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Effect of flow rate perturbations has been studied using the modified computer program CPAIR-P for time dependent corrosion rates in Pressurized Water Reactors (PWRs) having extended cycles. In these simulations, a decrease in the corresponding saturation values of corrosion product activity (CPA) is observed for higher pH values. Comparison of CPA’s behavior has been done for constant flow-rate case as well as for transients with elevated
^{10}B levels (~40%) in dissolved boric acid in coolant in two operating cycles. When the flow rate is decreased in the first cycle, the saturation value of CPA attains new higher values. Also, in the second operating cycle, the saturation values are about 12% higher when compared with the values in the first cycle.

Recent Pressurized Water Reactors (PWRs) are aiming at better performance of nuclear plants by increasing the fuel cycle length as high burn-up leads to better utilization of fuel as well as generation of higher revenues [

However, extended cycles put higher safety limits on fuel integrity for longer fuel residence time in core and corrosion induced cracking is one of the major reasons for material failure in PWRs [_{3}O_{4}), the pH levels of 7.3 - 7.4 are needed instead of 6.9. Also, high values of temperature in the system can cause highly corrosive coolant and decomposition of water further increases its corrosion [

In PWRs, the CPA mainly comes from short-lived ^{56}Mn and ^{24}Na. However; iron, molybdenum and cobalt make almost all of the activity after shutdown of reactor. ^{60}Co, ^{58}Co and ^{54}Mn show dependence on flow rate, pH values and boron [

Several studies have been carried out on coolant activation in nuclear reactors with focus on the flow rate & power transients. Reactor transient studies indicate that reactivity as well as flow rate perturbations result in neutron flux peaking [

Corrosion products | Reaction and neutron energy* | Activation cross-section and half-life | g-ray energy MeV (Intensity %)* |
---|---|---|---|

^{24}Na | ^{27}Al(n, α)^{24}Na (E_{n} > 11.6 MeV) ^{23}Na(n, g)^{24}Na (E_{n} is thermal) | 6 × 10^{−8} barn (5.3989 × 10^{4} s) 0.53 × 10^{−4} barn (5.3989 × 10^{4} s) | 1.368 (99.994) 2.754 (99.855) |

^{56}Mn | ^{55}Mn(n, g)^{56}Mn (E_{n} is thermal) | 13.4 barn (9.2808 × 10^{3} s) | 0.8467 (98.85) 1.8107 (26.9) 2.1131 (14.2) 2.5231 (1.02) |

^{59}Fe | ^{58}Fe(n, g)^{59}Fe (E_{n} is thermal) | 0.9 × 10^{−4} barn (1.6018 × 10^{5} s) | 0.1426 (1.02) 0.1923 (3.08) 1.0992 (56.5) 1.2916 (43.2) |

^{60}Co | ^{59}Co(n, g)^{60}Co | 2 × 10^{−3} barn (1.6638 × 10^{8} s) | 1.1732 (99.85) 1.3325 (99.98) |

^{99}Mo | ^{98}Mo(n, g)^{99}Mo E_{n} > 3.1 MeV | 0.45 × 10^{−4} barn (2.3751 × 10^{5} s) | 0.1811 (6.14) 0.3664 (1.20) 0.7395 (12.26) 0.7779 (4.3) |

*Interactive chart of Radionuclides NuDat 2.6, NNDC Databases, Brookhaven National Laboratory (http://www.nndc.bnl.gov/nudat2/chartNuc.jsp).

The time dependent CPA in primary loops of PWRs was carried out for flow rate and power changes using constant corrosion rate models [

In this work we focus on time dependent behavior for CPA in primary circuits of PWRs with extended cycles having flow rate transients and necessary changes were made in CPAIR-P code for nonlinear corrosion rates and pH values . Then for two extended operating cycles the CPA is estimated in the presence of both nonlinear corrosion rates and changes in pH values under flow rate transients.

Numerous studies have revealed that operating cycle in light water reactors is extendable to burnup value of 45 MWd/kgU in PWRs. The operating cycles of 18 to 24 month duration show an increase in the capacity factor from 3% to 7% [

The long operating cycles employ this scheme in which the coolant has higher pH in start of the cycle along with high values of boron and lithium concentrations. After that, steadily pH value is elevated to 7.4 and then kept constant till the end of cycle. Various scenarios for pH changes in a typical PWR versus effective full power days are shown as

Using deterministic simulation technique a mathematical model was developed and implemented into a computer code along with a suitable numerical integration method. The time derivative of active concentration is given by [

where, σ is the group constant. The effective one-group flux is given by ^{2}∙s) and ^{3}) represents the concentration of target nuclide in water. The^{3}. The values of concentrations of the activation products in primary coolant, piping and core are given as^{3}. The sum over j for

where, _{k} and removal rates from piping scale and from core surface are given by K_{p} and K_{c} respectively in #/cm^{2}∙s.

