Method for assisting in reaching a divergent state in a nuclear reactor

Abstract

The present disclosure relates to a method (100) for assisting in reaching a divergent state of a nuclear reactor (2), comprising steps of: - receiving (101) input data comprising a duration of stoppage of the reactor or a variation in a reactivity of the reactor with a previously measured initial boron concentration (CB0) in the reactor, a maximum boron concentration (CBDIV) in the reactor, a first parameter (Δρbars) representative of an effectiveness with which neutron-absorbing bars absorb neutrons and a second parameter (ε) representative of an effectiveness with which boron absorbs neutrons in the reactor, - based on the input data, generating (102) output data comprising flow rates (QREA) of dilution of the boron in the reactor to be applied in succession, and values of a third parameter (ITC) representative of a reactivity of the reactor, - causing the display of the output data by a display screen.

Description

[0001] DESCRIPTION

[0002] TITLE: Method for assisting in achieving a divergent state in a nuclear reactor

[0003] TECHNICAL FIELD

[0004] This disclosure relates to methods for assisting in the control of a nuclear reactor, as well as corresponding methods for controlling the reactor. More specifically, it aims to provide assistance during the start-up phase of a nuclear reactor, during which the reactor is brought from a subcritical state to a divergent state.

[0005] STATE OF THE ART

[0006] A nuclear unit is an electricity production unit comprising a nuclear reactor, a current-generating turbine, circuits supplying the current-generating turbine, and a control system enabling an operator to control electricity production.

[0007] As part of the fight against CO2 emissions, renewable energies are increasingly integrated into the electricity grid. By their very nature, they are linked to weather conditions, and therefore intermittent and fluctuating. The electricity grid is vast and interconnected, and the electrical frequency is controlled to provide a high-quality current. It therefore cannot absorb overly disparate and unpredictable sources of production. Nuclear power, which can be controlled, is thus used to complement renewable energies to ensure overall stability in electricity production, in line with consumption.Historically conceived as a means of baseload power generation, the control of nuclear reactors is therefore heavily impacted, as the operation of these reactors must adapt to increasingly shorter and more frequent time windows than in previous practice, in order to meet the growing number of power variation requests. Controlling a nuclear reactor requires knowing the current state of the reactor in order to reach a predetermined or desired operating point using the control tools available to the operator.

[0008] However, the physical phenomena occurring within a nuclear reactor are highly complex, requiring the application of multiple branches of physics, including nuclear physics, neutronics (e.g., the laws governing neutron populations), thermohydraulics (e.g., fluid mechanics and heat transfer), thermodynamics, and thermomechanics (the effects of stress on materials subjected to heat). These sciences are applied here to the core of nuclear reactors. As we can see, the phenomena that occur are diverse in nature and interact with one another.

[0009] Thus, for example, fission (nuclear physics) occurs through the interaction of a heavy nucleus with neutrons (neutronics). This fission produces heat that propagates through matter (thermal), which in turn transfers this heat to water, which carries it (thermohydraulics). Neutronics is the central branch here because it governs the generation of the aforementioned phenomena. It allows for the characterization of the neutron population, distributed spatially and temporally according to an energy spectrum that depends on the interaction with matter. These interactions include absorption (fissile, fertile, and sterile), scattering, reflection, and neutron leakage. A kinetic component must also be considered, related to the actual production of neutrons by fission, which is divided into prompt and delayed neutrons.These latter, which are in the minority and appear several seconds after prompt neutrons, are essential for enabling the control of a nuclear reactor.

[0010] The concepts of reactivity and criticality (measured using the effective multiplication coefficient Keff) of a nuclear reactor core are closely linked: a nuclear core is considered critical when the chain reaction is stabilized. In this case, one fission generates, on average, one other fission—no more, no less. If the number of fissions generated is less than 1, the core is said to be "subcritical." Conversely, a core in which one fission generates, on average, more than one fission is said to be "supercritical." The reactivity of a core, on the other hand, characterizes the deviation of the core's state from criticality. If the core is critical, the reactivity will be 0 (and the Keff ≥ 1). In the case of a subcritical core (Keff < 1), the reactivity will be negative, and vice versa. Various elements will have an impact on criticality and therefore reduce reactivity, including the presence in the core of certain species, including boron and control clusters.Other factors, on the contrary, will increase reactivity, such as a decrease in the moderator temperature in pressurized water reactors.

[0011] Starting up a nuclear reactor involves a so-called subcritical approach stage, during which an operator brings the core from a highly subcritical state to divergence, i.e. a slightly supercritical state of the core.

[0012] During the subcritical approach, the operator can modify the core criticality by manipulating several factors, including:

[0013] - a quantity of neutrophil control rods (or "clusters") inserted into the reactor, and

[0014] - the amount of boron present in the reactor.

[0015] More specifically, the operator can increase the reactivity of the core by decreasing the number of neutrophil rods inserted, and / or by diluting the boron present in the reactor.

[0016] During a subcritical approach that proceeds normally, the operator successively and progressively removes the neutrophil bars and boric acid in three phases:

[0017] 1. Removal of a large part of the neutrophil control bars,

[0018] 2. dilution of boric acid according to several successive decreasing flow rates, 3. extraction of the remaining control rods until divergence of the reactor is observed.

[0019] One challenge facing the operator is to carefully balance the use of the two reactor reactivity control methods. Indeed, the equilibrium between them must be maintained to avoid the need for substantial modifications to either control method immediately after criticality is reached. Furthermore, poor management of this balance can lead to a failure of core divergence or delay the point at which divergence is achieved. Finally, it is essential to precisely control the number of control rods inserted and the amount of boron in the reactor to prevent an increase in reactivity and, consequently, a divergence that deviates excessively from the criticality point, thus failing to meet applicable safety requirements.

[0020] EXPOSED

[0021] It is therefore necessary to allow an operator to perform a faster subcritical approach to a nuclear unit while preventing excessive divergence of the unit.

