressure where the values are larger than one. Thus, for Kn > 1, the collisions between the molecules and pore walls are dominant, and Knudsen diffusion takes place, and the membrane distillation coefficient is evaluated as:

M D Bm = wv ⎛ k ⎞ δ ⎝ RTm ⎠ ⎜

̇ Qmem = Jv ΔHv +

⎟

(6)

3τ

8RTm πMwv

Dk − v = Dk + Dv

(15)

where Q̇ mem is the heat flux across the membrane; ΔHv is the latent heat of vaporization; kmem, kwv, and kmt are the thermal conductivity of membrane, water vapor, and membrane material, respectively. Convective heat transfer across the feed thermal boundary layer, developed adjacent to the membrane surface, occurs from the bulk phase to the membrane surface, as:

(7)

Qḟ = hf (Tb − Tms )

(16)

where Q̇

f is the convective heat flux in the thermal boundary layer of the LiBr solution; hf is the convective heat transfer coefficient; Tb and Tms are the LiBr solution temperatures at the bulk phase and at the membrane surface, respectively. The convective heat transfer coefficient affects the temperature at

(8)

with 2 ε dp p τ 32 μ

(14)

with

where Mwv is the molecular weight of water; δ is the thickness of the membrane; Dk is the Knudsen diffusion coefficient; R is the gas constant; Tm is the mean temperature of the pore, which is estimated by the average temperature between the membrane surface and the vapor side; rp is the radius of pore. Knudsen-viscous diffusion occurs when there is no molecular diffusion through the pore [33]:

Dv =

km ⎛ ⎞ ⎜Tms, i − Tms, o ⎟ δ ⎝ ⎠

kmem = ε k wv + (1 − ε ) kmt dp ε

(13)

where Q̇ b is the heat flux by the decrease in temperature along the flowing direction; G is the mass flux of the feed LiBr solution; hb,in and hb,out are the bulk phase enthalpies at the inlet and outlet, respectively. The heat and mass transfer take place simultaneously during the water vapor desorption process via the HFM-G. The heat transfer is basically explained by two steps: the heat transfers through a thermal boundary layer of the feed LiBr solution in the HFM and across the membrane layer, where both values are identical at steady-state. The heat flux across the HFM is directly influenced by the mass flux of the water vapor and the conduction, such that:

with

Dk =

(12)

where Sh is Sherwood number. Dh is the hydraulic diameter identical to inner diameter of HFM. D is the mass diffusivity. Sc is the Schmidt number. μ is the dynamic viscosity.

with

λ=

μ ρ Dh

(9)

where Dk-v is the Knudsen-viscous diffusion coefficient Dv is the viscous diffusion coefficient. The concentration at the membrane surface increases due to the escape of water vapor from the solution stream. Thin film theory is widely considered to determine the concentration profile in the thermal boundary layer, as shown in Eq. (8) [22,8]:

J x ms = xb exp ⎜⎛ v ⎞⎟ ⎝ρ α⎠

(10)

where xms and xb are the concentrations of the LiBr solution at the membrane surface and at the bulk phase, respectively; ρ and α are the density and convective mass transfer coefficient, respectively. The convective mass transfer coefficient,α, is calculated by using the Sherwood number, a dimensionless number:

Sh =

α Dh = 0.13 Re 0.64 Sc 0.38 D

(11)

Fig. 3. Knudsen number in terms of submicron pore size and water vapor molecules for several working conditions.

with 419

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4. Experimental measurement

the membrane surface, directly influencing the mass transfer across the membrane. The Nusselt number has commonly been used for evaluating the convective heat transfer coefficient. The empirical heat transfer correlation for a laminar flow regime used in the membrane distillation process is shown in Eq. (17) [23,31]:

Nu = 4.36 +

0.036(Re Pr Dh / l) 1 + 0.0011(Re Pr Dh / l)0.8

4.1. Preparation of the HFM Fig. 5 illustrates the SEM images used to investigate the morphologies of the HFM used in this study, including the following views: (a) cross sectional, (b) enlarged cross sectional, (c) inner surface, and (d) outer surface. Table 2 lists the membrane parameters used in this study.

