DOI: 10.3303/CET2290003 
 

 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Paper Received: 29 December 2021; Revised: 2 March 2022; Accepted: 28 April 2022 
Please cite this article as: Ancione G., Mennuti C., Bragatto P., Milazzo M.F., Proverbio E., 2022, Application of statistical analysis for the 
identification of critical bottom areas due to corrosion in atmospheric storage tanks, Chemical Engineering Transactions, 90, 13-18 
DOI:10.3303/CET2290003 

CHEMICAL ENGINEERING TRANSACTIONS 

VOL. 90, 2022

A publication of 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Aleš Bernatík, Bruno Fabiano
Copyright © 2022, AIDIC Servizi S.r.l.
ISBN 978-88-95608-88-4; ISSN 2283-9216 

Application of Statistical Analysis for the Identification of 
Critical Bottom Areas Due to Corrosion in Atmospheric 

Storage Tanks 
Giuseppa Ancionea*, Canio Mennutib, Paolo Bragattob, Maria Francesca Milazzoa, 
Edoardo Proverbioa

Department of Engineering, University of Messina, Contrada di Dio, 98166 Messina, Italy a
 b Department of Technological Innovation, INAIL Workers’ Compensation Authority, via Fontana Candida, Monteporzio 

Catone Italy 
giusi.ancione@unime.it 

Equipment ageing containing hazardous substances is a criticality for the safe as leakages can give rise to 
serious accidental scenarios such as fires, explosions, and dispersions of chemicals into the environment. The 
attention towards this issue grows over the time and becomes significant when the equipment is reaching the 
end of its lifetime. Ageing management usually includes targeted and in-depth integrity controls performed at 
regular intervals. Atmospheric storage tanks of hydrocarbons are particularly critical as the control of the
bottom integrity requires not only the service interruption, but also the need for the inspectors to stay long time 
in hazardous environments during the time required for the thickness measurements. One of the main causes 
of perforation is corrosion. The whole bottom is in any case subjected to significant stress, therefore, the
thickness of the bottom plates must not be below a threshold value to avoid leakages. The aim of this work is
to investigate the entire bottom of an atmospheric storage tank to identify the most susceptible locations with 
respect to the deterioration due to localised corrosion. The assessment of the probability of perforation of the
bottom indicated the annular ring as the most critical. To achieve this objective, the latest inspection data have 
been used that allowed identifying the probabilities of leakage for the various homogeneous areas identified in 
the bottom. An estimate of the time to reach the critical thickness has also been given based on a recent
approach that combines the extreme value theory of with the Bayes theorem. 

1. Introduction
Atmospheric storage tanks of hydrocarbons are particularly critical because the control of the bottom integrity
requires that they must be taken out of service. Internal inspections are very costly and time consuming, in 
addition there is also the need for the inspectors to stay long time in hazardous environments for the execution
of thickness measurements. The localised corrosion is one of the main causes of the bottom perforation. The 
outer edge at the base of the tank, so-called annular ring, is particularly critical to corrosion because it 
includes the shell welding. Numerous standards (EEMUA, 2014; API, 2016) points that it is essential to 
monitor the thinning of the bottom plates of storage tanks as well as the annular ring to avoid leakages and 
catastrophic floor ruptures. The assessment of the integrity of annular ring can be made from the interior or 
the exterior of the tank. The inspection from the exterior with ultrasounds (UT) requires thoroughly removing
all corrosion products, this is not a safe operation, thus it is preferred to inspect them during planned bottom
inspections. Other in-service inspection methods are acoustic emissions, but these provide only indications of 
the potential evolution of damages. 
Several documents evidenced the relevance of equipment ageing in contributing to major accidents (Wood et 
al., 2013; Semmler, 2016; Gyenes and Wood, 2016; OECD, 2017; Pasman and Fabiano, 2021). In particular, 
the Seveso Directive explicitly requires the operators of major hazard accident establishments to demonstrate 
the adoption of proper management plans to control deterioration processes. To this scope, it would be useful 
for the operators to be able to make predictions about the future equipment condition, to calculate the 
probability of release due to ageing and to understand how long it is possible to safely extend the residual 

