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Cathodic protection system of copper–zinc–saline water in presence of bacteria
Desalination 270 (2011) 193–198
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Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l
Cathodic protection system of copper–zinc–saline water in presence of bacteria Aprael S. Yaro, Haidar Al-Jendeel, Anees A. Khadom ⁎ Department of Chemical Engineering, College of Engineering, Baghdad University, Aljaderia, 10071, Baghdad Governorate, Iraq
a r t i c l e
i n f o
Article history: Received 4 October 2010 Received in revised form 25 November 2010 Accepted 25 November 2010 Available online 18 December 2010 Keywords: Copper Zinc Weight loss Cathodic protection Microbiological corrosion
a b s t r a c t Rate of zinc consumption during the cathodic protection of copper pipeline which carries saline water was measured by weight loss technique in the absence and presence of bacteria. Variables studied were solution flow rate, temperature, time and NaCl concentration. It was found that within the present range of variables; the rate of zinc consumption increases with the increase of all operating conditions. The presence of bacteria increases the zinc consumption. Fourth order multi-term model and one-term model were suggested to represent the consumption data. Nonlinear regression analysis was used to estimate the coefficients of these models, while statistical analysis was used to determine the effect of each coefficient. Both models were representing the data successfully. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Equipment used in the desalination and cooling systems which uses saline water as a coolant suffers severely from corrosion owing to the presence of the highly aggressive chloride ions in high concentration. These structures are protected by cathodic protection with sacrificial anodes, therefore, hundreds of researches were done in the subject of cathodic protection system with sacrificial anode, but few of them were dealing with the presence of bacteria in these systems. These bacteria may cause a microbiological corrosion (MIC). Microbiological corrosion is the deterioration of materials which is caused directly or indirectly by bacteria, algae, moulds or fungi; singly or in combination. Microbiological corrosion refers to corrosion and the ensuing loss of metal caused by biological organisms. MIC can occur in any aqueous environments and it is a common problem in industrial processes due to the presence of microbes, adequate nutrients and corrosive byproducts [1]. Microorganisms pervade our environment and readily “invade” industrial systems wherever conditions permit. These agents flourish in a wide range of habitats and show a surprising ability to colonize water-rich surfaces wherever nutrients and physical conditions allow. Microbial growth occurs over the whole range of temperatures which are commonly found in water systems, and limited access to nitrogen and phosphorus is offset by a surprising ability to retain trace levels of these essential nutrients. A significant feature of microbial problems is that they can appear suddenly when conditions allow exponential growth of the organisms. Many
⁎ Corresponding author. Tel.: +964 790 2305786 (mobile). E-mail address: [email protected] (A.A. Khadom). 0011-9164/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2010.11.045
engineers continue to be surprised that such small organisms can lead to spectacular failures of large engineering systems [2]. A number of metals, such as structural steels, copper alloys etc., tend to corrode generally over the entire surface in the absence of crevices or galvanic effects. In such cases, corrosion is determined by the rate at which dissolved oxygen can be delivered to the metal surface. Biological organisms present in the aqueous medium often have the potential to increase or decrease oxygen transport to the surface; consequently, these organisms have a role in increasing or decreasing the general corrosion. Most MIC, however, manifests as localized corrosion because most organisms do not form in a continuous film on the metal surface. Microscopic organisms also tend to settle on metal surfaces in the form of discrete colonies or at least spotty, rather than continuous films. Biological organisms fall under two groups based on the type of corrosion they engender: (a) anaerobic corrosion that produces highly corrosive species as a part of their metabolism, and (b) aerobic corrosion that produces corrosive mineral acids. Sulfate reducing bacteria (SRB) from the genera desulfovibrio are a typical example of anaerobic MIC. Aerobic sulfur oxidizing bacteria of the type thiobacillus can create an environment of up to 10% sulfuric acid, thereby encouraging rapid corrosion [3]. The main use of seawater is for cooling purposes, but it is also used for Firefighting, oilfield water injection, and desalination plants [1]. Pseudomonas bacteria are now being found in these water systems in many parts of the country with maximum activity at pH 7.5–8.5 [4–6]. Until the last couple of years bacteria in these types of systems were of little concern and not often investigated. Now bacteria known as Pseudomonas have started to appear in main water supplies, where it has no significant health concerns, but can have a major effect on the water systems in commercial buildings. Pseudomonas is a biofilm or slime-producing bacteria and
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when left to proliferate can cause severe corrosion and blockages within the pipe work. This particularly affects modern buildings with smallbore pipe work and small orifices associated with control valves [7]. The biofilm can reduce the water flow and provide a habitat for other corrosion inducing bacteria that will lead to pitting and leaking of the pipe work. The net result of Pseudomonas in heating and chilled water systems is a decrease in their efficiency and increase down time and costs from repairing leaks. In this study experimental measurements were conducted on zinc electrode as sacrificial anode for cathodic protection of copper pipeline carrying saline seawater in the presence and absence of bacteria named scientifically as (Pseudomonas flourescens) was measured by weight loss technique. 2. Materials and methods Experimental work of sacrificial anode system was carried out to determine the consumption rate of zinc in cathodic protection using weight loss for various conditions of temperature (10–40 °C), flow rate (300–600 L/h), pH (8) , time (1–3 h), and NaCl (1–3.5%) in the presence and absence of bacteria (P. flourescens). 2.1. Electrodes Working electrode was a tube specimen of pure copper with dimensions of 30 cm length, 2 cm inside diameter and 0.2 cm thickness. While the anode electrode was zinc strip with dimensions of 30 cm length, 0.4 cm width and 0.08 cm thickness. These electrodes were cleaned by washing with hot water followed by distilled water. Specimens were abraded using emery paper grade 600, washed with water followed by distilled water. After each run, the zinc strip was rinsed in distal water, dried and reweighed [8]. 2.2. Preparation of culture media Pure culture of P. flourescens which were used in the experiments has been supplied by the Department of Biotechnology-Baghdad University. They were isolated from soil. P. flourescens were activated on nutrient agar at 32 °C overnight. Cells were harvested from cultures then inoculated into nutrient broth containing 0.5% peptic digest of animal tissue, 0.15% beef extract, 0.15% yeast extract and 0.5% sodium chloride dissolved in distilled water (pH 8) and incubated at 32 °C with rotary shaker (120 rpm) for 6 h [9,10].
