*Corr. Author’s Address: Jožef Stefan International Postgraduate School, Slovenia, ales.povse@petrol.si 282
Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 282-292 Received for review: 2023-06-08
© 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2024-02-06
DOI:10.5545/sv-jme.2023.682 Original Scientific Paper Accepted for publication: 2024-04-12
Evaluation of the Condition of the Bottom of the Tanks  
for Petroleum Products-Forecast of the Remaining Operating Life
Povše, A. – Skale, S. – V ojvodić Tuma, J.
Aleš Povše
1
 – Saša Skale
2
 – Jelena V ojvodić Tuma
3
1
Jožef Stefan International Postgraduate School, Slovenia 
2
SKALA, Saša Skale s.p., Slovenia 
3
Institute for Energy Engineering, Dr. Jelena V ojvodić Tuma s.p., Slovenia
Corrosion rate measurements in the tank enable us to develop a new model for predicting the remaining operating period of the tank. The 
empirical model for the study of bottom plate thicknesses and corrosion pits is more conservative than the standard linear model, as it 
considers the autocatalytic nature of the corrosion process. We used the double exponential distribution of maximum values (Gumbel's) to 
evaluate the maximum depth of pits, and the double exponential distribution of minimum values to evaluate the minimum values of the plate 
thickness. A comparison of the values of the parameters obtained using linear extrapolation and exponential models indicates the unreliability 
of linear extrapolation, since disregarding dynamic processes underestimates the actual rate of corrosion.
Keywords: pitting, storage tank bottom, time-dependent reliability, corrosion model
Highlights
• 	 The class of tank bottom metal plates can significantly affect on the prediction of the remaining operating period of the tank.
• 	 Improving the reliability of measurements of the condition of the tank bottom by statistical analysis of extreme values.
• 	 New model for predicting the remaining operating period of the tank.
• 	 Improving the reliability of the remaining tank operating period prediction model using actually calculated tank bottom 
corrosion rates.
• 	 The proposed model is more reliable than the established models and is consistent with the actual consequences of tank 
bottom corrosion.
0  INTRODUCTION
When storing fuels in tanks, complete bottom 
tightness must be ensured. A potential fuel spill can 
result in ecological and economic damage. From long-
standing monitoring of the condition of the internal 
surfaces of the tanks it follows that the presence of 
water makes the internal surfaces of the tanks the most 
congested. The presence of aqueous solutions at the 
bottom of the tank, in addition to general corrosion, 
allows the development of more problematic forms 
of local corrosion such as pitting and microbiological 
corrosion. Pitting may also appear independently from 
microbiological corrosion. Rapid progression of local 
forms of corrosion can lead to premature failure of 
the tank bottom, especially if adequate anti-corrosion 
protection system is not provided on surfaces 
contacting petroleum products. The combination of 
local corrosion and the absence of anti-corrosion 
protection system resulted in leaking of tank bottom 
constructed of nominal 8 mm carbon steel plates after 
6 years of tank operation.
During the regular periodic inspections of the 
tanks, it is necessary to reliably assess the progress 
of corrosion in the future operating period. The 
generally established methodology for predicting the 
remaining operational life of the tank bottom is based 
on non-destructive measurements of the thickness 
of the bottom plate with magnetic flux, ultrasound 
and measurements of the depth of corrosion damage 
with mechanical measures [1]. The corrosion rate 
is estimated from the measurements based on 
extrapolation to the previously known or initial 
condition of the tank bottom. The most unfavorable 
measured values, such as the minimum measured 
bottom plate thickness or the maximum measured 
depth of corrosion damage, are taken into account in 
the assessment. Construction of tank bottom must be 
also taken in account. In our case of double bottom 
tanks, with vacuumed interspace between bottoms, 
corrosion is limited to surfaces contacting petroleum 
products. In single bottom tanks can additional 
corrosion also occur from outside contacting soil or 
concrete. 
Corrosion rates estimated in this way are usually 
of the order of 0.1 mm/year to 0.2 mm/year [2] and 
[3]. This is significantly less than experience and data 
show us about the possible rates of pitting (0.5 mm/
year to 1.5 mm/year) or microbiological corrosion 
(0.5 mm/year to 2 mm/year) [2] and [3]. Therefore, the 
estimates of measurements carried out in accordance 
with standard methodology [1], significantly 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 282-292
283 Evaluation of the Condition of the Bottom of the Tanks for Petroleum Products-Forecast of the Remaining Operating Life 
underestimate the actual rate of corrosion progression 
in the presence of local form of corrosion.
One of the reasons for the unreliability of the 
standard corrosion prediction model is the lack of 
measurements of tank bottom plate thickness, as 
only a limited number of measurements are usually 
available. For this purpose, a statistical methodology 
of extreme values was developed for laboratory 
measurements during simulations of actual corrosion 
on objects. This, based on the hypothesis that the 
statistical distribution of measurements is the same 
on all parts of the surface, enables the evaluation 
of extreme values for the minimum bottom plate 
thickness or the maximum depth of corrosion damage. 
This approach improves the reliability of the corrosion 
progression prediction compared to the standard linear 
model.
The reliability of the prediction of the 
remaining service life of the tank bottom depends 
on the reliability of the assessment of the existing 
condition, the assessment of the corrosion rate and 
the adequacy of the model for the evaluation of 
the course of the corrosion rate. A linear model of 
corrosion progression with a constant corrosion rate 
is established in the technical regulations [1]. This is 
based on the lowest measured bottom plate thickness 
and an estimate of the corrosion rate based on a linear 
extrapolation to the previously known condition of the 
tank bottom. More reliable approach is use of extreme 
value estimates, again with linear extrapolation to a 
known initial state [4]. In case of accumulated data 
(databases), as is case for marine ships, prediction of 
thickness loss and corrosion rates can be estimated 
with statistical models [5] to [11]. In case of above 
ground storage tanks, in best case (but usually not), 
we have plate thickness measurements from previous 
tank inspection. 
Laboratory monitoring of corrosion processes 
has shown that the progression of corrosion can be 
described, depending on the nature of the corrosion, 
with two empirical models for passivation and active 
dissolution of steel. Laboratory empirical models 
are based on a large number of plate thickness 
measurements over at least three-time intervals, which 
are then correlated in an empirical model. In reality, 
however, this type of data is not available to us [12]. 
Long inspections intervals, currently lasting 
at least every 10 years, tank design and design 
imperfections, stored fuels and their quality, 
frequency of drainage, refill intervals, micro location 
of tank, cathodic protection of external tank bottoms 
contacting concrete foundations are some main factors 
which influence corrosion rates on internal surfaces 
of bottoms. During tank inspections we discovered 
significant differences on neighboring tanks of the 
same construction, age, design and stored fuel, 
probably due to variations of fuel quality. These are 
some main reasons, why laboratory simulations of 
internal tank exposure, progress of corrosion rates 
through time may significantly differ from reality 
and cannot be used for a reliable prediction for the 
remaining service life. 
In our previous work, we performed established 
electrochemical measurements (anodic polarization) 
in the studied tank before replacing the upper tank 
bottom. Measured spots plates were cut out and 
tank measurements verified in controlled laboratory 
conditions [13]. 
Replacing the bottom plates of the tank allowed 
us to measure the actual corrosion rates, while we 
were able to use the laboratory empirical model for 
active steel dissolution [13]. The empirical parameters 
of the model were evaluated based on extreme values 
of ultrasonic measurements of bottom plate thickness, 
pit depth and measured corrosion rates. The obtained 
corrosion progression model allowed us to predict the 
remaining service life of the tank bottom significantly 
more reliably compared to the standard linear model 
[1]. The results of our model were consistent with 
the observed actual condition of the reservoir bottom 
plates.
1  EXPERIMENT
Measurements of bottom plate thickness and pit depth 
were made at the bottom of an above-ground, double 
bottom tank for the storage of petroleum products 
with a volume of 55,000 m
3
. The tank was built in 
2006 [14] and [15]. After six years of operation, a 
bottom leak was detected. The measurements in the 
tank were carried out before the bottom plates were 
replaced. Corrosion was limited to surfaces contacting 
petroleum products. 
1.1  Measurements of the Remaining Bottom Plate 
Thickness
Measurements of the remaining bottom plate thickness 
(Tables 1 and 3) were carried out with an Elcometer 
204 Steel Ultrasonic Thickness Gauge, in accordance 
with the standard SIST EN 14127 [16]. The meter has 
a measuring range from 0.63 mm to 199.99 mm and a 
resolution of 0.01 mm and a reliability of ±2 %.
From 12 to 18 measurements were performed 
on each of the eleven measuring spots, in size 
approximately 1.5 m × 1.5 m. The nominal thickness 