[0022] To this end, a method is proposed to assist in achieving a divergent state of a nuclear reactor, the method being implemented by computer and comprising the following steps:

[0023] - receive input data including:

[0024] o a duration of nuclear reactor shutdown since the moment the nuclear reactor last underwent a shutdown, or a change in nuclear reactor reactivity with boron concentration in the nuclear reactor measured over a period ending with the moment the nuclear reactor reached a divergent state,

[0025] o an initial boron concentration measured in the nuclear reactor,

[0026] o a maximum boron concentration at which, for a predefined position of neutrophil control rods in the nuclear reactor, the nuclear reactor is in a divergent state, o a first parameter representing the efficiency of the neutrophil control rods in absorbing neutrons in the nuclear reactor, o a second parameter representing the efficiency of boron in absorbing neutrons in the nuclear reactor,

[0027] - From the input data, generate output data including:

[0028] o a plurality of values ​​for the boron dilution rate in the reactor to be applied successively, and

[0029] o a plurality of values ​​for a third parameter representing the reactivity of the nuclear reactor, each value of the third parameter being associated with a value among the plurality of values ​​for the boron dilution rate,

[0030] - cause the output data to be displayed on a display screen.

[0031] Thus, the proposed method for assisting boron dilution takes into account the neutron properties in the reactor core after fuel refueling, as well as the boron concentration before dilution. This allows for counting rate index and dilution flow rate values ​​such that divergence is reached more quickly, while respecting the safety constraints imposed on the operator due to the dilution being carried out in a plurality of successive stages at several dilution flow rates.

[0032] According to some embodiments, the input data further include a safety time, and the reactor is unsuitable for reaching the divergent state when the boron dilution rate remains equal, for a period less than or equal to the safety time, to a value chosen from the plurality of boron dilution rate values.

[0033] According to some embodiments, the input data further include a first boron dilution flow rate value equal to a maximum permitted boron dilution flow rate value for the nuclear reactor.

[0034] According to some embodiments, the output data generation is further performed such that, for any generated boron dilution flow rate, the nuclear reactor is unable to reach the divergent state without a change in the position of the control rods. This disclosure relates, in another aspect, to a method for controlling a nuclear reactor to reach a divergent state, the reactor comprising a set of control rods, the method comprising the steps of:

[0035] a. Removal from the reactor of part of the control rod assembly for the neutralization process,

[0036] b. dilution of boron present in the nuclear reactor, the dilution being carried out in successive steps, each step being carried out at a value of boron dilution flow rate up to a value of a third parameter representative of a reactivity of the nuclear reactor, each value of boron dilution flow rate and each value of the third parameter being obtained by means of the process of assisting the attainment of a divergent state as described above.

[0037] According to some embodiments, the divergent state is not reached at the end of the dilution, and the process includes, subsequent to the dilution, a further removal from the nuclear reactor of control rods from the nuclear reactor until the divergent state of the nuclear reactor is reached.

[0038] According to some embodiments, the input data for the process of assisting in reaching the divergent state include a target reactivity to be achieved in the reactor after the additional withdrawal.

[0039] According to some embodiments, the divergent state is reached during the dilution.

[0040] In another aspect, this disclosure relates to a computer program product comprising program code instructions for executing the steps of the process for achieving a divergent state as described above, when that program is executed by a computer. In another aspect, this disclosure relates to computer-readable memory storing instructions executable by the computer for executing the steps of the process for achieving a divergent state as described above.

[0041] DESCRIPTION OF THE FIGURES

[0042] Other aims and objectives will be exemplified by the following description, which is illustrative and in no way exhaustive, and in which:

[0043] [Fig. 1] schematically illustrates a nuclear reactor.

[0044] [Fig.2a] schematically illustrates a method of controlling a nuclear reactor, aimed at achieving a state of reactor divergence.

[0045] [Fig. 2b] schematically illustrates a method of assisting in reaching the divergent state, implemented within the framework of the control method of figure 2a.

[0046] [Fig. 3] represents a graph illustrating the evolution of a parameter representative of a count rate in the reactor as a function of reactivity.

[0047] [Fig. 4] schematically illustrates the temporal evolution of a boron concentration in reactor 2 and the deviation of boron concentration from a final concentration.

[0048] [Fig. 5] schematically illustrates dilution flow rates and count rate indices obtained using the process in Figure 2b.

[0049] [Fig. 6] schematically illustrates an evolution of a reactivity insertion rate as a function of reactivity in a reactor core.

[0050] Throughout the description that follows, the same reference symbols denote identical or similar elements.

[0051] DETAILED DESCRIPTION OF IMPLEMENTATION METHODS With reference to Figure 1, a nuclear power plant comprises one or more nuclear units 1.

[0052] Each nuclear unit 1 is an electricity production unit comprising a nuclear reactor 2, a current generating turbine 4 connected to the nuclear reactor 2, and a control system 6 enabling an operator to control the electricity production by the nuclear unit 1.

[0053] Nuclear reactor 2 is the site of a fission chain reaction, primarily involving uranium-235 nuclei and neutrons. The neutrons emitted during fission are too energetic to produce further fissions, so it is necessary to slow them down to lower energy levels, where the probability of fission is higher. To this end, nuclear reactor 2 includes a circuit to circulate water through the nuclear core, in order to slow the neutrons. The water acts as a moderator and also as a heat transfer fluid, carrying away the heat produced during fission.

[0054] Nuclear reactor 2 is known from the state of the art.

[0055] As is well known, nuclear reactor 2 includes neutron-absorbing rods, or neutron-absorbing rods. These rods are movable devices relative to the reactor frame in an axial direction to absorb neutrons and reduce the chain reaction as needed. The amount of neutrons absorbed by the neutron-absorbing rods depends on their position relative to the frame. The axial direction is typically vertical.

