**1.1. Conditions required for FAC**

It has been observed that the following conditions result in FAC degradation in nuclear or fossil power plants:


Failures and accidents due to FAC degradation have been reported at several nuclear power plants around the world since 1981 [1]. However, detailed analysis of the FAC related failures did not start before the severe elbow rapture downstream of a tee occurred at Surry Unit 2 power plant (USA) in 1989, which caused four fatalities and extensive plant damage and resulted in a plant shutdown. In 1999, an extensive steam leakage from the rupture of the shell side of a feed-water heater at the Point Beach power plant (USA) was reported by Yurmanov and Rakhmanov [2] (Figure 1). In 2004, a fatal pipe rupture downstream of an orifice in the condensate system due to FAC occurred in the Mihama nuclear power plant Unit 3 (Japan) [2]. More recently, the pipe failure downstream of a control valve at Iatan fossil power plant in 2007 resulted in two fatalities and a huge capital of plant loss as reported by Moore [3]. Although, a combination of lab research and attempts to correlate lab results with plant experience has been the major efforts made towards the study of FAC mechanism since the 1970's, the lab research only focused on understanding the mechanisms, and correlating experimental results in order to reduce the lab effort and to develop usable forms for the plant engineers. Several well cited correlations used to predict the actual corrosion rates due to FAC in piping systems and incorporated in computer software such as CHECWORKS developed by Electric Power Research Institute (EPRI). Following the abovementioned accidents, most utilities around the world have been following EPRI guideline of improving the flow water chemistry to slow down the rate of damage. Also, in the event of disposition of highly susceptible or damaged areas, utilities have typically taken the following initial steps:


154 Nuclear Power – Practical Aspects

straight piping component.

mechanical processes can be summarized as:

normally forms on the internal pipe wall surface.

components are made to contain at least 0.1% chromium.

are exposed to high velocities.

**1.1. Conditions required for FAC** 

fossil power plants:

etc.

greater than zero.

can however be avoided by a combination of improvements in: plant design, drying the

iii. **Flashing-induced erosion:** This form of erosion occurs when spontaneous vapour formation takes place due to sudden pressure changes. Locations where this type of

On the other hand, degradation mechanisms involve combined effect of chemical and

i. **Erosion-corrosion: In this mechanism** a combination of mechanical and chemical material degradation processes take place. The combined effect of the two processes is considered more severe especially in the case when copper alloy heat exchanger tubes

ii. **Flow-Accelerated Corrosion:** The pipe wall thinning due to this degradation mechanism in carbon steel piping is not due to the mechanical effect only, however, the wall thinning is mainly due to dissolution of normally protective magnetite film that

It has been observed that the following conditions result in FAC degradation in nuclear or

 Flow conditions: both single- and two-phase flow conditions, with water or watersteam mixture as the flowing liquid, at a temperature of > 95oC, and flow velocity is

 Chemistry condition: the flowing liquid should be such that a potential difference exists between the liquid and the carbon steel pipe wall. This difference will be responsible for the dissolution of the protective oxide layer in the flowing stream. A high magnetite solubility and subsequent rapid removal of the magnetite, is facilitated by either demineralised and neutral water or slightly alkalinized water under reducing conditions. Material: the pipe material must be carbon steel or low-alloy steel. General practice recommends that for a well-designed system, FAC will be effectively inhibited if steel

 Flow Geometry: FAC has been observed to occur downstream of flow-restricting or redirecting geometries like an orifice, sudden contraction, expansion, elbows, reducers,

Failures and accidents due to FAC degradation have been reported at several nuclear power plants around the world since 1981 [1]. However, detailed analysis of the FAC related

erosion occurs are found in drain and vent lines downstream of control valves. iv. **Cavitation erosion:** This type of erosion is caused by repeated growth and collapse of bubbles in a flowing fluid as a result of local pressure fluctuations. In the regions of higher pressures downstream, the sudden collapse of gas bubbles results in pressure spikes that may erode the material in their vicinity. These bubbles will however get reabsorbed along the piping system without causing any damage to the downstream

steam, and the use of more corrosion-resistant steels.

