Patent Number: 
Section: description

A practical method for determining the operating limit minimum critical power ratio (OLMCPR) of a Boiling Water Reactor (BWR) nuclear core is disclosed here. This practical improvement results in the realization of greater operating margins for the core which in turn results in more efficient and cost effective core operation and/or configurations. This is a more direct approach towards demonstrating compliance of a nuclear reactor with USNRC licensing requirements than processes conventionally used for such purposes. A data processing system is disclosed including a computer having memory and various I/O or display devices that is specifically programmed for providing simulation of transient operational events in a BWR and for a subsequent compilation and display of one or more response histogram(s) that incorporate all the inherent xe2x80x9cuncertaintiesxe2x80x9d associated with reactor plant initial state conditions and other parameter(s) of interest or importance. A method is used to calculate a generic bias in change in critical power ratio during a transient event (xcex94CPR/ICPR) and uses the resulting Probability Distribution Function (PDF) to predict a more accurate OLMCPR without first calculating a SLMCPR. From a large number of experimental trials that take many factors into account, a PDF for the transient xcex94CPR/ICPR is created and the standard deviation in xcex94CPR/ICPR is determined for each transient event. A nominal xcex94CPR/ICPR for the transient event starting from nominal initial conditions is also determined. Histograms of individual rod CPR values for the minimum point in the transient are created by drawing random values of initial CPR and transient xcex94CPR/ICPR uncertainty. The initial critical power ratios (ICPR) are converted, or translated, to MCPRs by a common random value of xcex94CPR/ICPR. From the MCPR values, the percentage of NRSBT is calculated for each trial. If the percentage of NRSBT is greater than 0.1%, initial operating conditions are changed and the process is repeated until the NRSBT is equal to 0.1%. The NRSBT distribution histogram is analyzed using statistical methods to determine the xe2x80x9ccentral tendencyxe2x80x9d of the distribution. Typically the mean or median is used as a statistic to quantify central tendency. The value of this statistic is defined here as the nominal value. In the discussions that follow, examples are given where the mean value is chosen as the nominal value although the present invention is not limited to this choice. Use of the median value or the value of some other statistic for central tendency as the nominal value is also contemplated as part of the present invention. The uncertainty in the nominal value of the statistic that is used to quantify central tendency is expressed in terms of a xe2x80x9cconfidence intervalxe2x80x9d for the nominal value. A confidence interval is defined such that there is a specified probability (usually of 50% or greater) that the interval contains the nominal value. For example, a 95% probability that the interval bounds the mean, defines a 95% confidence interval for the mean. The specified probability used to establish this confidence interval is called the xe2x80x9clevel of confidencexe2x80x9d or confidence level. The susceptibility to boiling transition during the transient is quantified statistically as either (1) the probability that a single rod in the core is susceptible to boiling transition or (2) the expected fraction of total rods in the core susceptible to boiling transition. Such a statistical relationship is possible because each individual trial value of NRSBT has been determined by summing the probabilities that individual fuel rods have CPR values less than 1.0 during the transient. The nominal value for each NRSBT distribution can also by the present invention be associated with the distribution of initial rod CPR values for all fuel rods in the core. It is by this process that a relationship can be established between the minimal initial MCPR value for all fuel rods in the core and the probability and confidence level that the fuel rods will be susceptible to boiling transition during the transient. The minimal initial MCPR value for the core when determined in this way using the probability and confidence level established by the USNRC design basis requirement for the number of rods not susceptible to boiling transition during the AOO transient, is by definition, the minimum Operating Limit MCPR required to demonstrate compliance. In accordance with one aspect, the present invention is a system including a data processing apparatus programmed to execute specific routines for simulating BWR core operating conditions and for calculating and statistically demonstrating the OLMCPR of a reactor in accordance with the improved method of the present invention as described in detail below. FIG. 8 shows a block diagram of an example data processing system, contemplated for performing the multi-dimensional simulation of reactor core transient response and for the direct evaluation of OLMCPR for a BWR reactor core in accordance with the present invention. Essentially, the system includes a central processing unit 801 (CPU), a storage memory 802, and a user interfacing I/O devices 803 and, optionally, one or more displays 804. Storage memory 802 includes a data base (not shown) of reactor plant state information, parameter values and routines for implementing multi-dimensional simulations of core operating conditions and evaluating OLMCPR in accordance with the improved method of the present invention as described herein below. A statistical study will be performed for each type of AOO, for each class of BWR plant type, and for each fuel type to determine the generic transient bias and uncertainty in the xcex94CPR/ICPR. Enough trials (on the order of one hundred) are made starting with the