Understanding and modelling the diffusion process of low molecular weight substances in polyethylene pipes

Water Research 157 (2019) 301e309

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Understanding and modelling the diffusion process of low molecular weight substances in polyethylene pipes Shima L. Holder*, Mikael S. Hedenqvist, Fritjof Nilsson** Department of Fibre and Polymer Technology e Polymeric Materials Division, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, Stockholm, 10044, Sweden

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 December 2018 Received in revised form 15 March 2019 Accepted 27 March 2019 Available online 30 March 2019

Peroxides are widely used as crosslinkers in polyethylene (PE) drinking water pipes. Cross-linked polyethylene (PEX) has better mechanical properties than PE, but peroxide decomposition by-products can migrate from PEX water pipes into the drinking water unless sufficient preventive actions are undertaken. This work systematically examines the migration of tert-Butyl methyl ether (MTBE), a dominating crosslinking by-product from PEX water pipes, into tap water by utilizing both experimental techniques and finite element (FEM) diffusion modeling. The effects of pipe geometry, tap water temperature (23e80
C), boundary conditions (air or water interface) and degasing (at 180
C) were considered. The MTBE diffusivity increased strongly with increasing temperature and it was concluded that a desired water quality can be achieved with proper degasing of the PEX pipes. As the FEM simulations were in excellent agreement with the experimental results, the model can accurately predict the MTBE concentration as a function of time, water temperature and PEX pipe geometry, and enable the pipe manufacturers to aid in ensuring desirable drinking water quality. © 2019 Elsevier Ltd. All rights reserved.

Keywords: PEX pipes Crosslinked polyethylene Polymers Diffusion model Diffusion coefficient Drinking water

1. Introduction Access to clean water for drinking is the most basic human right and commodity. The safety and quality of drinking water is often primarily associated with the source of the water (public water supplies, groundwater aquifers, desalination plants), but water quality can also deteriorate during the transport process from the water source to the end-user. Today's water pipes are much less toxic than the lead water pipes used during the height of the Roman
de, 2014; Empire (Delile, Blichert-Toft, Goiran, Keay, & Albare Hernberg, 2000), but nevertheless they can still have a negative impact on the final water quality since unhealthy contaminants can still leach from the water pipes into the drinking water. The kind of migrating chemicals is mainly determined by the initial pipe material, while the concentration of chemicals can be affected by other factors such as water temperature, pH, pipe dimension and exposure time between water and pipe. The ultimate aim of this report is to determine how the migration of undesirable chemicals from

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (S.L. (M.S. Hedenqvist), [email protected] (F. Nilsson). https://doi.org/10.1016/j.watres.2019.03.084 0043-1354/© 2019 Elsevier Ltd. All rights reserved.

Holder),

[email protected]

polymer-based water pipes into drinking water can be costefficiently minimized. Polyethylene (PE) is the most widely used polymer in the world, and the installation of PE-based water pipes in plumbing applications is steadily increasing globally (Rabaud and Rozental-Evesque, 2008; Trew, Tarbet, De Rosa, & UKWIR, 1995; UKWIR, 2002). These materials are flexible, inexpensive, corrosion resistant and have expected service lives greater than 100 years (Davis et al., 2006). In drinking water systems, PE-based water pipes are installed both in buried distribution systems and in building plumbing. A potential concern for the extensive use of PE materials is that organic chemicals can diffuse in, out, and through PE thereby adversely affecting the quality of drinking- and ground water. Drinking water distribution systems are vulnerable to intentional or unintentional contamination with neat solvents or organic chemicals, such that knowledge of the permeation of various chemicals into the polymer pipe is needed to assess the future use of the distribution system (Clark and Deininger, 2000). PE-based pipes that sorb organic chemicals can also release them into the water or to the ambient air resulting in long-term environmental contamination (Saquing et al., 2010). A significant amount of responsibility therefore falls to potable water system managers and designers, public health officials, and

