Corresponding author: Olga M. Gulina ( olga@iate.obninsk.ru ) Academic editor: Yury Korovin
© 2018 Valery I. Baranenko, Olga M. Gulina, Nikolaj L. Salnikov.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Baranenko VB, Gulina OM, Salnikov NL (2018) Flowaccelerated corrosion rate and residual life time estimation for the components of pipeline systems at nuclear power plants based on control data. Nuclear Energy and Technology 4(1): 3542. https://doi.org/10.3897/nucet.4.29850

As of today, large volumes of data related to nondestructive operational control are accumulated on NPPs. For ensuring safe operation of power units, optimization of scope and scheduling operational control it is necessary to continue development of guidance documents, software products, methodological guidance and operational documentation (
Approaches are examined to assessment of the rate of erosioncorrosion wear (flowaccelerated corrosion  FAC) according to the data of operational control. The present study was performed based on the data of thickness gauging of different elements of pipelines of NPPs with different types of reactor. Further development of ideas exposed in (
The implemented studies demonstrated efficiency of the developed procedures for pipeline welding zones. Analysis of known and newly developed procedures was performed for bends and ranking of these procedures according to the criterion of “conservatism of evaluation of residual lifetime” was executed.
Introduction of correction coefficients allows enhancing conservatism of calculations of lifetime characteristics as compared with calculations performed on the basis of nominal values of thicknesses; the result depends on the type and dimensions of the element, its geometry, as well as on the type of reactor.
Flowaccelerated corrosion (FAC), thickness gauging, evaluation of FAC rate, bends, welding, residual lifetime.
Substantiation of the methodology for calculation of FAC rate for NPP piping elements manufactured of carbon steel requires highquality analysis of data of operational control and taking into account significant number of factors (
Methodology for estimation of FAC rate presented in (
W _{FAC1} = [(S_{nom} × K_{11} × K_{12} – S_{min} × K_{2})] K_{safe}/ Δτ_{0}, (1)
where S_{nom} is the nominal wall thickness; K_{11} is the coefficient taking into account positive tolerance for wall thickness during manufacturing the pipeline; K_{12} is the coefficient taking into account contribution of corrosion products depositions in the nominal wall thickness; K_{2} is the coefficient taking into account corrosion products depositions to value of measured minimal wall thickness (S_{min}); K_{safe} is the safety factor; Δτ_{0} is the duration of operation of the element before the date of control. Geometrical features of such elements as bends and welding zones (
The purpose of the present study is the development of methodologies for evaluation of FAC rate taking into account geometrical features of such element as bends and welding zones.
Determination of correction coefficient for bends. Value of thickness measured during prestart control must be substituted in formula (1) in the calculations of FAC rates for extended elbow bends as the nominal thickness S_{nom}, otherwise the following dependence (
S _{bend} = S_{nom} (R – 0.2 D)/ (R + 0.3 D), (2)
where R is the radius of pipeline bend, mm; D is the pipeline outer diameter, mm; S_{bend} is the thickness of extended part of the bend, mm.
The following coefficient is introduced using dependence (2):
K _{bend} = 1 – [0.5 (1 – S_{bend}/ S_{nom})]. (3)
Dependence (3) takes into account that maximum thinning can be found on the section located beyond the extended part of the bend.
Determination of correction coefficient for welding zones. Large numbers of welding zones – WZ – are present on NPP power units. Quantities of fittings installed on power units of NPPs with VVER440, VVER1000, RBMK1000 and RBMK1500 reactors are presented in Table
Quantities of fittings installed on power units of NPPs with VVER440, VVER1000, RBMK1000 and RBMK1500 reactors.
