undergraduate research thesis

School of Chemical Engineering

CHEMENG 4054 Research Project

A New Risk Assessment for Microbiologically Influenced Corrosion of

Metals

Connor Skoss

Principal supervisor: Kenneth Davey

Co-supervisor: Samuel D. Collins

School of Chemical Engineering, University of Adelaide, Adelaide, SA 5005

Abstract

Microbiologically Influenced corrosion (MIC) is an electrochemically driven form of

corrosion that is initiated by the presence of microbial activity, which can lead to failure of

metals in chemical engineering processes. Existing risk assessment methods have several

disadvantages in being highly dependent on specific microorganism-metal systems, and do

not account for fluctuations in bacterial behaviour. A simplified MIC model was developed,

and is used for a new risk assessment of MIC using a probabilistic based risk framework that

can quantify random fluctuations as a distribution. This assessment was conducted for a

carbon-steel pipeline at standard operating conditions. The findings of this new risk

assessment framework were compared with traditional methods and found to offer significant

improvements by determining the frequency that MIC would occur over a particular operating

period. These findings have application to a wide range of industries involved in metal

selection and fluid flow through process equipment.

Keywords: carbon-steel pipe corrosion; Single Value Assessment (SVA); Fr13 risk

modelling; Microbiologically Influenced Corrosion (MIC)

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1.0 Introduction

This project uses a new risk assessment method for the microbiologically influenced

corrosion (MIC) of metals. Microbiological influenced corrosion (MIC) is an

electrochemically driven form of corrosion, which is influenced by the presence of

microorganisms. These microorganisms induce extensive pitting corrosion on the surface of

metals that significantly reduces equipment lifespan, and causes premature failures,

collectively costing the oil and gas industry $100 million globally (Javaherdashti et al., 2011).

The motivation of this project is to examine if the new risk methodology, the Friday 13th (Fr

13) framework, improving upon the practical limitations of existing mechanistic corrosion

risk models that do not adequately quantify the occurrence of natural fluctuations in steady-

state processes. This work is significant in being the first to attempt to develop a

comprehensive MIC risk assessment methodology that quantifies potential risk as a

distribution related to steady-state process parameters.

This project aims replicate the work undertaken by Collins et al. (2016), and extends upon the

limitations of this work. These include using an abiotic corrosion model to model biotic

bacterial corrosion behavior, and developing a more justified method of calculating Ecorr as a

multi-variable function of temperature and pH. These aims will be achieved using Fr 13, a

probabilistic risk assessment framework developed by Davey and others that quantifies

random fluctuations within a process, along with probability of a particular value physically

occurring. Using refined Monte Carlo (r- MC) sampling of the distributions ensures sampling

covers the entire range of the distribution and accounts for all possible scenarios. Analysis of

these distributions will allow the identification, of which process variables are the driving

parameters of MIC, and through second tier studies, how process changes can be implemented

to reduce the occurrence of MIC inducing an equipment failure.

2.0 Literature review

Studies on the effects of MIC were first motivated by the extensive corrosion in Holland’s

steel pipe waterways during the 1930s. Von Wolzogen Kuhr and Van der Flught (1934)

conducted an experiment to determine the origin of the corrosion. Having identified the

presence of sulphate reducing bacteria (SRB) within the river water samples, the authors

postulated the cathodic depolarisation theory (CDT) as the mechanism for how bacteria

groups such as SRB influence the corrosion of metals.

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In following studies several authors challenged CDT as an appropriate mechanistic model for

MIC. Wanklyn and Spruit (1951) examined SRB’s consumption of H2 in cathodic

depolarization leading to iron corrosion, and determined CDT did not adequately explain the

cathode charge measurements. In contrast, Iverson (1966) used the basis of Wanklyn and

Spruit’s study to further assess the validity of CDT by using cultured SRB in agar gel in a

nitrogen atmosphere, investigated several different types of metals. Iverson found the rate of

corrosion was smaller than anticipated, and unable to be fully attributed to CDT, but surmised

the broad theory was valid. The study was significant as being the first to develop a simple

corrosion model based on the experimental results.

De Waard et al. (1991) developed the deWaard-Milliams carbon dioxide corrosion model for

use in natural gas pipelines. Although not focused on MIC, the methodology for corrosion

modelling used by De Waard et al. (1991) provided a basis for further MIC studies that

shifted focus from assessing microorganism’s corrosion mechanisms, to creating a corrosion

model for MIC risk assessment. Pots et al. (2002) expanded upon the de Waard-Milliams

model to create a specific MIC corrosion that was incorporated into the HYDROCOR risk

assessment software. A key limitation of the Pots et al. (2002) model was the lack of

incorporation of appropriate biochemical parameters into the mechanistic model, which

affected the model accuracy. Studies by Maxwell and Campbell (2006) attempted to address

the limitation of the Pots et al. (2002) model by expanding the biochemical parameters used in

the model along with first-order bacterial kinetics to describe the sulfur-based biofilm growth

during the initial stages of MIC. The resultant modified model produced comparative results

to that of the original Pots et al. (2002) model, whilst the inclusion of bacterial kinetics

reduced the number of corrosion parameters from 11 to 4. Additionally, integration of the

bacterial kinetics helped address the initial problems by allowing the bacteria life cycle and

relative biocide effectiveness to be quantified. Smith et al. (2011) recognised the extensive

biochemical parameters associated with MIC was a large limitation in previous studies, and

investigated improving model accuracy through using a more appropriate model. This model

was fundamentally based around the Butler-Volmer kinetics to describe ion charge transfer.

Additionally, the Nernst diffusion model was incorporated to account for the mass transfer

process occurring during the corrosion. The resultant model produced reasonable qualitative

likeness with experimental data near the corrosion potential. However it was observed that a

larger overpotential in the system created more deviations between the model and

experimental values.

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Common issues with many of the models and generalised results, highlighted by the work of

Pots et al. (2002) and Maxwell and Campbell (2006), is that the mechanistic corrosion models

constructed were not sophisticated enough to take into account all the biological parameters.

These were compensated by making simplistic assumptions for biological variables that

cannot be accounted for in the models. This substantially reduces the accuracy and usefulness

of these models as a risk assessment tool. Both are unable to incorporate key variables as well

as not being able to quantify the natural fluctuations these variables undergo within the

system. Another issue noted is that in studies such as Smith et al. (2011), little analysis was

undertaken on how well the simulated MIC environment mimics MIC in real life, and how the

general findings can be applied. Lastly, the majority of studies almost exclusively focused on

the effects of SRB, where increasing evidence has shown APB to present equal, if not more

risk than SRB. This limits the effectiveness of the development of a corrosion risk model that

can accurately account for the effects from all the main corrosion inducing bacteria groups.

The traditional method used to create an MIC risk model is to use a deterministic approach to

solve a certain outcome, in this case occurrence of corrosion. The approach of linking the

operation parameters together in a mathematical expression and solving to find a particular

output is also known as Single Value Assessment (SVA) (Davey and Cerf, 2003). The use of

the deterministic SVA method has been the primary method employed by all previous work

used in developing an MIC risk model, including De Waard et al. (1991), Pots et al. (2002),

and Maxwell and Campbell (2006). The fundamental flaw with the use of SVA in chemical

engineering processes is that naturally occurring random fluctuations in inputs and their

potential impact on plant outcome behaviour cannot be implicitly accounted for, or quantified

using SVA (Davey and Zou, 2015). Although a new risk modelling methodology, several

studies have successfully used the Fr 13-risk assessment framework for steady state, single-

step unit-operations processes. These studies have not examined MIC specifically, however

lessons can be observed from the study’s findings and application of Fr 13 in terms of how is

could best be applied to further research on MIC.

The Fr 13 framework was used in the work undertaken by Davey (2015) to assess the fuel-to-

steam thermal efficiency of a coal-fired boiler (CFB), used to examine the potential risk of

reduced CFB efficiency from naturally occurring fluctuations. The unit-operations model was

used to simulate 20 key efficiency related parameters. The findings of the Fr 13 simulations

determined that 73 failures in CFB efficiency occurred per 10,000 operations. Further

sensitivity analysis determined that the undesirable impact on efficiency from fluctuations

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could be reduced by ensuring the consistency of the size and mixture of the coal be improved

across several feed batches.

Through its use in several different fields of chemical processing, the Fr 13-risk framework

has been able to significantly improve upon the use of the traditional SVA to conduct risk

analysis. Furthermore, the quantitative results produced using the MC method have a number

of advantages over other probabilistic risk analysis methods (Milazzo and Aven, 2012),

principally due to the ability to pinpoint individual parameters that are influencing the

processes failure rate, and then conduct second-tier simulations to target these parameters by

implementing design changes. A current limitation of Fr 13 is that the methodology is

generally limited to single step unit operations and hence may not be suitable for multi-step

unit operation processes (Davey and Zou, 2015). Based on various studies undertaken using

Fr13, there is no evidence that suggests the Fr 13 framework is unsuitable to be applied in

conducting a risk assessment for MIC using a single unit operation model.