[0056] Nuclear reactor 2, for example, includes two groups of neutrophil control rods:

[0057] • A first group of control bars, called group R, intended for controlling the core temperature,

[0058] • A power compensating group, called a GCP group: this group is itself made up of several subgroups of different absorption bars, and allows the power produced in the core to be modulated. The nuclear reactor may also include groups of rods designed to ensure, in a shutdown state of reactor 2, the subcriticality of reactor 2.

[0059] Nuclear reactor 2 can also use other absorbents, either intentionally introduced or produced by reactions within the core, to capture neutrons and prevent them from causing fission. These absorbents include boron (introduced in a dilute form into the moderator to limit the chain reaction). The operator can control the boron concentration in the moderator.

[0060] Generally, reactor 2 can be of any type incorporating chain reaction control means in the form of a diluted species around the fuel, such as boric acid. Dilution of this control means is necessary to achieve a divergent reactor state. Thus, reactor 2 can, in particular, be a pressurized water reactor, a boiling water reactor, or a CANDU reactor using boric acid diluted in the primary circuit water.

[0061] The control system 6 is designed to control the operation of nuclear reactor 2, in order to control the reactions that occur inside, and to be able to modulate the electrical power delivered by nuclear unit 1.

[0062] The control system 6 includes a communication interface 8, a human-machine interface 10, a processing unit 12 and a memory 14.

[0063] The communication interface 8 is suitable for communicating with components of the nuclear reactor 2 to be controlled or monitored. In particular, the control system 6 is capable of controlling the movement of the control rods to monitor their position, by sending them appropriate commands via the communication interface 8.

[0064] Communication interface 8 is also adapted to receive measurements acquired by sensors on nuclear reactor 2, in order to assess its operating status. Electrical power delivered by nuclear unit 1, when the thermal power generated by the reactor is sufficient to produce electricity, is among the measurements that can be received by communication interface 8.

[0065] The communication interface 8 is of any type, for example wired or wireless radio type.

[0066] The human-machine interface 10 is adapted to provide an operator with data generated by the processing unit 12 or measurements provided by the sensors of the nuclear reactor 2.

[0067] The human-machine interface 10 includes a display screen allowing this data to be presented to the operator, for example in graphical form or in table form.

[0068] The human-machine interface 10 also includes an input device allowing the operator to provide data that can be processed by the processing unit 12, and to initiate commands to the nuclear reactor 2.

[0069] The processing unit 12 is adapted to implement processing based on the received measurements. This processing will be described later. The processing unit 12 is also adapted to generate commands that can then be transmitted to the nuclear reactor 2 via the communication interface 8.

[0070] The processing unit 12 typically includes a processor configured to execute the code instructions of a computer program, thereby causing the implementation of these processes. The processor can be of any type (it may have one or more cores).

[0071] Figure 2a illustrates an example of process 110 aimed at enabling the reactor to reach a critical state. The term "subcritical approach" is generally used to designate a control phase, by an operator, of the nuclear reactor, the goal of this phase being to reach the divergent state.

[0072] Typically, control system 6 includes detectors capable of measuring neutron fluxes in reactor 2, called CNSs (for "source level chains"). The CNSs calculate these neutron fluxes by counting the neutrons exiting a vessel in reactor 2. The CNSs thus provide a measurement of the neutron flux called the "count rate," denoted N, corresponding to the number of neutrons detected during a given unit of time. A dimensionless indicator called the "inverse count rate" (or ITC) is also defined.

[0073] [Math. 1]

[0074]

[0075] Where No is the count rate at the beginning of the subcritical approach and N is the count rate at a given time t.

[0076] Thus, when the neutron flux increases, the ITC decreases. If the neutron flux increases between the initial time and time t by a factor of 100, then the ITC is 0.01.

[0077] According to the static 0D neutron model used in the process, the ITC has the property of being proportional to the reactivity p of reactor 2 at time t (typically expressed in per hundred thousand or pcm):

[0078] [Math. 2]

[0079]

[0080] Where po is the reactivity of reactor 2 at the initial time. ITC thus allows control of the approach to divergence (p = 0) and a decrease in flow rate as one gets closer to it. The objective is to achieve divergence in order to perform subsequent tests and then increase the reactor power in a controlled manner.

[0081] The physical model of reactor 2 implemented in this process, which models the subcritical approach, takes into account the main first-order physical effects on the reactivity of the reactor 2 core. The process 110 for reaching a divergent state includes an initial step 10 of removing some of the neutralizing control rods from reactor 2. Indeed, the subcritical approach includes such a step 10 before a step 20 of diluting boric acid in reactor 2, during which a process 100—more specifically, a process 100 that assists the operator in carrying out the dilution step 20 to reach the divergent state—is implemented. Process 100 is implemented by the treatment unit 12 to assist the operator. A non-limiting example of a method to help achieve divergence 100 as proposed is illustrated in Figure 2b.

[0082] At the end of the withdrawal step 10, the neutrophil bars are in an initial insertion position in reactor 2, corresponding to the position of the neutrophil control bars during the initiation of the process to help reach divergence 100.

[0083] The process 110 for achieving the divergent state may further include, subsequent to step 20, a step 30 of additional removal of neutrophil control rods, during which the remaining neutrophil control rods are gradually removed from the core of reactor 2 until a divergence of reactor 2 is observed. It is not necessary for all the control rods to be removed during the additional removal step 30 - indeed, it is possible that divergence will be reached before all the control rods are removed, in which case some of the rods may be removed while divergence has already been reached.

[0084] In some embodiments, however, core divergence is achieved directly during the dilution step 20, without the need for a further step 30 involving the removal of neutrophil bars to reach divergence. In this case, the dilution aid process 100 allows a divergent core state to be achieved during the dilution step 20. The details of how this can be implemented will be discussed later.

[0085] We will now describe in more detail the dilution aid process illustrated as an example in Figure 2b. This process 100 includes an initial step 101 of receiving input data necessary for the processing unit 12 to perform the calculations. Some of this data represents the neutron properties of the reactor core 2, while other data represents an initial state of the core at the initial time t0 at which the dilution step 20 begins.