Rate type | Value* |
---|---|

Deposition on core (ε_{c}Q_{c}) | 80.0 cm^{3} per second |

Deposition on piping (ε_{p}Q_{p}) | 13.7 cm^{3} per second |

Ion-exchanger removal (ε_{I}Q_{I}) | 500 to 781 cm^{3} per second |

Re-solution ratio for core (K_{c}) | 40.0 cm^{3} per second |

Re-solution ratio for piping (K_{p}) | 6.9 cm^{3} per second |

Volume of primary coolant (V_{w}) | 1.37 × 10^{7} cm^{3} |

Volume of scale on core (V_{c}) | 9.08 × 10^{6} cm^{3} |

Volume of scale on piping (V_{p}) | 1.37 × 10^{6} cm^{3} |

Total corrosion surface (S) | 1.01 × 10^{8} cm^{2} |

Average corrosion rate (C_{o}) | 2.4 × 10^{−13} gm per cm^{2} per s |

The temporal variation of dissolved boron in primary coolant are given by a parameter h(t):

here, _{0} and b_{0} are fractions in the initial and final phases of operation cycle. The residence time of primary coolant in core is represented by T_{c} while the time taken for circulating once in primary circuit is given by T_{L}. The temporal variation of concentration of target nuclide can be given as

where,

The removal rates by ion-exchanger, core deposition and leakage are function of primary coolant flow rate. The corresponding rate of the core scale activity is given by following model:

where, the volume of the scale on the reactor core surface is given by ^{3}). The ^{2}∙s). The temporal variation of concentration of target nuclide on the core scale (

The governing equation for the rate of change of active material on the piping scaling (

where, the scale volume on the piping is ^{3}). Then, the temporal variation of target nuclide on piping walls (

Using the above system of Equations (1)-(9), the CPAIR-P computer code [

The upgraded version of CPAIR-P code now simulates the CPA incorporating time dependent corrosion rates and primary coolant chemistry. This program uses the core design parameters to estimate the group constants (

In this work, computer simulations were done for a typical PWR with a clean system having none impurities [^{8} cm^{2} is in contact with the primary coolant. Also, in recent work [^{−13} g/cm^{2}-s. Such a PWR has coolant volume equal to 1.3 × 10^{7} cm^{3}. In this work we have used the same for the simulations.

In first part, the equilibrium value of removal rate of CPA by the ion-exchanger (^{3}/s. Consequently, the value of 600 cm^{3} per second was used for removal rate in this work. Behavior of dominant corrosion

Parameter | Value |
---|---|

Specific power (MW(th)/kg U | 33 |

Power density (MW(th)/m^{3}) | 102 |

Core height (m) | 4.17 |

Core diameter (m) | 3.37 |

Assemblies | 194 |

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 (Mg/s) | 18.3 |

Linear heat rate (kW/m^{2}) | 17.5 |

Coolant pressure (MPa) | 15.5 |

Inlet coolant temperature (˚C) | 293 |

Outlet coolant temperature (˚C) | 329 |

isotopes (^{56}Mn, and ^{60}Co) was observed and we saw that when reactor is operating the main contribution comes from ^{56}Mn and after the shutdown the cobalt isotopes dominate the activity.

Typical behavior of the pH-values for two cycles as a function of time is shown as ^{10}B in mixed in the chemical shim. When mixed B-10 is high the pH-value becomes also high in the system.

PWRs have in general nonlinear changes in the corrosion rate during their operation. This is in addition to the coolant chemistry effects. The following mathematical model is used for the first cycle:

The variable m represents slope having a constant value in the time interval

Similarly for the second cycle, the initial corrosion rate is non-zero because of a residual value from the first cycle which is enhanced by an increase in corrosion rate along with a opposing decrease due to effects of the pH-value. It is mathematically modeled by the following expression:

The values of 600, 1170 and 1200 days were used for c, d, and e respectively. The activity was then determined from the modified program CPAIR-P for both cycles. These simulations were carried out for various boron concentration scenarios. When h(t) = 1, the effect of pH-value is nominal and saturation values are largest of all cases. During first cycle, saturation values for Co-60 are 0.24 µCi/cm^{3} (core region), 0.10 µCi/cm^{3} (primary pipes) and 0.016 µCi/cm^{3} (primary coolant).

When the cross-sectional area for flow changes and/or the primary pump speed gets reduced then the flow rate transient occurs in the reactor. As a result the fuel, moderator and coolant temperatures change and start affecting the neutron flux. This further modifies the production of activated corrosion products and their loss terms. In this work, we have introduced a flow rate perturbation taking PWR operating at full power and the activated products has reached to their saturation values. Here we have not allowed the reactor to scram during these simulations to study the consequences of these simulations. Using the modified CPAIR-P program, the corrosion product activity was estimated in the coolant, primary pipe scale and in the reactor core. Flow rate changes were assumed to be linear and were started at time, t_{in} and remained effective for t_{max}-t_{in} time period. Such a model is introduced by the parameter g(t):

Flow rate decrease has a slope of α and t_{in} is the time of initiation of mass flow rate perturbation.

The mass flow rate perturbation is initiated at t_{0} = 300 d for several

^{60}Co for 40% ^{10}B in chemical shim. The results for the first cycle indicate that CPA approaches a higher final value. The new saturation value keeps on increasing when _{0}. Then, the new saturation activity in coolant increases from 0.011 µCi/cm^{3} to 0.017 µCi/cm^{3}. When the ion-exchanger purification rate,

The CPA under flow rate perturbations was investigated in primary loop of a

typical PWR with long operating cycle. These cycles affect the primary coolant chemistry in terms of operational levels of boron and optimum pH values. These simulations indicate that for the normal reactor operation conditions the values of specific CPA approach equilibrium value fairly quickly. The pH values, removal rates and cycle length affect the saturation level of CPA in the system. The CPA levels have been compared for flow rate transients in the presence of higher levels of ^{10}B in chemical shim. When the flow rate transient is applied, the saturation values of CPA go up. If the flow rate is allowed to change, _{0}. Then, the new saturation level in the coolant increases from 0.011 µCi/cm^{3} to 0.017 µCi/cm^{3}. The saturation values in the second operating cycle are about 12% higher when compared with values in the first cycle.

Nasir, R., Mirza, S.M. and Mirza, N.M. (2017) Evaluation of Corrosion Product Activity in a Typical PWR with Extended Cycles and Flow Rate Perturbations. World Journal of Nuclear Science and Technology, 7, 24-34. http://dx.doi.org/10.4236/wjnst.2017.71003