3.0 Method

A summary of the primary project tasks is described below:

1. Synthesise an abiotic MIC model based upon a simplified version of the Smith et al. (2011)

model and address the key limitation of the work of Collins et al. (2016) by creating a solver

loop to develop a more justified method of calculating Ecorr (free corrosion potential)

2. Solve the abiotic unit-operation model using the deterministic method of single value

assessment (SVA) using fixed values for temperature and pH. Then solve using the

probabilistic Fr 13 framework of Davey and co-workers

3. Compare and validate results against of other established corrosion models

4. Use the Fr 13 methodology to gain new insights into how random fluctuations affect MIC

through manipulating the input variables of temperature and pH

5. Determine the requirements to allow the abiotic corrosion model to be modified such that it

can become a biotic corrosion model, which will enhance the applicability of the risk model.

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3.1 Synthesis of Unit Operation Model

The generalised unit operation model will be heavily based upon the model constructed by

Smith et al. (2011) and the further modifications made by Collins (2016). The three-electrode

corrosion cell and potentiostat model of Smith et al. (2011) provides a realistic basis for

synthesis of a simplified unit-operations model of MIC corrosion, Fig. 1. The model is a

simplified version of steel corrosion subjected to synthetic water as MIC presented by Smith

et al. (2011).

Fig. 1 – Schematic of the three-electrode cell with synthetic water reproduced from Smith et

al. 2011)

The unit-operation model was derived using a system of linear equations based around the

Butler-Volmer kinetics, which described the charge transfer of the oxidation of iron along

with the Nernst diffusion model for the mass transfer process occurring during the corrosion

process. Complete breakdown of the unit-operation model is demonstrated in Appendix A.

It is assumed that the electrons formed by the oxidation of iron in the steel (Eq. [1]) are

consumed by the reduction of protons (Eq. [2]):

𝐹𝑒 → 𝐹𝑒!! + 2𝑒! [1]

𝐻! + 𝑒! → !!𝐻! [2]

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The transfer of charge (electrons) occurs only at the steel surface between the steel and the

water (electrolyte) because of the nature of electron transport. The overall corrosion reaction

is:

𝐹𝑒 + 2𝐻! → 𝐹𝑒!! + 𝐻! [3]

The charge transfer at the steel surface can be described by the Butler-Volmer equation (Gu,

2009) for current density due to the oxidation of iron (anodic process)

𝑗!",!! = 𝑗!,!! 𝑒𝑥𝑝!!,!! ∙!!! ∙!

!∙!∙ 𝜂!! − 𝑒𝑥𝑝

!!!,!! ∙!!! ∙!

!∙!∙ 𝜂!! [4]

From the expanded unit operation model in Appendix A, a simplified expression for MIC of a

carbon steel pipe can be described through Eq. [13], where 𝑗!" is equivalent to the number of

electrons produced in the oxidation of iron:

𝐶𝑅 = 1.155𝑗!" [13]

3.2 Single Value Assessment The unit-operation model-describing MIC for iron was solved using the deterministic and

single value assessment (SVA) (Sinnott, 2005; Davey, 2015). This is based on the use of

synthetic water using the two experimental input conditions detailed in Smith et al. (2011) of

T = 293.15 K and pH = 5.15. The output of this SVA is the corrosion rate of the carbon steel

pipe in mm yr-1.

Ones of the aims of this project is to address a limitation of the original work of Collins et al.

(2016), where Ecorr (free corrosion potential) was an assumed constant of -0.616 V vs SCE.

Ecorr is a multivariable function of temperature and pH, therefore this work attempted to

improve the accuracy of the findings by developing a more justifiable, calculated value of

Ecorr that will change if the input values of temperature and pH are varied. This was achieved

by creating a solver loop based around using the following Eq. [10] for overall charge

transfer, where the solver will converge on a value as close as possible to zero.

𝑗! = 𝑗!" + 𝑗!! = 0 [10]

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A domain was set such that Ecorr will only take values between - 0.4 and -1, the maximum

theoretical range Ecorr will take. Additionally, a parameter was set such that the Cs,Fe, surface

concentration of iron is always greater then Cb,,Fe, the concentration of iron in bulk solutions.

Any values that do not meet this constraint signify corrosion is no longer occurring. The

solver function is embedded within the Excel spreadsheet of the SVA. Each time an input

variable of temperature or pH is altered, the solver must be run to recalculate Ecorr. A

complete breakdown of the solver function, including instructions for use can be found in

Appendix B.

3.3 Friday 13th Framework

After the unit-operation model had been solved using the deterministic SVA method, it was

then solved using the probabilistic Fr 13 framework, and the two methods were compared.

The Fr 13 simulation (Davey et al. 2015) differs from the SVA method by considering input

parameters as distributions of values to mimic naturally occurring fluctuations within the

process, along with the probability of a particular value actually occurring. As with the SVA,

an output of the corrosion rate of the carbon steel pipe will be produced. However this output

will also be a distribution of particular outcomes that will include both desirable and

undesirable outcomes, i.e. intolerable levels of MIC.

A modified Monte Carlo (r-MC) (with Latin Hypercube) sampling of the distributions is used

to ensure sampling covers the entire range of the distribution. Vose (2008) determined the

standard MC sampling is unreliable due to its tendency to over-and under-estimate portions of

the distribution. When the sample size is large enough, the output distribution will be

approximately normal (Davey, 2015; Vose, 2008). For the simulations conducted in this

project 10 000 samples are considered sufficient (Collins et al., 2015).

As part of the Fr 13 framework a risk factor term, p, must be created to define which

outcomes in the distribution are desirable or not. This is called creating a failure definition.

For this work, a failure will be defined as any magnitude of MIC occurring, for all values p >

0 in the output distribution. This definition for a failure through the risk factor, p, can be

expressed in Eq. [14] below, where C𝑅′ is the corrosion obtained from the probabilistic Fr 13

simulation, and CR is the corrosion found in the SVA.

𝑝 = 𝐶𝑅′− 𝐶𝑅 [14]

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Eq. [14] is convenient because for all values p > 0, the corrosion is greater than acceptable.

However the definition of p can be further refined to more precisely describe MIC.

A more suitable mathematical form of the corrosion risk factor (Abdul-Halim & Davey, 2015;

Davey et al., 2015) can be expressed by Eq. [15].

𝑝 = 100 !"!

!"− 1 [15]

Eq. [15] can be considered more useful then Eq. [14], as it is dimensionless and because

corrosion rates greater than acceptable (i.e. failures) can be readily identified for all values p >

0. However, Eq. [15] can lastly be modified by including a measure of tolerance, shown in

Eq. [16], as a factor of design safety. There is no tolerance recommendation or guidelines

within the oil and gas industry, in the absence of conditional data, a tolerance of 25 % will be

used initially for all simulations. Part of this work will include examining the impact of

different tolerance levels. Eq. [16] will be used to define risk factor of the probabilistic Fr 13

model of MIC of the steel pipeline in water.

𝑝 = 100 !"!

!"− 1 −%𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 [16]

Computations for the Fr 13-risk model to determine the corrosion rate are to be carried out

using Microsoft Excel™ with a commercially available add-on @Risk™ (version 7.5,

Palisade Corporation). Excel is chosen as it is widely available and is generally well

understood across both academic and industry sectors. Furthermore, the distributions defining

naturally occurring fluctuations in the parameters can be manipulated using Excel formulae

(Abdul-Halim and Davey, 2016).

3.4 Second Tier Studies

The findings from the Fr 13 simulations may permit further insight into MIC of metals

through second tier studies (Davey, 2015) that aim to change an input parameter to reduce

failure rate. Several physical and chemical methods are used to remove or inactivate corrosion

inducing bacteria; one chemical method involves adding chlorine gas to the pipeline where it

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dissolves in the water to form hypochlorous acid (HOCl) and hyperchlorite (OCl-1) at

equilibrium of pH 7.5 (Tuthill et al., 1998). The addition of chlorine gas to the pipeline will

be simulated in the model by increasing the pH to 7.5.

This second tier study will also involve assessing the abiotic models responsiveness to pH

change by running a simulation at pH 3 where corrosion inducing bacteria should

theoretically thrive. The model will be solved with both SVA and the Fr 13 framework to

allow insight into whether or not the abiotic corrosion model can adequately model bacterial

fluctuations.

4.0 Results

Simulations were run in Microsoft Excel™ using the commercial add-on @Risk™. A

simulation was conducted for mid-range operating conditions commonly found in oil and gas

pipelines. Two simulations were then undertaken as second tier studies. The first was to

assess the effects of simulating the addition of chlorine gas to a pipeline to inactivate

corrosion inducing bacteria. The second simulation aimed to replicate ideal bacterial

conditions by reducing the pH 3. Each of these three simulations were then used to analyse

the effect tolerance has on failure rate by repeating each simulation at 0 % and 50 %

tolerance. These simulations analysing tolerance can be found in Appendix C.