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regulators to understand how and why PEX pipes can interfere with drinking water quality at the transport stage due to drinking water chemical interactions and variability in resistance to oxidation. The aforementioned is all the more important because there is very little that end-users, who this situation primarily impacts, can do to ensure that they are receiving good quality, contaminant-free drinking water. While most chemicals can be found at legal limits, scientists still articulate that these could pose long-term health risks and complications and in accumulated amounts. Albeit the European Drinking Water Directive (EUDWD) (1998) has not set strict limits on the majority of drinking water contaminants, with the rise of consumerism and the advent of global sustainable development, regulations that govern the drinking water quality and are focused toward the presence of migrants in newly produced PEX pipes (Kelley et al., 2014; Koch, 2004; Skjevrak et al., 2003) will be strengthened in the years to come (Mercea et al., 2018) and it can be in the interest of such businesses to be ‘ahead of the game’. The development of contaminant fate and transport models can help better establish and reduce the occurrence of PEX pipes which do not meet the minimum standards outlined in the DWD set by the European Commission for products in contact with drinking water (EDW, 2017). PEX pipes either undergo (1) peroxide crosslinking (PEX-A pipe, highest crosslinking degree); (2) silane crosslinking (PEX-B pipe); or (3) electron beam irradiation crosslinking (PEX-C pipe, lowest crosslinking degree) (Whelton et al., 2010), which causes polymer chains to bond with one another. Crosslinking improves the ability of PE pipes to resist mechanical failure at elevated temperatures (e.g. improved hot-water conveyance with PEX connection compared to HDPE pipes). Unfortunately, prior investigators have mainly focused on PEbased water pipe interactions with strictly nonpolar compounds (Mao et al., 2010; Ong, 2008; Selleck and Marinas, 1991; Vonk and Veenedaal, 1983; Whelton et al., 2010; Whelton et al., 2011). To date, little work has focused on PEX pipe water quality impacts, and no literature has been found enabling the fate and transport model development with more polar compounds such as tert-Butyl methyl ether (MTBE), which is sparingly soluble in water. Most studies have assumed specific compounds and exposed the pipes to them for modeling their uptakes, failing to first establish the fundamentals through directly investigating the chemicals that are migrating from the pipes without human influence (Ryssel et al., 2015). Furthermore, models have been developed for using neat contaminants and PE materials, but no studies or models have yet evaluated mass transfer of low concentration/dilute migrants, close to the real-world situation (Tang et al., 2013). Tert-Butyl methyl ether is one of the primary by-products of peroxide crosslinked PE pipes and even though these oxygen-containing aliphatic compounds exhibited high solubilities when tested as neat contaminants for their uptake in PEX compared to HDPE pipes (Tang et al., 2013), no further reports have been found in literature investigating the transport of the MTBE directly from PEX pipes. Due to the potentially negative effects of MTBE which is responsible for the taste and odour related problems and TBA metabolite formation, stronger regulations on the maximum allowed concentrations in the tap water at the point of use of the customer are desirable. Tougher water quality criteria are discussed both in the European Union (Deutsches Institut für Normung, 2005; Deutsches Institut für Normung, 2014; Federal Environment Agency, 2016) and the United States (Suffet, 2007; USFR, 2009; Whelton et al., 2010). In order to improve the tap water quality and fulfill the water quality regulations, increased knowledge and new predictive tools for simulating migration processes in PEX water pipes are needed. The goal of this work was to enable improved drinking water

quality by elucidating the chemical decomposition and migration of peroxide by-product in peroxide-crosslinked PEX pipes. The specific objectives were to: (1) determine the amount of MTBE in PEX pipes as a function of initial concentration, time, boundary conditions, pipe geometry and migration temperature, (2) understand the effect of heat treatment (degasing) on peroxide by-product release and finally, (3) develop a reliable finite element (FEM) diffusion model which can accurately predict the amount of chemical in the drinking water, using experimental migration data both as model input and for validation of the model. 2. Material and methods 2.1. Polymer preparation The polyethylene pipe grade polymer used was HDPE powder
having melt flow rate (MFR, 190 C/21.6 kg) of 2 g/10 min and 3 density of 0.954 g/cm . Crosslinked PE (PEX) pipes, manufactured in accordance with the international quality standard ISO 9001 and environmental standard ISO 14001 (ISO, 2015) for drinking water use, were prepared in 15  2.4 mm, 25  3.6 and 32  4.6 mm (Outer Diameter x Wall Thickness, OD x WT) dimensions. The PEX pipes had a density of 0.938 g/cm3 and peroxide crosslinking degree of approximately 85%. 2.2. PEX characterization TGA studies of the samples were conducted using a Mettler Toledo TG/DSC1 instrument. Pipe samples were carefully cut into small pieces (according to the sample holder size) with a total weight of 5e10 mg and underwent heating in 70 mL aluminium oxide crucibles from 30 to 850
C at a 10
C min1 heating rate, in nitrogen atmosphere with 50 mL min1 flow rate. A Mettler Toledo differential scanning calorimeter (DSC) was used for calorimetric measurements. The melting endotherms were determined using 5e10 mg of pipe sample in a covered aluminium pan, and nitrogen environment. Temperature was ramped at a rate of 10
C min1 from 80
C to 250
C, then 250
C to 80
C, and then 80
C to 250
C; the first heating cycle was used to obtain the melting temperature of each sample. 2.3. Data collection for model development and validation A combination of two regulatory standards described in the European Standard EN 12873 - Parts 1 and 2 (Deutsches Institut für Normung, 2005; Deutsches Institut für Normung, 2014; Federal Environment Agency, 2016) and the Chinese National Standard GB/T 17217-1998 (The Standardization Administration of the People's Republic of China, 1998) were used. In the European standard, a continuous migration process is used whereby water is stagnant in the pipe for retention times of more than 48 h, i.e. the continuous reaction between the pipe and water can be investigated to better understand compound migration in stagnant water. In the Chinese standard, a successive migration process is employed which mimics a more regular flow manner. In this study, a combined migration procedure was developed which fulfills both standards. Four series of migration experiments (S1eS4) were undertaken in total, as outlined in sections 2.3.1e2.3.4. In all of the experiments, 1 m long PEX pipes were filled with deionized water and the amount of chemical in the stagnant water was each day measured with Head-Space Gas Chromatography-Mass Spectrometry (HSGC-MS), after which the water was replenished.

