Pollutants removal from wastewaters through membrane distillation

Pollutants removal from wastewaters through membrane distillation

Desalination 183 (2005) 383–394 Pollutants removal from wastewaters through membrane distillation Cristiana Boi, Serena Bandini*, Giulio Cesare Sarti...

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Desalination 183 (2005) 383–394

Pollutants removal from wastewaters through membrane distillation Cristiana Boi, Serena Bandini*, Giulio Cesare Sarti Dipartimento di Ingegneria Chimica, Mineraria e delle Tecnologie Ambientali, Alma Mater Studiorum – Universita` di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy Tel. þ39 051 2093138; Fax þ39 051 581200; email: [email protected] Received 21 February 2005; accepted 10 March 2005

Abstract The Sweeping Gas Membrane Distillation process is considered for the treatment of wastewaters containing volatile organic compounds such as acetone and ethanol. The separation technique is based on the use of microporous hydrophobic membranes under conditions of non wettability, in which the membrane separates an aqueous phase from a stripping gas. A wide experimental investigation is performed to study the role of temperature, composition and flow rate of the liquid phase and the influence of the sweeping gas flow rate. Performances of flat PTFE membranes are studied in the case in which dry nitrogen is used as stripping agent. Liquid feed flow rate as well as nitrogen flow rate are identified as the major design quantities since they greatly affect the separation efficiency. A simplified mathematical model is developed to describe multicomponent mass transfer in the gas phases, in which a pseudo-binary diffusion approach is assumed; molecular diffusion is considered as the prevailing transport mechanism through the membrane. The results obtained are compared with the experiments and the validity range of the model is defined. Keywords: Membrane distillation; Sweeping gas; Volatile organic compounds; Porous hydrophobic membranes; Removal

1. Introduction The Sweeping Gas Membrane Distillation (SGMD) is a membrane-based separation *Corresponding author.

process which has been proposed for several purposes such as the production of ultrapure water from salt solutions and the selective removal of volatile organic compounds from aqueous streams [1–6]. A hybrid configuration between SGMD and Air Gap

Presented at the Conference on Desalination and the Environment, Santa Margherita, Italy, 22–26 May 2005. European Desalination Society. 0011-9164/05/$– See front matter Ó 2005 Elsevier B.V. All rights reserved doi:10.1016/j.desal.2005.03.041

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Membrane Distillation was also proposed as Termostatic SGMD in [7,8], in which the separation of azeotropic mixtures was also studied. The process is one of the various membrane distillation techniques, in which a microporous hydrophobic membrane separates an aqueous solution from a gas phase acting as a stripping agent (Fig. 1c). Under conditions of non wettability, evaporation takes place at the liquid–vapour interface located at the feed/membrane surface and vapours diffuse through a stagnant gas film entrapped within the membrane pores towards the sweeping gas phase downstream the membrane. Among the various membrane distillation techniques, SGMD and Vacuum Membrane Distillation [9] are certainly the most similar from the operative point of view. In both cases, the driving force of each permeating species is related to the corresponding partial pressure difference existing through the membrane which is sustained by a sweeping gas or by vacuum, respectively. As a consequence, it should be expected that the technological applications as well as the role of the main transport phenomena involved on the process efficiency could be quite similar. Nonetheless, for SGMD the mass transfer resistance in the gas phase can assume a relevant role; in addition, since the process operates at atmospheric pressure, molecular

diffusion is the prevailing mass transfer mechanism in the membrane with respect to Knudsen diffusion [3]. The process is here proposed for the purification of dilute wastewaters containing volatile organic compounds, in alternative to conventional separations such as distillation, carbon adsorption, gas stripping, in view of the lower energy demand with respect to conventional techniques. However, the process results economically advantageous only in those cases in which pollutants recovery is not required, since the condensation downstream the membrane unit is the most energy consuming step [10]. As a consequence, SGMD becomes a good alternative to biological abatement for the treatment of end-process streams containing various trace components for which recovery and separation would be remarkably expensive; in this case, the waste gas stream containing volatile organic compounds stripped from the aqueous streams can undergo a simple incineration process. Previous papers [1,2,5] established the process feasibility for the simple case of pure water, in flat as well as in shell and tube module configurations; the effect of operating variables was also experimentally investigated in [6] in the case of isopropanol-water mixtures. The prevailing role of liquid temperature on process performance, as well as the relevance of liquid and gas flow rates have

Fig. 1. SGMD process: (a) liquid side semicell; (b) flow pattern in each semicell; (c) detail of the porous membrane showing temperature and composition profiles in the external phases, with reference to the VOC.

