Zairyo-to-Kankyo, 52, 408-415 (2003)

論 文

Proposal of a New Stability Index Taking Account of

Corrosion Inhibiting Action of Silica and Derivation of

Empirical Equations Containing the New Index for

Corrosiveness and Scale Formation of Water

Makoto Yuasa*,**, Toshiharu Wake***, Takashi Fujieda*, Nobuyuki Momozawa* ,**, Aritomo Yamaguchi*, Yoshiaki Shibata***, Shintaro Someya***, and Akira Takahashi****

Faculty of Science and Technology, Tokyo University of Science**Institute of Colloid and Interface Science, Tokyo University of Scienc***Japan Organo, Corp.

A new stability index [an improved stability index (SI')] has been proposed that introduces corrosion inhibiting ability of silica in a broad range of temperature and pH into the conventional index of the corrosive action and scale formation of water, and new empirical equations [Eqs. 1-3] that characterize water were derived using the new index. The derived SI' was effective in the range of SI>6. The SI' was balanced at 0, and then SI'=0 differed from SI=6. In addition, a possibility was found for prediction and inhibition of corrosion of ferrous metals based on the equations by controlling the concentration of silica ([SiO2]).

y=K0{1-exp(-3.06•~10-1SI')} (1)

K0=(2.09T+1.872•~102)exp{-(-1.08•~10-4T+7.62•~10-3)[SiO2]} (2)

SI'=x-7.21{1-1.71•~10-1exp(-8.59•~10-3[SiO2])} (3)

[y: corrosion rate (V) (mdd), K0: constant affecting saturation value of corrosion rate (y) (mdd), T: temperature

(•Ž), [SiO2]: silica concentration (mg SiO2/dm3), x: stability index (SI) (-)]

Key words: stability index, empirical equations, corrosion inhibition, mild steel, water quality factor, silica

1. Introduction

Corrosion and scaling of ferrous plant materials caused

by water have been problems in water conduction plants

and water treatment systems including cooling water,

waste water treatment, industrial water treatment, and water demineralizing systems. For instance, we encounter

various problems including (1) corrosion of pipes due to

corrosive factors such as dissolved oxygen and chloride

ions caused by city or industrial water as circulating water

and (2) scaling problems such as blocking of pipes and reduction in the thermal conduction of heat exchangers

produced by concentration of dissolved substances and for-mation of insoluble salts due to evaporation of part of circu-

lating water1)-7) in the most frequently used open cooling

water systems ranging from those for small scale air-condi-

tioning in buildings to those for large scale cooling in com-

plexes. In order to overcome these problems, various anti-corrosion agents have so far been used in open cooling

water systems. These agents include (1) chromate and

phosphate salts against corrosion and (2) polyphosphate and phosphonate salts against scaling. In addition, they

are used widely with a small amount of other agents in

water conduction plants and water treatment systems so

that the combined agents give additive and synergetic

effects1)-9). Nevertheless, the demand for environmental

protection in recent years has made the use of these agents unfavorable due to the toxicity of chromate salts and the eutrophication of water by phosphate salts, and

hence the development of environment-friendly and less toxic anticorrosive agents and the reduction of added anti-

corrosive agent concentration are being required1)-7).

Many non-environment-pollutive oligomers and polymers with carboxylic acid groups are examined from these

points of view1)-7),10)-28). Moreover, the reduction of added anticorrosive agent concentration is one of the important

subjects to be examined and the elucidation of the relation

between water quality and metal corrosion in conformity with the present situation is necessary.

Calcium and silica have been known as possible anticor-

rosive components of water in water conduction plant and

water treatment systems including cooling water systems. These components have both advantages as corrosion

inhibitor and disadvantages as scale former, and calcium

carbonate has among others been regarded as the primary

component that causes scale problems, in addition to its anticorrosive action. Then, Langelier index (denoted

hereafter as saturation index)*1, Ryznar index [denoted

hereafter as stability index (SI)]*1, corrected Ryznar

index, and Larson index have been examined as an index

of the corrosiveness or scale formability of water1),4),29)-38

Silica has long been used in one-through cooling water sys-

tems because it is scarcely toxic and anticorrosive. Then, combined uses of silica with other agents are expected to

exhibit a high corrosion inhibiting action at lower concen-trations. Control of silica concentration in water is neces-

sary, however, because it deposits as scales. Moreover,

*2641, Yamazaki, Noda, 278-8510 Japan

**1-3, Kagurazaka, Shinjuku, Tokyo, 162-8601 Japan

***4-9, Kawagishi 1-chome, Toda, 335-0015 Japan

Vol.52, No.8 409

neither of the above-mentioned saturation index and stabil-

ity index (SI) takes into consideration the effect of silica.

