Sensitivity Analysis of the Pressure-Based Direct Integrity Test for

Nov 9, 2009 - Pressure-Based Direct Integrity Test for Membranes Used in Drinking. Water Treatment. JOHN G. MINNERY, †. JOSEPH G. JACANGELO, ‡,§...
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Environ. Sci. Technol. 2009 43, 9419–9424

Sensitivity Analysis of the Pressure-Based Direct Integrity Test for Membranes Used in Drinking Water Treatment JOHN G. MINNERY,† J O S E P H G . J A C A N G E L O , ‡,§ L E S L I E I . B O D E N , * ,† DONNA J. VORHEES,† AND WENDY HEIGER-BERNAYS† Department of Environmental Health, Boston University School of Public Health, 715 Albany Street, Boston, Massachusetts 02118, Department of Environmental Health Sciences, Division of Environmental Health Engineering, Johns Hopkins Bloomberg School of Public Health, 615 North Wolfe Street, Baltimore, Maryland 21205, and MWH, 40814 Stoneburner Mill Lane, Lovettsville, Virginia 20180

Received July 22, 2009. Revised manuscript received October 7, 2009. Accepted October 26, 2009.

We conducted a sensitivity analysis of the commonly employed pressure-based direct integrity test (DIT), the most sensitive test for defects in low-pressure hollow fiber (LPHF) microfiltration and ultrafiltration systems used in drinking water treatment. Incorporating uncertainty to assess the practice of DIT, we find the resolution in some tests may be insufficient to verify the presence of a barrier to oocysts of Cryptosporidium. Applying distributions and boundaries derived from literature and practice, we solved for the defect size resolution (DSR) using Monte Carlo and Probability Bounds Analysis for five commercial membrane designs. Surface tension was modeled using annual temperature profiles from three rivers. Contact angle measurement error and variability were derived from literature, respectively, as a standard deviation of 5.7° and ( 9.6° median change due to natural organic matter (NOM) fouling. These measures of contact angle uncertainty and variability were combined in a normal distribution with the discrete values currently applied. Additionally we considered model uncertainty, applying the maximum bubble pressure method, an established method of surface tension measurement in liquids in which the maximum air pressure in a submerged capillary is developed after the contact angle becomes zero prior to bubble formation. Where the DSR exceeds 3 µm the test design is not compliant with applicable drinking water regulations. Implications include uncertain and variable log-removal values (LRV) as determined by DIT due to the possible emergence of defects large enough to allow oocysts to pass without detection by the DIT. Specifically, we found the DSR may exceed 3 µm and may be as large as 8 µm. With the variable contact angle model, all lower bound possibilities are compliant, whereas the upper bound is over 80% noncompliant for * Corresponding author phone: (617)-638-4635; fax: (617)-6384857; e-mail: [email protected]. † Boston University School of Public Health. ‡ Johns Hopkins Bloomberg School of Public Health. § MWH. 10.1021/es902210r CCC: $40.75

Published on Web 11/09/2009

 2009 American Chemical Society

three of five commercial designs. Using the Maximum Bubble Pressure Method, the lower bounds in three designs start to exceed 3 µm for between 50 and 100% of the produced water, whereas the upper bounds of the DSR completely exceed 3 µm for four of five commercial designs examined.