S.L. Holder et al. / Water Research 157 (2019) 301e309

2.3.1. S1: determination of boundary conditions and starting concentrations The primary aim of the first migration experiment was to examine the boundary conditions at the pipe/water- and pipe/air interfaces. One set of PEX pipes with 32 mm OD and 4.6 mm WT were filled with deionized water and stored at 60
C for 31 days, similar to the drinking water testing standards outlined in European Standard EN 12873-1(2014) (Deutsches Institut für Normung, 2005; Deutsches Institut für Normung, 2014; Federal Environment Agency, 2016). The chemical concentration in the stagnant water was measured daily, thereafter the water was replenished. A second set of pipes, which were empty during the first 9 days and then filled with deionized water, were treated similarly. If the amount of released migrant (at a specific day) would be the same for both sets of pipes, then the boundary condition at the pipe/air interface would be effectively identical to the boundary condition at the pipe/water interface. The resulting data also enabled the determination of chemical starting concentrations and the proportions between di-tert-butyl peroxide (DTBP) and MTBE. 2.3.2. S2: comparison of migrant concentration with various pipe geometries The second experiment was also, together with S1, intended for determining the boundary conditions at the pipe walls. This objective was reached by investigating the influence of the PEX pipe wall thickness, because if a single diffusivity is used to fit experimental data for multiple geometries, a good fit between experiments and simulations can only be achieved if the boundary conditions are correct. Three pipes with 15, 25 and 32 mm OD and 2.4, 3.6 and 4.6 mm WT respectively were used. The study was conducted at 60
C for 30 days. 2.3.3. S3: influence of the water desorption temperature The aim of the third migration experiment was to determine the migrant diffusivity in the PEX pipe wall as a function of water temperature. PEX pipes with 32 mm OD and 4.6 mm WT were used to determine the migration at 23, 60 and 80
C respectively, for 31 days. 2.3.4. S4: influence of heat treatment (degasing) on migrant diffusion The goal of the fourth migration experiment was to determine the migrant diffusivity in the PEX pipe at 180
C to examine if proper degasing of the pipe could be a sufficient strategy for minimizing the chemical concentration in the tap water. Prior to the study, 4.6 mm thick PEX pipes were thermally treated in an oven (Heraeus, AE1030/BTC9090) with circulated nitrogen at 180
C for a maximum of 15 min. In order to determine the effect of degasing time on migrant concentration, the samples were heated for 2, 8 or 15 min, such that the diffusivity, D, at 180
C could be determined. Subsequently migration studies were carried out at 60
C. The results were additionally used for model validation. 2.4. Equipment and experimental setup Any vials, bottles and caps used were washed with concentrated nitric acid (Sigma-Aldrich), rinsed with deionized water and heated at 180
C for approximately 12 h. Migration studies were conducted in ovens (Memmert, Model 600) or at room temperature on shelves in the laboratory, and all pipes were sealed with Teflon-lined stoppers after filling with 18.2 MU deionized water. The water in the pipes was allowed to stand for 24 h, sampled, thoroughly drained, and then refilled with fresh 18.2 MU deionized water immediately; this continued for the duration of the experiments.

