# Parametric Study of Time-Dependent Corrosion Product Activity due to56Mn, 58Co, and 60Co in the Primary Coolant Circuit of a Typical Pressurized Water Reactor

Authors: Muhammad Rafique; Nasir M. Mirza; Sikander M. Mirza; Kimberlee J. Kearfott; Shahab A. Abbasi; Syed F. Naeem
Journal: Journal of Chemistry
 (2015)

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## Abstract

Results of a detailed study, based on the parametric analysis of activated corrosion products, in primary coolant of a typical pressurized water reactor (PWR) are presented. The parameters influencing time dependent buildup of corrosion product activity (CPA) in primary coolant loop of PWR were identified. The computer program CPAIR was used to accommodate for time dependent corrosion rates. The behaviors of56Mn, 58Co, and 60Co were studied over the reactor operational time. During the course of normal operation of reactor, the CPA is dominated by 56Mn, while 58Co and 60Co are the predominant radionuclides after reactor shutdown. Parametric study suggests that the total CPA is most sensitive to ion-exchanger removal rates. For a removal rate of 300 cm3-s−1, the specific activity due to 56Mn has the maximum value of 3.552 × 104 Bq-m−3 after 1,000 hours of reactor operation. This value decreases drastically to 8.325 × 103 Bq-m−3at removal rate of 900 cm3-s−1. Additionally, CPA due to 56Mn, 58Co, and 60Co shows strong dependence on removal rates from the core material surfaces. Variations in the values of radionuclide removal rates from piping surface and radionuclide removal rate from deposition on pipes showed only very small effects on CPA buildup.


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## Body

## 1. Introduction

Corrosion products activated by high neutron flux in the reactor core are the dominant contributors to the postshutdown radiation field (PSRF) for all water reactors. Pressurized water reactors (PWRs) have an order of magnitude higher PSRF values compared to gas-cooled reactors. Large PSRF values affect the plant availability factor by prolonging repair and maintenance schedules, entailing annual economic penalties of several billion US dollars [1].In the past, several authors [2–18] carried out investigations on the formation, transport, and deposition of radioactive corrosion products in various parts of PWRs. Several models were developed to simulate corrosion product transport and the buildup of activity in the primary coolant systems of PWRs. The PACTOLE program [4] was developed for predicting the time-dependent behavior of the activation of PWR corrosion products. Based upon experimental data, the CORA code was upgraded in 1985 [19] to model the transport of corrosion products in primary coolant loop of PWRs. The MIGA code was developed [20] on a strong understanding of the chemical thermodynamics that determines the most stable oxide phase likely to exist under the chemistry and temperature conditions in each region of the primary circuit. The DISER program [21] simulates corrosion product activity (CPA), assuming that the coolant contains solute, colloids, and particulate corrosion products. Song and Lee [22] investigated the generation mechanism of crud in the long term fuel cycle, using the COTRAN code, which simulates the behavior of the crud based on double layer concept model and solubility difference. The effects of flow and power transients on CPA were investigated by Mirza et al. and Deeba et al. using the code CPAIR [23, 24]. This was further modified to account for CPA under linearly and nonlinearly rising corrosion rate models by Mirza et al. [13, 14] and Rafique et al. [15].Malik et al. [25] studied CPA under flow rate transients, having extended burn-up cycles with time-dependent pH-level and boric acid variations. Their finding showed CPA buildup towards saturation following the mixing of boron in primary coolant and a decreasing trend following an increase in pH value. Another study by Malik et al. [26] showed that the use of enriched boric acid as chemical shim actually lowers the primary coolant activity when higher pH values are employed in coolant rather than natural boric acid.Lewis et al. [27] developed a physical model describing the coolant activity behavior of 99Tc during constant and reactor shutdown operations. Kang and coworkers [19] investigated the inventory of radioactivity in the typical 1,000 MWe Spanish PWR. Analysis was based on DORT models. Henshaw and coworkers [28] proposed a model for simulating thermal hydraulic and chemical conditions within fuel crud deposits. The unique feature of their model is that the chemistry is coupled to the thermohydraulics via the increase in the saturation temperature with the concentration of dissolved species. The model explains several crud scrape observations.Particulate fouling due to corrosion product sedimentation plays an important role in heat exchanger material integrity and water chemistry. Zebardast et al. [29] proposed a new experimental method for the detection of magnetite particles at temperatures up to 473 K.In-pile loops were used for the experimental study of possible improvements in the coolant chemistry for reducing the corrosion product dose rates [30, 31]. Those studies indicated that dissolution and crystallization cannot be modeled accurately enough in the absence of the required experimental coefficients for these processes. Those detailed studies revealed that the rate of corrosion in the reactor systems continues increasing as the time of reactor operation at full power increases. Access and frequent maintenance to areas near primary pumps then become very limited due to high radiation doses from primary water and pipe scale.In this work, parametric studies of CPA under normal reactor operation were carried out. The three radionuclides56Mn, 60Co, and 58Co were considered. Sensitive parameters are identified from the models, showing their effects on CPA buildup in the primary coolant of typical PWRs.