For each a simulation a summary table of the comparison of results produced from the

traditional SVA and the new Fr 13 simulation was generated. Rows 2 and 3-show

temperature and pH, the two model input parameters that are prone to natural fluctuations.

The physical system is fixed by constant parameters shown in rows 6 to 28. These constant

parameters, along with the input parameters were used to determine the calculated values

shown in rows 31 through to 46. The traditional SVA is read down column 2 where the

corrosion rate an annual figure of the corrosion of the carbon steel pipe (mm yr-1) is the output

in row 48. Meanwhile, the Fr 13 simulation is read down column 4 in which a normal

distribution has been used for both T and pH. These are represented by the @risk commands:

RiskNormal (mean, stdev, RiskTruncate(minimum, maximum)), these distributions model

how in operation the temperature and pH within a pipeline will vary randomly, but not outside

a certain range. Additionally, for each simulation a Risk Factor, p, distribution plot was

produced. This uses the definition that a failure, i.e. corrosion occurring, is represented by all

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values p > 0 to depict the amount of failures that would occur due to random fluctuations of

the input parameters, temperature and pH. The x-axis is the computed value of p from Eq.

[15] whilst the y-axis is the probability of p actually occurring.

Table 1 presents a summary comparison of results from the orthodox SVA and the new Fr 13

simulation of MIC of a carbon steel pipe at mid-range operating conditions of T = 293.15 K,

and pH = 5.15 for rows 2 and 3 respectively. The SVA output was 0.45 mm yr-1. The Fr 13

simulation, using a tolerance of 25 %, produced the same corrosion output as the SVA, whilst

these particular input parameter conditions produced a p value of 25. The corresponding

distribution of p values is shown in Fig. 1, which shows that from the 10 000 samples of

different temperature and pH values, 25 % or 2500 failures occurred. Shown in Appendix C

for Figs. C1 and C2, when using tolerances of 0 % and 50% for the Fr 13 simulations, failure

rate was found to be 50 % and 9 % respectively.

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Table 1 – SVA and Fr 13 Results (T = 293.15 K, pH = 5.15, Tolerance = 25 %)

Row Parameter SVA Fr 13 Simulation 1 Input 2 T (K) 293.15 293.15

RiskNormal(293.15,29.3,RiskTruncate(263.835,322.465))

3 pH 5.15 5.15 RiskNormal(5.15,0.515,RiskTruncate(4.63

5,5.665)) 4 5 Constants 6 αa,Fe (dimensionless) 0.4 0.4 Constant 7 αa,H+ (dimensionless) 0.6 0.6 Constant 8 αc,Fe (dimensionless) 0.6 0.6 Constant 9 αc,H+ (dimensionless) 0.4 0.4 Constant

10 nFe (dimensionless) 2 2 Constant 11 nH+ (dimensionless) 1 1 Constant 12 e(0,Fe) (A) 1.00E-07 1.00E-07 Constant 13 e(0,H+) (A) 1.00E-07 1.00E-07 Constant 14 A,E (m^2) 2.83E-03 2.83E-03 Constant 15 𝛾,Fe (dimensionless) 0.3 0.3 Constant 16 𝛾,H+ (dimensionless) 0.75 0.75 Constant 17 E°Fe (V vs SCE) -0.681 -0.681 Constant 18 E°H+ (V vs SCE) -0.241 -0.241 Constant 19 Cs,Fe (mol m-3) 1.00E-03 1.00E-03 Constant 20 Cs,H+ (mol m-3) 1.00E-07 1.00E-07 Constant 21 Cb,Fe (mol m-3) 1.01E-05 1.01E-05 Constant 22 DFe (m2 s-1) 7.98E-10 7.98E-10 Constant 23 DH+ (m2 s-1) 9.47E-09 9.47E-09 Constant 24 δN,Fe (m2) 7.23E-06 7.23E-06 Constant 25 δN,H+ (m2) 1.67E-05 1.67E-05 Constant 26 F (C mol-1) 96485 96485 Constant 27 R (J mol-1 K-1) 8.314 8.314 Constant 28 Tolerance (%) - 25 29 30 Calculations 31 Cb,H+ (mol m3) 7.08E-03 7.08E-03 Eq. [1] 32 j0,Fe (A m-2) 1.40E-04 1.40E-04 Eq. [5] 33 j0,H+ (A m-2) 0.00 0.00 Eq. [7] 34 Erev,Fe (V vs SCE) -7.68E-01 -7.68E-01 Eq. [6] 35 Erev,H+ (V vs SCE) -6.48E-01 -6.48E-01 Eq. [4] 36 jmt,Fe (A m2) 2.11E-02 2.11E-02 Eq. [9] 37 jmt,H+ (A m2) -3.87E-01 -0.387335386 Eq. [10] 38 jct,Fe (A m2) 3.66E-01 3.66E-01 Eq. [11] 39 jct,H+(A m2) 0.00 0.00 40 ηFe (V vs SCE) 2.48E-01 2.48E-01 41 ηH+ (V vs SCE) 0.13 0.13 Eq. [13] 42 Ecorr (V vs. SCE) -0.52 -0.52 43 jFe (A m-2) 0.39 0.39 Eq. [6] 44 jH+ (A m-2) -0.39 -0.39 Eq. [6] 45 jT (A m-2) 0.00 0.00 Eq. [6] 46 0.00 0.00 Eq. [6] 47 Output 48 CR (mm yr-1) 0.45 0.45 Eq. [13] 49 50 p - 25.00 Eq. [16]

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Fig. 1 – r-MC Risk Factor Distribution (T = 293.15 K, pH = 5.15, Tolerance = 25%)

Tables 2 presents a summary comparing results produced from the traditional SVA, and the

new Fr 13 simulation of chlorine gas being added to the pipeline where T = 293.15 K, and pH

= 7.5 for rows 2 and 3 respectively. The SVA output was 0.002 mm yr-1. The Fr 13

simulation, using a tolerance of 25 %, produced the same corrosion output as the SVA, while

the input parameter conditions produced a p value of -25. The corresponding distribution of p

values is shown in Fig. 2, which shows that from the 10 000 samples of different temperature

and pH values, 50 % or 5000 failures occurred. Shown in Appendix C for Figs. C5 and C6,

when using tolerances of 0 % and 50 % for the Fr 13 simulations, failure rate found to be 50

% and 47 % respectively.

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Table 2 – SVA and Fr 13 Results (T = 293.15 K, pH =7.5, Tolerance = 25 %)



3 pH 7.5 7.64 RiskNormal(7.5,0.75,RiskTruncate(6.95,8.4

5)) 4 5 Constants 6 αa,Fe (dimensionless) 0.4 0.4 Constant 7 αa,H+ (dimensionless) 0.6 0.6 Constant 8 αc,Fe (dimensionless) 0.6 0.6 Constant 9 αc,H+ (dimensionless) 0.4 0.4 Constant

10 nFe (dimensionless) 2 2 Constant 11 nH+ (dimensionless) 1 1 Constant 12 e(0,Fe) (A) 1.00E-07 1.00E-07 Constant 13 e(0,H+) (A) 1.00E-07 1.00E-07 Constant 14 A,E (m^2) 2.83E-03 2.83E-03 Constant 15 𝛾,Fe (dimensionless) 0.3 0.3 Constant 16 𝛾,H+ (dimensionless) 0.75 0.75 Constant 17 E°Fe (V vs SCE) -0.681 -0.681 Constant 18 E°H+ (V vs SCE) -0.241 -0.241 Constant 19 Cs,Fe (mol m-3) 1.00E-03 1.00E-03 Constant 20 Cs,H+ (mol m-3) 1.00E-07 1.00E-07 Constant 21 Cb,Fe (mol m-3) 1.01E-05 1.01E-05 Constant 22 DFe (m2 s-1) 7.98E-10 7.98E-10 Constant 23 DH+ (m2 s-1) 9.47E-09 9.47E-09 Constant 24 δN,Fe (m2) 7.23E-06 7.23E-06 Constant 25 δN,H+ (m2) 1.67E-05 1.67E-05 Constant 26 F (C mol-1) 96485 96485 Constant 27 R (J mol-1 K-1) 8.314 8.314 Constant 28 Tolerance (%) - 25 29 30 Calculations 31 Cb,H+ (mol m3) 3.16E-05 2.28E-05 Eq. [1] 32 j0,Fe (A m-2) 1.40E-04 1.40E-04 Eq. [5] 33 j0,H+ (A m-2) 0.00 0.00 Eq. [7]

34 Erev,Fe (V vs SCE) -7.68E-01 -7.68E-01 Eq. [6]

35 Erev,H+ (V vs SCE) -6.48E-01 -6.48E-01 Eq. [4]

36 jmt,Fe (A m2) 2.11E-02 2.11E-02 Eq. [9]

