Predictability of Al-Mn Alloy Exposure Time Based on Its As-Cast Weight and Corrosion Rate in Sea Water Environment

This paper presents the predictability of aluminium-manganese alloy exposure time based on its as-cast weight and corrosion rate in sea water environment. The validity of the derived model: 26.67 0.55 0.29       is rooted on the core expression: 0.0375 0.0206 0.0109       where both sides of the expression are correspondingly approximately equal. Statistical analysis of model-predicted and experimentally evaluated exposure time for each value of as-cast weight and alloy corrosion rate considered shows a standard error of 0.0017% & 0.0044% and 0.0140% & 0.0150% respectively. The depths of corrosion penetration (at increasing corrosion rate: 0.0104 0.0157 mm/yr) as predicted by derived model and obtained from experiment are 0.7208 × 10 & 1.0123 × 10 mm and 2.5460 × 10 & 1.8240 × 10 mm (at decreasing corrosion rate: 0.0157 0.0062 mm/yr) respectively. Deviational analysis indicates that the maximum deviation of the model-predicted alloy exposure time from the corresponding experimental value is less than 10%.


Introduction
The service performance of metals (or alloy), irrespective of the exposure environment is largely affected by their physical and mechanical properties such as hardness, weldability, toughness, malleability, ductility, resistance to fatique etc.It is therefore vital to consider these and other basic properties of metals or alloys when proposing their application for fabrication and other engineering purposes.
Researchers [1] have suggested the need to know the specific corrosion rates of different metals and alloys in different application environment in order to know the materials that can withstand outdoor structural applications.
The stability of metals or alloys in an aggressive environment has been reported [2] to basically depend on the protective properties of organic or inorganic films as well as on the layer of corrosion products.The scientists concluded that the ability of films to act as controlling barriers against different kinds of corrosion attack is dependent on film properties such as chemical composition, adhesion, conductivity, solubility, morphology and hygroscopicity.Several researchers [1,3] reported that the highlighted characteristic of films in turn depends on environmental variables such as atmospheric conditions, type and amount of pollutants as well as wet-dry cycle, the chemical composition and metallurgical history of the metals or alloys and physicochemical properties of coating.
Malfunctioning of engineering structures and equipment due to corrosion has been reported [4] to stem from tragic carelessness in plumbing, equipment manufacture and installation, with possibility of explosion, fire and spread of toxic materials in living environment.This is accompanied by some costs such as replacement of corroded equipment, disturbance in processes due to equip-ment corrosion, shutdown of plants due to replacement of corroded equipment, impurity in processed products due to corrosion as well as waste of the products of those vessels which are attacked by corrosion.The report indicates that about 70 percent of losses can be prevented by observing related principles and instructions.
One of the main problems in oil and gas industries is corrosion of pipelines and other engineering structures.This has always resulted in huge economic setback due to large sum of money spent in trying to combat it.Based on the forgoing, there is a great need to develop engineering materials that are corrosion resistant to avoid abrupt failure of the engineering structures.
Recently, the corrosion characteristics of selected ferrous metal samples (plain and alloyed ductile iron, low carbon steel and austenitic stainless steel) in crude oil were investigated by using weight loss method [5].Studies carried out during this work show that all the materials experience gain in weight within the first 10 days in the medium.This weight gain is attributed to the formation of hard and passive phases which acted as strong protective barriers to corrosion.It was also observed that the rate of corrosion decreased with increase in the number of days of exposure for all the coupons, this may be probably due to the deposition of corrosion products that tend to shield the corroding surface from further corrosion attack, thereby depressing the rate of corrosion.This result shows that despite of initial low corrosion resistance of plain ductile iron, it can still be considered, alongside other materials, for application in pipelines and storage facilities for crude oil.
Studies [6] on the corrosion behaviour of carbon steel under natural and stagnant seawater conditions have showed that the alloy is more corrosive in anaerobic stagnant sea-water conditions than that in aerobic conditions.The study also revealed that in both aerobic and anaerobic exposures, corrosion was more aggressive on horizontally oriented coupons compared to vertically oriented samples.
