Improving the accuracy of scaling from discs to cartridges for dead end microfiltration of biological fluids

Journal of Membrane Science 365 (2010) 347–355

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Improving the accuracy of scaling from discs to cartridges for dead end microfiltration of biological fluids Sal Giglia ∗ , Kevin Rautio, Greg Kazan, Kari Backes, Mark Blanchard, John Caulmare Millipore Corporation, 290 Concord Road, Billerica, MA 01821, United States

a r t i c l e

i n f o

Article history: Received 4 June 2010 Received in revised form 13 September 2010 Accepted 17 September 2010 Available online 25 September 2010 Keywords: Scalability Microfiltration Cartridge filter Process development Scale up

a b s t r a c t Manufacturers of microfiltration devices typically offer small scale sizing tools for initial evaluation of membrane filtration performance in process streams and for estimating membrane area requirements of the full scale process. Ideally, small scale devices should contain a minimum of membrane area to save valuable bioprocess fluid while also scaling linearly to the corresponding large scale devices. However, differences in flow geometries between small and large scale devices can confound scaling predictions, and variability in membrane and fluid properties can also add uncertainty in scaling estimations, necessitating the use of liberal safety factors that result in increased costs. In this study, the effects of design factors such as underdrain support structure of small scale devices on scalability to large scale devices were investigated. In addition, the impact of membrane variability on scalability was quantified, and a strategy for minimizing scalability uncertainty was assessed. Other contributing factors to filter scalability such as pleating effects and fittings losses were also examined. Successful scale-up was realized with minimal safety factor by: (a) proper small scale device design to maximize performance consistency and minimize non-membrane influences on performance; (b) employing models that simulate the effect of pleating on device performance; and (c) proper accounting of factors such as device variability and hydraulic effects associated with fittings and elevation. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Evaluations of the filterability of process streams through microfiltration membranes often utilize small discs to assess membrane performance. Measurements of flux and throughput per unit of membrane area can be used for initial estimates of cartridge requirements for the full scale process. Ideally, small scale devices should contain a minimum of membrane area to conserve valuable bioprocess fluid and scale linearly with their corresponding large scale devices. However, linear scale-up of small to large devices is sometimes not achieved in practice. Clean water flux in pleated cartridge devices has been reported to be up to about 50% lower than in small (47 mm) disc devices [1]. For some challenge stream conditions where significant fouling occurs, even greater discrepancies between disc and cartridge performance have been observed [2,3]. There are a number of factors that can confound scaling predictions, if they are not carefully measured and controlled. These factors include differences in flow geometries between small and large scale devices (including effective or fluid accessible

∗ Corresponding author. Tel.: +1 781 533 2564. E-mail address: sal [email protected] (S. Giglia). 0376-7388/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2010.09.032

membrane area), pressure losses associated with plumbing and elevation, variability in fluid properties, and variability in membrane properties. Proper accounting of some of these factors has been shown to decrease scaling discrepancies. For example, a model that considers the hydraulic properties of porous materials used as pleat supports was shown to closely predict flux loss associated with pleating [4]. Careful accounting for fittings pressure losses, and modeling filtration performance based on deduced membrane fouling mechanisms have also been shown to increase the reliability of scaling calculations [5]. However, even taking into consideration these issues, large safety factors (typically between about 1.3 and 2) are used to allow for such factors as variability in membrane performance and variability in process conditions [5,6]. A detailed analysis of filter sizing concluded that recommended safety factors relative to direct linear scale-up vary by application, but the range between about 1.3 and 2 was confirmed to be economically rational [7]. While large safety factors provide high assurance that a filtration system will not be undersized, this assurance comes at a cost in that some systems may be unnecessarily oversized. Reducing scale-up safety factors without compromising performance assurance would obviously be economically advantageous. Among the components that contribute to the necessity of large scale-up

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Table 1 Properties of 10-inch cartridges evaluated in this study. Device code

Membrane description

Pleat support material

Effective filtration area (m2 )