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284 Po vše,	A .	–	Sk ale,	S.	–	V o jv o d ić	T uma,	J.
of the tank bottom plate was 8 mm. According to the 
standard [17], for class C, a tolerance of 0 mm to +1.4 
mm is allowed. Due to the inclination of the bottom 
towards the center of the tank, corrosion loads are 
greatest in the middle of the tank, where we have the 
water phase zone [2], [3], [18], and [19]. A decrease in 
bottom plate thickness towards the center of the tank 
is expected.
1.2  Corrosion Pits Depth Measurements
Corrosion pits depths (Tables 2 and 4) were measured 
with a KS Tools digital depth gauge 300.0550 with 
a measurement range of 0 mm to 40 mm and a 
measurement uncertainty of ± 0.01 mm, the diameter 
of the needle was 2 mm.
We performed 14 to 18 measurements at eleven 
measurement spots, in size approximately 1.5 m × 1.5 
m. The deepest pit of 3.45 mm was measured at the 
measuring point number 11. Comparable to ultrasonic 
measurements, the depth of pits increases towards the 
center of the tank bottom.
1.3  Calculations and Evaluations of Measurements
From the extreme values of spot measurement series, 
we compiled an empirical cumulative distribution 
using the average ranking method [12]. This is 
optimized non-linearly with a selected statistical 
distribution [12] and [20]. The series of corrosion rates 
(Table 5) was evaluated with a normal distribution [12], 
[13], and [20]. Extreme values of the pit depth (Table 
4) and the remaining thickness of the bottom plates 
(Table 3) were evaluated with double exponential 
distributions of minimum and maximum values. 
The optimized empirical cumulative distributions 
allow us to estimate the maximum corrosion rate, the 
lowest residual thickness, and the deepest ulcers at the 
bottom of the tank (Table 6), with a chosen confidence 
of 99 % or return interval 100 with assumption that 
determined cumulative distributions are valid over all 
internal surfaces of upper tank bottom [12]. 
Corrosion is an electrochemical process for which 
the exponential model (kinetics of chemical reactions) 
applies [5], [7] to [12]:
 xa kt t
i
n
 
