Control rod is used to change the power in nuclear reactor. Certainly, the core at any moment can be made subcritical condition and shut downs when occurring to emergency instance in the core. The rod is grouped based on their function and located at different places in the core where their feature is maximized. Two methods of control rod calibration are the asymptotic period method and the rod-drop method, which were applied in this experiment. In the first method, the reactor is made supcritical by inserting the control rod to be calibrated a certain level. The rod drop method is to determine the subcritical; at the critical state, the rod to be calibrated is dropped into the core, and the resulting decay of neutron flux is observed and related to the reactivity. In this paper, the regulating rod will be calibrated according to the reactivity in OPR-1000 that corresponds to a certain control rod insert or withdraw, and the reactivity in power reactor depends on the integral and differential control rod group too. The core simulator OPR1000 is used to test those methods.
Core simulator OPR1000 is core nuclear power plant OPR1000 simulation. OPR1000 simulator for ShinKori-Unit 1, which will be operated at 2815 MWt, is being developed while the ShinKori-Units 1 and 2 are being built. OPR1000 simulator adopted the RELAP5 R/T code which ran in real-time mode. OPR1000 is the optimal multi-faceted, such as: time, the capacity to change the placement of the controls, temperature, power distribution and boric acid concentration [
The OPR1000 core consists of 177 fuel assemblies, which include 73 control element assemblies (CEAs), and 45 in-core instrument (ICI) thimbles. The core configuration is shown in
The asymptotic period method is frequently used to calibrate control rods, which are derived from the diffusion theory. It approximately requires two minutes for the transients to die to within 1% of the asymptotic period for periods less than 300 seconds [
The rod-drop method is used to reactivity determination [
The control rod moves vertically parallel to the z-axis of the cylindrical core as
H is the height of the core. The number of free neutrons decreases in reactivity which is caused by a differential rod slice dz being located at the position z is the larger:
- The maximum neutron flux
- The larger the macroscopic absorption cross section Σa;
- The larger the neutron flux density
- The longer the slice dz is.
The total probability of neutron product is depended on control rod position. The reactivity in the reactor is linear neutron product. So the differential reactivity
This equation for the differential control rod characteristic is:
C is a constant of proportionality. A control rod is moved into the reactor core by a finite length ∆z = z2 − z1will be changed the reactivity by:
Integration over the whole rod length up to the position z is the following function:
So the neutron flux distribution can be written:
and up to the full length 0… H gives, the integral reactivity is:
The asymptotic period method utilizes period measurements in the nearly super-critical region. By measuring the reactor period followed a reactivity change, the reactivity is found by using the inhour equation:
where T is period of time, Λ is the neutron reproduction time,
The neutron flux distribution is effected by control rod position, which depends on insert or withdraw control rod.
・ Boron swap;
・ Rod swap;
・ Subcritical rod worth.
There are two ways definite control rod worth that is integral rod worth and differential rod worth. The change of reactivity is the integral control rod worth for the displacement distance when a control rod moves from top to bottom of the core. The effect of inserting control rod is calculated by determining the reactivity change between the rod withdrawal state and the state at which rod be inserted from top to that part. In other method, differential rod worth, worth of each part of control rod is estimated based on reactivity change by inserting that part of control rod.
The rod test is inserting a small distance so that the reactor is slightly subcritical and the power starts to decrease. After a few minutes for the transients to die out, the reactor period is determined from the doubling time. Other rod is inserted into the reactor to bring it back to critical. The previous procedure is repeated until the rod test is calibrated along its whole length. From the observed periods are computed utilizing the inhour equation when the corresponding reactivity. Once the control rods are calibrated, it is possible to evaluate the magnitude of other reactivity changes by comparing the critical rod positions.
The error of this method is determined by propagation of errors. The results of control rod calibration that are approximately ±4% for the total rod worth but it is about 1% for slope of the rod calibration curve.
The rod-drop method must be dropped the rods from criticality, so the rod combinations limited that can be measured, and the rod-drop time is more difference theory.
The results showed that the asymptotic period method is accuracy and advantage. Until now, this method is the best method to use calibrated the control rod in the nuclear reactor.
Control rod worth (pcm) | R1 | R2 | R3 | R4 | R5 |
---|---|---|---|---|---|
Rod drop method | 957.25 | 825.62 | 751.64 | 450.39 | 291.11 |
Asymptotic period method | 898.16 | 809.34 | 729.26 | 443.9 | 289.21 |
Description | Measured Rod | Predicted Rod | Acc. Crit. (%) |
---|---|---|---|
Worth (pcm) | Worth (pcm) | [(P − M)/M] × 100 | |
Group 1 | 913.25 | 913.00 | ±10 |
Group A | 1811.69 | 1750.98 | ±15 or ±100 pcm* |
Group 2 | 756.47 | 784.00 | ±15 or ±100 pcm* |
Group 3 | 622.57 | 710.18 | ±15 or ±100 pcm* |
Group 4 | 456.36 | 514.44 | ±15 or ±100 pcm* |
Group 5 | 285.55 | 296.92 | ±15 or ±100 pcm* |
*If the predicted rod worth for each group is greater than or equal to 667 pcm, use the ±15% acceptance criteria; otherwise use the ±100 pcm acceptance criteria.
The results of the integral and differential worth were shown in
The slope of the curve (∆ρ/∆x) and therefore the amount of reactivity inserted per unit of withdrawal is greatest when the control rod is midway out of the core. This occurs because the area of greatest neutron flux is near the center of the core. Therefore, the amount of change in neutron absorption is greatest in this area. If the slope of the curve for integral rod worth in
When group 5 located at 252 cm in the core, it is effect to neutron flux distribution, and is shown in
The error of the simulation is around ±20 pcm. It can be seen that one control rod worth varies with the density, but the worth does not always rise when the density increases. It could be due to strong self-shielding effect of neutron absorbers. When clubbed control rod is inserted into the core, the effective absorption cross sections decrease. The result that the total worth of multiple control rods inserted into the reactor is not equal to the sum when each of them is inserted into the reactor respectively is shown.
The Core OPR1000 was used to simulate. The rod-drop method and the asymptotic period method were testing. The control rods were calibrated by asymptotic period method and the worth of regulating, and safety rods. According to this study, the integral and differential control rod worth and the total worth of five control rod groups with different position are also simulated. The effect of control rods to the axial and radial neutron flux was analyzed here. The simulation results are necessary for the control rod’s process and more than applications in the OPR1000 reactor.
We would like to thank Korea Hydraulic and Nuclear Power (KHNP), Hanyang University, and The Korea Nuclear Association (KNA) for supported Core Simulator OPR1000 that is the main equipment for this study.
Son N.A., Hoa N.D., Nguyen, T.T., Tuan, T.Q. and Raul, O.C. (2017) Control Rod Calibration and Worth Calculation for Optimized Power Reactor 1000 (OPR-1000) Using Core Simulator OPR1000. World Journal of Nuclear Science and Technology, 7, 15-23. http://dx.doi.org/10.4236/wjnst.2017.71002