SHF-A SHF-G SHC-A SHC-G SHR-A SHR-G SHRP-A SHRP-G

0.2 ␮m PES 0.2 ␮m PES 0.5/0.2 ␮m PES 0.5/0.2 ␮m PES 0.1 ␮m PES 0.1 ␮m PES 0.5/0.1 ␮m PES 0.5/0.1 ␮m PES

Polypropylene Polyester Polypropylene Polyester Polypropylene Polyester Polypropylene Polyester

0.49 0.57 0.50 0.54 0.60 0.69 0.49 0.54

Suffix codes: A – autoclavable; G – gamma irradiated.

safety factors are differences between small and large scale device designs, and variability in membrane performance. The performance of small scale devices where membrane area may be occluded (by the membrane support structure, for example) or where access by the process fluid to any part of the purported active membrane area is hindered will not easily translate into large scale performance. Scale-up uncertainties associated with such small scale device hydrodynamic effects can be minimized with a device design that ensures that non-membrane flow resistances are negligible over the allowed operating condition range of the device. A small scale device design that is free of significant non-membrane flow resistances should therefore allow for lower scale-up safety factors. The first part of this study will examine the effects of device design on small scale disc performance. Variability in membrane performance is another factor that can contribute significantly to large scale-up safety factors. In the case of microfiltration membrane filters, for example, there are many factors that influence membrane performance, including pore size distribution, membrane chemistry, membrane thickness, membrane porosity, and others. While membrane manufacturing processes are designed to control all of these factors to maximize uniformity and consistency, there inevitably will be some distribution within normal manufacturing conditions for all of these variables. This membrane variability limits device-to-device performance consistency and therefore limits the precision to which large scale performance can be predicted from small scale performance. While a minimum of membrane area in small scale devices is desirable for conserving process fluid, decreasing the small scale sample size may increase the probability that the small scale sample will not represent average membrane properties of the entire manufacturing population. In the second part of this study, a strategy for minimizing membrane variability effects, and which therefore allow for lower scale-up safety factors, is explored. 2. Materials and methods 2.1. Membranes and challenge streams The membranes used in this study were 0.1-␮m, 0.2-␮m and 0.5-␮m rated polyethersulfone (PES) membranes. The 0.5-␮m membranes were used only as pre-filter layers upstream of the sterilizing-grade 0.1-␮m and 0.2-␮m membranes. For the small scale tests, 25-mm discs were installed into OptiScale® -25 devices, which contain 3.5 cm2 of effective filtration area. Details of the 25mm device design are given in Section 3 of this paper. All of the large scale tests were performed on commercially available 10-inch pleated cartridges. Table 1 lists the cartridge types and relevant attributes. For all the clean water permeability tests, reverse osmosis purified water was used for both the small and large scale devices. For throughput testing, several challenge streams were used and are listed in Table 2. All solutions were prepared in 200–500 L quantities. The solution components were first mixed together in a 500 L

