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Empirical model for dissolved oxygen depletion during corrosion of drinking water copper pipes
Corrosion Science 52 (2010) 2250–2257
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Empirical model for dissolved oxygen depletion during corrosion of drinking water copper pipes Ignacio T. Vargas, Pablo A. Pastén, Gonzalo E. Pizarro * Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad, Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul Santiago, Chile
a r t i c l e
i n f o
Article history: Received 23 September 2009 Accepted 11 March 2010 Available online 15 March 2010 Keywords: A. Copper B. SEM B. XRD
a b s t r a c t Predictive models characterizing the evolution and interaction of key parameters of water chemistry are needed to better understand corrosion events in drinking water pipes. We performed experiments with new copper pipes under combinations of pH, dissolved oxygen (DO), temperature, chlorine, and dissolved inorganic carbon. We found that DO consumption during 24 h of stagnation was not limited by diffusion, thus the DO consumption rate in the bulk water could be used to probe the processes occurring at the pipe surface. We propose a quantitative dependency of the DO consumption rate on a rather limited set of physicochemical parameters. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Ageing and deterioration of piping in drinking water systems and the colonization of microorganisms on the surface of pipes have emerged as a relevant infrastructure maintenance and rehabilitation challenge worldwide for the next decades [1]. Copper has been the plumbing material of choice in household drinking water systems [2] because it is relatively resistant to corrosion [3] and it can limit biofilm growth on the inner surface of the pipes [4]. However, under specific water chemistry and operation conditions serious corrosion events can occur resulting in structural damages and release of dissolved copper into the tap water [4– 7]. Although copper is essential to the human diet, ingestion of copper could induce acute and chronic health effects. While high doses of copper induce acute effects to the gastrointestinal tract, long-term overexposure results in copper accumulation and liver damage. [8,9]. Quantitative predictive models are a key tool for predicting exposure to copper and for improving our conceptual understanding of copper corrosion. To predict events of copper release it is necessary to develop models that describe the evolution and reveal the relation between the key physicochemical parameters of corrosion during stagnation, the period of time that precedes the flushing of the pipe every time the tap is opened. Empirical expressions to estimate rates of corrosion and dissolution of corrosion by-products have been used and derived in several recent corrosion studies. For example, to covert electrode potentials to standard hydrogen electrode (SHE), Huang et al. use an empirical
* Corresponding author. Tel.: +56 2 354 4872; fax: +56 2 354 5876. E-mail address: [email protected] (G.E. Pizarro). 0010-938X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.corsci.2010.03.009
expression dependent on temperature [10]. Recently, a study of the dissolution rate of lead corrosion by product PbO2 derived an hydrogen ions and carbonate dependent expression to estimate the dissolution rate of PbO2 [11]. Likewise, Montañés et al. developed an experimental expression to estimate the dependence of the galvanic corrosion rate by the Reynolds number in copper/AISI pipe systems [12]. Thus, the development of empirical expressions based on the corrosion processes emerges as an important step in the construction of mechanistic models. Current knowledge of corrosion of copper pipes divides the phenomenon in three processes: (1) oxidation of metallic copper; (2) scale formation; and (3) dissolution and transport of dissolved copper form the surface to the bulk water [2,7]. The availability of dissolved oxygen (DO) limits the oxidation of metallic copper in the first process. The oxidation of metallic copper is an electrochemical phenomenon that involves two half-reactions. The anodic half-reaction is responsible for the release of metal ions into the water from the metal surface, leaving free electrons to consume oxygen and hydrogen ions (H+) by the cathodic half-reaction [13] (Fig. 1). Thus, the concentration of hydrogen ions in the water also controls the metallic copper oxidation. For pH values lower than 6 and DO concentrations greater than 2 mg/L, the metal may dissolve to form Cu2+, which is the most stable form of dissolved copper under these conditions [14]. Dissolved copper concentrations ranging from 0.05 to 1 mg/L have been observed in recent large-scale pilot studies [15,16]. These levels are significantly lower than the estimated dissolved copper concentration considering the total mass of oxygen available for the oxidation process. A reason for this observation could be the limitation imposed by the amount of available hydrogen ions in water [17]. In consequence, the consumption rate of DO and the kinetic of
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Fig. 1. The phenomenon of corrosion of copper consists of three processes: oxidation of metallic copper, scale formation, and dissolution and transport. The DO is consumed by the first process and the scale formation process contributes with hydrogen ions that are the limiting factor for the oxidation of metallic copper.
metallic copper oxidation are controlled by two mechanisms: the availability of hydrogen ions for consumption by the cathodic half-reaction and the scale formation. The scale formation (second process) is dependent on pH, DO, temperature and the ionic matrix of the water. When pH is greater than 6, cupric ions precipitate forming scales [2,18]. Pehkonen et al. [6] reported that the stability, thickness, and mass transfer properties of a film of corrosion by-products depend on DO and not only on pH. Moreover, the scale formation process is driven by a temperature dependent thermodynamic equilibrium: high temperatures favor the precipitation of corrosion by-products, decreasing dissolved copper concentrations [19]. The scale formation reactions release hydrogen ions into the water that are consumed by the oxidation of metallic copper process and the DO consumption, thus releasing more copper ions into the water. Hence, the kinetic of DO consumption is controlled by pH and temperature dependent scale formation reactions. The scale dissolution and transport of dissolved copper (third process) links the processes that occur in the metal-liquid interface (first and second processes) with the bulk water composition determining the events of high copper concentration in tap waters. Fig. 1 presents a conceptual model that includes the relationships between the three processes of corrosion of copper pipes and the copper released. The contribution of hydrogen ions by the scale formation processes allows the oxidation of metallic copper process. Therefore, temperature, pH, ionic content, and DO consumption are expected to show a complex dependency. Existing evidence has revealed only part of this interaction. During stagnation, DO concentration follows a first-order kinetic rate law (Eq. (1)) and the expression used to describe the DO consumption during stagnation follows an exponential form (Eq. (2)) [20,21]. An exponential model has showed good agreement to describe the DO consumption in old piping systems or under conditions of high levels of dissolved inorganic carbon (DIC) [17]. However, the exponential expression derived from experimental observations, has two limitations: (1) it is not clear whether diffusion controls the DO consumption based on bulk water measurements or if the exponential expression represents the processes at the solid-water interface; and (2) the rate of DO consumption used by this exponential model is represented by a constant (kox) that does not have a clear physical meaning and it has to be calibrated for each water. The objective of this paper is to address these limitations. We present an
empirical expression to calculate the rate of DO consumption that can be used for waters with different pHs, temperatures, DIC and chlorine concentrations. We expect that this will help to elucidate the mechanisms that control the kinetics of DO consumption and contribute to the construction of a mechanistic model for corrosion of copper that can be used under different conditions.
