Patent Number: 059129336
Section: description

BEST MODE FOR CARRYING OUT THE INVENTION 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. 1 shows a block diagram of an example data processing system, 100, 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, system 100 includes CPU 101, storage memory 102, and user interfacing I/O devices 103 and optionally one or more displays 104. Storage memory 102 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. In another aspect of present invention, a method of more accurately determining the OLMCPR of a BWR and for developing more efficient core designs and reactor operational procedures is provided by performing a direct evaluation of the OLMCPR during the simulation of postulated BWR operational events. In addition, the use of multi-dimensional modeling/simulation of BWR core thermal hydraulics for operational analysis in accordance with the method of the present invention results in a substantial benefit in terms of "margin" improvement in determining the operating limit minimum critical power ratio (OLMCPR). This improved method is described in greater detail below with reference to FIGS. 2 through 4. In accordance with thc present invention, the critical power ratio (CPR) is first calculated for all rods in all fuel channels in the reactor core using multi-dimensional modeling for the simulation and evaluation of postulated operational events (e.g., AOO transient events or some other anticipated event where the CPR values are expected to change). The multi-dimensional modeling consist of a multi-dimensional calculation of the power distribution and the thermal hydraulic conditions in the reactor core which enable the simultaneous calculation of the CPR for all fuel rods in all fuel channels in the reactor core. For the purposes of simplifying reactor modeling/simulation, fuel rods with similar characteristics may be combined to form a rod group, and fuel channels with similar characteristics may be combined to form a fuel channel group. An example of the effect of a CPR transient for different fuel rod groups or from different channel groups is illustrated in FIG. 2. In an initial phase, the CPR is determined explicitly for all rods (or rod groups) at all times during a transient. Then upon examining the CPR transient responses for the fuel rods, the minimum nominal value of the critical power ratio (MCPR) is determined for each fuel rod. There are inherent uncertainties associated with these nominal values due to uncertainties in the modeling methods, correlations and inputs and the uncertainty in the reactor plant state. The probability distributions for the calculated MCPR values are not assumed in advance since they are determined by how the CPR calculated values change as a result of changes in the inputs. Typically the resulting probability distributions are expected to approximate a normal distribution due to the random nature of competing effects; however, the present invention is not restricted to situations where the rod MCPR distributions are normal. An example is shown in FIG. 3 where the probability distribution associated with the CPR for a few fuel rods, R.sub.1 -R.sub.4, are illustrated. For any rod (i), the probability of the rod operating within the range of boiling transition, P.sub.i, can be calculated by the integral of the probability distribution function of the rod for CPR values that fall below unity--i.e., the area under the CPR probability distribution function P(CPR) of each rod in FIG. 3 for values of CPR that are less than unity. This is illustrated by shaded area 300 for the P(CPR) curve of rod R.sub.1 (which exhibits the lowest CPR of those depicted). By summing over all the probabilities for all rods, the total probable number of fuel rods susceptible to operating in the range of boiling transition can be determined. This summation of probabilities is represented by the following equation: ##EQU1## where, P.sub.i is the probability of rod i being in the thermal range of boiling transition; and NRSBT is the probability for the total number of fuel rods subject to operating in the range of boiling transition. The rod CPR probability distributions P(CPR) in these illustrations are intended to include uncertainties such as those attributed to the CPR correlation, the data used to develop the CPR correlation, and uncertainties in the calculations that implement the correlation. Such uncertainties include uncertainties associated with the particular thermal modeling methods used to evaluate the operational event (such as uncertainties associated with the proposed multi-dimensional modeling approach) and with uncertainties in knowing the exact state of the BWR. Consequently, the sensitivity of NRSBT value to a particular thermal modeling method and/or reactor plant state uncertainties is better evaluated by "perturbing" both plant state and modeling method parameters and then recalculating the resultant NRSBT. After performing a sufficiently large number of such perturbation