mixing tank and then transferred to a 1000 L pressure vessel. For testing of 25-mm discs, a 10 L sample of the solution was transferred to a 20 L pressure vessel. 2.2. Test method Both the 25-mm discs and the 10-inch cartridges were first tested for clean water permeability at 10 psid at about 21–25 ◦ C in a dead end (normal flow) configuration. All permeability values were adjusted to 23 ◦ C by correcting for viscosity using the following formula: x ◦ C (1) Lp23 ◦ C = Lpx ◦ C 23 ◦ C where Lp23 ◦ C is the water permeability at 23 ◦ C, Lpx ◦ C is the water permeability at temperature x, 23 ◦ C is the viscosity of water at 23 ◦ C, and x ◦ C is the viscosity of water at temperature x. Water flow rates for the 10-inch cartridges were measured using a Micro Motion F-series Coriolis flow meter. For the 25-mm discs, load cells (Tedea Huntleigh, 0–1 kg) were used to record the accumulation of permeated water with time. Water temperature was measured with an Omega J-type thermocouple and feed-to-permeate pressure differential was measured using Setra 0–170 kPad differential pressure transducers for both the 25-mm and 10-inch cartridge tests. All the instruments were connected to a data acquisition system which recorded data at 10 s intervals. The water permeability tests were run until an essentially steady-state flux condition was achieved, typically within 5 min. Throughput tests involving plugging solutions were run at a constant pressure differential of 69 ± 7 kPad, in dead end mode. The tests were run until the membrane permeability was reduced by at least 95% compared to the clean water permeability. The challenge streams were concentrated to achieve a high degree of plugging within about 30 min at the stated process conditions. For the 10inch cartridges, load cells capable of up to 200 kg were used to measure throughput volume. Feed-to-permeate pressure differential, temperature, and accumulated permeate mass with time data were collected using the data acquisition system. All 10-inch cartridges were installed into Millipore Series 3000 single round in-line stainless steel housings with 1.5-inch diameter Table 2 List of challenge streams for throughput tests. Membrane

Challenge stream

0.5/0.2 ␮m PES

0.3 g/L soy T in Hyclone® DMEM with 3.7 g/L sodium bicarbonate and 1 g/L Pluronic® F-68 surfactant 5 g/L Bacto tryptic soy broth in Hyclone DMEM, 3.7 g/L sodium bicarbonate, 1 g/L pluronic F-68 surfactant 2.0 g/L EMD soy in Gibco DMEM with 3.7 g/L sodium bicarbonate and 1 g/L pluronic F-68 surfactant

0.1 ␮m PES

0.5/0.1 ␮m PES

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349

Fig. 1. Membrane support configurations: (a) direct support of membrane may reduce effective filtration area; (b) porous backing that allows for improved utilization of membrane filtration area.

3. Small scale device design 3.1. Support structure The membrane support structure and the permeate underdrain design are critically important for accurate determination of membrane disc performance. Membrane discs must be supported against the pressure imparted by the process fluid but structures that occlude membrane area may render portions of the installed membrane partially or totally ineffective. Further, the impact of the occlusions may depend on the process conditions. As illustrated in Fig. 1a, liquid flow can circumvent blocked areas of membrane by permeating laterally within the membrane, but membrane performance can be compromised since the diverted lateral flow will compete with normal flow for membrane pore access. The lateral permeability may also be affected by the operating pressure, due to membrane compressibility, such that the effective area becomes dependent on pressure. Deformation of the membrane into the support structure could also occur, which would impact membrane performance. A method commonly used to eliminate direct contact between a rigid support structure and a membrane disc is to install an intermediate porous support, such as a non-woven porous structure. A porous support such as non-woven polypropylene that has high porosity and high normal and lateral permeability will act to direct the permeate from the membrane into the device permeate outlet without adding significant flow resistance (see Fig. 1b). Fig. 2 shows that a porous support greatly improves the efficiency of a 25-mm disc device, particularly at increased pressure operation.

50

40

-9

3

2

Water Permeability (x10 m /m -s-Pa )

inlet and outlet sanitary fittings. Pressure loss as a function of flow rate was measured for the empty housings into which “blank” (no membrane) cartridges were installed. Pressure drop through the housing and associated fittings was subtracted from the total inlet to outlet pressure difference to obtain the trans-membrane pressure differential (TMP) of cartridges installed into housings. The effective filtration area (EFA) of each cartridge was verified after permeability or throughput testing by dismantling the cartridge, unfolding the pleat pack, and measuring the surface area available for filtration.

30

20 w/ porous backing w/o porous backing

10

0 0

100

200

300

400

Pressure (kPa) Fig. 2. Comparison between effective water permeabilities of 25-mm 0.2 ␮m PES membrane discs with and without non-woven polypropylene support.

