Experimental study of the optimal vacuum pressure in vacuum assisted air gap membrane distillation process

Desalination 414 (2017) 63–72

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Experimental study of the optimal vacuum pressure in vacuum assisted air gap membrane distillation process Zhiyu Liu a,b,c, Qijun Gao a,c,⁎, Xiaolong Lu a,b,c,⁎⁎, Zhong Ma a,b,c, Hao Zhang a,b,c, Chunrui Wu a,c a b c

State Key Laboratory of Separation Membranes and Membrane Processes, Tianjin Polytechnic University, Tianjin 300387, PR China School of Material Science and Engineering, Tianjin Polytechnic University, Tianjin 300387, PR China Institute of Biological and Chemical Engineering, Tianjin Polytechnic University, Tianjin 300387, PR China

H I G H L I G H T S • • • •

A vacuum assisted air gap membrane distillation (VA-AGMD) process was designed. The optimal vacuum pressure (OVP) which can be achieved in air gap were obtained. Appropriate vacuum pressure can improve heat efficiency significantly. When T1 were 70.0 °C, 80.0 °C and 90.0 °C, OVP were 0.080 MPa, 0.060 MPa and 0.040 MPa, respectively.

a r t i c l e

i n f o

Article history: Received 16 January 2017 Received in revised form 21 March 2017 Accepted 22 March 2017 Available online xxxx Keywords: Air gap membrane distillation Vacuum pressure Non-condensable gases Heat and mass transfer

a b s t r a c t In this study, a vacuum assisted air gap membrane distillation process was designed to weaken the negative influence of non-condensable gases and improve the process performance. It was found that the applied vacuum (within a certain range of vacuum pressure) could remove the non-condensable gases and effectively improve the process performance. It was also found that water vapor cannot condense at the cooling surface in the module when the vacuum pressure is too high. Hence, the concept of optimal vacuum pressure was introduced and studied. The OVP was considered a critical factor to ensure that the VA-AGMD process was dominated by AGMD rather than by vacuum membrane distillation. The effect of some parameters on the optimal vacuum pressure was examined and is discussed in this paper. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Membrane distillation (MD) is a thermal-based membrane separation technology, and its mass transfer is driven by the vapor pressure difference across a hydrophobic membrane [1–3]. Based on the way the vapor is collected or removed from the permeate side, MD processes can be classified into four basic configurations: (i) direct contact membrane distillation (DCMD), collected by the permeate; (ii) vacuum membrane distillation (VMD), removed by vacuum pressure; (iii) air gap membrane distillation (AGMD), condensed in the air gap; (iv) sweeping gas membrane distillation (SGMD), removed by a sweeping gas [1–3].

⁎ Correspondence to: Q. Gao, State Key Laboratory of Separation Membranes and Membrane Processes, Tianjin Polytechnic University, Tianjin 300387, PR China. ⁎⁎ Correspondence to: X. Lu, School of Material Science and Engineering, Tianjin Polytechnic University, Tianjin 300387, PR China. E-mail addresses: [email protected] (Q. Gao), [email protected] (X. Lu).

http://dx.doi.org/10.1016/j.desal.2017.03.031 0011-9164/© 2017 Elsevier B.V. All rights reserved.

In typical AGMD configuration, there is a thin air gap between the membrane and cooling surface [4–6]. After passing through the membrane pores, the water vapor must move across the air gap, and finally condense at the cooling surface. The existence of an air gap helps to reduce conductive heat loss and improve heat efficiency. In AGMD process, condensation of the vapor and recovery of the latent heat can be simultaneously achieved inside the membrane module [7]. Therefore, AGMD has been considered as the most promising MD process in terms of heat recovery. However, the air gap increases mass transfer resistance [8], thereby reducing the distillate flux of the AGMD process. Under the same operating conditions, the flux of an AGMD process (with an air gap width of 5 mm) was only 1/8 of that from a DCMD process, as reported by Hsu [9]. It is known that non-condensable gases (such as air [10]) can to a certain extent dissolve in water. In MD process, the non-condensable gases (NCGs) that exist in the feed solution will be absorbed into the membrane pores, creating an additional diffusional resistance for vapor molecules and thereby reducing the distillate flux [1,4,11]. In an AGMD process, the NCGs will diffuse along with water vapor into the

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Nomenclature C Cp da df dm dh dw Dw-a g h ΔHv k kB Kn L m Nu P Pr q Q R Re S T t V v W λ δ σ ε τ ρ μ