[0086] Representative data on the neutron properties of the core include a boron concentration, known as the divergence boron concentration CBDIV. This is the divergence boron concentration evaluated with the neutrophil control rods in the position obtained at the end of the initial withdrawal step 10, this position remaining unchanged during the dilution step 20. The divergence boron concentration CBDIV depends, in particular, on the type of nuclear reactor 2 used and the fuel present in the nuclear reactor 2.

[0087] The data representing the neutron properties of the core also include parameters representing the effectiveness of the reactivity control means for reactor 2. A first parameter represents the effectiveness of the neutron control rods, that is, their ability to allow reactor 2 to reach criticality during the additional withdrawal stage 30. This first parameter can be expressed as a reactivity differential, Apbarres, which can vary depending on the type of fuel used. A second parameter, s, represents the effectiveness of boron in reactor 2, that is, the capacity of boron to absorb neutrons in the core, closely linked to the ability of boron dilution to allow reactor 2 to reach criticality during the boron dilution stage 20.

[0088] The representative data of the neutron properties CBDIV, Apbarres and s can, upstream of the implementation of process 100, be calculated by a calculation chain of reactor 2.

[0089] The representative data for the initial state of the core include the boron concentration (CBo) at the initial time when the dilution step 20 is initiated. The boron concentration (CBo) is measured, notably by titration. The representative data for the initial state may also include the reactor 2 shutdown time (DA) since the last time reactor 2 was shut down. Indeed, the reactor 2 shutdown time (DA) can be used to estimate a factor Y representing the difference between, on the one hand, the actual evolution of the ITC with reactivity and, on the other hand, a theoretical evolution corresponding to the OD model considered during process 100, which does not take into account the variation of the system's physical properties in space.Such a simulation of the y factor from the reactor shutdown time DA is appropriate for some reactors with secondary neutron sources with a half-life of the same order of magnitude as DA. For other reactors, the y factor will have to be adjusted according to the loading plan (arrangement of fuel assemblies in the reactor core).

[0090] The stopping time DA is taken into account in the calculation of the correction due to the half-life of 60 days of certain secondary sources, i.e. species not directly involved in the fission reaction but which can be activated by this reaction and thus produce additional neutrons which will be involved in subsequent fission reactions.

[0091] According to other embodiments, when subcritical approaches have previously been performed for reactor 2, data acquired during such prior subcritical approaches can be used to calculate the y factor. An example of such acquired data is shown in Figure 3, which illustrates different evolutions of the parameter

[0092]

[0093]

[0094] (in pcm x cp / s, cp being the number of counts) with the reactivity p. This parameter is directly representative of the evolution of the factor y =

[0095]

[0096] in reactor 2. A calculation of the Pox N o

[0097] factor y on the basis of measured data is particularly suitable in the case of a similar loading plan from one cycle to another.

[0098] Figure 3 illustrates more precisely the results obtained during a subcritical approach on a reactor comprising four NSCs. Three of the NSCs, corresponding to the three upper curves A, B, and C, are placed near active secondary sources, while the NSC corresponding to curve D is placed near an inactive secondary source. The lower values ​​of the parameter are observed.

[0099]

[0100] for the CNS near the inactive secondary source. Regarding the y factor, we will have y<1 for CNSs located near active sources (curves A, B, C) and y>1 for the CNS located near the inactive source (curve D).

[0101] After receiving all the input data in step 101, the proposed process 100 includes a step 102 for obtaining output data. A non-limiting example of the calculations used in step 102 will now be described.

[0102] A variation in the reactivity p of the core depends on the boron concentration at a given time t:

[0103] [Math. 3]

[0104] (t) = c(CB(t) - CB DIV )

[0105] The variation in the counting rate N is given by:

[0106] [Math. 4]

[0107]

[0108] The factor y is obtained either by estimation from the reactor shutdown time DA, or from real data obtained during a previous subcritical approach, as explained previously, or by simulation with a core calculation chain.

[0109] Thus, the calculated values ​​of CBDIV, Apbarres and s can be corrected to take into account the average deviations observed in the feedback from reactors of the same design as nuclear reactor 2.

[0110] The effect of transit in the reactor chemical and volumetric control circuit (RCV) on the dilution flow rate Qcore in the core affects the dilution flow rate, and is taken into account by means of the equation: [Math. 5]

[0111] Qcoeur() — QREA(^RCV)

[0112] where QREA is the boron dilution rate, and AtRcv is the RCV circuit transit time.

[0113] Furthermore, the effect of transit in the RCV circuit on the residual dilution reactivity is taken into account using the equation:

[0114] [Math. 6]

[0115] A ~ £ CBQREA&t RCV

[0116] Residual dilution ~ 7

[0117]

[0118] 1V1 RCP

[0119] with MRCP the mass of water contained in the primary circuit.

[0120] Thus, the reactivity insertion rate can be calculated, taking into account the boron concentration, the dilution rate, and the transit time in the RCV:

[0121] [Math. 7]

[0122] dp(t) _ £CBQ coeur (t') _ sCBQ REA (t-kt RCV )

[0123]

[0124] dt MRCP M RCP

[0125] The homogenizing effect of the primary circuit (i.e., the uniformization of the conditions – temperature, pressure – of the heat transfer fluid present in the primary circuit) with the pressurizer is taken into account via a fixed variation value Ap effet pZR of the target reactivity at the end of dilution.

[0126] The value Ap effet pZRis obtained by considering a model with two water masses, one corresponding to the primary circulation reactor (PCR) and the other to the pressurizer (PZR). The equations governing the CBs of the two water masses are as follows:

[0127] [Math. 8]MRCP dCB RCP — QREA dt BRCP QPZR dt BRCP + QPZR dt CB PZR

[0128] [Math. 9]

[0129] M PZ R dCB PZR — Q PZR dt CB RCP QPZR dt CB PZR

[0130] Or:

[0131] QPZR is the mass flow rate passing through the pressurizer

[0132] CBRCP is the boron concentration in the primary circulation reactor. CBPZR is the boron concentration in the pressurizer.

