Determination of Chemical Species Dominating the Corrosivity of Japanese Tap Water by Multiple Regression Analysis

Abstract

Japanese tap water is Ca²⁺-poor and SiO₂-rich in comparison with that of other counties. Thus, there have been few studies on its corrosivity. We sampled tap waters at 70 different sites and in different seasons in Japan, subjected the samples to chemical analysis and measured localized corrosion depth and the total corrosion loss of carbon steel placed in these waters. The average corrosion rate v_avg and maximum localized corrosion rate v_max were calculated. The ratio of v_max to v_avg, which was defined as localized corrosion factor LCF (=v_max/v_avg), was also studied. The multiple regression method was applied to obtain the dependence of v_avg (objective variable) on concentrations of chemical species (explanatory variables). In the same manner, the relation of v_max and LCF to concentrations of chemical species was derived. As a result, we showed that SiO₂ and SO₄²⁻ mainly dominate the corrosivity of Japanese tap water. In particular, as SO₄²⁻ increased, v_avg became larger and v_max became smaller. Also, as SiO₂ increased, v_max became larger and v_avg became smaller. The behavior of LCF was similar to that of v_max. The findings of this study will be useful for estimating the corrosivity of tap waters that have low Ca²⁺ and high SiO₂ concentrations.

1. Introduction

There are many steep mountains and volcanoes in Japan. Volcanoes are the cause of the high concentration of SiO₂ in river water. Meanwhile, the steep mountains result in fast-flowing rivers, and since CaCO₃ dissolves slowly into water, the concentration of Ca²⁺ is low, causing the tap water to be soft. Hori et al. [1] studied the hardness of tap waters in Japan and compared the results with those of European countries. They reported that total hardness at 16 places in France was 178 ± 68 mg/L as CaCO₃, at 11 places in Germany was 187 ± 71 mg/L as CaCO₃ and at 665 places in Japan was 48.9 ± 25.8 mg/L as CaCO₃. A more detailed study of tap water in European countries was conducted by Banks et al. [2,3], who showed that the average calcium hardness of 579 tap waters sampled in European countries was 60.1 mg/L (=149.9 mg/L as CaCO₃). Almost no report of calcium hardness in the US could be found; however, there have been some studies that investigated the hardness of river water in the US. Brigges et al. found that the mean hardness of river water at 344 sites was 223 mg/L as CaCO₃ [4]. In general, tap water is produced by treating river water, so it is reasonable to assume that tap water inherits the properties of river water, which explains why tap water in the US has high calcium hardness. On the contrary, Japanese tap water has low calcium hardness compared to that in European countries and America [1,2,3,4,5].

The relationship between corrosion rates and components in tap water has often been studied in laboratory settings. It is considered that Cl⁻ and SO₄²⁻ are corrosive and that HCO₃⁻ inhibits corrosion [6,7,8,9,10,11,12,13]. The effects of Cl⁻ and SO₄²⁻ in the concentration range of fresh water were reported by Takasaki et al. [10] and Agata et al. [12]. They found that when the concentrations of Cl⁻ and SO₄²⁻ are high enough, the corrosion rate almost becomes constant, while the rate increases when their concentrations are low [10,11]. In another similar study, Fujii et al. [13] added sodium chloride and sodium sulfate to tap water and found that the corrosivity did not change when the sum of Cl⁻ and SO₄²⁻ concentrations was above 20 mg/L.

Conventionally, the corrosivity of tap water is evaluated by corrosion indexes such as the Langelier Index (LI) [14,15], Ryzner Stability Index (RSI) [16] and Larson–Skold Index (LSI) [6,14,15,16,17,18]. However, according to the authors’ experience, these indexes do not always reflect actual corrosivity, particularly for Japanese tap water [19]. Nakamura et al. show that there is not always much of a relationship between the LI and RSI of Japanese tap water, average corrosion and localized corrosion of carbon steel [19]. We assume that this is due to the fact that conventional corrosion indexes were obtained on the basis of corrosion tests performed with tap water of high calcium hardness.