In addition to the porous support, the underdrain below the porous support should be designed to accommodate the permeate flow without adding significant flow restriction. The impact of underdrain design was evaluated using a 25-mm device configuration illustrated in Fig. 3. Two alternate underdrain structures were investigated. A computational fluid dynamic simulation (Fig. 4) indicated that design A (a pre-existing design used for nanofiltration membranes) would impart significant flow resistance for a high permeability microfiltration membrane (0.2 ␮m PES, Lp ∼ 1200 l/m2 h psi) operated at high pressure differential, whereas the more open design B would impart only a very small flow resistance relative to the membrane. This simulation result was verified empirically and the data is summarized in Fig. 5. Design B allows for an essentially pressure independent permeability. For scaling from small to large devices, precise measurement of permeability and filtration area is critically important for accurate scaling. For all the scaling tests reported in the remainder of this paper, design B was utilized.

Fig. 3. Device design for evaluating 25-mm membrane discs. The membrane frontal area is 3.5 cm2 .

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S. Giglia et al. / Journal of Membrane Science 365 (2010) 347–355

Fig. 4. Calculated pressure gradients using single layer PES 0.2 ␮m membrane operated at 345 kPa (50 psig). Values on grid represent distance in meters and values adjacent to color code sidebar represent water pressures in psig.

4. Minimization of membrane variability effects

For accurate scale-up, the membrane in the small scale device must be representative of the membrane in the large scale devices. However, as in any manufacturing process, there is a finite tolerance in acceptable performance from one lot of membranes to another. For example, a common quality control test that is used to release membranes for installation into devices is a water permeability test. Disc samples are cut from the cast membrane at intervals sufficient to adequately characterize membrane lot performance. In a well controlled manufacturing process, typically there is a normal distribution around the mean for water permeability or other key performance characteristic(s). The membrane in a scaling device could originate from anywhere within the acceptable membrane performance range. Accordingly, when estimating the required sizing of full scale devices, the variability in membrane performance must be accounted for, necessitating the use of liberal safety factors in scaling estimates.

This can be illustrated by considering a hypothetical distribution of membrane performances as shown in Fig. 6. In this example, average performance (either permeability or throughput capacity) of all membrane lots is normalized to one and the acceptable range of performance is defined as ±30% of the mean. One commonly employed approach is to use a small scale device containing membrane randomly selected from the population, which could perform at anywhere from 0.7 to 1.3. Similarly, a large scale device could perform at anywhere within the same 0.7–1.3 range. When scaling from a small scale to a large scale device, the possibility that the small scale device contains high end (1.3) membrane while the large scale device could contain low end (0.7) membrane must be accounted for. That is, a scaling safety factor of 1.3/0.7 = 1.86 must be applied to ensure that the large scale system is not undersized. In this situation, the worst case performance of the full system will be accurately estimated. However, it is also possible that the small scale device could contain membrane from the low end of the distribution (0.7) while the large scale device contains high end (1.3) membrane. Applying the same safety factor would result in a full system performance of (1.3/0.7)/(0.7/1.3), or 3.45. The result would be a filtration system that is oversized by a factor of 3.45. This value

Fig. 5. Effect of underdrain support structure on effective water permeability.

Fig. 6. Hypothetical distribution of membrane performance (permeability or throughput capacity, e.g.).

4.1. Effect of membrane variability on scaling uncertainty and safety factor

S. Giglia et al. / Journal of Membrane Science 365 (2010) 347–355

351

140

Measured Flow Rate (lpm)

120 100 80 SHRP-G SHRP-A SHC-G SHC-A SHF-A SHF-G SHR-A SHR-G

60 40 20 0 0

20

40

60

80

100

120

140

Predicted Flow Rate (lpm)

10

is defined as the scaling factor uncertainty ratio (Usf ) according to the following formula:

8

Usf =

Fh /Sl F S = h h Fl Sl Fl /Sh

(2)

where Fh is the full scale device high end potential performance, Fl is the full scale device low end potential performance, Sh is the scaling device high end potential performance, and Sl is the scaling device low end potential performance.