(17)

where Nu and Re are the Nusselt number and the Reynolds number, respectively; Pr is the Prandtl number; l is the distance from the HFM inlet. The temperature polarization effect leads to diffusive heat transfer resistance in the thermal boundary layer. The value of the temperature polarization coefficient, defined as the ratio of the temperature at the membrane surface to that at the bulk phase, approaching unity stands for an ideally designed HFM module that maximizes mass transfer performance, while a lower value signifies thermal dissipation through the thermal boundary layer. Enhancement in the temperature polarization coefficient is generally achieved with an increase in the feed flow rate or a decrease in the feed solution temperature.

4.2. Gas permeation test Evaluation of the membrane permeability is essential to characterize the mass transfer across the HFM layers. As shown in Eqs. (4)–(7), the membrane parameters determine the membrane distillation coefficient, Bm. The fibers are interlaced with each other, forming irregular pore sizes and shapes. The nominal membrane pore size is the first approximation for characterizing the mass transport, and thus, the determination of the pore size is the first and major requirement for evaluating the mass flux across the membrane. Fig. 6 shows a schematic of the experimental setup for the gas permeation test. A commercially used bundle of micro-porous polypropylene (PP) HFM capillaries was prepared, and an HFM module was made with transparent acrylic pipe (Ф 3.5 cm × L 35 cm). Nitrogen gas enters the lumen side of the HFM module's dead-end and is permeated to the shell side. A pressure regulator adjusts the pressure of the nitrogen gas in the lumen side, and a

3.4. Pressure drop Due to the desorption of water vapor, the temperature and concentration, in combination with the physical properties of the LiBr solution change in flow direction, the local pressure gradient, dp/dx, is expressed by Eq. (14):

f ρ dp = D u2 dx Dh 2

(18)

with

f=

64 Re

(19)

where dp is the frictional pressure drop through a single element of the HFM; fD is the Darcy friction factor for the laminar flow regime for a circular tube; dx is a single element of the HFM; u is the velocity of the solution. 3.5. Simulation procedure Fig. 4 shows a flow chart of the theoretical simulation of the heat and mass transfer of the HFM-G. The simulation begins with longitudinally splitting the HFM into tiny elements, dx. All the experimental operating conditions, such as the feed temperature, concentration, flow rate, and pressure at shell side, were recorded and used as input values for the simulation process. The heat balance (from Eqs. (13) and (14)) enables the evaluation of the mass flux of the water vapor across the HFM for a single element by determining the temperature and concentration at the membrane surface. The thermodynamic properties of the solution at the outlet of a single element of the HFM are then calculated and used as the feed physical properties for the next element. The above process is repeated until the summation of dx reaches the length of the HFM. The following assumptions were considered for the simulation.

• The process is a steady-state process. • The heat and mass transfer process is one-dimensional. • The mathematical model of one HFM represents the overall performance. • The membrane surface is in an equilibrium state with respect to the temperature and concentration of the LiBr solution. • Heat exchange does not take place with the surroundings. Fig. 4. Flow chart for the theoretical simulation of the heat and mass transfer on the HFM-G. 420

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Fig. 5. SEM images of the HFM used in this study: (a) cross sectional, (b) enlarged cross sectional, (c) inner surface view (interlaced fibers forming pores), and (d) outer surface view.

Table 2 Membrane parameters used in the experiments. Parameter

Value

Membrane material Inner diameter [µm] Outer diameter [µm] Membrane porosity [%] Number of HFMs Effective membrane length [cm]

polypropylene 390 540 50 380 25

Fig. 7. Experimental apparatus for the characteristics of the adiabatic desorption heat and mass transfer on the HFM-G.

evaluation of the nominal pore size because the nitrogen gas pushed all the air out from the pores and no molecular diffusion occurred. The nominal pore size is determined by solving Eq. (22) with respect to dp with the experimental permeability, Cm:

Cm =

MN2 ⎛ ε dp ⎜ RT ⎝ τ 3

8RT ε dP2 p ⎞ + ⎟ πMN2 τ 32 μ ⎠

(22)