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For each experiment, negative control test samples were prepared by placing deionized water into 50 mL amber glass bottles with Teflon-lined stoppers and left under identical test conditions as the PEX pipe samples. 2.5. Head-Space Gas Chromatography-Mass Spectrometry (HS-GCMS) analysis Water samples were collected in 40 mL glass vials with screw caps and stored at 4
C until analysis. In preparation of the internal standard (IS) solution, d8-Toluene was diluted in MeOH to obtain a final concentration of 5.43 mg L1. Of this solution, 25 mL was introduced into the headspace vials containing 10 mL of sample, and the vial was sealed; this was done for all analysed samples, including blank solutions and those used for obtaining calibration curves for each target substance. The analytes were quantified by HS-GC-MS on a Headspace sampler (Agilent, 7697A) with a 1 mL sample loop and 0.2 mm uncoated fused silica transfer line coupled to Agilent 7890A GC and 5975C MS systems. Prepared samples were placed into a 10 mL glass screw-top vial with polytetrafluoroethylene/silicone septa, evenly mixed, and allowed to equilibrate for 30 min at 30
C. Analytes were exposed to the sample headspace for 30 min and the evolved gases were injected into the GC-MS injection port where analysis took place; the transfer lines from the HS to the interface and from the interface to the GC were set at 110
C, and the sampling frequency was 20 s1. All GC-MS injections were performed with a 5:1 split ratio. A Rxi-624Sil MS (Restek, 13872) capillary column (60 m  320 mm i.d. x 1.8 mm film thickness) was used. Silarylene was used as the stationary phase at a maximum temperature of 300
C (splitless mode). Helium was used as carrier gas in the pressure control mode to ensure a column flow of 1.0 mL min1. The GC oven temperature program consisted of an isothermal step at temperature 30
C for 5 min, then raised at 20
C min 1 to 300
C and held for 30 min. Ionization was effectuated by electron impact (EI) at 70 eV, and an electron multiplier voltage (EMV) of 1 was used. The MS transfer line and oven temperatures were set to 280 and 150
C respectively. The ion source temperatures were 250
C and manifold temperature was 40
C. All analyses were performed in triplicate. The compounds in the GC/MS total ion chromatogram (TIC) were identified using NIST/ EPA/NIH Mass Spectral Library 2011. Qualitative analysis of the constituents was based on comparison of the obtained mass spectra with those of reference compounds in the NIST Mass Spectral Search Program (NIST Version 2.0). In scouting experiments, the acquisition was performed in Full-Scan mode in the 29 to 200 mass-to-charge ratio (m/z) range. In the final optimized method, the acquisition was in Selected Ion Monitoring (SIM) mode and DTBP (57 and 146 m/z) and MTBE (57 and 73 m/z were quickly identified. Calibration standards, DTBP (Luperox® DI, 98%) and MTBE (anhydrous, 99.8%) were obtained from Sigma Aldrich. Calibration curves were prepared for the two compounds. All standards were prepared and concentrated using the same IS solution as previously described for the samples. All results were fit to the calibration curve and normalized to the IS during data processing. For each substance, the calibration range, limit of detection (LOD) and limit of quantification (LOQ) in the HS-GC-MS method were as follows: DTBP: Calibration Range ¼ 0.01e0.23 mg/L; LOD ¼ 0.01 mg/L; LOQ ¼ 0.03 mg/L MTBE: Calibration Range ¼ 0.7e73 mg/L; LOD ¼ 1.0 mg/L; LOQ ¼ 3.1 mg/L

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S.L. Holder et al. / Water Research 157 (2019) 301e309 Table 1 Thermal characterization of PE materials.

2.6. FEM model development Finite element modeling (FEM) with COMSOL Multiphysics (supplemented with MATLAB) was used to compute the migrant concentration in the PEX pipe and in the water as a function of time. The pipe geometry was defined using the inner radius (ra), the outer radius (rb) and the pipe segment length (L). Due to the cylindrical symmetry and the high aspect ratio of the PEX pipe segments, the three-dimensional (3D) pipe geometry could be simplified to a one-dimensional (1D) problem in cylindrical coordinates. The diffusion equation, which describes the diffusion through the PEX pipe, then became: vcPipe / vt ¼ (1/r) $ v / vr $ (rD(T) $ (vcPipe / vr))