Housing ΔP (kPa)

Fig. 7. Defined performance range for small scale device reduces scale-up uncertainty.

SQRT(Housing ΔP (kPa))

Fig. 8. Water flow rate scaling predictions, excluding housing pressure losses and pleating effects.

6

3

2

1

0 0

4

40

80

120

160

Flow Rate (LPM)

2

4.2. Reducing membrane variability uncertainty By specifying only a narrow range of the distribution for scaling devices, the uncertainty in scaling from small scale to large scale devices is minimized (large scale devices can contain any qualified membrane, so the system must be sized to accommodate the full range of potential membrane performance especially if filters are replaced for each batch or are otherwise periodically replaced). For example, if only the middle third of the distribution range is selected for small scale devices, as illustrated in Fig. 7, then the performance of the small scale device will range from 0.9 to 1.1. Since the large scale devices will range from 0.7 to 1.3, the scaling safety factor will be (in accordance with Eq. (1)), (1.3/0.9)/(0.7/1.1) = 2.3, where Sh becomes the scaling device high end potential performance within the subset of the distribution, and Sl becomes the scaling device low end potential performance within the subset of the distribution. In this example, this method results in about a

0 0

20

40

60

80

100

120

140

160

Flow Rate (LPM) Fig. 9. Non-membrane pressure losses associated with housing and device construction. Inset shows expected linear relationship between square root of pressure drop and flow rate.

35% savings in scale-up sizing requirements compared to conventional random membrane selection used for scaling devices. It is not necessary that the membrane in the scaling device originate from the center portion of the membrane population. Any defined portion of the membrane population will reduce scaling uncertainty in accordance with Eq. (1).

Fig. 10. Pleated structures.

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Fig. 11. Pleated cartridge design and flow path.

120

400 350 300

Throughput (l/m2)

Measured Flow Rate (lpm)

100

80

60 SHRP-G SHRP-A SHC-G SHC-A SHF-A SHF-G SHR-A SHR-G

40

20

250 200 150 10" Cartridge 158-2 158-3 158-4 158-5 158-6

100 2g/L EMD soy in gibco DMEM, 3.7g/L sodium bicarbonate, 1g/L pluronic F-68

50 0 0

0 0

20

40

60

80

100

5

10

Predicted Flow Rate (lpm) Fig. 12. Water flow rate scaling predictions, accounting for housing pressure losses and pleating effects.

In a related approach, the scalability safety factor can be minimized by determining where, within the performance distribution, the small scale device lies (using either a surrogate or actual performance qualification test, for example), and then adjusting the scaling factor to reflect the portion of the distribution that the scaling device membrane originated from. In this approach, any

15

20

25

30

Time (min)

120

Fig. 14. Throughput comparison between 10-inch SHRP-G cartridge and corresponding 25-mm devices (158 series in legend).

membrane can reliably be used in scaling devices. Information about membrane performance is collected and the information is provided with the finished device. When the scaling device is evaluated in the process stream, this membrane performance data is used in determining the scaling factor. For example, using the hypothetical distribution in Fig. 6, assume that a specific membrane has a performance value of 0.9. The scaling factor simply would be (0.9/0.7) = 1.3. This factor represents the adjustment for the scal-

500

1.0 0.9

10" Cartridge 158-2 158-3 158-4 158-5 158-6

2g/L EMD soy in gibco DMEM, 3.7g/L sodium bicarbonate, 1g/L pluronic F-68

0.8 0.7 300

0.6

J/Jo

Measured Throughput (l)

400

200

SHRP-G SHRP-A SHC-G SHC-A SHR-A SHR-G

100

0.5 0.4 0.3 0.2 0.1

0

0.0 0

100

200

300

400

500

Predicted Throughput (l) Fig. 13. Predicted throughput of 10-inch devices from 25-mm device data. Challenge streams are listed in Table 2.

0

100

200

300

400

2

Throughput (l/m ) Fig. 15. Normalized flux decay (J/J0 ) comparison between 10-inch 0.5/0.1 ␮m cartridge and corresponding 25-mm devices (158 series in legend).

