The document discusses prognostic and deterministic analysis of thinning rates due to flow accelerated corrosion. It outlines developing a mechanistic model to predict thinning rates in nuclear power plant pipelines. The model considers factors like flow velocity, temperature, pH and water chemistry. Mathematical equations are presented for calculating the mass transfer coefficient and solubility driving force. CFD simulations are performed and results are validated against experimental data. Finally, the model is used to determine a 5.5 year time interval for maintenance scheduling to prevent pipe wall thickness from falling below the failure threshold.

1. Prognostic and Determistic Analysis of
thinning rate due to Flow Accelerated
Corrosion
Presented By : Akshay Murkute
Instructor : Dr. Yongming Liu

2. Outline
 Objectives
 Introduction
 Mathematical Model
 Validation and Verification
 Erosion simulation
 Maintenance Scheduling
 Future scope

3. Objectives
 Develop a mechanistic model and methodology to
predict the thinning rate of pipelines in Nuclear power
plant (CANDU) due to FAC
 Develop State Space model
 Compare the results with the experimental data
 Perform CFD simulations
 Time interval for Maintenance Scheduling

4. Flow Accelerated Corrosion
 Corrosion mechanism in which a normally protective
oxide layer on a metal surface dissolves in a fast
flowing water.[1]
 Rate of protective oxide layer (magnetite) dissolution
is greater than the rate of protective oxide formation,
when exposed to flowing water or wet steam.
 Causes wall thinning and pipe rupture over time.
[1] https://en.wikipedia.org/wiki/Flow-accelerated_corrosion

5. Spalling / pitting

6. Mechanism
Fe = Fe2+ + 2e–
2H2O + 2e– = 2 OH– + H2
Fe2+ + OH– = Fe(OH)+
2Fe(OH)+ + 2 H2O = 2 Fe(OH)2 + H2
Fe(OH)+ + 2 Fe(OH)2+ 3 OH– = Fe3O4 + 4 H2O
[1] “Guidelines for Controlling Flow-Accelerated Corrosion in Fossil and Combined Cycle Plants “ by EPRI

7. Hydrodynamics
 Flow Velocity (V)
 Reynolds Number (R)
 Mass transfer co-efficient (K)
 Turbulence intensity (TI)
 Surface shear stress (Ʈ)

8.  Increases turbulence
 Particle hitting pitting of
oxide layer
 Velocity
 Affects the solubility of the surface
Fe3O4
 Higher pH will reduce the amount of
corrosion and FAC
 pH

9. Mass transfer co-efficient
 Mass Transfer is the process of transporting material
(essentially magnetite) from the surface to the bulk of the
flowing water or water-steam flow
 The local mass transfer coefficient depends in a complex
manner on fluid velocity, fluid viscosity, flow geometry,
pipe/tube surface roughness and temperature
 Mass transfer is usually described by the dimensionless
parameters: Reynolds, Schmidt and Sherwood numbers

10. Temperature
 Affects:
o pH of the water or wet steam
o Solubility of the oxide
o The variables related to mass
transfer (Reynolds, Schmidt
and Sherwood numbers)
 FAC tends to peak at
temperatures in the range of
150–180°C (300–350°F
Reference: Corrosion 98 – paper 721 flow accelerated corrosion, R. D port Nalco Chemical Company

11. Geometry
 Locates where FAC will occur.
 Certain geometries affect mass transfer due to changes in local velocity
and turbulence.
 Eg: elbows, tight bends, reducer tees, locations downstream of flow
control orifices and valves
 Geometric enhancement factors are related to the turbulence created by
the particular geometry or fitting.
 Larger values denote a greater propensity for flow disturbance and
which increases the mass transfer coefficients.
 Regression equation for FAC resistance
R = 0.61 + 2.43 Cr + 1.64 Cu + 0.3 Mo , No FAC failure if R > 1

12. Mathematical Model

FAC = K ∆C
K = Mass transfer coefficient
∆C = Solubility driving force
𝐹𝐴𝐶 = 𝑓 T 𝑓 V 𝑓 pH 𝑓 𝑂 𝑓 ἀ 𝑓 𝐶𝑟 𝑓(𝐺)