It is then doubtful if these indexes can cope with the pre-

sent diversified water conditions.

We have investigated from the view point described

above the effects of water quality factors such as concen-

trations of silica, [SiO2] and chloride ion, [Cl-] on the sta-

bility index (SI), an index for the corrosiveness or scale

forming action of water, and the corrosion rate of mild

steel to gain the fundamental knowledge necessary to

construct a highly anticorrosive system with use of a

reduced concentration of anticorrosive agent39),40). We

proposed a new stability index [an improved stability index

(SI')] that combines the corrosion inhibiting action of sili-

ca in a broad range of temperature and pH of water with SI

and derived new empirical formulas (1)-(3) containing

the new index for the properties of water. We also made a

proposal for the way of inhibiting corrosion of ferrous met-

als in water conduction plants and water treatment systems

by controlling the concentration of silica added ([SiO2])

with the equations.

y=K0{1-exp(-3.06•~10-1SI')} (1)

where

K0=(2.09T+1.872•~102)

•~ exp{-(-1.08•~10-4T+7.62•~10-3)[SiO2]}

(2)

SI'=x-7.21{1-1.71•~10-1exp(-8.59•~10-3[SiO2])}

(3)

[y: corrosion rate (V) (mdd), K0: constant affecting satu-

ration value of corrosion rate (y) (mdd), T: temperature

(•Ž), [SiO2]: silica concentration (mg SiO2/dm3), x: sta-

bility index (SI) (-)].

2. Experimental

2.1 Materials

Table 1 lists the water qualities of the samples used.

Test solutions were prepared changing the concentrations

of SiO2 and Cl- according to the previous reports33),41)

using a water sample at a given stability index11),33)

obtained from its pH, calcium hardness (Ca2+), and M-

alkalinity*2. Aqueous H2SO4, CaSO4, NaHCO3, and NaCl

solutions were used to adjust the above parameters.

The steel test samples used were of SS 400 steel pre-

treated as previously reported42) [C 0.04mass%, Si extreme-

ly low percentage point, Mn 0.30mass%, P 0.02mass%, S

0.017mass%, Fe remaining percentage point, Japan Test

Panel Ind., 20•~80•~2mm, polished with emery paper

(#400)].

2.2 Corrosion weight loss test

The steel test samples were ultrasonically washed in ace-

tone and dried and their pre-weights were measured. The

samples were then immersed in a test solution (1dm3) for

7 days at different temperatures and atmospheric pressure

under stirring. After being withdrawn from the test solu-

tion, the samples were post-treated according to the previ-

ous report43) and their post-weights were measured.

Corrosion rate was calculated using the following equation:

V=w/(A•~t) (8)

where V is corrosion rate (mdd=mg/dm2/day), w is

weight loss (mg), A is surface area (dm2), and t is time of

test (day).

2.3 Numerical analysis

The relation among corrosion rate (V=y), SiO2 concen-

tration ([SiO2]), Cl- concentration ([Cl-]), and T was

numerically analyzed with a personal computer and its

effect was examined on the stability index (SI=x) and the

corrosion rate (V=y) in equations (1)-(3) when the water

quality factors, [SiO2] and [Cl-] are available.

3. Results and Discussion

3.1 Corrosion weight loss test

3.1.1 Scale forming water quality

Corrosion weight loss test was performed at T=25 and

40•Ž using the (CaCO3) scale forming water quality given

in Table 1. The results obtained at 25•Ž are shown in Fig.