Subscript a c f fw h m mm mol v va w wc

permeability coefficient, kg/(m2·h·Pa) specific heat capacity, kJ/(kg·°C) width of air gap, m thickness of condensate film, m thickness of membrane, m hydraulic diameter, m thickness of cooling wall, m diffusion coefficient of vapor molecules in the air, m2/s acceleration of gravity, m/s2 heat transfer coefficient, W/(m2·°C) enthalpy of water evaporation, kJ/kg thermal conductivity, W/(m·°C) Boltzman constant, 1.381 × 10−23 J/K Knudsen number length of membrane module, m molecular weight Nusselt number vapor pressure, Pa Prandtl number heat flux, J/m2 feed flow rate, L/h gas constant, 8.314 J/(mol·°C) Reynolds number surface area, m2 temperature, °C time, h diffusion volume, m3 velocity, m/s weight, kg mean molecular free path, m diameter of membrane pore, m collision diameter, m porosity tortuosity density, kg/m3 viscosity, Pa·s

air gap/air cold feed condensate film interface of condensate film and cooling wall hot feed membrane membrane material molecular diffusion vapor mixture of vapor and air water/cooling wall interface of cooling wall and cold feed side boundary layer

air gap, and then hinder the vapor diffusion and condensation heat transfer of water vapor [11–14]. These effects severely hamper the heat and mass transfer in the MD process. Therefore, it is necessary to remove NCGs to enhance the performance of the MD process. The predeaeration method, which applied in the Multi-stage Flash (MSF) is an effective way to solve the issue of NCGs in the MD process [15]. The most common way to remove the NCGs is by lowering the air pressure at the permeate side or air gap. In a VMD process, when

vacuum pressure is applied to remove the water vapor from the membrane module [16], the NCGs that exist in the membrane pores are also removed. Usually, the applied vacuum is lower than the saturation pressure of the hot feed and, as a result, the pressure difference across the membrane is very large. Meanwhile, the removal of the NCGs reduces the mass transfer resistance accordingly. Therefore, compared to the other three MD configurations, VMD can provide the largest driving force and the greatest distillate production [17,18]. In this case, the AGMD process is related to the principle of VMD that lowers the gas partial pressure in the air gap to remove the NCGs and improve the driving force [19,20]. This new process is a type of AGMD combined with VMD, but dominated by AGMD. Thus, to show its uniqueness, this process is called the vacuum assisted air gap membrane distillation (VA-AGMD) [21], as depicted in Fig. 1. Experimental studies by Alsaadi et al. [14], Guijt et al. [22] and Asghari et al. [23] indicated that the decline in the air gap pressure increased the distillate flux accordingly. Obviously, removing the NCGs can significantly enhance the distillate flux of the AGMD process. However, there are few studies focusing on the effect of the applied vacuum on the heat efficiency of the process. The heat efficiency of a thermal-based separation process is usually measured as the “gained output ratio” (GOR). Unfortunately, GOR of a conventional MD process was just 0.2–1.0 [24]. Further, a typical MD process consumes a large quantity of cooling water to condense vapor into pure water. High consumption of energy and cooling water seriously hinders the industrialization of the MD process. In recent years, some researchers have attempted to promote the heat efficiency of MD process. Lu [25] considered the heat recovery theory of the multiple effect distillation (MED) process and designed a novel MD process, which was referred to as multiple effect membrane distillation (MEMD). Undoubtedly, MEMD possesses the main technical merits of both MD and MED, which are efficient separation and heat recovery techniques, respectively. In the AGMD process, feed evaporation and heat recovery can be simultaneously achieved inside the module, similar to the function of MEMD. Therefore, the AGMD process can be regarded as a single-stage MEMD [26]. Thus, the study of the AGMD process must consider both membrane distillation flux (J) and heat efficiency (GOR). It is well known that when the environmental pressure is above the saturation pressure of the vapor, the vapor cannot be condensed into water. Therefore, in a VA-AGMD process, if the air gap pressure is lower than the saturation pressure of the cold feed temperature, the water vapor is ejected out of the module by the vacuum pump, instead

Fig. 1. Principle of the VA-AGMD process.