4.3. Transient experiment on the heat and mass transfer of the HFM-G Fig. 7 shows a schematic of the transient experimental apparatus, which is used to examine the heat and mass transfer characteristics of the HFM adiabatic desorption process. The feed weak LiBr solution is initially contained in a stainless steel-based reservoir and is fed by a solution pump (GB-P25, MICROPUMP). The first Coriolis flow meter (CA003, OVAL) measures the density, temperature, and flow rate of the feed LiBr solution. The feed solution is then heated by a heat exchanger and enters the HFM-G. The shell side of the HFM-G is connected with a condenser so that the pressure downstream of the water vapor desorption is controlled and also maintained by a heat rejection process. The pressure at the condenser is measured by a vacuum pressure transducer (CCMT-100D, ULVAC). The adiabatic desorption process takes place as long as the vapor pressure at the condenser is lower than the vapor pressure of the solution flowing along the HFMs, while the feed weak solution turns into a strong solution. Two Pt100 sensors (Class A, CHINO) measure the inlet and outlet solution temperatures to evaluate the adiabatic desorption heat transfer. The pressure drop via the HFM-G is measured by a differential pressure transducer (UNIK5000, GE). The density and concentration of the strong solution are measured by another Coriolis flow meter (CA003, OVAL). Prior to the density measurement by the second Coriolis flow meter, the strong solution undergoes a cooling process to prevent density measurement errors, which may occur if a temperature difference exists between the two Coriolis flow meters. All of the experimental data collected during the passage of experimental time was used as initial conditions to serve as a basis for comparison with the theoretical heat and mass transfer. The experimental operating conditions are shown in Table 3. Table 4 lists the measurement accuracy of the density, mass flow rate, temperature, and

Fig. 6. Experimental apparatus for the gas permeation test on the HFM-G.

digital difference manometer (GC62, NAGANO) measures the pressure difference from atmospheric pressure. The permeated nitrogen gas enters a bubble flow meter that is exposed to the atmosphere; as a result, the mass flow rates of the nitrogen are collected under several pressure differences across the HFMs, evaluating the permeability of the HFM, Cm, as:

Cm = ṁ N2

δ 1 Amem Δp

(20)

with

Amem =

πn l (do − di ) ln (do − di )

(21)

where Cm is the permeability of membrane; ṁ N2 is the mass flow rate of nitrogen gas permeated from capillaries of HFMs; Amem is the area of HFMs for nitrogen gas permeation; n is the number of the hollow fibers. The Knudsen-viscous diffusion model (Eq. (8)) was used for the 421

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Table 3 Range of experimental conditions. Parameter

Value

Temperature of feed solution [°C] Concentration of feed solution [%] Mass flux of feed solution [kg m−2 s−1] Pressure at condenser [kPa]

65–83 51–58 157–244 2.6–5.5

Table 4 Properties of sensors. Parameter

Measurement device

Accuracy

Range

Density Mass flow rate Temperature Temperature Pressure at condenser Pressure at reservoir Differential pressure

CA003, OVAL CA003, OVAL Pt sensor, CHINO T type, CHINO CCMT-100D, ULVAC CCMT-1000D, ULVAC UNIK5000, GE

± 0.0005 g/ml ± 0.1% for liquid ± 0.05 °C ± 0.5 °C ± 0.2% ± 0.005% F.S./°C ± 0.2% ± 0.005% F.S./°C ± 0.1% F.S.

0.3–2 g/ml 0.72–72 kg/h − 50 to 100 °C − 62 to 125 °C 1.3–13.3 kPa

Fig. 8. Experimental permeability results for the HFM-G, and the estimation of nominal pore size.

13–133 kPa 0–35 kPa

5. Results and discussion 5.1. Determination of nominal pore size

pressure.

The steady-state gas permeability was evaluated under several pressure differences across the HFM layers. Measuring the mass flow rate of nitrogen gas determined the permeability of the HFMs to characterize the mass transfer as shown in Fig. 8; as a result, the nominal pore size was also obtained based on the estimated permeability data to use the theoretical simulation process.

4.4. Data reduction Two Coriolis flow meters measure the density and temperature, evaluating the concentrations of the LiBr solution at the inlet and outlet of the HFM-G. The concentration of the LiBr solution is calculated by Eq. (23) [11]:

ρsol = A0 + A1 x + A2 x 2 − (A3 + A 4 x )(Tsol + 273)

(23)

5.2. Effect of the feed solution temperature on heat and mass transfer

where ρsol is the density of the LiBr solution; the constant values are A0 = 1145.36, A1 = 470.84, A2 = 1374.79, A3 = 0.333393, and A4 = 0.571749. In order to evaluate the desorption mass transfer, the mass conservation assumption was firstly determined. The mass of the LiBr salt, the non-volatile component, is conserved in a whole liquid solution stream and, thus, is estimated by measuring both the solution flow rate and the concentration at the inlet of the HFM-G as shown in Eq. (20):