1, in which the relationships are given between water quali-

ty factors, [SiO2] and [Cl-] and the corrosion rate of mild

steel, V [SI-water quality factors ([SiO2] and [Cl-])-corro-

siveness relationships]. The corrosion rate V decreased

with increasing [SiO2] but [Cl-] caused no change in the

rate at SI=4.4 as shown in Fig. 1-a. This can be under-

stood in terms of the [SiO2]-V relationship and the [Cl-]-

V relationship. Similar results were obtained at the other

SIs. This means that the corrosion rate depends more on

[SiO2] than [Cl-] in the experimental conditions used in

this work. The relationship [SiO2]-[Cl-]-V was not affect-

ed by changes in SI as seen from the SI-V relationship

(Fig. 2). This indicates that SiO2 and Cl- have no direct

effect on SI. Fig. 3 shows the results obtained at 40•Ž,

*1 saturation index and stability index are the indexes for calcium carbon-

ate (CaCO3) if it deposits as scales or dissolves and given by the follow-ing equations:

(saturation index)=pH-pHs (4)(stability index)=2pHs-pH (5)

pHs=(9.3+A+B)-(C+D) (6)where pH is measured pH value of solution and pHs is the pH value at which the solution is saturated with CaCO3, that is, the critical pH value at which scales begin to deposit, and is calculated using Eq. 6. A, B, C, and D are respectively the total solid matter coefficient, temperature coefficient, calcium hardness coefficient, and M-alkalinity coefficient (A

and D are obtained from the existing saturation index nomograms). Water quality is judged using the calculated saturation index and stabili-ty index as follows1),4),29)-38(stability index)<6[(saturation index)>0] (scaling tendency)(stability index)=6[(saturation index)=0] (7)(stability index)>6[(saturation index)<0] (corroding tendency)

*2 M-alkalinity is expressed as the mg/dm3 equivalent of acid needed to

neutralize the pH of sample to pH 4.8 or mg/dm3 of CaCO3 correspond-ing to the acid. M-alkalinity gives the total amount of alkaline sub-stances including hydroxides, carbonates, phosphates (2/3 amount), and silicates. Note here that M-alkalinity was altered to the acid con-sumption (pH 4.8) in 1989 JIS amendments41).

410 Zairyo-to-Kankyo

Table 1 Conditions of test soutions.

which indicate that the relationship [SiO2]-[Cl-]-V (three-

dimensional curved surface) shifts upward in the z-axis

direction. Thus, an increase in T caused an increase in V.

The other results were similar to those obtained at 25•Ž.

The above findings demonstrate that SiO2 affects V while

Cl- shows no effect on V at scale forming water quality.

In other words, only SiO2 affects V and the anticorrosive

action of SiO2 alone works in the experimental conditions.

The fact that V is unaffected by SI but depends on [SiO2]

(and T) would be due to missing the effect of anticorrosive

SiO2 on SI (due also to the previous disregard of SiO2

because of sufficient corrosion inhibition by CaCO3 scaling

alone in the experimental conditions where CaCO3 scales

Fig. 1 Relation of corrosion rate (V) of mild steel with water

quality factors as SiO2 and Cl- at various stability index (

SI) values and at 25•Ž using the scale forming water

quality. SI (-): 4.4 (a), 4.8 (b), 5.2 (c), 5.4 (d) and 5.8 (

e).

Fig. 2 Relationship between SI and V at 25•Ž using the scale

forming water quality in test solutions with Cl- {[Cl-]

(mg/dm3): 10 (a) and 500 (b)}. [SiO2] (mg/dm3): 10

(•¡), 50 (•œ), 100 (•£), 200 (•Ÿ) and 400 (•¥).

Fig. 3 Relation of V with water quality factors as SiO2 and Cl- at

various SI values and at 40•Ž using the scale forming

water quality. SI (-): 4.4 (a), 4.8 (b), 5.2 (c), 5.4 (d) and

5.8 (e).

Vol.52, No.8 411

Fig. 4 Relation of V with water quality factors as SiO2 and Cl- at

various SI values and at 55•Ž using the corrosive water

quality. SI (-): 7.8 (a), 8.7 (b), 9.1 (c), 10.4 (d), 13.1 (e)

and 14.1 (f).

are formed). A detailed investigation of the effect of SiO2

revealed that an increase in [SiO2] causes a decrease in V

at any SI in the experimental conditions (for example, Fig.

2) and SiO2 scale coats make up the corrosion that CaCO3

scale coats fail to prevent. That is, SiO2 contributes com-

plementarily and synergistically to corrosion inhibition.

3.1.2 Corrosive water quality

Corrosion weight loss tests were carried out at the cor-

rosive water quality given in Table 1 at 25, 40, and 55•Ž.

