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 of ^{56}Mn, ^{58}Co, and ^{60}Co were studied over the reactor operational time. During the course of normal operation of reactor, the CPA is dominated by ^{56}Mn, while ^{58}Co and ^{60}Co are the predominant radionuclides after reactor shutdown. Parametric study suggests that the total CPA is most sensitive to ionexchanger removal rates. For a removal rate of 300 cm^{3}s^{−1}, the specific activity due to ^{56}Mn has the maximum value of 3.552 × 10^{4} Bqm^{−3} after 1,000 hours of reactor operation. This value decreases drastically to 8.325 × 10^{3} Bqm^{−3 }at removal rate of 900 cm^{3}s^{−1}. Additionally, CPA due to ^{56}Mn, ^{58}Co, and ^{60}Co 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.
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 gascooled reactors. Large PSRF values affect the plant availability factor by prolonging repair and maintenance schedules, entailing annual economic penalties of several billion US dollars [
In the past, several authors [
Malik et al. [
Lewis et al. [
Particulate fouling due to corrosion product sedimentation plays an important role in heat exchanger material integrity and water chemistry. Zebardast et al. [
Inpile loops were used for the experimental study of possible improvements in the coolant chemistry for reducing the corrosion product dose rates [
In this work, parametric studies of CPA under normal reactor operation were carried out. The three radionuclides ^{56}Mn, ^{60}Co, and ^{58}Co were considered. Sensitive parameters are identified from the models, showing their effects on CPA buildup in the primary coolant of typical PWRs.
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 timedependent differential equations for modeling CPA in the primary circuits of PWRs appear in the literature [
In the above equations
If
The values of decay constant (
Activated corrosion products and their reaction properties [
Corrosion products  Reaction and neutron energy  Activation cross section and halflife 


^{56}Mn  ^{55}Mn(n, 
13.4 b (2.58 h)  9.2 × 10^{13} 
^{58}Co  ^{58}Ni(n, p) ^{58}Co (fast neutrons)  0.146 b (70.88 d)  9.02 × 10^{13} 
^{60}Co  ^{59}Co(n, 
20 b (5.3 y)  9.02 × 10^{13} 
The core residence time is given by
The loop time is approximated as
The corrosion source term appearing in the above equation is given by
The rate of change of active material concentration in primary coolants for each radionuclide is given by
The rate of activity buildup on core scale is given by
Here
The rate of buildup of target nuclide concentration on the core scale,
The rate of activity buildup in ionexchanger is expressed mathematically as
The rate of activity buildup in filters becomes
Using the above set of coupled differential equations ((
The computer code CPAIR, utilizing specifications of a typical PWR with power of 1,000 MWe, was considered [
Experimental values of exchange rates in a typical PWR [
Rate type  Value 

Deposition on core ( 
80.0 cm^{3}s^{−1} 
Deposition on piping ( 
13.7 cm^{3}s^{−1} 
Ionexchanger removal ( 
500.–781 cm^{3}s^{−1} 
Resolution ratio for core ( 
40.0 cm^{3}s^{−1} 
Resolution ratio for piping ( 
6.9 cm^{3}s^{−1} 
Volume of primary coolant ( 
1.37 × 10^{7} cm^{3} 
Volume of scale on core ( 
9.08 × 10^{6} cm^{3} 
Volume of scale on piping ( 
1.37 × 10^{6} cm^{3} 
Total corrosion surface ( 
1.01 × 10^{8} cm^{2} 
The design data values for a typical PWR under consideration are given in Table
Typical design specifications of a PWR [
Parameter  Value 

Specific power (MW(th)kg^{−1}U)  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  UO_{2} 
Clad type  Zircoloy 
Lattice pitch (mm)  12.6 
Fuel rod outer diameter (mm)  9.5 
Average enrichment (w%)  3.0 
Flow rate (Mgs^{−1})  18.3 
Linear heat rate (kWm^{−2})  17.5 
Coolant pressure (MPa)  15.5 
Inlet coolant temperature (°C)  293 
Outlet coolant temperature (°C)  329 
The plant surface area of ~10^{8} cm^{2} is exposed to the primary coolant for corrosion. In the presence of corrosion inhibitors, an equilibrium corrosion rate of 2.4 × 10^{−13} gcm^{−2}s^{−1} [
The purification rate due to an ionexchanger
During normal reactor operation at full power, the major contributor towards activity comes from the radionuclide ^{56}Mn. The ^{56}Mn activity saturates at about 150 h after start of the reactor. The saturation of ^{56}Mn activity was due to the fact that we assumed abundances of target nuclides
Specific activity due to each of the radionuclides (^{56}Mn, ^{58}Co, and ^{60}Co) changes significantly, in the primary coolant loop, with the assumed removal rates for the ionexchanger.
At removal rate of 300 cm^{3}s^{−1}, the specific activity due to ^{56}Mn reaches a maximum value (saturation value) of 3.552 × 10^{4} Bqcm^{−3} after 1,000 h of reactor operation as shown in Figure
Variation of specific activity in primary coolant of PWR with different values of ionexchanger removal rates.
These values indicate the fact that ionexchanger removal rates play an important role in controlling the specific activity in PWR primary coolant. So removal rates of 800 cm^{3}s^{−1} and greater are optimal values of ionexchanger removal rate. The parameter
The normalized specific activity due to ^{56}Mn was evaluated using a conventional removal rate of 600 cm^{3}s^{−1}. Specific activity due to ^{56}Mn at removal rates of 300, 400, 500, 700, 800, and 900 cm^{3}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
Normalized specific activity due to ^{56}Mn as a function of different removal rates.
Variations in the value of
Specific activities of ^{56}Mn, ^{58}Co, and ^{60}Co in primary coolant of PWR with different values of