(1)

where cPipe is the migrant concentration in the PEX pipe, t is the time, T is the temperature, and r is the radial position in the pipe (Crank, 1975). As a starting condition, it was defined that the boundary condition (bc) be ‘useOpenOuterbc ¼ 1’, where ‘0’ denotes that the change in concentration over time is equal to 0 (that is, 0 ¼ dcPipe(bc)/dt ¼ 0) and ‘1’ denotes that only the initial concentration at the boundaries (inner and outer pipe radius sides) is equal to 0 (that is, 1 ¼ cPipe,0(bc) ¼ 0). Furthermore, the initial conditions also assume that the migrating substance is uniformly distributed throughout the PEX pipe layer; that is, CPipe ¼ CPipe,0 for 0  x  L where L is the wall thickness. The diffusion coefficient D(T), which depend on both temperature, T, and the choice of migrant chemical (Adams et al., 2011), was determined by fitting the model to the results of migration experiments S1eS4. Due to the low chemical concentration, the diffusivity was considered concentration independent in the model. The initial concentration, cPipe,0, was determined from the experiments. Because of the simple cylindrical 1D pipe geometry, an equidistant mesh with 1  103 mm mesh elements was used. The storage time between pipe production and experiments was accounted for in the model. Once the pipe concentration was computed as a function of t (days), the concentration in the surrounding water was computed as follows, considering that the water was refreshed every day: mPipe(t) ¼ cPipe(t) $ VPipe

(2)

mWater(t) ¼ mPipe(0) - mPipe(t)

(3)

mRefreshedWater(t) ¼ mWater(t-1) - mWater(t)

(4)

cRefreshedWater(t) ¼ mRefreshedWater(t) / Vwater

(5)

where mPipe is the migrant mass in the pipe, as calculated by numerical integration of the concentration cPipe over the pipe volume, VPipe$Vwater is the volume of the water, cRefreshedWater is the concentration in the refreshed water, and mWater and mRefreshedWater are the accumulated masses of migrants in water and refreshed water, respectively. 3. Results and discussion 3.1. Physics of migration in PEX pipes The process of migration from the pipe to the water depends on the properties of both the polymer and the migrating compounds, and also on the migrant concentration in the water phase such that the driving force decreases with saturation. Table 1 presents the weight loss percentages of PE-based materials as well as the melting temperatures (Tm) and degradation temperatures (Tdeg)

Property (
C)

T10% T20% T50% T60% T70% T90% Tdeg, Tdeg Tm

b

onset

Type of PEa Neat PE

PE/AO resin

PEX1

PEX2

PEX3

PEX4

415 436 461 466 470 479 397 464 137

421 436 459 464 468 477 403 463 136

451 462 475 478 481 486 435 476 131

451 462 475 478 481 487 442 475 132

448 459 474 477 479 485 447 476 134

451 462 475 477 482 488 434 476 131

a AO ¼ antioxidant; PEX1 ¼ 2.4 mm; PEX2 ¼ 3.6 mm; PEX3 ¼ 4.6 mm; PEX4 ¼ 2.4 mm þ 180
C, 2 min. b Tx% ¼ temperature at which x % wt. loss occurs; Tdeg, onset ¼ onset temperature of degradation; Tdeg ¼ degradation temperature; Tm ¼ melting temperature.

derived from the TGA data, where the weight loss rate of sample was given as a function of temperature. The process of crosslinking PE showed a particularly strong impact such that the thermal stability, shown by increased temperatures at which weight loss occurred, was notably enhanced in PEX pipes compared to the neat PE powder and the PE/AO resin. The presence of crosslinks notably shifted the onset of thermal degradation toward higher temperatures than the neat PE. Neat PE powder and PE/AO resin generally exhibited the least thermal stability as they rapidly decomposed from T10% to T90% due to the absence of crosslinking networks conforming a more stable PE structure. The onset of thermal decomposition of all crosslinked pipes occurred at higher temperatures compared to those of the neat PE powder and PE/AO resin, supporting the stable nature of the peroxide crosslinking process for inferring thermal stability to PE pipes and resistance towards the onset of thermal degradation. The melting point of the crosslinked material was lower than the uncrosslinked material indicating thinner crystals in the former. Non-heat-treated PEX pipes possessed, as expected, similar thermal stabilities, regardless of pipe wall thickness, as temperature increased. Overall, thermal analysis revealed small differences in degradation temperature and its onset between non-heat-treated and heat-treated PEX samples, but greater differences between un-crosslinked and crosslinked samples. Degasing via heat treatment had no visible effect on the thermal stability of the PEX pipes, thereby demonstrating that heat treatment of PEX pipes does not significantly compromise their thermal integrity. Table 2 provides physicochemical properties of the migrants investigated in this study. Since MTBE is moderately miscible in water, this molecule is expected to be present in higher concentrations in the water phase than DTBP. Further compounding this effect, the molar volume decreases in the order of DTBP > MTBE. The migration rate is expected to increase with decreasing molecule size, since small compounds more easily penetrate the PEX structure. Furthermore, if these compounds are low polar or nonpolar, high compatibility and high solubilities are to be expected in PEX pipes since they are nonpolar. If both the molecular size and the dipole moment are similar for the substances, then the determining factor becomes the octanol/water (Kow) or the hexadecane-water (PHexadacane-Water) partition coefficient. However, while Log Kow is generally used throughout polymer research as a good proxy to assess chemical hydrophobicity and ability to stay in the PEX polymer and out of the water phase (Tang et al., 2013), octanol contains a polar hydroxyl moiety which is able to interact with polar molecules such as MTBE (Hale et al., 2010). As such, the hexadecane-water partition coefficient (estimated in this work using the commercial quantum chemical software COSMOtherm) is

