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Study on the heat and mass transfer in air-bubbling enhanced vacuum membrane distillation
Desalination 373 (2015) 16–26
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Desalination journal homepage: www.elsevier.com/locate/desal
Study on the heat and mass transfer in air-bubbling enhanced vacuum membrane distillation Chunrui Wu a,⁎, Zhengang Li a, Jianhua Zhang b, Yue Jia a, Qijun Gao a, Xiaolong Lu a,⁎ a b
State Key Laboratory of Separation Membranes and Membrane Processes, Institute of Biological and Chemical Engineering, Tianjin Polytechnic University, Tianjin 300160, P.R. China Institute of Sustainability and Innovation, Victoria University, PO Box 14428, Melbourne, Victoria 8001, Australia
H I G H L I G H T S • MD flux could be improved 100% by air-bubbling and gas–liquid two phase flow method. • Two phase flow pattern is the key factor affecting the performance of MD process. • Mathematic model based on flow pattern was built and AVMD performance was explained.
a r t i c l e
i n f o
Article history: Received 17 February 2015 Received in revised form 11 June 2015 Accepted 1 July 2015 Available online 10 July 2015 Keywords: Membrane distillation Vacuum membrane distillation Heat and mass transfer Hollow fiber membrane Two phase flow
a b s t r a c t Air-bubbling vacuum membrane distillation (AVMD) process was designed to boost the heat and mass transfer in membrane distillation (MD). Both effect of flow pattern on the performance of AVMD process and the heat and mass transfer mechanism in this process were studied in this paper. The results showed that the performance of VMD was improved obviously by air-bubbling method. The flux was doubled at certain feed velocity and gas/ liquid proportion. The study showed that flow pattern was the key factor affecting the mass and heat transfer efficiencies. The heat transfer coefficients, corresponding to the two main flow patterns in AVMD process, bubbly Pr ðμ b =μ w Þ0:14 λ=dÞ and slug flow ðh f slu ¼ 0:0632Re1:0420 Pr ðμ b =μ w Þ0:14 λ=dÞ, were flow ðh f bub ¼ 1:7527Re0:4215 tp tp obtained and employed in the modeling of AVMD process. The modeling results showed that the theoretical prediction of flux aligned with experimental results well, in which the error was within ±5%. Both variations of Temperature Polarization Coefficient (TPC) and Concentration Polarization Coefficient (CPC) in AVMD process were studied based on the obtained correlations. And the result showed that both TPC and CPC were significantly influenced by the flow patterns. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Membrane distillation (MD), an innovative separation process which combines distillation and membrane technology, has gained worldwide attention and been developed rapidly since it was invented in 1960s [1–3]. Compared to other desalination technology such as Reverse Osmosis and Multi-Flash, MD has quite a few distinctive advantages such as the ability of treating extra-high concentration solutions, high rejection for nonvolatile components, lower operating temperature and pressure, less distillation space requirement and the ability of using low grade heat [2,3]. Many processes and configurations of MD have been developed, and widely employed in sea and brackish water desalination, industrial wastewater treatment, food industry, petro chemistry, chemical engineering, et al. [4–8]. In MD process, water
⁎ Corresponding authors at:399# Binshui West Road, Xiqing District, Tianjin P.R. China. E-mail addresses: [email protected], [email protected] (C. Wu), [email protected] (X. Lu).
http://dx.doi.org/10.1016/j.desal.2015.07.001 0011-9164/© 2015 Elsevier B.V. All rights reserved.
1 3
1 3
molecules or other volatile components evaporate at the membrane pore entrance (feed side), cross the membrane pores in vapor phase, and finally condense in the cold side or be removed as vapor from the membrane module [9]. However, concentration and temperature polarization caused by liquid boundary layer are the major barriers inhibiting heat and mass transfer from the bulk stream to pore interface [10–13]. To solve the problem, different techniques have been developed. Teoh et al. [14] achieved 20–28% flux increase by adding baffles and spacers in membrane channel, and modifying the geometry of the hollow fiber in direct contact membrane distillation (DCMD) process. Yang et al. [15] achieved great flux increase by modifying hollow fiber membrane configurations in DCMD experiments in which the modules with undulating membrane surfaces (curly and spacer-knitted fibers) achieved up to 300% flux enhancement in laminar flow region. Liu et al. [16] designed coiled hollow fiber membrane modules for sweeping gas membrane distillation (SGMD) and the flux was improved by about 200%. Zhu et al. [3] obtained 25% flux enhancement by using ultrasonic technology in air gap membrane distillation (AGMD). Li et al. [17,18] found that cross-flow hollow fiber module could ensure a high heat transfer
C. Wu et al. / Desalination 373 (2015) 16–26
coefficient at low Reynolds number (Re) in both vacuum membrane distillation (VMD) and DCMD processes. By modifying the hot feed flow direction and the air gap configuration, Tian et al. [19] boosted the permeation flux up to 2.5-fold in comparison with the conventional design. Gas/liquid two phase flow technology has been well developed to minimize the boundary layer effect in microfiltration, ultrafiltration, membrane bioreactor and other traditional membrane separation processes [20–27]. Recently, Chen et al. [28] incorporated gas bubbling into DCMD process, and studied both its effect on reducing the concentration polarization and temperature polarization, and influence of bubble size distribution on the gas-bubbling performance [29]. Ding et al. [30] also found that the membrane fouling in DCMD for concentrating the extract of Chinese traditional medicine can be effectively controlled by optimizing gas bubbling parameters. Many models [1,13] have been developed to research the heat and mass transfer mechanism in MD. However, these models only studied single phase flow on either side of the membrane. Therefore, those models cannot be employed to explain the phenomenon in MD process that both gas and liquid phase exit in one stream (hot and/or cold stream). Influence of gas/liquid two phase flow on heat transfer has been established [31–33] in conventional heat transfer studies. However, in these researches, the mass transfer occurred simultaneously with heat transfer in MD has not been investigated. Although previous works confirmed experimentally in DCMD process that gas/liquid two phase flow was able to minimize boundary layer effect and enhance heat and mass transfer, there is no systematically theoretical study on the heat and mass transfer mechanism for bubbling-enhanced MD process, especially for VMD process. Therefore, it is necessary to develop the heat and mass transfer model suitable for bubbling-enhanced VMD process. In this paper, an air-bubbling enhanced vacuum membrane distillation (AVMD) process designed by our team [34,35] was studied experimentally and theoretically, and heat and mass transfer in this process was modeled. By combining the basic mechanism of MD process and the method of fitting gas/liquid two phase flow heat transfer correlations, the heat and mass transfer model suitable for AVMD process was established. Using the obtained heat and mass transfer correlations, the variations of TPC and CPC were studied at different patterns. 2. Theory In the gas/liquid two phase flow system, gas only intensifies mixing of feed solution and enhances surface shear rate, but the liquid boundary layer on the membrane surface still exists [36]. Furthermore, in the MD process, the liquid phase protrudes into the pores as a lid due to the hydrophobicity of the membrane [37], which makes the air bubble isolated from the pores. Therefore, it can be assumed that gas bubbles will not interfere with the mass transfer in membrane pores and alter the main principle of transmembrane mass transfer in AVMD process. Since liquid boundary layer still exists in the gas/liquid two phase flow system, the law of heat and mass transfer between the bulk phase and membrane interface in VMD process is also applicable to AVMD process. 2.1. Heat and mass transfer For VMD process, both Knudsen diffusion and Poiseuille flow make contributions to transmembrane mass transfer [38] and the MD flux J can be calculated as:
J¼
rε 1:064 τδ
sffiffiffiffiffiffiffiffiffi ! M r 2 ε MP m þ 0:125 P T fm −P T p RT m τδ μRT m
ð1Þ
17
where r is the membrane pore radius; ε is the membrane porosity; δ is the membrane thickness; τ is the pore tortuosity; μ is the dynamic viscosity of water vapor; M is the molecular weight of water; R is the gas constant; P(Tfm) and P(Tp) are the vapor pressure as function of Tfm and Tp; Tfm and Tp are the membrane interface temperature on the feed and the permeate sides; Tm is the average temperature in membrane pores, Tm = (Tfm + Tp) / 2; Pm is the average vapor pressure in membrane pores, Pm = [P(Tfm) + P(Tp)] / 2; P(Tfm) and P(Tp) can be calculated using the Antoine's equation (Eq. (2)) [13]: P T fmðpÞ ¼ exp 23:238−
! 3841 : T fmðpÞ −45
ð2Þ
With the measurable J and P(Tp) as well as other membrane parameters, the unknown parameter Tfm can be calculated via the combination of Eqs. (1) and (2) [9]. In MD system, the heat flux across the liquid boundary layer (feed side), Qf, can be expressed as Eq. (3): Q f ¼ h f A f T f −T fm
ð3Þ
where hf is heat transfer coefficient of the bulk phase; Tf is the temperature of the bulk phase, Tf = (Tin + Tout) / 2; Af is the effective inner surface area of the hollow fiber membranes, Af = πLd; L is the effective length of the membrane module; d is the inner diameter of hollow fiber membrane. The inlet temperature Tin can be measured and the outlet temperature Tout can be calculated via the combination of Eqs. (4) and (5): C p mðT in −T out Þ ¼ JΑm ΔΗ m ¼ ρl V l ¼ ρl U l Asec ¼ Retp
ð4Þ μg Asec ≈Retp μ l Asec =d μ g =μ l þ U g ρg =U l ρl d
ð5Þ
where Cp is specific heat of the feed; m is the mass flow rate of the feed solution; Am is the effective area of the transmembrane heat transfer, Am = πL(D − d) / ln(D/d), D is the outer diameter of hollow fiber membrane; Asec is the cross section area of the hollow fiber membranes based on the inner diameter of hollow fiber membrane; ρg and ρl are densities of air and water; Ug and Ul are superficial velocities of air and water; μg and μl are dynamic viscosities of air and water. ΔH is the latent heat of vapor at temperature of Tfm and it can be calculated via Eq. (6): ΔH ¼ 2258:4 þ 2:47 373:0−T fm :
ð6Þ
The overall heat-transfer flux across the membrane, Q, is expressed as Eq. (7): Q ¼ JΔHAm þ
hm Am T fm −T pm δ
ð7Þ
where hm is the thermal conductivity of hollow fiber membrane, hm = (1 − ε)hs + εhg; hs and hg are separately the thermal conductivity of polymer and gas (usually air); Tpm is the membrane surface temperature in the permeate side. Similar to VMD process, the contribution of the heat conduct through the membrane matrix in AVMD (i.e., hmAm(Tfm − Tpm) / δ) can be neglected due to the high vacuum degree in the permeate side [17]. Therefore, Eq. (7) can be simplified to Eq. (8):
Q ¼ JΔHAm :
ð8Þ
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Table 1 Parameters of the hollow fiber membrane. Inner diameter (mm)
Outer diameter (mm)
Membrane thickness (mm)
Pore radiusa (μm)
Tortuosity factora
Porosityb (%)
0.80
1.1
0.15
0.16
1.41
80
a
The two parameters were measured by gas permeation method [38]. The membrane porosity was measured by a gravimetric method [38].