37 jmt,H+ (A m2) -1.72E-03

-0.001242217 Eq. [10]

38 jct,Fe (A m2) -1.93E-02 -1.93E-02 Eq. [11]

39 jct,H+(A m2) 0.00 0.00 40 ηFe (V vs SCE) -1.04E-

01 -1.04E-01 41 ηH+ (V vs SCE) -0.22 -0.22 Eq. [13] 42 Ecorr (V vs. SCE) -0.87 -0.87 43 jFe (A m-2) 0.00 0.00 Eq. [6] 44 jH+ (A m-2) 0.00 0.00 Eq. [6] 45 jT (A m-2) 0.00 0.00 Eq. [6] 46 0.00 0.00 Eq. [6] 47 Output 48 CR (mm yr-1) 0.0020 0.002 Eq. [13] 49 50 p - -25.00 Eq. [16]

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Fig. 2 – r-MC Risk Factor Distribution (T = 293.15 K, pH =7.5, Tolerance = 25%)

Tables 3 presents a summary comparison of results produced from the traditional SVA and

the new Fr 13 framework simulating ideal bacterial pH conditions where T = 293.15 K, and

pH = 3 for rows 2 and 3 respectively. The SVA output was 18.79 mm yr-1. The Fr 13

simulation, using a tolerance of 25 %, produced the same corrosion output as the SVA, whilst

the input parameter conditions produced a p value of -25. The corresponding distribution of p

values is shown in Figure 2, which shows that from the 10 000 samples of different

temperature and pH values, 35 % or 3500 failures occurred. Shown in Appendix C for Figs.

C3 and C4, when using tolerances of 0 % and 50 % for the Fr 13 simulations, failure rate was

found to be 50 % and 25 % respectively.

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Table 3 – SVA and Fr 13 Results (T = 293.15 K, pH =3.0, Tolerance = 25 %)



3 pH 3 3 RiskNormal(3,0.3,RiskTruncate(2.7,3.3)) 4 5 Constants 6 αa,Fe (dimensionless) 0.4 0.4 Constant 7 αa,H+ (dimensionless) 0.6 0.6 Constant 8 αc,Fe (dimensionless) 0.6 0.6 Constant 9 αc,H+ (dimensionless) 0.4 0.4 Constant

10 nFe (dimensionless) 2 2 Constant 11 nH+ (dimensionless) 1 1 Constant 12 e(0,Fe) (A) 1.00E-07 1.00E-07 Constant 13 e(0,H+) (A) 1.00E-07 1.00E-07 Constant 14 A,E (m^2) 2.83E-03 2.83E-03 Constant 15 𝛾,Fe (dimensionless) 0.3 0.3 Constant 16 𝛾,H+ (dimensionless) 0.75 0.75 Constant 17 E°Fe (V vs SCE) -0.681 -0.681 Constant 18 E°H+ (V vs SCE) -0.241 -0.241 Constant 19 Cs,Fe (mol m-3) 1.00E-03 1.00E-03 Constant 20 Cs,H+ (mol m-3) 1.00E-07 1.00E-07 Constant 21 Cb,Fe (mol m-s3) 1.01E-05 1.01E-05 Constant 22 DFe (m2 s-1) 7.98E-10 7.98E-10 Constant 23 DH+ (m2 s-1) 9.47E-09 9.47E-09 Constant 24 δN,Fe (m2) 7.23E-06 7.23E-06 Constant 25 δN,H+ (m2) 1.67E-05 1.67E-05 Constant 26 F (C mol-1) 96485 96485 Constant 27 R (J mol-1 K-1) 8.314 8.314 Constant 28 Tolerance (%) - 25 29 30 Calculations 31 Cb,H+ (mol m3) 1.00E+0 1.00E+00 Eq. [1] 32 j0,Fe (A m-2) 1.40E-04 1.40E-04 Eq. [5] 33 j0,H+ (A m-2) 0.00 0.00 Eq. [7]



36 jmt,Fe (A m2) 2.11E-02 2.11E-02 Eq. [9]

37 jmt,H+ (A m2) -

5.47E+01

-54.71334483 Eq. [10]

38 jct,Fe (A m2) 1.63E+01 1.63E+01 Eq. [1]

39 jct,H+(A m2) 0.00 0.00 40 ηFe (V vs SCE) 3.68E-01 3.68E-01 41 ηH+ (V vs SCE) 0.25 0.25 Eq. [3] 42 Ecorr (V vs. SCE) -0.40 -0.40 43 jFe (A m-2) 16.27 16.27 Eq. [6] 44 jH+ (A m-2) -54.71 -54.71 Eq. [6] 45 jT (A m-2) -38.44 -38.44 Eq. [6] 46 38.44 38.44 Eq. [6] 47 Output 48 CR (mm yr-1) 18.79 18.79 Eq. [13] 49 50 p - -25.00 Eq. [16]

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Fig. 3 – r-MC Risk Factor Distribution (T = 293.15 K, pH =3.0, Tolerance = 25%)

Discussion

The 0.45 mm yr-1 corrosion output of the SVA in Table 1 is comparable to that of the value of

0.504 mm yr-1 determined by Collins et al. (2016). Similarly, it is supported by the findings of

Maxwell & Campbell (2006) that determined it is realistic that MIC has been found to induce

up to 10 mm yr-1 of corrosion to steel pipes. This validates the unit operation model as an

appropriate corrosion model when using deterministic risk assessments such as the SVA. The

Fr 13 simulations were found to be stable, where 10 000 r-MC samples were found to be

sufficient in simulating all possible practical combinations of scenarios that could occur with

MIC. If each of the simulation scenarios were thought of as one day, then Fig. 1 shows 2500

failures, where some magnitude of corrosion due to MIC occurred, this would be considered

unacceptable given (2500/10 000)*365.25 ≈ 91 failures per year or approximately one failure

every four days with a tolerance of 25 %. However, as Fig. 1 is a probabilistic distribution of

all possible outcomes, there is no reason the failure events will be equally spaced in time.

Regardless, this insight of predicting the theoretical number of occurrences of corrosion

occurring over a given time period is not available from traditional methods, such as the SVA.

Running the same simulation at lower and higher tolerances gave insight into how effectively

doubling the tolerance from 25 % to 50 % found failures reduce by approximately two-thirds

to 31 per tolerance year. Conversely, not having any tolerance level at all resulted in only a

50 % failure rate where it was anticipated to be higher. This is suggestive that in its current

mathematical expression, tolerance does not completely effectively model design safety.

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Similarly, as currently expressed within the p definition, it may be unrealistic in real operating

conditions to run a higher tolerance to achieve a more acceptable failure rate due to

limitations in implementing tighter design safety control on certain equipment.

The SVA results of the second tier studies supported literature (Maxwell and Campbell, 2006;

Javaherdashti et al., 2001) that corrosion inducing bacteria can be inactivated in basic pH

conditions, whilst thriving and therefore enhancing corrosion in more acidic pH

environments. However, the Fr 13 findings highlighted how traditional deterministic methods

such as SVA are not able to provide a complete risk analysis for processes prone to natural

fluctuations. The chlorine gas simulation at pH 7.5 showed corrosion became almost non-

existent at 0.002 mm yr-1 in the SVA, whereas the Fr 13 results found that failures still occur

48.5 % of the time. Therefore, chlorine is not as effective at fully deactivating bacteria, as the

SVA would suggest. These findings from the chlorine gas simulation are also supported from

the simulation of high acidic conditions of pH 3 where the SVA produced a very high

corrosion value of 18.79 mm yr-1, whilst the Fr 13 analysis determined a lower than

anticipated failure rate of 35 %, inferring that the bacteria cause corrosion less frequently, but

more severely. Moreover, modifying the tolerance for these studies saw only very minor

changes in failure rates. This is potentially representative of how the process should not be

run at these pH ranges long term, as no degree of design safety is fully effective. The findings

of both second tier studies are highly suggestive that the abiotic corrosion model is unable to

fully quantify fluctuations in bacterial behavior at the two extreme pH condition ranges.

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Conclusions The following conclusions were made:

1. Microbiologically influenced corrosion (MIC) of a carbon steel pipeline has been

shown to be responsive to a quantitative probabilistic risk assessment

2. The application of the probabilistic Fr 13 framework offers significant improvements

over existing corrosion risk modelling methods for conducting a comprehensive risk

assessment of the MIC of metals, and is applicable to corrosion prone environments in

Australia, such as the natural gas pipelines in Bass Strait

3. Based on a simplified abiotic corrosion model, the Fr 13 analysis found for standard

operating conditions of a pipeline, an unacceptably high frequency of corrosion

occurring, and equivalent to 91 days for each year of operation. This insight is not

available from traditional methods, such as SVA

4. The development and inclusion of the solver function to determine Ecorr improves

upon the accuracy of the original work of Collins et al. (2016) by providing a

justifiable mathematical method of calculating Ecorr at different pH and temperature

ranges

5. An abiotic corrosion model has significant limitations in quantifying fluctuations in

bacterial behaviour when using a probabilistic-based risk assessment

6. Incorporating biotic and material specific corrosion parameters into the unit-operation

model would enhance the applicability of this corrosion risk model to assess MIC for a

wider range of materials and corrosion-inducing bacterial species. This will require

conducting laboratory work that replicates that of Smith et al. (2011), but uses

additional metal samples and water solutions that replicate the environment in which

these metals are used.