0
() ,  (1)
where x is pit depth, t
i
 time at which local corrosion 
occurs, a
0
 initial value of pit depth, k and n empirical 
kinetic constants.
Derivation of Eq. (1) over time gives us the 
corrosion rate ( ν
corr
):
 v
dx
dt
nk tt
corr
t
i
n









() .
1
 (2)
Empirical kinetic constants (k, n) are calculated 
from the combination of Eqs. (1) and (2).
Table 1.  Bottom plate thickness measured by ultrasound [mm]
No
Measurement point
1 2 3 4 5 6 7 8 9 10 11
1 9.27 8.24 8.43 8.56 8.97 8.42 8.55 8.21 8.50 7.70 8.12
2 9.61 8.21 8.69 8.16 9.04 9.03 8.52 8.13 8.93 7.92 6.08
3 9.32 8.26 8.41 8.54 8.78 8.77 8.57 8.37 8.60 8.29 6.54
4 9.25 8.25 8.72 8.65 8.83 8.45 7.30 8.47 8.35 8.90 5.58
5 9.49 8.22 8.56 8.21 8.61 8.40 8.26 8.64 8.72 8.16 6.30
6 8.66 8.26 8.72 8.27 9.03 8.56 8.40 8.15 8.88 8.08 7.98
7 8.77 8.22 8.56 8.53 8.86 8.59 8.28 8.23 8.57 7.20 8.89
8 9.22 8.23 8.56 8.50 8.73 8.68 8.20 8.33 8.58 7.67 5.93
9 8.74 8.23 8.39 8.57 8.73 8.63 8.70 8.66 8.69 7.66 8.01
10 9.28 8.28 8.78 8.33 8.58 8.60 8.62 8.58 8.72 8.77 6.65
11 8.70 8.23 8.40 8.17 8.97 8.61 8.51 8.18 8.67 7.19 5.96
12 8.75 8.29 8.69 8.48 8.93 8.63 8.66 8.32 8.67 7.93 6.15
13 9.02 8.27 8.58 8.34 8.68 8.30 8.11 8.70 7.64 5.77
14 8.66 8.24 8.76 8.53 8.80 8.37 8.26 7.49 7.81 7.57
15 8.61 8.28 8.50 8.89 8.60  8.51 8.60 7.48 7.52
16 8.63 8.26 8.49    8.32 7.20 
17 9.31          
18 8.62          