b
According to Qf = Q, heat transfer coefficient on the feed side hf can be calculated via the combination of Eqs. (3) and (8): hf ¼
JΔHAm : T f −T fm A f
ð9Þ
In order to get J–T f theoretical curve, the relation between Pr and T was necessary. By fitting the data of pure water Prandtl number Pr at different temperature T [39], the relation between them can be expressed as: Pr ¼ 345:6866−2:7453 T þ 0:00737 T 2 −6:6464 10−6 T 3 :
ð10Þ
2.2. Modeling of heat and mass transfer in the feed side
Nu ¼ aRebtp Pr ðμ b =μ w Þ0:14
ð11Þ
1 3
where Nu = hfd/λ, Retp = Rel + Reg = dUlρl/μl + dUgρg/μg, Pr = Cpμ/λ; Retp is gas/liquid two phase flow Reynolds number; Rel and Reg are liquid and gas phase Reynolds numbers, Rel = dUlρl/μl, Reg = dUgρg/μg; a and b are parameters need to be calculated. Rearranging Eq. (11) and taking logarithm on both sides, it could be re-expressed as Eq. (12): Nu Pr ðμ b =μ w Þ0:14 1 3
¼ lga þ b lgRetp :
ð12Þ
When other experimental conditions had been given (i.e., the feed inlet temperature at 70 °C, vacuum pressure at 90 kPa and Ug/Ul = 0.50), and only varying Ul, the constants a and b could be obtained from the intercept and the slope by plotting lg[Nu / (Pr1/3(μb/μw)0.14)] against lgRetp. Hence, the heat transfer correlation suitable for AVMD process could be determined. As mentioned above, in the gas/liquid two phase flow system, liquid boundary layer on the membrane interface is still in continuous state. Therefore, the Chilton–Colburn analogy expressed as in Eq. (13) is applicable to calculate the solute mass transfer coefficient (ks) [36].
Sh Nu ¼ Sc Pr 1 3
Sh ¼ aRebtp Sc ðμ b =μ w Þ0:14 :
ð13Þ
1 3
where Sh = ksd/Ds, Sc = μ/(ρDs); Ds is solute diffusion coefficient.
ð14Þ
1 3
2.3. Calculation of TPC and CPC TPC refers to ratio of the temperature difference between the interfaces on both sides of the membrane, to the temperature difference between the bulky flows on both side of the membrane, which is an important factor to assess the thermal efficiency of MD process. In VMD (AVMD) process, TPC is usually simply defined as [40–42]: TPC ¼
According to the method from H. Groothuis et al. [31], Eq. (11) was used in our study for calculation of Nusselt Number Nu of the air/water two phase flow:
lg
Substituting Eq. (11) into Eq. (13) and Sh can be calculated by Eq. (14):
T fm : Tf
ð15Þ
The presence of solute in the feed reduces the partial pressure of the water vapor, so as to reduce the driving force in MD. As the existence of boundary layer and evaporation of the vapor to the permeate side, the solute concentration in the boundary layer becomes much higher (sometimes even saturated) than bulky flow, which is called concentration polarization (CP) phenomenon. The term concentration polarization coefficient, CPC, is defined to quantify the mass transport resistance within the concentration boundary layer on the feed side, and it refers to ratio of the salt concentration at the hot membrane surface to the salt concentration in the feed bulk solution. CPC can be calculated by the Eq. (16): CPC ¼
cfm J ¼ exp : ρks cf
ð16Þ
3. Experimental 3.1. Materials and equipment The hydrophobic polyvinylidene fluoride (PVDF) hollow fiber membranes fabricated by our team were used in the study, and the relevant membrane parameters were listed in Table 1. The hydrophobic hollow fiber membranes were fixed in a plastic cylindrical membrane module and relevant module specifications were listed in Table 2. The inlet temperature of feed solution was maintained by a thermostatic water bath (501A, Shanghai Jingke Co. Ltd. China), with a temperature accuracy of ± 0.1 °C. Mercurial thermometers with an accuracy of ± 0.1 °C were used for measuring the inlet and outlet temperature of feed flow. Electronic balance with an accuracy of ±0.1 g
Table 2 Specifications of hollow fiber membrane module. Module diameter (mm)
Module length (cm)
Effective fiber length (cm)
Membrane number
Membrane area (m2)
32
23
21
50
0.025
C. Wu et al. / Desalination 373 (2015) 16–26
Fig. 1. Flow chart of AVMD process. 1. water bath; 2. pump; 3. liquid flowmeter; 4. gas flowmeter; 5. pressurizer; 6. gas pump; 7. manometer; 8. thermometer; 9. hollow fiber membrane module; 10. buffer bottle 11. condenser; 12. vacuum pump; 13. product collection; 14. electronic balance.
was used for measuring the weight of the product water. To minimize the concentration polarization effect, pure water was used as the feed in the study of heat transfer mechanism. In the study of concentration polarization effect, the feed solution was 3.5 wt.% NaCl solution.
19
Fig. 3. Variation of MD flux with the increase of Ug/Ul at varied Ul. (Feed inlet temperature: 70 °C; vacuum pressure: 90 kPa). (★ bubbly flow, ▼▲●■ slug flow, ▽△○□ single phase flow).
was repeated three times and all data were the average of the three repeats.
4. Results and discussion 4.1. Determining the optimal Ug/Ul
3.2. Experimental setup and operation method The flow chart of AVMD experiment was shown in Fig. 1. Feed solution inlet temperature was controlled constant by the thermostatic water bath. The feed air was also heated by the thermostatic water bath to the same temperature of feed solution when the air passing through the copper tube immersed in the hot water. Feed solution was circulated through the lumen side of the hollow fiber membranes by a circulation pump. After pressure was stabilized by pressurizer, the clean air was injected into the inlet of the module. The velocities of the hot feed solution and air were controlled and monitored by liquid and gas flowmeters, respectively. A vacuum pump with a pressure controller was connected to the shell side of the module to create the vacuum and remove the permeation vapor. The water vapor pressure in the vacuum side was measured by a vacuum gauge. Each experiment
According to the conventional gas/liquid two phase flow heat transfer theory, flow pattern is the key factor affecting the heat transfer efficiency [43]. Therefore, it might also be the key factor affecting both heat and mass transfer efficiencies in the AVMD process. In vertical upward tubular channels, bubbly flow, slug flow, churn flow and annular flow will occur in sequence as increasing the gas/liquid velocity ratio (Ug /Ul ) [44]. Churn flow and annular flow will occur only when gas superficial velocity is more than 5 m/s and 10 m/s for vertical upward tubular channels [44]. However, in our experiments, gas superficial velocity was controlled less than 5 m/s. Thus, bubbly flow and/or slug flow were the dominant flow patterns in this study. In order to identify the flow pattern of gas/liquid two phase flow, methods, such as flow pattern maps and flow pattern discriminant,
Fig. 2. Relationship between flow pattern discriminant curve and straight lines of Ul = Ug/k.
