Subcritical core reactivity bias projection technique

Abstract

A method to determine a global core reactivity bias and the corresponding estimated critical conditions of a nuclear reactor core prior to achieving reactor criticality. The method first requires collection and evaluation of the inverse count rate ratio (ICRR) data; specifically, fitting measured ICRR vs. predicted ICRR data. The global core reactivity bias is then determined as the amount of uniform reactivity adjustment to the prediction that produces an ideal comparison between the measurement and the prediction.

Claims

1. A method of determining a global core reactivity bias for a nuclear reactor core and bringing the nuclear reactor core to a critical reactor state, the method comprising: predicting a combination of parameters expected to yield the critical reactor state of the nuclear reactor core, wherein the parameters comprise control rod position, soluble boron concentration, and coolant temperature; operating a nuclear reactor at a first subcritical state; measuring, using a source range detector, a first measured neutron flux value while the nuclear reactor is operating at the first subcritical state; adjusting the nuclear reactor to operate at a second subcritical state by repositioning at least one control rod of the nuclear reactor; measuring, using the source range detector, a second measured neutron flux value while the nuclear reactor is operating at the second subcritical state; predicting a first spatially-corrected neutron flux value for the first subcritical state and a second spatially-corrected neutron flux value for the second subcritical state; comparing each of the measured neutron flux values with the corresponding spatially-corrected neutron flux values to determine the global reactivity bias; wherein a spatial correction factor is not applied to the measured neutron flux values; updating the predicted combination of parameters by adjusting at least one of the parameters according to the global reactivity bias; and bringing the nuclear reactor core to the critical reactor state using the updated combination of parameters.

2. The method of claim 1, further comprising performing a regression analysis to determine a relationship between the measured neutron flux values and the corresponding spatially-corrected neutron flux values to determine the global reactivity bias; wherein the determined global reactivity bias is used to detect an anomaly associated with the nuclear reactor core without operating the reactor at a critical state.

3. The method of claim 1, wherein the first subcritical state and the second subcritical state are steady-state conditions.

4. The method of claim 1 wherein the predicted combination of parameters are updated without operating the nuclear reactor at the critical reactor state.

5. The method of claim 1, wherein operating the reactor at the first subcritical state occurs after an initial construction of the nuclear reactor.

6. The method of claim 1, wherein operating the nuclear reactor at the first subcritical state occurs after a refueling of the nuclear reactor.

7. The method of claim 2, wherein the anomaly associated with the nuclear reactor core is an anomalous reactivity behavior.

8. A processing device programmed to carry out the method of claim 1.

9. A machine readable medium comprising instructions for carrying out the method of claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) A further understanding of the disclosed concept can be gained from the following description of the preferred embodiments when read in conjunction with the accompanying drawings in which:

(2) FIG. 1 is a schematic representation of the primary side of a nuclear power generating system.

DESCRIPTION

(3) FIG. 1 illustrates the primary side of a nuclear electric power generating plant 10 in which a nuclear steam supply system 12 supplies steam for driving a turbine generator (not shown) to produce electric power. The nuclear steam supply system 12 has a pressurized water reactor 14 which includes a reactor core 16 housed within a pressure vessel 18. Fission reactions within the reactor core 16 generate heat, which is absorbed by a reactor coolant, light water, which is passed through the core. The heated coolant is circulated through hot leg piping 20 to a steam generator 22. Reactor coolant is returned to the reactor 14 from the steam generator 22 by a reactor coolant pump 24 through cold leg piping 26. Typically, a pressurized water reactor has at least two and often three or four steam generators 22 each supplied with heated coolant through a hot leg 20, which, along with the cold leg 26 and reactor coolant pump 2 form a primary loop. Each primary loop supplies steam to the turbine generator. One of such loops are shown in FIG. 1.

(4) Coolant returned to the reactor 14 flows downward through an annular downcomer, and then upward through the core 16. The reactivity of the core, and therefore the power output of the reactor 14, is controlled on a short term basis by control rods, which may be selectively inserted into the core. Long term reactivity is regulated through control of the concentration of a neutron moderator such as boron dissolved in the coolant. Regulation of the boron concentration affects reactivity uniformly throughout the core as the coolant circulates through the entire core. On the other hand, the control rods affect local reactivity and therefore, result in an asymmetry of the axial and radial power distribution within the core 16.