## 2. Mathematical Models

The purpose of the parametric analysis of CPA in the primary coolant loop of PWRs is to study the sensitivity of the model simulations to uncertainties in the values of model input data. This work identifies sensitive parameters occurring in mathematical models used for simulating the behavior of CPA.The governing time-dependent differential equations for modeling CPA in the primary circuits of PWRs appear in the literature [13–16, 18, 23, 24] and now are summarized. The rate of buildup of target nuclide concentration in coolant water can be written as(1)dNwdt=-x1Nw+x2Nw-x3Np-x4NcA2-A1+Sw,where(2)A1=σϕεNw,A2=g(t)Vw,x1=∑jεjQj=εIQI+εpQp+εcQc+εFQFand the quantities εIQI, εpQp, εcQc, and εFQF are removal rates due to ion-exchanger, deposition on pipes, deposition on core surfaces, and removal by filters, respectively. Similarly, the leakage rate from the kth leak is given by x2=∑klk, where the term lk is the rate at which primary coolant loop loses water from its kth leak (cm3-s−1). In addition, x3=Kp, where Kp is the rate at which isotopes are removed from the scale on piping (cm3-s−1), and x4=Kc, where Kc is the rate at which isotopes are removed from the scale on core material (cm3-s−1).In the above equationsx1 (the radionuclide removal rates due to ion-exchanger, deposition on pipes, deposition on core surfaces, and removal by filters), x2 (leakage rate from the kth leak), x3 (radionuclide removal from piping surface), and x4 (radionuclide removal rate from scales on core materials) are sensitive variables which change the time-dependent CPA in the primary coolant of PWR.Ifσ is the group constant for the production of isotope from target nuclide, then ϕε, the effective group flux (neutrons-cm−2-s−1), is defined by the equation (3)ϕε=1-exp⁡(-λTc)1-exp⁡(-λTL)ϕ0.The values of decay constant (λ) for 56Mn, 60Co, and 58Co are provided in Table 1. The group flux ϕ0 is averaged over the geometry of the core and has been estimated using LEOPARD [32] and ODMUG [33] programs in the CPAIR. The times Tc and TL are the core residence and loop times, respectively.Table 1
Activated corrosion products and their reaction properties [13].
Corrosion products
Reaction and neutron energy
Activation cross section and half-life
ϕ
0
56Mn
55Mn(n, γ) 56Mn (En is thermal)
13.4 b (2.58 h)
9.2 × 1013
58Co
58Ni(n, p) 58Co (fast neutrons)
0.146 b (70.88 d)
9.02 × 1013
60Co
59Co(n, γ) 60Co
20 b (5.3 y)
9.02 × 1013The core residence time is given by(4)Tc=HρAw(t),where H is the core height, A is the flow cross-sectional area in (cm2), ρ is the coolant density at operating temperatures, and w(t) is the time-dependent flow rate (g-s−1).The loop time is approximated asLpTc/H for the complete loop length Lp. Nw, Np, and Nc stand for the target nuclide concentration in water, on piping surfaces, and on core surfaces (atoms-cm−3); g(t) is flow rate perturbation parameter, defined as g(t)=w(t)/w0, where w(t) is the time-dependent flow rate and w0 is the steady state flow rate under normal operations. Because in this study transient conditions are avoided, in our subsequent study we will take value of g(t) equal to unity; that is, w(t)=w0. Vw is primary coolant volume.The corrosion source term appearing in the above equation is given by(5)Sw=C(t)SVwN0Afnfs,where C(t) is the time-dependent corrosion rate (gram cm−2-s−1), S is the area of system exposed to coolant for corrosion, N0 is Avogadro’s number (6.023 × 1023 atoms g-mole−1), and A is the atomic weight of the target nuclide (g). Here, fn and fs are abundances of target nuclides and chemical elements in the system, respectively.The rate of change of active material concentration in primary coolants for each radionuclide is given by(6)dnwdt=A1-A2x1+x2nw-A3nw+A2x3np+A2x3nc,where nw, np, and nc are the concentrations of the activated radionuclides in the primary coolant water, on the piping, and on the core surfaces, respectively, in atoms-cm−3.The rate of activity buildup on core scale is given by(7)dncdt=B1+B2y1nw-B2x4nc-A3nc,where B1=σϕ0Nc and B2=g(t)/Vc.HereVc is volume of the scale on the core (cm3). And y1=εcQc, where εcQc is removal rate from scales on core surfaces. Consider A3=λ.The rate of buildup of target nuclide concentration on the core scale,Nc, is given by (8)dNcdt=y1B2Nw-x4B2Nc-B1.It then follows that the rate of change of target nuclide on piping walls, Np, is(9)dNpdt=z1C1Nw-x3C1Np.The rate of deposition of active materials on the pipes is expressed as(10)dnpdt=C1z1nw-C1x3np-A3np,where C1=g(t)/Vp, with Vp equal to volume of scale on the piping (cm3). z1=εpQp, εpQp is removal rate from piping surface (cm3).The rate of activity buildup in ion-exchanger is expressed mathematically as(11)dnIdt=D1y2nw-A3n1,where D1=g(t)/VI, where VI is volume of ion-exchanger. y2=εIQI is removal rate by ion-exchanger.The rate of activity buildup in filters becomes(12)dnfdt=D2y3nw-A3nf,where D2=g(t)/Vf, Vf is volume of filter, and y3=εfQf is removal rate of filters.Using the above set of coupled differential equations ((1) through (12)), the computer program CPAIR (corrosion product activity in reactors) [15], using fourth-order Runge-Kutta method to find the activity values due to corrosion, was modified for this work.