Introduction Pressure-Based Direct Integrity Tests (DITs). Low-pressure hollow fiber (LPHF) membranes remove particulate and pathogens predominantly through a sieving action in processes to produce potable water. Water is filtered as it passes through pores in the fiber wall between 0.01 and 0.1 µm nominal diameter. The inner diameters of fibers are on the order of several hundred micrometers. LPHF membranes require DITs to comply with the additional treatment requirements of the Environmental Protection Agency’s (EPA) Long-term-2 Enhanced Surface Water Treatment Rule (LT2). This test for broken fibers, or defects, must be sensitive to breaches as small as 3 µm to determine the degree to which a system of membranes is a barrier to oocysts of the smallest known disinfectant-resistant waterborne pathogen, Cryptosporidium. Test frequency is determined by the state, whereas federal guidance recommends daily DITs as a minimum (1). The EPA’s Membrane Filtration Guidance Manual (1) describes the integrity monitoring requirements. State agencies often apply the guidance to regulate membrane applications regardless of the level of oocyst contamination in source waters. Additionally, the guidance manual may be adopted to set standards for the removal of other pathogens such as Giardia, or various bacteria. The pressure-based DIT is capable of detecting the smallest defects. Unlike complementary continuous indirect integrity monitoring (CIIM), such as with particle counters, direct tests evaluate the integrity of the barrier itself independent of the feedwater quality (2). DITs are used to verify challenge tests in which an organism, or suitable surrogate, is added to the feed stream at a known concentration and removed with an efficacy determined from the concentration measured in the permeate. Challenge tests are infrequent even on a pilot scale for reasons of security, cost, and technical difficulty. Pressure-based DITs are most common perhaps because they are able to take advantage of existing equipment such as pressure and flow meters to test integrity over large numbers of membranes. During a pressure-based DIT, air replaces water on one side of the membrane, the permeate or feed side. The basis of the DIT is the development of convective flow when the established air pressure overcomes the force of the surface tension of water in air, σ (N/m), acting in a cylindrical capillary (or defect) of diameter d (µm) and the material specific contact angle θ which modifies the directional component of counteracting forces (Figure 1). In practice (1) the pressure at which the test is conducted is given by eq 1 Ptest_end )

4 • σ • κ • cos θ • 103 + PBPmax d

(1)

where Ptest_end is the test pressure (kPa) at test completion, PBPmax is the maximum hydraulic head (kPa), and κ is the pore shape correction factor. Under LT2, d is normally fixed at 3 µm to ensure a barrier against Cryptosporidium oocysts. Pressures and surface tension vary by design and climate, respectively, but both are known and readily measured. Two variables in eq 1 are currently subject to considerable uncertainty: κ about which we know only a theoretical minimum and maximum, and θ about which we know only VOL. 43, NO. 24, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Cross section of pore during DIT: two models of the air-water-membrane interface at the point of bubble formation: (a) current and (b) the Maximum Bubble Pressure Method derived alternative. the value reported on the extremities of a virgin fiber (3). Absent evidence to the contrary, EPA guidance recommends conservative assumptions maximizing the test pressure: κ ) 1 and θ ) 0°. In polymeric membranes κ is a confounded factor of tortuous paths and noncylindrical pores with no established method of measurement (3). The conservative choice of κ ) 1 appears to be adopted universally, whereas nonconservative, nonzero, claims are made for the water contact angle, θ (3, 4). Generally, the reported contact angle is the angle measured from a small (e.g., 2 µL) water droplet on a membrane exposed to air, between the droplet-membrane surface and the droplet-air surface. The angle measured is a surrogate for the contact angle of interest: θ, the angle made by the interface, a fraction of a spherical surface of radius R, found in a cylindrical pore, or defect, of radius r (Figure 1a). Contact Angle Uncertainty. Contact angle measurements exhibit sensitivity to subtle uniform molecular changes on ideal, controlled surfaces (5, 6). Ascertaining representative contact angles on the surface of mass-produced membranes exposed over years to aquatic environments, water treatment, and cleaning processes, presents challenges. Surface and materials science regard the measurement as semiquantitative, useful for ranking materials in terms of relative hydrophobicity or hydrophilicity (7-11). Measurements are method dependent (9, 10, 12-16) and can lack reproducibility (5). Representative measurement may be limited by access to the separation surface, e.g., inside a small-bore fiber or subsurface pores in the bulk material (17, 18). Changes to the chemical composition of the membrane surface affect the contact angle. Polymers at the membrane surface may reorient (19) to minimize interfacial tension. The chemistry of a membrane surface may change due to exposure to algae and biological fouling (20), repeated chemical cleaning (21-25), and fouling (7, 26-31). Resultant changes in surface charge have been measured across porous membranes (see Supporting Information). Fouling by natural organic matter (NOM), a function of pretreatment operations (7) and both NOM and membrane composition, can increase or decrease the contact angle (7, 8, 11, 25, 32, 33). NOM has been associated with a seasonal change in contact angles (33). Surface roughness can increase or decrease the apparent contact angle (34-37). This is caused in part by air trapped between the dry surface and the droplet (37). Distributions of contact angles in commercial membranes have not been reported, nor has the long-term stability of surface chemistry. Where contact angle changes have been recorded for commercial membranes employed in municipal water treatment plants, the evaluations were experimental, bench, pilot-scale, or short-term (7, 33). 9420