Recently, corrosion studies have frequently used multivariate analysis for multiple regression [20,21]. Sobue et al. [20] applied multiple regression analysis to the relationship between chemical components and electrochemical impedance to determine the factors that significantly affect copper corrosion in tap water and found that free carbon dioxide (CO₂ aq) was the most accelerating corrosion factor. So et al. [21] used regression analysis to study corrosion factors in district heating water and presented a regression formula for predicting the corrosion depth as a function of pH, concentration of dissolved oxygen and time. Their study showed that multiple regression analysis can be applied to corrosion studies to determine the components in aqueous solutions that dominate corrosion [21].

In the present study, water quality measurements and corrosion tests for carbon steel were performed for 70 different tap waters in Japan sampled at different locations and in different months. The sources of the sampled tap water were ground water, surface water or their mixture. Moreover, multiple regression analysis for clarifying the relationship between chemical species and corrosion rates was conducted to determine the chemical species in tap water that dominate corrosivity.

2. Materials and Methods

2.1. Materials

Carbon steel ASTM A283 (JFE Steel Corporation, Tokyo, Japan) 50 mm × 25 mm × 3 mm polished with P400 [22] was used for the test specimens. The chemical composition of the specimens is shown in

Table 1. Chemical composition of test piece (carbon steel, SS400).

Element	Fe	C	Si	Mn	P	S
Content [wt%]	99.3	0.08	0.03	0.37	0.08	0.14

. The specimens were degreased with ethanol and acetone and covered with chemical-resistant adhesive tape except for the exposed areas. The boundary between the metal and the adhesive tape was painted with enamel resin. The exposed metal area was 4 cm² (2 cm × 2 cm). A schematic drawing of a test specimen is illustrated in Figure 1.

2.2. Sampling and Measurement of Tap Waters Used for Corrosion Tests

Seventy different Japanese tap waters were sampled and their pH, electrical conductivity, HCO₃⁻, Ca²⁺, Mg²⁺, Cl⁻, SO₄²⁻, NO₃⁻ and SiO₂ were measured. The pH was measured with a glass electrode. The electrical conductivity was measured by the method of two platinum electrodes whose surfaces were covered with platinum black. The concentration of HCO₃⁻ was determined from the value of M-alkalinity, which was determined by titration of bromocresol green–methyl red ethanol solution and sulfuric acid. The concentrations of Ca²⁺, Mg²⁺, Cl⁻, SO₄²⁻ and NO₃⁻ were quantitatively determined by ion chromatography. The concentration of SiO₂ was quantitatively analyzed by molybdenum yellow absorptiometry. Since Japanese tap water is treated with hypochlorous acid (0.1~1 mg/L) [23], the number of bacteria was not measured. Therefore, microbial corrosion was not taken into account. The corrosivity of these tap waters for carbon steel was evaluated by corrosion tests as follows.

2.3. Method of Immersion Test

The corrosivity of the sampled tap waters was evaluated by immersion tests. The testing time in this study was set according to common standards. The corrosion testing guidelines (i.e., ASTM G31-72 [24], Standard Practice for Laboratory Immersion Corrosion Testing of Metals and NACE Standard TM-01-69 [25], Test Method—Laboratory Corrosion Testing of Metals for the Process Industries) recommend that test periods (time, t (hours)) are longer than the following Equation (1):

t = 50/v

(1)

where v is conventional corrosion rate (mm y⁻¹) in test solutions. It is known that the corrosion rate of carbon steel immersed in neutral solutions (pH between 4 and 10) is about 0.1 mm y⁻¹ [26]. Therefore, at least 500 h is required for corrosion tests. For this reason, the specimens were immersed in 500 mL of the test solution for approximately 720 h. The experimental apparatus is shown in Figure 2. The temperature of the test solution was set at 25 °C. The solution was stirred at 300 rpm using a stirring bar controlled with a magnetic stirrer in the open-to-air state. Three specimens were placed in a vessel. The ratio of solution volume to specimen area was approximately 40 mL/cm². The corrosion test guidelines mentioned above require a solution volume to specimen area greater than 20 mL/cm². The ratio in this study meets this criterion. At the time of sampling and during the corrosion test, dissolved oxygen was not measured, since it was considered that the oxygen in the solution was in the saturated state by air because of its continuous stirring.