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 282-292
285 Evaluation of the Condition of the Bottom of the Tanks for Petroleum Products-Forecast of the Remaining Operating Life 
 n
dx
dt
tt
xa
t
i







 
 
0
, (3)
  k
xa
tt
n
dx
dt
tt
i
n
t
i
n

 
 







 

0
1 1
. (4)
For new plates are initial pit depths (a
0
) zero. In 
absence of intermediate measurements, we assumed 
that initial time (t
i
) for occurrences of local corrosion 
is also zero, which is valid in worst case scenario – 
immediate formation of pits. 
The quality of the correlation is evaluated with 
the coefficient of determination [20]:
 
R
FxFx
Fx F
eks i
I
n
eks i eks
I
n
2
2
1
2
1
1 
   



 








mod
,
 (5)
where R
2
 is coefficient of determination, F
eks
(x
i
) 
empirical cumulative distribution of measurements,  
F
mod
(x
i
) selected theoretical cumulative distribution 
and F
eks
 average value of empirical cumulative 
distribution of measurements.
2  RESULTS
Optimization of empirical cumulative distributions 
significantly improved coefficient of determination for 
both double exponential distributions and slightly for 
normal distribution. Extreme values were calculated 
from optimized empirical cumulative distributions for 
99 % confidence (Table 6), where  and  are location 
and scale parameters (Eq. (6) and (7)),  mean and  
standard deviation for normal distribution,  coefficient 
of determination (Eq. (5)) and  estimated extreme 
value. Statistically estimated extreme values in 
comparison to measured extreme values are more 
conservative and presented a more reliable state of 
tank bottom in worst case scenario – bottom leakage.
2.1  Evaluation of the Remaining Operating Time of the 
Tank Bottom
Corrosion damage can be roughly divided into 
two groups: uniform and local corrosion. Uniform 
corrosion results in a general reduction in bottom 
plate thickness. Localized corrosion causes corrosion 
damage in the form of pits and cracks.
The condition of the tank bottom, from the 
corrosion point of view, is evaluated by the remaining 
thickness of the bottom plate and the depth of the 
pits. Evaluating the time dependence of bottom 
plate thickness or pit depth requires at least two 
sets of measurements at different time periods. In 
practice, the problem of corrosion is only encountered 
during the prescribed periodical inspection of the 
condition of the tank. We do not have intermediate 
measurements, so a linear extrapolation of the rate 
determination to the new state of the tank is used to 
predict the remaining operating time of the tank. Most 
Table 2.  Pit depths [mm]
No
Measurement point
1 2 3 4 5 6 7 8 9 10 11
1 0.84 0.08 1.47 0.60 0.06 0.13 1.19 1.71 0.03 2.98 2.61
2 0.56 0.20 1.86 0.84 0.12 0.07 0.41 0.19 0.00 2.62 3.16
3 0.88 0.06 3.26 1.89 0.07 0.22 0.55 1.50 0.05 0.94 2.69
4 0.55 0.11 1.20 1.12 0.05 0.09 0.96 1.39 0.09 1.36 2.09
5 0.61 0.07 1.52 1.51 0.09 0.16 0.35 0.87 0.03 2.44 2.63
6 0.91 0.17 1.43 1.70 0.05 0.07 0.47 0.67 0.04 1.91 2.58
7 0.85 0.10 1.47 0.97 0.05 0.33 0.51 1.06 0.05 2.42 2.86
8 1.48 0.14 1.75 0.52 0.04 0.07 0.91 1.49 0.13 2.54 2.73
9 0.71 0.14 1.87 2.25 0.31 0.00 1.30 1.31 0.13 2.29 2.95
10 0.71 0.03 1.18 2.50 0.33 0.09 1.06 0.85 0.08 0.85 3.31
11 0.83 0.17 1.54 1.20 0.32 0.03 0.82 0.45 0.09 1.17 3.41
12 0.63 0.00 1.89 2.34 0.06 0.39 1.21 0.99 0.13 2.63 2.93
13 0.58 0.16 2.70 1.52 0.20 0.15 0.98 2.12 0.01 1.98 3.45
14 0.70 0.14 1.32 2.19 0.21 0.19 0.49 2.52 0.20 2.02 2.95
15 0.76 0.18 0.70 2.41 0.24 0.07 2.27 0.09 2.36 2.63
16 0.79 0.07 1.51 2.40 0.26  1.58 0.08 2.32 
17 0.45 0.11 1.30 2.34 0.41  2.43 0.12  
18 0.08 1.30        