Z. Liu et al. / Desalination 414 (2017) 63–72

of condensing at the cooling surface. In this case, VA-AGMD becomes a VMD process, and its vapor heat cannot be recovered. For this reason, to consider both J and GOR, it is important to study the critical air pressure in the air gap. The critical air pressure is defined as the optimal vacuum pressure (OVP) in the present work. The promoting effect of a specific vacuum pressure on the performance of the hollow fiber membrane VA-AGMD process has been reported in the latest literature [27], but the concept of OVP has not been discussed in this literature. In this study, a VA-AGMD process was designed based on the double-pipe AGMD module, which was reported in the previous work [28]. The effect of vacuum pressure P under different parameters on the performance of the VA-AGMD process was experimentally investigated. Further, the effect of these parameters on the optimal vacuum pressure was the focus of this study. The parameters included the temperature difference (ΔT) between the hot feed outlet temperature (T2) and the cold feed inlet temperature (T3), the hot feed temperature (T1), the hot feed flow rate (Q), and the air gap width (da). 2. Theory 2.1. Radial mass transfer Fig. 2 shows the mass transfer process of AGMD, which mainly includes mass transfer across the membrane and mass transfer across the air gap. (i) Mechanism of mass transfer across the membrane According to the Darcy's Law, the permeate flux Jm is proportional with the vapor pressure difference across the membrane [29], and it can be expressed as: J m ¼ C m  ΔP m ¼ C m  ðP mh −P ma Þ

ð1Þ

where Cm is the permeability coefficient of the hydrophobic membrane, ΔPm is the vapor pressure difference across the membrane, Pmh and Pma are the partial vapor pressures on both sides of the membrane, respectively. Saturated vapor pressure of water can be calculated by Antoine equation [26]:
P ðT Þ ¼ exp 23:1964−

 3816:44 ðT þ 273:15Þ−46:13

ð2Þ

A proper model is important for the accurate prediction of the mass transfer of gaseous components through porous media. Fickian, StefanMaxwell [30–33] and dusty-gas model have been widely used in modeling mass transfer in porous membrane [34]. In MD process, the mass transfer across the membrane is generally described by dusty gas model [35,36]. This model consists of the Knudsen diffusion, the

Fig. 2. Schematic diagram of the mass and heat transfer process of AGMD.

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Fig. 3. Mass transfer mechanism of MD process in the dusty gas model [36].

molecular diffusion and the Poiseuille flow as well as their combinations, as shown in Fig. 3. In conventional AGMD process, total pressure is approximately equal to 1 atm and operating temperature is under 100 °C, so the Poiseuille flow can be neglected [37]. Knudsen number (Kn) is defined as the ratio of the mean free path of the transported molecules to the membrane pore diameter [37]: Kn ¼

λ δ

ð3Þ

where λ is the mean molecular free path, δ is the membrane pore diameter. As a binary mixture of air and water vapor, the mean free path λ of the vapor molecules in air can be calculated at the average membrane temperature (Tm) [37,38]: λ¼

kB T m πððσ w þ σ a Þ=2Þ2  P T

1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ðmw =ma Þ

ð4Þ

where kB is the Boltzman constant (1.381 × 10−23 J/K), PT is the total pressure (1 atm for AGMD), σw and σa are the collision diameters of water vapor (2.641 × 10−10 m) and air (3.711 × 10−10 m), respectively, mw and ma are the molecular weights of water and air, respectively. At the membrane temperature of 70–90 °C in this study, the mean free path of vapor molecules in air is 0.117–0.124 μm, lightly smaller than the membrane pore diameter (0.16 μm).

Table 1 Parameters of the double-pipe AGMD modules. Parameters

Module #1

Module #2

Module #3

Module #4

Effective length of module, m Shell inside diameter, mm Number of membranes Number of copper tubes Inner/outer diameters of copper tube, mm Effective evaporation surface areaa, m2 Effective condensation surface areaa, m2 Air gap width, mm Packing densityb, % Cross-section area of the hot feed channel, m2 Cross-section area of the cold feed channel, m2

0.70

0.55

0.55

0.55

27 27 27 2.0/3.0

27 24 24 2.0/3.0

27 24 24 3.0/4.0

20 24 24 1.6/2.0

4.8 × 10−2

3.3 × 10−2

3.3 × 10−2

3.3 × 10−2

11.9 × 10−2

8.3 × 10−2

12.4 × 10−2

6.6 × 10−2

0.45 4.5 0.14 × 10−4

0.45 4.0 0.12 × 10−4

0.95 4.0 0.12 × 10−4

0.25 7.3 0.12 × 10−4

3.7 × 10−4

2.3 × 10−4

2.3 × 10−4

2.3 × 10−4

Note: a Based on the inner diameter of membrane and copper tube, respectively. b Ratio of total membrane cross-section area (based on outer diameter) to shell crosssection area (based on inner diameter).

