Study of mass transfer coefficient in membrane desalination

Desalination 407 (2017) 46–51

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Study of mass transfer coefficient in membrane desalination Jingcheng Cai, Fei Guo ⁎ School of Energy and Power Engineering, Dalian University of Technology, No.2 Linggong Road, Dalian 116024, China

H I G H L I G H T S • Feed temperature plays a dominant role on the permeate flux. • The mass transfer coefficient can be considered as a constant in membrane desalination process. • Estimation of permeate flux based on mass transfer coefficient

a r t i c l e

i n f o

Article history: Received 25 September 2016 Received in revised form 3 December 2016 Accepted 7 December 2016 Available online xxxx Keywords: Membrane desalination Mass transfer coefficient Diffusion Permeate flux

a b s t r a c t Membrane desalination (MD) is a thermally-driven separation process. The driving force in the MD process is the vapor pressure difference induced by the temperature difference across a hydrophobic membrane as a barrier. MD is a potential route to obtain high-quality fresh water from sea water or brine by using low-grade energy. It is important to estimate and predict the MD performance especially in terms of permeate flux under given conditions. This is very meaningful in MD plications. In this work, the MD performance was studied not only by varying the feed temperature but also by varying the coolant temperature in a lab scale AGMD system. The permeate flux and salt reject ratio were tested under various conditions. The mass transfer coefficient in porous membranes was studied in detail both theoretically and experimentally. A new approach to estimate the permeate flux was proposed based on the study of the mass transfer coefficient in MD systems. The estimation of MD performance in real applications can be much simplified based on this study. © 2016 Elsevier B.V. All rights reserved.

1. Introduction In recent years, membrane-based technologies have been rapidly growing in desalination related applications. Reverse osmosis (RO) and membrane desalination (MD) are two typical membrane-based water treatment technologies. RO exhibits great potential for water treatment worldwide due to its strong separation capability [1]. The main drawback of RO is the limited water recovery ratio and the high energy consumption [1,2]. MD is a thermally driven separation technology [3]. The driving force of MD is the vapor pressure across a hydrophobic membrane as a barrier. Comparing to the conventional technologies, such as mechanical vapor compression, multi effect distillation, multi stage flash vaporization, etc., MD process can be operated under relatively low temperature range (30 °C–80 °C) [4] which leads to a very low energy consumption. MD is very suitable for compact, solar powered desalination units providing small and medium range output [5,6]. The water recovery ratio of MD can reach 100% theoretically [7,8].

⁎ Corresponding author. E-mail address: [email protected] (F. Guo).

http://dx.doi.org/10.1016/j.desal.2016.12.013 0011-9164/© 2016 Elsevier B.V. All rights reserved.

The performance of MD is usually described by its permeate flux. Generally, higher permeate flux is preferred in desalination applications. To increase the permeate flux in MD, several approaches can be adopted, such as interrupting the temperature polarization [9–11], modifying the membrane surface [12–16], varying the thickness and structure of air gap spacer [17–20] in air gap membrane desalination (AGMD) systems, tilting the inclination angles of AGMD module [21, 22], increasing the flow rate of the feed [18,23] etc. The membrane used in MD process influences the permeate flux in several ways [24]. The effective surface area is less than the contact area between the feed water and membrane since the porosity of the membrane is not 100%. The vapor transport path is longer than the membrane thickness because of the membrane tortuosity. The momentum of the vapor molecules is decreased by the inside walls of the pores resulting in the resistance to the molecule diffusion. The permeate flux can be considered as a linear relation to the vapor pressure difference across the membrane according to Darcy's law [25]:
 N ¼ B f P fm −P pm

ð1Þ

where Pfm is the vapor pressure of the feed side, Ppm is the vapor pressure of the condensing side. Bf is mass transfer coefficient. In MD

J. Cai, F. Guo / Desalination 407 (2017) 46–51

process, Bf is governed by three basic mass transfer mechanisms (Table 1), which are Knudsen diffusion, Molecular diffusion, and a combination between them (Transition diffusion). The Knudsen number (Kn) indicates the dominant mass transfer mechanism in the pores [26]: Kn ¼

λ d

ð2Þ

where d is the mean pore size of the membrane; λ is the mean free path of a molecule [3,27]: kB T λ ¼ pffiffiffi 2πPσ 2

ð3Þ

where kB is the Boltzmann constant, σ is the collision diameter of the diffusion molecule. In Eq. (1), the vapor pressure (P) is calculated according to Antoine Equation: ln P ¼ A−

