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Mass transfer in spiral wound pervaporation modules
journal of MEMBRANE SCIENCE
ELSEVIEK
Journal of Membrane Science 92 ( 1994) 59-74
Mass transfer in spiral wound pervaporation modules Patrick J. Hickey, Charles H. Goading* Department of Chemical Engineering, Clemson University, Clemson, SC 29634-0909, USA
(Received August 27, 1993; accepted in revised form January 5, 1994)
Abstract Mass transfer performance correlations are needed for spiral wound membrane module feed spacers to determine the optimal flow velocity for each spacer, to find the most cost efficient spacer, and to compare spiral wound to other modules. The mass transfer characteristics of 15 feed spacers were determined experimentally. The mass
transfer correlations derived from the data indicate that a transitional flow regime exists in spacer-filled channels at the flow velocities evaluated. The use of a spacer increased the mass transfer coefficient to 1.5 to 4.0 times the coefficient obtained with an empty channel. There was only a modest increase in the performance of the spacer with the highest mass transfer coefficient when compared to the spacer with the lowest despite the fact that the friction loss characteristics of the spacers varied greatly. Attempts to define a characteristic dimension that would allow the consolidation of the mass transfer results from many spacers into a single equation were unsuccessful. Even spacers of a common design, i.e., diamond-shaped, required a unique equation to describe the mass transfer characteristics of each spacer. Ultraflo spacers from Nalle Plastics, Inc. provided the highest mass transfer coeffk cient per unit of pressure drop per unit length. However, the determination of the most cost effkient spacer will require the use of a detailed economic analysis. Keywords: Mass transfer; Spiral wound module; Pervaporation;
1. Introduction
Most industrial pervaporation units in use today consist of stainless steel plate and frame modules [ 11. These modules are used typically for solvent dehydration and can withstand high temperatures and corrosive environments, but they are also relatively expensive when compared with other types of membrane modules. Spiral wound modules are used commonly in reverse osmosis, ultrafiltration, and gas permeation [ 11. In applications where there is material compatibility, spiral wound modules are a less *Corresponding author.
Water treatment
expensive alternative to plate and frame modules. Commercial spiral wound modules have even been developed for some solvent dehydration applications [ 2 1. The major components of a spiral wound module are the feed and permeate spacers, the membrane, the permeate collection tube, and the shell. The performance of a spiral wound module for a given application is determined by the membrane, the module dimensions, and the spacers. Spacers (or turbulence promoters), which are usually plastic, net-like materials, are used to create flow channels between the membrane layers and to reduce liquid film resistances in applications which are mass transfer limited.
0376-7388/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI0376-7388(94)00043-X
P.J. Hickey, C.H. Gooding /Journal ofMembrane Science 92 (I 994) 59- 74
60
However, spacers also create larger pressure drops in flow channels. A detailed study of the friction loss characteristics of the spacers evaluated in this work has been presented previously [ 3 1. In principle, an optimal feed flow velocity should exist at which the benefit of enhanced mass transfer and the detriment of increased pressure drop are balanced. One potential application of pervaporation is the removal of volatile organic compounds (VOCs) from water (Fig. 1). Groundwater is susceptible to contamination due to chemical spills and underground storage tank leakage. Since half the drinking water used today in America comes from the ground, the remediation of contaminated groundwater has become a priority [ 41 . On the EPA’s first priority list of hazardous substances, 33 of the 100 chemicals were VOCs [ 5 1. VOCs are typically separated from water using a combination of air stripping and carbon adsorption. Air stripping can result in an objectionable level of air pollution, and carbon adsorption is a relatively expensive addon. Since many VOCs are sparingly soluble in water, pervaporation with organophilic membranes will produce a permeate concentration well above the organic solubility limit. As indicated in the process flow sheet in Fig. 1, the low solubility of both the VOC in water and water in the VOC then enhances the membrane separation and produces two product streams of nearly pure water and pure organic. The separation of dilute VOCs from water by
“8
voc
A
l
*
voc
.
voc
“A’ Fig. 1. Schematic diagram of the pervaporative VOCs from water.
removal of
pervaporation is typically a mass transfer limited process [ 6-9 1. On the feed side of the membrane, the transport of organic from the bulk liquid feed to the membrane interface is much slower than the transport of organic through the membrane. The mass transfer resistance on the permeate side of the membrane is usually assumed to be negligible since diffusivities in gases are much greater than in liquids. A balance between the benefit of enhanced mass transfer and the detriment of increased pressure drop is desired on the feed side. A spacer with low pressure drop characteristics is preferred on the permeate side. This mass transfer study is part of a research plan to determine optimal spiral wound module configurations and operating conditions for the removal of VOCs from water by pervaporation. Ultimately, the most efficient feed spacer can be determined using an optimization scheme developed by C&C and Lipski [ 7-9 ] with friction loss data reported previously [ 3, lo], and the mass transfer characteristics presented here. The overall optimization requires a module performance model [ 111 and an economic model [ lo].
2. Background 2.1. Literature review A review of the literature shows that minimal work has been published on the hydrodynamics of spacers. Glatzel and Tomaz [ 121 studied the heat transfer characteristics for flow through a spacer in a plate heat exchanger. Hicks [ 13 ] investigated the use of spacers for electrochemical applications. Belfort and Guter [ 141 used spacer filled channels to study the hydrodynamics of flow through spacers for electrodialysis. Schock and Miquel [ 15 ] studied various feed and permeate spacers from Nalle, Toray, FilmTec, and Desal. They conducted a limited number of reverse osmosis experiments with salt water using both a spiral wound module and a spacer-filled and developed dimensionless test cell correlations.
P.J. Hickey, C. H. Gooding /Journal ofMembrane Science 92 (1994) 59- 74
61
Light and Tran [ 16,171 evaluated a common diamond-shaped Vexar spacer from du Pont along with five other custom spacers using electrodialysis in a test cell. The custom spacers were cylindrical strands of stainless steel tubing suspended transverse to the flowing liquid between the upper and lower plate. Da Costa et al. [ 18 ] studied three spacers in various orientations by performing ultrafiltration with dextran T500 in a test cell. They concluded that at high flow rates through the spacers they tested, the friction loss results indicated turbulent flow behavior and the mass transfer results indicated laminar flow. To our knowledge, no one has published mass transfer correlations for spiral wound spacers based on pervaporation experiments. Furthermore, no one has obtained by any means and published detailed studies of the mass transfer characteristics of spacers available from American manufacturers.
the membrane and liquid film resistances for the removal of carbon tetrachloride from water using a relatively thick ( 165 ,um) poly (dimethylsiloxane ) (PDMS ) membrane. The membrane resistance (36 s/cm) was much less than the typical liquid film resistances ( 1OO- 1000 s/cm) for this separation. C&t and Lipski [ 7,9] also showed how several design and operating variables can influence the economics of pervaporation for the removal of VOCs from water. The variables that affect the efficiency of separation can be determined from the component flux equations. The organic flux through the membrane is proportional to the overall mass transfer coefficient from Eq. ( 1) and the chemical potential driving force. For Henry’s law behavior of organic in the feed and ideal gas behavior in the permeate, the organic flux is given by
2.2. Mass transfer
The water flux is a function of the water permeability in the membrane and the chemical potential driving force. For X, approaching one, Raoult’s law applies to water in the feed, yielding
C&C and Lipski [ 8,9] were among the first to show that pervaporation is typically limited by mass transfer on the liquid side of the membrane in the separation of dilute VOCs from water. For this application, the development of modules that achieve high mass transfer coefficients is most important. The choice of membrane is less critical, and relatively thick, commercially available membranes made of silicone rubber or polyethylene are sufficient or even preferable over thinner, composite materials since they are less expensive and permeate less water. C&e and Lipski proposed a resistance-in-series model to describe the mass transfer of dilute organic from the bulk liquid to the permeate vapor. The overall resistance is considered to be the sum of the resistances of the liquid film and membrane. 1
-= KO
I+--!KCL k
HS,D,
(1)
The liquid film resistance, l/k, is often dominant. For example, Gooding et al. [ 61 calculated
J,=K,,C(x,--
J=KC w
w
$$)
1-g (
PW >
(2)
(3)
Since water is abundant in the feed, there is no resistance to water in the liquid film, therefore K = P,&D, w CL,
(4)
For a given feed solution, module, and membrane, varying the feed flow rate or the membrane thickness, L,, will usually influence the separation. The water flux is inversely proportional to the membrane thickness but the effect of membrane thickness on organic flux varies. At low flow rates with high liquid film resistances, the membrane thickness has little effect on the organic flux. But as the flow rate is increased and the liquid film resistance is reduced, the membrane resistance can become important. The feed flow rate has no effect on the water flux but can have a significant effect on the or-
P. J. Hickey, C. H. Gooding /Journal
62
ganic flux in the application of dilute VOC removal from water. The relationship between the liquid mass transfer coefficient, k, and the flow rate is usually expressed as a dimensionless Sherwood number correlation. c
(5) The constants a, b, c, and e are particular to each module and to the flow regime. As shown in Eq. (5 ), the mass transfer coefficient is proportional to the volumetric flow rate to the power b, which is typically less than one. As the flow rate is increased, the mass transfer coefficient also increases. Ideally, the module can be operated at a flow rate where the liquid film resistance is negligible. However, since modules should be compared by total capital and operating costs, friction losses through the module must also be considered. Sherwood number correlations, as defined in Eq. (5 ), can be very useful for expressing the performance of a single type of geometric shape. However, unless a characteristic dimension can be defined for the flow channel which allows the mass transfer data from all spacers to be reduced to a single correlation, the comparison of Sherwood number correlation for different spacers may be misleading. In such cases, a spacer may have a lower Sherwood number than another spacer even though it produces a higher mass transfer coefficient. To avoid this situation it may be more useful to express the mass transfer data in a dimensional form, with the mass transfer coefficient correlated directly with the superlicial feed velocity. k=iiv’
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Science 92 (I 994) 59- 74
porative removal of VOCs from water through a silicone rubber membrane was used as a test separation. Due to the nature of the separation, the liquid film mass transfer coefficient cannot easily be measured directly. Two sets of experiments were required to decouple the liquid film and membrane resistances to organic transport. In each set of experiments the overall organic mass transfer rate was determined by measuring the rate of organic lost from a batch feed. This is believed to be the most reliable of several available methods of determining the overall mass transfer coefficient, K, [ 19 1. The experiments used to measure the rate of VOC removed from the feed were performed in a basic pervaporation test loop shown in Fig. 2. A batch feed is recirculated through a test cell containing a membrane. The mass transfer driving force is provided by a vacuum pump that reduces the pressure on the permeate side of the membrane. The permeate is collected in condensers, which are submerged in liquid nitrogen. The recirculation of the feed and a magnetic stirrer inside the feed tank keep the feed solution well mixed. The permeate pressure is maintained at N 1 mmHg to allow the assumption that the partial pressures of organic and water on the permeate side of the membrane are negligible. With this assumption, Eq. (2) can be combined with an unsteady state mass balance on the organic component of the feed in the batch system illustrated in Fig. 2 to yield (7)
(6)
For any particular set of flow conditions the exponent b in Eqs. (5 ) and (6 ) will be the same. 3. Determination of the overall VOC mass transfer coefficient The ultimate objective of this work was to determine liquid film mass transfer coefficients for flow through spacer-filled channels. The perva-
Fig. 2. Diagram of experimental
pervaporation
apparatus.