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been put in evidence. In parallel, a mathematical model was developed in the simple case of water/air systems, in analogy with the typical description of Direct Contact Membrane Distillation [1–5]. In this work the SGMD process is considered for the treatment of wastewaters containing volatile organic compounds such as acetone and ethanol, by using dry nitrogen as stripping agent. Performance of flat PTFE membranes is investigated with the aim to establish which are the major design variables among temperature, composition and flow rate of the liquid phase and flow rate of the sweeping gas. A simplified model is developed to describe multicomponent mass transfer both in the membrane and in the sweeping gas phase, in which a pseudo-binary diffusion approach is assumed. Validation of the model, which contains no adjustable parameters, is performed both in the case of binary systems such as water/nitrogen and in the case of ternary mixtures such as organicwater/nitrogen.

Fig. 2. SGMD experimental set-up.

385

2. Experimental methods and results 2.1. Materials and methods Experimental tests were performed using flat PTFE membranes, supported on highly porous polypropylene film, from Gelman Co. as TF200 (0.2 mm nominal pore diameter, 60% void fraction, 165 mm total thickness60 mm PTFE layer thickness). The membrane was located in the middle of a circular cell of 74 mm diameter divided in two chambers 2 mm deep (Fig. 1a). A 25 mm paper filter and a polypropylene mesh supported the membrane to prevent strain and breakage against the cell wall. The liquid feed entered the centre of the liquid side semicell perpendicularly to the membrane and flew outwards in the radial direction (Fig. 1b); the gas phase followed the same flow pattern symmetric with respect to the membrane. In such a configuration the membrane area useful for the process was 43 cm2. A flow sheet of the experimental set-up is reported in Fig. 2. The liquid was continuously recirculated to the membrane cell from a

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reservoir, sufficiently large (24 dm3) to keep the concentration nearly constant. The fresh gas stream was completely dried through a silica gel cartridge and fed to the membrane unit. For both phases, inlet temperature values were regulated through heat exchangers and the membrane unit was immersed in a thermostated bath. Gas stream pressure was kept close to the atmospheric value, whereas the pressure in the liquid side was kept higher than the gas stream through a sufficient liquid head. The total transmembrane flux was measured by the level decrease of a burette in the liquid side. Experiments were performed with pure water and with dilute binary solutions of acetone and ethanol in water, prepared from reagent-grade organics and distilled water; nitrogen was used as stripping agent in all cases. The gas permeate composition was measured by an on-line mass spectrometer; the liquid composition was measured by a refractometer. In all runs only minor differences between inlet and outlet temperatures and compositions in the liquid phase were observed; indeed the evaporation flux was always smaller than 1% with respect to the liquid flow rate. Therefore, in the elaboration of the experimental data temperature and composition in the liquid bulk will be taken as constant and equal to the respective inlet values. On the contrary, in the gas phase a remarkable variation of composition is observed and it will be accounted for in the following elaborations, while temperature variations are negligible between inlet and outlet sections of the membrane unit. 2.2. Results Experiments were performed in order to investigate the role of the main process variables. The research was prevailingly focussed on the investigation of the influence of liquid

and gas flow rates on SGMD of water-VOC mixtures, at different organic compositions; most of tests were performed at 35 C liquid temperature, whereas the gas temperature was varied in the range from 25 to 35 C. In Fig. 3 the permeate flux is reported as a function of the nitrogen flow rate, for the simple case of SGMD of pure water, at various liquid flow rates. The typical behaviour encountered also by other authors [2, 5, 6] is observed in which the water flux increases as the gas flow rate increases and as the liquid feed temperature increases. Of course, since SGMD is an evaporative process, it is greatly affected by the liquid temperature. However, fluid-dynamic conditions in the liquid phase are not relevant in determining the water flux: for example, at 200 dm3/h liquid flow rate, the flux increases from 1.08 to 1.60 kg/(m2h) as the gas flow rate increases from 0.22 to 0.63 m3/h at standard conditions, whereas at 0.63 m3/h gas flow water / dry nitrogen 2

, V L =200 dm 3 /h V L = 75 dm 3 /h

water flux ( kg/(hm2))

386

T L =35 °C

3

V L = 25 dm /h

1.5

3

1

200 dm 3 /h

25 dm /h

T L =25 °C

0.5

0 0.0

0.2

VG

0.4 0.6 ( m 3 (STP)/h)

0.8

Fig. 3. SGMD of water by dry nitrogen through TF200: average transmembrane flux vs. gas flow rate at standard conditions, at various temperatures and flow rates in the liquid side. Comparison between model predictions through equation (12) (lines) and the corresponding experimental results (symbols) open symbols: TG ¼ 258C; closed symbols: TG ¼ 328C.