(5) Conditions within the core 16 are monitored by several different sensor systems. These systems include an excore detector system 28, which measures neutron flux escaping from the reactor 14. The excore detector system 28 includes source range detectors used when the reactor is shut down, intermediate range detectors used during startup and shutdown, and power range detectors used when the reactor is above approximately 5% power. Incore detectors are also typically employed during power operation; however, they are not relevant to this application.

(6) Estimated critical conditions (ECC) are typically required as part of any reactor startup evolution. ECC is a combination of control rod and primary system conditions (e.g., soluble boron concentration, coolant temperature) that are expected to yield a critical reactor state. It is valuable, from a reactivity management perspective, that the ECC closely match the actual critical conditions of the core (i.e., the true combination of control rod position and primary system conditions that yield a critical reactor state). Furthermore, Plant Technical Specifications include a limiting condition for operation (also referred to as LCO) that the core reactivity be measured within a specified amount of the predicted core reactivity. The associated surveillances are performed prior to commencing power operation (typically >5% rated thermal power) after each core refueling, and generally every month afterward.

(7) Various ECC combinations can be determined by nuclear design predictions prior to reactor core operation. However, a more accurate ECC projection can be obtained through ICRR monitoring and evaluation prior to reactor criticality, which can identify the presence of any global core reactivity bias. The global core reactivity bias is defined as the difference between the predicted reactivity state of the core and the actual reactivity state of the core determined by measurement. Subsequently, the bias can be incorporated into an updated ECC projection prior to reactor criticality.

(8) ICRR monitoring is a common practice during shutdown/startup conditions that requires a baseline measurement from a neutron detector (M.sub.R). Following a reactivity manipulation (e.g., control rod withdrawal) and achievement of a new steady state condition (state point), another measurement is collected (M.sub.i). The ratio of M.sub.R/M.sub.i is defined as the ICRR for state point i. As additional reactivity manipulations occur, ICRR can be updated and monitored in terms of changes from the reference measurement, and in turn, how the reactor is progressing towards (or away from) reactor criticality. If the intent is to startup the reactor (i.e., bring the reactor to a critical state), positive reactivity is added to the core (e.g., control rod withdrawal, primary system soluble boron dilution), and the ICRR is expected to approach zero.

(9) As described in U.S. Pat. No. 6,801,593, due to the physics of the reactions occurring within the reactor core, the ICRR is not linear unless the reactor is very close to criticality; control rod position changes as part of pre-critical testing and the approach to criticality have a significant impact on the shape of the ICRR curve. Therefore, U.S. Pat. No. 6,801,593 provided a means of linearizing the measured ICRR with changes in control rod position or core conditions.

(10) The method described in U.S. Pat. No. 6,801,593 relied on use of spatially-corrected ICRR (ICRR.sub.SC) as the measurement parameter, which is a function of neutron detector measurements (M.sub.R/M.sub.i), but is dependent on nuclear design by way of spatial correction factors (SCFs). U.S. Pat. No. 6,801,593 defined SCF as a function of the static spatial factor and predicted eigenvalues obtained from subcritical, static calculations with and without fixed neutron sources.

(11) Because ICRR.sub.SC is partly dependent on design prediction, use of ICRR.sub.SC as the primary measurement parameter is inherently subject to masking effects, where an error or bias in the design prediction can influence the measurement as well. Hence, it is desirable from a reactor physics measurement standpoint to eliminate predictive components from measurement results in order to eliminate the potential for masking effects. Therefore, the disclosed concept first defines a linear relationship between measured ICRR (a “pure” measurement, M.sub.R/M.sub.i, and with no predictive component) and predicted ICRR (a “pure” prediction, with no measurement component, but that accounts for any spatial effects that may have resulted from changes in plant configuration or core conditions between measurements M.sub.R and M.sub.i).

