Patent Number: 048760579
Section: description

FIG. 1 shows a sectional view of a pressurized nuclear reactor vessel 2. The core of said nuclear reactor comprises: (a) Nuclear fuel (fissile materials) contained in jacketing and referred to as fuel rods 6, which are positioned vertically. (b) Sometimes, neutron-absorbing rods, often called consumable poison rods. The absorbing or fuel rods are maintained in mechanical structures, called assemblies. The core is constituted by assemblies and the network formed by the rods is generally regular. (c) A cooling fluid supplied by a feed pipe 8 and discharged by a discharge pipe 10 connected to a pump. This fluid flows vertically from top to bottom in the core and is constituted by water in the form .sub.1.sup.1 H.sub.2 8.sup.16 O having the property of slowing down the neutrons. In the case of a pressurized water system, the water can contain, in solution, neutron-absorbing nuclei and in particular boron nuclei .sub.5.sup.10 B. (d) Control rods 12 containing materials absorbing the neutrons which can be vertically displaced in the core during reactor operation. These control rods are used for the rapid control of the power in the core. A description will now be given of the inventive process with reference to the flowchart of FIGS. 2a and 2b. In order not to overburden the description, the simplified case will be assumed in which the neutron sources consist solely of fast fission neutrons. At the end of the description reference will be made to the general or kinetic case, in which the neutron sources also have delayed neutrons. This process involves a stage of determining the neutron flux .phi.(j,g), the power P(j) and the source S(j) in each mesh j by an iterative calculation, as well as a stage of using given physical quantities for controlling the core regulating means. The inventive process starts with an operation of initializing the values of the sources S(j), the neutron fluxes .phi.(j,g) and powers P(j). The initial value of the sources S(j) can be fixed in arbitrary manner, e.g. at 1. More advantageously they can be considered as equal, for the calculation of the neutron fluxes and powers at an instant t, to the value calculated according to the inventive process at a prior instant t' (t'&lt;t). In the first case, it is experimentally found that the first stage of the inventive process requires a number of iterations n of approximately 100, whereas in the second case n is approximately a few units. In the same way, the neutron fluxes .phi.(j,g) can be initially fixed at the value zero, but can be advantageously fixed at values determined at a preceding instant by the process of the invention. Finally, the powers P(j) are preferably preset to a value: ##EQU5## in which P is the total power of the core, which is known by measurements carried out thereon and v.sub.j is the volume of mesh j. Operation 16 in FIG. 2a notes the incrementation of the iteration index n. Each iteration consists of a sequence of operations 18-30 and ends by a convergence test 32. Operation 18 relates to the calculation of a first neutron flux component .phi..sup.0 (j,g) of the real neutron flux .phi.(j,g). Each first component .phi..sup.0 (j,g).sup.(n) at the nth iteration is expressed as a function of a predetermined coupling matrix [.psi.g] and sources S(j).sup.(n-1) calculated during the preceding iteration n-1. There are in all G coupling matrixes, one per velocity group g and each having a size K.times.K, in which K is the number of adjacent matrixes to a random matrix. The coupling matrixes [.psi.g] are associated with the influence field of neutron exchanges between meshes k, 1.ltoreq.k.ltoreq.K, adjacent to a mesh j (and including the latter) and mesh j. These predetermined coupling matrixes are calculated for a predetermined state of the core (also called reference medium), i.e. for predetermined interaction probabilities of the neutrons in the core. The terms .psi.g(j,k), 1.ltoreq.j.ltoreq.J and 1.ltoreq.k.ltoreq.K of the coupling matrixes [.psi.g] are defined by the following relation: ##EQU6## are the volumes of the meshes j and k and r=d(x.sub.j,x.sub.k) is the distance between a point x.sub.j of mesh j and a point x.sub.k of mesh k. The term .psi.g(r) represents the neutron flux in cm.sup.-2 at a point x.sub.j of mesh j at distance r=d(x.sub.j,x.sub.k) created by a source located at point x.sub.k of mesh k and emitting one neutron/second in accordance with a fission spectrum .chi..sub.g. The term .psi.g(j,k) represents the mean flux in mesh j produced by a source uniformly distributed in mesh k and emitting one neutron/second in accordance with the fission spectrum .chi..sub.g in the velocity group g. For a fission spectrum .chi..sub.g, the term .psi.g(r) can e.g. be determined in known manner on the basis of the ANISN transport code. The terms .psi.g(j,k) are then obtained by integration, which can introduce a certain imprecision in the values of terms .psi.g(j,k). It is possible to ensure that the values found are correct by proving that the equation: ##EQU7## is satisfied, which means that in the area formed by the K meshes, there is an absorption of one neutron (in the equation .SIGMA.a.sup.0,g is the effective macroscopic absorption section of the reference medium for group g). The first components of the neutron fluxes .phi..sup.0 (j,g).sup.