Name of the element  VVER440  VVER1000  RBMK1000  RBMK1500  
Odd power unit  Even power unit  Odd power unit  Even power unit  
Gate valves  74  246  1820  1145  886  886 
Shutoff valves  5448  6519  8715  8714  8135  7849 
Control valves  80  126  352  265  789  788 
Safety valves  65  172  135  135  119  119 
Check valves  338  421  609  429  896  896 
Total  6005  7484  11631  10688  10825  10538 
On straight sections of pipelines and on WZ with outer diameter less than 108 mm initial thickness is similar to nominal thickness. Technological boreholes creating conditions for highquality mating of joints during welding are drilled on WZ with outer diameter over 108 mm in accordance with industry standard OST 24.125.3189. Drilling bores is performed on the input and output WZ on the section with length equal to 50 mm (ОSТ 24.125.3089 1989).
Thickness S_{k} determining the wall thickness in the zone of weld joint along the length of 50 mm has on the average the value smaller than the thickness of the bore S_{r}^{*} by approximately 1.3 times. In the process of operational control thickness S_{k} can be taken as the minimum permissible value.
Values of S_{k} in the zone of boreholes for WZ of different types and dimensions, nominal thicknesses and boreholes S_{r}^{*} calculated according to diameters of boreholes (ОSТ 24.125.3089 1989) are presented in Table
S _{av} = SS_{i} / n_{meas} , (4)
where S_{i} is the wall thickness in the ith measurement point; n_{meas} is the number of measurement points. The following is determined in the calculation of coefficients K_{12} and K_{2}:
– Difference between the average and initial (nominal) thicknesses:
ΔS_{init} = S_{av} – S_{init} , (5)
– coefficient K_{12}:
K _{12} = (S_{init} – ΔS_{init})/ S_{init} , (6)
(if S_{av} < S_{init}, difference between the values will be negative and value of K_{12} will be larger than unity);
– coefficient K_{2}
K _{2} = (S_{min –} ΔS_{init}) / S_{min}. (7)
Calculation of FAC rate and residual lifetime. Corrosion rate aggravated by the flow W_{FAC} is calculated according to equation (1), nominal thicknesses are replaced with corresponding values of S_{bend} for bends and 0.9S_{nom} for welding zones. Residual lifetime of pipeline element is calculated according to the following equation:
t = (S_{min} – S_{perm})/W_{FAC} , (8)
where S_{perm} is the minimum permissible wall thickness of the element (
Thicknesses of boreholes and nominal thicknesses, ratios of thicknesses S_{r}^{*}/S_{nom} and S_{k}/S_{r}^{*} for control pressure and temperature.
p = 3.92 MPa, Т = 200°C  p = 5.89 MPa, Т = 275°C  
Item no.  D _{o}×S_{nom}, mm  S _{r}^{*}, mm  S _{k}, mm  S _{k}/S_{r}^{*}  S _{r}^{*}/S_{nom}  D _{o}×S_{nom}  S _{r}^{*}, mm  S _{k}, mm  S _{k}/S_{r}^{*}  S _{r}^{*}/S_{nom} 
1  108×6  5.5  3.6  0.655  0.917  108×6  5.5  3.7  0.673  0.917 
2  133×6.5  5.5  3.7  0.673  0.846  133×6.5  5.5  3.7  0.673  0.846 
3  159×7  5.5  4.0  0.727  1.071  159×7  5.5  4.0  0.727  0.786 
4  219×9  7.5  5.5  0.733  0.944  219×9  7.5  5.5  0.733  0.833 