S. Giglia et al. / Journal of Membrane Science 365 (2010) 347–355

10-inch Cartridge

5.1. Water permeability 50

-9

3

2

Water Permeability (x10 m /m -s-Pa)

5. Results and analysis

OptiScale-25

60

353

40

30

20

10

0 459

137

1056 3212 3218 5107 5139 1003 1014 7096 7427 8385

Cartridge ID Fig. 16. Comparison between water permeabilities derived from 10-inch cartridges and 25-mm devices. Error bars represent one standard deviation for a sample size of 5.

ing device with respect to the low end of the full distribution. Since the performance range of the scaling device is well defined and known, Sh and Sl are the same, so Eq. (2) reduces to: Usf =

Fh Fl

(3)

The scaling factor uncertainty ratio in this case becomes 1.3/0.7, or 1.86, which represents a 46% reduction compared to uninformed membrane selection. As a practical matter, membranes that represent typical (i.e., the center portion of the distribution) performance properties are preferred for sizing studies for flow and capacity (this differs from bacterial retention studies, where worst case membrane is a requirement). These membranes will most directly relate to the expected performance of large scale devices. Membrane device manufacturers will have upper and lower limits for acceptable membrane performance. Since these limits can be related to the average membrane performance, scaling safety factors can be applied to properly account for the potential range of device performance.

0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 00 1. 1 1. 2 1. 3

Frequency

Membrane Normalized ID Capacity A 1.12 B 0.99 C 1.04 D 1.02 E 0.96 F 0.71 G 1.06 H 0.69 I 0.88 J 0.80 K 0.90 L 0.80

Normalized Capacity Fig. 17. Capacity distribution of membrane lots. Membrane challenged with stream described in first row of Table 2.

Measured water flow rates of 10-inch cartridges containing 0.1␮m, 0.2-␮m, 0.5/0.1-␮m, and 0.5/0.2-␮m rated PES membranes are compared to simple calculated values in Fig. 8, based on direct linear scale-up from 25-mm devices. The simple calculated values are unadjusted for housing pressure losses and do not account for pleating effects. By this method, the 10-inch cartridges are shown to have lower nominal permeabilities than the corresponding 25mm devices, especially for the membranes/cartridges that have the higher permeabilities. As noted previously, the housing pressure losses must be accounted for to arrive at the actual TMP. Fig. 9 shows pressure losses associated with the cartridge housing. For the 0.2-␮m PES membrane single layer cartridge, housing losses were responsible for about 7% of the total pressure difference between the housing inlet and outlet. If unaccounted for, this will translate to a 7% error in scaling from small-scale to large-scale devices. Pleating effects also contribute to lower nominal permeability of cartridges [1,4,8]. As illustrated in Fig. 10, the feed fluid flows into the upstream support, parallel to the membrane, before traversing the membrane and then again flowing parallel to the membrane in the downstream support. The resistance to flow in both the upstream and downstream porous supports reduces the pressure difference across the membrane itself. In accordance with the semi-dense model described in Ref. [4], the reduction in flow rate due to pleating effects was calculated for each cartridge. The calculation parameters and results are summarized in Table 3. Pressure losses associated with the pleat pack support structure (outer cage and inner core, as depicted in Fig. 11) were measured as part of the empty shell pressure loss measurements (see Section 2.2). These pressure losses were found to be negligible and therefore not accounted for in the calculations. Fig. 12 shows that after accounting for pleating effects and housing pressure losses, there was good agreement (within 10%) between the predicted and measured permeate water flow rates for each of the membrane/cartridge types tested. The data in Fig. 12 was based on using membranes in both 25-mm devices and the corresponding 10-inch cartridge originating from the same manufacturing lot. In a typical process scale-up situation for a commercial application, this is unlikely to occur as the membranes in scale-down and scale-up devices may not necessarily be from the same lot. The consequences of this were discussed earlier and will be further addressed following the section on throughput scalability. 5.2. Throughput Bioprocess fluids representing high fouling applications were evaluated for all the membrane/cartridge types listed in Table 1, except for the single layer 0.2-␮m membrane, which is typically utilized in low fouling applications such as buffer filtration. Fig. 13 shows measured vs. predicted (based on 25-mm device data) throughput after 30 min of filtration time, at which point at least 95% flux decay had occurred. For these high plugging cases, the adjustments for housing pressure losses and pleating effects are negligible because the resistance through the plugged membrane relative to those effects is higher by more than two orders of magnitude. Example volume vs. time and flux vs. throughput curves are shown in Figs. 14 and 15. A fouling mechanism analysis of the throughput data based on the classical blocking models indicates that fouling behavior of both the 25-mm devices and the 10-inch cartridges were most consistent with the standard (gradual pore