(12) After collecting multiple ICRR measurements, measured ICRR can be compared to the predicted ICRR at each state point. It is then possible to quantify a global reactivity bias by determining the uniform reactivity adjustment to the predicted ICRR at each state point that results in ideal behavior, which is defined as a linear fit and a y-intercept of zero when performing a linear fit of measured ICRR versus predicted ICRR. Fundamentally, the prediction is adjusted to match measurement and the adjustment is used to correct the predictions for future evolutions (e.g., final approach to criticality).

(13) Recognizing that (1/M) theory is practically represented by monitoring changes in the measured neutron detector response from a baseline or reference condition, Equation (1) is a relationship familiar to nuclear reactor operators.
M.sub.R*(1−k.sub.R)∝M.sub.i*(1−k.sub.i)  (1)

(14) wherein, M.sub.R and M.sub.i are neutron detector responses at the reference state point condition and a subsequent state point condition i, respectively, and k.sub.R and k.sub.i are the K.sub.eff values at the reference state point condition and a subsequent state point condition i, respectively.

(15) Re-arrangement of terms yields a new Equation (2).

(16) $\begin{array}{cc}\frac{M_R}{M_i}\propto \frac{1-k_i}{1-k_R}& \left(2\right)\end{array}$
In this form, the left side of the equation is now only the ratio of measured count rates (“raw”, or not-spatially corrected, measured ICRR, I.sub.M, i). The right side of the equation is comprised of core eigenvalues that can be predicted by nuclear design calculations (predicted ICRR, I.sub.P, i) that take into account spatial effects resulting from changes in control rod positions or primary system conditions at the time of measurement. This separation of measurement from prediction is desirable in order to eliminate the potential for masking effects. In simplified form:
I.sub.M,i∝I.sub.P,i  (3)

(17) The true regression of Equation (3) can be written as:
I.sub.M=β.sub.1*I.sub.P+β.sub.0  (4)
The resultant estimate of the true regression, Equation (5), can be used as a basis for core design validation prior to at-power operation of the plant; specifically, incremental and total measured changes in ICRR can be compared to design prediction while the reactor is shutdown. The results evaluation is not subject to masking effects, and measured-to-predicted agreement (within pre-defined tolerance limits) demonstrates that the core is behaving as designed.
Î.sub.M=m*I.sub.P+b  (5)
Ideally, the as-built measured core is identical to the as-designed predicted core, so that β.sub.1 equals one and β.sub.0 equals zero in Equation (4). However, in practice, this is not likely to be the case; some non-trivial differences will likely be present in the line fit of measured vs. predicted ICRR response. Regardless of the cause, it is especially useful to quantify systematic reactivity bias so that it can be used for criticality forecasting and monitoring purposes.

(18) Returning to Equation (2), redefining the reference neutron detector measurement as a normalization constant (C) and rearrangement of terms yields the following:

(19) $\begin{array}{cc}{M}_i\propto \left[C.Math.\frac{1-k_R}{1-k_i}\right]& \left(6\right)\end{array}$
Equation (6) can be simplified and presented as a true regression by combining the normalization constant and predictive terms into a predicted detector response at state point i (P.sub.i) that also accounts for spatial effects as explained previously:
M.sub.i=β.sub.1*P.sub.i+β.sub.0  (7)
To quantify the global bias, the set of neutron detector measurements will be fit versus their corresponding predicted values. The resultant estimate of the true regression is defined in Equation (8).
{circumflex over (M)}.sub.i=m*P.sub.i+b  (8)

(20) In an ideal situation, the y-intercept of the measured vs. predicted neutron detector response is zero. Assuming the regression estimate is linear and the data points are tightly fit, the global measured-to-predicted reactivity bias can be estimated by determining the amount of reactivity adjustment required to drive the y-intercept (b) to zero for the line fit defined in Equation (8). The uniform reactivity adjustment across all state points (imparted via changes in the P.sub.i values) that produces a line fit with a y-intercept (b) of zero is the estimated core reactivity bias.
{circumflex over (M)}.sub.i={acute over (m)}*{acute over (P)}.sub.i  (9)

(21) Accordingly, the disclosed concept utilizes a direct comparison of raw subcritical neutron flux measurements with corresponding predictions at each state point condition. This differs from prior power reactor physics testing methodologies, which require correction of the measurement data prior to results evaluation; the benefit of this method, in employing complete separation of measurements and predictions, is the prevention of masking effects (i.e., elimination of interdependency between measurement and prediction).