Acknowledgements

I would like to thank Dr Davey, Dr Lavigne and Mr Collins, all of whom provided valuable

guidance and support throughout the project.

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Nomenclature

Numbers in parentheses after the description refer to the equation in which the symbol is first used or defined

CR Corrosion rate, mm yr-1 [12, 13]

Cb,H+ Concentration of species in bulk electrolyte = 10–pH x1000 mol m-3 [8]

Cs,H+ Concentration of species at steel surface = 10-6 mol m-3 [8]

DH+ Diffusion coefficient = 9.47 x 10-9 m2 s-1 [8]

E Potential, V [6]

Ecorr (V vs. SCE)

Free corrosion potential V [6]

Erev (V vs. SCE)

Reversible potential for species, V [7]

E°H+ (V vs. SCE)

Standard (equilibrium) potential = -0.241 V [7]

F Faraday constant = 96,485 C mol-1 [4]

ΔHH+ Enthalpy of activation = 30,000 J mol-1 for proton reduction [5]

J0,H+ Exchange current density, A m-2 [4]

jref0,H+ Reference exchange current density = 5 x 10-2 A m-2 [5]

MFe Molecular weight = 55.85 g mol-1 [12]

nH+ Number of electrons transferred in the process [4]

p Corrosion rate risk factor, dimensionless [16]

R Universal gas constant = 8.314 J mol-1 K-1 [4]

%tolerance Practical tolerance over design corrosion rate CR, % [16]

T Temperature of electrolyte, K [4]

TR Reference temperature = 293.15 K [5]

Greek Symbols

αa,H+ Anodic transfer symmetry function = 0.6 dimensionless [4]

αc,H+ Cathodic transfer symmetry function = (1 - αa,H+) = 0.4 dimensionless [4]

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δN,H+ Nernst diffusion layer thickness = 1.67 x 10-5 m [8]

ηH+ (V vs. SCE)

Overpotential, V [7]

ρFe Density of iron = 7,850 kg m-3 [12]

Subscripts

a Anodic symmetry function

c Cathodic symmetry function

T Total system parameter

References Abdul-Halim, N., Davey, K.R. (2015), A Friday 13th risk assessment of ultraviolet irradiation for potable water in turbulent flow, Food Control, 50, 770-777.

Chandrakash, S., Davey, K.R., O’Neill, B.K. (2015), An Fr 13 risk analysis of failure in a global food process – Illustration with milk processing, Asia-Pacific Journal of Chemical Engineering, 10, 526-541.

Collins, C., Davey, K.R., O’Neill, B.K., James T.G. Chu (2016), A new quantitative risk assessment of Microbiologically Influenced Corrosion (MIC) of carbon steel pipes used in chemical engineering, Chemeca 2016, 3386601

Davey, K.R. (2011), Introduction to fundamentals and benefits of Friday 13th risk modelling technology for food manufacturers, Food Australia, 63, 192-197.

Davey, K.R. (2015), A novel Friday 13th risk assessment of fuel-to-steam efficiency of a coal-fired boiler, Chemical Engineering Science, 127, 133-142.

Davey, K.R., Cerf, O. (2003), Risk modelling - An explanation of Friday13th syndrome (failure) in well-operated continuous sterilisation plant, in: Proceedings of the 31st Australasian Chemical Engineering Conference (Product and Processes for the 21st Century), Adelaide, Sept. 28 – Oct. 1, 2003.

Davey, K.R., Chandrakash, S., O'Neill, B.K. (2013), A new risk analysis of Clean-In-Place milk processing, Food Control, 29, 248-253.

Davey, K.R., Chandrakash, S., O'Neill, B.K. (2015), A Friday 13th failure assessment of clean-in-place removal of whey protein deposits from metal surfaces with auto-set cleaning times, Chemical Engineering Science, 126, 106-115.

Davey, K.R., Lavigne, O., Shah, P. (2016), Establishing an atlas of risk of pitting of metals at sea – demonstrated for stainless steel AISI 316L in the Bass Strait, Chemical Engineering Science, 140, 71-75.

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De Waard, C., Lotz, U., Miliams, D.E. (1991), Predictive model for CO2 corrosion engineering in wet natural gas pipelines, Corrosion, 47, 976–985

Gu, T., Zhao, K., Nesic, S. (2009), A New Mechanistic Model for MIC Based on a Biocatalytic Cathodic Sulfate Reduction Theory, in CORROSION 2009, Atlanta, March 22 - 26, 2009

Iverson, W.P., 1966, “Direct evidence for the cathodic depolarization theory of bacterial corrosion”, Science 151, 986-988. ISSN 00368075; 10959203

Javaherdashti, R., Raman-Singh, R.K., 2001, “Microbiologically Influenced Corrosion of Stainless Steels in Marine Environments: A Materials Engineering Approach. In: Proc. Engineering Materials”, Melbourne, Australia, Sept. 23-26.

Maxwell, S., Campbell, S. (2006), Monitoring the Mitigation of MIC Risk in Pipelines, in CORROSION 2006, San Diego, March 12 - 16, 2006.

Pots, B.F.M., John, R.C., Rippon, I.J., Thomas, M.J.J.S., Kapusta, S.D., Girgis, M.M., Whitman, T. (2002), Improvements on DeWaard-Milliams corrosion prediction and applications to corrosion management, in CORROSION 2002, Denver, April 7 – 11, 2002.

Roberge P.R., 2000, Handbook of Corrosion Engineering. McGraw-Hill, New York, pp. 35-54, 187-220, 335-336, 1047-1059. ISBN 0070765162

Von Wolzogen Kuhr C. A. H., Van Der Flught L S, 1934, “Graphitization of Cast Iron as an Electro biochemical Process in Anaerobic Soils,” Central Laboratory T. N. O., Holland

Vose, D., 2008, “Risk Analysis-A Quantitative Guide”, 2nd ed. John Wiley and Sons, Chichester, UK, pp. 64, 59, 34, 41-43, 19, 201-205 ff, 379 ff. ISBN: 9780470512845

Vose, D.J., 1998, “The application of quantitative risk assessment to microbial food safety”, J. Food Protect. 61 (5), 640-648. ISSN: 0362028X

Wanklyn, J.N., Spruit, C.J.P (1951), Influence of Sulphate-reducing Bacteria in the Corrosion Potential of Iron, Nature 169, 928-929

Weiss R., 1973, “Survival of Bacteria at Low pH and High Temperature” Indiana University, USA. Accessed 25/04/16 <http://mobile.tube.aslo.net/lo/toc/vol_18/issue_6/0877.pdf>

Xu J, Sun C, Yan M & Wang F, 2012, “Effects of Sulfate Reducing Bacteria on Corrosion of Carbon Steel Q235 in Soil-Extract Solution”, in International Journal of Electrochemical Science, Vol 7 (2012), pp. 11281 – 11296

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APPENDIX A

In Smith et al. (2011), a rotating disk electrode (RDE) was used as the working electrode

(WE) with the tip containing a sample of pipeline steel. A counter electrode (CE), made from

platinised titanium, was used as the electron sink/source, and a saturated calomel electrode

(SCE) reference electrode (RE) used for potential measurement. Synthetic produced water

was used to simulate MIC bacterial activity. This contained sulphate, chloride and hydrogen

sulphide.

It is assumed that the electrons formed by the oxidation of iron in the steel (Eq. [1]) are

consumed by the reduction of protons (Eq. [2]):

𝐹𝑒 → 𝐹𝑒!! + 2𝑒! [1]

𝐻! + 𝑒! → !!𝐻! [2]

The transfer of charge (electrons) occurs only at the steel surface between the steel and the

water (electrolyte) because of the nature of electron transport. The overall corrosion reaction

is:

𝐹𝑒 + 2𝐻! → 𝐹𝑒!! + 𝐻! [3]

The charge transfer at the steel surface can be described by the Butler-Volmer equation (Gu,

2009) for current density due to the oxidation of iron (anodic process)

𝑗!",!! = 𝑗!,!! 𝑒𝑥𝑝!!,!! ∙!!! ∙!

!∙!∙ 𝜂!! − 𝑒𝑥𝑝

!!!,!! ∙!!! ∙!

!∙!∙ 𝜂!! [4]

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The exchange current density is given by:

𝑗!,!! =!!,!!