2.3. Experimental procedure The apparatus shown in Fig. 1 was used to study the effect of the variables on the sacrificial anode cathodic protection system. In the absence of bacteria and before each run, the zinc strip was weighed and fixed at the inlet of the copper by rubber stopper and was electrically connected by an insulated copper wire to the copper tube outlet. The zinc strip is extending along the copper tube to ensure uniform current and potential distribution along the tube wall. After each run the zinc strip and copper pipe were rinsed in distilled water and brushed softly to remove the corrosion products, dried with clean tissue then immersed in Chloroxylenol, dried again, and then reweighted to determine the weight loss. The same procedure was repeated in the presence of bacteria, the bacterial cells were grown in nutrient broth for 6 h at 32 °C in a rotary shaker (120 rpm) then the absorbance of this broth was set to an A600 of O.D 0.15(243 × 107 bacteria/cm³) [9,10]. 2.4. Effect of cell concentration The bacterial inoculums prepared as mentioned in item 2.3 was used after determining the absorbance at 600 nm (A600). In order to study the effect of bacterial cell concentration the absorbance of the test solution was set to an A600 of 0.5, 0.15 and 0.05 (optical density) by using visible spectrophotometer. Viable counts were determined by serial dilution of cultures with normal saline (0.85%) and plating on nutrient agar. The three zinc strips were weighted and immersed in nutrient broth inoculated with bacterial suspensions of O.D 0.5, 0.15 and 0.05 respectively and then incubated overnight at 32 °C in a rotary shaker (120 rpm). Then the corrosion rates were measured by weighting the zinc strips after incubation. It was found that O.D. 0.5 gave the higher corrosion rate. Therefore, the whole tests have been carried out at this bacterial concentration with mixing ratio of 243 × 1010 bacteria to 1 L saline water. 3. Results and discussion Table 1 shows the rate of zinc consumption in the absence and presence of bacteria at different conditions. The data are distributed in this table and arranged in three sections. In Section I, at constant temperature (20 °C) and constant saline water concentration (3.5%), the zinc consumption increases with the increasing of time and flow rate. In Section II, at constant time (180 min) and constant saline water
Fig. 1. Schematic diagram of apparatus used in sacrificial anode test system.
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Temp. Flow rate NaCl Time Zinc consumption (mg/cm2) (°C) (L/h) (wt.%) (min) Bacteria absence Bacteria presence 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 Section II 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40 Section III 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
300 300 300 300 400 400 400 400 500 500 500 500 600 600 600 600 300 400 500 600 300 400 500 600 300 400 500 600 300 400 500 600 300 300 300 300 400 400 400 400 500 500 500 500 600 600 600 600
3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 1.0 2.0 2.5 3.5 1.0 2.0 2.5 3.5 1.0 2.0 2.5 3.5 1.0 2.0 2.5 3.5
50 100 150 180 50 100 150 180 50 100 150 180 50 100 150 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180
0.0016 0.0095 0.064 0.0918 0.0042 0.0265 0.0769 0.1172 0.0122 0.0626 0.1066 0.1814 0.0340 0.1008 0.1809 0.2515 0.0303 0.0547 0.0801 0.1252 0.0918 0.1172 0.1814 0.2515 0.1507 0.2021 0.2456 0.3077 0.1640 0.2170 0.2462 0.3343 0.0239 0.0865 0.1135 0.1507 0.0668 0.1496 0.1655 0.2021 0.0875 0.1714 0.2175 0.2456 0.104 0.2074 0.2706 0.3077
0.0021 0.0244 0.0753 0.1289 0.0058 0.0387 0.0849 0.1332 0.0143 0.0722 0.1332 0.2101 0.0389 0.1130 0.1931 0.2684 0.0669 0.0722 0.1130 0.1364 0.1289 0.1332 0.2101 0.2684 0.2048 0.2462 0.2849 0.3406 0.1656 0.2191 0.2483 0.3412 0.0891 0.1581 0.1798 0.2048 0.1167 0.1979 0.2143 0.2462 0.1305 0.2133 0.2589 0.2849 0.1395 0.2435 0.3050 0.3406
ln (zinc consumption rate) (mg/min.cm2)
-6.0
Table 1 Zinc consumption in sacrificial anode in the absence and presence of bacteria.
Section I
195
-6.2 -6.4 -6.6 -6.8 -7.0 -7.2 -7.4 -7.6 -7.8 -8.0
300 L/h 400 500 600
-8.2 -8.4
-8.6 0.00315 0.00320 0.00325 0.00330 0.00335 0.00340 0.00345 0.00350 0.00355
1/T (1/K) Fig. 2. Arrhenius plots for zinc consumption at different flow rate in the absence of bacteria.
3.1. Effect of temperature The increase in the rate of zinc dissolution with increasing saline water temperature may be due to several reasons; increasing saline water temperature leads to decreasing saline water viscosity with a consequent increase in oxygen diffusivity, which leads to increase the rate of mass transfer of dissolved oxygen to the cathode surface, then increasing the zinc consumption [8]. On the other hand, the decrease in saline water viscosity with increasing temperature improves the saline water conductivity with a consequent increase in corrosion current and the rate of corrosion. Another effect of temperature is that it increases the reaction rate according to Arrhenius equation [12]: −E= RT
ð3Þ
Rate = Ae
where A is frequency factor, E is activation energy, R is universal gas constant and T is absolute temperature. Figs. 2 and 3, show the Arrhenius plots of the rate of zinc consumption against reciprocal of absolute temperature. These figures were plotted as ln (zinc consumption rate) against 1/T with slope equal to −E/R, from which the values of activation energy were obtained. Table 2 shows that activation energy decreases as flow rate increases, and these values were lower in the presence of bacteria. This behavior indicates that zinc consumption reaction needs lower energy to occur.
concentration (3.5%), the variation of temperature and flow rate increases the zinc consumption. While in Section III, at constant time (180 min) and constant temperature (30 °C), both flow rate and saline water concentration lead to the increase of zinc consumption. The same behavior was observed in the presence of bacteria with more consumption of zinc. For the present system the electrochemical cell responsible for cathodic protection is Zn/NaCl/Cu. The anodic reaction is [11]: +2
Zn → Zn
ð1Þ
+ 2e
And the cathodic reaction which is an O2 reduction towards the wall of the copper pipe is assumed to predominate. O2 + 2H2 O + 4e → 4OH
−
ð2Þ
ln (zinc consumption rate) (mg/min.cm2)
-6.0 -6.2 -6.4 -6.6 -6.8 -7.0 -7.2 -7.4 -7.6
300 L/h 400 500 600
-7.8 0.00315 0.00320 0.00325 0.00330 0.00335 0.00340 0.00345 0.00350 0.00355
1/T (1/K) Fig. 3. Arrhenius plots for zinc consumption at different flow rates in the presence of bacteria.