P.J. Hickey, C. H. Gooding /Journal of Membrane Science 92 (I 994) 59- 74
Eq. (7) can be integrated to exploit an easier approach of feed loss measurement. In(:)
= (*)t
Fig. 3 is a semi-log plot of typical experimental data. The bulk feed organic concentration was analyzed intermittently using a gas chromatograph with a flame ionization detector. Samples were drawn from the feed bath through a 3 mm thick silicone septum. A stainless steel column filled with 1% SP-10000 on 60/80 mesh CarbopackTMpacking from Supelco was used in the gas chromatograph to separate the organic and water during analysis. With knowledge of the batch feed volume and the active membrane area, the overall organic mass transfer coefficient can be determined from the slope of the data plotted in the form of Eq. (8). The use of Eq. ( 8 ) requires that organic losses
Fig. 3. Example plot of mass transfer data and determination of K,.
63
from the feed, other than through the membrane, be negligible. Minimizing organic leaks from the experimental system is difficult because most VOCs of interest are very volatile and are sparingly soluble in water. Due to its relatively low volatility and high solubility in water, methylene chloride was used as the representative VOC for liquid film mass transfer experiments. Maintaining a tight seal on the feed tank and removing all air from the feed side of the experimental loop reduced the rate of organic leak greatly. The organic leak could not be eliminated totally for the apparatus used to determine the membrane permeability. When the organic leak is significant, the leak rate must be quantified. Assuming the VOC leak rate is proportional to the VOC feed concentration, Eq. (8) can be modified to incorporate a leak coefficient.
ln($) =-(K,‘y+“>l
(9)
To determine the leak coefficient, 1, the same experimental procedure described above is used but the permeate pressure is maintained at ambient conditions, thus removing the driving force for mass transfer through the membrane. Fig. 4 shows a typical semi-log plot of the data for a system with a significant organic feed leak. The relative significance of the leak rate and the uncertainty it introduces depends on the overall mass transfer rate of the particular experiment. In this work 1 was less than 20% of the mass transfer rate through the membrane in all cases and was typically much smaller.
4. Determination of membrane resistance 4. I. Experimental methods
Fig. 4. Example plot of experimental mass transfer data and determination of K, and i for an experimental system with a significant organic leak.
Experiments of the type described above give the total resistance to organic transport. Theoretically, the liquid film resistance can be eliminated by using very high feed flow velocities and very thick membranes, and the membrane resis-
64
P.J. Hickey, C. H. Gooding /Journal of Membrane Science 92 (I 994) 59- 74
tance is then determined directly. However, the extreme conditions necessary to accomplish this are not easily achieved in the pervaporation of VOCs. Values for the membrane resistances of various VOCs have been reported in the literature based on single experiments in a cell at a fast stirring rate and with thick membranes, but we believe the accuracy of data determined in this manner is dubious unless evidence is given to demonstrate that the liquid film resistance was negligible.
I
Retentate
The membrane resistance to organic transport can be determined using an extrapolative technique, the Wilson plot [ 20-221. To construct a Wilson plot, the feed flow rate is varied in a range over which the liquid film resistance is signiticant. Then the overall organic resistance, l/K,, is plotted versus the inverse of the volumetric flow rate raised to the power b. The exponent b is determined from the best linear fit of the data. The value 1/Qb is proportional to the liquid film resistance to organic transport. Therefore, as 1 /
4
I
Permeate +
Fig. 5. Diagram of MDS test cell used to determine membrane resistance.
P.J. Hickey, C.H. Gooding /Journal of Membrane Science 92 (I 994) S9- 74
Qb approaches zero the liquid film resistance also approaches zero, and the intercept of the graph represents the membrane resistance to organic transport. Our Wilson plot experiments were performed with a membrane test cell made by Membrane Development Specialists (an affiliate of Desal, Escondido, CA, see Fig. 5 ). The test cell consists of two PVC plates held together by four bolts. The test cell is unique in that the feed is delivered to the interior of the cell tangentially and flows in a spiral pattern to the exit in the center. The interior of the cell is tapered to maintain a constant feed velocity across the membrane. The leak rate from the experimental loop used for these experiments could not be eliminated, but it was quantified using the method outlined above. 4.2. Results and discussion Experiments were performed in the MDS test cell to determine the permeability of methylene chloride through a 127 pm thick Dow Corning Silastic membrane. The Wilson plot for this system is shown in Fig. 6. A membrane resistance of 22,670 s/m was determined from the intercept of the best fit line through the data. This equates to an overall mass transfer coefficient of 4.41 x low5 m/s when the liquid film is negligible. For this case, Eq. ( 1) becomes simplified and the permeability of the organic in the membrane is calculated to be
OF 0
I
0.005
I
I
0.010
0.015
0.020
l/Qbb,(Q in cm%ec)
Fig. 6. Wilson plot for methylene chloride and a 127 pm thick Dow Coming Silastic membrane determined with the MDS test cell and with b=0.684.
65
Table 1 Summary of membrane permeabilities obtained from Wilson plot experiments with MDS test cell
voc
Exponent Intercept H b (MPa) (s/m) (best fit)
1,2-Dichloroethane 0.692 Methylene chloride 0.684 Chloroform 0.705 Trichloroethylene
&IX,=+=
0.692
33,300 22,670 16,820 4,420
s&,x 10” (mol/msPa)
5.6
3.8
9.7 17 56
3.2 2.5 2.8
3.2x10-“=
(10)
To test the validity of the method further, the experiment was repeated with three other VOCs, chloroform, trichloroethylene, and 1,2-dichloroethane. The exponent b in the power law relationship between the liquid film mass transfer coefficient and the feed flow rate should be independent of the particular VOC as long as the solution is dilute. The results with all four VOCs were consistent as shown in Table 1, yielding an average b value of 0.69.
5. Spacer mass transfer characteristics 5.1, Experimental methods
A separate set of experiments was performed to determine the liquid film mass transfer coefficients for flow through spacers. Overall methylene chloride mass transfer coefficients were determined experimentally for each spacer at various flow rates. Using Eq. ( 1) and the membrane resistance to methylene chloride transport determined in the Wilson plot experiments, the values of the liquid film mass transfer coefficient were calculated. Dimensionless Sherwood number correlations [ Eq. (5 ) ] were developed with knowledge of the liquid film mass transfer coefficients and physical properties of the spacer and VOC. The dependency of the Sherwood number on the Schmidt number, SC, was not evaluated but was assumed to equal 0.33. The Schmidt number of a dilute aqueous methylene chloride solution at 20°C is 770. The exponent e in Eq.
P.J. Hi&v,
66
C. H. Gooding /Journal ofMembrane
(5) was assumed to be zero since the d/L term corrects for a developing mass transfer boundary layer in laminar flow and this correction should not be necessary for the tortuous flow path of a spacer-filled channel. A membrane test cell containing a spacer-filled channel was designed specifically for the liquid film resistance experiments of this study. The test cell, shown in Fig. 7, was constructed of plexiglass to allow for viewing of the flow channel. Most test cells described in the literature use a gasket to create a flow channel between two flat plates. However, the test cell used for this study is unique in that it has a flow channel cut into the upper plate, four smooth walls in the flow channel, and no gaskets. When spacers thinner than the flow channel were evaluated, a mylar plastic insert was placed in the void above the spacer to prevent channeling of the feed flow around the spacer. Visual dye tests were performed to confirm that the insert prevented flow channeling. The plexiglass plates were held together with two aluminum braces (Fig. 7). The braces and plates were bolted together with each bolt tightened to the same torque (75 in-lbs). The membrane was cut slightly larger than the flow channel and was placed on the lower plate of the test cell. The excess membrane provided a seal between the two plates and prevented leakage of the feed solution from the test cell without the use of gaskets. The active membrane area for this experimental system is defined by the area of the square permeate slit cut into the lower plate of the test cell, as shown in Fig.7. A spacer was placed into
lecd
mm
emuentport
Science 92 (1994) 59- 74
the permeate slit to keep the membrane flush with the surface of the lower plate. The low pressure in the permeate slit pulls the membrane down onto the spacer and forms a seal around the edge of the permeate slit. The empty slit channel height of the test cell, 2B, is 1.5 mm. The heights of the spacers tested ranged between 0.483 and 1.45 mm. The channel width, W, is 30 mm, or twenty times the maximum channel height, to allow the assumption of one-dimensional flow when the channel is empty (without spacers). Well above the feed chamlel cut into the upper plate, the feed and effluent ports were enlarged to cover the full channel width and thus distribute the flow evenly (Fig. 7). The length between the channel entrance and the front edge of the active membrane area is 60 mm, or forty times the maximum channel height. The length needed for laminar flow to develop completely in a thin slit is a function of the Reynolds number and the channel height [ 23 1,
L
6
=0.625+0.044
Re
(11)
The characteristic dimension used in Eq. ( 11) is the channel height, 2B. When performing calibration experiments with an empty feed channel, it is important to operate the system at Reynolds numbers that produce a fully developed flow before the active membrane area. The volumetric flow rate was determined by recording the time needed to till a 1000 ml volumetric flask. The velocity, v, used in the calculations is a superficial or approach velocity and is calculated by dividing the volumetric flow rate by the empty channel area, i.e., channel or spacer height times channel width. The VOC leak rate in this test cell and loop was so small that no leak could be detected over several hours of operation, the same duration as the mass transfer experiments. 5.2. Calibration
Fig. 7. Diagram of test cell used to determine transfer characteristics.
spacer mass
Before experiments were initiated to determine the feed side mass transfer characteristics
P.J. Hickey, C.H. Gooding /Journal ofMembrane Science 92 (I 994) 59- 74
of spacer-filled channels, calibration experiments were performed to test the experimental apparatus and ensure the validity of the experimental technique. The design of the spacer test cell assumed that the vacuum would provide a sufficient seal around the permeate slit without the use of a gasket and that the exposure of the dilute organic feed to non-active membrane area would not present a problem. A visual inspection of the cell showed that with vacuum on the permeate side, the membrane sealed well around the permeate slit. Flux experiments were also performed to validate this observation. Using a pure water feed, the water flux was determined by weighing the permeate collected in a liquid nitrogen condenser. The same experiment was done with the MDS membrane cell and the fluxes agreed within 5%. The significance of the comparison is that in the MDS cell all of the membrane exposed to the feed is also exposed to the permeate pressure. Therefore, this is further evidence that the seal was adequate, and there is no transport through the non-active membrane. The final calibration was done to ensure that the experimental and analytical techniques used to determine the liquid film mass transfer coefficients in the spacer cell were accurate, and that the non-active membrane area had no signiticant effect on the VOC. For laminar flow through conduits an accepted Sherwood number correlation, usually attributed to Leveque [ 241, is 0.33
Sh= 1.62 ReS+ (
>
(12)
where the characteristic dimension is the hydraulic diameter, d,,, defined as the cross-sectional area of the flow channel divided by the wetted perimeter of the flow channel. Mass transfer experiments were performed with the spacer cell empty (without any spacers) to determine K, and the results were adjusted using Eq. ( 1) and the membrane resistance obtained in the MDS test cell to get the liquid film mass transfer coefficient, k. For this flow channel, which is a thin, rectangular slit with the width much greater than the height, the hydraulic di-
67
K)
Fig. 8. Plot of experimental and theoretical Sherwood numbers as a function of Reynolds number for flow in a thin slit (the spacer test cell empty).
ameter can be approximated as two times the channel height. Fig. 8 shows a plot of the experimental and theoretical Sherwood numbers for laminar flow through the empty membrane cell. There is good agreement, which increases our confidence that the method is valid and that liquid film resistance experiments conducted with spacer-filled channels are accurate.