B T þC

ð4Þ

where A, B and C are constants (for water: A = 23.1964, B = 3816.44, C = −46.13) [3], T is temperature. If the free path of vapor molecules is large compared to the pore size of the membrane in this diffusion, the molecules hit the walls more often than to each other. This type of mass diffusion behavior is considered as Knudsen diffusion. When the Knudsen number (Kn) N10, the mass transfer is effectively modelled by Knudsen diffusion [28]. Then, the mass transfer coefficient (Bf) in the MD process equals to mass transfer coefficient of Knudsen diffusion (Bk): Bk ¼

  εd 8RT 1=2 Mw RTδ 3τ πMw

ð5Þ

where δ is the membrane thickness, ε is porosity, τ is tortuosity, Mw is molecular weight of water. ε can be determined by the SmolderFranken equation [29]: ρ ε ¼ 1− m ρp

ð6Þ

where ρm and ρp are the densities of the membrane and polymer material respectively. τ can be calculated from [30]: τ¼

ð2−ε Þ2 ε

ð7Þ

47

If the free path of vapor molecules is much smaller than the pore size of the membrane during the mass diffusion, intermolecular collisions start to limit the diffusion rate, collisions to the walls are rare. When the Knudsen number (Kn) b 0.01 [31], the mass transfer is considered as Molecular diffusion. Then, the mass transfer coefficient (Bf) in the MD process is fully governed mass transfer coefficient of Molecular diffusion (Bm): Bm ¼

1 ε Mw DP RT P a τδ

ð8Þ

where δ is the membrane thickness, ε is porosity, τ is tortuosity, Mw is molecular weight of water. P is total pressure inside the pore which equals to the partial pressure of air and water vapor. The values of P at various temperatures can be easily calculated based on the ideal gas law. Pa is the air pressure within membrane pore. The value of Pa can be calculated by subtracting the partial pressure of water vapor pressure from the total pressure. Water vapor pressure at a certain temperature can be calculated according to Antoine Equation (Eq. (4)). D is diffusion coefficient. The diffusion coefficient between air and water vapor is given by Fuller equation [32,33]: 1=2 1 þ Mw j D ¼ 1  10−7 h
1=3 i2 1=3 P ð∑vi Þ þ ∑v j T 1:75



1 Mwi

ð9Þ

where ∑v is the diffusion volume (air: 20.1, water vapor: 12.7) [27]; i and j represent the components of mixed gases. The diffusion coefficient D is approximately inversely proportional to the water vapor pressure inside the pores, so that the term DP remains almost constant when pressure changes, which is given by [37]: DP ¼ 1:89  10−5 T 2:072

ð10Þ

When 10 N Kn N 0.01, the mass transfer can be considered as a combination of Knudsen diffusion and Molecular diffusion (Transition diffusion) [3,24]. 1 1 1 ¼ þ Bt Bk Bm

ð11Þ

It has been widely reported that the permeate flux is affected by the temperature difference. Many studies have shown the increase in permeate flux with increasing temperature of the feed stream when the cooling stream is maintained at a fixed temperature [15–17,23]. In this work, MD performance was studied not only by varying the feed temperature but also by varying the coolant temperature in a lab-

Table 1 Typical diffusion mechanisms in MD process. Kn value

Diffusion

Mechanism

Kn N 10

Knudsen diffusion

Molecule-pore wall collisions

Kn b 0.01

Molecular diffusion

Molecule-molecule collisions

10 N Kn N 0.01

Transition diffusion

Molecules collide with each other as well as the pore wall

Schematic

48

J. Cai, F. Guo / Desalination 407 (2017) 46–51

Fig. 1. (a) Morphology of a PTFE membrane (pore size: 0.45 μm) characterized by SEM. (b) a schematic diagram of LEP unit. (c) LEP measurements of PTFE membranes (pore size: 0.22 μm, 0.45 μm; water contact angle: 135°, 125°) with a flow rate of 0.075 mL/min provided by a syringe pump.

scale AGMD system. The permeate flux and salt reject ratio were tested under various conditions. A new approach to estimate the permeate flux was proposed based on the study of the mass transfer mechanism in MD systems.

Emitech & Polaron Q150T) for 90 s to coating a very thin conductive layer of Au to enhance imaging.

2. Experimental

The hydrophobicity of the membranes was characterized by measuring water contact angle with a goniometer (model 500, RameHart). A droplet of 20 μL DI water was placed on a test membrane for contact angle measurement. The value of the contact angle of each sample was an average of 10 measurements. The measured water contact angle is the apparent contact angle which is usually larger than the material's intrinsic contact angle because of the air trapped between the water droplet and the cavities of the rough surface according to Cassie-Baxter theory.