2.4. Measurement of Corrosion

The corrosion products that formed on a test piece were removed with 7% hydrochloric acid containing 0.5% corrosion inhibitor for acid cleaning (Asahi Chemical Co., Ltd., Osaka, Japan, IBIT^® No. 2AS, Aqueous solution containing quaternary ammonium salts, nonionic surfactants, isopropyl alcohol, and benzyl trimethylammonium chloride). The average weight loss of the three specimens divided by the testing time was defined as v_avg. The localized corrosion depths were measured with a depth gauge (Mitsutoyo, Kanagawa, Japan, point micrometer). The depths of the five most significantly corroded areas were measured. The maximum value among them divided by the testing time was defined as v_max. In addition, the ratio of v_avg to v_max was calculated and defined as the localized corrosion factor (LCF). The above procedures are shown schematically in Figure 3.

2.5. Multiple Regression Analysis

The corrosive effect of the chemical species was evaluated on the basis of the actual corrosion rates and qualities of tested waters by multiple regression analysis [27]. The regression equation obtained from multiple regression analysis is given by

y = α + β1x1 + β2x2 + … + βpxp + ε

(2)

where y is the objective variable, corrosivity; p is the number of independent variables; α is the regression constant; β is the regression coefficient for xp; xp is the explanatory variable, the concentrations of various chemical species; and ε is random error [27].

In this study, several models with different numbers of explanatory variables were tested and the coefficient of determination (R2) with standard error (SE) of each model was compared. Based on the value of the regression variable x, the impact of that component on the corrosion rate was evaluated. Units of water constituents are given in mol/L and are normalized to a maximum value of 1. This means that the higher the regression coefficient x, the larger the impact on corrosion. The model for the regression analysis was tested for eight water species, H⁺, Ca²⁺, Mg²⁺, HCO₃⁻, Cl⁻, SO₄²⁻, NO₂⁻ and SiO₂ for the regression constant β, with the value of β reduced in steps until all variance expansion factors (VIFs) were less than 2 [28]. VIF calculations and multiple regression analysis were performed using Microsoft Excel (ver.2311, Microsoft Corporation, Redmond, WA, USA).

3. Results

3.1. Quality of Japanese Tap Waters

Histograms of the quality of Japanese tap waters and those of average value, maximum value and minimum value are shown in Figure 4 and

Table 2. Water quality of 70 different tap waters in Japan.

Species	Unit	Average	Maximum	Minimum
pH (25 °C)	-	7.46	8.1	7.0
Conductivity	mS/m	15.3	43.9	5.7
HCO3−	mg/L	43.6	106.1	13.4
	mmol/L	0.714	1.740	0.220
Ca2+	mg/L	13.0	28.4	3.6
	mmol/L	0.324	0.709	0.090
Mg2+	mg/L	3.1	17.2	0.7
	mmol/L	0.129	0.709	0.030
Cl−	mg/L	13.9	62	2
	mmol/L	0.391	1.749	0.056
SO42−	mg/L	14.9	41.4	1.3
	mmol/L	0.155	0.431	0.014
NO3−	mg/L	3.1	18	0.1
	mmol/L	0.050	0.290	0.002
SiO2	mg/L	17.1	59	2
	mmol/L	0.284	0.982	0.033

. The concentrations of components in Japanese tap water are widely distributed. Focusing on the concentrations of Ca²⁺ and SiO₂, the tap waters collected in this study had Ca²⁺ values in the range of 3.6–28.4 mg/L and SiO₂ in the range of 5–59 mg/L. In addition, the conductivity was distributed in the range of 5.7–43.9 mS/m. These results reflect the fact that there are many steep mountains and volcanoes in Japan, which typically lead to short rivers with water rich in SiO₂ but low in calcium compounds due to the high flow rate and low dissolution rate of CaCO₃ into water. As a result, Japanese tap waters are soft with lower levels of dissolved minerals than those in other countries. The solutions used in these corrosion tests reflect the characteristics of Japanese tap water [1]. Figure 5 shows the correlations among chemical species in tap water. In multiple regression analysis, it is desirable to reduce the correlations between the explanatory variables. Therefore, in the analysis, a few models with smaller VIFs were created by referring to Figure 5, which represents the strength of the correlations.