The corrosion behaviour of low carbon steel has also been investigated [7] in natural seawater and various synthetic seawaters.It was found that the steel corroded nearly four times faster in a 3.5% NaCl solution than in natural seawater for an exposure time of 21 days.The corrosion rate after immersion in synthetic seawaters was found to be similar to the corrosion rate after immersion in natural seawater.Calcium carbonate (aragonite) deposits were found on the surface of the steel after immersion in natural seawater and the synthetic seawaters.Some magnesium-containing deposits were also found after immersion in the natural seawater.These deposits act as a barrier against oxygen diffusion and thereby lower the corrosion rate.The morphology of the calcium carbonate deposits that formed during immersion in the natural seawater was found to be different from those formed during immersion in the solution.
It has been shown [8] that MnAl 6 formed from Al and Mn has almost the same electrode potential as aluminium and this compound is capable of dissolving iron which reduces the detrimental effect of Mn.Commercial Al-Mn alloys contains up to 1.25% manganese although the maximum solid solubility of this element in aluminium is as high as 1.82%.This limitation was imposed because the presence of iron as impurity reduces the solubility and there is a danger that large primary particles of MnAl 6 will form with a disastrous effect on local ductility.
Polmear [8] reported that Al-Mn alloys belong to the 3xxx series of alloys which are used for the manufacture of roofing sheets.These sheets are subject to corrosion because of the presence of moisture and oxygen in the atmosphere.The corrosion of this alloy is due to the strong affinity aluminium has for oxygen which results to its oxidation and subsequent formation of oxide film.Ekuma et al. [9] reported that with time, this film becomes passive to further oxidation and stable in aqueous media when the pH is between 4.0 and 8.5.It is important to state that the passive films can break and fall off, hence exposing the surface of the alloy to further corrosion.
Studies [4] on corrosion management indicate that it offers preventive strategies in two technical and nontechnical domains.Technical domains as preventive strategies are highly important.These includes: 1) Upgrading planning methods and using advanced planning ones to better corrosion management and so prevent avoidable corrosion costs.In this vein, planning methods must change and the best corrosion technologies must be available for planners.2) Improving corrosion technologies via research and development.Corrosion can be controlled in most industries by using scientific methods and new technological achievements.
Non-technical domain as preventive strategies includes: 1) Enhancing the employees' awareness about the high costs of corrosion and saving costs result in correct application of existing technologies and corrosion costs.Thus a lot of corrosion problems are due to lack of awareness about corrosion management and accountability of people in exchanging operations, inspection and maintenance of management system.2) Changing guidelines, protocols, standards and management methods to reduce corrosion costs by correct corrosion management, resulting in effective control of corrosion and safe operation and increase in shelf life of equipment.3) Amending and generalization of employees' instruction to introduce and identify corrosion control.4) Changing and amending wrong belief about not being able to do anything about corrosion and making new decisions in pre-venting this phenomenon.
The aim of this work is to ascertain the predictability of aluminium-manganese alloy exposure time based on its as-cast weight and corrosion rate in sea water environment.The model to be derived is expected to evaluate and predict directly the exact time (exposure time) at which the Al-Mn alloy should be exposed in the sea water environment putting into consideration its as-cast weight (alloy initial weight before corrosion) and corrosion rate in such environment.The essence of this work is to determine the exact exposure time for a weighed Al-Mn alloy whose corrosion rate in the sea water environment is already known.This rules out exposure of the alloy to the corrosive environment longer than necessary; a situation that could result to very disastrous, undue corrosion penetration on the alloy and invariably, failure.The success of this work would eventually reduce abrupt failure of Al-Mn alloy in sea water environment due to over exposure.

Materials and Methods
Materials used for this work are aluminium of 96% purity and pure granulated manganese.Details of the experimental procedure and associated process conditions are as stated in the previous report [10].