d½O2 ¼ kOX ½O2 dt
ð1Þ
½O2 ðtÞ ¼ ½O2 ð0Þ expft kOX g
ð2Þ
2. Materials and methods The experiments were conducted in copper pipes (1.95 cm internal diameter, type L, manufactured by MADECO-Chile under ASTMB88) filled with synthetic water prepared using MilliQ water, NaHCO3 (ACS grade, 99.7% pure, Merck KGaA, Darmstadt, Germany), and NaOCl (Reagent grade, available chlorine P4%, Sigma–Aldrich, St. Louis, MO.) to adjust chlorine concentration. The pH was adjusted to 6.5 with HNO3 (65%). Temperature was controlled during stagnation with a temperature control jacket. Fig. 2 shows the experimental set-up used to measure the DO concentration within the pipes under controlled temperature conditions. The pipes were preconditioned in three steps. Step 1: the pipes were filled with NaOH (0.1 M) to dissolve all oxides present on the inner surface of the pipe. Step 2: after two minutes with sodium hydroxide, the pipes were thoroughly rinsed three times with tap water to remove metallic copper particles. Step 3: the pipes were thoroughly rinsed three times with MiliQ water to clean the inner surface. Once the pipes were preconditioned, one end was closed with a rubber plug covered with laboratory plastic film to avoid the contact of water with the rubber. To determine the effect of transport by diffusion during stagnation, pipe experiments were conducted under stirred and non-stirred conditions. It was assumed that stirred conditions removed any diffusion limited transport. The mixed-stagnation was obtained introducing a small stirring bar inside the tested pipe during the stagnation time. Table 1 shows the specific conditions of the different stagnation conditions (i.e. pH, temperature, DIC, chlorine, stirred/non-stirred, and stagnation time) for the pipe tests made in this study.
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cence sensors consume no oxygen and can be reliably used in continuous measurements. The pH was determined by a Thermo Orion 420A pH meter with a ROSS Sure-flow Semi-Micro, epoxy body pH electrode (ORION, Model 8175). Chlorine was measured using the DPD method with a HACH DR/2010 portable spectrophotometer providing an analytical window of 0.02–2.00 mg/L that has been used in previous corrosion studies to determine chlorine [22,23]. Scanning electron microscopy (SEM) and energy dispersive Xray spectroscopy (EDX) were used to study the morphology and elemental composition of the corrosion by-products. Coupons of 0.5 0.5 cm were cut from the pipes for microscopic analysis. A LEO 1420VP scanning electron microscope coupled to an Oxford 7424 solid-state detector was used to obtain the micrographs and an estimation of the elemental composition. Additionally, grazing incidence X-ray diffraction (GI-XRD) was used to identify the nature of the scales. The corrosion by-products were identified by using a Bruker D8 Advance diffractometer with a 40 kV/30 mA copper cathode and a Sol-X detector. The experiments were performed continuously from 5° to 90° with a scan step size of 0.02°. 3. Results and discussion Our results are presented in four sections: (1) Surface analysis, (2) the effect of transport by diffusion, (3) the effect of pH and temperature, and (4) development of empirical model that includes the effect of these main parameters in the kinetic constant (kox) of DO consumption. Fig. 2. Experimental set-up used for the in situ dissolved oxygen measurements under controlled temperature conditions.
3.1. Surface analysis
During stagnation, the DO concentration was continuously measured every 15 min using a Luminescence Dissolved Oxygen (LDO) sensor connected to HQ40d multi meter (HACH Company, Loveland, CO). The LDO sensor was inserted at one end of the pipe (the opposite end was closed with a rubber stopper). The LDO sensor relies on the fluorescence quenching of rutenium complex trapped in a sol–gel matrix to measure the partial pressure of dissolved or gaseous oxygen. Unlike membrane electrodes, lumines-
SEM-EDX analysis of copper pipes tested with synthetic water of different DIC concentration (1.6, 7, and 14 mM of HCO3) suggests that copper carbonate hydroxide structures are formed over the metallic surface. SEM micrographs in Fig. 3 show the inner surface of new copper pipes after 24 h of stagnation in water with: 0 mM of HCO3 and 7 mM of HCO3. While Fig. 3a shows a compact and homogeneous film of corrosion by-products, Fig. 3b reveals formation of structures resembling ‘‘sea urchins” covering the inner surface of the pipe. The EDX analysis of these ‘‘sea urchin”
Table 1 Experimental conditions used for the dissolved oxygen consumption tests conducted with new copper pipes and synthetic water.
a
Test
pH
Temperature (°C)
DIC (mM.)
Chlorine (mM)
Stirring
Stagnation time (h)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
5.2 6.0 9.0 6.5 5.5 8.8 6.2 6.2 6.1 6.1 6.9 6.9 6.4 6.4 5.9 6 6.5 5.9 7.3 6.9 7.0 7.0 7.0
27.4 27.3 27.3 27.2 27.2 26.7 25.2 24 22.3 26 20 26.3 20 25.9 25.9 26 26.7 22–28a 25 25 25 25 25
14 14 14 14 14 14 0 0 19.2 19.2 14 14 7 7 3.5 1.6 0 3.5 1.6 1.6 1.6 1.6 1.6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.02 0.18 0.25 0.42
Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Stirred Non-stirred Stirred Non-stirred Stirred Non-stirred Stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred
50 50 50 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 8 8 8 8 8
Four hours alternate cycles at 22 and 28 °C.