S.L. Holder et al. / Water Research 157 (2019) 301e309 Table 2 Migrant characteristics in their standard state (25
C [77
F], 100 kPa) except where otherwise stated.

Formula m (debye)a, b Mm (g/mol) Mv (cm3) Mp (
C) Bp (
C) r (g/cm3) Sw (mg/L) Log Kow Log PHexadecane-Waterd

DTBP

MTBE

C8H18O2 0.920 146.23 173.4 40 111 0.796 171 (insoluble)c 3.20 2.61

C5H12O 1.361 88.15 119.1 109 55 0.740c 46000 (moderate)c 0.94 1.03

a m ¼ dipole moment; Mm ¼ Molar mass; Mv ¼ molar volume; Mp ¼ melting point; Bp ¼ boiling point; r ¼ Density; Sw ¼ water solubility; Log Kow ¼ octanol water partition coefficient; Log PHexadecane-Water ¼ hexadecane-water partition coefficient. b In benzene. c At 20
C. d (COSMOtherm, 2018).

a better measure of hydrophobicity when interactions with PE are studied; the higher the Log Kow or Log PHexadecane-Water, the higher the hydrophobicity. The properties of the migrating compounds have a direct influence on diffusivity values (Whelton et al., 2010), and are therefore as important as the molecular mobility of the polymer chains (Millet et al., 2016). Considering the full migrant properties presented, migrant concentration in the water during

Fig. 1. Illustration of the proposed mechanism for MTBE formation due to DTBP decomposition in PEX pipes and the migration into drinking water.

305

the studies is expected to increase in the order of DTBP < MTBE. In this work, the proposed FEM diffusion model considers that MTBE is a DTBP by-product as exemplified in Fig. 1. The basic model parameters such as initial concentrations and diffusion coefficients were obtained from experimental data, and where possible, compared to expected values. Furthermore, the relationship between the model parameters and the physicochemical characteristics of the compounds were analysed in order to determine their influence on the observed migration profiles. 3.2. Diffusion results for experiments and simulations In order to use the FEM diffusion model for predicting the migrant concentration in contact with the water as function of time, the boundary conditions, starting concentrations and temperature dependent diffusivity had to be determined. Migration experiments S1 and S2, which examined the effect of having the pipe in contact with air or water and the effect of changing pipe dimension, were used to evaluate the initial and boundary conditions described in Section 2.6. S1 was also used for determining the starting concentration in the pipe, while S3 and S4 were used to examine the temperature dependence of D and the effect of degasing the pipes respectively. The diffusion simulations were run in two steps, one for the degasing and storage phase and one corresponding to the conditions during the migration experiments. 3.2.1. Determination of boundary conditions and starting concentrations (S1) In Fig. 2, the data collected during migration study S1 is summarized, showing the concentration of migrants in the water (refreshed daily) versus time. As predicted in Section 3.1, the MTBE concentration was highest (z100 mg/L) and the DTBP concentration lowest (z1 mg/L). The MTBE concentration pattern showed a linear decrease in concentration of roughly one magnitude over 31 days in log-linear scale. Due to the low concentration of DTBP, it was difficult to assess its migration characteristics with HS-GCMS; however, the focus in this work was the analysis of MTBE data. At 60
C, the results for the initially empty pipes (Fig. 2a) were almost identical to the results for the continuously water-filled pipes (Fig. 2b), indicating that the boundary conditions at the pipe/airand pipe/water interfaces were effectively identical. The proportion of MTBE formation from DTBP decomposition was observed and included in the FEM model. 3.2.2. Comparison of migrant concentration at various pipe geometries (S2) In Fig. 3, the results of experiment S2 are summarized in three plots showing MTBE concentration versus time for three different

Fig. 2. DTBP and MTBE concentrations in continuously refreshed water during 31 days at 60
C for 4.6 mm thick PEX pipes undergoing migration (a) in air initially and water subsequently and (b) always in water.