5  273×10  8.5  6.5  0.765  1.100  273×10  8.5  6.5  0.765  0.850 
6  325×13  11  8.5  0.773  0.885  325×13  11.5  9.0  0.783  0.885 
7  377×13  11.5  9.0  0.783  0.962  426×14  12.5  9.0  0.720  0.893 
8  426×14  12.5  9.8  0.784  0.893  465×16  14.0  10.8  0.771  0.875 
9  465×16  14  10.8  0.771  0.875  
10  630×17  16  14.0  0.875  0.941  
11  Min  0.655  0.846  Min  0.673  0.786  
12  Average  0.754  0.943  Average  0.731  0.861  
13  Max  0.875  1.100  Max  0.783  0.917  
p = 8.44 MPa, Т = 300°C  p = 11.77 MPa, Т = 250°C  
Item no.  D _{o}×S_{nom}, mm  S _{r}^{*}, mm  S _{k}, mm  S _{k}/S_{r}^{*}  S _{r}^{*}/S_{nom}  D _{o}×S_{nom}  S _{r}^{*}, mm  S _{k}, mm  S _{k}/S_{r}^{*}  S _{r}^{*}/S_{nom} 
1  108×6  5.5  3.7  0.673  0.917  108×8  6.5  4.7  0.723  0.813 
2  133×8  7  5.8  0.829  0.875  133×8  7  5.8  0.829  0.875 
3  159×9  8.5  6.9  0.812  0.944  159×9  8.5  6.9  0.812  0.944 
4  219×13  12  9.5  0.792  0.923  219×13  12  9.5  0.792  0.923 
5  273×16  14.5  11.8  0.814  0.906  273×16  14.5  11.8  0.814  0.906 
6  325×19  17.5  14.2  0.811  0.921  325×19  17.5  14.2  0.811  0.921 
7  426×24  22  18.5  0.841  0.917  530×28  25  19.0  0.76  0.893 
8  530×28  25  19.0  0.760  0.893  
9  630×25  24  22.0  0.917  0.960  
10  Min  0.673  0.875  Min  0.723  0.813  
11  Average  0.805  0.917  Average  0.791  0.896  
12  Max  0.917  0.960  Max  0.829  0.944 
Values of wall thicknesses in circular points (Fig.
Measurements in axial direction were performed in one crosssection with step equal to 45° (corresponding to 12:00, 1:30, 3:00, 4:30, 6:00, 7:30, 9:00 и 10:30 “on a clock dial”). In accordance with Fig.
Wall thicknesses in circular points of WZ inlet , minimum, average and maximum thicknesses, number of measurements with values of thickness less than S_{nom} and S_{r}^{*}.
Item no.  Values of thicknesses in circular points, mm  Values of thicknesses  Number of measurements  
12:00  1:30  3:00  4:30  6:00  7:30  9:00  10:30  Min  Average  Max  < 24 mm  < 21.6 mm  
1  22.9  23.7  .30  22.6  22.7  22.6  22.4  24.2  22.4  23.1  24.2  7  0 
3  22.1  23.4  22.4  21.5  21.9  23.8  24.9  24.4  21.5  23.1  24.9  6  1 
5  22.2  24.5  24.2  22.7  22.2  22.8  20.4  21  20.4  22.5  24.5  6  2 
7  22.9  24.2  23.9  24.8  23.2  24.7  24.6  24.7  22.9  24.1  24.8  3  0 
9  22.3  24  25.2  23.6  21.8  23.5  23.2  21.9  21.8  23.2  25.2  6  0 
11  20.8  21.8  22.5  22.8  22.4  21.9  22.1  21.4  20.8  22.0  22.8  8  2 
13  24.8  24.4  21.5  20.9  22.3  21.6  21.5  22.7  20.9  22.5  24.8  6  3 
15  22.2  22  21.9  21.8  21.4  20.6  20.1  20.7  20.1  21.3  22.2  8  4 
Min  20.8  21.8  21.5  20.9  21.4  20.6  20.1  20.7  20.1  21.3  22.2  50  12 
Average  22.5  23.5  23.1  22.6  22.2  22.7  22.4  22.6  21.4  22.7  24.2  78.1%  18.8% 
Max  24.8  24.5  25.2  24.8  23.2  24.7  24.9  24.7  22.9  24.1  25.2 
Wall thicknesses in circular points of WZ outlet, minimum, average and maximum thicknesses, number of measurements with values of thickness less than S_{nom} and S_{r}^{*}.