(n) can be calculated on the basis of the coupling matrixes ].psi.g], notably according to the equation: ##EQU8## in which v.sub.k is the volume of mesh k. The predetermined interaction probabilities, i.e. associated with the reference medium are e.g. defined by predetermined values of the effective macroscopic sections .SIGMA.a.sup.0 (j,g), .SIGMA.s.sup.0 (j,g.fwdarw.g'), .SIGMA.t.sup.0 (j,g) and .SIGMA.f.sup.0 (j,g). Preferably .SIGMA.f.sup.0 (j,g) is chosen equal to zero. Each coefficient .psi.g(j,k) represents the flux in group g and mesh j, when one neutron is emitted per volume unit and time unit, in a homogeneous manner in mesh k in accordance with the fission spectrum, in a core for which the interaction probabilities of the neutrons are said predetermined interaction probabilities. The values are defined for each assembly type and are preferably chosen in such a way that the predetermined effective macroscopic sections are close to the real effective macroscopic sections in the core under normal operating conditions. This makes it possible to have a higher precision in the calculation of the neutron fluxes .phi.(j,g) and powers P(j). It is e.g. possible to choose a value for each predetermined effective macroscopic section equal to the mean value of the possible amplitude range for said effective macroscopic section. The following operation 20 of the process consists of evaluating second neutron flux components .phi..sup.1 (j,g).sup.(n) as a function of the real interaction probabilities of the neutrons in the core. In known manner, they are deduced from values of physical parameters describing the state of the core, the values of said physical parameters being in known manner either directly detectable by sensors, or evaluatable on the basis of indirect measurements. The generally known physical parameters are: (a) the position PBCq of each control rod q, 1.ltoreq.q.ltoreq.Q, in which Q is the total number of control rods, (b) the intake temperature .theta..sub.E of the cooling fluid into the core, (c) the pressure PR of the cooling fluid in the core, (d) the boron concentration C.sub.B in the core, (e) the total power P supplied by the core, (f) the description of the position of the assemblies of each type in the core and (g) the neutron fluxes .phi.(j,g).sup.(n-1) and the powers P(j).sup.(n-1) calculated at the preceding iteration instant n-1. On the basis of these physical parameters, it is possible to evaluate for each mesh j, a group of local parameters, such as: (a) the temperature of the fuel Tu(j), (b) the temperature of the cooling fluid .theta.(j), (c) the density of the cooling fluid (j), (d) the concentration Xe(j) in nuclei of .sub.54.sup.135 Xe, (e) the irradiation rate or the wear of the fuel I(j), (f) the state x.sub.m (j) (presence or absence) of a control rod of type m in mesh j, (g) a parameter p(j) characterizing the assemblies from the standpoint of their equivalent neutron properties (presence or absence of consumable poisons, initial .sub.92.sup.235 U enrichment, initial plutonium content, initial plutonium isotope composition, etc.). More specifically, the parameters Tu(j), .theta.(j) and (j) are calculated by relations expressing the thermal aspects of the fuel nucleus and the thermohydraulic aspects of the water in the rods on the basis of the physical parameters .theta..sub.E, PR, PBCq, P and powers P(j). The parameter Xe(j) is calculated on the basis of the neutron fluxes .phi.(j,g) by relations expressing the formation and disappearance of .sub.54.sup.135 Xe nuclei. The parameter I(j) is calculated by a time-based wear relationship. Reference can be made to the work "Nuclear Reactor Theory" by George I. Bell and Samuel Glasstone, Van Nostrand Reinhold Company for a description of methods for obtaining local parameters on the basis of physical parameters. The interaction probabilities of neutrons in the core, which can e.g. be defined by the effective macroscopic sections .SIGMA.s(j,g.fwdarw.g'), .SIGMA.a(j,g), .SIGMA.t(j,g) and .SIGMA.f(j,g), are then deduced in known manner from local parameters and the boron concentration C.sub.B. A method of calculating the effective macroscopic sections as a function of local parameters and C.sub.B is e.g. given in the document "Homogenization methods in reactor physics" issued by the International Atomic Energy Agency, Vienna, 1980. Following operation 20 relating to the evaluation of the effective real macroscopic sections, i.e. those corresponding to the effective values of the physical parameters of the core, in operation 22 second neutron flux components .phi..sup.1 (j,g).sup.(n) are calculated. The latter are expressed as a function of the first neutron flux component .phi..sup.0 (j,g).sup.(n), predetermined interaction probabilities of the neutrons in the core and real interaction probabilities of the neutrons in the core. For each mesh j, 1.ltoreq.j.ltoreq.J, this relation can be expressed by a linear system with G equations: ##EQU9## For each mesh, it is consequently a question of resolving a system of G equations with G unknowns .phi..sup.1 (j,g).sup.