2.1. Membranes The membranes that can be used for the AGMD system must meet the specific requirements by the definition of membrane desalination. The material must be hydrophobic or treated to be hydrophobic. The typical upper limit pore size should be controlled at around 1 μm to ensure the membranes can have a proper liquid entry pressure which should be high enough to stand the fluctuating pressures in the operation system. The membrane material should have a minimum mechanical and chemical stability and must not dissolve in the feed solution. Furthermore, the thermal conductivity of the material should be as low as possible to reduce the heat loss. However, it is always possible to optimize the membrane specifically to further improve the performance of membrane desalination. Commercial hydrophobic polytetrafluoroethylene (PTFE) membranes (Membrane Solutions, LLC, nominal pore size: 0.22 μm, 0.45 μm) were used in this work. The test membranes were cut into 5.5 cm × 6.5 cm for MD tests. A digital micrometer (211-101F from Guilin Guanglu Measuring Instrument Co., Ltd) was utilized to measure the thickness of the membrane. 2.2. Scanning electron microscopy The morphology of the test membranes (see Fig. 1a) was characterized by Scanning Electron Microscope (SEM) (FEI, QUANTA 450). The sample membranes were pretreated by a sputter coating unit (Quorum

2.3. Contact angle

2.4. Liquid entry pressure Liquid entry pressure (LEP) is the minimum pressure for feed liquid penetrating (wetting) the membranes. According to Young-Laplace equation [34,35] (Eq. (12)), LEP is dominated by surface tension of the test liquid, contact angle, and maximum pore size of the test membrane.

ΔP ¼ −

2γL cosθ rmax

ð12Þ

ΔP is the liquid entry pressure, γL is the liquid surface tension, θ is the contact angle, rmax is the maximum pore size. A custom-designed apparatus was applied to measure the LEP according to the previous study [15]. In this work, an air buffer cell was added on the unit to improve the stability and performance (Figs. 1b and S1 in Supplementary Information (SI)). The membrane was tested with a stainless steel filter holder (filter size, diameter: 13 mm; effective area: 64 mm2). The gauge pressure was recorded by a pressure transducer (CYYZ11-HK-67-RS-16-B-G, Beijing Star Sensor Technology CO., Ltd) linked to computer. The highest pressure in the recorded line was considered as the LEP. 2.5. Membrane desalination

Fig. 2. Schematic diagram of a lab-scale AGMD system used in this work.

Membrane distillation performance was characterized by a lab-scale Air Gap Membrane Distillation (AGMD) unit made of PTFE (10 cm × 10 cm) (Figs. 2 and S2 in SI). Polyethylene zigzag mesh was used as air gap spacer (thickness: ~2 mm). The effective area for distillation is about 90% of the total contact area because of the spacer mesh coverage. Silica gel sheet (1 mm and 2 mm) was used as sealing gasket. The condensing plate was made of stainless steel (thickness: ~2 mm). The feed was 3.5 wt% salt (NaCl) solution. The temperature of the feed was controlled by a water bath. Two magnetically driven pumps (MP-15R, Guangquan Machinery CO., Ltd.) were used to provide smooth circulating water. The flow rates of the feed and coolant were controlled by flow gauge (LZB, Changzhou Shuanghuan ThermoTechnical Instrument Co., Ltd.).

J. Cai, F. Guo / Desalination 407 (2017) 46–51

49

Fig. 3. Theoretical values of Bf calculated based on different diffusion mechanisms (δ = 160 μm, ε = 0.8, τ = 1.8).

The temperatures of the inlet and outlet were measured by mercurial thermometers (measuring range: − 30 °C– 100 °C; accuracy 1 °C) and thermal couples (WAP-194 PT100, Hangzhou Meacon Automation Technology Co., Ltd.). The values of pressure at the inlet and outlet of feed water were measured by digital pressure gauges (CYYZ11-HK-67-RS-16-B-G, Beijing Star Sensor Technology CO., Ltd.). The permeate water was collected and weighted by a digital mass balance connected to a computer with data recording (every 1 min). A chloride ion sensor (PXS-270, INESA Scientific Instrument Co., Ltd.) was used to measure the concentration of chloride ion. The salt rejection rate (Rs) was calculated from the concentration of chloride ion.

whole permeated flux trend in a MD process. Bcons can be obtained from experiment data according to Darcy's law.
 N ¼ Bcons P fm −P pm