5.3. Results and discussion After the membrane resistance to methylene chloride transfer was determined and the spacer test cell apparatus was calibrated, experiments were performed to determine liquid film mass transfer coefficients for flow through spacer-filled channels. These experiments were conducted at different feed flow velocities and with fifteen different feed spacers. A compilation of the spacer data, characteristics, and mass transfer correlations obtained in this work is shown in Table 2. The characteristic dimension used to describe the Sherwood and Reynolds numbers in the table for Eq. ( 5 ) is the thickness of the spacer, 28, and the characteristic velocity is the superficial velocity. Hickey and Gooding [ 3, lo] were able to reduce the friction loss data of several spacers to a single correlation by developing an equation to describe a hydraulic diameter for a channel filled with diamond-shaped spacers. Attempts to use this technique on our mass transfer data were not successful. Since the mass transfer characteristics of each spacer require a unique
P.J. Hickey, C.H. Gooding /Journal
68
Table 2 Spacer characteristics
ofMembrane
Science 92 (I 994) .59- 74
and mass transfer correlation constants obtained in this work for
Spacer (TP #)
I. Naltex MWN 2. Naltex Ultraflo’ 4. Naltex LWS 7. Maynard 6 150-7 8. Maynard 6145-I 9. Internet XN-43 11 10. National MO Grid” 12. Internet XN-1670 13. Internet XN-3235 14. Naltex ROF 15. Naltex 368 1 16. Naltex Ultraflo’ 18. Naltex Ultraflo’ 19. Naltex Ultraflo” 20. Naltex Uhraflo’
2B (mm)
1.10 1.10 0.508 0.762 0.559 0.762 1.20 0.991 0.483 0.762 0.762 0.762 1.14 1.45 0.762
t
0.86 0.89 0.87 0.86 0.87 0.86 NA NA NA 0.89 0.87 0.86 0.89 0.85 0.92
spi”
8x8 5x8 16x16 12x 12 15x15 12x 12 13x13 7x5 14x11 9x9 11x11 6x9 5x8 5x8 6x11
ConstantsforuseinEqs. ri x105
a
8.752 7.475 5.697 5.574 7.475 8.199 9.859 8.626 7.821 6.568 7.968 6.740 7.566 8.422 5.647
0.894 0.808 0.322 0.474 0.694 0.352 0.990 0.624 0.320 0.588 0.638 0.282 0.570 1.296 0.278
b
vx
2B between 0.67 and 6.67 cm2/s
(5)b, (6), (13)and(14) a’
b’
x 1o-6 0.413 0.405 0.435 0.408 0.395 0.511 0.423 0.455 0.484 0.401 0.418 0.516 0.460 0.379 0.49 1
3.21 0.482 0.561 0.552 0.817 0.639 0.868 1.00 0.577 0.325 0.43 I 0.182 0.254 0.268 0.240
a”
h”
x IO’O 1.755 1.484 1.585 1.481 1.462 1.617 1.527 1.713 1.178 1.497 1.616 I.338 1.551 1.611 1.568
0.273 I.551 1.016 1.010 0.883 1.289 1.120 0.863 1.355 2.022 1.849 3.695 2.978 3.140 2.353
- 1.34 - 1.08 -1.15 - 1.07 - 1.07 -1.11 -1.10 - 1.26 -0.69 - 1.10 - 1.20 -0.82 - 1.09 - 1.23 - 1.08
“The first spi (strands per inch) is for the thicker strand for Nahex Ultraflo and for the transverse strand for InterNet. bit is assumed that in Eq. (5) c is equal to 0.333 and e is equal to zero. ‘The heavy thread is parallel to flow and the minor thread is angled. dEvery fourth strand is a thicker strand.
correlation, there is no benefit to using a complicated channel dimension or flow velocity. A typical plot of the raw experimental data for various feed flow rates is shown for spacer TP 8 in Fig. 9. The best lit lines drawn through each data set had very high values of the correlation coefficient r, indicating accurate fits. Dimensionless Sherwood number versus Reynolds number correlations were derived from the experimental data. Two specific correlations for spacers TP 8 and TP 10 are shown in Fig. 10 along with a shaded area that represents the region where the data from all of the spacers lie. The Sherwood numbers for flow through the spacers were 1.5 to 4 times greater than the Sherwood numbers for flow through an empty, thin slit. Spacer TP 10, a unique diamond-shaped spacer whose strands are centered between the upper and lower walls of the channel, produced the highest mass transfer coefficients of all the spacers tested. Spacer TP 13 from Internet produced the greatest increase in mass transfer rates
as compared to an empty channel of the same height as the spacer. However, TP 13 is the thinnest of all the spacers evaluated at 2B= 0.483 mm and the thin channel height is penalized by higher friction loss. The range of data from all of the spacers in Table 2 is shown in Fig. 11 in terms of liquid film mass transfer coefficients and superficial feed velocities in the form of Eq. (6 ). Data from two specific spacers are shown to illustrate the typical lit and all of the data are documented elsewhere [ lo]. The liquid film mass transfer coefficients for all the spacers ranged from 2.0~ lop5 to 8.2~ lop5 m/s. As shown in Table 2, the exponent b in Eq. ( 5 ) ranged between 0.40 and 0.50 for most of the spacers evaluated. If the exponent b is an indication of the flow regime, then all of the spacers tested were in the transitional regime for the flow rates studied, closer to laminar flow than turbulent. Pressure drop correlations for these same spacers are also shown in Table 2 in the dimensional form
P.J. Hickey, C.H. Gooding /Journal ofMembrane Science 92 (I 994) 59- 74
AP -_=a’vb’ L
(13)
with AP/L in units of N/m3 and v in m/s. Additional details on these data are given elsewhere [ 3,101. The correlations also indicate that the flow through the spacers was in the transitional regime in the range of flows tested. There are no obvious correlations between the mass transfer and friction loss characteristics of the spacers. For example, to achieve similar liquid film mass transfer coefficients TP 10 creates approximately four times more pressure drop than TP 18 does. The results in Table 2 show that Naltex Ultraflo spacers will produce liquid film mass transfer coefficients in the same range as diamond-shaped spacers that produce much greater pressure drops. It would appear that using Ultraflo spacers in the feed channel would be more productive than using common diamond-shaped 4.0
4.1
a.2
In(?)
-0.3
-0.4
a.5
1
69
spacers unless a detailed economic analysis indicates that a small reduction in membrane area requirement will compensate for a large increase in feed pressure drop. To differentiate between spacers with similar mass transfer characteristics, a simplistic spacer efficiency was developed by dividing the mass transfer coefficient by the pressure drop per unit length. Dividing the two dimensional correlations, Eq. (6) by Eq. ( 13 ), yields a spacer mass transfer efficiency as a function of the feed velocity.
?#I=-
k
=a,‘vb”
AP ( L>
(14)
The values of a” and b” are reported in Table 2, and Fig. 12 shows a plot of the spacer efficiencies at a superficial flow velocity of 0.5 m/s. While the difference in mass transfer coefficients for all the spacers at a given velocity is small, the spacer efficiency can vary by as much as a factor of ten. Fig. 12 was developed with a simplistic approach, but it is helpful to show the diverse performance characteristics of the spacers. A detailed economic model will ultimately be needed to rank the spacers in terms of lowest cost of separation per volume of feed treated for specific applications. The relative ranking of the spacers will most likely change from Fig. 12 depending on the relative magnitudes of the capital and operating costs and hence the relative importance of increasing mass transfer and decreasing friction loss. For cases in which capital costs, i.e, membrane materials used, are relatively inexpensive, Ultraflo spacers will be attractive due to the lower friction loss characteristics. 5.4. Comparison with other reported results
1.5
2.0
lime (hr)
Fig. 9. An example of experimental mass transfer data, the log of the normalized feed concentration versus time for TP 8.
Mass transfer data from the literature obtained for several spacers in reverse osmosis and ultrafiltration experiments are shown in Table 3. Values of correlation parameters b and c in Table 3 were taken directly from the original work. It is not clear why the authors used the indicated values of c rather than the conventional value of
70
P. J. Hickey, C. H. Gooding /Journal
of Membrane
Science 92 (1994) 59- 74
I 100 Reynolds Number, Re Fig. 10. Experimental
Sherwood number versus Reynolds number correlations.
0.10
1.OO
Superficial Feed Velocity, v (m/s) Fig. 11. Experimental
data correlated in the form of Eq. (6).
0.33. The correlation parameters a in Table 3 are different than those presented in the referenced publications. The parameters were transformed to allow for direct comparison with the correlations presented in this work. They were determined on the basis of simple superficial velocities and with channel height or spacer thickness as the characteristic dimension. Fluid properties were evaluated at bulk feed flow conditions and parameter e was assumed to be zero. In their original work, Schock and Miquel [ 15 ] used a mean velocity and described the flow channel by a hydraulic diameter. This hydraulic diameter as defined by Schock and Miquel can be reduced to
be a simple function of the channel height and porosity, as shown by Hickey and Gooding 13,101
(15) Da Costa et al. [ 181 also defined the channel dimension using Eq. ( 15 ) and used a mean velocity to define the Reynolds number of the flow. Furthermore, Da Costa et al. determined fluid properties based on calculated feed concentrations at the membrane wall instead of bulk feed conditions, which can be measured analytically. The correlations published by Da Costa et al.