!!∙

!!,!!

!!,!!

!!! [5]

The overpotential is given by:

𝜂!! = 𝐸!"## − 𝐸!"#,!! [6]

The reversible potential is calculated using the Nernst equation (Roberge, 2000):

𝐸!"#,!! = 𝐸°!! +!.!∙!∙!!!! ∙!

∙ log 𝑐!,!! [7]

The mass transfer at the steel surface is described by a flux balance arising from the

dependency on diffusion and charge consumption (Smith et al., 2011):

!!",!!

!!! ∙!= −𝐷!!

!!,!!!!!,!!

!!,!! [8]

This can be rearranged to isolate the current density due to mass transfer to give:

𝑗!",!! = 𝑛!! ∙ 𝐹 ∙ −𝐷!!!!,!!!!!,!!

!!,!! [9]

Because the number of electrons produced in the oxidation of iron is balanced by the

reduction of protons (shown by Eq. [3]), the total current in the system i.e. the sum of the

current due to oxidation and reduction, must be zero, namely:

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𝑗! = 𝑗!" + 𝑗!",!! + 𝑗!",!! = 𝑗!" + 𝑗!! = 0 [10]

Eq. [10] can be rearranged to give:

𝑗!" = −𝑗!! [11]

The current density due to iron oxidation can be converted to corrosion rate using molecular

weight and density (Gu, 2009) to yield:

𝐶𝑅 = !!"!!∙!!"

∙ 𝑗!" [12]

Which can be simplified to:

𝐶𝑅 = 1.155𝑗!" [13]

Eqs. [1] through to [13] define the simplified unit-operations model for synthetic MIC

corrosion rate of a steel pipeline in water.

Fr 13 Risk Simulation

In contrast to the traditional single input of the SVA, to mimic naturally occurring

fluctuations in the system the probabilistic Fr 13-risk simulation considers the input

parameters as a distribution of values, together with the probability of that value actually

physically occurring.

This means that the output will be a distribution of probabilities of particular outcomes

(Davey, 2015; Davey et al., 2015; Abdul-Halim and Davey, 2015). Because all practically

possible inputs are simulated, the output will include unwanted outcomes i.e. ‘failed’

operations in which MIC occurs. A fundamental requirement of Fr 13 risk modelling is a

practical and unambiguous definition of risk and failure (Abdul-Halim, 2016; Davey, 2011).

An off-specification of an acceptable corrosion rate can be conveniently used as a corrosion

risk factor p such that:

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𝑃 = 𝐶𝑅′− 𝐶𝑅 [14]

Where CR’ is an instantaneous rate of corrosion (or mathematically more strictly, the CR

obtained using Fr 13 simulation). Eq. [14] is convenient because for all values p > 0 the

corrosion is greater than acceptable. However, a mathematically more convenient form of the

corrosion risk factor (Abdul-Halim & Davey, 2015; Davey, 2015; Davey et al., 2015) is

𝑝 = 100 !"!

!"− 1 [15]

Eq. [15] is computationally more convenient because it is dimensionless and because

corrosion rates greater than acceptable (i.e. failures) can be readily identified for all values

p>0.

Generally however, a design specification includes some measure of tolerance – a measure of

design safety. The corrosion risk factor of Eq. [15] can then be written as

𝑝 = 100 !"!

!"− 1 −%𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 [16]

Eqn.’s [1] through to [16] describe the unit operation corrosion model and that of the risk

factor definition utilised in the Fr 13 framework.

APPENDIX B

This appendix will address the construction and use of the solver function that is used to

recalculate Ecorr (free corrosion potential) when one or both of the input variables for

temperature and pH are changed.

A key limitation of the original work of Collins et al. (2016) was that Ecorr was incorporated

into the corrosion model as a constant value of -0.616 as seen in the below Table B1 in Row

5. This introduces a degree of error by treating Ecorr as a constant, where in reality Ecorr is a

multivariable function of the inputted temperature and pressure. Resultantly all calculated

values that use the fixed Ecorr value would also introduce errors that affect the accuracy and

validity of the overall corrosion value output.

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Table B1: Unit Operation Model Constants (Collins et al., 2016)

Row Parameter SVA Fr 13 simulation

4 Constants

5 Ecorr (V vs. SCE) -‐0.616 -‐0.616 Constant

6 αa,H+ (dimensionless) 0.6 0.6 Constant

7 αc, H+ (dimensionless) 0.4 0.4 Constant

8 nH+ (dimensionless) 1 1 Constant

9 jref0,H+ (A m-‐2) 0.05 0.05 Constant

10 ΔHH+ (J mol-‐1) 30000 30000 Constant

11 TR (K) 293.15 293.15 Constant

12 E°H+ (V vs SCE) -‐0.241 -‐0.241 Constant

13 Cs,H+ (mol m-‐3) 0.000001 0.000001 Constant

14 DH+ (m2 s-‐1) 9.47E-‐09 9.47E-‐09 Constant

15 δN,H+ (m) 0.0000167 0.0000167 Constant

16 F (C mol-‐1) 96485 96485 Constant

17 R (J mol-‐1 K-‐1) 8.314 8.314 Constant

18 tolerance (%) -‐ 50

It was determined the most efficient method to address the limitation of using a constant value

for Ecorr was to create a solver loop based around the below Eqn. [10] for the overall charge

transfer where Ecorr is defined by when 𝑗!" + 𝑗!! are in equilibrium which yields the free

corrosion potential. Figs. B1 and B2 depict the solver parameters as inputted in the solver

function, and the cells that return the value once the loop as converged as close as possible to

zero. These parameters were created to both define Ecorr so a value is converged upon quickly

and be able to be responsive to changes in the input variables of pH (i. e.C!,!! is converted

from the input pH) and temperature.

𝑗! = 𝑗!" + 𝑗!",!! + 𝑗!",!! = 𝑗!" + 𝑗!! = 0 [10]

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Fig.1 B1 displays the five solver parameters:

1. The first parameter is 𝐶!,!" ≥ 𝐶!,!". This ensures that if corrosion is occurring, then

the metal hasn’t completely corroded, in which case concentration of iron in the bulk

solution would be likely be greater then that of the surface of the metal

2. The second parameter, 𝐶!,!" ≥ 0.001 is described by Javaherdashti et al. (2001) as the

lowest recordable surface concentration of iron

3. The third parameter, 𝐶!,!".≤ 1e-05 represents the maximum concentration of iron in

the bulk solution

4. The fourth and fifth parameters both describe the domain of values that Ecorr may take

based on the findings of Simth et al. (2011) that found the range of values to be

-0.4 ≤ Ecorr ≤ -1.

Fig. B1: Solver Parameters

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Fig. B2: Solver Loop Input Cells for equating jT = 0

Instructions for Use:

Note: Based on 2014 Microsoft Excel on Apple running OS X Yosemite. Key different details

relevant for Windows users will be highlighted when necessary

1. Changing input parameters:

SVA – Adjust one or both inputs of temperature and pH

Fr 13 – Adjust one or both inputs of temperature and pressure by changing the

RiskNormal and RiskTruncate function such that: RiskNormal (mean, stdev,

RiskTruncate (minimum, maximum)).

Figure B3: Input parameters of temperature and pressure

2. Opening Solver Function:

SVA – Solver is a default add-in on Apple running Microsoft Excel. For Windows it

will need to be opened via selectable Add-Ins. By clicking ‘Solve’ the loop will

automatically begin running and attempt to find converge to the specified constraints.

Note, if the copy of Microsoft Excel is requiring an update, then running the loop will

likely shut the program down

à Tools à Solver à ‘Open Solver’ à Click ‘Solve’

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Fr 13 – Not necessary to open and run solver when undertaking Fr 13 when changing

the input parameters. It will run a separate loop automatically for every iteration

(where the user specifies the number of iteration) once the simulation initiates.

When using Windows however the following steps must be taken to ensure that the

solver is not running a single loop and using that value for all simulated iterations.

à Simulation Settings à Macros à Select ‘Excel Tool’ instead of ‘VBA Macros’

à Click ‘Run Macros’

Figure B4: Screenshot of Guide to Opening Solver for SVA

Figure B5: Screenshot of Guide to Running Solver for SVA

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APPENDIX C

Table C1 – SVA and Fr 13 Results (T = 293.15 K, pH =5.15, Tolerance = 0 %)



3 pH 5.15 5.15 RiskNormal(5.15,0.515,RiskTruncate(4.635,5.