Fig. 4 shows the results obtained at T=55•Ž that yielded

the largest changes in the relations between the water

quality factors, [SiO2] and [Cl-], and the corrosion rate of

mild steel, V(=y), in test solutions at different SIs [the

relationship SI-water quality factors ([SiO2] and [Cl-])-

corrosiveness]. V increased with increasing [SiO2] but not

with [Cl-] at SI=7.8 as shown in Fig. 4-a. This is under-

standable in terms of the [SiO2]-V relationship and the

[Cl-]-V relationship. Similar results were obtained at the

other SIs. Thus, the corrosion rate depends more on

[SiO2] than [Cl-] in the experimental conditions used in

this work. As SI decreased, the curved surface for the rela-

tionship [SiO2]-[Cl-]-V shited downward. This confirms

that the corrosiveness decreases with decreasing SI in test

solutions with added SiO2 and Cl-. This is comprehensi-

ble in terms of the SI-V relationship at each T (Fig . 5).

When T increased from 25 to 55•Ž, the relationship [SiO2]-

[Cl-]-V (three-dimensional curved surface) shifted

upward. The other tendencies were similar at all tempera-

tures.

3.2 Numerical analysis

Numerical analysis was conducted for the results to

examine the above-mentioned relationship SI-water quali-

ty factors ([SiO2] and [Cl-])-corrosiveness (no numerical

analysis was performed for the results obtained at the scale

forming water quality because only [SiO2] (and T) affected

V remarkably and no change in the SI-V relationship was

observed in the experimental conditions used in this

work).

3.2.1 Basic concepts

(1) Phenomena accompanying saturation

Conversion of the relationship [SiO2]-[Cl-]-V (Fig. 4)

to the SI-V relationship (Fig. 5) at each SI yields an

increasing trend of V with SI and its eventual stationary

state (or saturation state). This is a phenomenon accom-

panying saturation in mathematical terms. Fig. 6-a is a

conceptual diagram of the phenomenon accompanying sat-

uration. If y (V) on the ordinate is ƒ¿ against x (SI) on the

abscissa and converges onto ƒÀ, then

dy/dx=-ƒ¿(y-ƒÀ) (9).

The general solution for the above equation is

y=C1exp(-ƒ¿x)+ƒÀ (C1: integration constant) (10).

Since x is positive and larger than 6 in the experimental

conditions used in this work as mentioned above, Eq. 10

can be transformed into the following equation by chang-

ing the combination of constants and expressing x explicit-

ly:

y=K0[1-K1exp{-K2(x-K3)}] (11),

where K0-K3 are respectively constants affecting the satu-

ration value of y, characterizing y at x=K3 (equilibrium

state of x), giving the rate of change of y against x, and

denoting the effect of SiO2 on x.

(2) Upwardly and downwardly changing phenomena

Upwardly and downwardly changing phenomena shown

in Fig. 6-b can be expressed by Eq. 12 if n on the ordinate

is ƒÁ against m on the abscissa:

dn/dm=-ƒÁn (12)

The general solution of the equation is given by

n=C2exp(-ƒÁm) (C2: integration constant) (13).

The analysis was made using the above conceptions.

3.2.2 Effect of [Cl-] at corrosive water quality

Numerical analysis was performed using Eq. 11 at a fixed

[SiO2] to examine the effect of [Cl-] on the SI-V relation-

ship. Here, no analysis was made on the case without

412 Zairyo-to-Kankyo

Fig. 5 Relationship between SI and V at 25 (I), 40 (II) and 55

(III) •Ž using the corrosive water quality in test solutions

with Cl- {[Cl-] (mg/dm3): 10 (a) and 500 (b)}. [SiO2]

(mg/dm3): 10(•¡), 50(•œ), 100(•£), 200(•Ÿ) and

400(•¥).

Fig. 6 Concept figures of phenomena accompanying saturation (a) and upwardly and downwardly changing phenomena (b).