## 3. Methods and Assumptions

The computer code CPAIR, utilizing specifications of a typical PWR with power of 1,000 MWe, was considered [13–15, 34]. Initial impurity concentrations were assumed to be zero. The numerical values of experimental fractional exchange rates (εjQj/Vq) and resolution rates (Kj/Vq) assumed for this work are summarized in Table 2.Table 2
Experimental values of exchange rates in a typical PWR [13–15, 34].
Rate type
Value
Deposition on core (εcQc)
80.0 cm3-s−1
Deposition on piping (εpQp)
13.7 cm3-s−1
Ion-exchanger removal (εIQI)
500.–781 cm3-s−1
Resolution ratio for core (Kc)
40.0 cm3-s−1
Resolution ratio for piping (Kp)
6.9 cm3-s−1
Volume of primary coolant (Vw)
1.37 × 107 cm3
Volume of scale on core (Vc)
9.08 × 106 cm3
Volume of scale on piping (Vp)
1.37 × 106 cm3
Total corrosion surface (S)
1.01 × 108 cm2The design data values for a typical PWR under consideration are given in Table3 [13–15, 34]. The core averaged group fluxes have been computed using LEOPARD and ODMUG computer codes. The LEOPARD program is a zero-dimensional unit cell computer code with 54 fast and 172 thermal energy groups. Evaluated Nuclear Data (ENDF-IV) set has been used in the cross section library. In this work, equivalent cells of a typical PWR [34] have been employed to generate group constants for fuel cells and water holes. These cell-averaged group constants are then used in the one-dimensional multigroup diffusion theory based ODMUG code [33]. It calculates the group fluxes as a function of position in the reactor. These group fluxes are subsequently averaged over the core. Both LEOPARD and ODMUG are treated as subroutines of the CPAIR program.Table 3
Typical design specifications of a PWR [13–15, 34].
Parameter
Value
Specific power (MW(th)-kg−1U)
33
Power density (MW(th)-m−3)
102
Core height (m)
4.17
Core diameter (m)
3.37
Number of  assemblies
194
Number of rods per assembly
264
Fuel type
UO2
Clad type
Zircoloy
Lattice pitch (mm)
12.6
Fuel rod outer diameter (mm)
9.5
Average enrichment (w%)
3.0
Flow rate (Mg-s−1)
18.3
Linear heat rate (kW-m−2)
17.5
Coolant pressure (MPa)
15.5
Inlet coolant temperature (°C)
293
Outlet coolant temperature (°C)
329The plant surface area of ~108 cm2 is exposed to the primary coolant for corrosion. In the presence of corrosion inhibitors, an equilibrium corrosion rate of 2.4 × 10−13 g-cm−2-s−1 [13–15, 33–35] exists after 1 y operation of a reactor with a primary coolant volume of 1.3 × 107 cm3. The corrosion rate of 25 μg-s−1 has been used as normal equilibrium rate in subsequent studies.The purification rate due to an ion-exchangerεIQI was considered to be large enough to regard deposition, resolution, and leakage as second-order effects. Three radionuclides, 56Mn (soluble corrosion products, coming from impurities in the steel), 60Co, and 58Co (insoluble corrosion products), were considered.


