Journal of Electroanalytical Chemistry 812 (2018) 115–121

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Journal of Electroanalytical Chemistry

journal homepage: www.elsevier.com/locate/jelechem

On quantitative corrosion rate monitoring with ultrasound T

⁎
Fangxin Zou , Frederic B. Cegla
Non-Destructive Evaluation Group, Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK

A R T I C L E I N F O A B S T R A C T

Keywords: Wall-thickness loss rate (WTLR) is an important parameter that defines a corrosion process. The speed at which a
Corrosion monitoring WTLR can be determined is directly related to how quickly one can intervene in a process that is heading in the
Corrosion rate wrong direction. Ultrasonic testing has been widely used as a convenient and efficient technique for online
Ultrasound corrosion monitoring. One of the key performance parameters of ultrasonic corrosion monitoring is detection
Piezoelectric transducer
speed. While WTLRs can be determined by fitting linear lines to wall-thickness loss (WTL) measurements, the
Non-destructive evaluation
Structural health monitoring
presence of noise in the measurements makes it difficult to judge the confidence levels of the slopes that are
calculated this way. In this paper, a statistics based approach for assessing the detection speeds that are
achievable by ultrasonic corrosion monitoring systems is presented. Through the statistical analysis of experi-
mental data, a state-of-the-art laboratory setup is shown to be able to detect both WTLRs and changes in WTLR
that are of interest to industry (i.e. 0.1–0.2 mm/year) within 1–2 h.

1. Introduction genuine WTLs from measurement noise. In this paper, a statistical ap-
proach is used to assess the speeds at which corrosion processes and
In the US alone, corrosion costs the oil and gas industry billions of changes in corrosion rate can be detected. The approach quantifies the
dollars a year [1]. Corrosion induced component failures have caused confidence levels with which WTLRs and changes in WTLR can be es-
devastating environmental, social and financial consequences [2,3]. timated by linear line fitting. WTL measurements that were acquired
Online corrosion monitoring helps to improve the safety and the sus- during open-circuit corrosion processes, using the setup constructed by
tainability of assets. Conventional corrosion monitoring techniques, the authors, were quantitatively analysed to demonstrate the state-of-
such as linear polarisation resistance measurements [4,5] and weight the-art measurement capability of ultrasonic corrosion monitoring. The
loss measurements [6–8], are intrusive since they require probes to statistical approach offers a convenient way of evaluating the perfor-
access the interiors of closed vessels. Also, the estimation of wall- mances of ultrasonic corrosion monitoring systems.
thickness loss rates (WTLRs) by these techniques depends on a number
of assumptions (e.g. the chemical reactions that take place and the areas 2. State-of-the-art ultrasonic wall-thickness loss measurements
over which they occur) which often lead to loss of accuracy.
Ultrasonic testing (UT) offers a non-intrusive and more direct ap- Fig. 1 shows the ultrasonically measured WTLs of a 10 mm mild
proach for corrosion monitoring. In the past, UT could only be carried steel sample (BS 970:1983:080A15, UNS G10160) during open-circuit
out manually, and due to the uncertainties associated with transducer corrosion experiments. The experiments were conducted using the ul-
positioning and coupling, the method suffered from poor measurement trasonic monitoring setup constructed by the authors [13] which has a
repeatability (i.e. 0.1–0.5 mm) [9]. The use of permanently installed thickness measurement repeatability of ~20 nm over 1 h and that of
transducers has significantly improved the measurement repeatability ~40 nm over 24 h. The measurements were acquired at 1 min intervals.
of the method [10]. Ultrasonic wall-thickness loss (WTL) measurements The electrolytes used are distilled water, 0.1 M citric acid and 0.1 M
with micron level precision were subsequently reported [11,12]. Lately, acetic acid. The ultrasonic measurements were validated by optical
the authors constructed a state-of-the-art laboratory setup that is able to surface profile scans which were obtained by a white light inter-
achieve an unprecedented WTL measurement repeatability in the range ferometer (TMS-100 TopMap Metro.Lab, Polytec, Germany) after the
of 10s of nanometres [13]. corrosion experiments had finished. The procedure for carrying out the
The simplest way of determining WTLRs from ultrasonic WTL optical scans can be found in [13].
measurements is by linear least squares regression. When very small As shown in Fig. 1(a), distilled water had not caused any noticeable
WTLRs are to be determined, it is crucial to be able to differentiate WTL over the time frame of the experiment. The measurements that