3.2. Corrosivity of Japanese Tap Waters

Carbon steel specimens corroded in all 70 Japanese tap waters. The corrosion situation of some of the specimens was as shown in Figure 6. Corrosion was observed under the corrosion products, and the corrosion situation was different. Case 1 and Case 2 corroded almost uniformly; in contrast, uniform corrosion and localized corrosion pits were observed in Case 3. This result means that the corrosion situation of carbon steel depends on the water quality. The average corrosion rate v_avg, localized corrosion rate v_max and localized corrosion factor LCF obtained from corrosion tests are shown in Figure 7. The highest value of v_avg is 0.541 mm y⁻¹, the lowest is 0.105 mm y⁻¹, the mean is 0.302 mm y⁻¹ and the mode is 0.28 to 0.32 mmy⁻¹. The highest value of v_max is 4.16 mm y⁻¹, the lowest is 0.58 mm y⁻¹, the mean is 1.92 mm y⁻¹ and the mode is 0.5 to 1.0 mm y⁻¹. The highest value of LCF is 20.6, the lowest is 1.68, the mean is 7.08 and the mode is 2 to 4. Most notable among these results is the presence of tap water, which causes localized corrosion that progresses at a rate 20.6 times faster than average corrosion. These results show that corrosion rates are sensitive to the effects of water quality. Focusing on the shape of the distribution, v_avg was normally distributed. In contrast, the shape of v_max and LCF were skew distributed. The results indicate that most tap waters in Japan have low localized corrosivity, although a few have significantly high localized corrosivity.

3.3. Relationships between Water Quality and Corrosivity

The correlation coefficients (R) between v_avg, v_max and LCF for each chemical species in the tested waters are shown in

Table 3. Correlation coefficient (R) of corrosivity with chemical components in 70 different tap waters in Japan.

Corrosivity	H+	HCO3−	Ca2+	Mg2+	Cl−	SO42−	NO3−	SiO2
vavg	0.124	−0.166	0.102	−0.031	0.226	0.302	−0.243	−0.468
vmax	−0.081	0.005	−0.342	−0.211	−0.328	−0.432	−0.152	0.401
LCF	−0.145	0.066	−0.289	−0.111	−0.316	−0.440	0.030	0.506

. A close examination of these results clarifies the following. First, regarding v_avg, H⁺, Ca²⁺, Cl⁻ and SO₄²⁻ promoted corrosion because the correlation coefficients were positive. Meanwhile, HCO₃⁻, Mg²⁺, NO₃⁻ and SiO₂ inhibited corrosion because the correlation coefficients were negative. Next, with regard to v_max, since the correlation coefficients were positive, HCO₃⁻ and SiO₂ promoted corrosion. Ca²⁺, Mg²⁺, Cl⁻, SO₄²⁻ and NO₃⁻ inhibited corrosion because the correlation coefficients were negative. Finally, regarding LCF, since the correlation coefficients were positive, HCO₃⁻, NO₃⁻ and SiO₂ promoted localized corrosion. H⁺, Ca²⁺, Mg²⁺, Cl⁻ and SO₄²⁻ inhibited localized corrosion because the correlation coefficients were negative.

Focusing on the absolute values of the correlation coefficients, the values for SO₄²⁻ and SiO₂ were larger than those for the other species. This result suggests that these are dominant for the corrosion of carbon steel in tap water. The role of SiO₂ was also taken into consideration. Previous papers have reported that SiO₂ formed a film on zinc and copper [29]. If a similar film was formed on the iron surface, the corrosion inhibitive nature of SiO₂ could be explained. The suppressive effect of the SiO₂ obtained in the authors’ experiment was proved to be consistent with this assumption. Yuasa et al. [30] reported that the corrosion of carbon steel in artificial fresh water was inhibited by SiO₂. On the other hand, attention should be paid to the fact that v_max was an increasing function with respect to SiO₂. That is, SiO₂ promotes localized corrosion. Conventionally, it has been believed that HCO₃⁻ inhibits corrosion [6,7,10,11], but in fact it did not affect corrosion.