P.J. Hickey, C.H. Gooding / Journal ofMembrane Science 92 (1994) 59-74
71
Spacer, (TP #) Fig. 12. Mass transfer efficiencies of spacers for a superficial feed velocity of 0.5 m/s.
Table 3 Literature spacer characteristics TP
2B (mm)
Various Old 1.85 UFl 1.70 1.70 UF2 UF3 1.70 UF4 1.70 80-Mil-1 2.10 80-Mil-2 2.10
and correlation parameters
Eo. (5) a
b
c
0.069 a a a 0.020 0.025 0.033 0.029
0.875 0.53 0.49 0.52 0.59 0.50 0.62 0.66
0.25 0.60 0.59 0.60 0.60 0.59 0.58 0.58
“Could not be transformed
Range valid (d=2B)
Ref.
50
15 18 18 18 18 18 18 18
with available information.
predict very high Sherwood numbers at relatively low Reynolds numbers, but this is due to the unconventional description of fluid properties rather than high mass transfer characteristics. The results reported by Schock and Miquel [ 151 indicate a strong relationship between the Sherwood number and the Reynolds number (see Table 3). The exponent b from Eq. (5) in their correlation is 0.875, indicating flow in the turbulent regime. This b is twice the typical value determined for the spacers in this study (see Ta-
ble 2 ) . However, Schock and Miquel developed their correlation from data obtained with different membranes, spacers, and feed pressures, and it appears that the exponent b was not derived from a linear regression on all or any of the experimental data. Rather, their correlation was apparently determined by fixing the exponent b equal to 0.875 (perhaps based on common heat transfer correlations for turbulent pipe flow) and then allowing the other parameters in the Sherwood number correlation to be determined by a data fit. In our work a separate correlation was developed for each specific spacer using the same membrane and feed conditions. In the form of Eq. (5) the data from Da Costa et al. [ 18 ] were correlated with values of b ranging from 0.49 to 0.66, but Da Costa et al were unable to match the theoretical Reynolds number versus Sherwood number relationship when their apparatus was operated as an empty slit. Instead of an exponent b equal to 0.33 for the empty slit experiments, their data were fit with a correlation with b equal to 0.43. We believe that this overestimation in b was caused by the short entrance length used in their test cell. The channel entrance length in their cell was only 3 mm, or
72
P. J. Hickey, C. H. Gooding /Journal
twice the channel height. For the range of the Reynolds numbers of their empty slit experiments, an entrance length ten to forty times the channel height would be required according to Eq. ( 11). In the entrance region mass transfer is enhanced because the flow profile is not fully developed. In their subsequent studies of mass transfer characteristics of spacer-filled channels, an entrance region effect may have caused the correlations to overpredict the value of b as it did in the empty slit experiments. Da Costa disagrees with our analysis, however, stating that the entrance region is insignificant in a spacer-filled channel [ 25 1.
of Membrane
Attempts to consolidate the results of many spacers into a single correlation using a characteristic dimension for the spacer-tilled channel proved fruitless. Although this technique reduced friction loss results for diamond-shaped spacers into a single correlation, it did not work for the mass transfer results.
7. List of symbols correlation constant in Eq. ( 5 ) (-) correlation constant in Eq. (6 ) (-) correlation constant in Eq. ( 13 ) (- ) correlation constant in Eq. ( 14) (-) membrane area ( m2) bm correlation constant in Eqs. ( 5 ) and (6 ) (-) correlation constant in Eq. ( 13 ) (- ) b’ correlation constant in Eq. ( 14) (-) b” B ideal spacer strand diameter and half the channel thickness (m) correlation constant in Eq. ( 5 ) (-) C organic feed concentration (ppm) Co initial organic feed concentration ( ppm ) Cc% molar density of water ( mol/m3 ) C characteristic dimension (m) d hydraulic diameter ( m ) d,, diffusivity of permeant in membrane D (m2/s) correlation constant in Eq. (5 ) (-) s; Henry’s law constant, (Pa) molar flux ( mol/m2 s) J liquid film mass transfer coefficient (m/s) k overall mass transfer coefficient (m/s) K channel length (m ) L entry length (m) L, membrane thickness (m) L, A4 molecular weight (g/mol ) NA not available permeate pressure (Pa) P PW vapor pressure of water (Pa) volumetric flow rate (m3/s) Q correlation coefficient (- ) Reynolds number (-) L spi strands per inch (in- ’ ) sorption coefficient of permeant in mems brane ( mol/m3 Pa) SC Schmidt number (- ) a ii a’
I,
ti
6. Summary Mass transfer correlations were determined for 15 spacers with potential for use in the feed channel of spiral wound membrane modules built for pervaporation. Like the friction loss data determined for these spacers, the mass transfer results show that the hydrodynamics are in the transitional flow regime between laminar and fully turbulent flow. Spacer mass transfer coefficients are a function of the superficial flow velocity raised to the power b, where b ranged from 0.38 to 0.52. In this work the liquid film mass transfer coefficients determined for the spacers ranged from 2.0x 10m5 to 8.2x 10e5 m/s. The use of spacers in the flow channel enhanced mass transfer by 1.5 to 4 times over the mass transfer in an empty slit at similar superticial flow velocities. Despite the fact that the spacers had much different friction loss characteristics, the range of mass transfer coefficients produced by the spacers did not vary much for the flow velocities tested. Naltex Ultraflo spacers produced mass transfer coefficients in the same range as common diamond-shaped spacers despite the fact that Ultraflo spacers create much less pressure drop. Naltex Ultraflo spacers appear to have an economic advantage over most of the spacers, especially diamond-shaped ones, due to their low pressure drop at similar mass transfer coefficients.
Science 92 (I 994) S9- 74
P.J. Hickey, C. H. Gooding /Journal of Membrane Science 92 (I 994) 59- 74
Sh t u V
V W X
Y
Sherwood number (-) time (s) mean velocity v/t (m/s) superficial velocity (m/s) volume of batch feed ( m3 ) channel width (m) liquid mole fraction (-) vapor mole fraction (-)
7.1. Greek letters AP : p Q
pressure drop (N/m* ) porosity (-) leak coefficient ( m3/s) fluid viscosity (kg/m s) fluid density ( kg/m3)
7.2. Subscripts 0 W
organic water
Acknowledgments The authors thank Nalle Plastics, Inc., Maynard Plastics, InterNet, Inc., and National Netting, Inc. for providing spacers and pertinent information about them and Douglas Haugh for his assistance with the experiments.
References [ 1 ] M.C. Porter, Handbook of Industrial Membrane Technology, Noyes, Park Ridge, NJ, 1990. [ 21 J. Reale Jr., V.M. Shah and C.R. Bartels, The use of spiral wound modules in pervaporation, in R. Bakish (Ed. ) , Proc. 5th Int. Conf. Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1991, p.231. [ 3lP.J. Hickey and C.H. Gooding, Friction loss in spiral wound membrane modules, in: R. Bakish (Ed. ), Proc. 6th Int. Conf. on Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1992,~. 153. [4]L. Hooker, Danger below, Chem. Eng. Prog., 86( 5) ( 1990) 52. [ S]Federal Register, Vol. 52, No. 74, p. 12866, April 17, 1987.
13
[6]C.H. Gooding, P.J. Hickey and M.L. Crowder, Mass transfer characteristics of a new pervaporation module for water purification, in R. Bakish (Ed.), Proc. 5th Int. Conf. Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NH, 1991, p. 237. [ 71 P. C&C and C. Lipski, A technico-economical evaluation of pervaporation for water treatment, in R. Bakish (Ed. )., Proc. 4th Int. Conf. Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1989, p. 304. [ 81 P. Cote and and C. Lipski, Reducing concentration polarization in pervaporation for trace contaminant removal, in Proc. 1990 Int. Cong. Memb. Memb. Proc. Vol. I, 1990, p. 325. [ 91 P. C&C and C. Lipski, The use of pervaporation for the removal of organic contaminants from water, Environ. Prog., 9 (1990) 254. [ 1OlP.J. Hickey, The Optimization of Spiral Wound Membrane Modules for the Pervaporative Removal of Volatile Organic Compounds from Water, Dissertation, Clemson University, Clemson, SC, 1993. [ 11 ]P.J. Hickey and C.H. Gooding, Modeling spiral wound modules for the pervaporative removal of volatile organic compounds from water, J. Membrane Sci., 88 ( 1994) 47. [ 121 W.D. Glatzel and M.C. Tomaz, The effect of turbulence promoters on heat transfer and pressure drop in a plate heat exchanger, CSIR Special Report CHEM 53, 1966. [ 13lR.E. Hicks, Chemical Engineering Group, CSIR, Pretoria, South Africa, Reports CHEM 54,126, and 138, 1967-70. [ 14]G. Belfort and G.A. Guter, An experimental study of electrodialysis hydrodynamics, Desalination, 10 ( 1972) 221. [ 15]G. Schock and A. Miquel, Mass transfer and pressure loss in spiral wound modules, Desalination, 64 ( 1987) 339. [ 161 W.G. Light and T.V. Tran, Improvement of thin-channel design for pressure-driven membrane systems, Ind. Eng. Process Des. Dev., 20 ( 198 1) 33. [ 17lT.V. Tran and W.G. Light, Design and operational improvements for thin-channel membrane systems, in Proc. Second World Cong. Chemical Engineering, 1981, p. 492. [ 18lA.R. Da Costa, A.G. Fane, C.J.D. Fell and A.C.M. Franken, Optimal channel spacer design for ultraliltration, J. Membrane Sci., 62 (199 1) 275. [ 19 ] C. Gooding, P. Hickey, P. Dettenburg and J. Cobb, Mass transfer and permeate pressure effects in the pervaporation of VOCs from water, in: R. Bakish (Ed.), Proc. 6th Int. Conf. Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1992, p. 80. [ 201 E.E. Wilson, A basis for rational design of heat transfer apparatus, Trans. ASME, 37 ( 19 16 ) 47.
74
P.J. Hickey, C. H. Gooding /Journal of Membrane Science 92 (I 994) 59- 74
[ 2 1] P. Dettenburg, Mass transfer and permeate pressure effects in the pervaporation of trichloroethylene from water, Diplomarbeit, Clemson University, 1992. [ 221 R. Field and R. Burslem, The effect of concentration polarisation upon the performance of pervaporation membranes, in R. Bakish (Ed.), Proc. 6th Int. Conf.
Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1992, p. 275. [ 23lB.C. Sakiadis, Perry’s Chemical Engineers’ Handbook, 6th Ed., McGraw-Hill, New York, 1984, p. 5-35. [ 241 M.A. Leveque, Les lois de la transmission de chaleur par convection, Ann. Mines, 12: 13 (1928) 201. [ 25 ] A.R. Da Costa, Personal communication, March 199 1.