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Fig. 3. Scanning electron microscopy (SEM) images and Grazing incidence X-ray Diffraction (GI-XRD) of new copper pipes in stagnant conditions for 24 h. (a) 0 mM of HCO3. (b) 7 mM of HCO3. Post test analysis of the pipe inner surface suggests that carbonate in water results on malachite precipitation. Malachite formation results on surface coverage and subsequently passivation.
structures reveals an elemental composition of copper, oxygen, and carbonate (Cu = 21%, O = 61%, and Cu = 18%). These structures have been previously addressed by Vargas et al. [17] and Merkel et al. [20] and were identified by XAS and XRD as malachite (Cu(OH)2CuCO3), a copper carbonate hydroxide with passivating properties. Although, speciation of copper carbonates include azurite (Cu3(CO3)2 (OH)2), carbonates of Cu(I) (Cu2CO3) and Cu(II) (CuCO3), and malachite. Malachite is the only copper carbonate by-product that has been detected in real systems. In addition, thermodynamic calculations indicates that malachite is the solid by-product that dominates the speciation of Cu(II) between pH 5 and 9 [2]. According with GI-XRD analysis of the inner surface of the pipe tested with 0 mM of HCO3, the homogeneous and compact film of oxides observed by SEM is a layer of cuprite (Cu2O) that is coating the metallic copper (Fig. 3a). Through thermodynamic and kinetic studies, Ives and Rawson [13,21,24,25] report that the metallic copper is covered with a two layer cuprite film. This ‘‘duplex film model” proposes a first layer of 2 lm thick compact layer of cuprite followed by a second layer of high porosity. These structural differences induce an increase in the electrical resistance at the interface between the two cuprite layers, decreasing electrons availability in the porous film and consequently, leading oxidation and the subsequent precipitation of divalent copper scales as tenorite (CuO), cupric hydroxide (Cu(OH)2), or malachite (Cu2(CO3)(OH)2) [2]. In effect, GI-XRD analysis of the the inner surface of the pipe tested with 7 mM of HCO3 shows that the surface is composed by cuprite, tenorite and mainly malachite (Fig. 3b). Thus, the results of both SEM-EDX and GI-XRD suggest that, in presence of carbonate, an initial formation of a layer of cuprite is covered
progressively by the development of malachite ‘‘sea urchins”. These malachite structures might have passivation properties against the oxidation of the metallic surface [17]. Finally, is important to notice that for a complete surface characterization of hydrated samples with short-range ordering solid phases (e.g. cupric hydroxide); XRD has limitations and techniques such as X-ray absorption spectroscopy are required [7].
3.2. Effect of transport by diffusion The results confirm that DO depletion observed in the in situ experiments made in new copper pipes, represents the consumption of oxygen by the cathodic half-reaction (first process) and the contribution of diffusion to the overall oxygen transport is negligible. Fig. 4 shows the results of stirred and non-stirred tests of DO depletion performed for 4 different DIC concentrations (0, 7, 14, 19.2 mM). In all cases no significant differences were detected during 24 h of stagnation for mixed and non mixed conditions. The average coefficient of correlation (R2) obtained was 0.96. Table 2 presents the coefficient of correlation between stirred and nonstirred conditions for each pipe test. Thus, our experimental evidence suggests that for pipes of 1.95 cm of diameter the contribution of transport of oxygen by diffusion is negligible and the depletion of DO observed during stagnation is due to chemical reactions associated to the process of metallic copper oxidation. This allows us, for these conditions, to establish a direct relationship between the bulk water measurements with the processes that occur at the metal-liquid interface, where the possibility to determine water parameters (i.e. DO, pH, temperature) without perturbing the sample is analytically complex.
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Fig. 4. Stirred vs. non-stirred DO measurements in new copper pipes under different stagnation conditions. Open circles (s) represent stirred experiments and plus signs (+) represent non-stirred experiments. (a) DIC = 0 mM, (b) DIC = 7 mM, (c) DIC = 14 mM, (d) DIC = 19.2 mM.
Table 2 Coefficients of correlation between stirred and non-stirred experiments conducted with new copper pipes during 24 h of stagnation.
2
R
DIC = 0 mM
DIC = 7 mM
DIC = 14 mM
DIC = 19.2 mM
0.97
0.99
0.99
0.90
and (2) the scale formation process that incorporates hydrogen ions into the system, which is thermodynamically associated with the temperature of water. In the next paragraphs we discuss the results obtained in experiments performed to find the relationship between pH and temperature with the rate of DO consumption. The amount of available hydrogen ions in solution limits the occurrence of the cathodic half-reaction and, in consequence, the rate of oxidation of metallic copper decreases. Thus, the limitation of hydrogen ions is expressed also by changes in the DO consumption rate. Fig. 5a shows the DO depletion curves obtained for three different pHs (5.2, 6.0, and 9.0). In all cases the initial DO concentration was close to 0.25 mM (8 mg/L) at 27.5 ± 0.4 °C. After 50 h of stagnation it was 0, 0.06, and 0.2 mM, respectively. The oxygen mass consumed in these experiments varied considerably. For pH 5.2 it was 100%, while for pH 6.0 it was 75.5%, and pH 9.0 it was 17.4%. This important difference in the DO consumption rate corresponds to the concept of ‘‘corrosive water” used to describe waters with low pH and low levels of calcium and alkalinity [26]. Indeed, for the metallic surface oxidation, non-corrosive water (pH 9.0) does not consume as much DO as corrosive water (pH 5.2). This characteristic is clearly exemplified by DO consumption curves. Moreover, our results indicate that the effect of pH in the rate of DO consumption (kox) has a linear relation with a R2 = 0.93 (Fig. 5b), thus we propose that the DO consumption rate is intimately linked with the hydrogen ions available in solution. Assuming that during stagnation our pipe system, presented in Fig. 2, behaves as a closed system, total carbonate concentration in water is controlled by the initial addition of NaHCO3 and speciation by the Eqs. (3), (4), under standard conditions [27].
H2 CO3 ! HCO3 þ Hþ þ HCO3 ! CO2 3 þH
3.3. Effects of pH and temperature Experiments in copper pipes presented in Fig. 4 provides evidence to propose that the DO consumption follows a first-order kinetic rate law and has to be modeled by an exponential expression. However, the rate of oxygen consumption in Eq. (2) does not include the key chemical characteristics of the water. Fig. 4 shows diverse rates for experiments made under different conditions. The differences on the rates are attributed to the thermodynamic limitations of the oxidation process. Indeed, kox represents the kinetics of the metallic copper oxidation process, where the limitation of hydrogen ions in solution plays a fundamental role. As it was mentioned in the introduction section, hydrogen ions availability is controlled by: (1) the initial amount of hydrogen ions present in solution (initial pH)
pKa1 ¼ 6:3
ð3Þ
pKa1 ¼ 10:3
ð4Þ
A pH lower than 6.3 favors the presence of [H2CO3] that continuously provides hydrogen ions to the water. This production of H+ assists the cathodic reaction and the subsequent DO consumption. Using electrochemical impedance spectroscopy in an open carbonate system Sobue et al. (2003) found that the rate of copper corrosion increases with the concentration of free carbon dioxide which continuously provides water with hydrogen ions, inducing DO reduction [28]. Thus, hydrogen ions availability controlled by carbonate speciation could explain differences on the rate of DO depletion observed in Fig. 5. According to this assumption, it is expected to observe larger changes in kox for pHs lower to 6.3 and practically no changes for pHs close to 10.3. Higher temperatures favors the formation of scales on the inner surface of the copper pipe, decreasing the amount of copper released into the water [19]. The solid corrosion by-products formed (i.e. mal-
Fig. 5. pH affects DO consumption rate. (a) Experimental data obtained though in situ measurements. (b) The rate of DO depletion is correlated with the amount of hydrogen ions in water (R2 = 0.93).