4. Replace entire susceptible lines or the more susceptible portions with other components of FAC resistant material.

The recent review by Ahmed [4] highlighted the significant research conducted on investigating the effect of fluid chemical properties on flow accelerated corrosion (FAC) in nuclear power plants. He concluded that the hydrodynamic effects of single and two-phase flows on FAC have not been thoroughly investigated for many piping components. In order to determine the effect of the proximity between two components on the FAC wear rate, Ahmed [4] has investigated 211 inspection data for 90o carbon steel elbows from several nuclear power plants. The effect of the velocity as well as the distance between the elbows and the upstream components was discussed. Based on the analyzed trends obtained from the inspection data, the author indicated a significant increase in the wear rate of approximately 70% that was identified to be due to the proximity.

Furthermore, the repeated inspections in nuclear power plants have shown that piping components located downstream of flow singularities, such as sudden expansion or contractions, orifices, valves, tees and elbows are most susceptible to FAC damage. This is due to the severe changes in flow direction as well as the development of secondary flow instabilities downstream of these singularities [4]. Moreover, in two-phase flows, the significant phase redistributions downstream of these singularities may aggravate the problem. Therefore, it is important to identify the main flow and geometrical parameters require in characterizing FAC damage downstream of pipe fittings. These parameters are: the geometrical configuration of the components, piping orientation, and the flow turbulence structure which will affect the surface shear stress and mass transfer coefficients.

Flow Accelerated Corrosion in Nuclear Power Plants 157

For single phase flow, the secondary vortices and/or flow separation downstream of pipe fittings considered to be important parameters need to be analyzed and modelled while predicting the highest FAC wear rate location. For example; the secondary flows in elbows induce a pressure drop along the elbow wall that can significantly increase the wall mean and oscillatory shear stresses as discussed by Crawford et al. [5]. Also, orifices and valves promote turbulence close to the wall in the downstream pipe and thus enhance the rate of mass transfer at the wall [5]. These mechanisms have been identified as the governing

The hydrodynamics parameters controlling FAC in two-phase flows are considered more complex than for single-phase flows due to the complexity of two-phase distribution and the unknown interactions between the gas phase and the liquid [8]. These interactions play a major role in the mass, momentum, and energy transfer between the flow phases as explained by Hassan et al. [9]. Also, the inlet two-phase flow pattern plays an important role in the flow dynamics downstream of the orifices since the phase redistribution downstream depend on the upstream flow regime. For example, bubbles can have significant effects on the turbulent kinetic energy close to the wall, affecting the wall shear stress and pressure. Moreover, Jepson [10] showed that high velocity slugs can cause high turbulence and shear forces at the pipe wall and thus enhance the destruction of the

Computational fluid dynamic (CFD) analysis is used to predict turbulent fluid flow with great accuracy for many applications. However, only the recent advances in computational power have allowed the use of CFD for mass transfer and corrosion studies. This indicated that the accurate prediction of mass transfer near the wall requires resolving the mass transfer boundary layer which may be an order of magnitude smaller than the viscous sublayer. In order to perform the CFD calculations with good accuracy, fine near-wall grids with correct near-wall turbulence models can therefore provide mass transfer data for the corrosion species. In these cases corrosion is controlled by the mass transfer, relation between the wall mass transfer coefficient and corrosion rate can be derived as explained in details by Keating and Nesic [11]. Furthermore, in formulating the CFD codes, consideration is made to the hydrodynamic parameters affecting the mass transfer rate of the corrosion products to the bulk fluid and consequently the FAC rate. These hydrodynamic parameters are the flow velocity, pipe roughness, piping geometry, and steam quality or void fraction

The hydrodynamic effects of the working fluid on FAC have been investigated by many researchers using CFD. Bozzini [12] adopted numerical simulations for investigating wall erosion/corrosion inside a pipe bend for a four-phase flow that comprised of two immiscible liquids, gas and particulate solids. On the other hand, Chang et al. [13] suggested an evaluation scheme to estimate the load carrying capacity of thinned-wall pipes exhibiting FAC. In their study, they employed a steady-state incompressible flow CFD code to determine the pressure distributions as input conditions for a structural finite element

factors responsible for FAC as explained by Chen et al. [6].

protective inhibitor film.

for two-phase flow.

**Figure 1.** Examples of failures due to FAC worldwide (Yurmanov and Rakhmanov [2])

For single phase flow, the secondary vortices and/or flow separation downstream of pipe fittings considered to be important parameters need to be analyzed and modelled while predicting the highest FAC wear rate location. For example; the secondary flows in elbows induce a pressure drop along the elbow wall that can significantly increase the wall mean and oscillatory shear stresses as discussed by Crawford et al. [5]. Also, orifices and valves promote turbulence close to the wall in the downstream pipe and thus enhance the rate of mass transfer at the wall [5]. These mechanisms have been identified as the governing factors responsible for FAC as explained by Chen et al. [6].