 

^{56}Mn  ^{58}Co  ^{60}Co  
25  12118  21088  432 
30  12042  17753  362 
35  11965  15321  311 
40^{a}  11889  13476  273 
45  11813  12026  243 
50  11739  10858  219 
55  11666  9899  199 
Specific activity of ^{56}Mn as a function of reactor operation time in primary coolant of PWR with different values of
Normalized values of specific activities due to ^{56}Mn as a function of different resolutions rates from core surfaces are shown in Figure
Normalized specific activity of ^{56}Mn as a function of
Variation in the value of
Variation in specific activity of ^{58}Co in primary coolant of PWR with different values of
Normalized values of specific activities due to ^{58}Co as a function of different resolutions rates from core surfaces are shown in Figure
Normalized specific activity of ^{58}Co as a function of
Similarly specific activity due to ^{60}Co in primary coolant decreases with increasing values of
Specific activity of ^{60}Co in primary coolant of PWR with different values of
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 to ^{58}Co for
Specific activity of ^{58}Co on primary coolant piping surfaces of PWR with different values of
On piping surfaces of primary coolant loop the value of specific activity due to ^{60}Co for
Specific activity of ^{60}Co on primary coolant piping surfaces of PWR with different values of
While changing the value
Specific activity of ^{58}C0 and ^{60}Co with various

 

^{58}Co  ^{60}Co  
6.0  3595  268 
6.5  3605  269 
7.0^{b}  3612  270 
7.5  3621  271 
8.0  3629  271 
Specific activity of ^{58}Co in primary coolant of PWR with different values of
Specific activity of ^{60}Co in primary coolant of PWR with different values of
Effect of
Specific activity of ^{58}Co and ^{60}Co in primary coolant of PWR with different values of

Specific activity (Bq/cm^{3}) after 1000 hours of reactor operation  

^{58}Co  ^{60}Co  
10.7  3589  268 
11.7  3606  269 
12.7  3624  271 
13.7^{c}  3642  273 
14.7  3660  274 
15.7  3678  276 
16.7  3697  277 
Variation in specific activity of ^{58}Co in primary coolant of PWR with different values of
Specific activity of ^{60}Co in primary coolant of PWR with different values of
Some of the results of CPAIR have been compared with the code CRUDSIM/MIT [
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 burnup, longerlived 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.
During normal operation ^{56}Mn dominates the CPA, while ^{58}Co and ^{60}Co are the main contributors after shutdown.
The CPA shows a strong sensitive dependence on
The variation in other parameters, including
Excellent agreement was found between predictions of CPA using a modified version of CPAIR and CRUDSIM/MIT findings.
Target nuclide concentration in primary coolant water, atomscm^{−3} ((
Target nuclide concentration on inner walls of the piping, atomscm^{−3} ((
Target nuclide concentration on core surfaces, atomscm^{−3} ((
Radionuclide concentration primary water, atomscm^{−3} ((
Radionuclide concentration on the piping, atomscm^{−3} ((
Radionuclide concentration on the core surface, atomscm^{−3} ((
Removal rate due to ionexchanger (
Removal rate from deposition on pipes (
Removal rate from deposition on core surfaces (
Removal rate by filters (
Primary coolant loop water loss rate from the
Radionuclide removal rate from pipe scale, cm^{3}s^{−1} (
Radionuclide removal rate from core surface scale, cm^{3}s^{−1} (
Corrosion source term (
Timedependent corrosion rate, gcm^{−2}s^{−1} (
Area of system exposed to coolant for corrosion, 10^{8} cm^{2} (
Avogadro’s number, 6.023 × 10^{23} atomsg^{−1}mole^{−1} (
Target nuclide atomic weight (
Target nuclide abundance of target nuclide in system (
Chemical element abundance of chemical element in system (
Volume of the scale on the core, cm^{3}
Volume of scale in the piping, cm^{3}
Coolant water volume, cm^{3} ((
Thermal neutron flux averaged over the core geometry, neutronscm^{−2}s^{−1} (
The group constant for radionuclide production from target nuclides
The effective group flux, neutronscm^{−2}s^{−1}
Steady state flow rate under normal operations (
Timedependent flow rate (
The authors declare that there is no conflict of interests regarding the publication of this paper.
Muhammad Rafique is grateful to the Higher Education Commission of Pakistan for providing postdoctoral fellowship in the form of Grant 26(22)/PDFP/HEC/2013/14.