Fig. 4. Relationship between lg[Nu / (Pr1/3(μb/μw)0.14)] and lgRel of VMD process.
20
C. Wu et al. / Desalination 373 (2015) 16–26
have been developed. However, most of flow pattern maps contained only gas and liquid superficial velocities or other conversion parameters based on them. The other factors (pipe diameter, gravitational acceleration etc.) which affected the formation of flow patterns had not been involved in these flow pattern maps, which limited its application in identification of the flow pattern of gas/liquid two phase flow, especially in the transition area of the flow pattern. Therefore, the flow pattern discriminant proposed by Weisman [45] including gas and liquid superficial velocities, as well as pipe diameter and gravitational acceleration, was used to identify the flow pattern in AVMD process, which can be expressed as Eq. (17).
Ug Ug þ U pffiffiffiffiffiffi N0:45 pffiffiffiffiffiffi l gd gd
!0:78 ð17Þ
where g is gravitational acceleration, d is the pipe diameter. Substituting g = 9.81 m/s2 and d = 0.80 × 10− 3 m into inequality (17) and rearranging gave Eq. (18):
Fig. 5. Relationship between lg[Nu / (Pr1/3(μb/μw)0.14)] and lgRetp of AVMD process. (■ bubbly flow, △ slug flow).
4.2. Setup of heat transfer correlations 5:69U 1:282 −U g NU l : g
ð18Þ
Plotting the equation curve of 5.69Ug1.282 − Ug = Ul in Fig. 2 and the flow pattern discriminant curve was obtained. Defined the gas/liquid velocity ratio k = Ug/Ul, then Ul = Ug/k. Took different values of k, straight lines of Ul = Ug/k were also plotted in Fig. 2. In the range of 0 m/s b Ug b 1.0 m/s and 0 m/s b Ul b 1.5 m/s, Fig. 2 is divided into two parts by the discriminant curve. The upper left part belongs to bubbly flow region, the lower right part belongs to slug flow region. When k b 0.29, all data points fall into bubbly flow region; when k N 0.29, data points falling into slug flow region become more and more with the increase of k. Since the heat transfer enhancement effect of slug flow is much better than that of bubbly flow [45], the greater value of k (i.e., Ug/Ul) should be selected to make more data points fall into slug flow region, as shown in Fig. 2. The effect of Ug/Ul on MD flux was studied and the results were shown in Fig. 3. The flow pattern of each experimental point was determined according to the flow pattern discriminant and represented by different symbols (except for the solid star points for the bubbly flow, all the other solid points for the slug flow). As shown in Fig. 3, the air bubbling could enhance the flux of MD process, and the enhancement effect was affected by both Ul and Ug/Ul. For each given Ul, the obvious flux increase rate was observed as the flow pattern transiting from bubbly flow to slug flow. However, when Ug/Ul N 0.50, the trend of flux increase rate plateaued, and slightly declined after Ug/Ul N 0.65. The figure also showed that the enhancement effect of Ug/Ul became much obvious as at higher liquid flow rate. The main effect of air bubbles was to create even flow distribution, intensify mixing and enhance surface shear rate. In bubbly flow region (Ug/Ul was relative smaller), air bubbles increased the disturbance degree of feed solution which enhanced the heat and mass transfer efficiency, so as to increase the flux. As Ug/Ul increased to a certain value, the flow pattern transited to slug flow. Compared with the bubbly flow, slug flow could generate larger wake region to make surface shear rate higher and achieve better enhancement effect [43]. As Ug/Ul reached 0.50, gas slug should have occupied almost the entire cross section of the lumen, and would not possible increase any more. Therefore, there was not further enhancement effect that could be achieved when k was greater than 0.50. However, as the air ratio became higher, more heat was taken away by the air, which might reduce the flux. Based on the above analysis, there was an optimal Ug/Ul for AVMD process and it was 0.50 in our experiment.
Fitting equation shown in Fig. 4 represents heat transfer correlations in VMD process based on the method in Section 2.2, which is used for comparing the heat transfer change due to the air bubbling enhancement. The correlation constants of the AVMD process at k = 0.50 were also achieved by plotting lg[Nu/(Pr1/3(μb/μw)0.14)] against lgRetp in Fig. 5. In Fig. 4, it could be seen that lg[Nu / (Pr1/3(μb/μw)0.14)] against lgRel showed a good linear correlation in VMD process based on our experimental results. However, the obtained linear slope is about 0.35 in the laminar region (Rel b 2100), which is greater than the value (0.33) in the conventional study of heat transfer in the circular tube [46]. It might be resulted from the experimental conditions, because the measured vapor pressure value (actually was the total pressure) in the vacuum side was greater than the real vapor pressure value (should be partial pressure) due to existence of the air residual. Therefore, the calculated temperature in the vacuum side (Tp) was slightly higher than the real value. As a result, Tfm was slightly higher than the real value based on the measured flux. Based on the fixed temperature at the bulk phase (Tf) and the measured flux (J), heat transfer coefficient (hf) was slightly higher than the real value according to Eq. (9). Thus, the index of Rel was slightly larger than 0.33.
Fig. 6. Relationship between Tfm and Tp corresponding to different Retp. (Ug/Ul = 0.50; feed inlet temperature: 70 °C; vacuum pressure: 90 kPa).
C. Wu et al. / Desalination 373 (2015) 16–26
As shown in Fig. 5, the data did not present very good linear relationship in the overall range of the AVMD test as that of the VMD. However, when the tests fell into the same flow pattern region based on inequality (18), i.e., lgRetp b 2.66 (bubbly region) or lgRetp N 2.66 (slug flow region), the lgRetp showed good linear relationship to lg[Nu/(Pr1/3(μb/μw)0.14)]. Therefore, two fitting equations were used respectively for bubbly flow and slug flow, as shown in Eqs. (19) and (20): Bubbly flow: Pr Nubub ¼ 1:7527Re0:4215 tp
1 3
μb μw
0:14 :
ð19Þ
21
Slug flow: Pr Nuslu ¼ 0:0632Re1:0420 tp
1 3
μb μw
0:14 :
ð20Þ
The corresponding mass transfer correlations could be obtained according to Eq. (14). The critical transition Ug and Ul values between the bubbly and slug flow could be calculated by combining Ul = 5.69U1.282 − Ug and g the k value used in the experiments. Therefore, if k = 0.50, based on Retp = dUlρl/μl + dUgρg/μg, the critical Retp of flow pattern transition could be determined and it was Retp(c) = 457. Thus, when 0 b Retp b
Fig. 7. Calculation flow chart of implicit equations containing only J and Retp.
22
C. Wu et al. / Desalination 373 (2015) 16–26
457, the flow pattern was bubbly flow, Eq. (21) could be used to calculate the value of heat transfer coefficient at bubbly flow (hf bub): h f bub ¼ 1:7527Re0:4215 Pr ðμ b =μ w Þ0:14 λ=d: tp 1 3
ð21Þ
According to the data we measured in Fig. 5, the flow pattern was still slug flow when lgRetp b 3.6 (Retp b 4000). Therefore, when 457 b Retp b 4000, Eq. (22) could be used to calculate the value of heat transfer coefficient at slug flow (hf slu): 1:0420 h f slu ¼ 0:0632Retp Pr ðμ b =μ w Þ0:14 λ=d: 1 3
ð22Þ
listed in the figure. By comparing the experimental with the theoretical data of MD flux, it could be found that J–Retp theoretical data predicted the experimental results well, and the maximum error was within 5%. This demonstrated the feasibility of the obtained two phase flow heat transfer correlations in their application scope. Furthermore, it could be observed that the AVMD flux increase rate at slug flow was much higher than that of bubbly flow. Fig. 8 also showed that experimental values were all smaller than modeled ones, which might be caused by the heat lost of hollow fiber membrane module and/or the vapor pumped out by the vacuum pump. In addition, the experimental flux of the VMD process was also presented in Fig. 8, which was much lower than that of AVMD. It indicated that the heat transfer efficiency was enhanced greatly by the introduction of air bubbles.