156 Nuclear Power – Practical Aspects

require in characterizing FAC damage downstream of pipe fittings. These parameters are: the geometrical configuration of the components, piping orientation, and the flow turbulence structure which will affect the surface shear stress and mass transfer coefficients.

**Figure 1.** Examples of failures due to FAC worldwide (Yurmanov and Rakhmanov [2])

The hydrodynamics parameters controlling FAC in two-phase flows are considered more complex than for single-phase flows due to the complexity of two-phase distribution and the unknown interactions between the gas phase and the liquid [8]. These interactions play a major role in the mass, momentum, and energy transfer between the flow phases as explained by Hassan et al. [9]. Also, the inlet two-phase flow pattern plays an important role in the flow dynamics downstream of the orifices since the phase redistribution downstream depend on the upstream flow regime. For example, bubbles can have significant effects on the turbulent kinetic energy close to the wall, affecting the wall shear stress and pressure. Moreover, Jepson [10] showed that high velocity slugs can cause high turbulence and shear forces at the pipe wall and thus enhance the destruction of the protective inhibitor film.

Computational fluid dynamic (CFD) analysis is used to predict turbulent fluid flow with great accuracy for many applications. However, only the recent advances in computational power have allowed the use of CFD for mass transfer and corrosion studies. This indicated that the accurate prediction of mass transfer near the wall requires resolving the mass transfer boundary layer which may be an order of magnitude smaller than the viscous sublayer. In order to perform the CFD calculations with good accuracy, fine near-wall grids with correct near-wall turbulence models can therefore provide mass transfer data for the corrosion species. In these cases corrosion is controlled by the mass transfer, relation between the wall mass transfer coefficient and corrosion rate can be derived as explained in details by Keating and Nesic [11]. Furthermore, in formulating the CFD codes, consideration is made to the hydrodynamic parameters affecting the mass transfer rate of the corrosion products to the bulk fluid and consequently the FAC rate. These hydrodynamic parameters are the flow velocity, pipe roughness, piping geometry, and steam quality or void fraction for two-phase flow.

The hydrodynamic effects of the working fluid on FAC have been investigated by many researchers using CFD. Bozzini [12] adopted numerical simulations for investigating wall erosion/corrosion inside a pipe bend for a four-phase flow that comprised of two immiscible liquids, gas and particulate solids. On the other hand, Chang et al. [13] suggested an evaluation scheme to estimate the load carrying capacity of thinned-wall pipes exhibiting FAC. In their study, they employed a steady-state incompressible flow CFD code to determine the pressure distributions as input conditions for a structural finite element analyses in order to calculate local stresses. More recently, Ferng [14] developed an approach that used an erosion/corrosion model and three-dimensional single and two-phase flow models to predict locations of serious FAC in power plant piping systems. Their predictions agreed very well with plant measurements.

### **2. FAC rate and mass transfer**

The FAC process in carbon steel piping is described by three steps. In the first process, metal oxidation occurs at metal/oxide interface in oxygen-free water and explained by the following reactions:

$$\text{Fe} + 2\text{H}\_2\text{O} \rightarrow \text{Fe}^{2+} + 2\text{OH}^- + \text{H}\_2 \tag{1}$$

$$\text{Fe}^{2+} + 2\text{OH}^- \leftrightarrow \text{Fe} \text{(OH}\text{)}\_2 \tag{2}$$

Flow Accelerated Corrosion in Nuclear Power Plants 159

( – ) *w b FAC rate MTC C C* (5)

.. *b c Sh a Re Sc* (6)

./ *<sup>H</sup> Sh MTC d D* (7)

���� � ������ (8)

������������� � ���� (9)

Several research works [15-17] showed that MTC is one of the important parameters affecting FAC and the experimental data are often expressed in terms of Sherwood (*Sh*),

where *a*, *b* and *c* are related to mass transfer which occurs under a given flow condition and can only be obtained experimentally. Where (*Sh)* in the non-dimensional representation of