calculations a NRSBT histogram for the transient is compiled. An example of such an NRSBT histogram is illustrated in FIG. 4. Next, the number of rods susceptible to boiling transition at a given confidence level is statistically determined from mean and variance values that are obtained and calculated from the NSRBT histogram. The OLMCPR is then determined as the steady state initial minimum critical power ratio for all the fuel rods such that, in the event of a postulated worst case operational event, the calculated number of fuel rods susceptible to boiling transition is less than a predetermined value at a specified confidence level. For example, a contemporary USNRC regulations requirement for licensing of BWRs is the ability to demonstrate (with 50% confidence) that no more than 0.1% of the rods will be susceptible to boiling transition during the limiting AOO transient. Referring now to FIGS. 5A and 5B, a flow chart is depicted that illustrates the steps of the method of the present invention for determining an operating limit minimum critical power ratio (OLMCPR) so as to effectuate an improved core design. First, a potentially limiting postulated operational event is defined for evaluation (block 501). Next, the particular system "input" quantities that are ultimately to be perturbed are selected and/or defined (block 502). A direct evaluation of the OLMCPR for the postulated operational event in a BWR core is then preferably performed by a data processing system in accordance with the process steps shown within dashed-line box 500. The presently preferred embodiment for effectuating a direct evaluation of the OLMCPR, contemplated as being executed by data processing system 100, is now discussed in detail with reference to the computer implemented process steps shown within dashed box 500 in FIGS. 5A and 5B. Initially, as indicated at block 503, all (input) quantities are set to nominal values to establish a reference calculation during a first pass through the iterative part of the process. All other values needed to define the initial conditions for the transient are determined by a multi-dimensional steady-state simulation/calculation that is performed for each set of conditions (block 504). These conditions may be either the nominal reference conditions from step 503 or perturbed conditions from a subsequent iteration (such as established in block 510 described below). Next, a postulated operational event is simulated using a multi-dimensional model. Individual fuel rods or fuel rod groups from each fuel bundle or fuel bundle group in the core are simulated for the postulated operational event to determine the thermal operating characteristics of the fuel rods during the transient and calculate a profile of the CPR for each fuel rod as a function of time (block 505). CPR data for each rod is then stored, analyzed and the minimum CPR (MCPR) for each rod or group is selected from the transient simulation data (block 506). At this point, a probability distribution taking into account simulation uncertainties is determined using conventional techniques for each MCPR value corresponding to each rod or rod group (block 507). Next, the probability of the rod operating within the range of boiling transition, P.sub.i, is calculated from an integration of the probability distribution function for each rod for MCPR values that fall below unity and a value for the NRSBT is calculated in accordance with Equation (1) by summing CPR probability distributions for all rods where MCPR is less than 1.0 (block 508). Following this step, perturbations are introduced into the input values for the reactor plant initial state and the parameters for multi-dimensional simulation of the core (block 510). The NRSBT is then recalculated (blocks 504 through 508). The steps at blocks 504 through 510 are repeated for a predetermined number of perturbations (block 509) and the NRSBT values and other relevant values for all the transient simulations are recorded. After all perturbations have been completed a histogram of the recorded NRSBT values is compiled using results from all iterations (block 511). The nominal value for NRSBT is then calculated from the NRSBT histogram using a predetermined statistic measure that quantifies the central tendency of the NRSBT histogram (block 512). Next, a confidence interval for this nominal NRSBT value is calculated (block 513). Finally, the OLMCPR is selected as the minimal initial MCPR value such that the nominal NRSBT value is less than a prescribed cutoff value with a specified level of confidence--corresponding, for example, to the USNRC requisite 0.1% minimum at 50% confidence (block 514). The above processes may then be repeated for all known potentially limiting postulated operational events (block 515) and the OLMCPR ultimately used will be the maximum one of all transients evaluated (block 516). In other words the "limiting" histogram will provide the OLMCPR. While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.