ELSEVIEK
Journal of Membrane Science 92 ( 1994) 59-74
Mass transfer in spiral wound pervaporation modules Patrick J. Hickey, Charles H. Goading* Department of Chemical Engineering, Clemson University, Clemson, SC 29634-0909, USA
(Received August 27, 1993; accepted in revised form January 5, 1994)
Abstract Mass transfer performance correlations are needed for spiral wound membrane module feed spacers to determine the optimal flow velocity for each spacer, to find the most cost efficient spacer, and to compare spiral wound to other modules. The mass transfer characteristics of 15 feed spacers were determined experimentally. The mass
transfer correlations derived from the data indicate that a transitional flow regime exists in spacer-filled channels at the flow velocities evaluated. The use of a spacer increased the mass transfer coefficient to 1.5 to 4.0 times the coefficient obtained with an empty channel. There was only a modest increase in the performance of the spacer with the highest mass transfer coefficient when compared to the spacer with the lowest despite the fact that the friction loss characteristics of the spacers varied greatly. Attempts to define a characteristic dimension that would allow the consolidation of the mass transfer results from many spacers into a single equation were unsuccessful. Even spacers of a common design, i.e., diamond-shaped, required a unique equation to describe the mass transfer characteristics of each spacer. Ultraflo spacers from Nalle Plastics, Inc. provided the highest mass transfer coeffk cient per unit of pressure drop per unit length. However, the determination of the most cost effkient spacer will require the use of a detailed economic analysis. Keywords: Mass transfer; Spiral wound module; Pervaporation;
1. Introduction
Most industrial pervaporation units in use today consist of stainless steel plate and frame modules [ 11. These modules are used typically for solvent dehydration and can withstand high temperatures and corrosive environments, but they are also relatively expensive when compared with other types of membrane modules. Spiral wound modules are used commonly in reverse osmosis, ultrafiltration, and gas permeation [ 11. In applications where there is material compatibility, spiral wound modules are a less *Corresponding author.
Water treatment
expensive alternative to plate and frame modules. Commercial spiral wound modules have even been developed for some solvent dehydration applications [ 2 1. The major components of a spiral wound module are the feed and permeate spacers, the membrane, the permeate collection tube, and the shell. The performance of a spiral wound module for a given application is determined by the membrane, the module dimensions, and the spacers. Spacers (or turbulence promoters), which are usually plastic, net-like materials, are used to create flow channels between the membrane layers and to reduce liquid film resistances in applications which are mass transfer limited.
0376-7388/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI0376-7388(94)00043-X
P.J. Hickey, C.H. Gooding /Journal ofMembrane Science 92 (I 994) 59- 74
60
However, spacers also create larger pressure drops in flow channels. A detailed study of the friction loss characteristics of the spacers evaluated in this work has been presented previously [ 3 1. In principle, an optimal feed flow velocity should exist at which the benefit of enhanced mass transfer and the detriment of increased pressure drop are balanced. One potential application of pervaporation is the removal of volatile organic compounds (VOCs) from water (Fig. 1). Groundwater is susceptible to contamination due to chemical spills and underground storage tank leakage. Since half the drinking water used today in America comes from the ground, the remediation of contaminated groundwater has become a priority [ 41 . On the EPA’s first priority list of hazardous substances, 33 of the 100 chemicals were VOCs [ 5 1. VOCs are typically separated from water using a combination of air stripping and carbon adsorption. Air stripping can result in an objectionable level of air pollution, and carbon adsorption is a relatively expensive addon. Since many VOCs are sparingly soluble in water, pervaporation with organophilic membranes will produce a permeate concentration well above the organic solubility limit. As indicated in the process flow sheet in Fig. 1, the low solubility of both the VOC in water and water in the VOC then enhances the membrane separation and produces two product streams of nearly pure water and pure organic. The separation of dilute VOCs from water by
“8
voc
A
l
*
voc
.
voc
“A’ Fig. 1. Schematic diagram of the pervaporative VOCs from water.
removal of
pervaporation is typically a mass transfer limited process [ 6-9 1. On the feed side of the membrane, the transport of organic from the bulk liquid feed to the membrane interface is much slower than the transport of organic through the membrane. The mass transfer resistance on the permeate side of the membrane is usually assumed to be negligible since diffusivities in gases are much greater than in liquids. A balance between the benefit of enhanced mass transfer and the detriment of increased pressure drop is desired on the feed side. A spacer with low pressure drop characteristics is preferred on the permeate side. This mass transfer study is part of a research plan to determine optimal spiral wound module configurations and operating conditions for the removal of VOCs from water by pervaporation. Ultimately, the most efficient feed spacer can be determined using an optimization scheme developed by C&C and Lipski [ 7-9 ] with friction loss data reported previously [ 3, lo], and the mass transfer characteristics presented here. The overall optimization requires a module performance model [ 111 and an economic model [ lo].
2. Background 2.1. Literature review A review of the literature shows that minimal work has been published on the hydrodynamics of spacers. Glatzel and Tomaz [ 121 studied the heat transfer characteristics for flow through a spacer in a plate heat exchanger. Hicks [ 13 ] investigated the use of spacers for electrochemical applications. Belfort and Guter [ 141 used spacer filled channels to study the hydrodynamics of flow through spacers for electrodialysis. Schock and Miquel [ 15 ] studied various feed and permeate spacers from Nalle, Toray, FilmTec, and Desal. They conducted a limited number of reverse osmosis experiments with salt water using both a spiral wound module and a spacer-filled and developed dimensionless test cell correlations.
P.J. Hickey, C. H. Gooding /Journal ofMembrane Science 92 (1994) 59- 74
61
Light and Tran [ 16,171 evaluated a common diamond-shaped Vexar spacer from du Pont along with five other custom spacers using electrodialysis in a test cell. The custom spacers were cylindrical strands of stainless steel tubing suspended transverse to the flowing liquid between the upper and lower plate. Da Costa et al. [ 18 ] studied three spacers in various orientations by performing ultrafiltration with dextran T500 in a test cell. They concluded that at high flow rates through the spacers they tested, the friction loss results indicated turbulent flow behavior and the mass transfer results indicated laminar flow. To our knowledge, no one has published mass transfer correlations for spiral wound spacers based on pervaporation experiments. Furthermore, no one has obtained by any means and published detailed studies of the mass transfer characteristics of spacers available from American manufacturers.
the membrane and liquid film resistances for the removal of carbon tetrachloride from water using a relatively thick ( 165 ,um) poly (dimethylsiloxane ) (PDMS ) membrane. The membrane resistance (36 s/cm) was much less than the typical liquid film resistances ( 1OO- 1000 s/cm) for this separation. C&t and Lipski [ 7,9] also showed how several design and operating variables can influence the economics of pervaporation for the removal of VOCs from water. The variables that affect the efficiency of separation can be determined from the component flux equations. The organic flux through the membrane is proportional to the overall mass transfer coefficient from Eq. ( 1) and the chemical potential driving force. For Henry’s law behavior of organic in the feed and ideal gas behavior in the permeate, the organic flux is given by
2.2. Mass transfer
The water flux is a function of the water permeability in the membrane and the chemical potential driving force. For X, approaching one, Raoult’s law applies to water in the feed, yielding
C&C and Lipski [ 8,9] were among the first to show that pervaporation is typically limited by mass transfer on the liquid side of the membrane in the separation of dilute VOCs from water. For this application, the development of modules that achieve high mass transfer coefficients is most important. The choice of membrane is less critical, and relatively thick, commercially available membranes made of silicone rubber or polyethylene are sufficient or even preferable over thinner, composite materials since they are less expensive and permeate less water. C&e and Lipski proposed a resistance-in-series model to describe the mass transfer of dilute organic from the bulk liquid to the permeate vapor. The overall resistance is considered to be the sum of the resistances of the liquid film and membrane. 1
-= KO
I+--!KCL k
HS,D,
(1)
The liquid film resistance, l/k, is often dominant. For example, Gooding et al. [ 61 calculated
J,=K,,C(x,--
J=KC w
w
$$)
1-g (
PW >
(2)
(3)
Since water is abundant in the feed, there is no resistance to water in the liquid film, therefore K = P,&D, w CL,
(4)
For a given feed solution, module, and membrane, varying the feed flow rate or the membrane thickness, L,, will usually influence the separation. The water flux is inversely proportional to the membrane thickness but the effect of membrane thickness on organic flux varies. At low flow rates with high liquid film resistances, the membrane thickness has little effect on the organic flux. But as the flow rate is increased and the liquid film resistance is reduced, the membrane resistance can become important. The feed flow rate has no effect on the water flux but can have a significant effect on the or-
P. J. Hickey, C. H. Gooding /Journal
62
ganic flux in the application of dilute VOC removal from water. The relationship between the liquid mass transfer coefficient, k, and the flow rate is usually expressed as a dimensionless Sherwood number correlation. c
(5) The constants a, b, c, and e are particular to each module and to the flow regime. As shown in Eq. (5 ), the mass transfer coefficient is proportional to the volumetric flow rate to the power b, which is typically less than one. As the flow rate is increased, the mass transfer coefficient also increases. Ideally, the module can be operated at a flow rate where the liquid film resistance is negligible. However, since modules should be compared by total capital and operating costs, friction losses through the module must also be considered. Sherwood number correlations, as defined in Eq. (5 ), can be very useful for expressing the performance of a single type of geometric shape. However, unless a characteristic dimension can be defined for the flow channel which allows the mass transfer data from all spacers to be reduced to a single correlation, the comparison of Sherwood number correlation for different spacers may be misleading. In such cases, a spacer may have a lower Sherwood number than another spacer even though it produces a higher mass transfer coefficient. To avoid this situation it may be more useful to express the mass transfer data in a dimensional form, with the mass transfer coefficient correlated directly with the superlicial feed velocity. k=iiv’
of Membrane
Science 92 (I 994) 59- 74
porative removal of VOCs from water through a silicone rubber membrane was used as a test separation. Due to the nature of the separation, the liquid film mass transfer coefficient cannot easily be measured directly. Two sets of experiments were required to decouple the liquid film and membrane resistances to organic transport. In each set of experiments the overall organic mass transfer rate was determined by measuring the rate of organic lost from a batch feed. This is believed to be the most reliable of several available methods of determining the overall mass transfer coefficient, K, [ 19 1. The experiments used to measure the rate of VOC removed from the feed were performed in a basic pervaporation test loop shown in Fig. 2. A batch feed is recirculated through a test cell containing a membrane. The mass transfer driving force is provided by a vacuum pump that reduces the pressure on the permeate side of the membrane. The permeate is collected in condensers, which are submerged in liquid nitrogen. The recirculation of the feed and a magnetic stirrer inside the feed tank keep the feed solution well mixed. The permeate pressure is maintained at N 1 mmHg to allow the assumption that the partial pressures of organic and water on the permeate side of the membrane are negligible. With this assumption, Eq. (2) can be combined with an unsteady state mass balance on the organic component of the feed in the batch system illustrated in Fig. 2 to yield (7)
(6)
For any particular set of flow conditions the exponent b in Eqs. (5 ) and (6 ) will be the same. 3. Determination of the overall VOC mass transfer coefficient The ultimate objective of this work was to determine liquid film mass transfer coefficients for flow through spacer-filled channels. The perva-
Fig. 2. Diagram of experimental
pervaporation
apparatus.