In Equation (6), the velocity exponent varies between 0.8 for lower Reynolds numbers and 1.0 for very high Reynolds numbers. This difference in the velocity exponent is caused by the surface roughness. This indicates that the FAC rate increases as the surface roughness increases. It should be also noted that the experimental studies and the correlations developed for MTC were carried out under low flow rates conditions compared with common operating conditions in power generation industry. Therefore, the MTC data obtained in the literature for moderate and high Reynolds numbers at power plant

In the case of piping downstream orifices, Tagg et al. [18] described the wear enhancement profile empirically in terms of the maximum Sherwood number using Reynolds number at

On the other hand, the local enhancement profile downstream of the orifice at different axial

where ���� is the Sherwood number for the smooth straight pipe, *Shz* is the Sherwood

Another modelling approach for FAC prediction was carried by Remy et al., [21], to develop a criteria in order to avoid FAC damage. They model the FAC mechanism as a combination of two main mechanisms. These mechanisms are divided into two steps. In the first of which is the production of soluble ferrous ions, which is represented by a first-

eq K (C - C) *VC* (10)

����

����� � ���� � ���

locations (z) is described empirically by Coney [19] referred to by Chexal et al. [20] as:

����� �� � �� � ���

MTC as a function of the local hydrodynamic parameters and expressed as:

where: *dH =* hydraulic diameter, and *D* = diffusion coefficient of iron in water.

Reynolds (*Re*) and Schmidt (*Sc*) numbers as:

conditions can lead to significant errors.

the vena contracta section (���) as follows:

order reaction:

��� ����

number at any axial location (z), *Az* and *Bz* are empirical constants.

$$\text{C}\text{-}\text{5Fe} + \text{4H}\_2\text{O} \rightarrow \text{Fe}\_3\text{O}\_4 + \text{4H}\_2\tag{3}$$

The first process involves the solubility of the ferrous species through the porous oxide layer into the main water flow. This transport across the oxide layer is controlled by the concentration diffusion. The second step is described by the dissolution of magnetite at oxide/water interface as explained by the following reaction:

$$11/3Fe\_3O\_4 + \left(2-b\right)H^+ + 1/3H\_2 \leftrightarrow Fe\left(OH\right)\_b^{(2-b)+} + \left(4/3-b\right)H2O\tag{4}$$

where:

*Fe(OH)b(2-b)+* represents the different iron ferrous species *b=(0,1,2,3)* 

In the third step (Eq. 4), a diffusion process takes place where the ferrous irons transfer into the bulk flowing water across the diffusion boundary layer. In this process, the species migrated from the metal/oxide interface and the species dissolved at the oxide/water interface diffuse rapidly into the flowing water. In this case, the concentration of ferrous iron in the bulk water is very low compared to the concentration at the oxide/water interface.

It can be noticed that FAC mechanism involves convective mass transfer of the ferrous ions in the water. The convective mass transfer for single phase flow is known to be dependent on the hydrodynamic parameters near the wall interface such as flow velocity, local turbulence, geometry, and surface roughness. In addition, the physical properties of the transported species or the water do not affect the local transport rate in adiabatic flow especially when temperature changes in piping system are negligible. Over a limited length of piping component, FAC rate is considered as direct function of the mass flux of ferrous ions and can be calculated from the convective mass transfer coefficient (*MTC*) in the flowing water. Then, FAC rate is calculated from the MTC and the difference between the concentration of ferrous ions at the oxide/water interface (*Cw*) and the concentration of ferrous in the bulk of water (*Cb*) as:

$$FAC\text{ rate } = MTC(\text{ C}\_w - \text{ C}\_b) \tag{5}$$

Several research works [15-17] showed that MTC is one of the important parameters affecting FAC and the experimental data are often expressed in terms of Sherwood (*Sh*), Reynolds (*Re*) and Schmidt (*Sc*) numbers as:

$$Sh \, = \, a. \text{Re}^b \mathcal{S} \mathcal{C}^c \tag{6}$$

where *a*, *b* and *c* are related to mass transfer which occurs under a given flow condition and can only be obtained experimentally. Where (*Sh)* in the non-dimensional representation of MTC as a function of the local hydrodynamic parameters and expressed as:

$$Sh \, = \,\mathrm{MTC.d}\_{H} / \,\mathrm{D} \tag{7}$$

where: *dH =* hydraulic diameter, and *D* = diffusion coefficient of iron in water.