4.3. Validating heat transfer correlations 4.3.2. Setting up and validating J–Tf theoretical curve 4.3.1. Setting up and validating J–Retp theoretical curve 4.3.1.1. Determining the relationship between Tfm and Tp. For the heat and mass transfer across the membrane, the actual net driving force was related to the net temperature difference over the membrane which solely determined the flux. Keep other operating parameters (feed inlet temperature, vacuum pressure and gas/liquid velocity ratio k) constant and only change Ul, the membrane surface temperature was only determined by Retp at different flow patterns. In order to build the relationship between flux J and Retp, the relation between Tp and Tfm was necessary. At the given experimental conditions (the feed inlet temperature at 70 °C, vacuum pressure at 90 kPa and k = 0.50), varying Ul and Ug was varied, flux J and Tp at different Retp (100 b Retp b 3000) could be obtained experimentally. Then, Tfm at different Retp could be calculated by combining Eqs. (1) and (2). In Fig. 6, the relationship of T p against T fm was shown at the given k = 0.50. In Fig. 6, Tp and Tfm presented a good linear relationship which was independent from the flow pattern, and the fitting equation is shown in Eq. (23). T p ¼ 57:953 þ 0:8131T fm
ð23Þ
4.3.1.2. Comparison of J–Retp theoretical curve with experimental value. In order to draw J–Retp theoretical curves, the implicit equations containing only J and Retp were needed, and Fig. 7 showed the calculation flow chart of these implicit equations. According to these obtained implicit equations, J–Retp theoretical curves corresponding to bubbly flow and slug flow were drawn by Matlab software, as shown in Fig. 8. The experimental data were also
4.3.2.1. Determining the relationship between Tfm and Tp. In order to get J–Tf theoretical curves under different Ul, the relation between Tp and Tfm was also necessary. With a given experimental condition: vacuum pressure of 90 kPa and Ug/Ul of 0.50, AVMD flux J and Tp could be obtained experimentally by varying the feed inlet temperatures (333.15 K b Tin b 363.15 K). The relations (Eqs. (24a)–(24e)) between Tp and Tfm corresponding to different Ul can be obtained by using the same method as Section 4.3.1.1: U l ¼ 0:20 m=s : T p ¼ 24:256 þ 0:9088T fm
ð24aÞ
U l ¼ 0:60 m=s : T p ¼ 21:585 þ 0:9149T fm
ð24bÞ
U l ¼ 0:70 m=s : T p ¼ 19:1269 þ 0:9235T fm
ð24cÞ
U l ¼ 1:20 m=s : T p ¼ 15:9068 þ 0:9339T fm
ð24dÞ
U l ¼ 1:30 m=s : T p ¼ 15:0039 þ 0:937T fm :
ð24eÞ
4.3.2.2. Comparison of J–Tf theoretical curve with experimental value. In order to draw J–Tf theoretical curves, the equations with variables J and Tf are necessary, and Fig. 9 showed the calculation flow charts of these equations. In the range of 315 K b Tf b 355 K, based on these equations, J–Tf theoretical curves at different Ul drawn by Matlab software were shown in Fig. 10. By comparing with the experimental flux which was also listed in this figure, it could be found that the J–Tf theoretical curves at different Ul could predict MD flux very well, which demonstrated that
Fig. 8. Comparison of J–Retp theoretical curve and experimental value. (Ug/Ul = 0.50; feed inlet temperature: 70 °C; vacuum pressure: 90 kPa). (● two phase flow, ▲ single phase flow).
C. Wu et al. / Desalination 373 (2015) 16–26
23
Fig. 9. Calculation flow chart of equations containing only J and Tf.
4.4. Effect of operation parameters on TPC and CPC
was higher than that at bubbly flow. This further demonstrated that heat transfer efficiency at slug flow was much higher than that at bubbly flow. In addition, CPC decreased with increasing Retp and the CPC decrease rate was enhanced as the flow pattern transit from slug flow to bubbly flow. It was mainly because that slug flow could generate larger wake region and higher shear stress acting on membrane surface to reduce the thickness of concentration boundary layer. The results in Fig. 11 confirmed again that gas/liquid two phase flow could greatly intensify the heat and mass transfer process and diminish temperature polarization and concentration polarization effect in the boundary layer.
4.4.1. Effect of Retp on TPC and CPC Based on the obtained heat and mass transfer correlation, the corresponding TPC and CPC were calculated at varied Retp, and shown as the function of Retp in Fig. 11. In this figure, it could be seen that TPC increased with increasing Retp and the TPC increase rate at slug flow
4.4.2. Effect of Tf on TPC and CPC In Fig. 12, the influence of Tf on TPC and CPC was shown. It could be found that TPC decreased with the increase of Tf. When Tf increased, the flux was enhanced exponentially. As the overall heat transfer coefficient in the feed flow maintained almost unchanged, high temperature
the exponent of Pr in the equation Nu ¼ aRebtp Pr ðμ b =μ w Þ0:14 was suitable for AVMD process. In addition, it could be seen that similar to VMD process, AVMD flux also had an exponentially increasing trend with the increase of Tf due to the exponential relationship between temperature and vapor pressure (as shown in Eq. (2)) [9]. Like Fig. 8, experimental values of MD flux were all smaller than theoretical ones and the reasons might be the same. 1 3
24
C. Wu et al. / Desalination 373 (2015) 16–26
Fig. 10. Comparison of J–Tf theoretical curve and experimental value at varied Ul. (Ug/Ul = 0.50; vacuum pressure: 90 kPa).
difference across the feed flow was necessary based on Eq. (3), which enhanced the temperature polarization effect. From Fig. 12, it also could be seen that CPC increased with increasing Tf. When Tf increased, the water evaporates faster at the interface between feed solution and membrane pores, but the nonvolatile components could not pass through the membrane. However, the hydraulic condition (back mixing) was almost unchanged at different feed temperatures, which resulted in the increase of salt concentration in the boundary layer. Thus, CPC increased slightly with the increase of Tf which was similar to conventional MD process [47]. 5. Conclusion Air-bubbling was an effective method to enhance the performance of VMD process. The permeate flux was almost doubled at optimized conditions. According to the heat transfer correlation fitting method of gas/ liquid two phase flow, it was found that different flow patterns followed different heat transfer correlations in AVMD process and the corresponding heat transfer correlations were obtained experimentally:
Exponents of Retp in heat transfer correlations of bubbly flow and slug flow were significantly different. Heat and mass transfer efficiency of slug flow was much higher than that of the bubbly flow. Mass transfer correlations corresponding to different flow patterns were obtained by Chilton–Colburn analogy. Predicted flux of AVMD based on the obtained equations showed maximum difference less than 5%, compared to the experimental results. The variations of TPC and CPC in AVMD process were studied using the obtained heat and mass transfer correlations. According to the variation of TPC and CPC, the influence of flow pattern on TPC and CPC was also investigated. The results showed that flow pattern was the key factor affecting TPC and CPC. The TPC increase rate and CPC decrease rate both became higher when the flow pattern transited from bubbly flow to slug flow, which further validated the obtained heat and mass transfer correlations.
Pr ðμ b =μ w Þ0:14 λ=d ðslug flowÞ: h f slu ¼ 0:0632Re1:0420 tp
Nomenclature U superficial velocity (m/s) M molecular weight of water (kg/mol) d inner diameter of hollow fiber membrane (m) D outer diameter of hollow fiber membrane (m) r membrane pore radius (m) Tm average temperature in membrane pores (K)
Fig. 11. Effect of Retp on TPC and CPC. (feed inlet temperature: 70 °C; vacuum pressure: 90 kPa; Ug/Ul = 0.50). (△□ bubbly flow, ▲■ slug flow).
Fig. 12. Effect of Tf on TPC and CPC. (Feed inlet temperature: 70 °C; vacuum pressure: 90 kPa; Ug/Ul = 0.50).
h f bub ¼ 1:7527Re0:4215 Pr ðμ b =μ w Þ0:14 λ=d ðbubbly flowÞ; tp 1 3
1 3
C. Wu et al. / Desalination 373 (2015) 16–26
Pm Retp Rel Pr Fr Pe J Q C P T h R A L ΔH Nu Sh Sc Ds ks k Cp m V c
average vapor pressure in membrane pores (Pa) gas/liquid two phase flow Reynolds number liquid phase Reynolds number Prandtl number Froude number Peclet number MD flux (kg/(m2·s)) energy (W) MD coefficient (kg/(m2·s·Pa)) water vapor pressure (Pa) temperature (K) heat transfer coefficient (W/(m2·K)) gas constant (J/(mol·K)) area (m2) effective length of the membrane module (m) latent heat of water evaporation (kJ/kg) Nusselt number Sherwood number Schmidt number solute diffusion coefficient (m2/s) solute mass transfer coefficient (m/s) the gas/liquid velocity ratio heat capacity at constant pressure (J/(kg·K)) mass velocity (kg/(m2·s)) volume velocity (m3/(m2·s)) molar concentration (mol/L)
Greek symbols μ dynamic viscosity (kg/(m·s)) ρ density of the fluid (kg/m3) φ mean free path of water molecules (μm) ε fractional void volume of the membrane δ membrane thickness (m) τ pore tortuosity λ thermal conductivity (W/(m·K)) Subscripts tp two phase m membrane g gas l liquid f feed p the permeate side fm membrane surface on the feed side pm membrane surface in the permeate side bub bubbly flow slu slug flow b bulk phase w wall surface sec section in inlet out outlet Acknowledgment This study was supported by the National Natural Science Foundation of China (21106100, 21176188, 51278336), the Program for Chang-jiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRT13084) and Marine Science and Technology Project of Tianjin Province (KJXH2014-03). References [1] K.W. Lawson, D.R. Lloyd, Membrane distillation, J. Membr. Sci. 124 (1997) 1–25. [2] M.S. El-Bourawi, Z. Ding, R. Ma, M. Khayet, A framework for better understanding membrane distillation separation process, J. Membr. Sci. 285 (2006) 4–29.