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rate the flux increases only from 1.47 to 1.60 kg/(m2h) as the liquid flow rate increases from 25 to 200 d(m3/h). It is therefore selfevident that, in the geometry investigated, the fluid-dynamic conditions in the gas phase are remarkably relevant in determining the water flux, thus indicating that the mass transfer

resistance in the gas phase is the controlling transport mechanism. The SGMD of acetone-water and ethanolwater solutions are considered in Figs. 4 and 5, in which the effect of feed concentration as well as of the liquid and gas flow rates on distillate composition and total flux is reported.

acetone-water / dry nitrogen 0.7

3 1 bar

0.6

0.3 1

2 wt%

0.2 0.1

a)

0

0 0

0.2

0.4

0.6

0.8

1

5 1 bar

0.9 0.8

acetone wt%

2

2

0.4

10 wt%

4

5 wt%

2

0.7

total flux (kg/(m h))

acetone wt%

0.5

total flux (kg/(m h)

10 wt%

0.6 0.5

3

0.4 0.3

2

2 wt%

0.2

1

0.1 0

b)

0 0

0.2

0.4

0.6

0.8

3

V G (m (STP)/h) Fig. 4. SGMD of acetone-water mixtures by dry nitrogen through TF200: permeate acetone composition on gas free basis and total transmembrane flux are reported vs. the gas flow rate at standard conditions. TL = 35 C, TG = 33 C. (a) liquid flow rate = 25 dm3/h; (b) liquid flow rate = 200 dm3/h.

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2

0.5 5 wt %

ethanol wt %

2

total flux (kg/(m h))

1 bar

0.4

2 wt %

0.3

1 0.2 0.1 a)

0

0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.5

3

ethanol wt %

2

2 wt %

0.2 1 0.1

2

5 wt %

total flux (kg/(m h))

1 bar

0.4 0.3

b)

0.0

0 0

0.1

0.2

0.3

0.4

0.5

0.6

As the liquid flow rate increases, total flux greatly increases, whereas the organic composition in the permeate is not remarkably affected;  All the effects on total flux are enhanced as the volatility of the organic compound increases with respect to water. The experimental results presented are qualitatively suggestive of the important role of the polarization phenomena occurring both in the liquid phase and in the gas phase. However, the general behaviour observed puts in evidence that heat and mass transfer resistances in the liquid phase as well as mass transfer resistance in the gas phase affect water flux and organic flux in a different extent. Mass transfer in the gas phase can be reasonably considered the dominant phenomenon affecting water flux. On the contrary, the organic flux can be the result of the simultaneous effects of all the transport phenomena involved and the process can switch from mass transfer control in the liquid phase to mass transfer control in the gas phase, depending upon the fluid-dynamic conditions existing in the specific geometry. 

ethanol-water / dry nitrogen

0.7

0.8

V G (m 3 (STP) /h)

Fig. 5. SGMD of ethanol-water mixtures by dry nitrogen through TF200: permeate ethanol composition on gas free basis and total transmembrane flux are reported vs. the gas flow rate at standard conditions. TL = 35 C, TG = 33 C. (a) liquid flow rate = 25 dm3/h; (b) liquid flow rate = 200 dm3/h.

Also in this case, the behaviour observed is in good agreement with what obtained by other authors [6], and it can be summarized as follows:  As the organic composition in the liquid feed increases, total transmembrane flux and organic composition in the permeate increase;  As the sweeping gas flow rate increases, total flux increases and correspondingly the organic composition in the permeate decreases;

3. Model and predictions 3.1. Theory With reference to any membrane module cross section, the main physical phenomena involved in the SGMD process can be summarized as follows (Fig. 1c):  Heat and mass transfer from the liquid bulk to the membrane surface;  Evaporation of the liquid mixture at the L–V interface located on the liquid/membrane side;  Heat and mass transfer through the gas phase entrapped in the membrane;  Heat and mass transfer through the gas phase flowing downstream the membrane.