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Table 2 Activation energy of zinc consumption at different flow rates 3.5% saline water and 180 min. Flow rate (L/h)
300
400
500
600
Eabsence (kJ/mol) Epresence (kJ/mol)
41.7 29.4
34.8 23.6
27.6 22.3
23.5 19.8
3.2. Effect of time Table 1 shows that the rate of zinc consumption (dissolution) increases with the increase of time and this is a normal case because of the erosion–corrosion which accelerates the rate of deterioration of a metal resulting from relative movement between the corrosive fluid and the metal surface. On the other hand, the presence of P. flourescens increases the rate of zinc consumption because the aerobic bacteria (P. flourescens) accelerate anodic and cathodic reactions and the anodic oxidation was enhanced by the localized acidity at the anodic sites due to the excretion of organic/inorganic acids by microorganisms [13], therefore, by increasing bacteria exposure time, the amount of organic and inorganic acids will increase.
benefit from the absence of shear. At the other end, a fast moving fluid generates turbulence that provides enhanced mass transfer, but the accompanying high shear stress may be proved to be harmful to the cells and that may lead to the prevention of cell adhesion and thus biofilm formation. A sufficiently high shear stress may even detach an established biofilm [16]. Mild fluid flow offers the most favorable environment for cell adhesion and sessile growth and it likely yields the highest MIC corrosion rate [17]. Furthermore, the mass transfer coefficient can be expressed in terms of the dimensionless Reynolds (Re = ρude/μ), Schmidt (Sc = μ/ρD) and Sherwood (Sh = kdde/D) numbers [18]. Where ρ is the density, u is the linear velocity, de is the equivalent inner tube diameter, and μ is the dynamic viscosity. For single phase flow in a straight pipe, the correlation of Anederko et al. [19] can be used:
0:86
Sh = 0:0165Re
0:33
ð5Þ
Sc
Eq. (5) shows the variation of mass transfer coefficient, kd, with Re. It can be seen that the kd increases with increasing Re, that means the corrosion rate increases with increasing Re and then zinc consumption rate.
3.3. Effect of salt concentration 3.5. Statistical analysis It can be seen from Table 1 that the dissolution rate of zinc increases with increasing NaCl concentration. The increase in the rate of Zn dissolution with increasing NaCl concentration may be attributed to the increase of solution conductivity which raises the corrosion current and the rate of Zn corrosion. The high rates of Zn dissolution observed at 3.5%NaCl concentration are associated with high solution flow rates, these may be ascribed to the increase in solution conductivity [8]. Kuntia et al. [14] mentioned that changing the medium composition by the addition of sodium chloride (0.5% w/v) resulted in a faster decrease in the cell surface hydrophobicity. The formation, growth and reformation after detachment of the membraneattached biofilm were also slower in the presence of sodium chloride, confirming the cell growth studies, and this matches the results in this study.
Statistical analysis can be used to determine the effects of each variable on zinc consumption. One of these analyses is nonlinear regression of the data of Table 1. Second order model can be used to know whether the variables affect zinc consumption individually or if there is an interaction effect. Most of the probabilities can be taken into account, the main effect of each variable and the interaction effect:
Y = Co + C1 X1 + C2 X12 + C3 X1 X2 + C4 X1 X3 + C5 X1 X4 + C6 X2 + C7 X22 + C8 X2 X3 + C9 X2 X4 + C10 X3 + C11 X32 + C12 X3 X4 + C13 X4 +
ð6Þ
C14 X42
3.4. Effect of flow rate Table 1 shows the effect of solution flow rate on the zinc dissolution with time, different temperatures and NaCl concentrations, respectively. It can be seen that the dissolution rate of zinc increases with the increasing of the flow rate. This may be attributed to the decrease in the thickness of hydrodynamic boundary layer and diffusion layer across which dissolved oxygen diffuses to the tube wall of copper according to the following equation [8]:
Where Y is zinc consumption (mg/cm2), X1 is temperature (°C), X2 is flow rate (L/h), X3 is saline water concentration (%), X4 is time (min) and C0–C14 are model coefficients. This equation is used as a first model (model I). The foregoing model can be estimated using Levenberg– Marquardt estimation method. The following equation in the absence of bacteria (Eq. (7)) can be obtained with 0.9935 correlation coefficient: −6
2
Y = 8:32−51734:04X1 −0:000194X1 + 3:77 × 10 J = kd CO2
D = C δd O2
ð4Þ
+ 14781:54X1 X3 −0:00755X1 X4 −6:78 × 10 −7
× 10 Where J is mole flux of oxygen, kd is mass transfer coefficient, D is diffusivity of oxygen in saline water and δd is boundary layer thickness. Then the surface film resistance almost vanishes, oxygen depolarization, the products of corrosion and protective film are continuously swept away and continuous corrosion occurs. The flow rate of saline water may also caused erosion which is combined with electrochemical attack. In the presence of P. flourescens the effect of flow rate is important in bacterial corrosion process because it does not only affect the transfer of species to the metal surface but also influences the overall bacterial adhesion process and the transfer of nutrients to the metal surface [15]. Stagnant fluid offers the lowest mass transfer rates because convective mass transfer does not exist without fluid flow. However, cell adhesion and biofilm formation may