3.4. Extraction of Dominant Species Affecting Corrosivity of Waters

3.4.1. Constructing Multiple Regression Models

The explanatory variables were deleted step by step by considering the highest VIF. This operation was repeated with all VIFs that were less than two. First, model A consisted of H⁺, HCO₃⁻, Ca²⁺, Mg²⁺, Cl⁻, SO₄²⁻, NO₃⁻ and SiO₂. Ca²⁺ showed the highest VIF of 6.18. Therefore, Ca²⁺ was excluded from model A. This process brought model B. In the same manner, model C and model D were obtained. Finally, in model D, the VIF was less than two.

Table 4. VIF values among water species in each multiple regression model.

Model	H+	HCO3−	Ca2+	Mg2+	Cl−	SO42−	NO3−	SiO2
A	1.63	4.30	6.73	5.81	3.53	3.40	3.22	2.22
B	1.57	2.64	–	5.81	3.48	1.94	2.67	1.62
C	1.57	2.53	–	–	1.55	1.92	1.98	1.49
D	1.03	–	–	–	1.47	1.84	1.79	1.39

shows the results of this process. Multiple regression analysis was performed on models A to D with v_avg, v_max and LCF as the objective variables.

3.4.2. Multiple Regression Analysis on Chemical Species and v_avg

The R² and the regression coefficient for v_avg are shown in

Table 5. R² and regression coefficient in the multiple regression models for v_avg.

Model	R2	SiO2	NO3−	SO42−	Cl−	Mg2+	Ca2+	HCO3−	H+	b	SE
A	0.432	−0.224	−0.189	0.254	0.061	−0.018	0.020	−0.079	0.051	0.555	0.098
B	0.432	−0.230	−0.182	0.262	0.060	−0.018	–	−0.069	0.049	0.559	0.097
C	0.432	−0.232	−0.187	0.261	0.052	–	–	−0.071	0.049	0.560	0.096
D	0.427	−0.247	−0.208	0.251	0.039	–	–	–	0.076	0.535	0.096

. The R² varied from 0.427 to 0.432. The standard error (SE) was between 0.096 and 0.098. The explanatory variables with large regression coefficients were SiO₂, NO₃⁻ and SO₄²⁻. In addition, the p values obtained from the multiple regression analysis are shown in

Table 6. p values in each multiple regression model for v_avg.

Model	SiO2	NO3−	SO42−	Cl−	Mg2+	Ca2+	HCO3−	H+
A	1.85 × 10−2	0.123	8.31 × 10−3	0.614	0.929	0.899	0.548	0.445
B	4.66 × 10−3	0.099	3.91 × 10−4	0.619	0.929	–	0.502	0.448
C	2.78 × 10−3	0.048	3.39 × 10−4	0.515	–	–	0.478	0.445
D	1.03 × 10−3	0.021	3.98 × 10−4	0.614	–	–	–	0.145

. The p value means whether the coefficients of the explanatory variables are statistically significant or not. In this study, a p value of 0.05 or less was considered significant. Considering the p value of models C and D, it seems that SiO₂, NO₃⁻ and SO₄²⁻ affect v_avg significantly. This result shows that v_avg mainly dominated with these chemical species. Additionally, a negligible effect of Cl⁻ and HCO₃⁻ on v_avg was found. The signs of SiO₂ and NO₃⁻ were negative and that of SO₄²⁻ was positive. This means that SiO₂ and NO₃⁻ decrease the average corrosion rate, while SO₄²⁻ increases it.

3.4.3. Multiple Regression Analysis on Chemical Species and v_max

The R² and the regression coefficients for v_avg are shown in

Table 7. R² and regression coefficient in the multiple regression models for v_max.

Model	R2	SiO2	NO3−	SO42−	Cl−	Mg2+	Ca2+	HCO3−	H+	b	SE
A	0.474	0.592	−0.329	−0.283	−0.172	−0.038	−0.115	0.255	−0.012	0.446	0.165
B	0.472	0.627	−0.365	−0.328	−0.162	−0.037	–	0.195	−0.002	0.424	0.164
C	0.472	−0.232	−0.187	0.261	0.052	–	–	−0.071	0.049	0.560	0.163
D	0.461	0.661	−0.320	−0.301	−0.143	–	–	–	−0.075	0.496	0.163

. The R² varied from 0.474 to 0.461. The SE was between 0.163 and 0.165. Roughly, the explanatory variables with large regression coefficients were SiO₂, NO₃⁻ and SO₄²⁻. In addition, the p values are shown in

Table 8. p values in each multiple regression model for v_max.