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S.L. Holder et al. / Water Research 157 (2019) 301e309

Fig. 3. Log-lin plots of MTBE concentrations as a function of migration (60
C) time and pipe wall thickness, (a) 2.4, (b) 3.6 and (c) 4.6 mm. The curves correspond to the simulation fittings.

pipe dimensions (OD: 15, 25 and 32 mm; WT: 2.4, 3.6 and 4.6 mm). The migrant concentration in the refreshed water always decreased with time, with the decrease being more pronounced with decreasing pipe wall thickness. This result is expected since the size of the migrant reservoir increases with the volume of the pipe and thus also with the pipe thickness. Since study S1 indicated that the pipe/air- and the pipe/water boundary conditions were identical, one single D would be sufficient to fit all MTBE data in Fig. 3, assuming correct boundary conditions. Optimal fitting, as shown with curves in Fig. 3, was achieved by setting the concentrations to zero at both pipe surfaces. The boundary conditions are reasonable considering the comparatively large volume of the water reservoir, the daily refreshing of the water and the extremely slow diffusion inside the pipe wall as compared to the diffusivity in the water. Hence, the migration of MTBE was characterized as a process limited by its diffusion properties in the pipe; a diffusioncontrolled process. The fit yielded an MTBE diffusivity of D (60
C) ¼ 1.5  1012 m2/s. 3.2.3. Influence of water desorption temperature (S3) The results of migration experiment S3 are shown in Fig. 4,

where the concentration of MTBE in the refreshed water is plotted versus time for each migration temperature. When the water temperature was raised, the initial MTBE concentration in the water subsequently increased, while the final concentration decreased. After 30 days, the MTBE concentration had decreased ~8 times at 30
C and ~280 times at 80
C. These trends are explained by the expected increase in migrant diffusivity with increasing temperature (refer to S3 values in Table 3). 3.2.4. Influence of heat treatment on migrant diffusion (S4) Fig. 5 concludes the results of migration experiment S4, where the effect of degasing at 180
C was considered. The concentration of MTBE in refreshed water was plotted against time for 4.6 mm thick PEX pipes which had been heated at 180
C for 2, 8 and 15 min. After degasing, the standard migration experiments were performed at 60
C. The curves maintained a similar downward shift with increasing time from 2 to 15 min. The MTBE concentration decreased with degasing, and values remained within the same range of z99.3 mg/L by the end of migration day 21 regardless of degasing time, suggesting that 2 min was sufficient to achieve a reduction in the initial migrant concentration from 551 mg/L in S3

Fig. 4. Log-lin plots of migrant concentration in 4.6 mm (WT) PEX pipes in water at (a) 30, (b) 60 and (c) 80
C with corresponding curves showing simulation fittings.

Table 3 MTBE diffusion coefficients in the PEX pipe associated with experiments conducted in S1eS4. Experiment S1 S2

S3

S4

a b c d

PEX Pipe WT (mm) 4.6 4.6 2.4 3.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6

Heat Treatment Temperature (
C) e e e e e e e e 180 180 180

Air/water. Water only. MTBE diffusivity during heat treatment. MTBE diffusivity during water migration experiment.