Fig. 7 Relationship between SI and V at various [Cl-] and at 55•Ž

using the corrosive water quality in test solutions with

SiO2 {[SiO2] (mg/dm3): 10 (a), 50 (b), 100 (c), 200 (d)

and 400 (e)}. [Cl-] (mg/dm3): 0(•~), 10(•¡), 50(•œ),

100(•£), 300(•Ÿ) and 500(•¥).

added SiO2 because this case can be handled by the con-

ventional methods1),5),31),33),36),38). Fig. 7 shows the results

of analysis at 55•Ž as an example [the results of curve fit-

ting for the experimantal data on the SI-V relationship

using Eq. 11 (solid line)]. The SI-V relationship was the

same and represented by one curve at any [Cl-]. A simi-

lar tendency was obtained at the other temperatures (25

and 40•Ž). Thus, [Cl-] had a tendency not to affect the SI-

V relationship shown in Eq. 7 in the systems with added

SiO2.

3.2.3 Effect of [SiO2] at corrosive water quality

In order to examine the effect of [SiO2] on the SI-V rela-

tionship, numerical analysis was conducted at a fixed

[Cl-]. The analysis was carried out using the average

value of [Cl-] at respective [SiO2] since [Cl-] was found to

have no effect on V in the previous section. Fig. 8 shows

the results of analysis at each T [the results of curve fitting

using Eq. 11 for the experimental data on the SI-V relation-

ship (solid line)]. Fig. 9 shows the relationships between

the values of each K obtained from the curve fitting and

[SiO2]. K0 and K3 changed with increasing [SiO2] at any T

while K1 and K2 remained unchanged independently of

[SiO2].

Vol.52, No.8 413

Fig. 8 Relationship between SI and V at various [SiO2] and in test solution at 25 (I), 40 (II) and 55 (III) •Ž using the corrosive water

quality. [SiO2] (mg/dm3): 10(•¡), 50(•œ), 100(•£), 200(•Ÿ) and 400(•¥). Plots and solid lines in these figures are experi-

mental data and curve fitting data from analyses of numerical values, respectively.

Fig. 9 Relationship between [SiO2] and various K values deter-

mined by analyses of numerical values in test solution at

25 (I), 40 (II) and 55 (III) •Ž using the corrosive water

quality.

Discussion was made first on K1 and K2, both of which

are constant. K1 is unity because it is a constant character-

izing V(=y) at SI(=x)=K3, a value at the equilibrium state

of SI(=x), and represents conceptually a state where no

corrosion proceeds (V=0) and no CaCO3 scale is formed.

Here, K1=1 in Fig. 9, satisfying the present conditions and

showing the plausibility of Eq. 11 used in the numerical

analysis. K2 is a constant that represents the rate of

change of V(=y) against SI(=x). In other words, it is the

easiness with which V increases against SI. It has a value

of 3.06•~10-1 and remains constant while [SiO2] and T

change. This suggests that K2 relates to the SI-V relation-

ship in a similar manner in any test condition and hence

changes in [SiO2] and T would cause no change in the cor-

rosion inhibiting mechanism. These considerations lead to

a modification of Eq. 11 to

y=K0[1-exp{-3.06•~10-1(x-K3)}] (14).

Next, discussion was made about K0 and K3. Since K0

decreased with increasing [SiO2], the oxide has an anticor-

rosive effect. In particular, it shows a downwardingly

changing tendency (Fig. 9) as seen in Fig. 6-b and hence

it can be analyzed using Eq. 15 obtained by transformation

of Eq. 13:

K0=L0exp{-L1[SiO2]}(L0, L1: coefficients) (15).

Comparison of values of K0 at different temperatures indi-

cates that T has an effect to increase the saturation value of

corrosion, that is, a corrosion enhancing effect since an

increase in T causes an increase in K0. Then, the effect of

T on K0 must be taken into consideration. Numerical

analysis of K0 at each T yields the following equations:

K0=2.420•~102exp{-5.11•~10-3[SiO2]} (25•Ž) (16)

K0=2.657•~102exp{-2.96•~10-3[SiO2]} (40•Ž) (17)

K0=3.047•~102exp{-1.88•~10-3[SiO2]} (55•Ž) (18).

These results indicate that T affects both L0 and L1 and the

equations for L0-T and L1-T are

L0=2.09T+1.872•~102 (19)

L1=-1.08•~10-4T+7.62•~10-3 (20).

Substitution of these equations into Eq. 15 yields:

K0=(2.09T+1.872•~102)

•~ exp{-(-1.08•~10-4T+7.62•~10-3)[SiO2]} (21).

