Patent Number: 051715163
Section: description

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views, and more particularly to FIG. 1 thereof, the reactor core monitoring system according to the invention is shown which includes core 30 made up of a plurality of fuel cells, each fuel cell containing a plurality of fuel rods. FIG. 2 shows nine adjacent fuel segments A.sub.O -A.sub.g. The monitoring system also includes a monitoring and control means 31 which controls the operation of the reactor core 30 and monitors core state parameters such as the core flux and positions of the control rods, etc., of the reactor core 30. Monitor and control means 31 also includes a controller, which may include a microprocessor, and apparatus for moving the control rods 25 to required positions in the core. A detailed description of the controller and moving apparatus is omitted for brevity as they are believed to be well understood by those skilled in the art. In FIG. 3, a fuel segment 21 is shown having fuel rods 23 made of boiling water reactor fuel and arranged in 8 rows and 8 columns in a channel box 22 which is provided with two water rods 24 at its center. A control rod 25 is located at one corner of fuel segment A.sub.O. A typical fuel assembly (not shown) is made up of a number of fuel segments, for example 24, arranged one on top of the other. A fuel assembly is typically 5-6 meters long. The reactor contains a plurality of the fuel assemblies, for example 64, as will be understood by one skilled in the art. FIG. 4 illustrates a section of the reactor 30 with a plurality of fuel segments 21, each group of four having a control rod 25 disposed at a central position of the group, as is conventional in the art. Also shown in FIG. 4 is monitor 26, which is typically in the form of a rod. Monitor 26 provides information of the operation of the reactor core 30 to monitoring means 31. It is be understood that FIG. 4 is provided for illustration purposes only, and the dimensions and positions of the fuel segments 21, control rods 25, and monitor 26 do not necessarily reflect the actual dimensions positions, and arrangement in a reactor core. A memory device 33 stores the nuclear constants in an infinite lattice, the local power distribution in an infinite lattice, and the R factor in an infinite lattice, etc., which were previously found by solving the heterogeneous neutron diffusion equation in an infinite lattice consisting only of the fuel segment in question, of the fuel segments arranged in the core 30 of the atomic reactor. This heterogeneous neutron diffusion equation in an infinite lattice is that typically used in the design calculations of a fuel assembly. Several memory devices are capable of storing the various required data, as will be apparent to one skilled in the art. In this embodiment, a single memory such as a read-only memory is used, but a separate memory may be used for each of the nuclear constants, local power distribution and R factor. The nuclear constants in the infinite lattice are stored in nuclear constant storage area 33A of memory device 33. The local power distribution in the infinite lattice is stored in local power distribution storage area 33B of memory device 33. The R factor in the infinite lattice is stored in R factor storage area 33C of memory device 33. The nuclear constants in infinite lattice stored in nuclear constant storage area 33A include the average spectral index F of a fuel segment in infinite lattice, the average macroscopic removal area S of thermal neutrons in a fuel segment, and the average diffusion coefficient D in a fuel segment. The local power distribution obtained by solving the heterogeneous neutron diffusion equation of a fuel segment in infinite lattice and the R factor for critical quality calculated from this are stored in storage areas 33B and 33C, respectively, as functions of the void fraction and exposure in tabular form or by fitting. In some cases, the local power distribution in infinite lattice which is stored in storage area 33B may be the local power of all the fuel rods in each of the fuel segments. Usually, however, the position, exposure, and void fraction points, etc., of several representative fuel rods or large local power in infinite lattice found by the fuel assembly design calculation are stored and the largest values of these are taken as the thermally most limiting local power of fuel rods of each of the fuel segments. The various parameters from reactor core monitoring means 31 are input to a core performance determining means 32 which determines the global power distribution of the core 30. The global power distribution, and consequently the channel power distribution, in a BWR core are determined by solving coupled nuclear thermal-hydraulics equations. Next, a core neutron diffusion determining means 34 determines the difference of thermal neutron flux between the thermal neutron flux at the position of a fuel rod and the thermal neutron flux in infinite lattice in a fuel segment under consideration, of the various fuel segments in reactor core 30. This core neutron from nuclear constant storage area 33A and the global power distribution from core performance determining means 32 Of all the fuel segments whose global power distribution obtained by core performance determining means 32 is indicated, a particular fuel segment is selected for consideration. The diffusion equation for thermal neutron flux of a system wherein each of the fuel segments is homogenized is then solved in a two-dimensional region defined in the core and constituted of the fuel segment under consideration and the neighboring fuel segments surrounding it. This diffusion equation is expressed by the following equation (4) by a two-group neutron diffusion model, where the first group is the fast group and the second group is the thermal group. EQU -v.sup.2 .PSI.