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Membranes are fabricated from common polymers with proprietary modifications to increase flux, improve hydrophilicity, or reduce fouling. Regardless of specific chemistries, the literature provides a measure of random error in the contact angle measurement by way of reported sample standard deviations, δs. The population standard deviation can be determined from δp ) δs (n 0.5), where n is the number of repeat measurements or samples. Similarly measures of change that may occur due to surface effects can be obtained from ∆θ ) θe - θo, where θo represents the initial surface state and θe is the contact angle after a surface effect, e.g., fouling. An Alternative Model of the Bubble Point. We propose an alternative model for the bubble point from an area of interfacial science concerned with the measurement of surface tension in complex liquids. The concept follows from an established method known as the Maximum Bubble Pressure Method (38-40) and has been validated with LPHF membranes (41). The method suggests that once the applied pressure is great enough to overcome the force of surface tension modified by the commonly measured static θ, the interfacial surface would move along the capillary wall until the contact line reaches the edge of a pore. The air-water interfacial surface has a spherical curvature of radius R ) r/cos(θ), where r is the radius of the capillary (38). To create a bubble one must increase the pressure further to distort the interfacial surface, reducing the radius of curvature and the contact angle until the maximum bubble pressure is reached. The maximum bubble pressure occurs when a semisphere is formed by the interface, when θ ) 0. This is because the interfacial component of total pressure, Pi ) 2σ/R, is maximized when R is minimized, when R ) r (38) (Figure 1b). Thereafter, the interfacial resistance drops and a bubble is released. The wettability of the pore affects the bubble frequency and volume (42). To implement this approach we used θ ) 0. Variability and Uncertainty. Variability is distinguished from uncertainty (43-45). Uncertainty can be reduced through research, empirical measurement, and expert consensus. Uncertainty when quantified is a measure of incertitude, or ignorance (44). Variability can not be reduced and refers to a quantity for which the value may change within a known degree of randomness (44). To account for uncertainty with Monte Carlo analysis one may treat unknowns as variables with an assumed probability distribution. This method has been criticized for mixing frequentist and subjectivist concepts of probability; for treating uncertainty as a randomly distributed variable to generate a single cumulative distribution function. With uncertainty, a single distribution implies a range and

distribution of likelihood that is not justified by the state of knowledge. Another approach is the 2-Dimensional Monte Carlo method where simulations of known variables are nested within another simulation from which different values for the uncertain variable distribution are selected. Probability Bounds Analysis combines interval arithmetic and probability theory (46, 47). Where there is no uncertainty and the distributions are known for all parameters, the outcome of a Probability Bounds Analysis is identical to that of Monte Carlo (46). When accounting for uncertainty, Probability Bounds Analysis uses probability-boxes, solutions that enclose the neighborhood of all possible cumulative distribution functions that would be generated with a comprehensive 2-D Monte Carlo simulation (48). The width of a probability-box is function of what is not known, the uncertainty. The Probability Bounds Analysis program (RiskCalc) (46) can simultaneously propagate uncertainty of various types in numerous parameters, including the type of distribution, the parameters of a known distribution (e.g., the mean, or the standard deviation of a normal distribution), and uncertainty about dependencies between variables in the model (46-49). The aggregate probabilistic information is preserved in the shape of the boundaries of the probabilitybox. The flexibility and comprehensiveness of Probability Bounds Analysis is advantageous when precise parameter values, distributions or dependencies can not be specified due to limited availability of, or nonexistent, empirical data (49). Objective. The objectives of our analysis are to assess the DIT designs for five major commercial systems of LPHF membranes used in drinking water treatment facilities; to determine compliance with the requirements of LT2. Here we consider 5 commercial designs, each from a different manufacturer of membranes, labeled A through E. Each design has established a test pressure to meet or exceed that expected from eq 1. We used 1-dimensional Monte Carlo analysis as well as Probability Bounds Analysis to determine the range and distribution of defect size resolution (DSR) in each design. Our method provides a unique perspective on the importance of current data gaps and assumptions in the regulation of LPHF membranes providing a barrier to Cryptosporidium oocysts. We present here for the first time an accounting of both the back pressure and variable contact angles in the assessment of DITs practiced by industry, a treatment of θ > 90°, and an application of the Maximum Bubble Pressure Method to the determination of resolution in pressure-based integrity tests.