158 Nuclear Power – Practical Aspects

following reactions:

where:

predictions agreed very well with plant measurements.

oxide/water interface as explained by the following reaction:

*Fe(OH)b(2-b)+* represents the different iron ferrous species *b=(0,1,2,3)* 

**2. FAC rate and mass transfer** 

ferrous in the bulk of water (*Cb*) as:

analyses in order to calculate local stresses. More recently, Ferng [14] developed an approach that used an erosion/corrosion model and three-dimensional single and two-phase flow models to predict locations of serious FAC in power plant piping systems. Their

The FAC process in carbon steel piping is described by three steps. In the first process, metal oxidation occurs at metal/oxide interface in oxygen-free water and explained by the

2

<sup>2</sup>

The first process involves the solubility of the ferrous species through the porous oxide layer into the main water flow. This transport across the oxide layer is controlled by the concentration diffusion. The second step is described by the dissolution of magnetite at

> <sup>2</sup> 3 4 <sup>2</sup> 1/3 2 1/3 4/3 2 ) *<sup>b</sup>*

In the third step (Eq. 4), a diffusion process takes place where the ferrous irons transfer into the bulk flowing water across the diffusion boundary layer. In this process, the species migrated from the metal/oxide interface and the species dissolved at the oxide/water interface diffuse rapidly into the flowing water. In this case, the concentration of ferrous iron in the bulk water is very low compared to the concentration at the oxide/water interface.

It can be noticed that FAC mechanism involves convective mass transfer of the ferrous ions in the water. The convective mass transfer for single phase flow is known to be dependent on the hydrodynamic parameters near the wall interface such as flow velocity, local turbulence, geometry, and surface roughness. In addition, the physical properties of the transported species or the water do not affect the local transport rate in adiabatic flow especially when temperature changes in piping system are negligible. Over a limited length of piping component, FAC rate is considered as direct function of the mass flux of ferrous ions and can be calculated from the convective mass transfer coefficient (*MTC*) in the flowing water. Then, FAC rate is calculated from the MTC and the difference between the concentration of ferrous ions at the oxide/water interface (*Cw*) and the concentration of

*<sup>b</sup> Fe O b H H Fe OH bHO* (4)

2 2 *Fe H O Fe OH H* 2 2 (1)

<sup>2</sup> *Fe OH Fe OH* <sup>2</sup> (2)

2 34 2 3 4 4 *Fe H O Fe O H* (3)

In Equation (6), the velocity exponent varies between 0.8 for lower Reynolds numbers and 1.0 for very high Reynolds numbers. This difference in the velocity exponent is caused by the surface roughness. This indicates that the FAC rate increases as the surface roughness increases. It should be also noted that the experimental studies and the correlations developed for MTC were carried out under low flow rates conditions compared with common operating conditions in power generation industry. Therefore, the MTC data obtained in the literature for moderate and high Reynolds numbers at power plant conditions can lead to significant errors.

In the case of piping downstream orifices, Tagg et al. [18] described the wear enhancement profile empirically in terms of the maximum Sherwood number using Reynolds number at the vena contracta section (���) as follows:

$$Sh\_{max} = 0.27 \cdot Re\_o^{0.67} \cdot \text{Sc}^{0.33} \tag{8}$$

On the other hand, the local enhancement profile downstream of the orifice at different axial locations (z) is described empirically by Coney [19] referred to by Chexal et al. [20] as:

$$\frac{Sh\_{\rm z}}{Sh\_{fd}} = 1 + A\_{\rm Z} \left[ 1 + B\_{\rm Z} \left( \frac{Re\_0^{0.66}}{0.0165 \cdot Re^{0.06}} - 21 \right) \right] \tag{9}$$

where ���� is the Sherwood number for the smooth straight pipe, *Shz* is the Sherwood number at any axial location (z), *Az* and *Bz* are empirical constants.