[0133] These equations transform into a first-order differential system with constant coefficients:

[0134] [Math. 10]

[0135] dCB RCP Q d n QPZR QPZR R P

[0136] LÜRCP + TT LüpzR

[0137]

[0138] dt MRCP 1V1 RCP

[0139] [Math. 11]

[0140] dCB PZR QPZR QPZR „„

[0141] '■'DpzR

[0142]

[0143] dt MPZR RCP M PZR

[0144] This system is therefore of the form:

[0145] [Math. 12]

[0146] ® = M[CB],

[0147] dt

[0148] with:

[0149] [Math. 13]

[0150] '-Qdil-QPZR QPZR

[0151] CBRCP MRCP MRCP

[0152] [CB] =

[0153] CB PZR QPZR -QPZR

[0154]

[0155] MPZR M PZR. The solution therefore takes the form:

[0156] [Math. 14]

[0157] [CB]=[CB0]e Mt

[0158] The flow rate in the pressurizer is related to the power P C f r of heaters configured to maintain a predefined water temperature in the pressurizer. Water enters the pressurizer by spraying from the primary circulation reactor, at the TRCP temperature in that reactor, and exits through an expansion leg at a saturation temperature T sa t. Thus, at equilibrium, the heat balance in the pressurizer can be expressed as follows:

[0159] [Math. 15]

[0160] P

[0161]

[0162] (cf. QaspersionCpCTsat TRCP)

[0163] Thus, the spray flow rate Qaspersion is directly proportional to the power of the heaters. This is why, during the subcritical approach, all available heaters are put into operation in order to maximize the spray flow rate and thus minimize the time required to reach equilibrium in boron concentration.

[0164] The mass of water contained in the MPZR pressurizer is given by the following formula:

[0165] [Math. 16]

[0166]

[0167] MpzR Vjambe expansion * Pmoy + VpZR * Psat with

[0168] [Math. 17]

[0169] _ (Psat + PRCP)

[0170] Pmoy

[0171]

[0172] 2

[0173] WHERE - Vexpansion leg and VPZR are respectively the volumes of water contained in the expansion leg and in the pressurizer,

[0174] - Psat and PRCP are the densities, respectively, of the water contained in the expansion leg and in the pressurizer.

[0175] Based on the design values ​​and results obtained for the dilution and flow rate changes of the power plants, these equations are modeled. The results for a pressurized water reactor with an electrical production capacity of 1300 MWe are shown as an example in the graph in Figure 4. This graph represents:

[0176] - In the upper part, the time evolution of the boron concentration, in ppm, of the pressurizer (curve I), the primary circuit without the pressurizer (curve II), and the reactor with a primary circuit without considering the pressurizer (curve III). - In the lower part, the time evolution of the difference in boron concentration, in ppm, of curve II, relative to the final boron concentration obtained at the end of a phase of the dilution step 20 (final CB of curve II). These results show that the effect of homogenizing the primary circuit with the pressurizer leads to an increase in boron concentration of approximately 3.6 ppm (i.e., approximately a decrease in reactivity of 26 pcm) after the end of the residual dilution, and that it takes approximately 100 minutes for the primary circuit to reach a boron concentration less than 0.5 ppm from its equilibrium value.Such a decrease in reactivity is noticeable during physical tests at zero power, and justifies waiting for the primary to reach equilibrium before starting the measurement of boron concentration and the measurement of the isothermal temperature coefficient.

[0177] As an example, based on these results, we can estimate that, for a 1300 MWe pressurized water reactor, the effect due to the pressurizer is Ap effet pZR = -25 pcm. The output data for process 100 dilution aid include QREA dilution rates and / or ITCs at which a change in the dilution rate must be made.

[0178] Preferably, the process obtains in step 102 both a plurality of QREA dilution flow rates and the ITCs at which one of these dilution flow rates is changed to the next dilution flow rate. However, some embodiments only include the calculation of the ITCs for flow rate changes, with the QREA dilution flow rates then being specified as input data in the receiving step 101. This is useful when the operator knows from experience which QREA dilution flow rates should be used, but wants to know more precisely when to implement each of the QREA dilution flow rates.

[0179] Advantageously, the algorithm for determining QREA and ITC implemented in the dilution aid process 100 can be such that it ensures a response time Atoperator for the operator—that is, a duration available to the operator, at a given dilution rate, to react in order to avoid divergence due to residual dilution—this duration being greater than a threshold value. This threshold value can, for example, be between 20 and 30 minutes. Indeed, the risk of an unwanted divergence during dilution is a major problem with known prior art control processes, and taking into account the response time Atoperator therefore significantly improves the safety of the proposed process. The response time Atoperator takes into account the insertion rate of the reactivity dp / dt as well as the deduction of the transit time t RCV in the RCV circuit:

[0180] [Math. 18]

[0181] ^

[0182]

[0183] operator &tp=o ^RCV

[0184] OR

[0185] [Math. 19]

[0186] n Ar c P=o - ~ dp ~ p , •

[0187]

[0188] ' dt

[0189] The time spent at each dilution rate must be manageable by the operator and at least greater than the transit time in the RCV. Therefore, the implementation time for each rate must exceed a chosen duration. Rate changes occur at a given ITC, the difference in ITC over a time interval [ti, t]. 1+ i] given being:

[0190] [Math. 20]

[0191] P

[0192]

[0193] M f ) i+ 1 -f \-Ny rThe algorithm can also predict the cessation of dilution at a target subcriticality (reactivity) Ap bie, close to criticality, taking into account the residual dilution:

[0194] [Math. 21]

[0195] Target Pstop (also known as TAP residual dilution)

[0196] Where pstop dii is the reactivity at which the dilution stop command is transmitted. This allows the inertia of reactor 2 to be taken into account.