Item no.  Values of thicknesses in circular points, mm  Values of thicknesses  Number of measurements  
12:00  1:30  3:00  4:30  6:00  7:30  9:00  10:30  Min  Average  Max  < 24 mm  < 21.6 mm  
2  22.6  20.5  20.9  22.2  23.3  23.1  22.2  23.8  20.5  22.3  23.8  8  2 
4  22.2  22.4  22.6  25.4  25.5  21.3  21.4  20.3  20.3  22.6  25.5  6  3 
6  20.2  21.1  24.2  24.9  24.1  22.2  21  21.4  20.2  22.4  24.9  5  4 
8  25.5  23.8  23.8  24  23.5  23.1  22  23.6  22.0  23.7  25.5  6  0 
10  25.3  24.1  22.4  24.9  24.8  24.4  24.2  25.5  22.4  24.5  25.5  1  0 
12  22.3  21.4  21.8  22.1  22.4  22.8  22.4  23.3  21.4  22.3  23.3  8  1 
14  22.8  23  23.1  23.8  23.7  24.3  24.3  23.6  22.8  23.6  24.3  6  0 
16  22.2  22.8  22.3  22.5  24.1  22.5  21.8  21.3  21.3  22.4  24.1  7  1 
Min  20.2  20.5  20.9  22.1  22.4  21.3  21  20.3  20.2  22.3  23.3  47  11 
Average  22.9  22.4  22.6  23.7  23.9  23.0  22.4  22.9  21.4  23.0  24.6  73.4%  17.2% 
Max  25.5  24.1  24.2  25.4  25.5  24.4  24.3  25.5  22.8  24.5  25.5 
It follows from Tables
Results of calculations performed using formulas (5) – (8) are presented in Tables
Estimated value of residual lifetime obtained using the formula for the nominal thickness S_{nom} (W_{FAC1} and Т_{1}) is by 1.8 times less than the value obtained taking into account the borehole (W_{FAC2} and Т_{2}).
Use of borehole thickness instead of S_{nom} results in the estimated value of residual lifetime larger by approximately 1.9 times, i.e. similarly to the picture for WZ inlet. Values of FAC rate and residual lifetime for WZ inlet without correction coefficients are presented in Table
Analysis of Table
Values characterizing residual lifetime of WZ inlet of pressure pipelines of feed electric pump and emergency feed pumps.
Item no.  ΔS_{in}= S_{av} –S_{in}, mm  K_{12}  K_{2}  S_{min}  W_{FAC1}, mm/yr  Т_{1}, years  W_{FAC2}, mm/yr  Т_{2}, years  Т_{2}/Т_{1} 
3  1.5  0,931  0,930  21,5  0,095  20,3  0,074  31,5  1,55 
5  0.9  0,958  0,907  20,4  0,163  11,6  0,172  11,7  1,01 
11  0.4  0,981  0,949  20,8  0,170  8,6  0,140  13,5  1,56 
13  0.9  0,958  0,93  20,9  0,144  7,0  0,129  16,6  2,37 
15  –0.3  1,014  0,949  20,1  0,230  2,9  0,205  6,9  2,38 
Average  1.8 
Values characterizing residual lifetime of WZ outlet of pressure pipelines of feed electric pump and emergency feed pumps 426×24 mm.
Item no.  S_{min}, mm  C_{12}  C_{2}  S_{min}×C_{2}, mm  Diff.  W_{FAC1}, mm/year  Residual lifetime Т1, years  W_{FAC2}, mm/year  Residual lifetime Т_{2}, years  Т_{2}/Т_{1} 
2  20.5  0,968  0,921  18,9  2  0,276  7,24  0,161  12,4  1,71 
4  20.3  0,954  0,898  18,2  1,8  0,294  6,12  0,184  9,78  1,60 
6  20.2  0,963  0,902  18,2  1,7  0,304  5,59  0,193  8,8  1,57 
12  21.4  0,968  0,963  20,6  2,9  0,198  14,64  0,087  33,3  2,27 
16  21.3  0,963  0,953  20,3  2,8  0,207  13,5  0,097  28,8  2,13 
Average  1.86 
FAC rate and residual lifetime for WZ inlet (W_{FAC11}) and outlet (W_{FAC21}) without correction coefficients.