665)) 4 5 Constants 6 αa,Fe (dimensionless) 0.4 0.4 Constant 7 αa,H+ (dimensionless) 0.6 0.6 Constant 8 αc,Fe (dimensionless) 0.6 0.6 Constant 9 αc,H+ (dimensionless) 0.4 0.4 Constant

10 nFe (dimensionless) 2 2 Constant 11 nH+ (dimensionless) 1 1 Constant 12 e(0,Fe) (A) 1.00E-07 1.00E-07 Constant 13 e(0,H+) (A) 1.00E-07 1.00E-07 Constant 14 A,E (m^2) 2.83E-03 2.83E-03 Constant 15 𝛾,Fe (dimensionless) 0.3 0.3 Constant 16 𝛾,H+ (dimensionless) 0.75 0.75 Constant 17 E°Fe (V vs SCE) -0.681 -0.681 Constant 18 E°H+ (V vs SCE) -0.241 -0.241 Constant 19 Cs,Fe (mol m-3) 1.00E-03 1.00E-03 Constant 20 Cs,H+ (mol m-3) 1.00E-07 1.00E-07 Constant 21 Cb,Fe (mol m-3) 1.01E-05 1.01E-05 Constant 22 DFe (m2 s-1) 7.98E-10 7.98E-10 Constant 23 DH+ (m2 s-1) 9.47E-09 9.47E-09 Constant 24 δN,Fe (m2) 7.23E-06 7.23E-06 Constant 25 δN,H+ (m2) 1.67E-05 1.67E-05 Constant 26 F (C mol-1) 96485 96485 Constant 27 R (J mol-1 K-1) 8.314 8.314 Constant 28 Tolerance (%) - 0 29 30 Calculations 31 Cb,H+ (mol m3) 7.08E-03 7.08E-03 Eq. [1] 32 j0,Fe (A m-2) 1.40E-04 1.40E-04 Eq. [5] 33 j0,H+ (A m-2) 0.00 0.00 Eq. [7] 34 Erev,Fe (V vs SCE) -7.68E-01 -7.68E-01 Eq. [6] 35 Erev,H+ (V vs SCE) -6.48E-01 -6.48E-01 Eq. [4] 36 jmt,Fe (A m2) 2.11E-02 2.11E-02 Eq. [9]

37 jmt,H+ (A m2)

-3.87E-01 -

0.387335386

Eq. [10]

38 jct,Fe (A m2) 3.66E-01 3.66E-01 Eq. [11] 39 jct,H+(A m2) 0.00 0.00 40 ηFe (V vs SCE) 2.48E-01 2.48E-01 41 ηH+ (V vs SCE) 0.13 0.13 Eq. [13] 42 Ecorr (V vs. SCE) -0.52 -0.52 43 jFe (A m-2) 0.39 0.39 Eq. [6] 44 jH+ (A m-2) -0.39 -0.39 Eq. [6] 45 jT (A m-2) 0.00 0.00 Eq. [6] 46 0.00 0.00 Eq. [6] 47 Output 48 CR (mm yr-1) 0.45 0.45 49 50 p - 0.00 Eq. [16]

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3 pH 5.15 5.15 RiskNormal(5.15,0.515,RiskTruncate(4.63

5,5.665)) 4 5 Constants 6 αa,Fe (dimensionless) 0.4 0.4 Constant 7 αa,H+ (dimensionless) 0.6 0.6 Constant 8 αc,Fe (dimensionless) 0.6 0.6 Constant 9 αc,H+ (dimensionless) 0.4 0.4 Constant

10 nFe (dimensionless) 2 2 Constant 11 nH+ (dimensionless) 1 1 Constant 12 e(0,Fe) (A) 1.00E-07 1.00E-07 Constant 13 e(0,H+) (A) 1.00E-07 1.00E-07 Constant 14 A,E (m^2) 2.83E-03 2.83E-03 Constant 15 𝛾,Fe (dimensionless) 0.3 0.3 Constant 16 𝛾,H+ (dimensionless) 0.75 0.75 Constant 17 E°Fe (V vs SCE) -0.681 -0.681 Constant 18 E°H+ (V vs SCE) -0.241 -0.241 Constant 19 Cs,Fe (mol m-3) 1.00E-03 1.00E-03 Constant 20 Cs,H+ (mol m-3) 1.00E-07 1.00E-07 Constant 21 Cb,Fe (mol m-3) 1.01E-05 1.01E-05 Constant 22 DFe (m2 s-1) 7.98E-10 7.98E-10 Constant 23 DH+ (m2 s-1) 9.47E-09 9.47E-09 Constant 24 δN,Fe (m2) 7.23E-06 7.23E-06 Constant 25 δN,H+ (m2) 1.67E-05 1.67E-05 Constant 26 F (C mol-1) 96485 96485 Constant 27 R (J mol-1 K-1) 8.314 8.314 Constant 28 Tolerance (%) - 50 29 30 Calculations 31 Cb,H+ (mol m3) 7.08E-03 7.08E-03 Eq. [1] 32 j0,Fe (A m-2) 1.40E-04 1.40E-04 Eq. [5] 33 j0,H+ (A m-2) 0.00 0.00 Eq. [7] 34 Erev,Fe (V vs SCE) -7.68E-01 -7.68E-01 Eq. [6] 35 Erev,H+ (V vs SCE) -6.48E-01 -6.48E-01 Eq. [4] 36 jmt,Fe (A m2) 2.11E-02 2.11E-02 Eq. [9] 37 jmt,H+ (A m2) -3.87E-01 -0.387335386 Eq. [10] 38 jct,Fe (A m2) 3.66E-01 3.66E-01 Eq. [11] 39 jct,H+(A m2) 0.00 0.00 40 ηFe (V vs SCE) 2.48E-01 2.48E-01 41 ηH+ (V vs SCE) 0.13 0.13 Eq. [13] 42 Ecorr (V vs. SCE) -0.52 -0.52 43 jFe (A m-2) 0.39 0.39 Eq. [6] ]44 jH+ (A m-2) -0.39 -0.39 Eq. [6] 45 jT (A m-2) 0.00 0.00 Eq. [6] 46 0.00 0.00 Eq. [6] 47 Output 48 CR (mm yr-1) 0.45 0.45 49 50 p - -50.00 Eq. [16]

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3 pH 7.5 7.641987129 RiskNormal(7.5,0.75,RiskTrun

cate(6.95,8.45)) 4 5 Constants 6 αa,Fe (dimensionless) 0.4 0.4 Constant 7 αa,H+ (dimensionless) 0.6 0.6 Constant 8 αc,Fe (dimensionless) 0.6 0.6 Constant 9 αc,H+ (dimensionless) 0.4 0.4 Constant

10 nFe (dimensionless) 2 2 Constant 11 nH+ (dimensionless) 1 1 Constant 12 e(0,Fe) (A) 1.00E-07 1.00E-07 Constant 13 e(0,H+) (A) 1.00E-07 1.00E-07 Constant 14 A,E (m^2) 2.83E-03 2.83E-03 Constant 15 𝛾,Fe (dimensionless) 0.3 0.3 Constant 16 𝛾,H+ (dimensionless) 0.75 0.75 Constant 17 E°Fe (V vs SCE) -0.681 -0.681 Constant 18 E°H+ (V vs SCE) -0.241 -0.241 Constant 19 Cs,Fe (mol m-3) 1.00E-03 1.00E-03 Constant 20 Cs,H+ (mol m-3) 1.00E-07 1.00E-07 Constant 21 Cb,Fe (mol m-3) 1.01E-05 1.01E-05 Constant 22 DFe (m2 s-1) 7.98E-10 7.98E-10 Constant 23 DH+ (m2 s-1) 9.47E-09 9.47E-09 Constant 24 δN,Fe (m2) 7.23E-06 7.23E-06 Constant 25 δN,H+ (m2) 1.67E-05 1.67E-05 Constant 26 F (C mol-1) 96485 96485 Constant 27 R (J mol-1 K-1) 8.314 8.314 Constant 28 Tolerance (%) - 50 29 30 Calculations 31 Cb,H+ (mol m3) 3.16E-05 2.28E-05 Eq. [1] 32 j0,Fe (A m-2) 1.40E-04 1.40E-04 Eq. [5] 33 j0,H+ (A m-2) 0.00 0.00 Eq. [7] 34 Erev,Fe (V vs SCE) -7.68E-01 -7.68E-01 Eq. [6] 35 Erev,H+ (V vs SCE) -6.48E-01 -6.48E-01 Eq. [4] 36 jmt,Fe (A m2) 2.11E-02 2.11E-02 Eq. [9] 37 jmt,H+ (A m2) -1.72E-03 -0.001242217 Eq. [10] 38 jct,Fe (A m2) -1.93E-02 -1.93E-02 Eq. [11] 39 jct,H+(A m2) 0.00 0.00 40 ηFe (V vs SCE) -1.04E-01 -1.04E-01 41 ηH+ (V vs SCE) -0.22 -0.22 Eq. [13] 42 Ecorr (V vs. SCE) -0.87 -0.87 43 jFe (A m-2) 0.00 0.00 Eq. [6] 44 jH+ (A m-2) 0.00 0.00 Eq. [6] 45 jT (A m-2) 0.00 0.00 Eq. [6] 46 0.00 0.00 Eq. [6] 47 Output 48 CR (mm yr-1) 0.0020 0.00 49 50 p - -50.00 Eq. [16]