ð15Þ

The temperature inside the membrane in MD process is usually in a range lower than the feed temperature and higher than coolant temperature [4,11,36]. We take 20 °C–55 °C as the membrane temperature in the present work. The Bf value changes slightly in this temperature range as shown in Table 3. By taking account in all the operation errors, Bf can be considered as constant during a test condition. The permeate flux in a MD process can be obtained directly from Bf and water vapor pressure difference across the membrane. Therefore, only one experiment is needed to obtain the Bf value which can be used to predict the

where N is the permeate flux, Bcons is the constant mass transfer coefficient (kg/m2/Pa/s), Pfm is water vapor pressure of the feed side, Ppm is water vapor pressure of the permeate side. The values of Pfm and Ppm can be calculated according to Antoine Equation (Eq. (4)) A set of experiments were conducted to verify the theoretical estimation as shown in Fig. 4. The calculated lines fit the experimental data under various conditions. For a fixed coolant temperature (10 °C), Bf value is calculated to be 1.1 × 10− 7 kg/m2/pa/s when the feed temperature is set at 38 °C. Fig. 5 shows the effect of coolant temperature on permeate flux under fixed feed temperatures. The feed water temperature of each experiment was kept at 48 °C, 52 °C, 56 °C, respectively. The chloride iron concentration of the permeate water was measured to be b 10 ppm, which indicates the salt rejection ratio N99.9%. Under fixed feed temperature, the permeate flux increases with the decrease of the coolant temperature. The only variable of the permeate flux is Ppm under a fixed feed temperature according to Eq. (15). When temperature is below 20 °C, water vapor pressure is almost linear fit with temperature according to Antoine's equation. Therefore, the permeate flux increases with the coolant temperature almost linearly according to Eq. (15). The lines are almost in the same trend as shown in Fig. 5. The distance between the lines are almost constant because the vapor pressure change is almost a straight line within 48 °C–56 °C. The experiment results apparently fit the theoretical analysis. As shown in Figs. 4 and 5, increasing the feed temperature is more effective on the permeate flux enhancement compared to decreasing the coolant temperature at the same temperature difference. This is because water vapor pressure is about a power function of temperature. Water vapor pressure increases dramatically with temperature. Therefore, the feed temperature plays a dominant role on the permeate flux. Lower the coolant temperature has insignificant influence on the permeate flux, but can lower the energy efficiency of the whole MD process. The flow rate of the feed also affects the permeate flux. As shown in Fig. 6, increasing flow rate of the feed can effectively improve the flux as the thickness of the thermal boundary layer can be reduced by

Table 2 Parameters of fitting equation of Bf on temperature.

Table 3 Variation of Bf in the temperature of 20 °C–55 °C.

−

Rs ¼ 1−

½Cl perm

ð13Þ

−

½Cl feed

3. Results and discussion The permeate flux can be calculated with various Bf according to Eq. (1). Bf is associated with δ, ε, τ, d, and T. For a test membrane in a MD system, the values of δ, ε, τ, d are fixed. T is the only variable determining Bf. As shown in Fig. 3, Bf from various models can be obtained based on the given conditions. The values of Bm, and Bt show insignificant increase, while Bk shows a slightly decrease tendency. The fitting parameters (Table 2) show that Bk is almost of linear fitting to temperature. Bm and Bt are power function of temperature. Then, Bf can be obtained as a power function of temperature. B f ¼ a þ bT

c

ð14Þ

Pore size

Bf

a

b

c

R2

Pore size

Bf

Variation (kg/m2/pa/s)

Error (%)

0.45 μm

Bk Bm Bt Bk Bt

1.854E−6 4.848E−7 3.792E−7 9.064E−7 3.096E−7

−2.614E−9 1.631E−17 5.620E−17 −1.278E−9 4.700E−17

1 5.340 4.891 1 4.804

0.9982 0.9971 0.9989 0.9982 0.9996

0.45 μm

Bm Bt Bk Bk Bt

4.43E−8 2.20E−8 1.28E−7 4.84E−8 1.12E−8

9.0 5.7 5.6 5.6 3.6

0.22 μm

0.22 μm

50

J. Cai, F. Guo / Desalination 407 (2017) 46–51

Fig. 4. The experimental data and the theoretical estimation of permeate flux under various feed temperature conditions. The coolant temperature is fixed at (a) 10 °C and (b) 20 °C. (pore size: 0.45 μm, air gap: 2 mm).