⁎
Corresponding author.
E-mail addresses: f.zou11@imperial.ac.uk (F. Zou), f.cegla@imperial.ac.uk (F.B. Cegla).

https://doi.org/10.1016/j.jelechem.2018.02.005
Received 30 November 2017; Received in revised form 1 February 2018; Accepted 5 February 2018
Available online 06 February 2018
1572-6657/ © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).
F. Zou, F.B. Cegla Journal of Electroanalytical Chemistry 812 (2018) 115–121

Passivation
acetic acid
Passivation
citric acid

(a) (b)
Fig. 1. (a) Ultrasonic measurements of the WTLs of the sample during the experiments with distilled water (black), 0.1 M citric acid (blue) and 0.1 M acetic acid (red). The mean thickness
changes calculated from the optical profile scans of the corrosion surfaces are shown as error bars. (b) Measurements that were acquired in the first 30 min. (For interpretation of the
references to colour in this figure legend, the reader is referred to the web version of this article.)

PN –
bounded PDRC=95%
by black
line and
PR –

corrosion process
red curve
bounded

Detection of
by black
line and
blue
curve

(a) (b)
Fig. 2. (a) PDF curves of the reference and the new WTLRs that are determined up until a given time instant. (b) PDRC curve for WTLRs.

were acquired during the experiment with distilled water are therefore the consideration of confidence levels that automated, on-the-spot de-
indicative of the noise level of the measurement system that was em- tection of corrosion processes and changes in corrosion rate is achieved.
ployed. The two acidic solutions, on the other hand, had resulted in The statistical approach is equally applicable to analysing field mea-
micron level WTLs. During the two acidic corrosion processes, the effect surements which expectedly have lower measurement repeatability and
of surface passivation, which caused WTLRs to change, was observed at hence result in longer detection times. Also, it is capable of making
the 2nd and the 7th hour respectively. It is worth mentioning that predictions of the response times of ultrasonic corrosion monitoring
surface passivation occurs when corrosion products gradually deposit systems.
onto the corroding surface. This leads to the formation of a corrosion-
inhibiting passivation layer which hinders further diffusion of ions and
3. Detection of statistically significant wall-thickness loss rates
hence slows down corrosion kinetics.
While it is relatively easy to retrospectively identify the two cor-
Consider a set of N WTL measurements which have a variance of
rosion processes and calculate the WTLRs from the WTL measurements
σw2. The standard deviation (σr) of all the WTLRs that can be calculated
by linear least squares regression, it is not straightforward to do so at
from these WTL measurements is given by
the onsets of the changes (without a large number of a priori mea-
surements) since the presence of noise introduces uncertainty to the
σw2
linearly fitted WTLRs. As illustrated in Fig. 1(b), the two acidic corro- σr = N
∑i = 1 (ti − t )
sion processes cannot be clearly identified in the first 15–20 min since (1)
the WTL measurements lie within the noise level of the ultrasonic setup.
where ti is the sampling time instant of the ith WTL measurement, and t
Therefore, in this paper, a statistical approach for confidently de-
is the mean value of all the sampling time instants.
termining WTLRs and changes in WTLR is described, and it is through
A quantity named the probability of detecting a real change (PDRC)

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Table 1
Times of detection for the corrosion processes recorded.

Electrolyte Corrosion WTLR Time of detection (min)

stage (mm/
year) Experimental Predicted

σw = 20 nm σw = 40 nm

Citric acid Pre- ~3 11 8 13

passivation
~1 mm/year Post- ~1 21 17 26
passivation
Acetic acid Pre- ~4 8 7 11
passivation
Post- ~1.8 12 11 18
passivation

form, PDRC is expressed as

PN (t )
PDRC (t ) =
Fig. 3. Illustration of the alignment of the reference and the new measurements that were PR (t ) + PN (t ) (2)
considered for the detection of corrosion processes.
where, as illustrated in Fig. 2(a), PN is the area bounded by a certain
threshold and the probability density function (PDF) curve of the
[14] is introduced to calculate the probability that a WTLR, measured
WTLRs that are determined from a set of new WTL measurements that
at time t, genuinely represents a corrosion process or a change in cor-
are acquired up until time t, and PR is the area bounded by the same
rosion rate as opposed to the result of measurement noise. In equation
threshold and the PDF curve of the WTLRs that are determined from an

(a) (b)

(c) (d)
Fig. 4. PDRC curves for (a) pre-passivation and (b) post-passivation corrosion process with citric acid, and (c) pre-passivation and (b) post-passivation corrosion process with acetic acid.