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Fig. 4. Configuration of the double-pipe AGMD module.

When 0.01 b Kn b 10, the Knudsen diffusion and the molecular diffusion existed simultaneously. The permeability coefficient of the Knudsen diffusion [39,40] can be described as: C Kn ¼


0:5 1 8mw εδ 3 πRðT m þ 273:15Þ dm τ

ð5Þ

where ε is the membrane porosity, dm is the thickness of the membrane, τ is the membrane pore tortuosity, R is the gas constant (8.314 J/ (mol·°C))。. The permeability coefficient of the molecular diffusion can be written as [40]: C mol ¼

Dw−a P tm ε mw Pm dm τ RðT m þ 273:15Þ

ð6Þ

where Ptm is the total pressure in the membrane pore, Pm is the logmean air pressure at both sides of the membrane, Dw-a is the diffusion coefficient of the vapor molecules in air and can be calculated by Fuller equation [41]: Dw−a ¼

T m 1:75 ð1=mw þ 1=ma Þ1=2  2 P V a 1=3 þ V w 1=3

ð7Þ

where Vw and Va are the diffusion volumes of water vapor and air, respectively.

So the total permeability coefficient Cm can be written as [40]:


 1 1 −1 þ C Kn C mol sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# (" )−1 3dm τ πRðT m þ 273:15Þ τdm P m RðT m þ 273:15Þ þ ¼ ε εδ 8mw Dw−a P tm mw

Cm ¼

ð8Þ

(ii) Mechanism of mass transfer across the air gap The permeate flux Ja is proportional with the vapor pressure difference across the air gap, and it can be expressed as:   J a ¼ C a  ΔP a ¼ C a  P ma −P af

ð9Þ

where Ca is the permeability coefficient in the air gap, ΔPa is the vapor pressure difference across the air gap, Pma and Paf are the partial vapor pressures at both sides of the air gap, respectively. Only the molecule diffusion existed in the air gap, so Ca can be described as [8]: Ca ¼

Dw−a P ta ε mw Pa da τ RðT a þ 273:15Þ

ð10Þ

where Pta is the total pressure in the air gap, Pa is the log-mean air pressure at both sides of the air gap, da is the air gap width, Ta is the air gap temperature. In typical AGMD process, the partial pressure of the NCGs in the membrane pores and the air gap is close to atmospheric pressure, so

Fig. 5. Schematic diagram of the VA-AGMD process.

Z. Liu et al. / Desalination 414 (2017) 63–72

67

Fig. 6. Effect of the vacuum pressure P on the performance of the VA-AGMD process. (T1 = 90.0 °C, ΔT = 10.0 °C and Q = 4.0 L/h)

the mass transfer process is controlled by the molecule diffusion. When the air gap is under vacuum pressure, pressure gradients will exist in air gap, so the viscous flow cannot be ignored any more. After the NCGs is completely removed, the molecule diffusion will eventually disappear [36].

(i) Heat transfer within the hot side boundary layer. The heat transfer within the hot side boundary per unit area is calculated by the following equation:

hh  dh kh

ð12Þ

Re  Pr 

0:33 ð13Þ

Re ¼

vh dh ρh μh

ð14Þ

Pr ¼

Cpμ h kh

ð15Þ

where vh, ρh, μh and Cp are the velocity, density, viscosity and the specific heat capacity of the hot feed, respectively. (ii) Heat transfer across the membrane Heat transfer across the membrane includes heat conduction and vapor latent heat through the membrane pores [8,43]. qm ¼ J m  ΔH v þ

where Nu is the Nusselt number, dh is the hydraulic diameter of the hot feed, kh is the thermal conductivity of the hot feed.

dh L

where Re and Pr are Reynolds number and Prandtl number, respectively, and can be described as [42]:

ð11Þ

where hh is the heat transfer coefficient of the hot feed, Th and Tmh are the bulk temperature of hot feed and the membrane/hot feed interface temperature, respectively. The heat transfer coefficient hh can be calculated by Nusselt equation [42]: Nu ¼


Nu ¼ 1:86

2.2. Radial heat transfer

qh ¼ hh ðT h −T mh Þ

Due to the low strength of hollow fiber membrane, the velocity of hot feed in the lumen of membrane must be lower than 0.6 m/s, in this case, the fluid is at laminar flow state. So Nu can be calculated by [42]:

km ðT −T ma Þ dm mh

ð16Þ

where ΔHv is the evaporation enthalpy of water, km is the thermal

Fig. 7. Schematic diagram of the effect of the vacuum pressure on the AGMD process.