X22
−5
+ 8:21 × 10
−4
−6
X2 X3 + 2:76 × 10
X1 X2
X2 + 3:33
X2 X4 −10:13X3
ð7Þ
−0:015X32 −2463:5X3 X4 + 8622:5X4 + 5:28 × 10−6 X42
The analysis of variance (F-test) was used for testing the significance of each effect in Eq. (10) [20]. The calculations are given in Table 3. An estimate of the variance S2b is obtained by dividing the experimental error variance S2r by the sum of squares of each effect ΣX2, as follows, S2r ∑e2 and γ = N – n is degree of freedom. The where, S2r = S2b = γ ∑X 2 significance of effects may be estimated by comparing the values of the ratio (C2/S2b) with the critical value of the F-distribution at 95% confidence level (F0.95 = 6.61). If the ratio C2/S2b N 6.61 then the effect is significant. Thus, according to the results shown in Table 3, it appears
Table 3 Analysis of variance. Effect
X1 X21 X1 X2 X1 X3 X1 X4 X2 X22 X2 X3 X2 X4 X3 X23 X3 X4 X4 X24
∑ X2
Coefficients, C
3.28 × 1004 2.97 × 1007 7.05 × 1009 3.10 × 1005 9.63 × 1008 1.00 × 1007 2.71 × 1012 1.05 × 1008 2.81 × 1009 4.86 × 1002 5.63 × 1014 1.27 × 1018 1.31 × 1017 4.03 × 1009
C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14
8.32 − 51734.04 −1.94×10−4 3.77 × 10− 6 14781.55 −7.55×10−3 −6.78×10−4 3.33 × 10− 7 8.21 × 10− 5 2.76 × 10− 6 − 10.13 − 0.015 − 2463.5 8622.5 5.28 × 10− 6
Variance S2 S2b = ∑Xr 2
F-value = C2/S2b
F0.95 = 6.61
2.69 × 10− 05 2.97 × 10− 08 1.25 × 10− 10 2.85 × 10− 06 9.16 × 10− 10 8.83 × 10− 08 3.30 × 1001 8.45 × 10− 09 3.14 × 10− 12 1.82 × 10− 03 1.57 × 10− 04 6.95 × 10− 08 6.75 × 10− 07 2.19 × 10− 10
9.95 × 1011 1.28 × 1000 1.10 × 1001 7.67 × 1011 6.23 × 1004 5.21 × 1001 3.41×10− 13 7.90×10− 01 2.43 × 1000 5.65 × 1004 1.44 × 1000 8.73 × 1011 1.11 × 1013 0.13 × 1000
S* NS* NS S S S NS NS NS S NS S S NS
Predicted zinc consumption by model I and II (mg/cm2)
A.S. Yaro et al. / Desalination 270 (2011) 193–198
197
0.40 line equations: MI = 0.0066+0.958*x MII = 0.0231+0.8657*x
0.35 0.30 0.25 0.20 0.15 0.10 0.05
Model I Model II
0.00 -0.05 -0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Observed zinc consumption by experiment (mg/cm2)
*S: significant effect, NS: not significant effect. Fig. 5. Predicted zinc consumption by model II against the experimental one in the presence of bacteria.
that most effects are not significant. The best response function is then conveniently written as follows: Eq. (9) can be rewritten and can be used as a second model (model II): Y = 8:32−51734:04X1 + 14781:54X1 X3 −0:00756X1 X4 −4
−6:78 × 10
X2 −10:135X3 −2463:5X3 X4 + 8622:5X4
ð8Þ
Analysis of variance shows that most of the interaction effects were canceled, and the main effect of each variable was the dominated one. Another model can be suggested to represent the consumption data. This model depends on pervious discussion mentioned earlier. Instead of using a multi-term model (Eq. (6)), a one-term model can be used. A similar model was suggested successfully in our previous research [21] for the corrosion of copper alloy as a function of two variables. In the present work the modified form for zinc consumption as a function of four variables was suggested. It was found that zinc consumption varies exponentially with absolute value of temperature (according to Arrhenius equation), in the same way it is extrusive proportional to time, flow rate and salt concentration, therefore;
Predicted zinc consumption by model I and II (mg/cm2)
1 Zinc consumption ∝ exp ðtimeÞð flow rateÞðsalt conc:Þ temp:
ð9Þ
0.40 0.35 0.30
C1 C2 C3 C4 X X X X1 2 3 4
ð10Þ
This equation can be estimated using the foregoing estimation method producing the following equation with 0.9766, correlation coefficient:
Y = 1:7 × 10
−5
2450 1:24 0:65 1:74 exp − X2 X3 X4 X1
ð11Þ
Although Eq. (11) has lower correlation coefficients, it is easier and practical since it deals with only one term. The coefficient C1 in the model can be compared with the slope of the Arrhenius equation (−E/R). Activation energy value by model II equals to 20.37 kJ/mol, within the range of activation energy which is given in Table 2. Fig. 4 shows the predicted zinc consumption by models I and II against the experimental values. The same models and statistical analysis can be repeated for cases when bacteria are present. Fig. 5 shows the estimated zinc consumption against the experimental one. 4. Conclusion
line equations: MI = 0.0022+0.9805*x MII = 0.0163+0.8957*x
The zinc consumption during cathodic protection of copper pipe which carries saline water increased with the increase of all studied operating conditions. The presence of bacteria increases the zinc consumption. Fourth order multi-term model represents the data with high correlation coefficient. Statistical analysis was a very helpful way to reduce the terms of this model. One-term model was simpler and more practical than the first model. The optimum zinc consumption was at 20 °C, 300 L/h, 3.5% NaCl and 50 min. While maximum zinc consumption was observed at maximum operating conditions (i.e. at 40 °C, 600 L/h, 3.5% NaCl and 180 min). Future work may be needed to find a new solution or treatment to saline water containing bacteria.
0.25 0.20 0.15 0.10 0.05 Model I Model II
0.00 -0.05 -0.05
Y = C0 exp
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Observed zinc consumption by experiment (mg/cm2)
Fig. 4. Predicted zinc consumption by model II against the experimental one in the absence of bacteria.