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(a) (b)

(c)
Fig. 5. Illustration of the reason for the mismatch between initial PDRC values. The data makes use of the measurements that were acquired during the pre-passivation corrosion process
with citric acid. (a) PDF curves drawn with pre-defined mean WTLRs and measurement repeatability. (b) Comparison of true (pre-defined) and temporarily fitted mean WTLR. (c) PDF
curves drawn with temporarily fitted mean WTLRs and measurement repeatability.

equal number of reference WTL measurements. In this work, the passivation acidic corrosion processes were shifted in time and in space
threshold was set to two times the standard deviation of the reference to begin at the origin as demonstrated in Fig. 3.
WTLRs. As shown in Fig. 2(b), a corrosion process or a change in cor- Fig. 4 shows the predicted and the experimentally obtained PDRC
rosion rate is defined as detected when the PDRC value is stably > 95%. curves for the four different segments of corrosion processes. The pre-
It is also possible to use Eqs. (1) and (2) to predict the amount of dictions were attained using σw = [20, 40 nm], WTLR = 0 for the re-
time that a measurement system will take to detect a given corrosion ference measurements, WTLR = [3, 1, 4, 1.8 mm/year] for the new
process. This is done by inputting the pre-determined measurement measurements, and sampling intervals of 1 min. The times of detection
repeatability of the measurement system, the WTLR of the corrosion that are determined from the predicted and the experimentally ob-
process, and the sampling intervals at which measurements are ac- tained PDRC curves are given in Table 1. The experimental values lie in
quired. between the predictions which outline the expected variability.
It is observed from Fig. 4 that while the initial values of the pre-
dicted PDRC curves are close to 50%, the experimentally obtained
4. Application of statistics based detection to state-of-the-art
curves begin from 0. The predicted curves were constructed using mean
experimental data
WTLRs and measurement repeatability that were pre-defined. For a
given corrosion process, the PDF curves of the new and the reference
The WTL measurements that were acquired during each of the two
WTLRs assume the same shape, and for a small number of measure-
acidic corrosion processes can be divided into two segments of data by
ments, they have much overlap (Fig. 5(a)), resulting in PR and PN being
the onset of surface passivation. The mean WTLRs that were calculated
similar and hence PDRC being close to 0.5. On the other hand, the
by linear least squares regressions are ~3 and ~1 mm/year for the pre-
experimentally obtained PDRC curves were constructed in situ using
and the post-passivation corrosion process with citric acid, and ~4 and
mean WTLRs and measurement repeatability that were determined
~1.8 mm/year for those with acetic acid. The speeds at which the four
based on a priori WTL measurements. In this case, when only a small
different segments of corrosion processes could be detected were
number of measurements are present, the temporarily fitted WTLR is
evaluated. The ultrasonic measurements that were acquired during the
very likely to be different from the true value though its confidence
experiment with distilled water were used as the reference data. The
level may be quite high (Fig. 5(b)). The consequence of this is that the
WTL measurements that were acquired during each of the two post-

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(a) (b)

(c)
Fig. 6. Illustration of the reason for the fluctuation in experimentally obtained PDRC values. The data makes use of the measurements that were acquired during the post-passivation
corrosion process with citric acid. (a) PDF curves drawn with pre-defined mean WTLRs and measurement repeatability. (b) Comparison of the mean WTLRs that were determined in situ
using different numbers of WTL measurements. (c) PDF curves drawn with temporarily fitted mean WTLRs and measurement repeatability. For (a) and (c), solid line: based on first 10
measurements, dashed line: based on first 20 measurements, dotted line: based on first 30 measurements.