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Z. Liu et al. / Desalination 414 (2017) 63–72

The thickness df can be calculated by [44]: 0

10:33 3μ f  J  A df ¼ @ gρ f ρ f −ρv

ð20Þ

where μf is the viscosity of the distillate, g is the acceleration of gravity, ρf and ρv are the densities of the distillate and the vapor, respectively. (v) Heat transfer across the cooling wall Heat transfer across the cooling wall can be described as: qw ¼

Fig. 8. Effect of the vacuum pressure P on the specific energy consumption. (T1 = 90.0 °C, ΔT = 10.0 °C and Q = 4.0 L/h).

conductivity of the membrane, dm is the thickness of the membrane and Tma is the membrane/air gap interface temperature. Since porous membrane consists of matrix and pores, so its thermal conductivity km is related with porosity, and can be expressed as: km ¼ ð1−ε Þkmm þ εkva

ð17Þ

where kmm and kva are the thermal conductivities of the membrane material and the gas mixture, respectively. (iii) Heat transfer across the air gap. In the air gap, heat transfer also consists of heat conduction and vapor latent heat transfer, and can be described as [8,43]: qa ¼ J a  ΔH v þ

 kva  T ma −T af da

ð18Þ

where da is the air gap width, Taf is the air gap/condensate film interface temperature. (iv) Heat transfer within the condensate film A thin condensate film will be formed when water vapor condensed into distillate at the cooling wall. Heat transfer within the condensate film can be written as: qf ¼

 kf  T −T fw d f af

ð19Þ

where kf is the heat conductivity of the distillate, df is the film thickness, Tfw is the condensate film/cooling wall interface temperature.

 kw  T −T wc dw fw

ð21Þ

where kw and dw are the heat conductivity and thickness of the cooling wall, respectively, Twc is the cooling wall/cold feed interface temperature. (vi) Heat transfer within the cold feed boundary layer The whole heat transfer process is completed after heat transported from the boundary layer to the bulk cold feed. qc ¼ hc ðT wc −T c Þ

ð22Þ

where hc is the heat transfer coefficient of the cold feed, and calculated by the same way with hh which is described in Eq. (12), Tc is the cold feed temperature. 2.3. Temperature polarization In the AGMD process, due to the existence of temperature boundary layer, the temperature difference (Tmh − Taf) across the membrane and the air gap is lower than the temperature difference between the bulk temperature of hot feed (Th) and cold feed (Tc). It leads to that the actual driving force is much lower than the theoretical one. This phenomenon is known as temperature polarization and described by the temperature polarization coefficient (TPC) [45]: TPC ¼

T mh −T af T h −T c

ð23Þ

3. Experimental 3.1. Membranes and modules The hydrophobic polyvinylidene fluoride (PVDF) hollow fiber membranes were fabricated by our research team. The details of the membrane preparation process and membrane properties have been

Fig. 9. Effect of the vacuum pressure P on the performance of the VA-AGMD process under various ΔT (Module #1, T1 = 90.0 °C and Q = 4.0 L/h).

Z. Liu et al. / Desalination 414 (2017) 63–72

69

Fig. 10. Effect of the vacuum pressure P on the performance of the VA-AGMD process under various T1 (Module #1, ΔT = 10.0 °C and Q = 12.0 L/h).

described in the previous works [3,46]. The mean pore size, porosity and inner/outer diameters of the membrane are 0.16 μm, 85% and 0.8/ 1.1 mm, respectively. Table 1 lists the parameters of the double-pipe AGMD modules. The configuration of the module is depicted in Fig. 4. Tap water was used as the feed solution, and its electrical conductivity is about 530 μS/cm. 3.2. Experimental apparatus The schematic of the VA-AGMD process is depicted in Fig. 5. To reduce heat loss, the entire circulatory system was wrapped with insulation cotton. In the thermostat (CS501, Shanghai Jinping Instrument Co., Ltd., Shanghai, China, 1500 W), the feed solution was heated to a constant temperature T1. It was then pumped into the lumen of the hollow fiber membranes at a constant flow rate Q by the magnetic pump (MP-55RZ, Zhejiang Xishan Pump Co., Ltd., Zhejiang, China, 90 W) and adjusted by the rotameter. After the vapor evaporated from the feed and diffused across the membrane into the air gap, the feed temperature dropped to T2. After that, the feed exited the module and flowed into Condenser 1; thus, its temperature further dropped to T3. Then, the feed flowed into the shell side of the copper tubes as cold feed. In the module, the cold feed flowed counter-currently to the hot feed. Thus, the cold feed can absorb the vapor heat and gradually warm up. Meanwhile, the vapor was condensed into pure water. Finally, the feed with temperature T4 flowed back into the feed tank. The vacuum pump (SHB-IIIA, Beijing Zhongxingweiye Instrument Co., Ltd., Beijing, China, 180 W) was used to control the air gap pressure (vacuum pressure) P. The vacuum degree was monitored by the mercury nanometer. The