P.J. Hickey, C. H. Gooding /Journal of Membrane Science 92 (I 994) 59- 74
Eq. (7) can be integrated to exploit an easier approach of feed loss measurement. In(:)
= (*)t
Fig. 3 is a semi-log plot of typical experimental data. The bulk feed organic concentration was analyzed intermittently using a gas chromatograph with a flame ionization detector. Samples were drawn from the feed bath through a 3 mm thick silicone septum. A stainless steel column filled with 1% SP-10000 on 60/80 mesh CarbopackTMpacking from Supelco was used in the gas chromatograph to separate the organic and water during analysis. With knowledge of the batch feed volume and the active membrane area, the overall organic mass transfer coefficient can be determined from the slope of the data plotted in the form of Eq. (8). The use of Eq. ( 8 ) requires that organic losses
Fig. 3. Example plot of mass transfer data and determination of K,.
63
from the feed, other than through the membrane, be negligible. Minimizing organic leaks from the experimental system is difficult because most VOCs of interest are very volatile and are sparingly soluble in water. Due to its relatively low volatility and high solubility in water, methylene chloride was used as the representative VOC for liquid film mass transfer experiments. Maintaining a tight seal on the feed tank and removing all air from the feed side of the experimental loop reduced the rate of organic leak greatly. The organic leak could not be eliminated totally for the apparatus used to determine the membrane permeability. When the organic leak is significant, the leak rate must be quantified. Assuming the VOC leak rate is proportional to the VOC feed concentration, Eq. (8) can be modified to incorporate a leak coefficient.
ln($) =-(K,‘y+“>l
(9)
To determine the leak coefficient, 1, the same experimental procedure described above is used but the permeate pressure is maintained at ambient conditions, thus removing the driving force for mass transfer through the membrane. Fig. 4 shows a typical semi-log plot of the data for a system with a significant organic feed leak. The relative significance of the leak rate and the uncertainty it introduces depends on the overall mass transfer rate of the particular experiment. In this work 1 was less than 20% of the mass transfer rate through the membrane in all cases and was typically much smaller.
4. Determination of membrane resistance 4. I. Experimental methods
Fig. 4. Example plot of experimental mass transfer data and determination of K, and i for an experimental system with a significant organic leak.
Experiments of the type described above give the total resistance to organic transport. Theoretically, the liquid film resistance can be eliminated by using very high feed flow velocities and very thick membranes, and the membrane resis-
64
P.J. Hickey, C. H. Gooding /Journal of Membrane Science 92 (I 994) 59- 74
tance is then determined directly. However, the extreme conditions necessary to accomplish this are not easily achieved in the pervaporation of VOCs. Values for the membrane resistances of various VOCs have been reported in the literature based on single experiments in a cell at a fast stirring rate and with thick membranes, but we believe the accuracy of data determined in this manner is dubious unless evidence is given to demonstrate that the liquid film resistance was negligible.
I
Retentate
The membrane resistance to organic transport can be determined using an extrapolative technique, the Wilson plot [ 20-221. To construct a Wilson plot, the feed flow rate is varied in a range over which the liquid film resistance is signiticant. Then the overall organic resistance, l/K,, is plotted versus the inverse of the volumetric flow rate raised to the power b. The exponent b is determined from the best linear fit of the data. The value 1/Qb is proportional to the liquid film resistance to organic transport. Therefore, as 1 /
4
I
Permeate +
Fig. 5. Diagram of MDS test cell used to determine membrane resistance.
P.J. Hickey, C.H. Gooding /Journal of Membrane Science 92 (I 994) S9- 74
Qb approaches zero the liquid film resistance also approaches zero, and the intercept of the graph represents the membrane resistance to organic transport. Our Wilson plot experiments were performed with a membrane test cell made by Membrane Development Specialists (an affiliate of Desal, Escondido, CA, see Fig. 5 ). The test cell consists of two PVC plates held together by four bolts. The test cell is unique in that the feed is delivered to the interior of the cell tangentially and flows in a spiral pattern to the exit in the center. The interior of the cell is tapered to maintain a constant feed velocity across the membrane. The leak rate from the experimental loop used for these experiments could not be eliminated, but it was quantified using the method outlined above. 4.2. Results and discussion Experiments were performed in the MDS test cell to determine the permeability of methylene chloride through a 127 pm thick Dow Corning Silastic membrane. The Wilson plot for this system is shown in Fig. 6. A membrane resistance of 22,670 s/m was determined from the intercept of the best fit line through the data. This equates to an overall mass transfer coefficient of 4.41 x low5 m/s when the liquid film is negligible. For this case, Eq. ( 1) becomes simplified and the permeability of the organic in the membrane is calculated to be
OF 0
I
0.005
I
I
0.010
0.015
0.020
l/Qbb,(Q in cm%ec)
Fig. 6. Wilson plot for methylene chloride and a 127 pm thick Dow Coming Silastic membrane determined with the MDS test cell and with b=0.684.
65
Table 1 Summary of membrane permeabilities obtained from Wilson plot experiments with MDS test cell
voc
Exponent Intercept H b (MPa) (s/m) (best fit)
1,2-Dichloroethane 0.692 Methylene chloride 0.684 Chloroform 0.705 Trichloroethylene
&IX,=+=
0.692
33,300 22,670 16,820 4,420
s&,x 10” (mol/msPa)
5.6
3.8
9.7 17 56
3.2 2.5 2.8
3.2x10-“=
(10)
To test the validity of the method further, the experiment was repeated with three other VOCs, chloroform, trichloroethylene, and 1,2-dichloroethane. The exponent b in the power law relationship between the liquid film mass transfer coefficient and the feed flow rate should be independent of the particular VOC as long as the solution is dilute. The results with all four VOCs were consistent as shown in Table 1, yielding an average b value of 0.69.
5. Spacer mass transfer characteristics 5.1, Experimental methods
A separate set of experiments was performed to determine the liquid film mass transfer coefficients for flow through spacers. Overall methylene chloride mass transfer coefficients were determined experimentally for each spacer at various flow rates. Using Eq. ( 1) and the membrane resistance to methylene chloride transport determined in the Wilson plot experiments, the values of the liquid film mass transfer coefficient were calculated. Dimensionless Sherwood number correlations [ Eq. (5 ) ] were developed with knowledge of the liquid film mass transfer coefficients and physical properties of the spacer and VOC. The dependency of the Sherwood number on the Schmidt number, SC, was not evaluated but was assumed to equal 0.33. The Schmidt number of a dilute aqueous methylene chloride solution at 20°C is 770. The exponent e in Eq.
P.J. Hi&v,
66
C. H. Gooding /Journal ofMembrane
(5) was assumed to be zero since the d/L term corrects for a developing mass transfer boundary layer in laminar flow and this correction should not be necessary for the tortuous flow path of a spacer-filled channel. A membrane test cell containing a spacer-filled channel was designed specifically for the liquid film resistance experiments of this study. The test cell, shown in Fig. 7, was constructed of plexiglass to allow for viewing of the flow channel. Most test cells described in the literature use a gasket to create a flow channel between two flat plates. However, the test cell used for this study is unique in that it has a flow channel cut into the upper plate, four smooth walls in the flow channel, and no gaskets. When spacers thinner than the flow channel were evaluated, a mylar plastic insert was placed in the void above the spacer to prevent channeling of the feed flow around the spacer. Visual dye tests were performed to confirm that the insert prevented flow channeling. The plexiglass plates were held together with two aluminum braces (Fig. 7). The braces and plates were bolted together with each bolt tightened to the same torque (75 in-lbs). The membrane was cut slightly larger than the flow channel and was placed on the lower plate of the test cell. The excess membrane provided a seal between the two plates and prevented leakage of the feed solution from the test cell without the use of gaskets. The active membrane area for this experimental system is defined by the area of the square permeate slit cut into the lower plate of the test cell, as shown in Fig.7. A spacer was placed into
lecd
mm
emuentport
Science 92 (1994) 59- 74
the permeate slit to keep the membrane flush with the surface of the lower plate. The low pressure in the permeate slit pulls the membrane down onto the spacer and forms a seal around the edge of the permeate slit. The empty slit channel height of the test cell, 2B, is 1.5 mm. The heights of the spacers tested ranged between 0.483 and 1.45 mm. The channel width, W, is 30 mm, or twenty times the maximum channel height, to allow the assumption of one-dimensional flow when the channel is empty (without spacers). Well above the feed chamlel cut into the upper plate, the feed and effluent ports were enlarged to cover the full channel width and thus distribute the flow evenly (Fig. 7). The length between the channel entrance and the front edge of the active membrane area is 60 mm, or forty times the maximum channel height. The length needed for laminar flow to develop completely in a thin slit is a function of the Reynolds number and the channel height [ 23 1,
L
6
=0.625+0.044
Re
(11)
The characteristic dimension used in Eq. ( 11) is the channel height, 2B. When performing calibration experiments with an empty feed channel, it is important to operate the system at Reynolds numbers that produce a fully developed flow before the active membrane area. The volumetric flow rate was determined by recording the time needed to till a 1000 ml volumetric flask. The velocity, v, used in the calculations is a superficial or approach velocity and is calculated by dividing the volumetric flow rate by the empty channel area, i.e., channel or spacer height times channel width. The VOC leak rate in this test cell and loop was so small that no leak could be detected over several hours of operation, the same duration as the mass transfer experiments. 5.2. Calibration
Fig. 7. Diagram of test cell used to determine transfer characteristics.
spacer mass
Before experiments were initiated to determine the feed side mass transfer characteristics
P.J. Hickey, C.H. Gooding /Journal ofMembrane Science 92 (I 994) 59- 74
of spacer-filled channels, calibration experiments were performed to test the experimental apparatus and ensure the validity of the experimental technique. The design of the spacer test cell assumed that the vacuum would provide a sufficient seal around the permeate slit without the use of a gasket and that the exposure of the dilute organic feed to non-active membrane area would not present a problem. A visual inspection of the cell showed that with vacuum on the permeate side, the membrane sealed well around the permeate slit. Flux experiments were also performed to validate this observation. Using a pure water feed, the water flux was determined by weighing the permeate collected in a liquid nitrogen condenser. The same experiment was done with the MDS membrane cell and the fluxes agreed within 5%. The significance of the comparison is that in the MDS cell all of the membrane exposed to the feed is also exposed to the permeate pressure. Therefore, this is further evidence that the seal was adequate, and there is no transport through the non-active membrane. The final calibration was done to ensure that the experimental and analytical techniques used to determine the liquid film mass transfer coefficients in the spacer cell were accurate, and that the non-active membrane area had no signiticant effect on the VOC. For laminar flow through conduits an accepted Sherwood number correlation, usually attributed to Leveque [ 241, is 0.33
Sh= 1.62 ReS+ (
>
(12)
where the characteristic dimension is the hydraulic diameter, d,,, defined as the cross-sectional area of the flow channel divided by the wetted perimeter of the flow channel. Mass transfer experiments were performed with the spacer cell empty (without any spacers) to determine K, and the results were adjusted using Eq. ( 1) and the membrane resistance obtained in the MDS test cell to get the liquid film mass transfer coefficient, k. For this flow channel, which is a thin, rectangular slit with the width much greater than the height, the hydraulic di-
67
K)
Fig. 8. Plot of experimental and theoretical Sherwood numbers as a function of Reynolds number for flow in a thin slit (the spacer test cell empty).
ameter can be approximated as two times the channel height. Fig. 8 shows a plot of the experimental and theoretical Sherwood numbers for laminar flow through the empty membrane cell. There is good agreement, which increases our confidence that the method is valid and that liquid film resistance experiments conducted with spacer-filled channels are accurate.