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Contents lists available at ScienceDirect
Desalination journal homepage: www.elsevier.com/locate/desal
Study on the heat and mass transfer in air-bubbling enhanced vacuum membrane distillation Chunrui Wu a,⁎, Zhengang Li a, Jianhua Zhang b, Yue Jia a, Qijun Gao a, Xiaolong Lu a,⁎ a b
State Key Laboratory of Separation Membranes and Membrane Processes, Institute of Biological and Chemical Engineering, Tianjin Polytechnic University, Tianjin 300160, P.R. China Institute of Sustainability and Innovation, Victoria University, PO Box 14428, Melbourne, Victoria 8001, Australia
H I G H L I G H T S • MD flux could be improved 100% by air-bubbling and gas–liquid two phase flow method. • Two phase flow pattern is the key factor affecting the performance of MD process. • Mathematic model based on flow pattern was built and AVMD performance was explained.
a r t i c l e
i n f o
Article history: Received 17 February 2015 Received in revised form 11 June 2015 Accepted 1 July 2015 Available online 10 July 2015 Keywords: Membrane distillation Vacuum membrane distillation Heat and mass transfer Hollow fiber membrane Two phase flow
a b s t r a c t Air-bubbling vacuum membrane distillation (AVMD) process was designed to boost the heat and mass transfer in membrane distillation (MD). Both effect of flow pattern on the performance of AVMD process and the heat and mass transfer mechanism in this process were studied in this paper. The results showed that the performance of VMD was improved obviously by air-bubbling method. The flux was doubled at certain feed velocity and gas/ liquid proportion. The study showed that flow pattern was the key factor affecting the mass and heat transfer efficiencies. The heat transfer coefficients, corresponding to the two main flow patterns in AVMD process, bubbly Pr ðμ b =μ w Þ0:14 λ=dÞ and slug flow ðh f slu ¼ 0:0632Re1:0420 Pr ðμ b =μ w Þ0:14 λ=dÞ, were flow ðh f bub ¼ 1:7527Re0:4215 tp tp obtained and employed in the modeling of AVMD process. The modeling results showed that the theoretical prediction of flux aligned with experimental results well, in which the error was within ±5%. Both variations of Temperature Polarization Coefficient (TPC) and Concentration Polarization Coefficient (CPC) in AVMD process were studied based on the obtained correlations. And the result showed that both TPC and CPC were significantly influenced by the flow patterns. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Membrane distillation (MD), an innovative separation process which combines distillation and membrane technology, has gained worldwide attention and been developed rapidly since it was invented in 1960s [1–3]. Compared to other desalination technology such as Reverse Osmosis and Multi-Flash, MD has quite a few distinctive advantages such as the ability of treating extra-high concentration solutions, high rejection for nonvolatile components, lower operating temperature and pressure, less distillation space requirement and the ability of using low grade heat [2,3]. Many processes and configurations of MD have been developed, and widely employed in sea and brackish water desalination, industrial wastewater treatment, food industry, petro chemistry, chemical engineering, et al. [4–8]. In MD process, water
⁎ Corresponding authors at:399# Binshui West Road, Xiqing District, Tianjin P.R. China. E-mail addresses: [email protected], [email protected] (C. Wu), [email protected] (X. Lu).
http://dx.doi.org/10.1016/j.desal.2015.07.001 0011-9164/© 2015 Elsevier B.V. All rights reserved.
1 3
1 3
molecules or other volatile components evaporate at the membrane pore entrance (feed side), cross the membrane pores in vapor phase, and finally condense in the cold side or be removed as vapor from the membrane module [9]. However, concentration and temperature polarization caused by liquid boundary layer are the major barriers inhibiting heat and mass transfer from the bulk stream to pore interface [10–13]. To solve the problem, different techniques have been developed. Teoh et al. [14] achieved 20–28% flux increase by adding baffles and spacers in membrane channel, and modifying the geometry of the hollow fiber in direct contact membrane distillation (DCMD) process. Yang et al. [15] achieved great flux increase by modifying hollow fiber membrane configurations in DCMD experiments in which the modules with undulating membrane surfaces (curly and spacer-knitted fibers) achieved up to 300% flux enhancement in laminar flow region. Liu et al. [16] designed coiled hollow fiber membrane modules for sweeping gas membrane distillation (SGMD) and the flux was improved by about 200%. Zhu et al. [3] obtained 25% flux enhancement by using ultrasonic technology in air gap membrane distillation (AGMD). Li et al. [17,18] found that cross-flow hollow fiber module could ensure a high heat transfer
C. Wu et al. / Desalination 373 (2015) 16–26
coefficient at low Reynolds number (Re) in both vacuum membrane distillation (VMD) and DCMD processes. By modifying the hot feed flow direction and the air gap configuration, Tian et al. [19] boosted the permeation flux up to 2.5-fold in comparison with the conventional design. Gas/liquid two phase flow technology has been well developed to minimize the boundary layer effect in microfiltration, ultrafiltration, membrane bioreactor and other traditional membrane separation processes [20–27]. Recently, Chen et al. [28] incorporated gas bubbling into DCMD process, and studied both its effect on reducing the concentration polarization and temperature polarization, and influence of bubble size distribution on the gas-bubbling performance [29]. Ding et al. [30] also found that the membrane fouling in DCMD for concentrating the extract of Chinese traditional medicine can be effectively controlled by optimizing gas bubbling parameters. Many models [1,13] have been developed to research the heat and mass transfer mechanism in MD. However, these models only studied single phase flow on either side of the membrane. Therefore, those models cannot be employed to explain the phenomenon in MD process that both gas and liquid phase exit in one stream (hot and/or cold stream). Influence of gas/liquid two phase flow on heat transfer has been established [31–33] in conventional heat transfer studies. However, in these researches, the mass transfer occurred simultaneously with heat transfer in MD has not been investigated. Although previous works confirmed experimentally in DCMD process that gas/liquid two phase flow was able to minimize boundary layer effect and enhance heat and mass transfer, there is no systematically theoretical study on the heat and mass transfer mechanism for bubbling-enhanced MD process, especially for VMD process. Therefore, it is necessary to develop the heat and mass transfer model suitable for bubbling-enhanced VMD process. In this paper, an air-bubbling enhanced vacuum membrane distillation (AVMD) process designed by our team [34,35] was studied experimentally and theoretically, and heat and mass transfer in this process was modeled. By combining the basic mechanism of MD process and the method of fitting gas/liquid two phase flow heat transfer correlations, the heat and mass transfer model suitable for AVMD process was established. Using the obtained heat and mass transfer correlations, the variations of TPC and CPC were studied at different patterns. 2. Theory In the gas/liquid two phase flow system, gas only intensifies mixing of feed solution and enhances surface shear rate, but the liquid boundary layer on the membrane surface still exists [36]. Furthermore, in the MD process, the liquid phase protrudes into the pores as a lid due to the hydrophobicity of the membrane [37], which makes the air bubble isolated from the pores. Therefore, it can be assumed that gas bubbles will not interfere with the mass transfer in membrane pores and alter the main principle of transmembrane mass transfer in AVMD process. Since liquid boundary layer still exists in the gas/liquid two phase flow system, the law of heat and mass transfer between the bulk phase and membrane interface in VMD process is also applicable to AVMD process. 2.1. Heat and mass transfer For VMD process, both Knudsen diffusion and Poiseuille flow make contributions to transmembrane mass transfer [38] and the MD flux J can be calculated as:
J¼
rε 1:064 τδ
sffiffiffiffiffiffiffiffiffi ! M r 2 ε MP m þ 0:125 P T fm −P T p RT m τδ μRT m
ð1Þ
17
where r is the membrane pore radius; ε is the membrane porosity; δ is the membrane thickness; τ is the pore tortuosity; μ is the dynamic viscosity of water vapor; M is the molecular weight of water; R is the gas constant; P(Tfm) and P(Tp) are the vapor pressure as function of Tfm and Tp; Tfm and Tp are the membrane interface temperature on the feed and the permeate sides; Tm is the average temperature in membrane pores, Tm = (Tfm + Tp) / 2; Pm is the average vapor pressure in membrane pores, Pm = [P(Tfm) + P(Tp)] / 2; P(Tfm) and P(Tp) can be calculated using the Antoine's equation (Eq. (2)) [13]: P T fmðpÞ ¼ exp 23:238−
! 3841 : T fmðpÞ −45
ð2Þ