buffer tank was used to protect the vacuum pump. After all the conditions (such as T2, T3, and P) attained a steady state, the distillate was collected and weighted every 6 min. A conductivity meter was used to measure the conductivity of the distillate to monitor any leakage in the module. A clamp meter (LA812201, Shanghai Lao A Tools Co., Ltd., Shanghai, China) was used to evaluate the energy consumption during the experiments. Each test was repeated thrice and the averages were reported [27]. 3.3. Performance of VA-AGMD process The performance of the VA-AGMD process is mainly characterized by J and GOR. Moreover, the specific energy consumption (SEC) is introduced to evaluate the energy consumption during the experiments. (i) J J is a significant parameter for characterizing the production capacity of the MD process, kg/(m2·h):

J¼

W St

ð24Þ

where W is the weight of the distillate water, kg, S is the effective surface area of the hollow fiber membrane (based on the inner diameter), m2, and t is the operating time, h. In this study, only the distillate that condensed inside the module was calculated. (ii) GOR.

Fig. 11. Effect of the vacuum pressure P on the performance of the VA-AGMD process under various Q (Module #1, T1 = 90.0 °C and ΔT = 10.0 °C).

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GOR is used to evaluate the heat efficiency of the MD process: GOR ¼

J  S  ΔH J  S  ΔH ¼ Q in Q  C p  ðT 1 −T 4 Þ

Table 2 Change of T4 with P under various da.

ð25Þ

where Qin is the heat input from the thermostat, kJ, Cp is the specific heat of the hot feed, kJ/(kg·°C), Q is the flow rate, L/h, T1 and T4 are the hot feed inlet temperature and the cold feed outlet temperature, respectively, °C, and ΔH is the evaporation enthalpy of the hot feed, kJ/kg, which can be calculated by [47]: ΔH ¼ 2258:4 þ 2:47½373:0−ðT þ 273:15Þ

ð26Þ

where T is the mean temperature of the hot feed in the module, °C. (iii) SEC SEC is the ratio of the total energy consumption in the operating time to the weight of the distillate, KWh/m3: SEC ¼

EC W

ð27Þ

where EC is the total energy consumption, KWh. 4. Results and discussion In all the experiments, the electrical conductivity of the distillate was under 15 μS/cm indicated that no leakage in the module, and thus, it is not mentioned in the following sections. The effect of vacuum pressure P under different parameters (T1, ΔT, Q, and da) on the performance of the VA-AGMD process was experimentally investigated. Moreover, the effect of these parameters on the optimal vacuum pressure was the focus of this study. 4.1. Effect of vacuum pressure P The effect of P on J and GOR is illustrated in Fig. 6. As can be observed, first, J and GOR showed a growing trend when P increased. However, in the change curves of J and GOR, there appeared an inflection point when P increased further. Beyond the inflection point, both J and GOR dropped significantly. The reasons for this phenomenon will be discussed in the Section 4.1.1 and Section 4.1.2. 4.1.1. Promoting of evaporation in the VA-AGMD process It is well known that the mass transfer driving force of MD process is the vapor pressure difference across the membrane. The increase of P in the air gap causes the vapor pressure difference to increase. Therefore, the driving force for the mass transfer is enhanced. Moreover, according to the Antoine equation, the boiling point of water is directly

P (MPa)