(22) Additionally, the disclosed concept utilizes regression statistics of raw neutron detector measurements to corresponding predictions, and quantitative measured-to-predicted criteria on such, to detect various core anomalies while the plant is in a subcritical condition and prior to the plant achieving criticality. The benefit of this approach is that it provides an added measure of safety since anomalous core conditions can be detected during hot standby testing and can be anticipated during the final approach to criticality.

(23) Furthermore, the disclosed concept utilizes a method of determining the reactivity bias between the predicted core and actual core by determining the uniform analytical reactivity adjustment (systematic global reactivity bias) required to reconcile the measured neutron flux data with predictions. This differs from previous power reactor physics test methodologies, for which the reactivity difference is determined based on measured reactivity at critical reactor conditions. The benefit of this approach is that it provides a way to identify anomalous reactivity indication/behavior in the subcritical state as a means of providing reactivity management guidance and/or accident prevention. Also, this method directly provides a reactivity bias offset on the predictive model used in the plant safety analysis.

(24) Application of this method requires neutron detector measurements and corresponding core condition predictions that are provided by existing core design codes and account for the subcritical neutron flux distribution. The basic uses of this method are to monitor and project the subcritical state of the core. Associated applications include monitoring of negative reactivity conditions or shutdown margin, and forecasting of estimated critical conditions prior to plant startup. The method amounts to Subcritical Physics Testing, which integrates the monitoring and forecasting function to ultimately execute a series of measured-to-predicted comparisons to confirm the as-built core is operating consistent with design following refueling; results that could only previously been achieved during low power testing after the reactor went critical.

(25) A key piece of information needed for the safe and efficient operation of a subcritical reactor core is the negative reactivity of the core; that is, the amount that the core is subcritical, also known as the shutdown margin. Prior to development of the methodology described herein, this information has only been inferred, and not directly measured.

(26) The basic uses of this method are to project and monitor the negative reactivity of a subcritical core for any static configuration of interest, i.e., a steady-state combination of control rod position and primary system conditions, through the use of neutron detector signal measurements and advanced subcritical core predictions. A series of subcritical measured-to-predicted comparisons during plant startup forms the basis for the integrated application of this methodology, i.e., the measured-to-predicted comparisons are performed at a number of steady-state subcritical conditions, each of which is referred to as a state point.

(27) This method is performed at static and subcritical conditions (vs. the dynamic and critical conditions for traditional low power physics testing). This method is revolutionary in that it is not just an extension of the steps performed during low power physics testing. However, this method achieves the same objective as low power physics testing; following refueling and prior to returning to normal operation, testing is performed to determine if the operating characteristics of the core are consistent with design predictions as a means to ensure the core can be operated as designed.

(28) While achieving the same objective as low power physics testing, performing this method yields inherent safety, human performance, and test performance benefits over low power physics testing. Performing measurements at static and subcritical conditions inherently enhances plant safety and reactivity management. This method is seamlessly integrated into routine plant startup activities as opposed to necessitating infrequently performed tests and evolutions and special test exceptions to plant operations, which improves test reliability and human performance. Therefore, this method-based core design verification offers broad benefits for essentially any plant type.

(29) It is to be appreciated that methods as described herein can be carried out by a processor or processing device of a computer system or by other means of carrying out the function. Thus, a processor with the necessary instructions programmed directly therein or on a machine readable medium accessed thereby for carrying out such a method or element of a method forms a means for carrying out the method or element of a method. Furthermore, an element described herein of an apparatus embodiment is an example of a means for carrying out the function performed by the element for the purpose of carrying out the invention.

(30) While specific embodiments of the disclosed concept have been described in detail, it will be appreciated by those skilled in the art that various modifications and alternatives to those details could be developed in light of the overall teachings of the disclosure. Accordingly, the particular embodiments disclosed are meant to be illustrative only and not limiting as to the scope of the disclosed concept which is to be given the full breadth of the appended claims and any and all equivalents thereof.