Heat Treatment Time (min) e e e e e e e e 2 8 15

Migration Condition (
C) a

60 60b 60 60 60 30 60 80 60 60 60

D (109 m2/s)c

D (1012 m2/s)d

e e e e e e e e 1 1 1

1.5 1.5 1.5 1.2 1.5 1.3 1.5 3.5 0.8 0.8 0.8

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derived for MTBE, it should be noted that in four studies, the geometric mean detection threshold and as such, the recommended taste and odour thresholds of MTBE in drinking water varies from 24 to 135 mg/L and 15e180 mg/L respectively (WHO, 2005), whereas the European Commission states a threshold of 15 mg/L (EC, 2001). Specifically, in the US, the primary drinking water standards for MTBE vary from state to state and range from 10 to 240 mg/L (NEIWPCC, 2003), while the health advisory range for organoleptic (taste and odour) effects suggested by the U.S Environmental Protection Agency (EPA) were 20 mg/L - 40 mg/L (EPA, 2008). It is evident that MTBE threshold values vary and this must be acknowledged since degasing conditions should be chosen to meet the specific regional/national threshold values. It should also be acknowledged that complicating factors (e.g. disinfectant residuals, biofilm and scale presence, and water flow velocity) in real water distribution systems can influence the aging and degradation of PEX pipes (Dear and Mason, 2006; Whelton and Dietrich, 2009; Colin et al., 2009a, 2009b). While these factors are beyond the aims of the present work, their influence may be explored in future work as an extension to this study, providing a wholestic tool which benefits both pipe manufacturers and drinking water sectors. 3.2.5. Summary of the diffusion results Table 3 summarizes the MTBE diffusivities in PEX from experiments S1 e S4. Diffusivities were computed by fitting the developed FEM model to the experimental desorption data of Figs. 3 and 4, using a zero-boundary MTBE concentration (typical concentration profiles were as shown in Fig. 6). Essentially all diffusivities from the S1 and S2 experiments were identical, confirming the correctness of using zero concentration boundary conditions and considering a diffusion-controlled migration process. The computed diffusivity D(60
C) ¼ 1.5  1012 m2/s was close to a previously reported diffusivity (2.0  1012 m2/s), corrected for temperature using the Piringer's model (Crompton, 2007). It was also shown that D increases, as expected, with increasing migration temperature in the range 30e80
C for MTBE (S3). The diffusivities between the different degasing times were desirably consistent. Since D(60
C) only decreased slightly with degasing treatment (S4), it can be concluded that D was at least not strongly concentration dependent, as suggested in previous studies (Adams et al., 2011). For any migration curve, a reduction in the starting concentration c0 will thus result in a reduced final concentration with exactly the same factor. Consequently, one of the most costeffective ways to reduce the chemical emissions from PEX pipes is to reduce c0 through degasing of the pipes. To conclude, the FEM diffusion model can now accurately predict the migrant concentration in drinking water as function of pipe geometry and migration temperature. The model can thus be used as a valuable tool for minimizing the amounts of chemicals migrating from PEX pipes into tap water. Fig. 5. Simulation and experimental data on the 4.6 mm (WT) PEX pipe showing the MTBE concentration as a function of migration time at 60
C. Figures a, b, and c show the results for 2 (____), 8 (_ _ _) and 15 (€) min degasing at 180
C respectively.

(reference 4.6 mm WT pipe; 60
C migration) to z355 mg/L after degasing. Using this experimental data, the FEM model was used to compute the MTBE diffusivity during both the degasing and migration processes. MTBE diffusivity during the degasing treatment at 180
C, D(180
C), was 1  109 m2/s, while diffusivity during the migration period, D(60
C), was 0.8  109 m2/s, in good agreement with migration studies conducted throughout experiments S1eS3. While an official health-based guideline value has not been

4. Conclusions A combined experimental and simulation strategy was used for predicting the migration of chemicals from peroxide-crosslinked water pipes into drinking water. The decomposition product, MTBE, from the common DTBP peroxide crosslinking of PE was focused on in this study. Physical properties of PEX pipes were determined with TGA and DSC, while HS-GC-MS was used to measure the concentration of chemicals in the drinking water as a function of time. The experimental migration results were reasonable, considering the physical properties of the compounds. A FEM diffusion model was developed for analyzing the migration, providing predictions in good agreement with experimental migration validation data. Proper boundary conditions, initial

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Fig. 6. Concentration profiles of MTBE in the 4.6 mm (WT) PEX pipe during degasing treatment at 180
C (a & b) and after day 26 of 60
C migration (c & d).

concentrations, partitioning coefficients and temperaturedependent diffusion coefficients were established by fitting the FEM model to experimental results of tailor-made migration experiments. Assuming an even distribution of migrants along the length of the pipe, the model can accurately predict the concentration of chemicals in tap water as a function of time, migration temperature and PEX pipe geometry. Degasing was found to be an efficient strategy for reducing the migrant concentration in the PEX pipes and the model can already be used for predicting ideal degasing times, although complementary degasing experiments will be needed for computing D(T) over the whole temperature range of relevance and for additional validation of the model. Due to the prediction power of the new FEM diffusion model, the results of this study can enable PEX pipe producers to optimize their production processes, ultimately playing their part in ensuring a desirable water quality and an augmented public health. Declaration of interests None. References Adams, W.A., Xu, Y., Little, J.C., Fristachi, A.F., Rice, G.E., Impellitteri, C.A., 2011. Predicting the migration rate of dialkyl organotins from PVC pipe into water. Environ. Sci. Technol. 45 (16), 6902e6907. https://doi.org/10.1021/es201552x. Clark, R.M., Deininger, R.A., 2000. Protecting the nations critical infrastructure: the vulnerability of U.S. Water supply systems. J. Contingencies Crisis Manag. 8 (2), 73e80. https://doi.org/10.1111/1468-5973.00126.

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