0 0.02 0.03 0.04

T4 (°C) 0.25 mm

0.45 mm

0.95 mm

79.0 79.4 79.7 79.7

79.5 79.7 79.7 79.8

79.0 79.5 79.5 79.7

proportional to the ambient pressure. Thus, the vacuum is conducive to the production of water vapor. Furthermore, a part of the NCGs were removed by the applied vacuum, which effectively weakened the mass transfer resistance. Therefore, J improves with the increase in P. The removal of the NCGs enables the water vapor to reach the cooling surface more easily and reduces the NCGs' concentration at the cooling surface. Consequently, the temperature and partial pressure of the vapor near the cooling surface increased, and the temperature difference across the condensate film increased accordingly [14]. Thus, the condensation heat transfer coefficient could be improved. Moreover, the increase in J means that more heat from the hot feed was used for evaporation, and additional vapor heat can be recovered by the cold feed. Therefore, with the increase in P, GOR also increased. 4.1.2. Weakening of condensation in the VA-AGMD process As shown in Fig. 6, when P further increased, both J and GOR dropped significantly. Theoretically, when the partial pressure of vapor is lower than the saturation pressure of the cold feed, the water vapor is ejected out the module by the vacuum pump, instead of condensing at the cooling surface. Certainly, along the axial direction of the module, the cold feed temperature decreased gradually from top to bottom, which means that the saturation pressure of the cold feed also decreased gradually. That is to say, when P reaches the saturation pressure of the cold feed in the upper side, a part of the vapor cannot condense at the corresponding cooling surface, as depicted in Fig. 7. Thus, this non-condensing vapor can only move down with the applied vacuum, occupying the space of the lower-temperature vapor and condensing at the colder surface. Such phenomenon was repeated continuously along the vertical direction of the air gap, until some vapor was ejected from the module. The heat recovery efficiency inside the module was one of the main aspects in the present work, and thus, only the vapor heat that was recovered by the cold feed in the module was considered. Then, only the weight of the distillate that is condensed inside the module was counted. Therefore, the overall amount of water vapor would increase when P increased to a large degree; however, the percent of vapor that condensed inside the module dropped and, as consequence, J decreased

Fig. 12. Effect of the vacuum pressure P on the performance of the VA-AGMD process under various da (Module #2, #3 and #4, T1 = 90.0 °C, ΔT = 10.0 °C and Q = 12.0 L/h).

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significantly. Because some vapor condensed in condenser 2 and its heat could not be recovered by the cold feed, T4 considerably decreased. Thus, GOR dropped as well. Hence, the inflection point of the change curve of J and GOR is OVP, which will be discussed in the following sections. 4.1.3. Specific energy consumption Regarding energy consumption, SEC of the VA-AGMD process was higher than that of the AGMD process, as can be seen in Fig. 8. This occurs because removing the NCGs by the vacuum pump also requires energy. Obviously, in the VA-AGMD process, when P increased from 0.02 MPa to 0.04 MPa, SEC was accordingly reduced. As mentioned in Section 4.1.1, J increased with the increase in P, and the weight of the distillate increased. Meanwhile, the energy consumed by the vacuum pump remained nearly constant, at approximately 233.2 W. Therefore, the specific energy consumption showed a negative correlation with P (under OVP). When P became equal to OVP, compared to the AGMD process, SEC of the VA-AGMD process did not increase significantly. For example, for module #1, SECs of AGMD and VA-AGMD were 120.9 KWh/ m3 and 140.2 KWh/m3, respectively. Such a result suggested that running a VA-AGMD process under OVP would not consume excessive energy. On the other hand, when P was higher than OVP, the effective weight of the distillate decreased and T4 dropped considerably, which caused the thermostat to consume more energy to keep T1 constant. Thus, the specific energy consumption increased significantly. 4.2. The optimal vacuum pressure of VA-AGMD process 4.2.1. Effect of temperature difference (ΔT) As can be seen in Fig. 9, when ΔT values were 3.0 °C, 5.0 °C and 10.0 °C, the optimal vacuum pressures in the air gap could reach 0.030 MPa, 0.040 MPa, and 0.040 MPa, respectively. Theoretically, as mentioned above, when T1 remained constant, a larger ΔT led to a lower cold feed temperature. Meanwhile, according to the Antoine equation, the saturation pressure of water decreases with a decrease in its temperature. Therefore, as ΔT increased, OVP improved. When the vacuum pressure achieved OVP, J could increase by 17.6%–22.4%, and GOR could increase by 20.0%–31.8%. It can be seen that the increase of GOR was more significant than J. The reason for such a phenomenon is that the vacuum pressure ensured that the vapor heat could easily to be absorbed by the cold feed, as mentioned in Section 4.1.1, and then T4 increased which means (T1–T4) dropped. If J increased and (T1–T4) dropped, according to Eq. (25), GOR increased more prominently than J. Such a result further proved that an appropriate vacuum pressure could significantly improve the heat efficiency. 4.2.2. Effect of hot feed temperature (T1) As shown in Fig. 10, when T1 values were 70.0 °C, 80.0 °C and 90.0 °C, the optimal vacuum pressures could reach 0.080 MPa, 0.060 MPa and 0.040 MPa, respectively. That is to say, with lower hot feed temperatures, the OVPs in the air gap were larger. The reason is that when ΔT was kept constant, a lower T1 led to a lower cold feed temperature, which means a lower saturation pressure of the cold feed. Thus, OVP increased. In the meantime, with the increase in P, the volume fraction of the NCGs decreased. Therefore, the promotion of J and GOR were more significant when T1 was lower. When T1 was 70.0 °C, J and GOR could be increased by about 50.0%. 4.2.3. Effect of feed flow rate (Q) Fig. 11 shows that all the OVPs were 0.04 MPa under different feed flow rates. It must be pointed out that OVP was influenced by temperature polarization. As mentioned in Section 2.2 (i), the fluid of the MD process was at laminar flow state. For example, when the feed flow rate was 12.0 L/h, the corresponding flow velocities of the hot feed vh and the cold feed vc were 0.25 m/s and 0.01 m/s respectively, and the corresponding Reynolds numbers Re were 606.7 and 252.6,