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3 pH 7.5 7.641987129 RiskNormal(7.5,0.75,RiskTruncate(6.95,8.45)) 4 5 Constants 6 αa,Fe (dimensionless) 0.4 0.4 Constant 7 αa,H+ (dimensionless) 0.6 0.6 Constant 8 αc,Fe (dimensionless) 0.6 0.6 Constant 9 αc,H+ (dimensionless) 0.4 0.4 Constant

10 nFe (dimensionless) 2 2 Constant 11 nH+ (dimensionless) 1 1 Constant 12 e(0,Fe) (A) 1.00E-07 1.00E-07 Constant 13 e(0,H+) (A) 1.00E-07 1.00E-07 Constant 14 A,E (m^2) 2.83E-03 2.83E-03 Constant 15 𝛾,Fe (dimensionless) 0.3 0.3 Constant 16 𝛾,H+ (dimensionless) 0.75 0.75 Constant 17 E°Fe (V vs SCE) -0.681 -0.681 Constant 18 E°H+ (V vs SCE) -0.241 -0.241 Constant 19 Cs,Fe (mol m-3) 1.00E-03 1.00E-03 Constant 20 Cs,H+ (mol m-3) 1.00E-07 1.00E-07 Constant 21 Cb,Fe (mol m-3) 1.01E-05 1.01E-05 Constant 22 DFe (m2 s-1) 7.98E-10 7.98E-10 Constant 23 DH+ (m2 s-1) 9.47E-09 9.47E-09 Constant 24 δN,Fe (m2) 7.23E-06 7.23E-06 Constant 25 δN,H+ (m2) 1.67E-05 1.67E-05 Constant 26 F (C mol-1) 96485 96485 Constant 27 R (J mol-1 K-1) 8.314 8.314 Constant 28 Tolerance (%) - 0 29 30 Calculations 31 Cb,H+ (mol m3) 3.16E-05 2.28E-05 Eq. [1] 32 j0,Fe (A m-2) 1.40E-04 1.40E-04 Eq. [5] 33 j0,H+ (A m-2) 0.00 0.00 Eq. [7]



36 jmt,Fe (A m2) 2.11E-02 2.11E-02 Eq. [9]

37 jmt,H+ (A m2) -1.72E-03 -0.001242217 Eq. [10]

38 jct,Fe (A m2) -1.93E-02 -1.93E-02 Eq. [11]

39 jct,H+(A m2) 0.00 0.00 40 ηFe (V vs SCE) -1.04E-

01 -1.04E-01 41 ηH+ (V vs SCE) -0.22 -0.22 Eq. [13] 42 Ecorr (V vs. SCE) -0.87 -0.87 43 jFe (A m-2) 0.00 0.00 Eq. [6] 44 jH+ (A m-2) 0.00 0.00 Eq. [6] 45 jT (A m-2) 0.00 0.00 Eq. [6] 46 0.00 0.00 Eq. [6] 47 Output 48 CR (mm yr-1) 0.0020 0.00 49 50 p - 0.00 Eq. [16]

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10 nFe (dimensionless) 2 2 Constant 11 nH+ (dimensionless) 1 1 Constant 12 e(0,Fe) (A) 1.00E-07 1.00E-07 Constant 13 e(0,H+) (A) 1.00E-07 1.00E-07 Constant 14 A,E (m^2) 2.83E-03 2.83E-03 Constant 15 𝛾,Fe (dimensionless) 0.3 0.3 Constant 16 𝛾,H+ (dimensionless) 0.75 0.75 Constant 17 E°Fe (V vs SCE) -0.681 -0.681 Constant 18 E°H+ (V vs SCE) -0.241 -0.241 Constant 19 Cs,Fe (mol m-3) 1.00E-03 1.00E-03 Constant 20 Cs,H+ (mol m-3) 1.00E-07 1.00E-07 Constant 21 Cb,Fe (mol m-3) 1.01E-05 1.01E-05 Constant 22 DFe (m2 s-1) 7.98E-10 7.98E-10 Constant 23 DH+ (m2 s-1) 9.47E-09 9.47E-09 Constant 24 δN,Fe (m2) 7.23E-06 7.23E-06 Constant 25 δN,H+ (m2) 1.67E-05 1.67E-05 Constant 26 F (C mol-1) 96485 96485 Constant 27 R (J mol-1 K-1) 8.314 8.314 Constant 28 Tolerance (%) - 50 29 30 Calculations 31 Cb,H+ (mol m3) 1.00E+0

0 1.00E+00 Eq. [1]

32 j0,Fe (A m-2) 1.40E-04 1.40E-04 Eq. [5] 33 j0,H+ (A m-2) 0.00 0.00 Eq. [7]



36 jmt,Fe (A m2) 2.11E-02 2.11E-02 Eq. [9]

37 jmt,H+ (A m2) -

5.47E+01

-54.71334483 Eq. [10]

38 jct,Fe (A m2) 1.63E+01 1.63E+01 Eq. [11]

39 jct,H+(A m2) 0.00 0.00 40 ηFe (V vs SCE) 3.68E-01 3.68E-01 41 ηH+ (V vs SCE) 0.25 0.25 Eq. [13] 42 Ecorr (V vs. SCE) -0.40 -0.40 43 jFe (A m-2) 16.27 16.27 Eq. [6] 44 jH+ (A m-2) -54.71 -54.71 Eq. [6] 45 jT (A m-2) -38.44 -38.44 Eq. [6] 46 38.44 38.44 Eq. [6] 47 Output 48 CR (mm yr-1) 18.79 18.79 49 50 p - -50.00 Eq. [16]

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10 nFe (dimensionless) 2 2 Constant 11 nH+ (dimensionless) 1 1 Constant 12 e(0,Fe) (A) 1.00E-07 1.00E-07 Constant 13 e(0,H+) (A) 1.00E-07 1.00E-07 Constant 14 A,E (m^2) 2.83E-03 2.83E-03 Constant 15 𝛾,Fe (dimensionless) 0.3 0.3 Constant 16 𝛾,H+ (dimensionless) 0.75 0.75 Constant 17 E°Fe (V vs SCE) -0.681 -0.681 Constant 18 E°H+ (V vs SCE) -0.241 -0.241 Constant 19 Cs,Fe (mol m-3) 1.00E-03 1.00E-03 Constant 20 Cs,H+ (mol m-3) 1.00E-07 1.00E-07 Constant 21 Cb,Fe (mol m-3) 1.01E-05 1.01E-05 Constant 22 DFe (m2 s-1) 7.98E-10 7.98E-10 Constant 23 DH+ (m2 s-1) 9.47E-09 9.47E-09 Constant 24 δN,Fe (m2) 7.23E-06 7.23E-06 Constant 25 δN,H+ (m2) 1.67E-05 1.67E-05 Constant 26 F (C mol-1) 96485 96485 Constant 27 R (J mol-1 K-1) 8.314 8.314 Constant 28 Tolerance (%) - 0 29 30 Calculations 31 Cb,H+ (mol m3) 1.00E+00 1.00E+00 Eq. [1] 32 j0,Fe (A m-2) 1.40E-04 1.40E-04 Eq. [5] 33 j0,H+ (A m-2) 0.00 0.00 Eq. [7] 34 Erev,Fe (V vs SCE) -7.68E-01 -7.68E-01 Eq. [6] 35 Erev,H+ (V vs SCE) -6.48E-01 -6.48E-01 Eq. [4] 36 jmt,Fe (A m2) 2.11E-02 2.11E-02 Eq. [9] 37 jmt,H+ (A m2) -5.47E+01 -54.71334483 Eq. [10] 38 jct,Fe (A m2) 1.63E+01 1.63E+01 Eq. [11] 39 jct,H+(A m2) 0.00 0.00 40 ηFe (V vs SCE) 3.68E-01 3.68E-01 41 ηH+ (V vs SCE) 0.25 0.25 Eq. [13] 42 Ecorr (V vs. SCE) -0.40 -0.40 43 jFe (A m-2) 16.27 16.27 Eq. [6] 44 jH+ (A m-2) -54.71 -54.71 Eq. [6] 45 jT (A m-2) -38.44 -38.44 Eq. [6] 46 38.44 38.44 Eq. [6] 47 Output 48 CR (mm yr-1) 18.79 18.79 49 50 p - 0.00 Eq. [16]

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Fig. C1: r-MC Risk Factor Distribution (T = 293.15 K, pH =5.15, Tolerance = 0 %)


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Fig. C3: r-MC Risk Factor Distribution (T = 293.15 K, pH =3, Tolerance = 0 %)

Fig. C4: r-MC Risk Factor Distribution (T = 293.15 K, pH =3, Tolerance = 50 %)

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undergraduate research thesis

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