Another modelling approach for FAC prediction was carried by Remy et al., [21], to develop a criteria in order to avoid FAC damage. They model the FAC mechanism as a combination of two main mechanisms. These mechanisms are divided into two steps. In the first of which is the production of soluble ferrous ions, which is represented by a firstorder reaction:

$$V\_{\mathbb{C}} = \text{ K ( $\mathbb{C}\_{eq}$  -  $\mathbb{C}$ )}\tag{10}$$

*VC =* total corrosion rate, *K* = reaction rate constant, *Ceq* = the soluble ion concentration at oxide water interface. The second step of FAC is correlated to the transfer of ferrous ion into the bulk water, which is a convective transport phenomenon that can be modelled as:

$$F\_{\text{IF}} = \text{ } \& \text{(C - C\_{\text{eq}})}\tag{11}$$

Flow Accelerated Corrosion in Nuclear Power Plants 161

(16)

This model is mainly an improved version of Berge's model considering the diffusion through the porous oxide layer and incorporating both oxide thickness (δ) and porosity (Ѳ), and also

(C ) eq rate \* 1 (1 )(1 )

For FAC under two-phase flow condition, Remy et al. [21] indicated that same correlations used for single-phase flow calculations are also applicable in two-phase flow calculations. The only difference in the analysis is the calculation of actual Reynolds number, using the actual water velocity taking into account the void fraction between the steam and water.

EPRI report [3] incorporated the idea of Remy et al. [21] on the use of single phase correlations in clculating FAC under two-phase flow conditions. Calculation begin by

> Re *<sup>H</sup> L L*

<sup>1</sup> . <sup>1</sup> *<sup>L</sup> L Q x <sup>V</sup> A*

The flow is considered to be a single phase liquid flow when the steam quality (x) and the steam void fraction (α) are both equal to zero (0), while α = 1 implies no presence of liquid, hence *ReL* = 0 and no FAC damage is expected. Under two-phase flow conditions, when (*α* ) is greater than (*x)*, and *ReL*> *Re*, the mass transfer coefficient increases and consequently FAC

In two-phase flow the void fraction is usually not equal to steam quality because the liquid and the vapour phases are moving with different velocities, and sometimes in different directions. If homogeneous flow is assumed, the two phase's velocities are assumed to be equal, which results in a steam quality-void fraction relationship as a function of pressure. However, due to the fact that the homogeneous flow assumption is not suitable for many industrial applications, more sophisticated models were developed by researchers to relate steam quality to void fraction. One of the most cited model is the Chexal-Lellouche void

> *g O gj*

*j Cj V*

*L <sup>d</sup> <sup>V</sup>* 

> 

(17)

(18)

(19)

*K fk D*

*C*

considers diffusion of iron hydroxides through the pores, to determine the FAC rate as:

*FAC*

determining Reynolds number for the liquid phase, *ReL*, as follows:

**3. FAC modelling in two-phase flow** 

Where the liquid velocity expressed as:

wear rate increases.

model:

ii. MIT model

where: *FIF* = the ferrous ion flux, *MTC* = mass transfer coefficient, *C* ͚ = ferrous ion concentration in the bulk flow. These two steps are assumed to be equal at equilibrium state, and can be expressed in terms of the combined equation:

$$V\_{\mathbb{C}} = \text{ 2K(MTC)} \text{ (C}\_{\text{eq}}\text{-C)} \text{(MTC + 2K)}\tag{12}$$

which was finally reduced to:

$$T\_L = \text{ } \mathbf{kC\_{eq}}\tag{13}$$

*TL* is the thickness loss kinetic which is mainly correlated to the FAC wear rate. This conclusion of linear relationship between FAC rate and concentration was early refuted by Poulson [22], giving reasons in favour of non-linearity. These reasons including:


A comprehensive report on FAC in power plants, by EPRI [3], presents empirical models that have been used successfully to predict components that are most likely to wear, and provide reasonable estimates of pipe wall-thinning. These models are however computerbased due to the large amount of information that needs to be processed. These models are represented in the following two groups:

i. Berge model

The model assumed that the chemical dissolution of the magnetite at the oxide/water interface occurs in accordance with the following equation:

$$DR = \text{ } K \text{ ( $\mathbb{C}\_{eq} - \mathbb{C}\_{S}$ )}\tag{14}$$

where *DR* is the ferrous iron production rate; *K* is the reaction rate constants or (kinetics); *Ceq*, is the equilibrium concentration of magnetite; and *CS*, is the magnetite concentration at oxide/water interface. Finally, the FAC rate is given as:

$$\text{FAC rate} \, = \text{2K} \, (\text{C}\_{\text{eq}} \text{-} \text{C}\_{\text{S}}) \, \tag{15}$$