13

mailto:giusi.ancione@unime.it


useful lifetime (RUL). The knowledge of the probability of leakage from the bottom plates and the annular ring 
of atmospheric storage tanks allows integrating these accidental scenarios into the safety report of major 
accident hazard establishments. 
The aim of this work is to investigate the entire bottom of an atmospheric storage tanks to identify the most 
susceptible areas to the deterioration due to localised corrosion. This is possible the elaborating data from the 
latest inspection in order to identify the probabilities of leakage for the various critical areas. An estimate of the 
time to reach the critical floor thickness (bottom plates including its annular ring of the tank) has also been 
made based on a recent approach that combines the extreme value theory of with the Bayes theorem 
(Milazzo et al., 2022). Thickness measurements are obtained by means of field inspections with different 
measurement techniques such as ultrasounds and magnetic flux leakage. This study has been developed 
within the MAC4PRO project, which supported by the Italian Workers’ Compensation Authority (INAIL), and 
focuses on a wider investigation context, including civil infrastructures and industrial structures. The paper is 
structured in the following sections: Section 2 discusses the methodology for the assessment of the probability 
of leakage from the bottom and the residual useful lifetime; Sections 3 presents the case-study investigated in 
this study; Section 3 shows the results of the application and the discussion; finally, Section 4 provides some 
conclusions and future remarks. 

2. Methodology 
The proposed approach for the assessment of the perforation probability of the bottom of atmospheric storage 
tanks and the residual lifetime uses the extreme value theory and the Bayesian inference (Milazzo et al. 
2022;). The input data to the model is the thickness measurements obtained through field inspections. The 
studied area is divided firstly in homogeneous areas and then into smaller parts. For each part, the minimum 
thickness is identified. After, the sets of the maximum corrosion values are obtained for each homogeneous 
area, the Gumbel distribution (Gumbel, 1958) is used to estimate the probability of the critical depth for each 
area: 

( ) exp exp
x

F x
β

α
 −  

= − −  
    

(1) 

where F(x) is the cumulative probability function; α and β are respectively the scale and the location 
parameters of the distribution. 
 
To determine α and β, a reduced variate (y) is introduced to make the linearization of the Gumbel function 
(Gumbel plot). The parameters α and β are obtained from the slope and the intercept of the line representing 
the Gumbel plot: 

 
x

y
β

α
−

=  (2) 

( )1ln ln ( )y F y= −  (3) 
where F(y) is the cumulative probability. 
 
The Bayesian inference allows estimating a posterior probability of the scale and position parameters 
 χ”(α|xmax), and λ”(β|xmax) at a given time. This is possible by means of inspection data, i.e. the likelihood 
functions f(xmax|α) and f(xmax|β), and the a priori probabilities χ’(α), and λ’(β) which includes the knowledge 
deriving from inspections made for tanks with similar characteristics. The following correlations represent the 
Bayesian inference: 

max
max

max

'( ) ( | )
''( | )

'( ) ( | )
f x

x
f x d

χ α α
χ α

χ α α α
⋅

=
⋅ ⋅∫  

(4) 

max
max

max

'( ) ( | )
''( | )

'( ) ( | )
f x

x
f x d

λ β β
λ β

λ β β β
⋅

=
⋅ ⋅∫  

(5) 

Once the prediction of the parameters of the Gumbel distributions have been obtained, a new plot position is 
constructed that represents the expected trend after a given time. By using the past and expected plot 
positions, the probability (y axis) that corrosion is less or equal to a given value (x axis) can be read. If several 
inspections are available, it possible for a certain probability to draw the graph corrosion vs. time. The 

14



corrosion rate is the slope of the curve and is not constant. Finally, the curve allows also estimating the 
residual useful life (RUL), associated to the same probability, which is obtained by intersecting the curve 
corrosion vs. time with the threshold limit for the thickness of the bottom and annular ring. 