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 282-292
286 Po vše,	A .	–	Sk ale,	S.	–	V o jv o d ić	T uma,	J.
of material is lost due to uniform corrosion. Local 
corrosion represents only small portion of overall loss 
but presents major threat for tank bottom tightness 
due to significantly higher corrosion rates. Local 
corrosion rates, with time, can vary from decreasing 
(passivation) to increasing (active dissolution). In 
absence of localized corrosion, linear extrapolation to 
initial known state of tank bottom may provide good 
corrosion rate estimate. But in case of presence of 
local corrosion, even one pit is enough for loss of tank 
bottom tightness. For evaluation of remaining service 
life, model for active dissolution is more appropriate. 
[1], [4], [12], and [21] to [23].
2.2  Estimate Bottom Plate Thickness
The plate thickness on the bottom was evaluated using 
a double exponential distribution of the minimum 
values [12]. 
A double exponential distribution of minimum 
values was used to estimate the thickness of the 
bottom plate:
Table 3.  Recapitulation of minimum bottom plate thicknesses [mm] 
Measurement spot 1 2 3 4 5 6 7 8 9 10 11
Number of measurements 18 16 16 15 15 14 12 16 15 16 15
Average thickness [mm] 9.00 8.25 8.58 8.45 8.81 8.57 8.38 8.34 8.58 7.85 6.87
Mean thickness [mm] 8.90 8.25 8.56 8.50 8.80 8.60 8.52 8.32 8.67 7.76 6.54
Standard deviation [mm] 0.34 0.02 0.13 0.2 0.16 0.19 0.38 0.18 0.33 0.51 1.05
Minimum measured thickness [mm] 8.61 8.21 8.39 8.16 8.58 8.30 7.30 8.11 7.49 7.19 5.58
Table 4.  Recapitulation of maximum depth of corrosion pits [mm]
Measurement spot 1 2 3 4 5 6 7 8 9 10 11
Number of measurements 17 18 18 17 17 15 14 17 17 16 15
Average pit depth [mm] 0.76 0.11 1.63 1.66 0.17 0.14 0.80 1.38 0.08 2.05 2.87
Mean pit depth [mm] 0.71 0.11 1.49 1.70 0.12 0.09 0.87 1.39 0.08 2.31 2.86
Standard deviation [mm] 0.23 0.06 0.58 0.69 0.12 0.11 0.33 0.68 0.05 0.64 0.36
Maximum measured pit depth [mm] 1.48 0.20 3.26 2.50 0.41 0.39 1.30 2.52 0.20 2.98 3.45
Table 5.  Corrosion rates in the tank [mm/year] [4] 
Measurement spot 1 2 3 4 5 6 7 8 9 10 11
Corrosion rate 0.33 0.35 0.82 0.37 1.34 0.91 0.93 1.15 1.15 1.59 1.17
Table 6.  Optimisation and estimation of extreme values for pit depth, plate thickness and corrosion rate with 99 % confidence
Distribution
Pit depth Plate thickness Corrosion rates
Double exponential of max. Double exponential of min. Normal
Theoretical Optimised Theoretical Optimised Theoretical Optimised
λ( μ
(*)
) [mm] 1.1125 1.0165 7.9060 8.2588 0.9191 0.9399 
a / ( σ
(*)
) [mm] 1.0026 1.5104 0.6931 0.6323 0.4218 0.5183 
R
2
 [-] 0.758 0.937 0.869 0.928 0.938 0.945
x [mm] 5.7 8.50 4.7 5.1 1.9 2.1 
Table 7.  Empirical model parameters calculation for active dissolution – Eq. (1), and Figs. (3), (4) and (5)
Time  
[years]
Pit Depth Plate thickness
Measured Estimated Measured / 
(1)
nominal Class C Estimated / 
(1)
nominal Class C
0 8.0 mm(1) 9.4 mm(1) 8.0 mm(1) 9.4 mm(1)
7 3.5 mm 8.5 mm 5.6 mm 5.1 mm
Empirical calculated parameters for Eq. (1):
n 4.3420 1.7624 6.1901 3.9215 5.1655 3.4837
k 0.0007386 0.2754 0.00001421 0.001854 0.0001250 0.004891