With the measurable J and P(Tp) as well as other membrane parameters, the unknown parameter Tfm can be calculated via the combination of Eqs. (1) and (2) [9]. In MD system, the heat flux across the liquid boundary layer (feed side), Qf, can be expressed as Eq. (3): Q f ¼ h f A f T f −T fm
ð3Þ
where hf is heat transfer coefficient of the bulk phase; Tf is the temperature of the bulk phase, Tf = (Tin + Tout) / 2; Af is the effective inner surface area of the hollow fiber membranes, Af = πLd; L is the effective length of the membrane module; d is the inner diameter of hollow fiber membrane. The inlet temperature Tin can be measured and the outlet temperature Tout can be calculated via the combination of Eqs. (4) and (5): C p mðT in −T out Þ ¼ JΑm ΔΗ m ¼ ρl V l ¼ ρl U l Asec ¼ Retp
ð4Þ μg Asec ≈Retp μ l Asec =d μ g =μ l þ U g ρg =U l ρl d
ð5Þ
where Cp is specific heat of the feed; m is the mass flow rate of the feed solution; Am is the effective area of the transmembrane heat transfer, Am = πL(D − d) / ln(D/d), D is the outer diameter of hollow fiber membrane; Asec is the cross section area of the hollow fiber membranes based on the inner diameter of hollow fiber membrane; ρg and ρl are densities of air and water; Ug and Ul are superficial velocities of air and water; μg and μl are dynamic viscosities of air and water. ΔH is the latent heat of vapor at temperature of Tfm and it can be calculated via Eq. (6): ΔH ¼ 2258:4 þ 2:47 373:0−T fm :
ð6Þ
The overall heat-transfer flux across the membrane, Q, is expressed as Eq. (7): Q ¼ JΔHAm þ
hm Am T fm −T pm δ
ð7Þ
where hm is the thermal conductivity of hollow fiber membrane, hm = (1 − ε)hs + εhg; hs and hg are separately the thermal conductivity of polymer and gas (usually air); Tpm is the membrane surface temperature in the permeate side. Similar to VMD process, the contribution of the heat conduct through the membrane matrix in AVMD (i.e., hmAm(Tfm − Tpm) / δ) can be neglected due to the high vacuum degree in the permeate side [17]. Therefore, Eq. (7) can be simplified to Eq. (8):
Q ¼ JΔHAm :
ð8Þ
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C. Wu et al. / Desalination 373 (2015) 16–26
Table 1 Parameters of the hollow fiber membrane. Inner diameter (mm)
Outer diameter (mm)
Membrane thickness (mm)
Pore radiusa (μm)
Tortuosity factora
Porosityb (%)
0.80
1.1
0.15
0.16
1.41
80
a
The two parameters were measured by gas permeation method [38]. The membrane porosity was measured by a gravimetric method [38].
b
According to Qf = Q, heat transfer coefficient on the feed side hf can be calculated via the combination of Eqs. (3) and (8): hf ¼
JΔHAm : T f −T fm A f
ð9Þ
In order to get J–T f theoretical curve, the relation between Pr and T was necessary. By fitting the data of pure water Prandtl number Pr at different temperature T [39], the relation between them can be expressed as: Pr ¼ 345:6866−2:7453 T þ 0:00737 T 2 −6:6464 10−6 T 3 :
ð10Þ
2.2. Modeling of heat and mass transfer in the feed side
Nu ¼ aRebtp Pr ðμ b =μ w Þ0:14
ð11Þ
1 3
where Nu = hfd/λ, Retp = Rel + Reg = dUlρl/μl + dUgρg/μg, Pr = Cpμ/λ; Retp is gas/liquid two phase flow Reynolds number; Rel and Reg are liquid and gas phase Reynolds numbers, Rel = dUlρl/μl, Reg = dUgρg/μg; a and b are parameters need to be calculated. Rearranging Eq. (11) and taking logarithm on both sides, it could be re-expressed as Eq. (12): Nu Pr ðμ b =μ w Þ0:14 1 3
¼ lga þ b lgRetp :
ð12Þ
When other experimental conditions had been given (i.e., the feed inlet temperature at 70 °C, vacuum pressure at 90 kPa and Ug/Ul = 0.50), and only varying Ul, the constants a and b could be obtained from the intercept and the slope by plotting lg[Nu / (Pr1/3(μb/μw)0.14)] against lgRetp. Hence, the heat transfer correlation suitable for AVMD process could be determined. As mentioned above, in the gas/liquid two phase flow system, liquid boundary layer on the membrane interface is still in continuous state. Therefore, the Chilton–Colburn analogy expressed as in Eq. (13) is applicable to calculate the solute mass transfer coefficient (ks) [36].
Sh Nu ¼ Sc Pr 1 3
Sh ¼ aRebtp Sc ðμ b =μ w Þ0:14 :
ð13Þ
1 3
where Sh = ksd/Ds, Sc = μ/(ρDs); Ds is solute diffusion coefficient.
ð14Þ
1 3
2.3. Calculation of TPC and CPC TPC refers to ratio of the temperature difference between the interfaces on both sides of the membrane, to the temperature difference between the bulky flows on both side of the membrane, which is an important factor to assess the thermal efficiency of MD process. In VMD (AVMD) process, TPC is usually simply defined as [40–42]: TPC ¼
According to the method from H. Groothuis et al. [31], Eq. (11) was used in our study for calculation of Nusselt Number Nu of the air/water two phase flow:
lg
Substituting Eq. (11) into Eq. (13) and Sh can be calculated by Eq. (14):
T fm : Tf
ð15Þ
The presence of solute in the feed reduces the partial pressure of the water vapor, so as to reduce the driving force in MD. As the existence of boundary layer and evaporation of the vapor to the permeate side, the solute concentration in the boundary layer becomes much higher (sometimes even saturated) than bulky flow, which is called concentration polarization (CP) phenomenon. The term concentration polarization coefficient, CPC, is defined to quantify the mass transport resistance within the concentration boundary layer on the feed side, and it refers to ratio of the salt concentration at the hot membrane surface to the salt concentration in the feed bulk solution. CPC can be calculated by the Eq. (16): CPC ¼
cfm J ¼ exp : ρks cf
ð16Þ
3. Experimental 3.1. Materials and equipment The hydrophobic polyvinylidene fluoride (PVDF) hollow fiber membranes fabricated by our team were used in the study, and the relevant membrane parameters were listed in Table 1. The hydrophobic hollow fiber membranes were fixed in a plastic cylindrical membrane module and relevant module specifications were listed in Table 2. The inlet temperature of feed solution was maintained by a thermostatic water bath (501A, Shanghai Jingke Co. Ltd. China), with a temperature accuracy of ± 0.1 °C. Mercurial thermometers with an accuracy of ± 0.1 °C were used for measuring the inlet and outlet temperature of feed flow. Electronic balance with an accuracy of ±0.1 g
Table 2 Specifications of hollow fiber membrane module. Module diameter (mm)
Module length (cm)
Effective fiber length (cm)
Membrane number
Membrane area (m2)
32
23
21
50
0.025
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Fig. 1. Flow chart of AVMD process. 1. water bath; 2. pump; 3. liquid flowmeter; 4. gas flowmeter; 5. pressurizer; 6. gas pump; 7. manometer; 8. thermometer; 9. hollow fiber membrane module; 10. buffer bottle 11. condenser; 12. vacuum pump; 13. product collection; 14. electronic balance.
was used for measuring the weight of the product water. To minimize the concentration polarization effect, pure water was used as the feed in the study of heat transfer mechanism. In the study of concentration polarization effect, the feed solution was 3.5 wt.% NaCl solution.
19
Fig. 3. Variation of MD flux with the increase of Ug/Ul at varied Ul. (Feed inlet temperature: 70 °C; vacuum pressure: 90 kPa). (★ bubbly flow, ▼▲●■ slug flow, ▽△○□ single phase flow).
was repeated three times and all data were the average of the three repeats.
4. Results and discussion 4.1. Determining the optimal Ug/Ul
3.2. Experimental setup and operation method The flow chart of AVMD experiment was shown in Fig. 1. Feed solution inlet temperature was controlled constant by the thermostatic water bath. The feed air was also heated by the thermostatic water bath to the same temperature of feed solution when the air passing through the copper tube immersed in the hot water. Feed solution was circulated through the lumen side of the hollow fiber membranes by a circulation pump. After pressure was stabilized by pressurizer, the clean air was injected into the inlet of the module. The velocities of the hot feed solution and air were controlled and monitored by liquid and gas flowmeters, respectively. A vacuum pump with a pressure controller was connected to the shell side of the module to create the vacuum and remove the permeation vapor. The water vapor pressure in the vacuum side was measured by a vacuum gauge. Each experiment
According to the conventional gas/liquid two phase flow heat transfer theory, flow pattern is the key factor affecting the heat transfer efficiency [43]. Therefore, it might also be the key factor affecting both heat and mass transfer efficiencies in the AVMD process. In vertical upward tubular channels, bubbly flow, slug flow, churn flow and annular flow will occur in sequence as increasing the gas/liquid velocity ratio (Ug /Ul ) [44]. Churn flow and annular flow will occur only when gas superficial velocity is more than 5 m/s and 10 m/s for vertical upward tubular channels [44]. However, in our experiments, gas superficial velocity was controlled less than 5 m/s. Thus, bubbly flow and/or slug flow were the dominant flow patterns in this study. In order to identify the flow pattern of gas/liquid two phase flow, methods, such as flow pattern maps and flow pattern discriminant,
Fig. 2. Relationship between flow pattern discriminant curve and straight lines of Ul = Ug/k.