3. Case-study 
The methodology has been applied to an atmospheric storage tank containing diesel fuel (Figure 1a), located 
in a storage depot of an Italian Seveso site. The measures of thickness have been taken for the 135 carbon 
steel plates of the tank bottom and in three locations points of the annular ring (external side, central and 
internal side for the main cardinal directions and some intermediate directions) (Figure 1b). The nominal 
thickness of bottom plates is 8 mm, whereas it is 8.5 mm for the annular ring. The circular covered area of the 
tank is about 1855 m2 with a radius of 24.3 m. The tank is in-service since the 1965. Two non-destructive 
inspections, carried out for the bottom and the annual ring, have been analysed for this study. Between the 
first and second bottom inspections, no plate changes have been carried out. A summary of the statistics of 
the inspection data is shown in Table 1. 
 

a)  b)  

Figure 1: a) Scheme of a typical atmospheric storage tank with fixed roof [API 650] and b) location map of the 
measured points during the annular ring inspections. 

Table 1: Statistics for the inspection data for annular ring and bottom plates. 

Component ID inspection Year Technique 
Average 

thickness [mm] 
Minimum 

thickness [mm] 
Standard 
deviation 

Bottom 
plates 

1 1990 UTM 6.84 6.1 0.21 

2 2019 MFL 5.1 0.4 1.82 

Annular ring 
1 2002 UTM 7.27 5.8 0.67 

2 2008 UTM 6.37 4.2 1.05 

4. Results and discussion 
The sets of maximum corrosion depths deriving from the inspection of the bottom and the annular ring have 
been used for the estimation of the parameters of the Gumbel distributions and the subsequent analysis gave 
the corrosion rate and RUL by applying the methodology described in Section 2.  

4.1 Application of the extreme value theory 

Figure 2a) and 2b) gives the plot positions constructed by using the inspections 1 and 2 respectively for the 
bottom plates and the annular ring. The parameters of the Gumbel distributions have been obtained (Table 2). 
The values of scale and location parameters of the bottom plates and the annular ring refer to different years, 
therefore, an annual increase has been calculated for them (∆). 
It can be observed that the scale parameter (α), which represents the dispersion of pits over the surface, 
grows in similar way for both the bottom and the annual ring; whereas the location parameter (β), which is the 
most frequent pit depth, significatively increases for the annular plates (~50% for the annular ring and ~19% of 

15



the bottom plates). This investigation confirms that the annular ring is the most critical area of an atmospheric 
storage tank containing hydrocarbons. 

a)    b)  

Figure 2: Plot positions for inspection 1 and 2 respectively for: a) bottom plates and b) annular ring. 

Table 2: Gumbel parameters. 

Year 
Bottom plates Annular plates 

Scale parameter 
(α) 

Position parameter 
(β) 

Scale parameter 
(α) 

Position parameter 
(β) 

2002 0.527 1.926 0.876 1.076 
2008 0.715 2.292 1.186 1.613 

∆ 0.188 0.366 0.309 0.538 
∆(%) 35.6% 19.0% 35.3% 50.0% 

4.2 Model validation 

The approach has already been validated for the bottom plates in a previous work (Milazzo, et al., 2022). In 
this study the validation has been made for the annular ring area by using the data collected during the first 
inspection (2002). The prediction of the distribution parameters has been done at the time of the second 
inspection in order to compare the result with the actual parameters. Figure 3 shows the a priori and posteriori 
distributions of the distribution parameters. Table 3 shows the results of the Bayesian inference and compare 
them with those obtained from the application of the approach presented in Section 2. 

 a)  b)  

Figure 3: A priori and posteriori distributions for: a) the scale parameter, b) the location parameter. 