Item no.  S_{min}, mm  W_{FAC11}, mm/year  Т_{11}, years  Item no.  S_{min}, mm  W_{FAC21}, mm/year  Т_{21}, years  Т_{11/}Т_{1}  Т_{21/}Т_{2} 
3  21.5  0.004  750  2  20,5  0,045  44  23,8  3,5 
5  20.4  0.050  38  4  20,3  0,054  33  3,2  3,4 
11  20.8  0.033  70  6  20,2  0,058  29  5,2  3,3 
13  20.9  0.029  82  12  21,4  0,008  362  4,9  10,8 
15  20.1  0.062  25  16  21,3  0,012  233  3,6  8,1 
Average  8.1  5.8 
Bends. For calculating FAC rate and residual lifetime of bends let us examine the data of measurements performed in 1995, 1996, 2000 and 2002 on bends 06K and 16K of feedwater pipelines 273×16 mm of the Dukovany NPP during implementation of operational control. Selection of the bends was predetermined by the large number of measurements performed on each of the elements (from 276 to 394) (
W _{1} = (S_{nom} – S_{min})K_{safe}/ Δτ_{0}. (9)
The formula W_{2} = [(S_{nom}×K_{11}×K_{12} – S_{min}×K_{2})]×K_{safe}/ Dt_{0} (
FAC rate and residual lifetime for bends without taking (9) into consideration and with correction coefficients (1).
Bend  Year  T_{op}, years  S_{min}  S_{av}  ΔS  C_{12}  C_{2}  W_{1}  Τ_{1}  W_{2}  Τ_{2}  T_{1}/T_{2} 
06K  1996  11,7  12,95  16,32  0,32  0,98  0,975  0,236  26  0,329  18,7  1,39 
2002  17,7  13,5  16,13  0,13  0,992  0,990  0,128  52  0,190  35,2  1,47  
16K  1995  10,7  13,84  16,17  0,17  0,989  0,987  0,183  38,4  0,285  24,7  1,55 
1996  11,7  13,95  16,23  0,23  0,985  0,983  0,159  44,9  0,250  28,6  1,56  
2000  15,7  13,76  16,22  0,22  0,986  0,984  0,130  53,5  0,198  35,15  1,52  
Average  1.5 
Formula for estimation of FAC rate suggested in (
W _{3} = (1,25×S_{nom} – 0,95×S_{min})K_{safe}/ Dt_{0} (10)
was also applied with respect to the examined bends. Corresponding values of the rate W_{3} and residual lifetime Т_{3} are presented in Table
Estimated values of ECW rate and remaining lifespan for bends obtained according to formula (10).
Bend  Year  S_{min}  S_{av}  ΔS  0.95×S_{min}  W_{3}  Т_{3}  Т_{3}/Т_{2} 
06K  1996  12.95  16.32  0.32  12.3  0.598  10.3  0.55 
2002  13.5  16.13  0.13  12.825  0.368  18.2  0.517  
16K  1995  13.84  16.17  0.17  13.148  0.582  12.1  0.49 
1996  13.95  16.23  0.23  13.25  0.524  13.6  0.475  
2000  13.76  16.22  0.22  13.07  0.401  17.3  0.492 
In accordance with formula (2) thickness of extended part of the bend is equal to
S _{bend}=S_{nom}(R – 0.2D)/(R + 0.3D),
where R is the bend radius. For the examined bends (90°) R = 1370 mm. Then S_{bend} = 14.5 mm and the value of factor K_{bend} = 1 – [0.5×(1 – S_{bend} / S_{nom})] = 0.953.