Boundary and Initial Conditions
Consider solid Al-Mn alloy exposed to sea water environment and interacting with some corrosion-induced agents.The sea water is assumed to be affected by unwanted dissolved gases.Range of exposed time considered: 0.0384 -0.0767 yrs (336 -672 hrs).Initial weight range considered: 0.0121 -0.0137 kg (12.0754 -13.7434 g).Purity of aluminium used: 96%.Concentration of manganese addition: 4%.Details of experiment and other process conditions are as stated in the experimental technique [10].
The boundary conditions are: aerobic environment to enhance Al-Mn alloy oxidation (since the sea water contains oxygen).At the bottom of the exposed alloy, a zero gradient for the gas scalar are assumed.The exposed alloy is stationary.The sides of the solid are taken to be symmetries.

Results and Discussions
The derived model is Equation (4).Computational analysis of Table 1 gave rise to Tables 2 and 3.The derived model is two-factorial in nature because it is a constituent of two input process factors: as-cast weight (initial alloy weight) and corrosion rate.This implies that the predicted exposure time for the Al-Mn alloy in sea water environment is dependent on just two factors: as-cast weight and corrosion rate of the alloy.

Model Validation
The validity of the model is strongly rooted on Equation (2) (core model equation) where both sides of the equation are correspondingly approximately equal.Table 2 also agrees with Equation (2) following the values of 0.0375α and γ + 0.0206β -0.0109 evaluated from the experimental results in Table 1.Furthermore, the derived model was validated by comparing the exposure time predicted by the model and that obtained from the experiment [10].This was done using various analytical techniques.

Computational Analysis
Computational analysis of the experimental and modelpredicted exposure time was carried out to ascertain the degree of validity of the derived model.This was done by comparing the depth of corrosion penetration obtained by calculations involving experimental results, and predicted directly by the model.The depth of corrosion penetration for Al-Mn alloy during the period of exposure in the sea water environment C D (mm) was calculated from the equation; Δβ = Change in the corrosion rates β 2 , β 1 within a range of exposure time: α 1 -α 2 .Δα = Change in the alloy exposure time α 2 , α 1 .
On other hand, substituting model-predicted results of points (0.0520, 0.0157) and (0.0788, 0.0062) for (α 1 , β 1 ) and (α 2 , β 2 ) respectively, during decreasing corrosion rate (as in Figure 2) into Equation (5) gives −2.5460 × 10 −4 mm.The negative signs preceding the magnitudes of the depth of corrosion penetration do not indicate that the depth of the penetration is negative, but that the corrosion penetration occurred when the alloy corrosion rate is decreasing and so are discarded.Based on the foregoing, the depths of corrosion penetration during the period corrosion rate was decreasing as obtained from experiments [10] and derived model are 1.8240 × 10 −4 and 2.5460 × 10 −4 mm respectively.

Statistical Analysis
Statistical analysis of model-predicted and experimentally evaluated exposure time for each value of as-cast weight and alloy corrosion rate considered shows a standard error (STEYX) of 0.0017% & 0.0044% and 0.0140% & 0.0150% respectively.The standard error was evaluated using a Microsoft Excel [12].Furthermore, as a way validating the derived model, regression model (highlighted from [12]) was used to predict the corresponding exposure time for the values of as-cast weight and corrosion rate considered, and the results are shown in Figures 3 and 4. On the other hand, the standard error in predicting the exposure time for each value of corrosion rate considered is 0.0119%.
The correlations between exposure time and as-cast weight as well as exposure time and corrosion rate as obtained from derived model, regression model and experimental results [10] were calculated.This was done by considering the coefficients of determination R 2 from Figures 1-6, using the equation: The evaluated correlations are shown in Tables 4 and  5.The model was also validated by comparing its results of evaluated correlations between exposure time and ascast weight as well as exposure time and corrosion rate with that evaluated using experimental and regression model-predicted results.Tables 4 and 5 show that the correlation results from experiment, derived model (D-MoD) and R-MoD are in proximate agreement.

Graphical Analysis
Results predicted by the regression model were plotted;   Comparative analysis of expo ment [10] and derived model revealed deviations on the part of the model-predicted values relative to values obtained from the experiment.This is attributed to the fact that the surface properties of the alloy and the physiochemical interaction between the alloy and corrosion induced agents (in the sea water) were not considered during the model formulation.This necessitated the introduction of correction factor, to bring the model-predicted corrosion rate to those of the corresponding experimental values.