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Fig. 6. Temperature affects the rate of DO consumption. The figure shows experiments of DO depletion in a pipe with cycles of different temperature during stagnation. DO concentration (s), temperature (h). The values of kox are expressed in h1.
achite) might have passivating properties by limiting ion transport between the metallic surface and the water. However, an increase in the formation of scales is also linked to an increase of hydrogen ions released into the water close to the metal–liquid interface (Fig. 1), which favors the oxidation process, enhancing the DO consumption rates. Fig. 6 shows the effect of changes in temperature on the DO consumption rates. During 24 h of stagnation, the temperature was changed in 4 h cycles of hot water (28 ± 1 °C) and cold water (22 ± 1.5 °C). The DO consumption rate in hot water was greater compared to cold water, evidencing the relationship between temperature and the oxidation rate (R2 = 0.98). Indeed, Fig. 6 shows that slight differences in the average temperature of each cycle are reflected in differences in the value of kox.
3.4. Empirical model for dissolved oxygen depletion To solve the limitations of the expression used to represent the behavior of DO during stagnation (Eq. (2)), we propose an expression to calculate kox that includes the effect of pH and temperature on the DO consumption rate (Eq. (5)). This expression for calculating kox (h1) depends on the concentration of hydrogen ions (with [H+] in M), temperature (with T in K), and is controlled by three parameters: a, b, and c. Least square optimization of the experimental data to Eq. (5) yielded values of 278 (K), 9 104 (M1 K1 h1), and 6.25 104 (K1 h1) for parameters a, b, and c respectively. Fig. 7 shows the results obtained in experiments performed in copper pipes with waters with different pHs and temperatures during stagnation. The model described with good
agreement (R2 = 0.97) the DO consumption for experiments performed with pHs between 5 and 9. The sum of squares for the residual was calculated in 0.149. Moreover, the correction by temperature, expressed by a, reproduces the changes in the rate of DO consumption associated to changes in the temperature measured during stagnation. 1
kox ðh Þ ¼ ðT aÞðb½Hþ þ cÞ
ð5Þ
Even though our experiments were performed at temperatures between 20 and 28 °C, we expect the model to represent DO consumption rates for cold and hot water (temperatures between 15 and 40 °C). Temperatures in an interior wall of a house would be over 15–25 °C while hot water temperatures are commonly about 40 °C [19]. Additionally, to check the applicability of the empirical model, we made experiments for water with different DIC and chlorine concentrations. Our previous work [17] proposes that high concentrations of DIC might passivate de oxidation process though the formation of a homogeneous malachite film that covers the inner surface of the copper pipe limiting the transport of copper ions from the metallic surface to the water. Fig. 8a shows the results of experiments performed with new pipes and water with different DIC concentrations. Consistently, the DO consumption follows a first-order kinetic law for all cases where the water contains enough DIC to form malachite. For pH 6.3 and 26 °C (average experimental conditions), our empirical model represents the data obtained for water with presence of DIC. On the other hand, and in agreement with our previous work [17], data for water with absence of DIC and pH 6.5 follows a zero-order kinetic rate law.
Fig. 7. The empirical model proposed for DO consumption has a good agreement (R2 = 0.97) with the experimental data for values of pH between 5 and 9 during 10 h of stagnation.
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Fig. 8. The empirical model proposed for DO consumption is applicable to waters with different DIC and chlorine concentrations. The dashed line represents the model estimation for DO stagnation (average experimental conditions), (a) different DIC concentrations; (b) different chlorine concentrations.
Drinking water generally has a residual chlorine concentration between 0.2 and 2 mg/L of Cl2 from disinfection [29]. Although chlorine is an important oxidant agent responsible for the corrosion of copper competing with dissolved oxygen, our results do not provide evidence of a significant influence on the rate of DO consumption in the range of chlorine concentration found in typical tap water. Fig. 8b presents the results of experiments made with new pipes and water with different residual chlorine concentrations, DIC = 1.6 mM and pH about 7.2. Thus, the model presented can be used for waters with different concentrations of DIC and chlorine. 4. Conclusions Our results suggest that the corrosion processes of copper pipes dominate the consumption of DO within the pipe and the effect of transport by diffusion is negligible for pipes of 1.95 cm diameter. In consequence the DO consumed in the oxidation process could be modeled by an expression based on the DO depletion observed in the bulk water. The experimental results evidence the effect of pH and temperature on the kinetics of DO consumption within the pipe. Based on these results, a general expression for DO consumption was developed. The expression for DO consumption presented can be used to describe the DO depletion in waters with different pHs, temperatures, DIC, and chlorine concentrations without previous calibration. Our expression has a good agreement with the experimental data for values of pH between 5 and 9 during the first 10 h of stagnation. Although the analytical expression for the rate of DO consumption (kox) developed in this work is based on an empirical approach, it includes the main parameters that control the kinetics of metallic copper oxidation: pH and temperature. In addition, in situ estimations of atmospheric corrosion rates through non destructive methods, such as DO consumption measurements, have been used in recent archeological studies on copper, steel, and cast iron with very good results [30,31]. This is due to the fact that corrosion rates and oxygen depletion rates are stoiquiometrically linked through the redox couple reaction. Thus, using basic water chemistry parameters our model can predict the corrosion rate of metallic copper pipes found in typical household drinking water systems. Acknowledgements This research was funded by CONICYT Grant 24080013/2008 and FONDECYT project 1080578/2008. References [1] M.A. Shannon, P.W. Bohn, M. Elimelech, J.G. Georgiadis, B.J. Marinas, A.M. Mayes, Science and technology for water purification in the coming decades, Nature 452 (7185) (2008) 301–310.