#### ii. MIT model

160 Nuclear Power – Practical Aspects

which was finally reduced to:

solutions,

and 3), and

i. Berge model

*VC =* total corrosion rate, *K* = reaction rate constant, *Ceq* = the soluble ion concentration at oxide water interface. The second step of FAC is correlated to the transfer of ferrous ion into the

where: *FIF* = the ferrous ion flux, *MTC* = mass transfer coefficient, *C* ͚ = ferrous ion concentration in the bulk flow. These two steps are assumed to be equal at equilibrium state,

eq 2K(MTC) (C - C)/(MTC 2K) *VC* (12)

eq kC *<sup>L</sup> T* (13)

*TL* is the thickness loss kinetic which is mainly correlated to the FAC wear rate. This conclusion of linear relationship between FAC rate and concentration was early refuted by

a. removal of a surface film above a critical value of *K*, e.g. carbon steel in nitrate

c. coupling of reactions, where flow effects *K*, which changes the corrosion potential and also the oxide solubility (∆C). This leads to a dependency on *Kn* (where *n* is between 1

d. dual control, e.g. situations in which the rate is partially controlled by activation such as copper alloys in seawater, or alternatively by two transport processes. This tends to

A comprehensive report on FAC in power plants, by EPRI [3], presents empirical models that have been used successfully to predict components that are most likely to wear, and provide reasonable estimates of pipe wall-thinning. These models are however computerbased due to the large amount of information that needs to be processed. These models are

The model assumed that the chemical dissolution of the magnetite at the oxide/water

eq S *DR* K (C - C ) (14)

where *DR* is the ferrous iron production rate; *K* is the reaction rate constants or (kinetics); *Ceq*, is the equilibrium concentration of magnetite; and *CS*, is the magnetite concentration at

eq S *FAC* rate 2K (C - C ) (15)

Poulson [22], giving reasons in favour of non-linearity. These reasons including:

b. interactions of anodic and cathodic areas, e.g. iron in Nacl or FeCl3 solutions,

k (C - C ) *IF F* (11)

bulk water, which is a convective transport phenomenon that can be modelled as:

and can be expressed in terms of the combined equation:

lead to a dependency on *Kn*, where *n* is less than 1.

interface occurs in accordance with the following equation:

oxide/water interface. Finally, the FAC rate is given as:

represented in the following two groups:

This model is mainly an improved version of Berge's model considering the diffusion through the porous oxide layer and incorporating both oxide thickness (δ) and porosity (Ѳ), and also considers diffusion of iron hydroxides through the pores, to determine the FAC rate as:

$$F\text{AC rate} = \frac{\theta(\mathbb{C}\_{\text{eq}} - \mathbb{C}\_{\text{co}})}{\left(1\not{k}\stackrel{\bullet}{\text{K}} + (1 - f)(1\not{k} + \delta\not{f}D)\right)}\tag{16}$$

#### **3. FAC modelling in two-phase flow**

For FAC under two-phase flow condition, Remy et al. [21] indicated that same correlations used for single-phase flow calculations are also applicable in two-phase flow calculations. The only difference in the analysis is the calculation of actual Reynolds number, using the actual water velocity taking into account the void fraction between the steam and water.

EPRI report [3] incorporated the idea of Remy et al. [21] on the use of single phase correlations in clculating FAC under two-phase flow conditions. Calculation begin by determining Reynolds number for the liquid phase, *ReL*, as follows:

$$\text{Re}\_L = V\_L \frac{d\_H}{\nu\_L} \tag{17}$$

Where the liquid velocity expressed as:

$$V\_L = \left(\frac{Q}{A\rho\_L}\right) \left(\frac{1-\chi}{1-\alpha}\right) \tag{18}$$

The flow is considered to be a single phase liquid flow when the steam quality (x) and the steam void fraction (α) are both equal to zero (0), while α = 1 implies no presence of liquid, hence *ReL* = 0 and no FAC damage is expected. Under two-phase flow conditions, when (*α* ) is greater than (*x)*, and *ReL*> *Re*, the mass transfer coefficient increases and consequently FAC wear rate increases.

In two-phase flow the void fraction is usually not equal to steam quality because the liquid and the vapour phases are moving with different velocities, and sometimes in different directions. If homogeneous flow is assumed, the two phase's velocities are assumed to be equal, which results in a steam quality-void fraction relationship as a function of pressure. However, due to the fact that the homogeneous flow assumption is not suitable for many industrial applications, more sophisticated models were developed by researchers to relate steam quality to void fraction. One of the most cited model is the Chexal-Lellouche void model:

$$\left< \alpha \right> = \frac{\left< j\_{\rm g} \right>}{C\_O \left< j \right> + \overline{V\_{\rm gj}}} \tag{19}$$

where:

〈*j*〉 and 〈*jg*〉 are the mixture and vapour volumetric fluxes.