Average value of the ratio Т_{3}/Т_{2} = 0.5, i.e. calculation of FAC rate according to the formula presented in the new edition of the regulatory document (RD) (
Formula for calculating FAC rate taking into account the bend geometry W_{4} is similar to formula (1) with corresponding replacement of S_{nom} with S_{bend}:
W _{4} = [(S_{bend}×K_{11}×K_{12}×K_{bend} – S_{min}×K_{2})]×K_{safe}/ Dt_{0}. (11)
Estimated value of residual lifetime for the described case (Т_{4}) is by 3.5 times larger than that obtained using formula (1) for straight sections (Table
Thus, residual lifetime calculated according to RD is by approximately tree times less than that calculated using the formula for bends.
Estimated values of FAC rate and residual lifetime (W_{4} and Т_{4}) for bends obtained according to formula (1) taking into account the bend geometry.
Bend  Year  S_{min}  S_{ср}  ΔS  C_{12}  C_{2}  W_{4}  Т_{4}  Т_{4}/Т_{2}  Т_{3}/Т_{4} 
06K  1996  12.95  16,32  0,32  0,98  0,975  0,205  28,4  2,75  0,362 
2002  13.5  16,13  0,13  0,992  0,990  0,107  61,4  3,37  0,296  
16K  1995  13.84  16,17  0,17  0,989  0,987  0,149  46  3,8  0,263 
1996  13.95  16,23  0,23  0,985  0,983  0,127  54,4  4  0,25  
2000  13.76  16,22  0,22  0,986  0,984  0,106  63,5  3,67  0,272  
Average  3.5  ~ 0.3 
Summary of results for bends are presented in Table
As the final result the most conservative estimation was obtained using the formula taken from RD (W_{3}) and the most optimistic estimation was obtained with introduction of correction coefficients for bends (W_{4}). Reasonable conservatism was demonstrated in this case with introduction of correction coefficients for bends similar to those for straight sections (W_{2}), i.e. without taking the geometry into account. However, it is difficult enough to substantiate this result and, therefore, the whole set of results must be used in order to make decision on the implementation of the next control when already expired time gets close to the minimum among the calculated values of time.
Residual lifetime for bends (summary of results).
Bend  Year of measurement  S_{min}  S_{av}  Т_{1}  Т_{2}  Т_{3}  Т_{4} 
06K  1996  12,95  16,32  26  18,7  10,3  28,4 
2002  13,5  16,13  52  35,2  18,2  61,4  
16K  1995  13,84  16,17  38,4  24,7  12,1  46 
1996  13,95  16,23  44,9  28,6  13,6  54,4  
2000  13,76  16,22  53,5  35,15  17,3  63,5 
1. Methodologies were developed for calculating the rates of flowaccelerated corrosion and residual lifetime for bends and welding zones with introduction of correction coefficients taking into account the effects on the corrosion process produced by the manufacturing technology, as well as influence of depositions of corrosion products.
2. Reasonable conservatism of the calculations is ensured by introduction of correction coefficients and geometry of the elements. It was demonstrated that calculated results obtained taking these correction factors into account are not overly pessimistic.
3. Values of correction coefficients introduced in the calculation dependences are determined on the basis of processing the data of operational control. Calculation of FAC rate and residual lifetime of the WZ are performed using nominal thickness and borehole thickness as the initial value of thickness. Use of borehole thickness instead of nominal thickness results in the estimation of residual lifetime which is by approximately 1.9 times larger both for WZ inlet and outlet of pressure pipelines of feed electric pump and emergency feed pumps with size type 426×24 mm.
4. Calculation without introduction of correction coefficients for the borehole thickness produce estimated values of residual lifetime which are smaller by approximately eight times for WZ inlet and by 5.8 times for outlet. Therefore, calculation methodology with introduction of correction coefficients and application of borehole thickness as the initial thickness is certainly recommended for welding zones.
5. Data of measurements performed on bends of feedwater pipelines 06K and 16K 273×16 mm of the Dukovany NPP performed in the course of operational control in 1995, 1996, 2000 and 2002 are examined for calculation of FAC rate and residual lifetime. The following four formulas for calculating FAC rate were examined: for straight sections without corrections, for straight sections with introduction of correction factors, with introduction of correction factors for bends and the formula recommended in RD (