[0197] According to one embodiment, in order to allow the chaining of subsequent tests after the additional removal step 30 without requiring a new insertion of boron into the core ("reborication"), the treatment unit 12 receives as input a target reactivity of the core, either once the neutrophil control bars have been completely removed from the reactor 2 after the additional removal step 30, or after the dilution step 20. This data can be a setpoint, requested from the operator and specified by the latter via the human-machine interface 10 before initiation of the process 100. For example, the target reactivity value after the complete removal of the control bars is 60 pcm.

[0198] The algorithm for obtaining dilution flow rates and ITC can, for example, take this setpoint into account thanks to the theoretical efficiency of the neutralizing rods, calculated during calculations implemented during fuel refueling, thanks to the average bias of the measurements and the target reactivity value, i.e., at the end of the dilution step (Δρ). cible ), or when the control bars have been completely removed (known as "all bars up" reactivity ρ StepTBH ), of the reborication effect due to the Ap pressurizer effet pZR and a provision for uncertainty Apincertitude.

[0199] [Math. 22]

[0200] .-. Cctl eu l I -biais > pStepTBH | ^peffet PZR incertitude A

[0201]

[0202] Target bars ^P bars + Ap

[0203] Based on the preceding equations, the treatment unit 12 calculates the change in transfer coefficients (ITCs) at which the dilution flow rate QREA must be modified, as well as, where applicable, the plurality of successive dilution flow rates QREA. An example of the evolution of the dilution flow rate over time is illustrated in Figure 5, corresponding to the implementation of the dilution aid process 100, for which the treatment unit calculates three dilution flow rates Qo, Qi, and Qz. Curve X illustrates the evolution of the reactor pump flow rate, while curve XI illustrates the flow rate at the core Qcoeur, after transit through the RCV. The flow rate at the core Qcoeur exhibits a lag corresponding to the transit time at the RCV AtRcv.

[0204] Naturally, process 100 can, according to certain embodiment variants, include obtaining in step 102 a larger number of ITCs of dilution flow change and, where appropriate, corresponding QREA dilution flow rates, in particular 4 to 5 ITC values ​​and QREA dilution flow rates.

[0205] According to one embodiment, the calculation is first performed for the last dilution flow rate used before divergence is reached (and therefore before dilution is stopped), as well as for the ITC at which dilution must be stopped (ITCstop n). In the example in Figure 5, this last dilution flow rate is Qz, and the corresponding ITCstop dii is ITC3.

[0206] Using equations 3 and 4, the dilution stop reactivity is expressed as a function of the corresponding ITC and the initial boron concentration CBo, at the initiation of the dilution aid process 100:

[0207] [Math. 23]

[0208] ρ stop dil= ε(CB0− CB DIV (N0 / N γ) stop dil

[0209]

[0210] ' ' stop dil

[0211] The reactivity resulting from the residual dilution is determined from equation 6:

[0212] [Math. 24]

[0213] Δρresidual dilution≈ −εCBQ2 REA Δt RCV / M RCP

[0214] Residual dilution ~ « Æ

[0215]

[0216] 1V1 RCP

[0217] The boron concentration at the end of the residual dilution is very close to the divergence boron concentration. Therefore, we can take CBDIV as an approximation and rewrite equation 21 in the form:

[0218] [Math. 25] / N o ECB DIV Q? EA to t RCV ^Pbarres = ~< CB0- CB DIV ) A + -

[0219]

[0220] VV 'stop dll lvl RCP

[0221] Here we see that the ITCstop dii and the flow rate Q.2 are linked by an equation. To determine them unambiguously, an additional equation must be added. For example, the operator delay principle from equation 18 can be used for this purpose:

[0222] [Math. 26]

[0223] _ ~ P

[0224] ^operator -J - ^RCV

[0225]

[0226] ' dt

[0227] The reactivity p at the time the dilution is stopped is that given by equation 23 and the rate of insertion of the reactivity is given by equation 7 applied to Qz with CB = CBDIV:

[0228] [Math. 27]

[0229] i cfD r} heart

[0230] dpi _ _>

[0231]

[0232] dt ~

[0233] Thus, equation 26 can be rewritten as:

[0234] [Math. 28]

[0235] M RCPFNRT

[0236] ncoeur ro — CB D I V ) ( Y j — ^operator Q2 + ^RCV

[0237]

[0238] V2 L ts DIV 'stop said

[0239] We thus obtain a second equation relating the ITC at the end of dilution and the final dilution flow rate. We can now determine the two values ​​unambiguously by solving the system of two equations with two unknowns:

[0240] [Math. 29]

[0241] ^Pbarres^ RCP

[0242] Q2 REA

[0243]

[0244] GCB DIV ^operator Q2

[0245] [Math. 30]^ÏRCV

[0246] N o \ ^Pbarres I 1 + operator Q2

[0247]

[0248] - ' / V v Y ' ) stop dil ​​e(CB0CB DIV )

[0249] We can now calculate Q1 and ITC2 by applying the principle of sufficient duration of Q.2 and respecting the operator delay principle with Q1.

[0250] We now consider equation 20. To obtain the derivative of the ITC as a function of time present in equation 20, we combine equations 4 and 7:

[0251] [Math. 31]

[0252] , (N0A

[0253] d \N Y ) _ _ CB Q Heart

[0254]

[0255] dt ~ (CB0- CB DIV réelle )M RCP

[0256] so that equation 20 becomes:

[0257] [Math. 32]

[0258] / M) \ (N o \ f tl+1 CBQ REA (t — At RCV )

[0259] I — y I — I — y I — I - CLT

[0260]

[0261] \WJ t2 \N / stop says Jti ÇCBQ — CB DI V^)M R CP

[0262] Since the boron concentration varies little over the time interval [t2, tstopdii], we obtain, with good approximation, taking into account the change in flow rate at the core:

[0263] [Math. 33]

[0264] / M) \ (N o CB2Q REA At RCV + CB stop di iQ REA (t stopdii — t2— At RCV )

[0265]

[0266] \W / 12\N ) stop dil ​​(CB0CB DIV )M RCP

[0267] where AtQ2 = tstopdii - 12 is the duration chosen to stay at the Oz flow rate.