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Table 3 Values for pleat effect calculations. See Nomenclature section of symbol explanations. Device code

Pleat length (cm)

ku (×10−7 cm2 )

kd (×10−7 cm2 )

bu (cm)

bd (cm)

Disca Lp (×10−9 m3 /m2 s Pa)

Pleat scaling factor

SHF-A SHF-G SHC-A SHC-G SHR-A SHR-G SHRP-A SHRP-G

0.89 0.89 1.15 1.15 1.15 1.15 1.15 1.15

8.75 5.60 8.75 5.60 8.75 5.60 8.75 5.60

8.75 5.60 8.75 5.60 8.75 5.60 8.75 5.60

0.020 0.019 0.020 0.019 0.020 0.019 0.020 0.019

0.029 0.019 0.029 0.019 0.029 0.019 0.029 0.019

50 50 36 36 24 24 20 20

0.95 0.89 0.94 0.87 0.96 0.91 0.97 0.92

a

Typical values.

plug) blocking model, described by Eqs. (4) and (5) [9]: V=

1

J = J0

J0 t



+

1−

Ks 2

Ks V 2

−1 (4)

2 (5)

where V is the volume filtered, t is time, J is the flux, J0 is the initial flux, and Ks is the standard blocking constant. Table 4 shows that the blocking constants derived from the throughput data of the 25-mm devices are in good agreement with those of the 10-inch cartridges. It is clear that the throughput behavior of the 25-mm devices was consistent with that of the 10-inch cartridges. 5.3. Membrane variability and scale-up safety factor The comparisons between 25-mm device and 10-inch cartridge performance in the preceding subsections show device scaling effects when the same membrane lot is used. In practice, however, a scale-down device will be used to estimate system sizing for devices that can include membrane from anywhere within the product specification range. As discussed in Section 4, the scaleup safety factor must account for the potential ranges of both small scale and large scale performance. But by using the principles discussed in Section 4.2 (designating only membranes that have performance properties within a narrow and well defined range of the overall distribution) the scale-up safety factor can be substantially reduced. To demonstrate this, a series of twelve 10-inch 0.2-␮m membrane cartridges and membrane rolls were selected at random from a one year period of commercially manufactured membranes and devices. Each membrane roll manufactured during this period had been characterized for water permeability as part of routine quality control testing. One membrane roll was selected as representative of the center portion of the membrane performance distribution (water permeability within 2% of the mean of the overall population of membrane rolls). All the cartridges and membrane discs (as installed into 25-mm devices) were tested for water permeability. One cartridge and five 25-mm devices were manufactured and tested from each membrane roll. As shown in Fig. 16, the withinlot permeabilities of the 25-mm devices closely tracked their corresponding 10-inch cartridges. However, the 25-mm devices permeabilities ranged from 44 to 56 × 10−9 m3 /m2 s Pa and the 10inch cartridge permeabilities (adjusted for external pressure loss Table 4 Best fit values of filtration data to standard blocking law constants. 25-mm devices data is average of 5 devices. Device

J0 (×10−6 m3 /m2 s)