## 4. Results and Discussion

During normal reactor operation at full power, the major contributor towards activity comes from the radionuclide56Mn. The 56Mn activity saturates at about 150 h after start of the reactor. The saturation of 56Mn activity was due to the fact that we assumed abundances of target nuclides (fn) and chemical elements (fs) in the system equal to 1 and 0.5, respectively. Its saturation value is 8.325 × 10−3 Bq-cm−3 and it makes the primary coolant as a 2.453 × 107 Bq source (including coactivity) within 150–230 h of reactor operation at full power.


### 4.1. Effect of Ion-Exchanger Removal Rates (εIQI) on CPA Buildup in Primary Coolant Loop

Specific activity due to each of the radionuclides (56Mn, 58Co, and 60Co) changes significantly, in the primary coolant loop, with the assumed removal rates for the ion-exchanger.At removal rate of 300 cm3-s−1, the specific activity due to 56Mn reaches a maximum value (saturation value) of 3.552 × 104 Bq-cm−3 after 1,000 h of reactor operation as shown in Figure 1. Specific activities at removal rates of 400, 500, 600, 700, 800, and 900 cm3-s−1 result in CPA values of (2.49, 1.868, 1.465, 1.188, 0.984, 0.832) × 104 Bq-cm−3, respectively.Figure 1
Variation of specific activity in primary coolant of PWR with different values of ion-exchanger removal rates.These values indicate the fact that ion-exchanger removal rates play an important role in controlling the specific activity in PWR primary coolant. So removal rates of 800 cm3-s−1 and greater are optimal values of ion-exchanger removal rate. The parameter εIQI is the most sensitive parameter for the mathematical models above. By changing values of εIQI there will be considerable change in the coolant activity.The normalized specific activity due to56Mn was evaluated using a conventional removal rate of 600 cm3-s−1. Specific activity due to 56Mn at removal rates of 300, 400, 500, 700, 800, and 900 cm3-s−1 was 2.42, 1.7, 1.27, 0.81, 0.67, and 0.57 times the conventional removal rate, respectively. Normalized specific activity as a function of different removal rates is shown in Figure 2.Figure 2
Normalized specific activity due to56Mn as a function of different removal rates.