5.3. Results and discussion After the membrane resistance to methylene chloride transfer was determined and the spacer test cell apparatus was calibrated, experiments were performed to determine liquid film mass transfer coefficients for flow through spacer-filled channels. These experiments were conducted at different feed flow velocities and with fifteen different feed spacers. A compilation of the spacer data, characteristics, and mass transfer correlations obtained in this work is shown in Table 2. The characteristic dimension used to describe the Sherwood and Reynolds numbers in the table for Eq. ( 5 ) is the thickness of the spacer, 28, and the characteristic velocity is the superficial velocity. Hickey and Gooding [ 3, lo] were able to reduce the friction loss data of several spacers to a single correlation by developing an equation to describe a hydraulic diameter for a channel filled with diamond-shaped spacers. Attempts to use this technique on our mass transfer data were not successful. Since the mass transfer characteristics of each spacer require a unique
P.J. Hickey, C.H. Gooding /Journal
68
Table 2 Spacer characteristics
ofMembrane
Science 92 (I 994) .59- 74
and mass transfer correlation constants obtained in this work for
Spacer (TP #)
I. Naltex MWN 2. Naltex Ultraflo’ 4. Naltex LWS 7. Maynard 6 150-7 8. Maynard 6145-I 9. Internet XN-43 11 10. National MO Grid” 12. Internet XN-1670 13. Internet XN-3235 14. Naltex ROF 15. Naltex 368 1 16. Naltex Ultraflo’ 18. Naltex Ultraflo’ 19. Naltex Ultraflo” 20. Naltex Uhraflo’
2B (mm)
1.10 1.10 0.508 0.762 0.559 0.762 1.20 0.991 0.483 0.762 0.762 0.762 1.14 1.45 0.762
t
0.86 0.89 0.87 0.86 0.87 0.86 NA NA NA 0.89 0.87 0.86 0.89 0.85 0.92
spi”
8x8 5x8 16x16 12x 12 15x15 12x 12 13x13 7x5 14x11 9x9 11x11 6x9 5x8 5x8 6x11
ConstantsforuseinEqs. ri x105
a
8.752 7.475 5.697 5.574 7.475 8.199 9.859 8.626 7.821 6.568 7.968 6.740 7.566 8.422 5.647
0.894 0.808 0.322 0.474 0.694 0.352 0.990 0.624 0.320 0.588 0.638 0.282 0.570 1.296 0.278
b
vx
2B between 0.67 and 6.67 cm2/s
(5)b, (6), (13)and(14) a’
b’
x 1o-6 0.413 0.405 0.435 0.408 0.395 0.511 0.423 0.455 0.484 0.401 0.418 0.516 0.460 0.379 0.49 1
3.21 0.482 0.561 0.552 0.817 0.639 0.868 1.00 0.577 0.325 0.43 I 0.182 0.254 0.268 0.240
a”
h”
x IO’O 1.755 1.484 1.585 1.481 1.462 1.617 1.527 1.713 1.178 1.497 1.616 I.338 1.551 1.611 1.568
0.273 I.551 1.016 1.010 0.883 1.289 1.120 0.863 1.355 2.022 1.849 3.695 2.978 3.140 2.353
- 1.34 - 1.08 -1.15 - 1.07 - 1.07 -1.11 -1.10 - 1.26 -0.69 - 1.10 - 1.20 -0.82 - 1.09 - 1.23 - 1.08
“The first spi (strands per inch) is for the thicker strand for Nahex Ultraflo and for the transverse strand for InterNet. bit is assumed that in Eq. (5) c is equal to 0.333 and e is equal to zero. ‘The heavy thread is parallel to flow and the minor thread is angled. dEvery fourth strand is a thicker strand.
correlation, there is no benefit to using a complicated channel dimension or flow velocity. A typical plot of the raw experimental data for various feed flow rates is shown for spacer TP 8 in Fig. 9. The best lit lines drawn through each data set had very high values of the correlation coefficient r, indicating accurate fits. Dimensionless Sherwood number versus Reynolds number correlations were derived from the experimental data. Two specific correlations for spacers TP 8 and TP 10 are shown in Fig. 10 along with a shaded area that represents the region where the data from all of the spacers lie. The Sherwood numbers for flow through the spacers were 1.5 to 4 times greater than the Sherwood numbers for flow through an empty, thin slit. Spacer TP 10, a unique diamond-shaped spacer whose strands are centered between the upper and lower walls of the channel, produced the highest mass transfer coefficients of all the spacers tested. Spacer TP 13 from Internet produced the greatest increase in mass transfer rates
as compared to an empty channel of the same height as the spacer. However, TP 13 is the thinnest of all the spacers evaluated at 2B= 0.483 mm and the thin channel height is penalized by higher friction loss. The range of data from all of the spacers in Table 2 is shown in Fig. 11 in terms of liquid film mass transfer coefficients and superficial feed velocities in the form of Eq. (6 ). Data from two specific spacers are shown to illustrate the typical lit and all of the data are documented elsewhere [ lo]. The liquid film mass transfer coefficients for all the spacers ranged from 2.0~ lop5 to 8.2~ lop5 m/s. As shown in Table 2, the exponent b in Eq. ( 5 ) ranged between 0.40 and 0.50 for most of the spacers evaluated. If the exponent b is an indication of the flow regime, then all of the spacers tested were in the transitional regime for the flow rates studied, closer to laminar flow than turbulent. Pressure drop correlations for these same spacers are also shown in Table 2 in the dimensional form
P.J. Hickey, C.H. Gooding /Journal ofMembrane Science 92 (I 994) 59- 74
AP -_=a’vb’ L
(13)
with AP/L in units of N/m3 and v in m/s. Additional details on these data are given elsewhere [ 3,101. The correlations also indicate that the flow through the spacers was in the transitional regime in the range of flows tested. There are no obvious correlations between the mass transfer and friction loss characteristics of the spacers. For example, to achieve similar liquid film mass transfer coefficients TP 10 creates approximately four times more pressure drop than TP 18 does. The results in Table 2 show that Naltex Ultraflo spacers will produce liquid film mass transfer coefficients in the same range as diamond-shaped spacers that produce much greater pressure drops. It would appear that using Ultraflo spacers in the feed channel would be more productive than using common diamond-shaped 4.0
4.1
a.2
In(?)
-0.3
-0.4
a.5
1
69
spacers unless a detailed economic analysis indicates that a small reduction in membrane area requirement will compensate for a large increase in feed pressure drop. To differentiate between spacers with similar mass transfer characteristics, a simplistic spacer efficiency was developed by dividing the mass transfer coefficient by the pressure drop per unit length. Dividing the two dimensional correlations, Eq. (6) by Eq. ( 13 ), yields a spacer mass transfer efficiency as a function of the feed velocity.
?#I=-
k
=a,‘vb”
AP ( L>
(14)
The values of a” and b” are reported in Table 2, and Fig. 12 shows a plot of the spacer efficiencies at a superficial flow velocity of 0.5 m/s. While the difference in mass transfer coefficients for all the spacers at a given velocity is small, the spacer efficiency can vary by as much as a factor of ten. Fig. 12 was developed with a simplistic approach, but it is helpful to show the diverse performance characteristics of the spacers. A detailed economic model will ultimately be needed to rank the spacers in terms of lowest cost of separation per volume of feed treated for specific applications. The relative ranking of the spacers will most likely change from Fig. 12 depending on the relative magnitudes of the capital and operating costs and hence the relative importance of increasing mass transfer and decreasing friction loss. For cases in which capital costs, i.e, membrane materials used, are relatively inexpensive, Ultraflo spacers will be attractive due to the lower friction loss characteristics. 5.4. Comparison with other reported results
1.5
2.0
lime (hr)
Fig. 9. An example of experimental mass transfer data, the log of the normalized feed concentration versus time for TP 8.
Mass transfer data from the literature obtained for several spacers in reverse osmosis and ultrafiltration experiments are shown in Table 3. Values of correlation parameters b and c in Table 3 were taken directly from the original work. It is not clear why the authors used the indicated values of c rather than the conventional value of
70
P. J. Hickey, C. H. Gooding /Journal
of Membrane
Science 92 (1994) 59- 74
I 100 Reynolds Number, Re Fig. 10. Experimental
Sherwood number versus Reynolds number correlations.
0.10
1.OO
Superficial Feed Velocity, v (m/s) Fig. 11. Experimental
data correlated in the form of Eq. (6).
0.33. The correlation parameters a in Table 3 are different than those presented in the referenced publications. The parameters were transformed to allow for direct comparison with the correlations presented in this work. They were determined on the basis of simple superficial velocities and with channel height or spacer thickness as the characteristic dimension. Fluid properties were evaluated at bulk feed flow conditions and parameter e was assumed to be zero. In their original work, Schock and Miquel [ 15 ] used a mean velocity and described the flow channel by a hydraulic diameter. This hydraulic diameter as defined by Schock and Miquel can be reduced to
be a simple function of the channel height and porosity, as shown by Hickey and Gooding 13,101
(15) Da Costa et al. [ 181 also defined the channel dimension using Eq. ( 15 ) and used a mean velocity to define the Reynolds number of the flow. Furthermore, Da Costa et al. determined fluid properties based on calculated feed concentrations at the membrane wall instead of bulk feed conditions, which can be measured analytically. The correlations published by Da Costa et al.