Acknowledgment This work was supported by Baghdad University, Chemical Engineering Department, which is gratefully acknowledged. Also special thank to Mrs. Areej S. Dawood for her assistance during this study.
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Cathodic protection system of copper–zinc–saline water in presence of bacteria Aprael S. Yaro, Haidar Al-Jendeel, Anees A. Khadom ⁎ Department of Chemical Engineering, College of Engineering, Baghdad University, Aljaderia, 10071, Baghdad Governorate, Iraq
a r t i c l e
i n f o
Article history: Received 4 October 2010 Received in revised form 25 November 2010 Accepted 25 November 2010 Available online 18 December 2010 Keywords: Copper Zinc Weight loss Cathodic protection Microbiological corrosion
a b s t r a c t Rate of zinc consumption during the cathodic protection of copper pipeline which carries saline water was measured by weight loss technique in the absence and presence of bacteria. Variables studied were solution flow rate, temperature, time and NaCl concentration. It was found that within the present range of variables; the rate of zinc consumption increases with the increase of all operating conditions. The presence of bacteria increases the zinc consumption. Fourth order multi-term model and one-term model were suggested to represent the consumption data. Nonlinear regression analysis was used to estimate the coefficients of these models, while statistical analysis was used to determine the effect of each coefficient. Both models were representing the data successfully. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Equipment used in the desalination and cooling systems which uses saline water as a coolant suffers severely from corrosion owing to the presence of the highly aggressive chloride ions in high concentration. These structures are protected by cathodic protection with sacrificial anodes, therefore, hundreds of researches were done in the subject of cathodic protection system with sacrificial anode, but few of them were dealing with the presence of bacteria in these systems. These bacteria may cause a microbiological corrosion (MIC). Microbiological corrosion is the deterioration of materials which is caused directly or indirectly by bacteria, algae, moulds or fungi; singly or in combination. Microbiological corrosion refers to corrosion and the ensuing loss of metal caused by biological organisms. MIC can occur in any aqueous environments and it is a common problem in industrial processes due to the presence of microbes, adequate nutrients and corrosive byproducts [1]. Microorganisms pervade our environment and readily “invade” industrial systems wherever conditions permit. These agents flourish in a wide range of habitats and show a surprising ability to colonize water-rich surfaces wherever nutrients and physical conditions allow. Microbial growth occurs over the whole range of temperatures which are commonly found in water systems, and limited access to nitrogen and phosphorus is offset by a surprising ability to retain trace levels of these essential nutrients. A significant feature of microbial problems is that they can appear suddenly when conditions allow exponential growth of the organisms. Many
⁎ Corresponding author. Tel.: +964 790 2305786 (mobile). E-mail address: [email protected] (A.A. Khadom). 0011-9164/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2010.11.045
engineers continue to be surprised that such small organisms can lead to spectacular failures of large engineering systems [2]. A number of metals, such as structural steels, copper alloys etc., tend to corrode generally over the entire surface in the absence of crevices or galvanic effects. In such cases, corrosion is determined by the rate at which dissolved oxygen can be delivered to the metal surface. Biological organisms present in the aqueous medium often have the potential to increase or decrease oxygen transport to the surface; consequently, these organisms have a role in increasing or decreasing the general corrosion. Most MIC, however, manifests as localized corrosion because most organisms do not form in a continuous film on the metal surface. Microscopic organisms also tend to settle on metal surfaces in the form of discrete colonies or at least spotty, rather than continuous films. Biological organisms fall under two groups based on the type of corrosion they engender: (a) anaerobic corrosion that produces highly corrosive species as a part of their metabolism, and (b) aerobic corrosion that produces corrosive mineral acids. Sulfate reducing bacteria (SRB) from the genera desulfovibrio are a typical example of anaerobic MIC. Aerobic sulfur oxidizing bacteria of the type thiobacillus can create an environment of up to 10% sulfuric acid, thereby encouraging rapid corrosion [3]. The main use of seawater is for cooling purposes, but it is also used for Firefighting, oilfield water injection, and desalination plants [1]. Pseudomonas bacteria are now being found in these water systems in many parts of the country with maximum activity at pH 7.5–8.5 [4–6]. Until the last couple of years bacteria in these types of systems were of little concern and not often investigated. Now bacteria known as Pseudomonas have started to appear in main water supplies, where it has no significant health concerns, but can have a major effect on the water systems in commercial buildings. Pseudomonas is a biofilm or slime-producing bacteria and
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when left to proliferate can cause severe corrosion and blockages within the pipe work. This particularly affects modern buildings with smallbore pipe work and small orifices associated with control valves [7]. The biofilm can reduce the water flow and provide a habitat for other corrosion inducing bacteria that will lead to pitting and leaking of the pipe work. The net result of Pseudomonas in heating and chilled water systems is a decrease in their efficiency and increase down time and costs from repairing leaks. In this study experimental measurements were conducted on zinc electrode as sacrificial anode for cathodic protection of copper pipeline carrying saline seawater in the presence and absence of bacteria named scientifically as (Pseudomonas flourescens) was measured by weight loss technique. 2. Materials and methods Experimental work of sacrificial anode system was carried out to determine the consumption rate of zinc in cathodic protection using weight loss for various conditions of temperature (10–40 °C), flow rate (300–600 L/h), pH (8) , time (1–3 h), and NaCl (1–3.5%) in the presence and absence of bacteria (P. flourescens). 2.1. Electrodes Working electrode was a tube specimen of pure copper with dimensions of 30 cm length, 2 cm inside diameter and 0.2 cm thickness. While the anode electrode was zinc strip with dimensions of 30 cm length, 0.4 cm width and 0.08 cm thickness. These electrodes were cleaned by washing with hot water followed by distilled water. Specimens were abraded using emery paper grade 600, washed with water followed by distilled water. After each run, the zinc strip was rinsed in distal water, dried and reweighed [8]. 2.2. Preparation of culture media Pure culture of P. flourescens which were used in the experiments has been supplied by the Department of Biotechnology-Baghdad University. They were isolated from soil. P. flourescens were activated on nutrient agar at 32 °C overnight. Cells were harvested from cultures then inoculated into nutrient broth containing 0.5% peptic digest of animal tissue, 0.15% beef extract, 0.15% yeast extract and 0.5% sodium chloride dissolved in distilled water (pH 8) and incubated at 32 °C with rotary shaker (120 rpm) for 6 h [9,10].