Materials and Methods Determining DSR. To determine DSR, we rearrange eq 1, the EPA equation for determination of the final test pressure, Ptest_end, to solve for d, which we now call the DSR of the pressure test: DSR )

4 • σ • κ • abs(cos(θ)) • 103 Ptest_end - PBP

(2)

where PBP, is either the fixed maximum PBPmax to evaluate strict compliance, or the continuous function of height PBP(h) to recognize that the DSR varies with height for each productive element of membrane at elevation h on the vertical hydraulic gradient of the system during the test; and the absolute value of the cosine is used to account for static components of surface tension resisting displacement by air pressure whether θ < 90° or θ > 90° (see Supporting Information). The product of our 1-dimensional Monte Carlo analysis is the cumulative distribution function which expresses all information as variability in the DSR. The output from the Probability Bounds Analysis is a probability-box which

envelops a range of possible distributions, expressing both the variability and uncertainty for the DSR. The value of a distribution at the DSR of 3 µm establishes the fraction of systems in compliance, if determined using PBPmax. Or if determined using PBP(h), it is the fraction of water filtered by membranes that have been evaluated using a test of integrity that is capable of detecting defects 3 µm or smaller. The remaining fraction is the risk of water being produced by systems, or by membranes, for which the integrity test could only detect defects larger than 3 µm. Analysis was conducted using @Risk and Risk Calc (see Supporting Information). Data and Models. Data used in the analysis can be found in the Supporting Information. Surface tension, a function of water temperature, was calculated from three regressions on annual profiles from three rivers (50-52) and ranged from 0.0718 to 0.0756 N/m. Temperature ranged from 0 to 27.5 °C. The pore shape correction factor, κ, may be any value between 1.0 and 0 (1). To our knowledge no attempt to further quantify this variable exists in the literature and all DIT designs use the conservative value κ ) 1. Here κ was modeled as a scalar 1.0, a uniform distribution between 0 and 1 with Monte Carlo, and a variable bounded between 1.0 and 0 with Probability Bounds Analysis. DIT test pressures and contact angles used in industry practice have been reported (3, 4). All pressure-based DITs occur with one side of the membrane in air and the other in water creating a hydrostatic gradient across the membrane that varies vertically along the height of the membrane. The hydrostatic back pressure was estimated from the vertical dimensions of each membrane module or cassette, plus an estimated 0-0.6 m of hydrostatic head to overhead permeate pipe or tank level (7, 53). The upper bound of the back pressure is the sum of the hydrostatic head at the bottom of the membrane, hLmax, and that above the membrane, ho, up to the permeate collecting pipe or, for submerged membranes, up to the water level of the tank. A triangular distribution between 0, 0.3, and 0.6 m of head is used to estimate ho, and hL is a known triangular distribution from 0 to hLmax. Thus the maximum back pressure, PBPmax ) ho + hLmax, and the back pressure at elevation h is PBP(h) ) ho+ hL. Manufacturers A and E have two membranes with different hLmax, hLmax_1 < hLmax_2, so we used a triangular distribution for hLmax between 0, hLmax_1, and hLmax_2. C and E have stackable membranes, stacked up to 8-high and 3-high, respectively. Using Monte Carlo, hLmax equaled the full height of the maximum stack, where as in Probability Bounds Analysis, hLmax equaled 1 stack or the maximum stack. Contact angle variability was derived from changes in contact angles reported due to natural organic matter (NOM) fouling. A histogram was generated, ranging from 0° to 102°, with median 9.6°. Contact angle random error was derived from values reported for error or sample standard deviation. These were converted into population standard deviations that ranged from 0.8° to 56°. A histogram and a beta function was generated and the mode, or most likely, population standard deviation was 5.7°. For each commercial design, the contact angle was represented with a normal distribution where the mean was determined as the reported value ( 9.6° and standard deviation 5.7°. For analysis with B, who has not reported a contact angle, we employ a uniform distribution and probability-box between 0 and 180°.