[0268] As with Q, respecting the operator delay principle with the Q1 throughput allows us to obtain the value of Q1 and of en giving a

[0269]

[0270] second equation to solve the system: [Math. 34]

[0271] M RCP / N n \

[0272] n REAr R (CB0- CB DIV ) -M ^operator Q1 "h At RE y

[0273]

[0274] Q1 LB DIV \7V / t 2

[0275] The value of the primary boron concentration CB2 at the change in flow rate is given by the combination of equations 3 and 4:

[0276] CB2— CB DIV + (CB0— CB DIV ) (~jrpYj

[0277]

[0278] 7V / 12

[0279] To avoid dependence on the (-y) term of CB2 in order to solve more easily \N 7 t 2

[0280] For the following equations, we simplify equation 31 with the following approximation:

[0281] [Math. 35]

[0282] C

[0283]

[0284] B2~ CB stop dil + 40 ppm

[0285] We then solve the following system of equations, derived from equations 33 and 34, to obtain (-y) and Q? EA depending on other parameters:

[0286] N 7 12

[0287] [Math. 36]

[0288] MRCP(CB Q — CB DIV ) y) _ - ht,

[0289] oREA rn operator Q1 + ' L HAS A / L -RCV < vi LB DIV / N o \ / N o CB2Qx EA to t RCV + CB stop d ii(atQ2— at t RCV ^Q REA

[0290]

[0291] 't2 'N ' stop of the (CB0- CB DIV )M RCP

[0292] We manipulate the first term to obtain:

[0293] [Math. 37]

[0294] / NQ \ _ (At O operator IQ + &tRcv)Qi EA CB DIV \N Y ) t2 'MRCP(CB0— CB DIV ) No \ _ / No \ BB2QREA^RCV + CB stap d uÇàtQ2— ^RCV^QREA

[0295]

[0296] •N / f2 'N / st O p d u (CB0— CB DIV ^M RCP Then, we substitute this value of (-y) into the second part of equation 37:

[0297] \N / t 2

[0298] [Math. 38]

[0299] (At O pe ra IQ test + &t RC v)Q? EA CB DIV / NQ X MRCP(C#0 — CB DIV ) \N / stop dil

[0300] _ CB2Q REA to t RCV + CB stop dij(AtQ2— at t RCV ^Q REA

[0301]

[0302] (CB0— CBpuy^Mjfcp This equation simplifies to:

[0303] [Math. 39]

[0304] MRCP (CB0CB DIV ) Ç NY^ S DÜ + CB stop diiÇ^Q2 ^ÏRCV^QREA (£ EA

[0305]

[0306] ( (to operator Q1 + ^RCV^BB DIV — CB2 at RC y ]

[0307] The value of (-y) is obtained by substituting the value of Q? EA obtained

[0308] \N / t2

[0309] previously in the first equation of the system of equation 37:

[0310] [Math. 40]

[0311] No = / No \ BB2Q REA to t RCV + CBstap dilÇ^Q2 ^RCV^QREA

[0312]

[0313] N / f2 ' N / st O p dil ​​(CB0— CB DIV ^M RCP

[0314] We then proceed in the same way to obtain ( \— N y / ) tl and Q EA from the example in Figure 6 starting from (-y) and Q? EA :

[0315]

[0316] \ N / t2

[0317] [Math. 41]

[0318] Q0 REA = M RCP (CB0− CB DIV (N0 / N γ) t2 + CB2(Δt Q1 − Δt RCV )Q1 REA

[0319] VO

[0320] (Δt operator Q0 + Δt RCV )CB DIV − CB1Δt RCV

[0321] I + CB2(At çl — at RCV ^Q REA

[0322]

[0323] ti t2 (CB0— CBpuy^MpcpTJ

[0324] if Q EA Q max , so we take Qmax instead of Q EA to determine (-y), Qmax being the maximum possible flow rate (i.e. permitted, for example by the design of the REA pumps or the safety requirements in force) for reactor 2. Indeed, the first dilution flow rate used can be the maximum possible flow rate Qmax, so as to allow the divergence state to be reached more quickly.

[0325] The number of flow rates required to achieve a flow rate greater than or equal to Qmax varies depending on the values ​​of the parameters Qmax, MRCP, CBDIV, Apbarres, AtoperatorQi, and AtQi. Qmax, AtRcv, and MRCP are related to the reactor design, while CBDIV and Apbarres are derived from the core design to be started. The values ​​of AtoperatorQi and AtQi must be chosen with regard to the safety of the installation. The initial tests carried out used a value of 20 minutes for all these parameters. The results obtained with these values ​​were conclusive.

[0326] Figure 6 illustrates the evolution of the insertion velocity of the reactivity dp / dt as a function of the core reactivity p COEur. Curves IVa, Va, and Via illustrate the trajectory followed by the operator for heart control, taking into account the ITC and QREA dilution rates calculated by processing unit 12. Curves IVb, Vb, and Vlb illustrate the reactivity and the reactivity insertion rate into the heart itself (taking into account the transit time in the RCV relative to the trajectory followed by the operator). The vertical curves correspond to ITC values. For the example given, an operator delay of 20 minutes was considered (corresponding to curves VII and VIII for control and the heart, respectively). For information purposes, curve IX, representing a zero operator delay, is also shown.

[0327] When the process 110 for achieving a divergent state does not include a supplementary removal step 30 of the remaining neutrophil control bars, what is called a "divergence on dilution" is achieved; that is, the divergence is reached at the end of a boron dilution step 20. The target is not a negative reactivity leading to the raised divergence of the remaining neutrophil control bars, but rather a positive reactivity target leading directly to divergence during the dilution.