2.3. Experimental procedure The apparatus shown in Fig. 1 was used to study the effect of the variables on the sacrificial anode cathodic protection system. In the absence of bacteria and before each run, the zinc strip was weighed and fixed at the inlet of the copper by rubber stopper and was electrically connected by an insulated copper wire to the copper tube outlet. The zinc strip is extending along the copper tube to ensure uniform current and potential distribution along the tube wall. After each run the zinc strip and copper pipe were rinsed in distilled water and brushed softly to remove the corrosion products, dried with clean tissue then immersed in Chloroxylenol, dried again, and then reweighted to determine the weight loss. The same procedure was repeated in the presence of bacteria, the bacterial cells were grown in nutrient broth for 6 h at 32 °C in a rotary shaker (120 rpm) then the absorbance of this broth was set to an A600 of O.D 0.15(243 × 107 bacteria/cm³) [9,10]. 2.4. Effect of cell concentration The bacterial inoculums prepared as mentioned in item 2.3 was used after determining the absorbance at 600 nm (A600). In order to study the effect of bacterial cell concentration the absorbance of the test solution was set to an A600 of 0.5, 0.15 and 0.05 (optical density) by using visible spectrophotometer. Viable counts were determined by serial dilution of cultures with normal saline (0.85%) and plating on nutrient agar. The three zinc strips were weighted and immersed in nutrient broth inoculated with bacterial suspensions of O.D 0.5, 0.15 and 0.05 respectively and then incubated overnight at 32 °C in a rotary shaker (120 rpm). Then the corrosion rates were measured by weighting the zinc strips after incubation. It was found that O.D. 0.5 gave the higher corrosion rate. Therefore, the whole tests have been carried out at this bacterial concentration with mixing ratio of 243 × 1010 bacteria to 1 L saline water. 3. Results and discussion Table 1 shows the rate of zinc consumption in the absence and presence of bacteria at different conditions. The data are distributed in this table and arranged in three sections. In Section I, at constant temperature (20 °C) and constant saline water concentration (3.5%), the zinc consumption increases with the increasing of time and flow rate. In Section II, at constant time (180 min) and constant saline water
Fig. 1. Schematic diagram of apparatus used in sacrificial anode test system.
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Temp. Flow rate NaCl Time Zinc consumption (mg/cm2) (°C) (L/h) (wt.%) (min) Bacteria absence Bacteria presence 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 Section II 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40 Section III 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
300 300 300 300 400 400 400 400 500 500 500 500 600 600 600 600 300 400 500 600 300 400 500 600 300 400 500 600 300 400 500 600 300 300 300 300 400 400 400 400 500 500 500 500 600 600 600 600
3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 1.0 2.0 2.5 3.5 1.0 2.0 2.5 3.5 1.0 2.0 2.5 3.5 1.0 2.0 2.5 3.5
50 100 150 180 50 100 150 180 50 100 150 180 50 100 150 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180
0.0016 0.0095 0.064 0.0918 0.0042 0.0265 0.0769 0.1172 0.0122 0.0626 0.1066 0.1814 0.0340 0.1008 0.1809 0.2515 0.0303 0.0547 0.0801 0.1252 0.0918 0.1172 0.1814 0.2515 0.1507 0.2021 0.2456 0.3077 0.1640 0.2170 0.2462 0.3343 0.0239 0.0865 0.1135 0.1507 0.0668 0.1496 0.1655 0.2021 0.0875 0.1714 0.2175 0.2456 0.104 0.2074 0.2706 0.3077
0.0021 0.0244 0.0753 0.1289 0.0058 0.0387 0.0849 0.1332 0.0143 0.0722 0.1332 0.2101 0.0389 0.1130 0.1931 0.2684 0.0669 0.0722 0.1130 0.1364 0.1289 0.1332 0.2101 0.2684 0.2048 0.2462 0.2849 0.3406 0.1656 0.2191 0.2483 0.3412 0.0891 0.1581 0.1798 0.2048 0.1167 0.1979 0.2143 0.2462 0.1305 0.2133 0.2589 0.2849 0.1395 0.2435 0.3050 0.3406
ln (zinc consumption rate) (mg/min.cm2)
-6.0
Table 1 Zinc consumption in sacrificial anode in the absence and presence of bacteria.
Section I
195
-6.2 -6.4 -6.6 -6.8 -7.0 -7.2 -7.4 -7.6 -7.8 -8.0
300 L/h 400 500 600
-8.2 -8.4
-8.6 0.00315 0.00320 0.00325 0.00330 0.00335 0.00340 0.00345 0.00350 0.00355
1/T (1/K) Fig. 2. Arrhenius plots for zinc consumption at different flow rate in the absence of bacteria.
3.1. Effect of temperature The increase in the rate of zinc dissolution with increasing saline water temperature may be due to several reasons; increasing saline water temperature leads to decreasing saline water viscosity with a consequent increase in oxygen diffusivity, which leads to increase the rate of mass transfer of dissolved oxygen to the cathode surface, then increasing the zinc consumption [8]. On the other hand, the decrease in saline water viscosity with increasing temperature improves the saline water conductivity with a consequent increase in corrosion current and the rate of corrosion. Another effect of temperature is that it increases the reaction rate according to Arrhenius equation [12]: −E= RT
ð3Þ
Rate = Ae
where A is frequency factor, E is activation energy, R is universal gas constant and T is absolute temperature. Figs. 2 and 3, show the Arrhenius plots of the rate of zinc consumption against reciprocal of absolute temperature. These figures were plotted as ln (zinc consumption rate) against 1/T with slope equal to −E/R, from which the values of activation energy were obtained. Table 2 shows that activation energy decreases as flow rate increases, and these values were lower in the presence of bacteria. This behavior indicates that zinc consumption reaction needs lower energy to occur.
concentration (3.5%), the variation of temperature and flow rate increases the zinc consumption. While in Section III, at constant time (180 min) and constant temperature (30 °C), both flow rate and saline water concentration lead to the increase of zinc consumption. The same behavior was observed in the presence of bacteria with more consumption of zinc. For the present system the electrochemical cell responsible for cathodic protection is Zn/NaCl/Cu. The anodic reaction is [11]: +2
Zn → Zn
ð1Þ
+ 2e
And the cathodic reaction which is an O2 reduction towards the wall of the copper pipe is assumed to predominate. O2 + 2H2 O + 4e → 4OH
−
ð2Þ
ln (zinc consumption rate) (mg/min.cm2)
-6.0 -6.2 -6.4 -6.6 -6.8 -7.0 -7.2 -7.4 -7.6
300 L/h 400 500 600
-7.8 0.00315 0.00320 0.00325 0.00330 0.00335 0.00340 0.00345 0.00350 0.00355
1/T (1/K) Fig. 3. Arrhenius plots for zinc consumption at different flow rates in the presence of bacteria.