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Contents lists available at ScienceDirect
Corrosion Science journal homepage: www.elsevier.com/locate/corsci
Empirical model for dissolved oxygen depletion during corrosion of drinking water copper pipes Ignacio T. Vargas, Pablo A. Pastén, Gonzalo E. Pizarro * Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad, Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul Santiago, Chile
a r t i c l e
i n f o
Article history: Received 23 September 2009 Accepted 11 March 2010 Available online 15 March 2010 Keywords: A. Copper B. SEM B. XRD
a b s t r a c t Predictive models characterizing the evolution and interaction of key parameters of water chemistry are needed to better understand corrosion events in drinking water pipes. We performed experiments with new copper pipes under combinations of pH, dissolved oxygen (DO), temperature, chlorine, and dissolved inorganic carbon. We found that DO consumption during 24 h of stagnation was not limited by diffusion, thus the DO consumption rate in the bulk water could be used to probe the processes occurring at the pipe surface. We propose a quantitative dependency of the DO consumption rate on a rather limited set of physicochemical parameters. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Ageing and deterioration of piping in drinking water systems and the colonization of microorganisms on the surface of pipes have emerged as a relevant infrastructure maintenance and rehabilitation challenge worldwide for the next decades [1]. Copper has been the plumbing material of choice in household drinking water systems [2] because it is relatively resistant to corrosion [3] and it can limit biofilm growth on the inner surface of the pipes [4]. However, under specific water chemistry and operation conditions serious corrosion events can occur resulting in structural damages and release of dissolved copper into the tap water [4– 7]. Although copper is essential to the human diet, ingestion of copper could induce acute and chronic health effects. While high doses of copper induce acute effects to the gastrointestinal tract, long-term overexposure results in copper accumulation and liver damage. [8,9]. Quantitative predictive models are a key tool for predicting exposure to copper and for improving our conceptual understanding of copper corrosion. To predict events of copper release it is necessary to develop models that describe the evolution and reveal the relation between the key physicochemical parameters of corrosion during stagnation, the period of time that precedes the flushing of the pipe every time the tap is opened. Empirical expressions to estimate rates of corrosion and dissolution of corrosion by-products have been used and derived in several recent corrosion studies. For example, to covert electrode potentials to standard hydrogen electrode (SHE), Huang et al. use an empirical
* Corresponding author. Tel.: +56 2 354 4872; fax: +56 2 354 5876. E-mail address: [email protected] (G.E. Pizarro). 0010-938X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.corsci.2010.03.009
expression dependent on temperature [10]. Recently, a study of the dissolution rate of lead corrosion by product PbO2 derived an hydrogen ions and carbonate dependent expression to estimate the dissolution rate of PbO2 [11]. Likewise, Montañés et al. developed an experimental expression to estimate the dependence of the galvanic corrosion rate by the Reynolds number in copper/AISI pipe systems [12]. Thus, the development of empirical expressions based on the corrosion processes emerges as an important step in the construction of mechanistic models. Current knowledge of corrosion of copper pipes divides the phenomenon in three processes: (1) oxidation of metallic copper; (2) scale formation; and (3) dissolution and transport of dissolved copper form the surface to the bulk water [2,7]. The availability of dissolved oxygen (DO) limits the oxidation of metallic copper in the first process. The oxidation of metallic copper is an electrochemical phenomenon that involves two half-reactions. The anodic half-reaction is responsible for the release of metal ions into the water from the metal surface, leaving free electrons to consume oxygen and hydrogen ions (H+) by the cathodic half-reaction [13] (Fig. 1). Thus, the concentration of hydrogen ions in the water also controls the metallic copper oxidation. For pH values lower than 6 and DO concentrations greater than 2 mg/L, the metal may dissolve to form Cu2+, which is the most stable form of dissolved copper under these conditions [14]. Dissolved copper concentrations ranging from 0.05 to 1 mg/L have been observed in recent large-scale pilot studies [15,16]. These levels are significantly lower than the estimated dissolved copper concentration considering the total mass of oxygen available for the oxidation process. A reason for this observation could be the limitation imposed by the amount of available hydrogen ions in water [17]. In consequence, the consumption rate of DO and the kinetic of
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Fig. 1. The phenomenon of corrosion of copper consists of three processes: oxidation of metallic copper, scale formation, and dissolution and transport. The DO is consumed by the first process and the scale formation process contributes with hydrogen ions that are the limiting factor for the oxidation of metallic copper.
metallic copper oxidation are controlled by two mechanisms: the availability of hydrogen ions for consumption by the cathodic half-reaction and the scale formation. The scale formation (second process) is dependent on pH, DO, temperature and the ionic matrix of the water. When pH is greater than 6, cupric ions precipitate forming scales [2,18]. Pehkonen et al. [6] reported that the stability, thickness, and mass transfer properties of a film of corrosion by-products depend on DO and not only on pH. Moreover, the scale formation process is driven by a temperature dependent thermodynamic equilibrium: high temperatures favor the precipitation of corrosion by-products, decreasing dissolved copper concentrations [19]. The scale formation reactions release hydrogen ions into the water that are consumed by the oxidation of metallic copper process and the DO consumption, thus releasing more copper ions into the water. Hence, the kinetic of DO consumption is controlled by pH and temperature dependent scale formation reactions. The scale dissolution and transport of dissolved copper (third process) links the processes that occur in the metal-liquid interface (first and second processes) with the bulk water composition determining the events of high copper concentration in tap waters. Fig. 1 presents a conceptual model that includes the relationships between the three processes of corrosion of copper pipes and the copper released. The contribution of hydrogen ions by the scale formation processes allows the oxidation of metallic copper process. Therefore, temperature, pH, ionic content, and DO consumption are expected to show a complex dependency. Existing evidence has revealed only part of this interaction. During stagnation, DO concentration follows a first-order kinetic rate law (Eq. (1)) and the expression used to describe the DO consumption during stagnation follows an exponential form (Eq. (2)) [20,21]. An exponential model has showed good agreement to describe the DO consumption in old piping systems or under conditions of high levels of dissolved inorganic carbon (DIC) [17]. However, the exponential expression derived from experimental observations, has two limitations: (1) it is not clear whether diffusion controls the DO consumption based on bulk water measurements or if the exponential expression represents the processes at the solid-water interface; and (2) the rate of DO consumption used by this exponential model is represented by a constant (kox) that does not have a clear physical meaning and it has to be calibrated for each water. The objective of this paper is to address these limitations. We present an
empirical expression to calculate the rate of DO consumption that can be used for waters with different pHs, temperatures, DIC and chlorine concentrations. We expect that this will help to elucidate the mechanisms that control the kinetics of DO consumption and contribute to the construction of a mechanistic model for corrosion of copper that can be used under different conditions.