(n), 1.ltoreq.g.ltoreq.G. The number G of velocity groups is in general a few units. Thus, the linear system can be simply resolved by reversing the associated matrix of size G.times.G. Operations 18 and 22 respectively supply the first neutron flux components .phi..sup.0 (j,g).sup.(n) and the second neutron flux components .phi..sup.1 (j,g).sup.(n). The neutron fluxes .phi.(j,g).sup.(n) are then calculated as the sum of the first and second components by operation 24. In the particular case, which frequently occurs in practice, where the number of velocity groups is equal to 2 (G=2) and in which there is no rise of neutrons of group 2 (slow velocities) into group 1 (fast velocities) during a diffusion, the neutron fluxes .phi.(j,g).sup.(n) for velocities g=1 and g=2 can be more rapidly calculated in direct manner on the basis of first neutron flux components .phi..sup.0 (j,g).sup.(n) by the following expressions: ##EQU10## In the particular case where G=2, it is consequently not necessary to explicitly calculate the second neutron flux components .phi..sup.1 (j,g).sup.(n), so that operation 22 is eliminated. The knowledge of the neutron fluxes .phi.(j,g).sup.(n) makes it possible to evaluate th new values S(j).sup.(n) of the sources. Initially, operation 26 is used for determining new sources NS(j).sup.(n) as a function of the neutron fluxes .phi.(j,g).sup.(n) and effective fission section .SIGMA.f(j,g), according to relation: ##EQU11## in which .nu. is the mean number of new neutrons produced by one fission. Secondly (operation 28), an updated value is calculated of sources S(j) by: ##EQU12## From this is deduced by operation 30 the value of the power given off by each mesh j in accordance with relation: ##EQU13## Thus, at the end of operation 30, the neutron flux .phi.(j,g).sup.(n), the source S(j).sup.(n) and the power given off P(j).sup.(n) are obtained for each mesh j 1.ltoreq.j.ltoreq.J. A test 32 is then performed to determine whether there is convergence of the calculated values, or whether it is necessary to perform a new iteration. The test can e.g. apply to sources S(j) and to the multiplication rates of the neutrons in the core, said rate being defined by .lambda..sup.(n) =NS.sup.(n) /S.sup.(n-1). For the sources S(j), there is a comparison for each mesh j, of the relative increase .vertline.S(j).sup.(n) -S(j).sup.(n-1) /S(j).sup.(n-1) .vertline. with a constant factor .epsilon. having a value equal to e.g. 10.sup.-4. In the same way, there is a comparison of the increase of the multiplication rate .vertline.(.lambda..sup.(n) -.lambda..sup.(n-1))/.lambda..sup.(n-1) .vertline. with a constant factor .eta. having a value e.g. equal to 10.sup.-5. If the two comparisons indicate that there is convergence, the process is continued by operation 34. In the opposite case, operation 16 is repeated to start a new iteration. If convergence occurs, the values P(j).sup.(n) and .phi.(j,g).sup.(n) are respectively allocated to parameters P(j) and .phi.(j,g) (operation 34). These values are then used for controlling the core by acting on the position of the control rods and/or on the boron concentration. More specifically, the values P(j) and .phi.(j,g) make it possible to accurately evaluate the physical limits of the core and to compare them in conventional manner with thresholds respecting the safety criteria of the reactor. This comparison leads to an action on the control rods and/or the boron concentration and/or the transmission of an alarm signal. In the preceding description, the neutron sources only had neutrons directly resulting from fission. In practice, account can also be taken of sources formed from delayed neutrons. This only slightly modifies the equations defining the fluxes .phi..sup.0 (h,g), .phi..sup.1 (j,g) and the new sources NS(j). Thus, the kinetic case consists of taking into account the sources S.sub.k.sup.PREC linked with delayed neutron precursors and the flux variation term ##EQU14## in which v is the mean neutron velocity. In order to take account of delayed neutrons, it is necessary to introduce a time index m, the calculations being performed iteratively (n being the iteration index) at each time t equal to t.sub.0 +m..DELTA.t. The first flux component .phi..sup.0 (j,g).sup.(n,m) is defined by ##EQU15## in which .psi.g(j,k).sup.PREC represents the mean flux in mesh j for the velocity group g, associated with a source uniformly distributed in mesh k and emitting one neutron per second in accordance with the emission spectrum of the delayed neutron .chi..sub.g.sup.PREC. Thus, the first flux component appears as the sum of two fluxes, each produced by a particular neutron source. These sources are calculated by the following equations: ##EQU16## in which .beta. is the total number of delayed neutrons per fission neutron and ##EQU17## in which .lambda.i is the radioactive decay constant of the precursor and Ci(j).sup.(n,m) is the concentration of the precursor i in mesh j at instant t.sub.0 +m..DELTA.t and at iteration n. The second neutron flux component .phi..sup.1 (j,g).sup.(n,m) is obtained as in the preceding description by the resolution of a linear system: ##EQU18## in which .phi.(j,g).sup.(m-1) is the neutron flux obtained on time iteration m-1 and v.sub.g is the mean neutron velocity of the velocity group g. Finally, the new sources Nw(j).sup.(n,m) are defined by ##EQU19##