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Table 2 Activation energy of zinc consumption at different flow rates 3.5% saline water and 180 min. Flow rate (L/h)
300
400
500
600
Eabsence (kJ/mol) Epresence (kJ/mol)
41.7 29.4
34.8 23.6
27.6 22.3
23.5 19.8
3.2. Effect of time Table 1 shows that the rate of zinc consumption (dissolution) increases with the increase of time and this is a normal case because of the erosion–corrosion which accelerates the rate of deterioration of a metal resulting from relative movement between the corrosive fluid and the metal surface. On the other hand, the presence of P. flourescens increases the rate of zinc consumption because the aerobic bacteria (P. flourescens) accelerate anodic and cathodic reactions and the anodic oxidation was enhanced by the localized acidity at the anodic sites due to the excretion of organic/inorganic acids by microorganisms [13], therefore, by increasing bacteria exposure time, the amount of organic and inorganic acids will increase.
benefit from the absence of shear. At the other end, a fast moving fluid generates turbulence that provides enhanced mass transfer, but the accompanying high shear stress may be proved to be harmful to the cells and that may lead to the prevention of cell adhesion and thus biofilm formation. A sufficiently high shear stress may even detach an established biofilm [16]. Mild fluid flow offers the most favorable environment for cell adhesion and sessile growth and it likely yields the highest MIC corrosion rate [17]. Furthermore, the mass transfer coefficient can be expressed in terms of the dimensionless Reynolds (Re = ρude/μ), Schmidt (Sc = μ/ρD) and Sherwood (Sh = kdde/D) numbers [18]. Where ρ is the density, u is the linear velocity, de is the equivalent inner tube diameter, and μ is the dynamic viscosity. For single phase flow in a straight pipe, the correlation of Anederko et al. [19] can be used:
0:86
Sh = 0:0165Re
0:33
ð5Þ
Sc
Eq. (5) shows the variation of mass transfer coefficient, kd, with Re. It can be seen that the kd increases with increasing Re, that means the corrosion rate increases with increasing Re and then zinc consumption rate.
3.3. Effect of salt concentration 3.5. Statistical analysis It can be seen from Table 1 that the dissolution rate of zinc increases with increasing NaCl concentration. The increase in the rate of Zn dissolution with increasing NaCl concentration may be attributed to the increase of solution conductivity which raises the corrosion current and the rate of Zn corrosion. The high rates of Zn dissolution observed at 3.5%NaCl concentration are associated with high solution flow rates, these may be ascribed to the increase in solution conductivity [8]. Kuntia et al. [14] mentioned that changing the medium composition by the addition of sodium chloride (0.5% w/v) resulted in a faster decrease in the cell surface hydrophobicity. The formation, growth and reformation after detachment of the membraneattached biofilm were also slower in the presence of sodium chloride, confirming the cell growth studies, and this matches the results in this study.
Statistical analysis can be used to determine the effects of each variable on zinc consumption. One of these analyses is nonlinear regression of the data of Table 1. Second order model can be used to know whether the variables affect zinc consumption individually or if there is an interaction effect. Most of the probabilities can be taken into account, the main effect of each variable and the interaction effect:
Y = Co + C1 X1 + C2 X12 + C3 X1 X2 + C4 X1 X3 + C5 X1 X4 + C6 X2 + C7 X22 + C8 X2 X3 + C9 X2 X4 + C10 X3 + C11 X32 + C12 X3 X4 + C13 X4 +
ð6Þ
C14 X42
3.4. Effect of flow rate Table 1 shows the effect of solution flow rate on the zinc dissolution with time, different temperatures and NaCl concentrations, respectively. It can be seen that the dissolution rate of zinc increases with the increasing of the flow rate. This may be attributed to the decrease in the thickness of hydrodynamic boundary layer and diffusion layer across which dissolved oxygen diffuses to the tube wall of copper according to the following equation [8]:
Where Y is zinc consumption (mg/cm2), X1 is temperature (°C), X2 is flow rate (L/h), X3 is saline water concentration (%), X4 is time (min) and C0–C14 are model coefficients. This equation is used as a first model (model I). The foregoing model can be estimated using Levenberg– Marquardt estimation method. The following equation in the absence of bacteria (Eq. (7)) can be obtained with 0.9935 correlation coefficient: −6
2
Y = 8:32−51734:04X1 −0:000194X1 + 3:77 × 10 J = kd CO2
D = C δd O2
ð4Þ
+ 14781:54X1 X3 −0:00755X1 X4 −6:78 × 10 −7
× 10 Where J is mole flux of oxygen, kd is mass transfer coefficient, D is diffusivity of oxygen in saline water and δd is boundary layer thickness. Then the surface film resistance almost vanishes, oxygen depolarization, the products of corrosion and protective film are continuously swept away and continuous corrosion occurs. The flow rate of saline water may also caused erosion which is combined with electrochemical attack. In the presence of P. flourescens the effect of flow rate is important in bacterial corrosion process because it does not only affect the transfer of species to the metal surface but also influences the overall bacterial adhesion process and the transfer of nutrients to the metal surface [15]. Stagnant fluid offers the lowest mass transfer rates because convective mass transfer does not exist without fluid flow. However, cell adhesion and biofilm formation may
X22
−5
+ 8:21 × 10
−4