PDF curve of the new WTLRs falls within that of the reference WTLRs,
and hence the threshold (i.e. two times the standard deviation of the
reference WTLRs) lies outside the PDF curve of the new WTLRs. This in
turn leads to PN = 0 and PDRC = 0.
Another observation that can be made from Fig. 4 is that the pre-
dicted PDRC curves converge smoothly, whereas the experimentally
obtained curves fluctuate before arriving at convergence. Since the
mean WTLRs and the measurement repeatability that were used to
~3 mm/year construct the predicted curves were pre-defined, the overlap between
the PDF curves of a given pair of reference and new WTLRs decreases
gradually with increasing number of measurement (Fig. 6(a)). Conse-
quently, PR and PN part, and PDRC converges to a value that is close to
1. In contrast, the mean WTLRs and the measurement repeatability that
was determined in situ from a small number of experimental WTL
~1 mm/year measurements exhibit fluctuation (Fig. 6(b)). This gives rise to varying
PDF curves (Fig. 6(c)) which then output varying PN and PDRC.
One of the key purposes of online corrosion rate monitoring is to
identify accelerated component degradations so that appropriate cor-
Fig. 7. Illustration of the reference and the new measurements that were considered for rosion control strategies can be applied on time to mitigate further
the detection of changes in corrosion rate. The data makes use of the measurements that
excessive structural losses. In order to ensure that the mitigation stra-
were acquired during the corrosion process with acetic acid.
tegies applied are effective, it is essential to be able to detect the
changes in corrosion rate that they will have led to.

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(a) (b)
Fig. 8. PDRC curves for the changes in corrosion rate in the corrosion processes with (a) citric acid and (b) acetic acid.

Table 2 changes in corrosion rate in the two acidic corrosion processes are
Times of detection for the changes in corrosion rate recorded. displayed in Fig. 8. The predicted curves were constructed using
σw = [20, 40 nm], WTLR = [3, 4 mm/year] for the reference mea-
Electrolyte Change in WTLR (mm/ Time of detection (min)
year)
surements, WTLR = [1, 1.8 mm/year] for the new measurements, and
Experimental Predicted sampling intervals of 1 min. The discrepancies between the predicted
and the experimentally obtained curves can also be attributed to the
σw = 20 nm σw = 40 nm aforementioned reasons. Table 2 shows that the times of detection that
Citric acid ~2 13 11 17
are determined from the experimental results lie within the predicted
Acetic acid ~2.2 11 10 16 variability.

The mean WTLRs of the two acidic corrosion processes changed at 5. Evaluation of ultrasonic corrosion monitoring systems
the 140th and the 455th minute respectively due to surface passivation.
Assume that these changes were caused by the application of some The results presented thus far suggest that the statistics based ap-
corrosion mitigation strategies. In order to construct the PDRC curves of proach is effective in evaluating the capabilities of ultrasonic corrosion
the post-change corrosion processes, the pre-change WTL measure- monitoring systems to detect corrosion processes and changes in cor-
ments were used reversely as the reference measurements as demon- rosion rate. It is worth mentioning that the approach is only sensitive to
strated in Fig. 7. The reversion allowed the measurements that are absolute changes in WTLR, meaning that, in theory, a corrosion process
closer to the onsets of the changes to be contrasted against earlier in the that take places at 2 mm/year requires the same amount of time to be
construction of the PDRC curves. detected as a change in corrosion rate from 1 to 3 mm/year does.
The predicted and the experimentally obtained PDRC curves for the Therefore, the time that it takes to complete the monitoring of a

(a) (b)
Fig. 9. Detectability of absolute changes in corrosion rate with respect to (a) measurement repeatability (sampling time increment: 1 min) and (b) sampling time increment (measurement
repeatability: 20 nm). The variability of the detection speeds that are achievable by the setup constructed by the authors are bounded by the blue and the red curve in (a). (For
interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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corrosion control cycle is essentially equivalent to the sum of the times Acknowledgement
that it takes to detect all the absolute changes in corrosion rate that are
involved. This work was supported by the Engineering and Physical Sciences
Fig. 9 shows the detection speeds that can be achieved at different Research Council [grant number EP/K033565/1].
values of measurement repeatability and different sampling intervals. It
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