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 282-292
287 Evaluation of the Condition of the Bottom of the Tanks for Petroleum Products-Forecast of the Remaining Operating Life 
 Fx
x
I 
  
 











1e xp exp,


 (6)
where F
–I 
(x) is the cumulative distribution function of 
the minimum values,  the location parameter, and  is 
the distribution width parameter.
Fig. 1.  Estimate of minimum bottom plate thickness
The measured minimum values for each 
measurement spots were subjected to empirical 
cumulative distribution using the average ranking 
method. This was optimized as double exponential 
distribution of minimum values, using the Newton-
Raphson algorithm (Fig. 1). The minimum bottom 
plate thickness 5.1 mm (with 99 % confidence) was 
estimated from an optimized double exponential 
cumulative distribution of minimum values.   
2.3  Evaluation of the Maximum Depth of Pits
The pit depths on the bottom were evaluated using 
a double exponential distribution of the maximum 
values [12]. 
We used (Gumbel's) distribution to evaluate the 
maximum depth of pits:
 Fx
x
I
 
 











expe xp ,


 (7)
where F
–I 
(x) is the cumulative distribution function of 
maximum values, λ is the location parameter, α is the 
distribution width parameter.
The maximum measured depths for each 
measurement site were subjected to empirical 
cumulative distribution using the average ranking 
method. This was optimized as double exponential 
distribution of maximum values with the Newton-
Raphson algorithm (Fig. 2). The maximum pit depth 
8.5 mm (with 99 % confidence) was estimated 
from the optimized double exponential cumulative 
distribution of maximum values.
Fig. 2.  Evaluation of the maximum depth of pits
3  DISCUSSION
The definition of time models for the evaluation 
of the remaining operating life of the bottom of the 
tanks requires the implementation of many series 
of measurements of corrosion parameters (plate 
thickness, depth of pits) after different time periods 
of operation, which are usually not available or have 
not been carried out. Therefore, linear extrapolation 
is used to predict the remaining service life of tank 
bottoms. In the past, the relatively poor reliability 
of linear extrapolation of corrosion parameters led 
to the development of statistical methods for the 
evaluation of extreme values, which allowed us to 
make more reliable estimates of the remaining service 
life. The statistics of extreme values allow us to more 
conservatively predict critical corrosion parameters, 
such as the minimum bottom plate thickness and the 
maximum depth of pits [12]. Especially in case of 
local corrosion presence.
Evaluating corrosion rate allowed us to use a real-
time model to predict the remaining service life of the 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 282-292
288 Po vše,	A .	–	Sk ale,	S.	–	V o jv o d ić	T uma,	J.
tank. Compared to linearly extrapolated time models, 
exponential time models allow for a more reliable 
prediction of the remaining operating life of the tank. 
In our case, the estimation of corrosion rate, based 
on the linear extrapolation of bottom plate thicknesses, 
to the initial design state, was in the range from 0.6 
mm/year to 0.7 mm/year. The rate of corrosion in the 
linear extrapolation of pit depths was in the range of 
0.5 mm/year to 1.2 mm/year. 
Estimated rate of corrosion (2.1 mm/year) from 
empirical normal distribution and even max. measured 
corrosion rate (1.6 mm/year) are significantly higher 
than estimation with linear extrapolation. Even with 
additional 1.4 mm from upper allowed initial thickness 
of plates, we failed to estimate actual corrosion rates 
in tank, with linear extrapolation of extreme values.  
Therefore, we are of the opinion that from the point of 
view of predicting the remaining operating life of the 
tank, empirical model for active dissolution [12] is a 
better solution. 
3.1  Prediction of the Remaining Operating Life of a Tank 
Bottom
The established and prescribed way of predicting 
the remaining operating life of the tank bottom is 
based on linear extrapolation of the established 
tank condition [4], and [24]. The rate of corrosion is 
evaluated linearly, based on comparison with previous 
measurements of bottom plate thickness and depth of 
pits or to the initial design state. When evaluating the 
state of the tank bottom, estimated extreme statistical 
values [4], [12], [21], [22], and [25] are conservatively 
used instead of direct measurements.
To predict the remaining operating life, in 
addition to the condition assessment, an assessment 
of the corrosion rate based on transient measurements 
or even the condition of the initial design of the 
tank bottom is essential. The long intervals between 
prescribed periodical inspections (10 years or more) 
and the high costs associated with carrying out 
inspections practically make it impossible for us to 
carry out more frequent condition measurements. 
Fig. 3.  Prediction of service life from ultrasonic bottom plate thickness measurements: Comparison of empirical model (Eq. (1))  
with established linear extrapolation model, based on minimal measured and minimal estimated plate thickness to initial state;  
Effect of Class C plate thickness tolerances on service life is also presented