nominal conditions, using random variations in the model and plant parameters. Uncertainties in initial conditions that contribute to the xcex94CPR/ICPR (e.g., core power) are also included in the perturbations. The data are utilized to determine bias and standard deviation on the transient xcex94CPR/ICPR. A flow chart for the process of the present invention is shown in FIG. 9. Block 909 remains unvaried throughout the calculation of the OLMCPR, and the xcex94CPR/ICPR for individual transient events for each reactor type and fuel type must be determined before the process is used. FIG. 10 shows the resulting graph of xcex94CPR/ICPR for one specific type of AOO. Histogram 1000 shows the number of trials 1002 with a resulting CPR 1001 for each rod versus the corresponding CPR 1001 values. The PDF 1003 represents the distribution of CPR before the transient event. Each CPR value then changes according to individual xcex94CPR/ICPR 1006 values. The aggregate of the transient CPR values yields the PDF 1004 during the transient event. The nominal xcex94CPR/ICPR 1005 is defined to be the difference in the nominal CPR value of the PDF 1003 and the nominal CPR value of the PDF 1004. The calculation of the OLMCPR is as follows. Step 1: Assume a set of base core operating conditions using the parameters to run the plant generates a core MCPR equal to the OLMCPR as shown by block 901. Step 2: Using the parameters, such as core power, core flow, core pressure, bundle power and others, that predict a general bundle CPR set forth in block 907, determine the ICPR for each bundle in the core, as shown by block 902. Step 3: Using parameters, such as rod placement within each bundle and rod power distribution, that change each bundle CPR into individual rod CPR values set forth in block 908, determine the ICPR for each rod in the core, as shown by block 903. Step 4: Using a randomly drawn individual xcex94CPR/ICPR 1006 value from the graph of the appropriate transient represented in FIG. 10, MCPR values are projected for corresponding values of ICPR according to Equation 4. In FIG. 11, this process is represented by Shift 1109. Histogram 1100 shows the number of rods at a specific CPR value 1102 versus the corresponding CPR value 1101. The histogram 1107 is translated to histogram 1108 during the transient using a randomly selected xcex94CPR/ICPR 1006 value. Lowest CPR value 1105 becomes lowest CPR value 1106, and lowest CPR rod PDF 1103 becomes lowest CPR rod 1104.                               MCPR          i                =                              ICPR            i                    ⁡                      (                          1              -                                                (                                                            Δ                      ⁢                                              xe2x80x83                                            ⁢                      C                      ⁢                                              xe2x80x83                                            ⁢                      P                      ⁢                                              xe2x80x83                                            ⁢                      R                                                              I                      ⁢                                              xe2x80x83                                            ⁢                      C                      ⁢                                              xe2x80x83                                            ⁢                      P                      ⁢                                              xe2x80x83                                            ⁢                      R                                                        )                                1                                      )                                              (                  Equation          ⁢                      xe2x80x83                    ⁢          4                )             Step 5: Using the ECPR probability distribution shown as PDF 1104 and set forth in block 910, determine the percentage of NRSBT in the core by summing the probabilities of each rod in the core that is subject to boiling transition as shown by block 905. This summation is performed using Equation 3, shown above. Step 6: Vary the parameters set forth in blocks 907 and 908 for a set number of Monte Carlo statistical trials as shown by block 906. Compile the statistics from all the trials from steps 2 through 5 to generate a probability distribution of NRSBT. Step 7: Compare the value of percentage of NRSBT to 0.1% as shown in block 911. If the percentage is greater than 0.1%, reset the core parameters to different initial conditions in order to comply with the USNRC regulations as shown in block 912. Similar to Step 1 and block 901, the new initial conditions are assumed to generate the OLMCPR. The determination of NRSBT restarts and runs until the value of NRSBT is equal to 0.1%. Similarly, if the percentage is less than 0.1%, the core parameters are reset to increase the value of NRSBT in order to operate the core more efficiently or to reduce effluents. Step 8: If the percentage of NRSBT equals 0.1%, the assumed value of OLMCPR, which equals core MCPR, complies with the USNRC regulations as shown by block 913. Accordingly, the operating core conditions are set as the assumed parameters. Two assumptions are made for the above estimation of OLMCPR. First, in performing step 4, shown in FIG. 11 as shift 1109 and in FIG. 9 as block 904, the inventors assume that random draws from the xcex94CPR/ICPR distribution are permissible for a perturbation in the initial conditions. Therefore, variations in xcex94CPR/ICPR must be independent of perturbations in initial conditions or have a negative correlation, so that the interaction tends to diminish the individual effects. Second, in performing step 