d½O2 ¼ kOX ½O2 dt
ð1Þ
½O2 ðtÞ ¼ ½O2 ð0Þ expft kOX g
ð2Þ
2. Materials and methods The experiments were conducted in copper pipes (1.95 cm internal diameter, type L, manufactured by MADECO-Chile under ASTMB88) filled with synthetic water prepared using MilliQ water, NaHCO3 (ACS grade, 99.7% pure, Merck KGaA, Darmstadt, Germany), and NaOCl (Reagent grade, available chlorine P4%, Sigma–Aldrich, St. Louis, MO.) to adjust chlorine concentration. The pH was adjusted to 6.5 with HNO3 (65%). Temperature was controlled during stagnation with a temperature control jacket. Fig. 2 shows the experimental set-up used to measure the DO concentration within the pipes under controlled temperature conditions. The pipes were preconditioned in three steps. Step 1: the pipes were filled with NaOH (0.1 M) to dissolve all oxides present on the inner surface of the pipe. Step 2: after two minutes with sodium hydroxide, the pipes were thoroughly rinsed three times with tap water to remove metallic copper particles. Step 3: the pipes were thoroughly rinsed three times with MiliQ water to clean the inner surface. Once the pipes were preconditioned, one end was closed with a rubber plug covered with laboratory plastic film to avoid the contact of water with the rubber. To determine the effect of transport by diffusion during stagnation, pipe experiments were conducted under stirred and non-stirred conditions. It was assumed that stirred conditions removed any diffusion limited transport. The mixed-stagnation was obtained introducing a small stirring bar inside the tested pipe during the stagnation time. Table 1 shows the specific conditions of the different stagnation conditions (i.e. pH, temperature, DIC, chlorine, stirred/non-stirred, and stagnation time) for the pipe tests made in this study.
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cence sensors consume no oxygen and can be reliably used in continuous measurements. The pH was determined by a Thermo Orion 420A pH meter with a ROSS Sure-flow Semi-Micro, epoxy body pH electrode (ORION, Model 8175). Chlorine was measured using the DPD method with a HACH DR/2010 portable spectrophotometer providing an analytical window of 0.02–2.00 mg/L that has been used in previous corrosion studies to determine chlorine [22,23]. Scanning electron microscopy (SEM) and energy dispersive Xray spectroscopy (EDX) were used to study the morphology and elemental composition of the corrosion by-products. Coupons of 0.5 0.5 cm were cut from the pipes for microscopic analysis. A LEO 1420VP scanning electron microscope coupled to an Oxford 7424 solid-state detector was used to obtain the micrographs and an estimation of the elemental composition. Additionally, grazing incidence X-ray diffraction (GI-XRD) was used to identify the nature of the scales. The corrosion by-products were identified by using a Bruker D8 Advance diffractometer with a 40 kV/30 mA copper cathode and a Sol-X detector. The experiments were performed continuously from 5° to 90° with a scan step size of 0.02°. 3. Results and discussion Our results are presented in four sections: (1) Surface analysis, (2) the effect of transport by diffusion, (3) the effect of pH and temperature, and (4) development of empirical model that includes the effect of these main parameters in the kinetic constant (kox) of DO consumption. Fig. 2. Experimental set-up used for the in situ dissolved oxygen measurements under controlled temperature conditions.
3.1. Surface analysis
During stagnation, the DO concentration was continuously measured every 15 min using a Luminescence Dissolved Oxygen (LDO) sensor connected to HQ40d multi meter (HACH Company, Loveland, CO). The LDO sensor was inserted at one end of the pipe (the opposite end was closed with a rubber stopper). The LDO sensor relies on the fluorescence quenching of rutenium complex trapped in a sol–gel matrix to measure the partial pressure of dissolved or gaseous oxygen. Unlike membrane electrodes, lumines-
SEM-EDX analysis of copper pipes tested with synthetic water of different DIC concentration (1.6, 7, and 14 mM of HCO3) suggests that copper carbonate hydroxide structures are formed over the metallic surface. SEM micrographs in Fig. 3 show the inner surface of new copper pipes after 24 h of stagnation in water with: 0 mM of HCO3 and 7 mM of HCO3. While Fig. 3a shows a compact and homogeneous film of corrosion by-products, Fig. 3b reveals formation of structures resembling ‘‘sea urchins” covering the inner surface of the pipe. The EDX analysis of these ‘‘sea urchin”
Table 1 Experimental conditions used for the dissolved oxygen consumption tests conducted with new copper pipes and synthetic water.
a
Test
pH
Temperature (°C)
DIC (mM.)
Chlorine (mM)
Stirring
Stagnation time (h)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
5.2 6.0 9.0 6.5 5.5 8.8 6.2 6.2 6.1 6.1 6.9 6.9 6.4 6.4 5.9 6 6.5 5.9 7.3 6.9 7.0 7.0 7.0
27.4 27.3 27.3 27.2 27.2 26.7 25.2 24 22.3 26 20 26.3 20 25.9 25.9 26 26.7 22–28a 25 25 25 25 25
14 14 14 14 14 14 0 0 19.2 19.2 14 14 7 7 3.5 1.6 0 3.5 1.6 1.6 1.6 1.6 1.6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.02 0.18 0.25 0.42
Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Stirred Non-stirred Stirred Non-stirred Stirred Non-stirred Stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred Non-stirred
50 50 50 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 8 8 8 8 8
Four hours alternate cycles at 22 and 28 °C.