### 4.2. Effect of Radionuclide Removal Rate from Core Surface Scale (Kc) on CPA Buildup in Primary Coolant Loop

Variations in the value ofKc change the value of CPA in primary circuit of PWR. At Kc=25 cm3-s−1 the specific activity due to 56Mn in primary coolant becomes 1.21 × 104 Bq-cm−3, which decreases at higher values of Kc and becomes 1.16 × 104 Bq-cm−3 at Kc=55 cm3-s−1. The variation of 56Mn specific activity with Kc is depicted in Figure 3 and saturation values are listed in Table 4.Table 4
Specific activities of56Mn, 58Co, and 60Co in primary coolant of PWR with different values of Kc.
K
c (cm2/s)
Specific activity (Bq/cm3) after 1000 hours of reactor operation
56Mn
58Co
60Co
25
12118
21088
432
30
12042
17753
362
35
11965
15321
311
40a
11889
13476
273
45
11813
12026
243
50
11739
10858
219
55
11666
9899
199
aActual experimental value of resolution value for core in a typical PWR.Figure 3
Specific activity of56Mn as a function of reactor operation time in primary coolant of PWR with different values of Kc.Normalized values of specific activities due to56Mn as a function of different resolutions rates from core surfaces are shown in Figure 4. A conventional value of Kc=40 cm3-s−1 was chosen and specific activity due to 56Mn at resolution rates of 25, 30, 35, 45, 50, and 55 cm3-s−1 was found as a factor of 1.019, 1.012, 1.006, 0.99, 0.987, and 0.981 with the conventional chosen resolution rate activity.Figure 4
Normalized specific activity of56Mn as a function of Kc.Variation in the value ofKc also changes the amount of radioactivity due to 58Co in primary coolant. The specific activity due to 58Co decreases with increasing the values of Kc. For Kc=25 cm3-s−1 the specific activity due to 58Co has the value 2.11 × 104 Bq-cm−3 after 1,000 hours of reactor operation, and this value decreases to 0.989 × 104 Bq-cm−3 at Kc=55 cm3-s−1 as shown in Figure 5 and Table 4. The resolution rates must also be considered a sensitive parameter.Figure 5
Variation in specific activity of58Co in primary coolant of PWR with different values of Kc.Normalized values of specific activities due to58Co as a function of different resolutions rates from core surfaces are shown in Figure 6. A conventional value of Kc=40 cm3-s−1 was chosen and specific activity due to 58Co at resolution rates of 25, 30, 35, 45, 50, and 55 cm3-s−1 was found as a factor of 1.56, 1.31, 1.14, 0.89, 0.81, and 0.73 with the conventional chosen resolution rate activity.Figure 6
Normalized specific activity of58Co as a function of Kc.Similarly specific activity due to60Co in primary coolant decreases with increasing values of Kc. For Kc=25 cm3-s−1 the specific activity has the value 432 Bq-cm−3 after 1,000 h of reactor operation. This value decreases to 199 Bq-cm−3 at Kc=55 cm3-s−1 as shown in Figure 7 and Table 4.Figure 7
Specific activity of60Co in primary coolant of PWR with different values of Kc.


### 4.3. Effect of Radionuclide Removal Rate from Core Surface Scale (Kc) on CPA Buildup on Piping Surface

Activated corrosion products once produced may get deposited on piping surfaces of primary coolant loop over the period of reactor operation, thereby becoming the potential source of radiation field. On piping surfaces of primary coolant loop the value of specific activity due to58Co for Kc=25 cm3-s−1 has the value 5.81 × 104 Bq-cm−3 after 1,000 h of reactor operation, and this value decreases radically to 2.838 × 104 Bq-cm−3 at Kc=55 cm3-s−1 as shown in Figure 8.Figure 8
Specific activity of58Co on primary coolant piping surfaces of PWR with different values of Kc.On piping surfaces of primary coolant loop the value of specific activity due to60Co for Kc=25 cm3-s−1 has the value 4847 Bq-cm−3 after 1,000 h of reactor operation, and this value decreases radically to 2331 Bq-cm−3 at Kc=55 cm3-s−1, as illustrated in Figure 9.Figure 9
Specific activity of60Co on primary coolant piping surfaces of PWR with different values of Kc.