P.J. Hickey, C.H. Gooding / Journal ofMembrane Science 92 (1994) 59-74
71
Spacer, (TP #) Fig. 12. Mass transfer efficiencies of spacers for a superficial feed velocity of 0.5 m/s.
Table 3 Literature spacer characteristics TP
2B (mm)
Various Old 1.85 UFl 1.70 1.70 UF2 UF3 1.70 UF4 1.70 80-Mil-1 2.10 80-Mil-2 2.10
and correlation parameters
Eo. (5) a
b
c
0.069 a a a 0.020 0.025 0.033 0.029
0.875 0.53 0.49 0.52 0.59 0.50 0.62 0.66
0.25 0.60 0.59 0.60 0.60 0.59 0.58 0.58
“Could not be transformed
Range valid (d=2B)
Ref.
50
15 18 18 18 18 18 18 18
with available information.
predict very high Sherwood numbers at relatively low Reynolds numbers, but this is due to the unconventional description of fluid properties rather than high mass transfer characteristics. The results reported by Schock and Miquel [ 151 indicate a strong relationship between the Sherwood number and the Reynolds number (see Table 3). The exponent b from Eq. (5) in their correlation is 0.875, indicating flow in the turbulent regime. This b is twice the typical value determined for the spacers in this study (see Ta-
ble 2 ) . However, Schock and Miquel developed their correlation from data obtained with different membranes, spacers, and feed pressures, and it appears that the exponent b was not derived from a linear regression on all or any of the experimental data. Rather, their correlation was apparently determined by fixing the exponent b equal to 0.875 (perhaps based on common heat transfer correlations for turbulent pipe flow) and then allowing the other parameters in the Sherwood number correlation to be determined by a data fit. In our work a separate correlation was developed for each specific spacer using the same membrane and feed conditions. In the form of Eq. (5) the data from Da Costa et al. [ 18 ] were correlated with values of b ranging from 0.49 to 0.66, but Da Costa et al were unable to match the theoretical Reynolds number versus Sherwood number relationship when their apparatus was operated as an empty slit. Instead of an exponent b equal to 0.33 for the empty slit experiments, their data were fit with a correlation with b equal to 0.43. We believe that this overestimation in b was caused by the short entrance length used in their test cell. The channel entrance length in their cell was only 3 mm, or
72
P. J. Hickey, C. H. Gooding /Journal
twice the channel height. For the range of the Reynolds numbers of their empty slit experiments, an entrance length ten to forty times the channel height would be required according to Eq. ( 11). In the entrance region mass transfer is enhanced because the flow profile is not fully developed. In their subsequent studies of mass transfer characteristics of spacer-filled channels, an entrance region effect may have caused the correlations to overpredict the value of b as it did in the empty slit experiments. Da Costa disagrees with our analysis, however, stating that the entrance region is insignificant in a spacer-filled channel [ 25 1.
of Membrane
Attempts to consolidate the results of many spacers into a single correlation using a characteristic dimension for the spacer-tilled channel proved fruitless. Although this technique reduced friction loss results for diamond-shaped spacers into a single correlation, it did not work for the mass transfer results.
7. List of symbols correlation constant in Eq. ( 5 ) (-) correlation constant in Eq. (6 ) (-) correlation constant in Eq. ( 13 ) (- ) correlation constant in Eq. ( 14) (-) membrane area ( m2) bm correlation constant in Eqs. ( 5 ) and (6 ) (-) correlation constant in Eq. ( 13 ) (- ) b’ correlation constant in Eq. ( 14) (-) b” B ideal spacer strand diameter and half the channel thickness (m) correlation constant in Eq. ( 5 ) (-) C organic feed concentration (ppm) Co initial organic feed concentration ( ppm ) Cc% molar density of water ( mol/m3 ) C characteristic dimension (m) d hydraulic diameter ( m ) d,, diffusivity of permeant in membrane D (m2/s) correlation constant in Eq. (5 ) (-) s; Henry’s law constant, (Pa) molar flux ( mol/m2 s) J liquid film mass transfer coefficient (m/s) k overall mass transfer coefficient (m/s) K channel length (m ) L entry length (m) L, membrane thickness (m) L, A4 molecular weight (g/mol ) NA not available permeate pressure (Pa) P PW vapor pressure of water (Pa) volumetric flow rate (m3/s) Q correlation coefficient (- ) Reynolds number (-) L spi strands per inch (in- ’ ) sorption coefficient of permeant in mems brane ( mol/m3 Pa) SC Schmidt number (- ) a ii a’
I,
ti
6. Summary Mass transfer correlations were determined for 15 spacers with potential for use in the feed channel of spiral wound membrane modules built for pervaporation. Like the friction loss data determined for these spacers, the mass transfer results show that the hydrodynamics are in the transitional flow regime between laminar and fully turbulent flow. Spacer mass transfer coefficients are a function of the superficial flow velocity raised to the power b, where b ranged from 0.38 to 0.52. In this work the liquid film mass transfer coefficients determined for the spacers ranged from 2.0x 10m5 to 8.2x 10e5 m/s. The use of spacers in the flow channel enhanced mass transfer by 1.5 to 4 times over the mass transfer in an empty slit at similar superticial flow velocities. Despite the fact that the spacers had much different friction loss characteristics, the range of mass transfer coefficients produced by the spacers did not vary much for the flow velocities tested. Naltex Ultraflo spacers produced mass transfer coefficients in the same range as common diamond-shaped spacers despite the fact that Ultraflo spacers create much less pressure drop. Naltex Ultraflo spacers appear to have an economic advantage over most of the spacers, especially diamond-shaped ones, due to their low pressure drop at similar mass transfer coefficients.
Science 92 (I 994) S9- 74
P.J. Hickey, C. H. Gooding /Journal of Membrane Science 92 (I 994) 59- 74
Sh t u V
V W X
Y
Sherwood number (-) time (s) mean velocity v/t (m/s) superficial velocity (m/s) volume of batch feed ( m3 ) channel width (m) liquid mole fraction (-) vapor mole fraction (-)
7.1. Greek letters AP : p Q
pressure drop (N/m* ) porosity (-) leak coefficient ( m3/s) fluid viscosity (kg/m s) fluid density ( kg/m3)
7.2. Subscripts 0 W
organic water
Acknowledgments The authors thank Nalle Plastics, Inc., Maynard Plastics, InterNet, Inc., and National Netting, Inc. for providing spacers and pertinent information about them and Douglas Haugh for his assistance with the experiments.
References [ 1 ] M.C. Porter, Handbook of Industrial Membrane Technology, Noyes, Park Ridge, NJ, 1990. [ 21 J. Reale Jr., V.M. Shah and C.R. Bartels, The use of spiral wound modules in pervaporation, in R. Bakish (Ed. ) , Proc. 5th Int. Conf. Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1991, p.231. [ 3lP.J. Hickey and C.H. Gooding, Friction loss in spiral wound membrane modules, in: R. Bakish (Ed. ), Proc. 6th Int. Conf. on Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1992,~. 153. [4]L. Hooker, Danger below, Chem. Eng. Prog., 86( 5) ( 1990) 52. [ S]Federal Register, Vol. 52, No. 74, p. 12866, April 17, 1987.
13
[6]C.H. Gooding, P.J. Hickey and M.L. Crowder, Mass transfer characteristics of a new pervaporation module for water purification, in R. Bakish (Ed.), Proc. 5th Int. Conf. Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NH, 1991, p. 237. [ 71 P. C&C and C. Lipski, A technico-economical evaluation of pervaporation for water treatment, in R. Bakish (Ed. )., Proc. 4th Int. Conf. Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1989, p. 304. [ 81 P. Cote and and C. Lipski, Reducing concentration polarization in pervaporation for trace contaminant removal, in Proc. 1990 Int. Cong. Memb. Memb. Proc. Vol. I, 1990, p. 325. [ 91 P. C&C and C. Lipski, The use of pervaporation for the removal of organic contaminants from water, Environ. Prog., 9 (1990) 254. [ 1OlP.J. Hickey, The Optimization of Spiral Wound Membrane Modules for the Pervaporative Removal of Volatile Organic Compounds from Water, Dissertation, Clemson University, Clemson, SC, 1993. [ 11 ]P.J. Hickey and C.H. Gooding, Modeling spiral wound modules for the pervaporative removal of volatile organic compounds from water, J. Membrane Sci., 88 ( 1994) 47. [ 121 W.D. Glatzel and M.C. Tomaz, The effect of turbulence promoters on heat transfer and pressure drop in a plate heat exchanger, CSIR Special Report CHEM 53, 1966. [ 13lR.E. Hicks, Chemical Engineering Group, CSIR, Pretoria, South Africa, Reports CHEM 54,126, and 138, 1967-70. [ 14]G. Belfort and G.A. Guter, An experimental study of electrodialysis hydrodynamics, Desalination, 10 ( 1972) 221. [ 15]G. Schock and A. Miquel, Mass transfer and pressure loss in spiral wound modules, Desalination, 64 ( 1987) 339. [ 161 W.G. Light and T.V. Tran, Improvement of thin-channel design for pressure-driven membrane systems, Ind. Eng. Process Des. Dev., 20 ( 198 1) 33. [ 17lT.V. Tran and W.G. Light, Design and operational improvements for thin-channel membrane systems, in Proc. Second World Cong. Chemical Engineering, 1981, p. 492. [ 18lA.R. Da Costa, A.G. Fane, C.J.D. Fell and A.C.M. Franken, Optimal channel spacer design for ultraliltration, J. Membrane Sci., 62 (199 1) 275. [ 19 ] C. Gooding, P. Hickey, P. Dettenburg and J. Cobb, Mass transfer and permeate pressure effects in the pervaporation of VOCs from water, in: R. Bakish (Ed.), Proc. 6th Int. Conf. Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1992, p. 80. [ 201 E.E. Wilson, A basis for rational design of heat transfer apparatus, Trans. ASME, 37 ( 19 16 ) 47.
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P.J. Hickey, C. H. Gooding /Journal of Membrane Science 92 (I 994) 59- 74
[ 2 1] P. Dettenburg, Mass transfer and permeate pressure effects in the pervaporation of trichloroethylene from water, Diplomarbeit, Clemson University, 1992. [ 221 R. Field and R. Burslem, The effect of concentration polarisation upon the performance of pervaporation membranes, in R. Bakish (Ed.), Proc. 6th Int. Conf.
Pervaporation Processes in the Chemical Industry, Bakish Materials Corp., Englewood, NJ, 1992, p. 275. [ 23lB.C. Sakiadis, Perry’s Chemical Engineers’ Handbook, 6th Ed., McGraw-Hill, New York, 1984, p. 5-35. [ 241 M.A. Leveque, Les lois de la transmission de chaleur par convection, Ann. Mines, 12: 13 (1928) 201. [ 25 ] A.R. Da Costa, Personal communication, March 199 1.