Ks (m−1)

r2

10-inch cartridge 25-mm devices

890 830

4.3 4.0

0.999 0.995

and pleating effects) ranged from 47 to 54 × 10−9 m3 /m2 s Pa (due to averaging effects, a narrower range would be expected in cartridges that contain approximately 1500 times more membrane area than 25-mm devices). Without a priori knowledge of what part of the membrane population is represented by the membrane in the scale-down device, and to guard against potential system undersizing, it is assumed that a small-scale device may represent the high end of the population, and that the scaled-up system may utilize cartridges that contain membrane from the low end of the population. For the set of membranes in this example, this would require a safety factor of 56/44 = 1.27 to allow for membrane variability effects alone (an additional 10–40% safety factor may also be required to account for other uncertainties and effects such as variability in processing conditions and process fluid properties) [7]. However, if the scale-down device is known to contain membrane that has performance properties within ±2% of the population mean (the designated membrane in this example had a measured permeability of 51 as compared to the population mean of 50 × 10−9 m3 /m2 s Pa), then the safety factor need only be 50 × 1.02/44 = 1.16. Compared to random membrane selection for scale-down devices, utilizing a defined scale-down property strategy results a nearly 10% savings in system size without compromising the level of scaled-up system performance assurance. Membrane batches can be similarly characterized for throughput capacity. Fig. 17 shows the distribution of capacities for 12 membrane batches of 0.5-␮m rated microfiltration membrane (used as a prefilter layer upstream of a 0.2-␮m rated membrane). The range of capacities is about ±25% of the mean. If membrane is selected at random for use in small-scale devices, then the scaling factor uncertainty ratio is 2.8. Designating only membranes that have capacity within 2% of the mean (in this case membrane K, which has a capacity of 0.90 compared to the population mean of 0.91) reduces the scaling factor uncertainty ratio to 1.7. Since membrane batches are routinely characterized for both permeability and capacity, and the quantity of membrane required for small scale devices is a tiny fraction of the membrane used to manufacture large scale devices, manufacturing small scale devices only from membrane that represents a narrow range of the performance distribution is a feasible strategy that can readily be implemented in manufacturing. 6. Conclusions Scaling predictions of large-scale membrane filtration device performance from small scale device performance must account for a number of factors, including differences in flow geometries between small and large scale devices, extra-membrane flow resistances, and non-idealities in fluid accessible membrane area. Variability in membrane and fluid properties can also add uncertainty in scaling estimations. In this study, effects of device design factors such as membrane underdrain support structure of small scale devices were

S. Giglia et al. / Journal of Membrane Science 365 (2010) 347–355

investigated, the impact of membrane variability on scalability was quantified, and a strategy for minimizing scalability uncertainty was assessed. Other contributing factors to filter scalability, such as the effect of fittings losses were also examined in this study. It was found that successful scale-up could be realized by: (a) proper small scale device design; (b) employing models that simulate the effect of pleating on device performance; (c) defining the minimum allowance for membrane performance variability; and (d) proper accounting of hydraulic effects associated with fittings and elevation. Excellent agreement was found between measured and predicted 10-inch cartridge performance using small-scale 25-mm devices and within-lot membrane. Using small scale (25mm) devices with membrane from a well defined portion of the known manufactured membrane distribution can significantly reduce scaling uncertainties associated with membrane variability. This allows for lower scale-up safety factors and translates directly into savings in system size and cost.

Nomenclature bd bu Fh Fl J J0 kd ku

thickness, downstream support thickness, upstream support full scale device high end potential performance full scale device low end potential performance flux (m/s) initial flux (m/s) lateral permeability, downstream support lateral permeability, upstream support

Ks Lp Sh Sl t Usf V

355

standard blocking constant (m−1 ) water permeability (m s−1 Pa−1 ) small scale device high end potential performance small scale device low end potential performance time (s) scaling factor uncertainty ratio volume filtered (m3 /m2 )

Greek letter  viscosity (Pa s)

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