### 4.4. Effects of Radionuclide Removal Rate from Piping Scales (Kp) on CPA Buildup in Primary Coolant Loop

While changing the valueKp, change in CPA in primary coolant has been observed. For the CPA due to 58Co has value 3626 Bq-cm−3, which decreases to 3589 Bq-cm−3 at Kp=8.0 as shown in Figure 10. Similarly for 60Co specific activity has the value 270 Bq-cm−3 at Kp=6.0, and this value decreases to the value 266 Bq-cm−3 at Kp=8.0 as shown in Figure 11 and Table 5.Table 5
Specific activity of58C0 and 60Co with various Kp values.
K
p (cm2/s)
Specific activity (Bq/cm3) after 1000 hours of reactor operation
58Co
60Co
6.0
3595
268
6.5
3605
269
7.0b
3612
270
7.5
3621
271
8.0
3629
271
bActual experimental value of resolution rate for piping in a typical PWR.Figure 10
Specific activity of58Co in primary coolant of PWR with different values of Kp.Figure 11
Specific activity of60Co in primary coolant of PWR with different values of Kp.


### 4.5. Effects of Removal Rate from Deposition on Piping Surfaces (EPQP) on CPA Buildup in Primary Coolant Loop

Effect ofEPQP on CPA due to 58Co and 60Co in primary coolant has also been studied. For 58Co the specific activity has the value 3697 Bq-cm−3, and this value decreases to 3589 Bq-cm−3 for EPQP=10.7 after 1,000 h of reactor operation, as shown in Figure 12 and Table 6. For 60Co the specific activity has the value 277 Bq-cm−3, and this value decreases to 268 Bq-cm−3 for EPQP=10.7 after 1,000 h of reactor operation, as shown in Figure 13.Table 6
Specific activity of58Co and 60Co in primary coolant of PWR with different values of EPQP.
E
p
Q
p (cm2/s)
Specific activity (Bq/cm3) after 1000 hours of reactor operation
58Co
60Co
10.7
3589
268
11.7
3606
269
12.7
3624
271
13.7c
3642
273
14.7
3660
274
15.7
3678
276
16.7
3697
277
cActual experimental value of resolution rate from deposition on piping.Figure 12
Variation in specific activity of58Co in primary coolant of PWR with different values of EPQP.Figure 13
Specific activity of60Co in primary coolant of PWR with different values of EPQP.Some of the results of CPAIR have been compared with the code CRUDSIM/MIT [31]. The same data were used to simulate the CPA using CPAIR program, resulting in 2.02 × 104 Bq-cm−3 estimated for the stainless steel letdown filters, whose function is to retain corrosion products 58Co, 60Co, and 56Mn. Because solubility is a function of temperature and the temperature of the filters is less than that of the bulk coolant, the filter activity concentrations are not necessary representatives of actual coolant activity concentrations. The filter results, however, are very similar to the value of 1.85 × 104 Bq-cm−3 reported elsewhere [31].


## 4.1. Effect of Ion-Exchanger Removal Rates (εIQI) on CPA Buildup in Primary Coolant Loop

Specific activity due to each of the radionuclides (56Mn, 58Co, and 60Co) changes significantly, in the primary coolant loop, with the assumed removal rates for the ion-exchanger.At removal rate of 300 cm3-s−1, the specific activity due to 56Mn reaches a maximum value (saturation value) of 3.552 × 104 Bq-cm−3 after 1,000 h of reactor operation as shown in Figure 1. Specific activities at removal rates of 400, 500, 600, 700, 800, and 900 cm3-s−1 result in CPA values of (2.49, 1.868, 1.465, 1.188, 0.984, 0.832) × 104 Bq-cm−3, respectively.Figure 1
Variation of specific activity in primary coolant of PWR with different values of ion-exchanger removal rates.These values indicate the fact that ion-exchanger removal rates play an important role in controlling the specific activity in PWR primary coolant. So removal rates of 800 cm3-s−1 and greater are optimal values of ion-exchanger removal rate. The parameter εIQI is the most sensitive parameter for the mathematical models above. By changing values of εIQI there will be considerable change in the coolant activity.The normalized specific activity due to56Mn was evaluated using a conventional removal rate of 600 cm3-s−1. Specific activity due to 56Mn at removal rates of 300, 400, 500, 700, 800, and 900 cm3-s−1 was 2.42, 1.7, 1.27, 0.81, 0.67, and 0.57 times the conventional removal rate, respectively. Normalized specific activity as a function of different removal rates is shown in Figure 2.Figure 2
Normalized specific activity due to56Mn as a function of different removal rates.