4, the inventors assume that the transient change in the xcex94CPR/ICPR applies to all rods. A demonstration analysis shows that the xcex94CPR/ICPR is not sensitive to the uncertainty in core power, core flow, core pressure, feedwater temperature, and rod peaking factor (R-factor). Of these, one of the most important parameters in the currently approved process is core power. This parameter actually results in an effect opposite the effect on ICPR. If the power increases, the ICPR will decrease but the xcex94CPR/ICPR will also decrease. This will result in an MCPR that would be higher than derived through the currently approved process. Another conservative factor is the intended use of the nominal xcex94CPR/ICPR. If the core was adjusting to a limiting rod pattern to maximize the number of contributing bundles, as is done for the currently approved process, the xcex94CPR/ICPR is 4% lower. Table 1 shows the impact of uncertainty in critical ICPR values on xcex94CPR/ICPR values. Column 101 lists the critical parameter quantities that affect the xcex94CPR/ICPR. Column 102 lists the percentage uncertainty of each parameter corresponding to the standard deviation of the associated PDF. "sgr" is the standard deviation of the PDF corresponding to the uncertainty in parameter quantity. Column 103 lists the change in the xcex94CPR/ICPR corresponding to a change of one standard deviation of each parameter. The xcex94CPR/ICPR is not sensitive to the other unknown parameter in the currently approved process. The axial power distribution is also part of the local power distribution (TIP uncertainty) calculation in the currently approved process. For a very large change in axial power shape (nearly two times higher power in the bottom of the bundle), the sensitivity to xcex94CPR/ICPR is less than 2%, which is insignificant. The other assumption to be validated is that a constant value of xcex94CPR/ICPR can be applied to rods at different ICPR values. As described above, the transient MCPR distribution will be obtained by transforming the ICPR distribution using Equation 4. To further validate this assumption, a specific set of calculations were performed. Benchmark calculations were made for a transient event that included the uncertainties in core power and channel pressure drop as initial conditions, as well as uncertainties in the model. Core power and channel pressure drop uncertainties were chosen, because they are the only currently approved process compatible uncertainties that are also varied in generating the generic uncertainty probability distribution function. MCPR distributions during the transient were generated for two fuel bundles in the core through ninety-eight transient calculations. The two bundles are very close in ICPR values and have identical xcex94CPR/ICPR values. To verify the translation process, ninety-eight Monte Carlo calculations were then performed where only the core power and pressure drop were varied to generate a PDF of ICPRs at the initial operating state. FIG. 12 shows histogram 1200, which is the number of rods 1202 at a certain CPR versus the corresponding CPR 1201 value. PDF 1203 is the ICPR distribution that was created using the Monte Carlo calculations varying core power and pressure drop. PDF 1205 is the corresponding transient MCPR distribution after the process of the invention transformation was applied. PDF 1204 is the reference ICPR distribution. PDF 1206 is the transient MCPR distribution when applying the currently approved process. PDF 1205 and PDF 1206 are very similar in both the most probably value of MCPR and the associated standard deviation of each distribution. Since there is a strong resemblance between the two resulting MCPR distributions, the transformation using the process of the invention is valid. It has been demonstrated that: (1) the xcex94CPR/ICPR is independent relative to the uncertainties that affect the ICPR, or the covariance is such that it is conservative to assume independence and (2) the transient MCPR distribution can be determined by applying the transient xcex94CPR/ICPR uncertainty to the rod ICPR distribution using the proposed approach. An example of the process of the invention is described by FIG. 13. In FIG. 13, histogram 1300 shows the number of rods 1302 of a certain CPR value versus the corresponding CPR value 1301. The PDF 1303 shows the resulting ICPR values from a set of approximately ninety-eight ICPR trials with all uncertainties applied. Ninety-eight new trials were run to generate a xcex94CPR/ICPR distribution for the specific transient event in order to translate the ICPR values to MCPR values. This xcex94CPR/ICPR distribution is not shown in FIG. 13. The xcex94CPR/ICPR distribution was applied using the process of the invention to the ICPR PDF 1303 to obtain the MCPR PDF 1304. The NRSBT was determined using the process of the invention, and the OLMCPR was determined to be 1.26. As a comparison, using the currently approved process, the SLMCPR was determined to be 1.10. Thus, the process described herein is more conservative than the first stage of the currently approved process. Ultimately, however, the currently approved process generates a unnecessarily conservative value after the error factor is added to the SLMCPR value, which yields a OLMCPR value needlessly larger than the process of the invention. Although the improved methods, as described herein below, are preferably implemented using a high speed data processing system capable of processing simulation routines that require highly accurate calculations and multiple reiterations, the present invention is not intended as limited to any one particular type of computer or data processing system. Any generic data processing system having sufficient, speed, storage memory and programmable computational capabilities for implementing statistical data analysis/reduction may be utilized to implement the present invention.