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Fig. 3. Scanning electron microscopy (SEM) images and Grazing incidence X-ray Diffraction (GI-XRD) of new copper pipes in stagnant conditions for 24 h. (a) 0 mM of HCO3. (b) 7 mM of HCO3. Post test analysis of the pipe inner surface suggests that carbonate in water results on malachite precipitation. Malachite formation results on surface coverage and subsequently passivation.
structures reveals an elemental composition of copper, oxygen, and carbonate (Cu = 21%, O = 61%, and Cu = 18%). These structures have been previously addressed by Vargas et al. [17] and Merkel et al. [20] and were identified by XAS and XRD as malachite (Cu(OH)2CuCO3), a copper carbonate hydroxide with passivating properties. Although, speciation of copper carbonates include azurite (Cu3(CO3)2 (OH)2), carbonates of Cu(I) (Cu2CO3) and Cu(II) (CuCO3), and malachite. Malachite is the only copper carbonate by-product that has been detected in real systems. In addition, thermodynamic calculations indicates that malachite is the solid by-product that dominates the speciation of Cu(II) between pH 5 and 9 [2]. According with GI-XRD analysis of the inner surface of the pipe tested with 0 mM of HCO3, the homogeneous and compact film of oxides observed by SEM is a layer of cuprite (Cu2O) that is coating the metallic copper (Fig. 3a). Through thermodynamic and kinetic studies, Ives and Rawson [13,21,24,25] report that the metallic copper is covered with a two layer cuprite film. This ‘‘duplex film model” proposes a first layer of 2 lm thick compact layer of cuprite followed by a second layer of high porosity. These structural differences induce an increase in the electrical resistance at the interface between the two cuprite layers, decreasing electrons availability in the porous film and consequently, leading oxidation and the subsequent precipitation of divalent copper scales as tenorite (CuO), cupric hydroxide (Cu(OH)2), or malachite (Cu2(CO3)(OH)2) [2]. In effect, GI-XRD analysis of the the inner surface of the pipe tested with 7 mM of HCO3 shows that the surface is composed by cuprite, tenorite and mainly malachite (Fig. 3b). Thus, the results of both SEM-EDX and GI-XRD suggest that, in presence of carbonate, an initial formation of a layer of cuprite is covered
progressively by the development of malachite ‘‘sea urchins”. These malachite structures might have passivation properties against the oxidation of the metallic surface [17]. Finally, is important to notice that for a complete surface characterization of hydrated samples with short-range ordering solid phases (e.g. cupric hydroxide); XRD has limitations and techniques such as X-ray absorption spectroscopy are required [7].
3.2. Effect of transport by diffusion The results confirm that DO depletion observed in the in situ experiments made in new copper pipes, represents the consumption of oxygen by the cathodic half-reaction (first process) and the contribution of diffusion to the overall oxygen transport is negligible. Fig. 4 shows the results of stirred and non-stirred tests of DO depletion performed for 4 different DIC concentrations (0, 7, 14, 19.2 mM). In all cases no significant differences were detected during 24 h of stagnation for mixed and non mixed conditions. The average coefficient of correlation (R2) obtained was 0.96. Table 2 presents the coefficient of correlation between stirred and nonstirred conditions for each pipe test. Thus, our experimental evidence suggests that for pipes of 1.95 cm of diameter the contribution of transport of oxygen by diffusion is negligible and the depletion of DO observed during stagnation is due to chemical reactions associated to the process of metallic copper oxidation. This allows us, for these conditions, to establish a direct relationship between the bulk water measurements with the processes that occur at the metal-liquid interface, where the possibility to determine water parameters (i.e. DO, pH, temperature) without perturbing the sample is analytically complex.
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Fig. 4. Stirred vs. non-stirred DO measurements in new copper pipes under different stagnation conditions. Open circles (s) represent stirred experiments and plus signs (+) represent non-stirred experiments. (a) DIC = 0 mM, (b) DIC = 7 mM, (c) DIC = 14 mM, (d) DIC = 19.2 mM.
Table 2 Coefficients of correlation between stirred and non-stirred experiments conducted with new copper pipes during 24 h of stagnation.
2
R
DIC = 0 mM
DIC = 7 mM
DIC = 14 mM
DIC = 19.2 mM
0.97
0.99
0.99
0.90
and (2) the scale formation process that incorporates hydrogen ions into the system, which is thermodynamically associated with the temperature of water. In the next paragraphs we discuss the results obtained in experiments performed to find the relationship between pH and temperature with the rate of DO consumption. The amount of available hydrogen ions in solution limits the occurrence of the cathodic half-reaction and, in consequence, the rate of oxidation of metallic copper decreases. Thus, the limitation of hydrogen ions is expressed also by changes in the DO consumption rate. Fig. 5a shows the DO depletion curves obtained for three different pHs (5.2, 6.0, and 9.0). In all cases the initial DO concentration was close to 0.25 mM (8 mg/L) at 27.5 ± 0.4 °C. After 50 h of stagnation it was 0, 0.06, and 0.2 mM, respectively. The oxygen mass consumed in these experiments varied considerably. For pH 5.2 it was 100%, while for pH 6.0 it was 75.5%, and pH 9.0 it was 17.4%. This important difference in the DO consumption rate corresponds to the concept of ‘‘corrosive water” used to describe waters with low pH and low levels of calcium and alkalinity [26]. Indeed, for the metallic surface oxidation, non-corrosive water (pH 9.0) does not consume as much DO as corrosive water (pH 5.2). This characteristic is clearly exemplified by DO consumption curves. Moreover, our results indicate that the effect of pH in the rate of DO consumption (kox) has a linear relation with a R2 = 0.93 (Fig. 5b), thus we propose that the DO consumption rate is intimately linked with the hydrogen ions available in solution. Assuming that during stagnation our pipe system, presented in Fig. 2, behaves as a closed system, total carbonate concentration in water is controlled by the initial addition of NaHCO3 and speciation by the Eqs. (3), (4), under standard conditions [27].
H2 CO3 ! HCO3 þ Hþ þ HCO3 ! CO2 3 þH
3.3. Effects of pH and temperature Experiments in copper pipes presented in Fig. 4 provides evidence to propose that the DO consumption follows a first-order kinetic rate law and has to be modeled by an exponential expression. However, the rate of oxygen consumption in Eq. (2) does not include the key chemical characteristics of the water. Fig. 4 shows diverse rates for experiments made under different conditions. The differences on the rates are attributed to the thermodynamic limitations of the oxidation process. Indeed, kox represents the kinetics of the metallic copper oxidation process, where the limitation of hydrogen ions in solution plays a fundamental role. As it was mentioned in the introduction section, hydrogen ions availability is controlled by: (1) the initial amount of hydrogen ions present in solution (initial pH)
pKa1 ¼ 6:3
ð3Þ
pKa1 ¼ 10:3
ð4Þ
A pH lower than 6.3 favors the presence of [H2CO3] that continuously provides hydrogen ions to the water. This production of H+ assists the cathodic reaction and the subsequent DO consumption. Using electrochemical impedance spectroscopy in an open carbonate system Sobue et al. (2003) found that the rate of copper corrosion increases with the concentration of free carbon dioxide which continuously provides water with hydrogen ions, inducing DO reduction [28]. Thus, hydrogen ions availability controlled by carbonate speciation could explain differences on the rate of DO depletion observed in Fig. 5. According to this assumption, it is expected to observe larger changes in kox for pHs lower to 6.3 and practically no changes for pHs close to 10.3. Higher temperatures favors the formation of scales on the inner surface of the copper pipe, decreasing the amount of copper released into the water [19]. The solid corrosion by-products formed (i.e. mal-
Fig. 5. pH affects DO consumption rate. (a) Experimental data obtained though in situ measurements. (b) The rate of DO depletion is correlated with the amount of hydrogen ions in water (R2 = 0.93).