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289 Evaluation of the Condition of the Bottom of the Tanks for Petroleum Products-Forecast of the Remaining Operating Life 
on the nominal and the maximum allowable thickness 
(Fig. 3). For example, depending on plate thickness 
interval, corrosion rates (9.4 mm to 5.1 mm) per 7 
years or (8.0 mm to 5.1 mm) per 7 years. Even much 
greater than the difference in estimated corrosion rates 
between the minimum measured and the minimum 
statistically estimated bottom plate thickness.
The reliability of the corrosion rate estimation 
when intermediate measurements are not available can 
also be strongly influenced by the time of corrosion 
initiation. The later the time of initiation, the higher the 
corrosion rate. When evaluating the rate of corrosion 
based on measurements of the depth of corrosion 
damage, the influence of thickness tolerances for the 
bottom plate class does not apply, since there are no 
corrosion pits at the start of operation. The influence 
of the bottom plate class is shown in the prediction of 
the remaining service life, since the exceeded nominal 
thickness of the bottom plate cannot reliably predict 
failure.
The problem of predicting the remaining operating 
life is therefore only encountered when corrosion is 
discovered at the bottom of the tank.
The material for bottom plate is standardized 
into classes that, among other things, define thickness 
tolerances. The most demanding class "C" according 
to EN 10029 [17] is usually used for the bottom of 
the tanks, which does not allow negative deviations 
from the nominal plate thickness. However, it allows 
limited positive deviations. In the case of our tank 
bottom, plate with a nominal thickness of 8 mm was 
used, which allows a maximum thickness of 9.4 mm.
In the case where the initial state of the bottom 
plate is defined only nominally, when evaluating the 
corrosion rate, we are confronted with the designed 
state, where the thickness of the bottom plate is 
defined in the interval between the nominal and the 
maximum permissible thickness of the bottom plate. 
In our case, the projected bottom plate thickness is 
between 8 mm and 9.4 mm. There is a significant 
difference between the corrosion rates estimated based 
Fig. 4.  Prediction of operating life based on corrosion pit depth measurements: Comparison of empirical model (Eq. (1))  
with established linear extrapolation model, based on maximal measured and maximal estimated pit depth to initial state

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 282-292
290 Po vše,	A .	–	Sk ale,	S.	–	V o jv o d ić	T uma,	J.
The linear corrosion prediction is also strongly 
influenced by the initiation time of local corrosion. 
From the point of view of the linear prediction of 
the corrosion rate, based on the designed state, due 
to the lack of knowledge of the initiation time, we 
underestimated the corrosion rate.
Linear predictions of the remaining operating 
life of the tank bottom, in the absence of intermediate 
measurements of the tank condition, are not reliable.
When evaluating the measurements with the 
double statistic of extreme values, we found an 
interesting difference between ultrasound and pit depth 
measurements. The difference between the measured 
and estimated extreme values is significantly higher 
and thus more conservative when measuring the 
depth of pits than when measuring the bottom plate 
thickness (Figs. 3 and 4).
Evaluating the rate of corrosion in conjunction 
with an assessment of the condition of the tank 
allows us to use the empirical model (Eq. (1), Table 
7) to predict the remaining service life of the tank 
bottom. Unreliability of the initial plate thickness and 
unknown initiation time only affect the shape of the 
empirical model curves for plate thickness, (Figs. 3 
and 4).
With the empirical model of bottom plate 
thicknesses (Fig. 3), the unreliability of initial 
plate thickness is reflected in significantly smaller 
differences compared to linear models. The empirical 
model that considers the minimum initial bottom plate 
thickness is more conservative compared to the model 
that considers the maximum allowable thickness, due 
to higher value of parameter . Curve shape parameters  
are significantly above value 1. Corrosion rates (Eq. 
(2)) increase through time. Parameter  is corrosion 
rate constant rather than corrosion rate as in linear 
approximations of empirical model in Eq. (1).
The exponential model for pit depth is more 
conservative compared to the linear model, but 
the difference is significantly smaller compared to 
Fig. 5.  Comparison of models for predicting the remaining service life of the tank bottom: Informative comparison of empirical models  
(Eq. (1)) for pit depth and plate thickness measurements; For direct comparison of reliability, steel plate thickness reduction is calculated as 
difference between initial plate state and empirical model for plate thickness (red and green curve); Additional lines for linear extrapolation, 
based on statistically estimated values for maximal pit depth and minimal plate thickness are added