Another model developed by Kuo-Tong et al. [23] to predict FAC damage locations on High pressure (HP) turbine exhaust steam line. Their choice of High pressure (HP) turbine exhaust steam line as a case study was based on the plant measured data of pipe thickness which indicated HP lines as a good example where serious FAC takes place under two phase flow conditions. They reported that FAC phenomenon strongly depends on the piping layout and local flow conditions. They proposed a new mathematical approach to simulate FAC wear rate. The approach includes the use of 3D two-phase flow hydrodynamic CFD model to simulate the two-phase flow behaviour in HP lines, integrated with FAC Models to investigate the impact of the local parameters on FAC damage. The improvement of their new approach over the previous work is the ability to account for the multi-dimensional characteristics applied to FAC wear rate prediction. This is consider a great advantage in predicting FAC compared to the previous codes such as CHECKWORK or CAECE program which are based on empirical correlations that are dependent on the global flow conditions in the piping lines. In developing their code, the following assumptions were adopted:

Flow Accelerated Corrosion in Nuclear Power Plants 163

(20)

*vY J S* (22)

(21)

(23)

) are

(25)

*k*

turbulent pipe flow is assumed in order to determine MTC profiles downstream of the orifice. ANSI specifications of orifice were used to construct the geometrical model. Since the experimental condition in the present study is carried out for straight pipe section fabricated from hydrocal (CaSO4.½H2O) downstream of an orifice to simulate faster effect of mass transfer rates. The Solution is obtained for Renormalization Group (RNG) *K-Ɛ* differential viscosity model for turbulent flow in conjunction with the species transport

The velocity field of the incompressible viscous flow is obtained using the one dimensional

*i i j i j j ij j uP u u u u x xx x*

.( ) . *i i <sup>i</sup>*

In Equation (11), the Boussinesq eddy viscosity assumption [25] is used for modeling the

 

*i i u x*

Species mass transport equation for a steady process with no chemical reaction is:

[( / ) ( )] 2 / 3 *ij t i j j i ij*

The turbulence kinetic energy ( *k* ) and the turbulence kinetic energy dissipation rate (

22 2 <sup>2</sup> ( ) / 2, ( / ) *i j k u v w vu z* 

Therefore, the equation for turbulence kinetic energy can be also expressed as follows:

*Uk r Vk kz r kr*

*zr z r*

 

[( / )( / ) [( / )( / )] () ( ) (1 / ) [1 / ] *eff k eff k*

*r r G*

 (26)

*uu U z U z k*

is defined as the "turbulent viscosity" and expressed as:

<sup>2</sup> ( / ) *<sup>t</sup> Cf k* 

 

Reynold's stress. The eddy viscosity model relation is expressed as:

i i <sup>u</sup> 0 0 x

> 1 Re

is the diffusion flux of species *i,* and arises due to concentration gradient, and *<sup>i</sup> S*

 

(24)

 

equations using FLUENT CFD code.

Continuity equation:

Momentum equation:

where: *<sup>i</sup> J* 

where *<sup>t</sup>* 

is the source term.

defined as follows:

 

 

Reynolds averaged governing equations as follows:


Their final hydrodynamic CFD models include two-fluid 3D continuity and momentum equations. Closure relations such as the mixture *k-e* turbulent models, two-phase constitutive equations were also used. The developed FAC model claimed to include droplet impingement model, which was used to simulate the mechanically-assisted form of material degradation.

In a similar two-phase flow analysis applied to the extraction piping system connecting the low-pressure turbine (LPTB) and feed water heater (FWH) at boiling water reactors (BWR), Yuh et al. [24] developed a code to predict FAC wear in BWR piping system. Their mathematical approach is very similar to the work done by Kuo-Tong et al. [23], with the exception to the addition of corrosion model used. They obtained the local distributions of fluid parameters including two-phase flow velocities, void fractions, turbulent properties, and pressure. These results were further used to establish the relation for droplet kinetic energy that represents the FAC damage. The comparison of between their model and the plant measured data show qualitatively a good agreement.