Results and Discussion Allowing for uncertainty and variability, our analysis reveals that DITs may not necessarily detect defects greater than 3 µm, and may even miss defects as large as 8 µm. Our analysis indicated that four of the commercial DIT designs may not be in compliance regardless of whether the contact angle is variable or zero. We present here results for cases where κ VOL. 43, NO. 24, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 2. Probability Bounds Analysis (PBA) enveloping Monte Carlo (MC) analysis for the D design, for DSR, when K ) 1 and θ is normally distributed.

FIGURE 3. Probability Bounds Analysis, the upper bounds of probability-boxes for DSR, when K ) 1 and θ is normally distributed for all five designs. ) 1, the back pressure varies with elevation, PBP(h), and the annual temperature profile is based on Irondequoit Creek (52). With these options fixed we present two approaches to the contact angle, first the normal distribution using the as reported (3) mean contact angle minus 9.6° (due to NOM fouling) with standard deviation 5.7° and second, applying the Maximum Bubble Pressure Method, the contact angle θ ) 0°. Both contact angle models indicate that noncompliance is possible for four of five designs, however when the contact angle is zero at the bubble point, the uncertainty is reduced (the probability-boxes are smaller) and compliance possibilities are lower. Variable Contact Angle. For the normally distributed contact angle, the Monte Carlo simulations for B, C, D, and E all exceed DSR > 3 µm, indicating 96%, 99%, 23%, and 31% compliance, respectively. The lower and upper limits of DSR probability-boxes were 0 to 1.3, 0 to 3.5, 0.3 to 3.5, 1.2 to 4.9, and 0.1 to 6.1 µm, for commercial designs A to E, respectively. The Monte Carlo result is always enveloped by the probability-box (Figure 2). The upper bounds of the probabilityboxes reveal that noncompliance may occur in all but one design (Figure 3). The lower bounds of all probability-boxes lie entirely below the EPA requirement, revealing that it is possible that compliance requirements would be satisfied for all designs (not shown). Maximum Bubble Pressure Method. For θ ) 0°, Figure 4 shows the Monte Carlo analysis for B and E, each enveloped by their respective probability-boxes. The Monte Carlo results for C, D, and E all lie above 3 µm (not shown). The lower and upper limits of DSR probability-boxes were 1.4 to 2.1, 2.5 to 3.4, 2.9 to 4.3, 2.8 to 5.1, and 4.2 to 7.9 µm, for commercial designs A to E, respectively. The upper bounds of the probability-boxes reveal noncompliance may occur in all but one design (not shown). The probability-box for B straddled the EPA requirement (Figure 4), whereas that of A was 100% compliant, situated between a DSR of 1 and 2 µm (not shown). C and D were largely noncompliant with less than half of the lower bound below 3 µm (not shown). E was entirely noncompliant (Figure 4). Temperature and Pore Shape Correction Factors. Differences between and within annual temperature profiles 9422