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Also in the simple case of binary mixtures here considered, mass transfer through the membrane is represented by the multicomponent diffusion of organic compound and water vapors through a stagnant film of gas, which should be described by the Stefan-Maxwell equations [11]. The same kind of problem should be solved to describe mass transfer in the sweeping gas phase. A simplified approach is developed to describe mass transfer in the gas phase, in which the pseudo-binary diffusion model [12] is assumed. In this model any coupling effects between VOC and water are neglected. In other words, the gas phases inside and outside the membrane are treated as dilute solutions of organic and water in nitrogen and molecular diffusion is considered as the prevailing mechanism. With reference to the membrane scheme reported in Fig. 1(c), mass transfer of the i-th component (both water and organic) through the membrane can be described by equation (1): Jt ¼ kim cm ln

Ji =Jt  yi2 Ji =Jt  yiI

ð1Þ

in which kim is a sort of mass transfer coefficient of the i-th component in the membrane and cm represents the total mole concentration in the membrane pores; in the case of prevailing molecular diffusion [3,13], they are calculated according to equation (2): Jt Ji =Jt  yiG ¼ ln kjG cG Ji =Jt  yi2

ð2Þ

Pm and Tm represent average values of pressure and temperature in the membrane pores, respectively. Similarly, mass transfer of the i-th component through the liquid phase and through

the gas phase can be described through the film theory model [14] represented by equations (3) and (4), respectively. Jt Ji =Jt  xiI ¼ ln kiL cL Ji =Jt  xib

ð3Þ

Jt Ji =Jt  yiG ¼ ln kiG cG Ji =Jt  yi2

ð4Þ

in which kiL and kiG are the mass transfer coefficients of the i-th component in the liquid and in the gas phase, respectively. The heat required for the evaporation, occurring at the liquid/membrane interface, is supplied by the heat flux through the liquid stream; heat balance across the evaporation surface can be coupled with the corresponding heat balance at the membrane/gas phase surface and the following relationship can be obtained: hL ðTL  TI Þ ¼ i Ji i þ UG ðTI  TG Þ

ð5Þ

in which hL is the heat transfer coefficient in the liquid phase and UG represents the overall heat transfer coefficient in the gas phase, accounting for heat transfer in the membrane (hm) and in the sweeping gas (hG) as follows: 1 1 1 ¼ þ ; UG hm hG

hm ¼

T kST ð1  "Þ þ kG " 

ð6Þ

Generally speaking, since the ratio hm =hG varies in the range from 20 to 100 for the PTFE and PP membranes typically used in MD processes [13, 15], the temperature difference across the membrane is relatively low and quite negligible with respect to the temperature difference across the sweeping gas phase. As a consequence, the properties appearing in equation (2) of the model can be calculated at the corresponding value of TI.

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Table 1 Transport correlations for radial flow geometry Correlation j = 1.61Re

Flow regime

Notation

0.35 IN

m Re ¼ 2b



ðRbc Þ

Nu Pr1=3

1=3

¼

ðRbc Þ

Sh Sc1=3

1=3

[9, 17] 1=3 ShiG ¼ 3:56Re0:265 SciG G

ð13Þ

500 < Re < 5000

c Nu ¼ hR kT

Sh ¼ kDi Ri c ð14Þ

Equations (1), (3), (4) and (5), coupled with the relationships describing the liquid-vapour equilibrium conditions existing at the liquid/ membrane interface, embody the local mathematical description of the SGMD process. Once the membrane parameters (/) are known, and the suitable relationships for both heat and mass transfer coefficients are available for the specific cell geometry, the model can be used in a completely predictive way. 3.2. Model application and discussion The validity of the model presented is here proved by comparing the values of total flux and permeate composition predicted by the model equations with the corresponding quantities measured in the experimental runs reported in section 2. For the specific geometry of the cell with radial flow, transport correlations were developed basing on VMD data [9] and are synthetically reported in Table 1, as equation (13). They were obtained for liquid phases and in fluid-dynamic conditions corresponding to high Reynolds numbers, so that they can be used with confidence to predict heat and mass transfer coefficients in the liquid feed. Calculations of the mass transfer coefficient in the sweeping gas phase were performed based on the SGMD data with pure water reported in Fig. 3. To this purpose, heat and mass balance equations should

250 < ReG < 1200

be solved for the specific radial geometry. Since the variations of temperature and composition in the liquid side are relatively low as well as the variations of the gas phase temperature, only mass balances in the permeate side have to be solved to account for the composition variation in the sweeping gas phase between inlet and outlet sections of the membrane unit. Therefore, indicating with r the radial coordinate of the cell, in the case of dilute solutions, mass balance of the i-th component in the permeate side can be written as: dnG dyiG i ffi nN2 ¼ Ji 2r dr dr