Model	SiO2	NO3−	SO42−	Cl−	Mg2+	Ca2+	HCO3−	H+
A	3.69 × 10−4	0.113	7.79 × 10−2	0.405	0.913	0.665	0.254	0.915
B	1.43 × 10−5	5.23 × 10−2	7.40 × 10−3	0.427	0.913	–	0.263	0.984
C	6.52 × 10−6	2.03 × 10−2	6.48 × 10−3	0.189	–	–	0.259	0.982
D	1.01 × 10−6	3.72 × 10−2	1.07 × 10−2	–	–	–	0.277	0.395

. In models B, C and D, p values less than 0.05 were obtained for SiO₂, SO₄²⁻ and NO₃⁻. As with v_avg, v_max mainly dominated with these chemical species. Focusing on the sign of the regression coefficient, SiO₂ was positive, while SO₄²⁻ and NO₃⁻ were negative. Therefore, it can be said that SiO₂ increases the localized corrosion rate, while SO₄²⁻ and NO₃⁻ decrease it.

3.4.4. Multiple Regression Analysis on Chemical Species and LCF

The R² and the regression coefficients for LCF are shown in

Table 9. R² and regression coefficient in the multiple regression models for LCF.

Model	R2	SiO2	NO3−	SO42−	Cl−	Mg2+	Ca2+	HCO3−	H+	b	SE
A	0.557	0.617	−0.003	−0.421	−0.145	0.030	−0.107	0.125	−0.129	0.394	0.155
B	0.556	0.651	−0.037	−0.463	−0.135	0.031	–	0.069	−0.119	0.373	0.154
C	0.556	0.654	−0.029	−0.462	−0.121	–	–	0.073	−0.119	0.371	0.153
D	0.554	0.669	−0.008	−0.452	−0.108	–	–	–	−0.147	0.398	0.152

, and the p values are shown in

Table 10. p values in each multiple regression model for LCF.

Model	SiO2	NO3−	SO42−	Cl−	Mg2+	Ca2+	HCO3−	H+
A	8.74 × 10−5	0.987	5.95 × 10−3	0.454	0.925	0.666	0.548	0.228
B	2.21 × 10−6	0.830	9.44 × 10−5	0.479	0.923	–	0.669	0.249
C	6.94 × 10−7	0.846	7.97 × 10−5	0.337	–	–	0.646	0.246
D	1.58 × 10−7	0.956	7.21 × 10−5	–	–	–	0.376	0.077

. The results show similar trends to v_max. The SE was between 0.152 and 0.155. The R² was between 0.554 and 0.557, which is higher than that of v_avg and v_max. The explanatory variables with large regression coefficients were SiO₂ and SO₄²⁻. LCF mainly dominated with these chemical species. Moreover, being focused on p values, SiO₂ and SO₄²⁻ values were below 0.05 and significantly smaller. This indicates that it may be possible to determine the corrosivity based on only two variables. Focusing on the sign of the regression coefficient, SiO₂ was positive and SO₄²⁻ was negative. The larger the LCF, the more localized the corrosion, so it can be assumed that SiO₂ localizes the corrosion, while SO₄²⁻ causes uniform corrosion.

4. Conclusions

Tap waters sampled at 70 different places and in different seasons in Japan were subjected to chemical analysis, and the corrosion of carbon steel in these waters was studied. The average corrosion rate v_avg, the maximum v_max and the LCF (=v_max/v_avg) were discussed. v_avg was in the range of 0.105 mm y⁻¹ to 0.54 mm y⁻¹, v_max was 0.58 mm y⁻¹ to 4.16 mm y⁻¹ and LCF was 1.68 to 20.1. Multiple regression analysis was carried out by setting chemical species as explanatory variables and LCF and corrosion rates as objective variables. We succeeded in showing that SiO₂ and SO₄²⁻ dominate the corrosivity of Japanese tap water. In particular, as SO₄²⁻ increased, v_avg became larger and v_max became smaller. Also, as SiO₂ increased, v_max became larger and v_avg became smaller. LCF behaved similarly to v_max. The authors expect that the findings of this study will be useful for estimating the corrosivity of tap waters with low Ca²⁺ and high SiO₂ concentrations.