16



Table 3: Actual and expected Gumbel parameters for the inspection of 2008. 
 Scale parameter (α) Position parameter (β) 

Actual values 1.186 1.613 
Values from Bayesian inference 1.225 1.630 

4.3 Estimate of the RUL 

Once the most critical part of the bottom of the atmospheric tank has been identified the RUL has been 
estimated. By means of the Bayesian inference the distribution parameters and the corrosion rate in 2022 
have been predicted by assuming that no replacement has been made since the last inspection and that the 
surrounding conditions have not been modified (repairs, partial or total replacements of plates, change of the 
type of substance stored inside, etc.). Since the nominal thickness of the plates is 8.5 mm, a critical threshold 
of 6 mm has been used to define the residual useful lifetime of the equipment as suggested in EEMUA (2014). 
In Figure 4a) the actual and expected plot positions are reported, whereas in Figure 4b) a detail of the Gumbel 
cumulative probability curves is shown. Finally, Figure 5 shows the corrosion rate and the RUL associated with 
a probability of 90%. The corrosion rate has been estimated to be 0.22 mm/year. The RUL for the equipment 
after the second inspection of the annular plates (i.e. in 2008) is about 7 years.  
 

a)     b)   

Figure 4: a) Actual and expected plot positions for the annual ring, b) Actual and expected Gumbel cumulative 
probability distributions for the annual ring (detail). 

5. Conclusions 
The approach allows identifying the most critical area based on the analysis of inspection data and thus on the 
conditions detected. At the same time the establishment operator can make forecast about the evolution of the 
degradation of the whole bottom tank based on the estimation of the probability of the residual thickness. The 
approach supports in planning the next inspection by reducing the out-service time and the exposure of 
operators (maintenance workers and inspectors) to a dangerous environment if the degradation of the tank 
has been well-controlled. 

17



 

Figure 5: Residual Useful Lifetime (probability 90%). 

Acknowledgments 

This work has been funded by INAIL within the BRIC/2018, ID = 11 framework, project MAC4PRO. The 
authors thank unem - Unione Energie per la Mobilità - for providing the data used in this study as part of the 
agreement INAIL-unem. 

References 

API, American Petroleum Institute, 2007, Welded Tanks for Oil Storage, API Standard 650, 11th ed., New 
York, US.  

API, American Petroleum Institute, 2016, Risk-Based Inspection Technology, API Recommended Practice API 
RP 581, 3rd ed., New York, US. 

EEMUA, the Engineering Equipment and Materials Users Association, 2014, Users’ Guide to the Inspection, 
Maintenance and Repair of above Ground Vertical Cylindrical Steel Storage Tanks, Standard EEMUA no. 
159. 

Gyenes, Z., Wood, M.H., 2016, Lessons Learned from Major Accidents Relating to Ageing of Chemical Plants, 
Chemical Engineering Transactions, 48, 733-738. 

Milazzo M.F., Ancione G., Bragatto P., Proverbio E., 2022 (forthcoming), An approach for the estimation of the 
Residual Useful Lifetime of atmospheric storage tanks in oil industry, submitted to the Journal of Loss 
Prevention in the Process Industries 

OECD, Organisation for Economic Cooperation and Development, 2017, Ageing of hazardous installations, 
OECD Environment, Health and Safety Publications - Series on Chemical Accidents, no. 29. 

Pasman, H.J., Fabiano, B., 2021, The Delft 1974 and 2019 European Loss Prevention Symposia: Highlights 
and an impression of process safety evolutionary changes from the 1st to the 16th LPS, Process Safety 
and Environmental Protection, 147, 80-91. 

Semmler, R., 2016, Aging equipment in facilities and daily maintenance-latent risks on sites with major 
accident hazards directive 2012/18/EU, Chemical Engineering Transactions, 48, 523-528. 

Wood, M.H., Arellano, A.V., Van Wijk, L., 2013, Corrosion Related Accidents in Petroleum Refineries, 
European Commission Joint Research Centre Report no. EUR 26331. 

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	lp-2022-abstract-139.pdf
	Application of Statistical Analysis for the Identification of Critical Bottom Areas Due to Corrosion in Atmospheric Storage Tanks