13. K - calculation

D = Diffusivity
𝛾 = Kinematic viscosity
𝑑 = diameter of pipe
ε = Roughness
Mass transfer Sherwood number (Sh) = 𝐾(𝑑/𝐷)
Reynolds number(Re) = 𝑉(𝑑/𝛾)
Schmitt number (Sc) = 𝛾/𝐷.
Component enhancement factor = 16.73*(Re)-0.19

14. ∆C (solubility driving force)
 Depends on temperature, pH and water chemistry
 Defined within specific range
 ∆C = 0.0026*T2 - 1.3973*T + 195.09………(pH=9.5-11)
 ∆C = -5e-06*T3 + 0.006*T2 - 2.3307*T + 314.33……..(pH < 9.5)
Reference: F. H. Sweeton and C. F. Baes Jr., “The solubility of magnetite and hydrolysis of ferrous ion in aqueous solutions at elevated
temperatures,”The Journal of ChemicalThermodynamics, vol. 2, no. 4, pp. 479–500, 1970
0
20
40
60
80
100
120
140
0 50 100 150 200 250 300 350
Solubilityppb
Temperature (C)
Solubility vs temp

15. CANDU Reactor
 Outlet feeder Input data
Temperature= 310 ˚C
pH = 10.6
Velocity (V)= 8-16.5 m/s
Dissolved O2 ̴ 0 ppb
Diameter (d) = 2.5 in
Reference : A Mechanistic Model for Predicting Flow-assisted and General Corrosion of Carbon Steel in Reactor Primary Coolants D. H. Lister* and
L. C. Lang**
Node Diagram for CANDU circuit

16. Comparison
Diameter (cm) Bend Angle Coolant Velocity (m/s) Experimental FAC(um/a) Calculated
FAC(um/a)
6.4 42 10.5 50.2 50.43
6.4 73 10.4 59.0 63.5
6.4 73 12.3 75.6 75.9
6.4 73 15.6 105.9 96
6.4 73 16.2 110.0 99.4
6.4 73 17.5 123.1 107
5.0 42 15.8 94.9 90.7
5.0 73 11.9 74.8 89.2

17. Comparison
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12 14 16 18 20
FACrate(um/a)
Velocity (m/s)
FAC rate vs Velocity
 Experimental
 Calculated

18. CANDU Reactor
FAC (mm) vs Time (years) Mass transfer vs Temp

19. Erosion Simulation
CFD Set up

20. Geometry and Meshing
Inflation at the interface of Wall-fluid

21. Convergence plot

22. Mass transfer co-efficient
Erosion Particle tracking

23. Verification

24. Validation with Velocity
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 2 4 6 8 10 12 14 16 18
Thinningrate
Velocity
Thinning rate vs Velocity
0.0005
0.00055
0.0006
0.00065
0.0007
0.00075
0.0008
0.00085
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
MTC
Velocity
MTC vs Velocity
Experimental data Calculated data
Reference: “A Mechanistic Model for Predicting Flow-assisted and General Corrosion of Carbon Steel in Reactor Primary Coolants by D. H. Lister and L. C. Lang”

25. 25Reference: “A Mechanistic Model for Predicting Flow-assisted and General Corrosion of Carbon Steel in Reactor Primary Coolants by D. H. Lister and
L. C. Lang”
Maintenance Scheduling
Node Diagram of Nuclear primary circuit

26. 26
Mathematical Model for Flow Accelerated Corrosion
FACrate = (1000*K*∆C +4.85)*10^3
I
II
III
Condition Stages
Stage 1 : >= 6.7
Stage 2 : 6.7< T <=6.4
Stage 3 : 6.4 < T <=6.1
Failure condition

27. 27
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
0 1 2 3 4 5 6 7 8 9 10 11
Thicknessinmm
Time in years
Thickness vs Time
Maintenance Scheduling Interval
Assumptions:
1. 10% randomness in the variables
2. Initial Condition is 6.7 mm
3. Do nothing maintenance alternative
4. 10% failure probability
5. Both variables of line are randomized
Result:
Time interval of Maintenace
= 8.5 – 3
= 5.5 years
Time interval

28. Thank you!