−6
X2 X3 + 2:76 × 10
X1 X2
X2 + 3:33
X2 X4 −10:13X3
ð7Þ
−0:015X32 −2463:5X3 X4 + 8622:5X4 + 5:28 × 10−6 X42
The analysis of variance (F-test) was used for testing the significance of each effect in Eq. (10) [20]. The calculations are given in Table 3. An estimate of the variance S2b is obtained by dividing the experimental error variance S2r by the sum of squares of each effect ΣX2, as follows, S2r ∑e2 and γ = N – n is degree of freedom. The where, S2r = S2b = γ ∑X 2 significance of effects may be estimated by comparing the values of the ratio (C2/S2b) with the critical value of the F-distribution at 95% confidence level (F0.95 = 6.61). If the ratio C2/S2b N 6.61 then the effect is significant. Thus, according to the results shown in Table 3, it appears
Table 3 Analysis of variance. Effect
X1 X21 X1 X2 X1 X3 X1 X4 X2 X22 X2 X3 X2 X4 X3 X23 X3 X4 X4 X24
∑ X2
Coefficients, C
3.28 × 1004 2.97 × 1007 7.05 × 1009 3.10 × 1005 9.63 × 1008 1.00 × 1007 2.71 × 1012 1.05 × 1008 2.81 × 1009 4.86 × 1002 5.63 × 1014 1.27 × 1018 1.31 × 1017 4.03 × 1009
C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14
8.32 − 51734.04 −1.94×10−4 3.77 × 10− 6 14781.55 −7.55×10−3 −6.78×10−4 3.33 × 10− 7 8.21 × 10− 5 2.76 × 10− 6 − 10.13 − 0.015 − 2463.5 8622.5 5.28 × 10− 6
Variance S2 S2b = ∑Xr 2
F-value = C2/S2b
F0.95 = 6.61
2.69 × 10− 05 2.97 × 10− 08 1.25 × 10− 10 2.85 × 10− 06 9.16 × 10− 10 8.83 × 10− 08 3.30 × 1001 8.45 × 10− 09 3.14 × 10− 12 1.82 × 10− 03 1.57 × 10− 04 6.95 × 10− 08 6.75 × 10− 07 2.19 × 10− 10
9.95 × 1011 1.28 × 1000 1.10 × 1001 7.67 × 1011 6.23 × 1004 5.21 × 1001 3.41×10− 13 7.90×10− 01 2.43 × 1000 5.65 × 1004 1.44 × 1000 8.73 × 1011 1.11 × 1013 0.13 × 1000
S* NS* NS S S S NS NS NS S NS S S NS
Predicted zinc consumption by model I and II (mg/cm2)
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197
0.40 line equations: MI = 0.0066+0.958*x MII = 0.0231+0.8657*x
0.35 0.30 0.25 0.20 0.15 0.10 0.05
Model I Model II
0.00 -0.05 -0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Observed zinc consumption by experiment (mg/cm2)
*S: significant effect, NS: not significant effect. Fig. 5. Predicted zinc consumption by model II against the experimental one in the presence of bacteria.
that most effects are not significant. The best response function is then conveniently written as follows: Eq. (9) can be rewritten and can be used as a second model (model II): Y = 8:32−51734:04X1 + 14781:54X1 X3 −0:00756X1 X4 −4
−6:78 × 10
X2 −10:135X3 −2463:5X3 X4 + 8622:5X4
ð8Þ
Analysis of variance shows that most of the interaction effects were canceled, and the main effect of each variable was the dominated one. Another model can be suggested to represent the consumption data. This model depends on pervious discussion mentioned earlier. Instead of using a multi-term model (Eq. (6)), a one-term model can be used. A similar model was suggested successfully in our previous research [21] for the corrosion of copper alloy as a function of two variables. In the present work the modified form for zinc consumption as a function of four variables was suggested. It was found that zinc consumption varies exponentially with absolute value of temperature (according to Arrhenius equation), in the same way it is extrusive proportional to time, flow rate and salt concentration, therefore;
Predicted zinc consumption by model I and II (mg/cm2)
1 Zinc consumption ∝ exp ðtimeÞð flow rateÞðsalt conc:Þ temp:
ð9Þ
0.40 0.35 0.30
C1 C2 C3 C4 X X X X1 2 3 4
ð10Þ
This equation can be estimated using the foregoing estimation method producing the following equation with 0.9766, correlation coefficient:
Y = 1:7 × 10
−5
2450 1:24 0:65 1:74 exp − X2 X3 X4 X1
ð11Þ
Although Eq. (11) has lower correlation coefficients, it is easier and practical since it deals with only one term. The coefficient C1 in the model can be compared with the slope of the Arrhenius equation (−E/R). Activation energy value by model II equals to 20.37 kJ/mol, within the range of activation energy which is given in Table 2. Fig. 4 shows the predicted zinc consumption by models I and II against the experimental values. The same models and statistical analysis can be repeated for cases when bacteria are present. Fig. 5 shows the estimated zinc consumption against the experimental one. 4. Conclusion
line equations: MI = 0.0022+0.9805*x MII = 0.0163+0.8957*x
The zinc consumption during cathodic protection of copper pipe which carries saline water increased with the increase of all studied operating conditions. The presence of bacteria increases the zinc consumption. Fourth order multi-term model represents the data with high correlation coefficient. Statistical analysis was a very helpful way to reduce the terms of this model. One-term model was simpler and more practical than the first model. The optimum zinc consumption was at 20 °C, 300 L/h, 3.5% NaCl and 50 min. While maximum zinc consumption was observed at maximum operating conditions (i.e. at 40 °C, 600 L/h, 3.5% NaCl and 180 min). Future work may be needed to find a new solution or treatment to saline water containing bacteria.
0.25 0.20 0.15 0.10 0.05 Model I Model II
0.00 -0.05 -0.05
Y = C0 exp
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Observed zinc consumption by experiment (mg/cm2)
Fig. 4. Predicted zinc consumption by model II against the experimental one in the absence of bacteria.
Acknowledgment This work was supported by Baghdad University, Chemical Engineering Department, which is gratefully acknowledged. Also special thank to Mrs. Areej S. Dawood for her assistance during this study.
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