Deviation (Dn) of modelth
the experiment [10] is given by -100 Correction factor (Cr) is the negative i.e.Figures 11 and 12 show that the maximum deviation of the mode-predicted exposure time from onding experimental values is less than 10% and quite within the acceptable deviation limit of experimental results.These figures show that least and highest magnitudes of deviation of the model-predicted exposure time (from the corresponding experimental values) are 0% and −9.57% which corresponds to exposure times: 0.0384 and 0.0520 yr, alloy as-cast weight; 0.0121 and 0.0125 kg and alloy corrosion rates; 0.0104 and 0.0157 mm/yr respectively.
Comparative analysis of Figures 11-14 indicates that the orientation site that of the deviation of model-predicted exposure time (Figures 11 and 12).This is because correction factor is the negative of the deviation as shown in Equations ( 8) and (19).It is believed that the correction factor takes care of the effects of the surface properties of the alloy which were not considered during the model formulation.to exposure times: 0.0384 and 0.0520 yr, alloy Aluminium-manganese alloy exposure time was evalubased on its as-cast weight and cor-ct predicted exposure time are 0 and +9.57% which corresponds as-cast weight; 0.0121 and 0.0125 kg and alloy corrosion rates; 0.0104 and 0.0157 mm/yr respectively.It is important to state that the deviation of model predicted results from that of the experiment is just the magnitude of the value.The associated sign preceding the value signifies that the deviation is deficit (negative sign) or surplus (positive sign).

Figure 1 .Figure 2 .
Figure 1.Coefficient of determination between alloy exposure time and its corrosion rate as obtained from the experiment [10].

Figure 3 .Figure 4 .Figure 5 .Figure 6 .
Figure 3. Coefficient of determination between alloy exposure time and its as-cast weight as predicted by regression model.
ET AL.  312    Comparative graphical analysis of Figures7 and 8

3. 5 .
Deviational Analysis sure time from the experi-shows very close alignment of the curves from derived model and experiment.Figures 9 and 10 also indicate a close alignment of curves from derived model (MoD), regression model (R-MoD) predicted results as well as experimental (ExD).

Figure 7 .Figure 8 .Figure 9 .Figure 10 .
Figure 7.Comparison of the alloy exposure time (relative to its as-cast weight) as obtained from experiment [10] and derived model.
where: P CR = Model-predicted exposure ti y the corre-me (yr); E CR = Exposure time obtained from experiment [10] (yr); Cr = Correction factor (%); Dn = Deviation (%).Introduction of the corresponding values of Cr from Equation (9) into the model gives exactl sp the corresp of the curve in Figures 13 and 14 is oppo onding experimental corrosion rate.

Figure 11 .Figure 12 .Figure 13 .Figure 14 .
Figure 11.Variation of model-predicted alloy exposure time (relative to its as-cast weight) with its associated devi ation from experimental values.
ated and predicted rosion rate in sea water environment.The validity of the derived model was rooted on the core expression: of the expression are correspondingly approximately equal.Statistical analysis of model-predicted and experimentally evaluated exposure time for each value of as-cast weight and alloy corrosion rate considered shows a standard error of 0.0017% & 0.0044% and 0.0140% & [1] C. E. Ekuma and N. E. Idenyi, "Statistical Analysis of the Influence of tion of Corrosion from Its Param of Physics, Vol. 1, 0.0150% respectively.The depths of corrosion penetration (at increasing corrosion rate: 0.0104 -0.0157 mm/yr) as predicted by derived model and obtained from experiment are 0.7208 × 10 −4 & 1.0123 × 10 −4 mm and 2.5460 × 10 −4 & 1.8240 × 10 −4 mm (at decreasing corrosion rate: 0.0157 -0.0062 mm/yr) respectively.Deviational analysis indicates that the maximum deviation of the model-predicted alloy exposure time from the corresponding experimental value is less than 10%.

Table 1 ,
gave rise to Table 2 which indicate that: