Method and system for direct evaluation of operating limit minimum critical power ratios for boiling water reactors

A system for determining an operating limit minimum critical power ratio (OLMCPR) of a boiling water reactor (BWR), said system comprising a computer including a storage memory and I/O devices, said memory having stored therein rules for simultaneously simulating and evaluating thermal operating characteristics for a plurality of fuel rods during an anticipated operational occurrence of the reactor and a data base of one or more parametric quantities representing reactor plant operational state values and/or fuel rod modeling parameters, said computer programmed to:

• (i) simulate an anticipated operational occurrence for the reactor;
• (ii) determine a minimum critical power ratio (MCPR) for each individual fuel rod simulated;
• (iii) calculate a probability distribution P(MCPR) of potential MCPR values for each MCPR value;
• (iv) calculate a value for a number of fuel rods subject to boiling transition (NRSBT) by summing portions of probability distributions corresponding to values for MCPR where MCPR<1.0 for all rods simulated, then repetitively calculate further values for NRSBT after perturbing one or more of said parametric quantities for a predetermined number of different perturbations;
• (v) develop a histogram of calculated NRSBT values over all perturbations;
• and
• (vi) select the OLMCPR from a minimal MCPR such that, for a simulation of the most limiting operational event, the nominal NRSBT value at a prescribed level of confidence as determined from analysis of the histogram determined from step (v) remains less than a predetermined cutoff value.

A method for evaluating the operating limit minimum critical power ratio (OLMCPR) of a boiling water reactor (BWR), comprising the steps, executed by a computer, of:

• a) setting a minimum critical power ratio (MCPR) for each of a plurality of individual nuclear fuel rods used in the reactor;
• b) calculating a value for a total number of fuel rods subject to boiling transition (NRSBT);
• c) perturbing one or more reactor plant state value and/or fuel rod modeling parameter and recalculating a value for NRSBT;
• d) performing step (c) for a predetermined number of perturbations;
• e) developing a histogram of NRSBT values determined in steps (b), (c) and (d);
• and
• f) selecting the OLMCPR from a minimal MCPR such that, for a simulation of the most limiting operational event, the nominal NRSBT value at a prescribed level of confidence as determined from analysis of the histogram determined from step (v) remains less than a predetermined cutoff value.

For a nuclear fuel core of a Boiling Water Reactor, wherein fuel design and/or core configuration are contingent upon an operating margin for the reactor, said operating margin being determined by a process for evaluating an operating limit minimum critical power ratio (OLMCPR), an improved process for evaluating an OLMCPR and operating a Boiling Water Reactor which results in an improved operating margin for the reactor, comprising the steps of:

• a) developing in a memory of a computer system a histogram of NRSBT (number of fuel rods subject to boiling transition) values, corresponding to a plurality of computer simulations of a transient operational occurrence in a reactor, said simulations providing values for a critical power ratio (CPR) for one or more fuel rods for a multiple of different parametric quantities for said reactor;
• b) selecting a nominal NRSBT value, based on a central tendency of NRSBT distribution, statistically determined by said computer system from the histogram of NRSBT values developed in step (a);
• c) selecting a confidence interval for the nominal NRSBT value;
• d) selecting an OLMCPR value from a minimal CPR such that during a simulation of a limiting transient operational occurrence the nominal NRSBT value remains less than a predetermined cutoff value;
• and
• e) effecting said Boiling Water Reactor operation by applying the OLMCPR selected in step (d) as an operational control parameter.

For a nuclear fuel core of a Boiling Water Reactor, wherein fuel rod design and/or core configuration are contingent upon an operating margin for the reactor, said operating margin being determined by a process for evaluating an operating limit minimum critical power ratio (OLMCPR), a improved process for evaluating an OLMCPR and operating a Boiling Water Reactor that results in an increased operating margin for the reactor, comprising the steps, executed by a computer, of:

• a) developing in a memory of said computer a histogram of NRSBT (number of fuel rods subject to boiling transition) values, corresponding to a plurality of computer simulations of a transient operational occurrence in a reactor, said simulations providing values for a critical power ratio (CPR) for one or more fuel rods for a multiple of different parametric quantities for said reactor;
• b) calculating a nominal NRSBT value, based on a central tendency of an NRSBT distribution, from the histogram of NRSBT values obtained in step (a);
• c) selecting a confidence interval for the nominal NRSBT value;
• d) selecting an OLMCPR for the reactor as the initial minimal MCPR such that during a simulation of a transient the nominal NRSBT value remains less than a predetermined cutoff value;
• and
• e) effecting Boiling Water Reactor operation by applying the OLMCPR selected in step (d) as an operational control parameter.

A method for statistically demonstrating an operating limit minimum critical power ratio (OLMCPR) of a boiling water reactor (BWR) for compliance with licensing requirements, said reactor characterized by one or more parametric quantities indicative of design constraints and operating conditions, comprising the steps of:

• a) programming a computer to determine an OLMCPR value for a boiling water reactor, said computer programmed at least to:
• i) develop a histogram of NRSBT (number of fuel rods subject to boiling transition) values, corresponding to a plurality of simulations of a transient operational occurrence in a reactor, said simulations providing values for a critical power ratio (CPR) for one or more fuel rods over a multiple of randomly selected variations in the parametric quantities for said reactor;
• ii) calculate a nominal NRSBT value from the histogram of NRSBT values;
• and
• iii) select an OLMCPR for the reactor corresponding to a minimal MCPR such that during a simulation of a transient the nominal NRSBT value remains less than a predetermined cutoff value;
• and
• b) providing said OLMPCR value to an output device for display, recordation or storage.

For use in controlling a Boiling Water Reactor having a nuclear fueled core characterized by an operating limit minimum critical power ratio (OLMCPR) value, a method for determining said OLMCPR value comprising the steps of:

• a) using a computer to simulate transient operational occurrences which might occur during the operation of a Boiling Water Reactor;
• developing a histogram of NRSBT values from a computer simulation of a transient operational occurrence in a Boiling Water Reactor, the simulation providing values for a critical power ratio (CPR) for one or more fuel rods;
• c) determining a nominal NRSBT value, based on a central tendency of an NRSBT distribution, from the histogram of NRSBT values obtained in step (a);
• d) selecting a confidence interval for the nominal NRSBT value;
• and
• e) selecting an OLMCPR for the reactor as the initial minimal MCPR such that during a simulation of a transient the nominal NRSBT value remains less than a predetermined cutoff value.