enhancing the flow turbulence. The mass transfer coefficients are calculated to be 0.8 × 10− 7 kg/m2/pa/s, 1.1 × 10− 7 kg/m2/pa/s, and 1.3 × 10−7 kg/m2/pa/s, respectively, according to Eq. (15) under feed flow rates of 1 L/min, 1.6 L/min, and 3.8 L/min. The increase of the mass transfer coefficient results in better MD performance in terms of permeate flux. The theoretical estimations fit the experimental results well under various feed flow rates (see Fig. 6). The polymer spacer mesh in the AGMD system provides an air gap between the membrane and the condensation plate. This configuration has the highest energy efficiency, but the mass transfer flux is generally low compared to DCMD system because the air gap also increases the resistance to the mass transfer. Decreasing the thickness of the air gap leads to an increase of the mass transfer flux. When the spacer mesh is removed, the membrane directly attaches on the condensation plate. The condensed permeate water can still drop out along the condensation plate without mixing with the cooling liquid. This configuration is very close to a DCMD system. Fig. 7 shows the experimental results and the theoretical estimation of the MD performance in terms of permeate flux without using a spacer mesh in the AGMD system. For fixed coolant temperatures at 10 °C and 20 °C, the values of mass transfer coefficient can be calculated to be 6.2 × 10−7 kg/m2/pa/s and 5.9 × 10−7 kg/m2/pa/s respectively according to Eq. (15). A lower coolant temperature can promote the permeate flux very slightly. The permeate flux is about six times larger than that with a spacer mesh (~2 mm in thickness). This is because the decrease of the resistance to the mass transfer caused by the air gap. The theoretical estimations fit the experimental data very well even without a spacer mesh in the AGMD system.

4. Conclusions The effect of feed temperature and coolant temperature on permeate flux in MD system was studied in detail theoretically and experimentally. We have shown that the feed temperature plays a dominant role on the permeate flux while the coolant temperature (usually b 25 °C) has insignificant influence on the permeate flux. This is consistent with the thermal properties of water vapor pressure. In low temperature zone (roughly between 0 °C–25 °C), the water vapor pressure and its variation are both small. We have also shown that the mass transfer coefficient can be considered as a constant in a MD process by studying the possible water molecules diffusion mechanisms in porous membranes. The related experiment results under various given conditions are in consistent with the theoretical analysis. This opens up a new approach to estimate and predict the permeate flux in MD process. And the estimation of MD performance in real applications can be simplified based on this study. Nomenclature constant mass transfer coefficient (kg/m2/Pa/s) Bcons mass transfer coefficient (kg/m2/Pa/s) Bf mass transfer coefficient of Knudsen diffusion (kg/m2/Pa/s) Bk mass transfer coefficient of Molecular diffusion (kg/m2/Pa/s) Bm mass transfer coefficient of Transition diffusion (kg/m2/Pa/s) Bt d mean pore size of the membrane (m) D diffusion coefficient (m2/s) Boltzmann constant (1.381 × 10−23 J/K) kB Knudsen number Kn

Permeate flux (kg/m2/hr)

8 7

Feed: 56 o C

6

Feed: 52o C

5

Feed: 48 o C

4 3

0

4 8 12 16 Coolant temperature ( oC)

20

Fig. 5. The effect of coolant temperature on permeate flux under fixed feed temperatures. (pore size: 0.45 μm, air gap: 2 mm).

Fig. 6. The MD performance in terms of permeate flux under various feed flow rates: (i) 1 L/min, (ii) 1.6 L/min, (iii) 3.8 L/min. (pore size: 0.45 μm, air gap: ~2 mm).

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51

Fig. 7. The MD performance in terms of permeate flux without a spacer mesh under different coolant temperatures (a) 10 °C, (b) 20 °C. (pore size: 0.45 μm).

Mw N P Pa Pfm Ppm R Rs rmax T [Cl−]feed [Cl−]Perm ΔP

molecular weight of water (g/mol) permeate flux (kg/m2/h) total pressure (Pa) air pressure within membrane pore (Pa) vapor pressure of the feed side (Pa) vapor pressure of the permeate side (Pa) the universal gas constant (take as 8.3144 m2 kg/s2/K/mol) salt rejection rate (%) maximum pore radius (m) temperature (°C) mass concentration of chloride ion in feed mass concentration of chloride ion in permeate side liquid entry pressure (Pa)

Greek letters γL δ ε θ λ νi νj ρm ρp σ τ

liquid surface tension (N/m) membrane thickness (μm) membrane porosity (%) contact angle (o) mean free path of a molecule (m) diffusion volume of i component (m3/mol) diffusion volume of j component (m3/mol) density of the membrane (kg/m3) density of polymer material (kg/m3) collision diameter of the diffusion molecule (2.641 × 10−10 m) tortuosity of the membrane

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