K3 is the value of SI when V is 0 and it increases from 6

(equilibrium state) to about 7 with increace in [SiO2] as

shown in Fig. 9. This suggests that addition of SiO2 causes

changes in the value of SI at V=0, namely, the equilibrium

value of corrosion. Since K3 remains unchanged while T

changes, it depends merely on [SiO2]. Since K3 converges

without being affected by T as seen in Fig. 9, it can be con-

414 Zairyo-to-Kankyo

sidered to behave as the situation in Fig. 6-a. Then, refer-

ring to Eq. 11

K3=M0[1-M1exp{-M2([SiO2]-M3)}] (22).

[M0, M1, M2, M3: constants]

Analyzing Eq. 22 in a way similar to that used for Eq. 11

gives

K3=7.21{1-1.71•~10-1exp(-8.59•~10-3[SiO2])}

(23).

Referring to the conditions of Eqs. 21 and 23, Eq. 14

becomes

y=K0[1-exp{-3.06•~10-1(x-K3)}] (14),

where

K0=(2.09T+1.872•~102)

•~ exp{-(-1.08•~10-4T+7.62•~10-3)[SiO2])}

(21)

K3=7.21{1-1.71•~10-1exp(-8.59•~10-3[SiO2])}

(23).

3.2.4 Correction of stability index: improved stabili-

ty index (SI')

The results obtained in the previous section suggest the

necessity of corrections for the existing index of corrosive-

ness, SI, in SiO2-containing water systems since [SiO2]

affects both V(=y) and SI(=x). Taking account of the

finding that SI increases from 6 to about 7 with increase in

[SiO2] and of the relation of Eq. 11, a new stability index

(improved stability index), SI', is expressed as

SI'=SI-K3=x-K3 (24).

Using Eq. 24, Eqs. 14, 21, and 23 eventually become respec-

tively

y=K0{1-exp(-3.06•~10-1SI')} (1)

where

K0=(2.09T+1.872•~102)

•~ exp{-(-1.08•~10-4T+7.62•~10-3)[SiO2]}

(2)

SI'=x-7.21{1-1.71•~10-1exp(-8.59•~10-3[SiO2])} (3).

[y: corrosion rate (V) (mdd), K0: constant affecting satu-

ration value of corrosion rate (y) (mdd), T: temperature

(•Ž), [SiO2]: silica concentration (mg SiO2/dm3), x: stabili-

ty index (SI) (-)].

The derived SI' was effective in the range of SI>6. The SI'

was balanced at 0, and then SI'=0 differed from SI=6.

Using Eqs. 1-3 makes it possibe (1) to predict the value of

V and hence the corrosiveness for water at a given temper-

ature and corrosion indexes including SI and (2) to control

the value of V through regulation of [SiO2] and inhibit cor-

rosion. Thus, an improved stability index (SI') was pro-

posed as a new index for the corrosiveness of water to pre-

dict and control of ferrous metal corrosion in water con-

duction plants and water treatment systems including cool-

ing water, waste water treatment, industrial water treat-

ment, and pure water treatment systems and reasonable

empirical equations [Eqs. 1-3] for the SI'-V relationship

were derived taking account of the effect of [SiO2].

4. Conclusions

In order to gain fundamental knowledge necessary to

construct a more effective anticorrosive system than

before through lowering the concentration of added corro-

sion inhibitor for ferrous metals in water conduction plants

and water treatment systems, the effects of [SiO2] and

[Cl-], water quality factors, were examined on the stability

index SI, an index for the corrosiveness or scale forming

action of water, and the corrosion rate of mild steel. A new

stability index [an improved stability index (SI')] has been

proposed that introduces anticorrosive action of SiO2 in a

wide range of temperature and pH into the existing index

for the corrosiveness or scale forming action of water, and

new empirical equations [Eqs. 1-3] that characterize water

were derived using the new index. The derived SI' was

effective in the range of SI>6. The SI' was balanced at 0,

and then SI'=0 differed from SI=6. In addition, a possibil-

ity was found for the prediction and inhibition of corrosion

of ferrous metal by controlling the concentration of added

SiO2 as corrosion inhibitor based on the equations derived.

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(Manuscript received January 21, 2 0 0 3 ; in final form May 6, 2 0 0 3 )