Fig. 4. Relationship between lg[Nu / (Pr1/3(μb/μw)0.14)] and lgRel of VMD process.
20
C. Wu et al. / Desalination 373 (2015) 16–26
have been developed. However, most of flow pattern maps contained only gas and liquid superficial velocities or other conversion parameters based on them. The other factors (pipe diameter, gravitational acceleration etc.) which affected the formation of flow patterns had not been involved in these flow pattern maps, which limited its application in identification of the flow pattern of gas/liquid two phase flow, especially in the transition area of the flow pattern. Therefore, the flow pattern discriminant proposed by Weisman [45] including gas and liquid superficial velocities, as well as pipe diameter and gravitational acceleration, was used to identify the flow pattern in AVMD process, which can be expressed as Eq. (17).
Ug Ug þ U pffiffiffiffiffiffi N0:45 pffiffiffiffiffiffi l gd gd
!0:78 ð17Þ
where g is gravitational acceleration, d is the pipe diameter. Substituting g = 9.81 m/s2 and d = 0.80 × 10− 3 m into inequality (17) and rearranging gave Eq. (18):
Fig. 5. Relationship between lg[Nu / (Pr1/3(μb/μw)0.14)] and lgRetp of AVMD process. (■ bubbly flow, △ slug flow).
4.2. Setup of heat transfer correlations 5:69U 1:282 −U g NU l : g
ð18Þ
Plotting the equation curve of 5.69Ug1.282 − Ug = Ul in Fig. 2 and the flow pattern discriminant curve was obtained. Defined the gas/liquid velocity ratio k = Ug/Ul, then Ul = Ug/k. Took different values of k, straight lines of Ul = Ug/k were also plotted in Fig. 2. In the range of 0 m/s b Ug b 1.0 m/s and 0 m/s b Ul b 1.5 m/s, Fig. 2 is divided into two parts by the discriminant curve. The upper left part belongs to bubbly flow region, the lower right part belongs to slug flow region. When k b 0.29, all data points fall into bubbly flow region; when k N 0.29, data points falling into slug flow region become more and more with the increase of k. Since the heat transfer enhancement effect of slug flow is much better than that of bubbly flow [45], the greater value of k (i.e., Ug/Ul) should be selected to make more data points fall into slug flow region, as shown in Fig. 2. The effect of Ug/Ul on MD flux was studied and the results were shown in Fig. 3. The flow pattern of each experimental point was determined according to the flow pattern discriminant and represented by different symbols (except for the solid star points for the bubbly flow, all the other solid points for the slug flow). As shown in Fig. 3, the air bubbling could enhance the flux of MD process, and the enhancement effect was affected by both Ul and Ug/Ul. For each given Ul, the obvious flux increase rate was observed as the flow pattern transiting from bubbly flow to slug flow. However, when Ug/Ul N 0.50, the trend of flux increase rate plateaued, and slightly declined after Ug/Ul N 0.65. The figure also showed that the enhancement effect of Ug/Ul became much obvious as at higher liquid flow rate. The main effect of air bubbles was to create even flow distribution, intensify mixing and enhance surface shear rate. In bubbly flow region (Ug/Ul was relative smaller), air bubbles increased the disturbance degree of feed solution which enhanced the heat and mass transfer efficiency, so as to increase the flux. As Ug/Ul increased to a certain value, the flow pattern transited to slug flow. Compared with the bubbly flow, slug flow could generate larger wake region to make surface shear rate higher and achieve better enhancement effect [43]. As Ug/Ul reached 0.50, gas slug should have occupied almost the entire cross section of the lumen, and would not possible increase any more. Therefore, there was not further enhancement effect that could be achieved when k was greater than 0.50. However, as the air ratio became higher, more heat was taken away by the air, which might reduce the flux. Based on the above analysis, there was an optimal Ug/Ul for AVMD process and it was 0.50 in our experiment.
Fitting equation shown in Fig. 4 represents heat transfer correlations in VMD process based on the method in Section 2.2, which is used for comparing the heat transfer change due to the air bubbling enhancement. The correlation constants of the AVMD process at k = 0.50 were also achieved by plotting lg[Nu/(Pr1/3(μb/μw)0.14)] against lgRetp in Fig. 5. In Fig. 4, it could be seen that lg[Nu / (Pr1/3(μb/μw)0.14)] against lgRel showed a good linear correlation in VMD process based on our experimental results. However, the obtained linear slope is about 0.35 in the laminar region (Rel b 2100), which is greater than the value (0.33) in the conventional study of heat transfer in the circular tube [46]. It might be resulted from the experimental conditions, because the measured vapor pressure value (actually was the total pressure) in the vacuum side was greater than the real vapor pressure value (should be partial pressure) due to existence of the air residual. Therefore, the calculated temperature in the vacuum side (Tp) was slightly higher than the real value. As a result, Tfm was slightly higher than the real value based on the measured flux. Based on the fixed temperature at the bulk phase (Tf) and the measured flux (J), heat transfer coefficient (hf) was slightly higher than the real value according to Eq. (9). Thus, the index of Rel was slightly larger than 0.33.
Fig. 6. Relationship between Tfm and Tp corresponding to different Retp. (Ug/Ul = 0.50; feed inlet temperature: 70 °C; vacuum pressure: 90 kPa).
C. Wu et al. / Desalination 373 (2015) 16–26
As shown in Fig. 5, the data did not present very good linear relationship in the overall range of the AVMD test as that of the VMD. However, when the tests fell into the same flow pattern region based on inequality (18), i.e., lgRetp b 2.66 (bubbly region) or lgRetp N 2.66 (slug flow region), the lgRetp showed good linear relationship to lg[Nu/(Pr1/3(μb/μw)0.14)]. Therefore, two fitting equations were used respectively for bubbly flow and slug flow, as shown in Eqs. (19) and (20): Bubbly flow: Pr Nubub ¼ 1:7527Re0:4215 tp
1 3
μb μw
0:14 :
ð19Þ
21
Slug flow: Pr Nuslu ¼ 0:0632Re1:0420 tp
1 3
μb μw
0:14 :
ð20Þ
The corresponding mass transfer correlations could be obtained according to Eq. (14). The critical transition Ug and Ul values between the bubbly and slug flow could be calculated by combining Ul = 5.69U1.282 − Ug and g the k value used in the experiments. Therefore, if k = 0.50, based on Retp = dUlρl/μl + dUgρg/μg, the critical Retp of flow pattern transition could be determined and it was Retp(c) = 457. Thus, when 0 b Retp b
Fig. 7. Calculation flow chart of implicit equations containing only J and Retp.
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C. Wu et al. / Desalination 373 (2015) 16–26
457, the flow pattern was bubbly flow, Eq. (21) could be used to calculate the value of heat transfer coefficient at bubbly flow (hf bub): h f bub ¼ 1:7527Re0:4215 Pr ðμ b =μ w Þ0:14 λ=d: tp 1 3
ð21Þ
According to the data we measured in Fig. 5, the flow pattern was still slug flow when lgRetp b 3.6 (Retp b 4000). Therefore, when 457 b Retp b 4000, Eq. (22) could be used to calculate the value of heat transfer coefficient at slug flow (hf slu): 1:0420 h f slu ¼ 0:0632Retp Pr ðμ b =μ w Þ0:14 λ=d: 1 3
ð22Þ
listed in the figure. By comparing the experimental with the theoretical data of MD flux, it could be found that J–Retp theoretical data predicted the experimental results well, and the maximum error was within 5%. This demonstrated the feasibility of the obtained two phase flow heat transfer correlations in their application scope. Furthermore, it could be observed that the AVMD flux increase rate at slug flow was much higher than that of bubbly flow. Fig. 8 also showed that experimental values were all smaller than modeled ones, which might be caused by the heat lost of hollow fiber membrane module and/or the vapor pumped out by the vacuum pump. In addition, the experimental flux of the VMD process was also presented in Fig. 8, which was much lower than that of AVMD. It indicated that the heat transfer efficiency was enhanced greatly by the introduction of air bubbles.