## 4.2. Effect of Radionuclide Removal Rate from Core Surface Scale (Kc) on CPA Buildup in Primary Coolant Loop

Variations in the value ofKc change the value of CPA in primary circuit of PWR. At Kc=25 cm3-s−1 the specific activity due to 56Mn in primary coolant becomes 1.21 × 104 Bq-cm−3, which decreases at higher values of Kc and becomes 1.16 × 104 Bq-cm−3 at Kc=55 cm3-s−1. The variation of 56Mn specific activity with Kc is depicted in Figure 3 and saturation values are listed in Table 4.Table 4
Specific activities of56Mn, 58Co, and 60Co in primary coolant of PWR with different values of Kc.
K
c (cm2/s)
Specific activity (Bq/cm3) after 1000 hours of reactor operation
56Mn
58Co
60Co
25
12118
21088
432
30
12042
17753
362
35
11965
15321
311
40a
11889
13476
273
45
11813
12026
243
50
11739
10858
219
55
11666
9899
199
aActual experimental value of resolution value for core in a typical PWR.Figure 3
Specific activity of56Mn as a function of reactor operation time in primary coolant of PWR with different values of Kc.Normalized values of specific activities due to56Mn as a function of different resolutions rates from core surfaces are shown in Figure 4. A conventional value of Kc=40 cm3-s−1 was chosen and specific activity due to 56Mn at resolution rates of 25, 30, 35, 45, 50, and 55 cm3-s−1 was found as a factor of 1.019, 1.012, 1.006, 0.99, 0.987, and 0.981 with the conventional chosen resolution rate activity.Figure 4
Normalized specific activity of56Mn as a function of Kc.Variation in the value ofKc also changes the amount of radioactivity due to 58Co in primary coolant. The specific activity due to 58Co decreases with increasing the values of Kc. For Kc=25 cm3-s−1 the specific activity due to 58Co has the value 2.11 × 104 Bq-cm−3 after 1,000 hours of reactor operation, and this value decreases to 0.989 × 104 Bq-cm−3 at Kc=55 cm3-s−1 as shown in Figure 5 and Table 4. The resolution rates must also be considered a sensitive parameter.Figure 5
Variation in specific activity of58Co in primary coolant of PWR with different values of Kc.Normalized values of specific activities due to58Co as a function of different resolutions rates from core surfaces are shown in Figure 6. A conventional value of Kc=40 cm3-s−1 was chosen and specific activity due to 58Co at resolution rates of 25, 30, 35, 45, 50, and 55 cm3-s−1 was found as a factor of 1.56, 1.31, 1.14, 0.89, 0.81, and 0.73 with the conventional chosen resolution rate activity.Figure 6
Normalized specific activity of58Co as a function of Kc.Similarly specific activity due to60Co in primary coolant decreases with increasing values of Kc. For Kc=25 cm3-s−1 the specific activity has the value 432 Bq-cm−3 after 1,000 h of reactor operation. This value decreases to 199 Bq-cm−3 at Kc=55 cm3-s−1 as shown in Figure 7 and Table 4.Figure 7
Specific activity of60Co in primary coolant of PWR with different values of Kc.


## 4.3. Effect of Radionuclide Removal Rate from Core Surface Scale (Kc) on CPA Buildup on Piping Surface

Activated corrosion products once produced may get deposited on piping surfaces of primary coolant loop over the period of reactor operation, thereby becoming the potential source of radiation field. On piping surfaces of primary coolant loop the value of specific activity due to58Co for Kc=25 cm3-s−1 has the value 5.81 × 104 Bq-cm−3 after 1,000 h of reactor operation, and this value decreases radically to 2.838 × 104 Bq-cm−3 at Kc=55 cm3-s−1 as shown in Figure 8.Figure 8
Specific activity of58Co on primary coolant piping surfaces of PWR with different values of Kc.On piping surfaces of primary coolant loop the value of specific activity due to60Co for Kc=25 cm3-s−1 has the value 4847 Bq-cm−3 after 1,000 h of reactor operation, and this value decreases radically to 2331 Bq-cm−3 at Kc=55 cm3-s−1, as illustrated in Figure 9.Figure 9
Specific activity of60Co on primary coolant piping surfaces of PWR with different values of Kc.