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respectively. Under laminar flow, a boundary layer was formed at the interface of the fluid and channel wall when the feed flowed in the channel. Because of the boundary layer, the heat transfer process of MD was affected by temperature polarization. As shown in Fig. 2 and Section 2.3, the actual driving force (Tmh − Taf) of the AGMD process was lower than the apparent driving force (Th − Tc). In this study, the measuring temperature T4 was the bulk temperature of the cold feed outlet (Tc), and its corresponding Taf could be far higher, because of temperature polarization. In this case, when the air gap pressure was lower than the saturation pressure at Taf, instead of T4, some water vapor could not condense at the cooling surface and was ejected from the module along with the NCGs. Theoretically, the increase of Q might weaken the effect of temperature polarization. Thus, Taf could get close to T4. However, the flow velocity of the cold feed was lower than 0.01 m/s even if Q was 12.0 L/h. At this point, the feed flow velocity was too low to weaken the temperature polarization. Therefore, there was still a large gap between Taf and T4. As a result, the increase of Q did not cause the OVP to increase accordingly. 4.2.4. Effect of air gap width (da) As can be seen from Fig. 12, under different air gap widths, the OVPs were 0.04 MPa. The air gap width can affect the mean temperature of the feed in the module (which is the reason for the variations of J and GOR). However, when other conditions were kept constant, the changes of T4 were very light, as observed in Table 2. Therefore, because OVP was closely related to T4 (Taf), all OVPs were 0.04 MPa under different air gap widths. 5. Conclusions This study showed that applying vacuum (within a certain range of vacuum pressure) that can remove the NCGs and effectively increase the vapor pressure difference, the VA-AGMD process could significantly improve J and GOR. Compared to AGMD, J and GOR of the VA-AGMD process could be increased by 20%–50%, and the specific energy consumption did not increase significantly. On the other hand, when the vacuum pressure was too large, water vapor could not condense at the cooling surface in the module and its vapor heat could not be recovered. The optimal vacuum pressure is then a critical factor to ensure that the VA-AGMD process is dominated by AGMD, rather than VMD. Within the experimental range, when T1 values were 70.0 °C, 80.0 °C and 90.0 °C, the OVPs in the air gap could reach 0.080 MPa, 0.060 MPa, and 0.040 MPa, respectively. The results showed that in a VA-AGMD process, it is necessary to select an appropriate vacuum pressure according to the operating conditions. Additionally, we believe that in a large-scale application, with the help of highly efficient thermostat and pumps, the total energy consumption of the VA-AGMD process can be further reduced. Acknowledgement The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (Grant No. 51278336 and 51578376), Tianjin Science and Technology Support Program of China (Grant No. 15ZCZDSF00070), The Science and Technology Plans of Tianjin (No·15PTSYJC00240), The Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) of Ministry of Education of China (Grand No. IRT13084), and The Marine Science and Technology Project of Tianjin Province (KJXH2014-03). References [1] A. Alkhudhiri, N. Darwish, N. Hilal, Membrane distillation: a comprehensive review [J], Desalination 287 (8) (2012) 2–18. [2] E. Drioli, A. Ali, F. Macedonio, Membrane distillation: recent developments and perspectives [J], Desalination 356 (2015) 56–84.

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