ð7Þ

in which nG i and nN2 represent molar flow rates of the i-th component and nitrogen in the sweeping gas stream, respectively. In addition, equations (1) and (4) can be coupled as indicated in equation (8), and an overall mass transfer coefficient in the gas phase can be defined in a straightforward way (equation (9)). G ln Jt ¼ KiOV

1 G KiOV

¼

Ji =Jt  yiG Ji =Jt  yiI

1 1 þ kim cm kiG cG

ð8Þ

ð9Þ

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Equation (8) can be also rewritten and rearranged in a linearized form, as indicated in equation (10), without loosing precision, in view of the low compositions of the i-th component in the gas phase (yiI, yiG <<1) and of the relatively high composition in the corresponding permeate stream (Ji/Jt>>yil). Ji =Jt  yiG G Jt ¼ KiOV ln Ji =Jt  yiI  yiI  yiG G ¼ KiOV ln 1 þ Ji =Jt  yiI yiI  yiG G ffi KiOV Ji =Jt  yiI

ð10Þ

Finally, (10) can be inserted into equation (7), thus obtaining: 8 > <

nN2

dyiG Ji G yiI  yiG rdr ¼ 2 KiOV dr Jt Ji =Jt  yiI

> : y ðr ¼ 0Þ ¼ yIN iG iG

ð11Þ

Since experimentation puts in evidence that TL, TG and xib are remarkably constant values in the feed side semicell, TI as well as yiI can be reasonably assumed as independent of the radial coordinate; as a consequence equation (11) can be easily integrated. As numerical calculations suggest, the ratio Ji/Jt can be taken as constant and equal to the ratio of the respective average values /, so that the relationship reported in equation (12) is obtained:

ln

G yiI  yOUT R2c KiOV hJi i iG ¼ ; hJt i nN2 ðyiI  hJi i=hJt iÞ yiI  yIN iG ð12Þ Pi ðTI Þi ðTI ; xiI ÞxiI yiI ¼ PG

Equation (12) coupled with equation (3) and (5) represents the integration of the model equation for the specific geometry

391

of the cell with radial flow and it can be used to simulate the membrane performances under the operative conditions investigated. On the other hand, the same equation set can be used to calculate the water mass transfer coefficient in the gas phase, kwG. First, equation (12) can be used coupled with equation (5) to calculate the corresponding value G and TI through the elaboration of of KwOV the SGMD data obtained for the case of pure water, simply imposing Ji = Jw = Jt; secondly, equations (2) and (9) can be used to obtain kwG. The calculated water mass transfer coefficients in the gas phase, kwG, are well-fitted by the power law relationship reported in Table 1 as equation (14). Such correlation was obtained by using equation (13) to calculate the corresponding heat transfer coefficients in the liquid phase, whereas the contribution of the gas phase to the heat flux, appearing in equation (5), was neglected (as it can be easily calculated from the experimental data)., Calculations were performed considering  = 0.6, d = 60 mm and w = 2.27; the tortuosity factor was estimated based on membrane permeability measurements performed both in membrane extraction [16] and in direct osmosis [13] experiments. A graphical representation of the quality of the fitting procedure is reported in Fig. 3, in which water flux values predicted through the set of equations (3), (5) and (12) are compared with the corresponding experimental values. Finally, the model represented by equations (3), (5) and (12) is used to predict permeate composition and total flux in the case of acetone-water as well as of ethanolwater mixtures for all the operative conditions inspected. The same membrane parameters used in the case of pure water simulations were considered; correspondingly

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equations (13) and (14) of Table 1 were used for the calculation of heat and mass transfer coefficients. Van Laar and NRTL equations were used to calculate the L–V equilibrium conditions; their respective parameters were taken from [18]. The results obtained are reported in Fig. 6. Apparently, the agreement is qualitatively satisfactory, above all in the case of total flux, both for acetone-water and total flux 6 a)

flux in kg/(h m 2 )

5 calculated flux

1 bar

4 3 acetone 2 wt% acetone 10 wt% ethanol 2 wt% ethanol 5wt% acetone 5 wt%

2 1 0 0

1

2

3 4 measured flux

5

6

composition 1 b)