[0328] To this end, equations 18 and 19 can be enriched with a variable p ma x corresponds to the reactivity value that we do not want to exceed:

[0329] [Math. 42]

[0330]

[0331] Δt opérateur = Δt ρ=ρmax − Δt RCV

[0332] [Math. 43]

[0333] Δt ρ=ρmax =

[0334] (ρ max − ρ) / (dρ / dt)

[0335]

[0336] / dt

[0337] According to certain variations of the dilution aid method 100, some of the approximations taken into account in the calculation can be eliminated by making the calculation equations more complex. This allows for a more precise ITC calculation, at the cost of longer calculation times.

[0338] One of the main approximations is the inclusion of an approximate CB in the expression of the insertion speed of the reactivity of equations 24, 27, 31.

[0339] By not simplifying equation 24, we obtain:

[0340] [Math. 44]

[0341] A EC (CB DIV + (CB0- CB DIV ) (JTY) ~ \ \ JV / stO 'j Q2 REA ^RCV p of the / ^Residual dilution ~ «7

[0342]

[0343] 1V1RCP This then gives the following equation, which replaces equation 25:

[0344] [Math. 45]

[0345] ^Pbarres CB^iyJ I y I

[0346] ' ' stop dil ​​E (cB DIV + (CB0- CB DIV ) (JTY) 'j Q2 EA ^RCV \ ' stop dil / Djy

[0347]

[0348] By not simplifying equation 27, it becomes:

[0349] [Math. 46]

[0350]

[0351] This leads to the equation in the following form, which replaces equation 28:

[0352] [Math. 47]

[0353] / z A7 \ \ (CB0CBpyy) ( y ) operator Q2 + ^RCV Q^ oeur [CB D1V + (CB0- CB DIV (jfr) stop dil ) V N ' stop dil

[0354]

[0355] To solve the system of 2 equations and 2 unknowns in equations 45 and 46, we must then solve one equation from the second part. ème or 3ème degree...

[0356] Another approximation is to take a fixed value for Ap effet pZR whereas this actually depends on the dilution parameters (CBDIV, CBO,...)

[0357] To resolve this dependency, we can recalculate Ap effet PZR using the results Q0, Q1, Q2, ITCO, ITC1, ITC2 obtained, then repeat the calculation of Δρ effet PZR until convergence towards a stabilized value in a few iterations.

[0358] In some embodiments, the dilution aid process 100 is implemented on the dilutions preceding the divergences during the cycle. If the shutdown time of nuclear unit 1 before divergence is less than 48 hours, it is then advantageous to take into account the variation in xenon reactivity in the calculations, as xenon then has a non-negligible neutrophilizing effect.

Claims

DEMANDS 1. A method (100) for assisting in achieving a divergent state of a nuclear reactor (2), the method being implemented by computer and comprising the steps of: receive (101) input data including: a nuclear reactor shutdown duration (2) from a moment when the nuclear reactor last underwent a shutdown or a change in the reactivity of the nuclear reactor (2) with a boron concentration in the nuclear reactor (2) measured during a period ending with a moment when the nuclear reactor reached a divergent state, an initial boron concentration (CBo) measured in the nuclear reactor (2), a maximum boron concentration (CBDIV) at which, for a predefined position of neutrophil control rods in the nuclear reactor (2), the nuclear reactor (2) is in a divergent state, a first parameter (Apbarres) representative of the efficiency of the neutrophil control rods in absorbing neutrons in the nuclear reactor (2), a second parameter(s) representative of the efficiency of boron in absorbing neutrons in the nuclear reactor (2), From the input data, generate (102) output data including: a plurality of boron dilution rate (QREA) values ​​in the reactor to be applied successively, and a plurality of values ​​of a third parameter (ITC) representative of a reactivity of the nuclear reactor (2), each value of the third parameter (ITC) being associated with a value among the plurality of values ​​of the boron dilution rate (QREA), cause the output data to be displayed on a display screen.

2. A method according to claim 1, wherein the input data further include a safety time, and wherein the reactor is unsuitable for reaching the divergent state when the boron dilution rate remains equal, for a period less than or equal to the safety time, to a value chosen from the plurality of boron dilution rate values ​​(QREA).

3. A method according to any one of claims 1 and 2, wherein the input data further comprise a first boron dilution flow rate value (Qo REA) equal to a maximum permissible boron dilution flow rate value (Qmax) for the nuclear reactor (2).

4. Method according to any one of claims 1 to 3, wherein the generation (102) of output data is further carried out such that, for any generated boron dilution flow rate value (QREA), the nuclear reactor is unsuitable for reaching the divergent state in the absence of a change in the position of the neutrophilizing rods.

5. A method for controlling (110) a nuclear reactor (2) to achieve a divergent state of the nuclear reactor (2), the reactor comprising a set of control rods, the method comprising the steps of: a. removal (10) from reactor (2) of part of the neutrophil control rod assembly, b. dilution (20) of boron present in the nuclear reactor (2), the dilution being carried out in successive steps, each step being carried out at a boron dilution rate value (QREA) up to a value of a third parameter (ITC) representative of a reactivity of the nuclear reactor (2), each boron dilution rate value (Q REA ) and each value of the third parameter (ITC) being obtained by means of the method for assisting in reaching a divergent state (100) according to any one of claims 1 to 4.

6. Control method (110) according to claim 5, wherein the divergent state is not reached after dilution (20), the method comprising, subsequent to dilution (20), a further removal (30) from the nuclear reactor (2) of neutralizing control rods present in the nuclear reactor (2) until the divergent state of the nuclear reactor (2) is reached.

7. Piloting method (110) according to the preceding claim, wherein the input data of the method for assisting in reaching the divergent state (100) include a target reactivity to be achieved in the reactor (2) at the end of the additional withdrawal (30).

8. Piloting method (110) according to claim 5, wherein the divergent state is reached during the dilution (20).

9. A computer program product comprising program code instructions for executing the steps of the process according to any one of claims 1 to 4, when this program is executed by a computer.

10. Computer-readable memory storing instructions executable by the computer for executing the steps of the process according to any one of claims 1 to 4.

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