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Fig. 6. Temperature affects the rate of DO consumption. The figure shows experiments of DO depletion in a pipe with cycles of different temperature during stagnation. DO concentration (s), temperature (h). The values of kox are expressed in h1.
achite) might have passivating properties by limiting ion transport between the metallic surface and the water. However, an increase in the formation of scales is also linked to an increase of hydrogen ions released into the water close to the metal–liquid interface (Fig. 1), which favors the oxidation process, enhancing the DO consumption rates. Fig. 6 shows the effect of changes in temperature on the DO consumption rates. During 24 h of stagnation, the temperature was changed in 4 h cycles of hot water (28 ± 1 °C) and cold water (22 ± 1.5 °C). The DO consumption rate in hot water was greater compared to cold water, evidencing the relationship between temperature and the oxidation rate (R2 = 0.98). Indeed, Fig. 6 shows that slight differences in the average temperature of each cycle are reflected in differences in the value of kox.
3.4. Empirical model for dissolved oxygen depletion To solve the limitations of the expression used to represent the behavior of DO during stagnation (Eq. (2)), we propose an expression to calculate kox that includes the effect of pH and temperature on the DO consumption rate (Eq. (5)). This expression for calculating kox (h1) depends on the concentration of hydrogen ions (with [H+] in M), temperature (with T in K), and is controlled by three parameters: a, b, and c. Least square optimization of the experimental data to Eq. (5) yielded values of 278 (K), 9 104 (M1 K1 h1), and 6.25 104 (K1 h1) for parameters a, b, and c respectively. Fig. 7 shows the results obtained in experiments performed in copper pipes with waters with different pHs and temperatures during stagnation. The model described with good
agreement (R2 = 0.97) the DO consumption for experiments performed with pHs between 5 and 9. The sum of squares for the residual was calculated in 0.149. Moreover, the correction by temperature, expressed by a, reproduces the changes in the rate of DO consumption associated to changes in the temperature measured during stagnation. 1
kox ðh Þ ¼ ðT aÞðb½Hþ þ cÞ
ð5Þ
Even though our experiments were performed at temperatures between 20 and 28 °C, we expect the model to represent DO consumption rates for cold and hot water (temperatures between 15 and 40 °C). Temperatures in an interior wall of a house would be over 15–25 °C while hot water temperatures are commonly about 40 °C [19]. Additionally, to check the applicability of the empirical model, we made experiments for water with different DIC and chlorine concentrations. Our previous work [17] proposes that high concentrations of DIC might passivate de oxidation process though the formation of a homogeneous malachite film that covers the inner surface of the copper pipe limiting the transport of copper ions from the metallic surface to the water. Fig. 8a shows the results of experiments performed with new pipes and water with different DIC concentrations. Consistently, the DO consumption follows a first-order kinetic law for all cases where the water contains enough DIC to form malachite. For pH 6.3 and 26 °C (average experimental conditions), our empirical model represents the data obtained for water with presence of DIC. On the other hand, and in agreement with our previous work [17], data for water with absence of DIC and pH 6.5 follows a zero-order kinetic rate law.
Fig. 7. The empirical model proposed for DO consumption has a good agreement (R2 = 0.97) with the experimental data for values of pH between 5 and 9 during 10 h of stagnation.
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Fig. 8. The empirical model proposed for DO consumption is applicable to waters with different DIC and chlorine concentrations. The dashed line represents the model estimation for DO stagnation (average experimental conditions), (a) different DIC concentrations; (b) different chlorine concentrations.
Drinking water generally has a residual chlorine concentration between 0.2 and 2 mg/L of Cl2 from disinfection [29]. Although chlorine is an important oxidant agent responsible for the corrosion of copper competing with dissolved oxygen, our results do not provide evidence of a significant influence on the rate of DO consumption in the range of chlorine concentration found in typical tap water. Fig. 8b presents the results of experiments made with new pipes and water with different residual chlorine concentrations, DIC = 1.6 mM and pH about 7.2. Thus, the model presented can be used for waters with different concentrations of DIC and chlorine. 4. Conclusions Our results suggest that the corrosion processes of copper pipes dominate the consumption of DO within the pipe and the effect of transport by diffusion is negligible for pipes of 1.95 cm diameter. In consequence the DO consumed in the oxidation process could be modeled by an expression based on the DO depletion observed in the bulk water. The experimental results evidence the effect of pH and temperature on the kinetics of DO consumption within the pipe. Based on these results, a general expression for DO consumption was developed. The expression for DO consumption presented can be used to describe the DO depletion in waters with different pHs, temperatures, DIC, and chlorine concentrations without previous calibration. Our expression has a good agreement with the experimental data for values of pH between 5 and 9 during the first 10 h of stagnation. Although the analytical expression for the rate of DO consumption (kox) developed in this work is based on an empirical approach, it includes the main parameters that control the kinetics of metallic copper oxidation: pH and temperature. In addition, in situ estimations of atmospheric corrosion rates through non destructive methods, such as DO consumption measurements, have been used in recent archeological studies on copper, steel, and cast iron with very good results [30,31]. This is due to the fact that corrosion rates and oxygen depletion rates are stoiquiometrically linked through the redox couple reaction. Thus, using basic water chemistry parameters our model can predict the corrosion rate of metallic copper pipes found in typical household drinking water systems. Acknowledgements This research was funded by CONICYT Grant 24080013/2008 and FONDECYT project 1080578/2008. References [1] M.A. Shannon, P.W. Bohn, M. Elimelech, J.G. Georgiadis, B.J. Marinas, A.M. Mayes, Science and technology for water purification in the coming decades, Nature 452 (7185) (2008) 301–310.
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