ṁ LiBr = ṁ sol, in x in

Fig. 9 presents the experimental desorption mass flux of the water vapor in terms of the feed solution temperature for several feed concentrations. An increase in the feed solution temperature led to an increase in the mass flux due to the exponential increase in the vapor pressure, which is dependent on temperature, i.e., the Antoine equation [29]. For example, the desorption mass flux was enhanced by approximately 2.7, 3.2, 3.9, and 5.8 times for the solution concentrations of 51%, 52%, 53%, and 54%, respectively, as the solution temperature was increased from approximately 65 to 82 °C. The lower feed

(24)

where ṁ LiBr and ṁ sol,in are the mass flow rate of LiBr salt and inlet weak solution, respectively; xin is the concentration of solution at inlet, defined as ṁ LiBr / (ṁ LiBr + ṁ w, in). The amount of desorbed water vapor across the HFMs is estimated by the difference between the measured value of the inlet solution flow rate and the calculated outlet solution flow rate by measuring the outlet concentration as:

ṁ wv = ṁ sol, in −

ṁ LiBr x out

(25)

where ṁ wv is the mass flow rate of the desorbed water vapor; xout is the concentration of the solution at the outlet. Thus, the mass flux of the water vapor across the HFMs is determined as function of the total interfacial area for water vapor desorption, as shown in Eq. (26):

Jv =

ṁ vapor Amem

Fig. 9. Experimental desorption mass flux of the water vapor with respect to the feed solution temperature for several feed concentrations (Gfeed = 152.9 kg m−2 s−1, Pcond = 4.7 ± 0.3 kPa).

(26)

where Jv is the mass flux of water vapor across HFMs. 422

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concentration also caused a higher desorption mass flux due to the higher vapor pressure of the solution. For example, in the case with a solution temperature of 82 °C, the mass flux increased by approximately 2.3 times, while the solution concentration varied from 57% to 51%. This is because the vapor pressure of the solution increases from approximately 8.1 to 13.8 kPa under the above case, and as a result, the difference in the driving force of the mass transport results in approximately 2.6 times the designated condenser pressure. Fig. 10 depicts the temperature drops through the adiabatic desorption process for several conditions. The sensible heat is supplied as latent heat to evaporate the water vapor at the liquid-vapor interface, and thus, a large temperature drop takes place in the flow direction. Because the higher feed temperature and the lower feed concentration gave rise to a higher mass flux, the temperature drops became larger for the entire concentration range. This is due to the use of more sensible energy for the latent heat of vaporization for higher feed temperatures and lower concentrations. It was observed that for a concentration of 51%, the feed solution temperature increased from approximately 65 to 82 °C, as the temperature drop was varied from 7.8 to 22.4 °C.

(i.e., the liquid phase of the solution is permeated into the pores) if the solution pressure becomes higher than the breakthrough pressure (Eq. (2)). Furthermore, to prevent the large pressure drop by the phase change of the solution during the preheating process, the solution pressure must be larger than the static equilibrium pressure. As a result, considering the breakthrough pressure and phase change, the pressure drop is an important factor to avoid malfunction during the desorption process in the HFM-G. 5.6. Comparison of experimental heat and mass transfer with theoretical results All of the experimental initial conditions influencing the heat and mass transfer, such as feed solution temperature, concentration, mass flow rate, and condenser pressure, were collected during the series of experiments. The obtained data were used as initial operating conditions to conduct the theoretical simulation process. Fig. 16 depicts the comparison of the experimental desorption mass flux with the theoretical simulation results. The result shows that at the lower driving force (i.e., strong concentration and low temperature of the feed solution), the theoretical model over-predicted while at the higher driving force, under-predicted the experimental desorption mass fluxes. Especially, at extremely low driving force, the theoretical desorption mass flux was much higher than the experimental one (in some case, 90% over predicted). This is because the theoretical model had the value of the desorption mass flux as long as the driving force exists (even extremely small value of the driving force exists); however, in the experimental works, the lower driving force generated the large uncertainty of measurement; furthermore, the pressure drop at the shell side of the HFM module caused further lowering driving force of mass flux (i.e., the frictional pressure drop is higher than the driving force). It is well known that the specific volume of water vapor, occupying the condenser, is very large, resulting in the significant pressure drop. For example, the driving force for 70 °C and 58% feed concentration with 4.0 kPa condenser pressure is less than 0.5 kPa. In such cases, the theoretical model calculated even small values of the desorption mass flux, but the experimental data under such extremely small driving forces were hardly obtained. The experimental temperature drop via the adiabatic desorption process was also compared with the simulated results, as shown in Fig. 17.