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 282-292
291 Evaluation of the Condition of the Bottom of the Tanks for Petroleum Products-Forecast of the Remaining Operating Life 
models for bottom plate thickness based on ultrasound 
measurements.
Reliable comparison of bottom plate thickness 
model with pit depth models is not possible (Fig. 5). 
Ultrasonic measurements on the uneven surface of 
the bottom plate give us the thickness between the 
apparent plane in the pit profile and the bottom surface 
of the bottom plate. Initial interval of plate thickness 
prevents any reliable estimation of uniform corrosion. 
Pit depth measurements do not consider thickness 
loss due to uniform corrosion and are limited by the 
diameter of the depth gauge needle. 
Depth of pits or the thinning of the bottom plate 
at which the bottom of the tank fails is equal to the 
nominal thickness of the bottom plate. The exception 
is the empirical models, which considers the initial 
thickness of plates 9.4 mm (Fig. 5). In our case, after 
seven years of operation of the tank, we were faced 
with a leak in the bottom of the tank, which is also 
confirmed by the statistical analysis of the depth of 
the pits.
4  CONCLUSION
In the experiment, we compared different models 
for predicting the remaining operational life of the 
tank bottom. Conventional linear time models for 
predicting the remaining operating life of the tank 
bottom [4], and [24] are not reliable in the case of local 
forms of corrosion.
Empirical model in Eq. (1) enables us to make 
better predictions of the remaining operational life of 
the tank bottom, which require the implementation of 
several series of measurements of the tank's condition 
during its operational period. In practice, data on the 
state of the tank bottom within the legally prescribed 
inspection intervals are not available to us. Therefore, 
the use of an exponential model to predict the 
remaining operating life based on the actual state of 
the tank bottom is not possible.
The exponential model of pit depths increase is 
more conservative than the linear model. The bottom 
plate thickness measurements, even after extreme 
values analysis, fail to predict tank bottom failure as 
the minimum estimated bottom plate thickness was 
5.1 mm. The reason for this is probably related to the 
geometry of the probe of the ultrasonic meter and the 
rugged topography of the bottom plate surfaces.
When determining the condition of the bottom of 
the tank with ultrasound, the performance of reliable 
measurements requires additional grinding of the 
bottom plate surfaces to the depth of the pit, otherwise 
the measurement is not reliable due to the relatively 
large surface area of the measuring probe. Therefore, 
models for predicting the remaining service life of 
the tank bottom based on ultrasonic measurements 
(without grinding) of bottom plate thicknesses 
fail in case of local corrosion. The assessment of 
the remaining service life based on measurements 
of the depth of pits is more reliable and faster in 
the case of local corrosion, as it does not require 
additional preparation of the bottom plate surface for 
measurements.
In the water phase, the presence of salts or micro-
organisms results in significantly higher corrosion 
rates than would be expected from the values 
published in the literature [2], [3], [26], [27]. This 
confirms the established requirement for adequate 
service and anti-corrosion protection of tank bottoms 
[28], [29], and [30].
Some empirical cumulative distributions obtained 
in other tanks showed bi-modal distribution patterns, 
when we observed different types of local corrosion 
on separate parts of bottom. Further studies will be 
focused on possible influence of type of corrosion 
on empirical distributions to improve estimation of 
extreme pit depths. 
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