0.9 0.8

1 bar

for ethanol-water mixtures. With regard to the quality of the distillate composition prediction, we observe that the calculated values are systematically higher than the measured ones; in the case of acetone-water mixtures the deviation is more evident at the lower composition values, that is at the higher gas flow rates. The errors seem to be ascribable to the calculation of the organic flux as a function of the gas flow rate, which is predicted much more dependent on the gas flow rate than in the experimental runs, whereas water flux is correctly predicted. In other words, the effect of mass transfer resistance in the gas phase on the organic flux is predicted higher than the real one, although the same kind of prediction is substantially good for the water flux. Nonetheless the model presented is certainly an approximated interpretation of the physical phenomena involved, the approach proposed allows a simple description of the process, which can be easily extended to multicomponent systems. Since the total flux is correctly predicted, the model can be used for predictive purposes, for process optimization and it could be particularly useful in those cases in which a feasibility study of the process is pursued.

calculated

0.7 0.6

4. Conclusions

0.5 0.4

acetone 2 wt% acetone 10 wt% ethanol 2wt% ethanol 5 wt% acetone 5 wt%

0.3 0.2 0.1 0 0

0.1

0.2 0.3

0.4 0.5 0.6 measured

0.7 0.8 0.9

1

Fig. 6. SGMD of ethanol-water and acetone-water mixtures by dry nitrogen through TF200: comparison between predicted and measured values. TL = 35 C, TG = 33 C, VL = 200 dm3/h. (a) total transmembrane flux; (b) organic composition on gas free basis in the permeate.

The SGMD process was experimentally studied as a separation technique to remove volatile organic compounds from aqueous streams; acetone-water and ethanol-water mixtures were investigated as typical; dry nitrogen was used as stripping agent. Flat PTFE membranes were tested in a circular cell with radial flow in both feed and permeate sides. Since the process, like all the membrane distillation processes, is an evaporative process, it is greatly affected by the liquid feed temperature.

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However, the separation efficiency is strictly related to the fluid-dynamic conditions existing in the phases external to the membrane. As a general trend, an appreciable permeation rate increase is observed with increasing the gas flow rate, which is paralleled by a remarkable decrease in the permeate organic composition. On the contrary, both permeation rate and composition benefit by an increase of the liquid feed flow rate. That is a clear indication of the relevance of the resistances offered to the transport phenomena by the liquid as well as by the gas phase. As a qualitative indication, we can conclude that water flux is remarkably affected by the mass transfer resistance in the stripping gas phase, whereas the organic flux is the result of the concomitant effects of all the transport resistances existing both in the liquid phase and in the gas phase. On the other hand, the role of the membrane in the separation efficiency is relatively modest. Therefore, it is self-evident that a good module design will be the basic requirement for a successful application of the process on an industrial scale. A simplified mathematical model was finally developed to describe multicomponent mass transfer in the gas phases, in which a pseudo-binary diffusion approach was assumed, neglecting every interaction between the transport of water and organic compounds in the presence of a stagnant gaseous film. Molecular diffusion was considered as the prevailing transport mechanism through the membrane. The predictive ability of the model was tested both in the case of binary systems such as water/nitrogen and in the case of ternary mixtures such as organic-water/nitrogen. The most interesting result is a remarkable precision in the prediction of the total flux; the most critical aspect is a relevant overestimation of the organic flux, with

393

respect to the values obtained in the experimentation. However, although the model presented is an approximated interpretation of the physical phenomena involved, the approach proposed allows a simple description of the process, which can be easily extended to multicomponent systems. Since the total flux is correctly predicted, the model can be used for predictive purposes, for process optimization and it could be particularly useful in those cases in which a feasibility study of the process is analyzed. Acknowledgements Financial support by Italian Ministry of Education University and Research (MIUR ex 60%) is acknowledged. Notation b c D h k kT KOV J m n P P* r R Rc T U V x y

radial semicell thickness (m) mole concentration (mol/m3) diffusivity (m2/s) heat transfer coefficient (W/(m2 K)) mass transfer coefficient (m/s) thermal conductivity (W/(m K)) overall mass transfer coefficient defined in equation (9) (mol/(m2 s)) molar flux (mol/(m2 s)) mass flow rate (kg/s) molar flow rate (mol/s) pressure (Pa) vapor pressure (Pa) radial coordinate (m) universal gas constant radial cell radius (m) temperature (K) overall heat transfer coefficient defined in equation (6) (W/(m2K)) volume flow rate (m3/s) mole fraction in the liquid phase mole fraction in the gas phase

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tortuosity factor membrane thickness (m) porosity activity coefficient molar latent heat of vaporization (J/mol) dynamic viscosity (Pa s)

Subscripts and superscripts 2 b G i I L m S w IN OUT

gas/membrane interface liquid bulk gas phase i-th component feed/membrane interface liquid phase membrane membrane polymer water inlet section outlet section

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