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FIGURE 4. Probability Bounds Analysis (PBA) enveloping Monte Carlo (MC) analysis for DSR, when K ) 1, and θ ) 0° for B and E designs. had negligible effect. Assumptions of independence between the surface tension and contact angle had no impact. When probability-boxes were generated for κ ) 0 or 1, the lower bounds were DSR ) 0 µm for all designs. Using a uniform κ distribution the Monte Carlo distribution starts at zero. If κ was found to be 0.38, or lower, all designs examined here would be compliant. Limitations. The variability introduced to claimed contact angle values represent the central tendencies of data derived from literature. For the population standard deviation, we use the mode of the curve fit over the distribution, and for the change due to NOM fouling we used the median change observed. Equally large changes in the contact angle are observed due to roughness, hydrolysis, and oxidation. Thus, the variability considered here does not encompass the full range of possibilities. The different outcomes reveal that a 1-dimensional Monte Carlo analysis may underestimate or overestimate risk by disregarding uncertainty, or by assuming the distribution of an uncertain variable. The upper bounds of the probabilitybox may overestimate the risk if in practice the uncertainty is lower than shown. For example, if test pressure and back pressure are the only sources of uncertainty, the designs involving a range of test pressures may choose the higher test pressure when the back pressure is highest therefore maximizing the denominator in eq 2 and existing on the lowest bound DSR curve. Similarly the lower bounds of the probability-box may underestimate the risk. Faced with the uncertainty that creates upper and lower bounds, interpretation must consider the entire probability-box. Questions arise about the representativeness of the distribution of standard deviations and contact angle changes obtained by pooling values from various membranes, experimental and commercial, and values obtained using various methods of measurement. Criticism of the applicability of these pooled values to individual commercial membranes is appropriate; the magnitude and direction of variability, due to measurement error, manufacturing variability, effects of fouling, is valid. Finally, where there is uncertainty, Probability Bounds Analysis provides the upper and lower bounds but does not identify the location of the “true” distribution within the probability-box. This provides a visual characterization of the uncertainty around the partially subjective risk of noncompliance estimated using Monte Carlo. The true DSR distribution may differ within one design on a site by site basis. Significance. Under LT2, a single membrane system may be relied upon to provide up to 4-log removal in new systems and 5.5-log removal of Cryptosporidium oocysts in previously approved systems. This is a level greater than that of any other water treatment technology (54). DITs are used to ensure integrity is maintained as fibers deteriorate or break, to identify and isolate defects, and for the daily determination of log removal values (LRV).

To ensure compliance with LT2, the pressure at completion of the integrity test could be increased until the DSR probability-box is entirely below 3 µm. This may increase maintenance requirements as well as costs of warranty and operation. Alternatively, regular challenge tests could be implemented. The degree to which a DSR > 3 increases the risk of exposure to Cryptosporidium has not been assessed here. The EPA uses 3 µm for the oocyst’s dimension (1, 4), and while some species are as small as 3 µm, those hosted in humans range from 4.4 to 7.4 µm (55, 56). Issues of pathogen shape, flexibility, and compressibility also warrant attention (57, 58). Even in the noncompliant scenarios identified in this study, some removal is likely to occur through direct adhesion of oocysts to membranes (59), sieving, and adsorption, by matter deposited on the membrane (60). Membrane deterioration affecting water quality will eventually be detected by indirect methods (2). However, these methods can be insensitive to cut fibers (e.g., 1 or 3 cut from 1250 or 22,400 intact fibers, respectively) (2, 61) and by extension to a number of defects on the order of 100 µm, depending on the dilution from intact fibers. The health risks posed by these hazards are limited by the prevalence of such undetected defects, the remaining oocyst removal efficiency, and the efficacy of CIIM to identify problems. High LRVs can be maintained with a number of broken fibers, depending on the size of the system. Given that the DSR is well below the fiber diameter, all broken fibers will be discovered by DIT.

Acknowledgments Thanks to Richard W. Clapp, Boston University School of ´ cole Supe´rieure de Physique et de Public Health; Jose Bico, E Chimie Industrielles de la Ville de Paris; and Takeshi Matsuura, Faculty of Engineering, University of Ottawa. J.M. discloses that he has worked with several membrane manufacturers and recently joined the Safe Drinking Water Branch, Ontario Ministry of the Environment.

Supporting Information Available Detailed information used in determination of the DSR. This material is available free of charge via the Internet at http:// pubs.acs.org.

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