4.3. Validating heat transfer correlations 4.3.2. Setting up and validating J–Tf theoretical curve 4.3.1. Setting up and validating J–Retp theoretical curve 4.3.1.1. Determining the relationship between Tfm and Tp. For the heat and mass transfer across the membrane, the actual net driving force was related to the net temperature difference over the membrane which solely determined the flux. Keep other operating parameters (feed inlet temperature, vacuum pressure and gas/liquid velocity ratio k) constant and only change Ul, the membrane surface temperature was only determined by Retp at different flow patterns. In order to build the relationship between flux J and Retp, the relation between Tp and Tfm was necessary. At the given experimental conditions (the feed inlet temperature at 70 °C, vacuum pressure at 90 kPa and k = 0.50), varying Ul and Ug was varied, flux J and Tp at different Retp (100 b Retp b 3000) could be obtained experimentally. Then, Tfm at different Retp could be calculated by combining Eqs. (1) and (2). In Fig. 6, the relationship of T p against T fm was shown at the given k = 0.50. In Fig. 6, Tp and Tfm presented a good linear relationship which was independent from the flow pattern, and the fitting equation is shown in Eq. (23). T p ¼ 57:953 þ 0:8131T fm
ð23Þ
4.3.1.2. Comparison of J–Retp theoretical curve with experimental value. In order to draw J–Retp theoretical curves, the implicit equations containing only J and Retp were needed, and Fig. 7 showed the calculation flow chart of these implicit equations. According to these obtained implicit equations, J–Retp theoretical curves corresponding to bubbly flow and slug flow were drawn by Matlab software, as shown in Fig. 8. The experimental data were also
4.3.2.1. Determining the relationship between Tfm and Tp. In order to get J–Tf theoretical curves under different Ul, the relation between Tp and Tfm was also necessary. With a given experimental condition: vacuum pressure of 90 kPa and Ug/Ul of 0.50, AVMD flux J and Tp could be obtained experimentally by varying the feed inlet temperatures (333.15 K b Tin b 363.15 K). The relations (Eqs. (24a)–(24e)) between Tp and Tfm corresponding to different Ul can be obtained by using the same method as Section 4.3.1.1: U l ¼ 0:20 m=s : T p ¼ 24:256 þ 0:9088T fm
ð24aÞ
U l ¼ 0:60 m=s : T p ¼ 21:585 þ 0:9149T fm
ð24bÞ
U l ¼ 0:70 m=s : T p ¼ 19:1269 þ 0:9235T fm
ð24cÞ
U l ¼ 1:20 m=s : T p ¼ 15:9068 þ 0:9339T fm
ð24dÞ
U l ¼ 1:30 m=s : T p ¼ 15:0039 þ 0:937T fm :
ð24eÞ
4.3.2.2. Comparison of J–Tf theoretical curve with experimental value. In order to draw J–Tf theoretical curves, the equations with variables J and Tf are necessary, and Fig. 9 showed the calculation flow charts of these equations. In the range of 315 K b Tf b 355 K, based on these equations, J–Tf theoretical curves at different Ul drawn by Matlab software were shown in Fig. 10. By comparing with the experimental flux which was also listed in this figure, it could be found that the J–Tf theoretical curves at different Ul could predict MD flux very well, which demonstrated that
Fig. 8. Comparison of J–Retp theoretical curve and experimental value. (Ug/Ul = 0.50; feed inlet temperature: 70 °C; vacuum pressure: 90 kPa). (● two phase flow, ▲ single phase flow).
C. Wu et al. / Desalination 373 (2015) 16–26
23
Fig. 9. Calculation flow chart of equations containing only J and Tf.
4.4. Effect of operation parameters on TPC and CPC
was higher than that at bubbly flow. This further demonstrated that heat transfer efficiency at slug flow was much higher than that at bubbly flow. In addition, CPC decreased with increasing Retp and the CPC decrease rate was enhanced as the flow pattern transit from slug flow to bubbly flow. It was mainly because that slug flow could generate larger wake region and higher shear stress acting on membrane surface to reduce the thickness of concentration boundary layer. The results in Fig. 11 confirmed again that gas/liquid two phase flow could greatly intensify the heat and mass transfer process and diminish temperature polarization and concentration polarization effect in the boundary layer.
4.4.1. Effect of Retp on TPC and CPC Based on the obtained heat and mass transfer correlation, the corresponding TPC and CPC were calculated at varied Retp, and shown as the function of Retp in Fig. 11. In this figure, it could be seen that TPC increased with increasing Retp and the TPC increase rate at slug flow
4.4.2. Effect of Tf on TPC and CPC In Fig. 12, the influence of Tf on TPC and CPC was shown. It could be found that TPC decreased with the increase of Tf. When Tf increased, the flux was enhanced exponentially. As the overall heat transfer coefficient in the feed flow maintained almost unchanged, high temperature
the exponent of Pr in the equation Nu ¼ aRebtp Pr ðμ b =μ w Þ0:14 was suitable for AVMD process. In addition, it could be seen that similar to VMD process, AVMD flux also had an exponentially increasing trend with the increase of Tf due to the exponential relationship between temperature and vapor pressure (as shown in Eq. (2)) [9]. Like Fig. 8, experimental values of MD flux were all smaller than theoretical ones and the reasons might be the same. 1 3
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Fig. 10. Comparison of J–Tf theoretical curve and experimental value at varied Ul. (Ug/Ul = 0.50; vacuum pressure: 90 kPa).
difference across the feed flow was necessary based on Eq. (3), which enhanced the temperature polarization effect. From Fig. 12, it also could be seen that CPC increased with increasing Tf. When Tf increased, the water evaporates faster at the interface between feed solution and membrane pores, but the nonvolatile components could not pass through the membrane. However, the hydraulic condition (back mixing) was almost unchanged at different feed temperatures, which resulted in the increase of salt concentration in the boundary layer. Thus, CPC increased slightly with the increase of Tf which was similar to conventional MD process [47]. 5. Conclusion Air-bubbling was an effective method to enhance the performance of VMD process. The permeate flux was almost doubled at optimized conditions. According to the heat transfer correlation fitting method of gas/ liquid two phase flow, it was found that different flow patterns followed different heat transfer correlations in AVMD process and the corresponding heat transfer correlations were obtained experimentally:
Exponents of Retp in heat transfer correlations of bubbly flow and slug flow were significantly different. Heat and mass transfer efficiency of slug flow was much higher than that of the bubbly flow. Mass transfer correlations corresponding to different flow patterns were obtained by Chilton–Colburn analogy. Predicted flux of AVMD based on the obtained equations showed maximum difference less than 5%, compared to the experimental results. The variations of TPC and CPC in AVMD process were studied using the obtained heat and mass transfer correlations. According to the variation of TPC and CPC, the influence of flow pattern on TPC and CPC was also investigated. The results showed that flow pattern was the key factor affecting TPC and CPC. The TPC increase rate and CPC decrease rate both became higher when the flow pattern transited from bubbly flow to slug flow, which further validated the obtained heat and mass transfer correlations.
Pr ðμ b =μ w Þ0:14 λ=d ðslug flowÞ: h f slu ¼ 0:0632Re1:0420 tp
Nomenclature U superficial velocity (m/s) M molecular weight of water (kg/mol) d inner diameter of hollow fiber membrane (m) D outer diameter of hollow fiber membrane (m) r membrane pore radius (m) Tm average temperature in membrane pores (K)
Fig. 11. Effect of Retp on TPC and CPC. (feed inlet temperature: 70 °C; vacuum pressure: 90 kPa; Ug/Ul = 0.50). (△□ bubbly flow, ▲■ slug flow).
Fig. 12. Effect of Tf on TPC and CPC. (Feed inlet temperature: 70 °C; vacuum pressure: 90 kPa; Ug/Ul = 0.50).
h f bub ¼ 1:7527Re0:4215 Pr ðμ b =μ w Þ0:14 λ=d ðbubbly flowÞ; tp 1 3
1 3
C. Wu et al. / Desalination 373 (2015) 16–26
Pm Retp Rel Pr Fr Pe J Q C P T h R A L ΔH Nu Sh Sc Ds ks k Cp m V c
average vapor pressure in membrane pores (Pa) gas/liquid two phase flow Reynolds number liquid phase Reynolds number Prandtl number Froude number Peclet number MD flux (kg/(m2·s)) energy (W) MD coefficient (kg/(m2·s·Pa)) water vapor pressure (Pa) temperature (K) heat transfer coefficient (W/(m2·K)) gas constant (J/(mol·K)) area (m2) effective length of the membrane module (m) latent heat of water evaporation (kJ/kg) Nusselt number Sherwood number Schmidt number solute diffusion coefficient (m2/s) solute mass transfer coefficient (m/s) the gas/liquid velocity ratio heat capacity at constant pressure (J/(kg·K)) mass velocity (kg/(m2·s)) volume velocity (m3/(m2·s)) molar concentration (mol/L)
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