## 4.4. Effects of Radionuclide Removal Rate from Piping Scales (Kp) on CPA Buildup in Primary Coolant Loop

While changing the valueKp, change in CPA in primary coolant has been observed. For the CPA due to 58Co has value 3626 Bq-cm−3, which decreases to 3589 Bq-cm−3 at Kp=8.0 as shown in Figure 10. Similarly for 60Co specific activity has the value 270 Bq-cm−3 at Kp=6.0, and this value decreases to the value 266 Bq-cm−3 at Kp=8.0 as shown in Figure 11 and Table 5.Table 5
Specific activity of58C0 and 60Co with various Kp values.
K
p (cm2/s)
Specific activity (Bq/cm3) after 1000 hours of reactor operation
58Co
60Co
6.0
3595
268
6.5
3605
269
7.0b
3612
270
7.5
3621
271
8.0
3629
271
bActual experimental value of resolution rate for piping in a typical PWR.Figure 10
Specific activity of58Co in primary coolant of PWR with different values of Kp.Figure 11
Specific activity of60Co in primary coolant of PWR with different values of Kp.


## 4.5. Effects of Removal Rate from Deposition on Piping Surfaces (EPQP) on CPA Buildup in Primary Coolant Loop

Effect ofEPQP on CPA due to 58Co and 60Co in primary coolant has also been studied. For 58Co the specific activity has the value 3697 Bq-cm−3, and this value decreases to 3589 Bq-cm−3 for EPQP=10.7 after 1,000 h of reactor operation, as shown in Figure 12 and Table 6. For 60Co the specific activity has the value 277 Bq-cm−3, and this value decreases to 268 Bq-cm−3 for EPQP=10.7 after 1,000 h of reactor operation, as shown in Figure 13.Table 6
Specific activity of58Co and 60Co in primary coolant of PWR with different values of EPQP.
E
p
Q
p (cm2/s)
Specific activity (Bq/cm3) after 1000 hours of reactor operation
58Co
60Co
10.7
3589
268
11.7
3606
269
12.7
3624
271
13.7c
3642
273
14.7
3660
274
15.7
3678
276
16.7
3697
277
cActual experimental value of resolution rate from deposition on piping.Figure 12
Variation in specific activity of58Co in primary coolant of PWR with different values of EPQP.Figure 13
Specific activity of60Co in primary coolant of PWR with different values of EPQP.Some of the results of CPAIR have been compared with the code CRUDSIM/MIT [31]. The same data were used to simulate the CPA using CPAIR program, resulting in 2.02 × 104 Bq-cm−3 estimated for the stainless steel letdown filters, whose function is to retain corrosion products 58Co, 60Co, and 56Mn. Because solubility is a function of temperature and the temperature of the filters is less than that of the bulk coolant, the filter activity concentrations are not necessary representatives of actual coolant activity concentrations. The filter results, however, are very similar to the value of 1.85 × 104 Bq-cm−3 reported elsewhere [31].


## 5. Conclusions

Corrosion products are strong contributors to radiation levels produced in personnel working environment of PWR, and thus the estimation of corrosion product activity (CPA) is important. Higher burn-up, longer-lived reactor cores make the problem more critical. In this work, a parametric study of CPA in primary coolant of a typical PWR was carried out using the CPAIR computer code. Conclusions based upon those numerical simulations include the following.(i)
During normal operation56Mn dominates the CPA, while 58Co and 60Co are the main contributors after shutdown.(ii)
The CPA shows a strong sensitive dependence onKc.(iii)
The variation in other parameters, includingKp, lk, and εpQp, only weakly affects the CPA.(iv)
Excellent agreement was found between predictions of CPA using a modified version of CPAIR and CRUDSIM/MIT findings.



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*Source: 809672-2015-04-06.xml*