5.3. Effect of the feed solution mass flux on the heat and mass transfer As shown in Fig. 11, the desorption mass flux is enhanced by a larger mass flux of the feed solution. A higher feed solution mass flux generates a higher value for the temperature polarization coefficient, for which the temperature difference between the bulk and membrane surface (i.e., the heat transfer resistance in the thermal boundary layer) becomes smaller. Note that the rate of increase in the mass flux was reduced with an increase in the feed solution flux. This means that the enhancement of input energy is not exactly proportional to the mass flux performance because the larger sensible energy is not entirely used in the adiabatic desorption process for certain membrane parameters. The desorption mass flux was enhanced from approximately 2.5 to 4 kg m−2 h−1 as the mass flux of the feed solution increases from 157.3 to 239.8 kg m−2 s−1 for a 51% concentration of the feed solution. As shown in Fig. 12, the temperature drop via the desorption process decreases with an increase in the mass flux of feed solution. The explanation for this is that not all of the sensible input energy was used for the evaporation of the water vapor as the feed solution flux increased. For the solution concentration of 51%, for instance, the solution temperature dropped by 23.4 °C for a feed mass flux of 157.3 kg m−2 s−1, and a temperature drop of 18.5 °C was found for a feed mass flux of 239.8 kg m−2 s−1.

5.7. Mass transfer characteristics with respect to a simultaneous change in the feed solution temperature and mass flux

5.4. Effect of the condenser pressure on heat and mass transfer

As shown in Fig. 18, the feed solution temperature directly

The effect of the condenser pressure on the mass flux performance is shown in Fig. 13. The condenser pressure is directly related to the driving force of the desorption mass flux, and as a result, the enhancement of desorption was found with a decrease in the condenser pressure. The feed solution concentration also inversely influences the mass flux. The temperature drop decreases with higher condenser pressures due to the lower mass flux performance, as shown in Fig. 14. 5.5. Pressure drop via the HFM-G The pressure drop of the LiBr solution via the HFM-G used in this study is shown in Fig. 15. It was found that the pressure drop linearly increases with an increase in the solution velocity. The solution concentration also influences the solution pressure drop through the HFMs mainly due to the change in density and viscosity of the solution. The calculation values by the Darcy friction pressure drop, considering the change of the thermodynamic properties in the flow direction, is also shown in Fig. 15. It is noteworthy that the pressure drop resists the flow of the solution through the HFMs, and thus, a larger solution pressure is mandatory against the larger pressure drop; however, the HFM is wet

Fig. 10. Experimental temperature drop by adiabatic desorption with respect to the feed solution temperature for several feed concentrations (Gfeed = 152.9 kg m−2 s−1, Pcond = 4.7 ± 0.3 kPa). 423

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Fig. 11. Experimental desorption mass flux of the water vapor with respect to the mass flux of the feed solution for several feed concentrations (Tfeed = 80 °C, Pcond = 4.7 ± 0.3 kPa).

Fig. 14. Experimental temperature drop by adiabatic desorption with respect to the pressure at the permeate side for several feed concentrations (Tfeed = 80 °C, Gfeed = 183.6 kg m−2 s−1).

Fig. 12. Experimental temperature drop by the adiabatic desorption with respect to mass flux of the feed solution for several feed concentrations (Tfeed = 80 °C, Pcond = 4.7 ± 0.3 kPa).

Fig. 15. Pressure drop of the solution via the HFMs with respect to the solution velocity for several concentrations (Tfeed = 80 °C, Pcond = 2.4 kPa).

Fig. 13. Experimental desorption mass flux of the water vapor with respect to the pressure at the permeate side for several feed concentrations (Tfeed = 80 °C, Gfeed = 183.6 kg m−2 s−1).

Fig. 16. Comparison of the experimental desorption mass flux with the theoretical simulation results (xfeed = 51–58%).

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transfer characteristics in terms of the HFM dimensions. The number of HFMs is adjusted for a given volume to increase the liquid-vapor mass transfer interfacial area and control performance. As shown in Fig. 20, increases in the number and length of the HFMs enlarge the concentration difference; however, the curve for the concentration difference becomes nearly flat and hardly increases with increasing length and number of the HFMs. The change in the number of HFMs is associated with the solution velocity, and the change in the length of the HFMs is directly related to a decrease in the driving force in the flowing direction. Therefore, with larger HFM-G dimensions, the driving force of the mass flux drastically decreases in the flowing direction as the solution temperature relatively easily decreases by the adiabatic desorption process; as a result, a given HFM could have a certain maximum concentration difference regardless of the dimension increase of the HFM-G. The mass flux of the water vapor across the HFMs decreases with increases in the number and length of the HMFs, as shown in Fig. 21. Note that the sensible energy input provides the energy for the adiabatic desorption process and is readily used as the dimension of the HFM-G increases. This indicates that the desorption process no longer occurs at certain point in the HFMs due to the extremely low driving force. As a result, the mass transfer rate per unit HFM area decreases with larger dimensions of the HFM-G.

Fig. 17. Comparison of the experimental desorption temperature drop with the theoretical simulation results (xfeed = 51–58%).

6. Conclusion A hydrophobic HFM-G was proposed as the mechanism for the water vapor desorption process in a VARs. The HFM-G is effectively used not only for stationary applications, but also for portable applications with several advantages:

• Compactness with enhanced heat and mass transfer • Lightness and corrosion-free due to the use of a non-metallic-based structure • Functionality under harsh driving conditions This paper mainly focused on the physical characteristics of the hydrophobic HFM, theoretical mechanism of the adiabatic desorption of water vapor from the perspective of heat and mass transfer, experimental works, and feasibility of the HFM-G for practical use.

Fig. 18. Concentration increase via adiabatic desorption in terms of the simultaneous change in the feed solution temperature and mass flux (xfeed = 57%, Pcond = 7.0 kPa).

• The characteristics of gas permeation across the HFMs were ex-

influences the concentration difference between the inlet and outlet of the HFM-G at a constant condenser pressure. The concentration difference, however, decreases with an increasing feed solution flux because the membrane distillation efficiency, defined as the ratio of the desorbed water vapor to the energy input, decreases under certain membrane parameters. This is directly related to the circulation ratio, which is a critical factor that is highly responsible for determining the size and cost of the system. Fig. 19 describes the desorption water vapor mass flux in terms of both the mass flux and temperature of the feed solution. It is known that as the mass flux and the temperature of the feed solution increase, the desorption mass flux is drastically enhanced. Under certain feed solution temperatures, the higher mass flux improved the cooling capacity by obtaining larger amounts of water vapor, but the COP of the HFM-G-based VARs decreased with a higher feed solution flux [14]. In summary, a higher feed solution temperature has the potential to considerably enhance the performance of VARs, as well as increase the performance of the HFM-G. On the other hand, the flow rate of the LiBr solution is a necessary consideration in terms of the circulation ratio, cooling capacity, and the COP of VARs.

•

5.8. Mass transfer characteristics with respect to a simultaneous change in the dimension of the HFM-G

perimentally investigated and depicted the nominal pore size of the HFMs used in this work. A transient experimental method was proposed to examine the adiabatic desorption heat and mass transfer of the HFM-G. The experimental heat and mass transfer results demonstrated that higher

Fig. 19. Mass flux via adiabatic desorption in terms of the simultaneous change in the feed solution temperature and mass flux (xfeed = 57%, Pcond = 7.0 kPa).

Figs. 20 and 21 present the theoretical prediction of the mass 425

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Fig. 20. Concentration increase via adiabatic desorption in terms of the simultaneous change in the number and length of the HFM-G (Tfeed = 100 °C, xfeed = 57%, Gfeed = 917 kg m−2 s−1, Pcond = 7.0 kPa).

Fig. 21. Mass flux via adiabatic desorption in terms of the simultaneous change in the number and length of the HFM-G (Tfeed = 100 °C, xfeed = 57%, Gfeed = 917 kg m−2 s−1, Pcond = 7.0 kPa).

•

•

feed temperatures led to an exponential increase in both the mass flux and adiabatic temperature drop due to the increase in irreversibility. The increase in the feed solution mass flux and the decrease in condenser pressure also enhanced the mass transfer performance. All of the experimental operating condition data were collected in a series of experiments and were used to conduct the theoretical simulation works. From the results, it was found that the theoretical model had a particular trend with experimental data. We are not sure right away to explain the intersected trend, but also pursue to find which parameters (e.g., physical membrane parameters, or theoretical model) influence this phenomenon. The future work should include the developed prediction for further investigation. The prediction of the mass transfer characteristics in terms of the feed properties and the dimension of the HFMs enabled the consideration of the system performance with respect to several conditions.

Acknowledgement This paper is based on the results obtained from a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

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