+K.sup.2 .PSI.=K.sup.2 F.PHI. . . . (4) where .PSI. is the thermal neutron flux PA1 .gradient..sup.2 is the Laplace operator, and EQU K.sup.2 =S/D; . . . (5) PA1 F is the average spectral index of the fuel segment in infinite lattice, PA1 .PHI. is the average fast neutron flux of the fuel segment, PA1 S is the average macroscopic removal area, and PA1 D is the average diffusion coefficient of the fuel segment for thermal neutrons. PA1 .delta.P(x,y)=the change in local power distribution and PA1 .delta.P.sub.av =the average change in local power distribution. and where The spectral index F is defined as the ratio of the thermal neutron flux to the fast neutron flux. In equations (4) and (5), the composition in a fuel segment is assumed to be homogeneous. For the nuclear constants, the fuel segment average values obtained by the design calculation of the fuel assembly in infinite lattice are used. Also, the fast neutron flux .PHI. is assumed to be spatially flat within a fuel segment. F.PHI. on the right-hand side in equation (4) expresses the thermal neutron flux when there is no gradient of the thermal neutrons, i.e., in the case of a homogenized infinite lattice. This is provisionally called the asymptotic thermal neutron flux. Diffusion equation (4) is a partial differential equation and can usually be solved numerically by a finite difference method. An example of such a method is given in: L. A. Hageman; "Numerical Methods and Techniques used in the Two-Dimensional Neutron-Diffusion Program PDQ-5", WAPD-TM-364 (1963). The boundary conditions used are the conditions of outer boundary mirror symmetry of the regions defined within the core and the four-side periodic boundary condition, etc. These boundary conditions do not strictly hold, but, in a narrow region such as is in question, it is justifiable to regard the fast neutron flux as practically uniform and the thermal neutron flux as becoming an asymptotic value at a distance of about 1/2 of one side of a fuel segment, so the neutron flux distribution can be obtained with sufficient accuracy for this purpose by these boundary conditions. In order to shorten the calculation time, diffusion equation (4) can be solved analytically under the approximation of fixed boundary conditions. An example of such a method of solution is disclosed in Early Japanese Patent Publication Sho. 62-106396 "Device for Monitoring Local Power Peaking Coefficient". In this method of solution, in ordinary light water reactor fuel, the effect of adjacent fuel segments on the value of the thermal neutron flux decreases with the distance r from the boundary with the adjacent fuel segment practically in the form exp(-Kr) and becomes a practically negligible magnitude at about 1/2 of the fuel segment width. Using this to specify an approximate boundary condition, the difference between the thermal neutron flux at fuel rod position (x,y) in a fuel segment and the asymptotic thermal neutron flux F.PHI. is given by equation (6). ##EQU1## where, as shown in FIG. 2, A.sub.O indicates the fuel segment under consideration and A.sub.1 to A.sub.4 indicate the four fuel segments adjacently facing this fuel segment A.sub.O in the radial direction. Also in equation (6), ##EQU2## indicates the sum of the variables F.sub.n and r.sub.n (n=1 to 4) for these fuel segments A.sub.1 to A.sub.4, and r.sub.n is the length of a perpendicular dropped from a fuel rod at a position (x,y) in fuel segment A.sub.O under consideration onto the boundary line with the adjacent fuel segment A.sub.n (n=1 to 4). F.sub.O is the average spectral index of the fuel segment under consideration, and F.sub.n is the average spectral index of the respective adjacent fuel segments A.sub.n (n=1 to 4). In equation (6) the effect of the fuel segments A.sub.5 to A.sub.8 that are diagonally adjacent to the fuel segment in question is neglected, but, if greater accuracy is required, an analytic solution can be obtained by the following equation using boundary conditions taking into account the effects of these fuel segments A.sub.5 to A.sub.8. ##EQU3## Here, the subscript m indicates the two respective facing adjacent fuel segments A.sub.m on both sides of fuel segments A.sub.5 to A.sub.8 that are diagonally adjacent fuel segment A.sub.O under consideration. For example, in the case of fuel segment A.sub.5 that is diagonally adjacent fuel segment A.sub.O, the two fuel segments A.sub.1 and A.sub.4 correspond to A.sub.m. .delta.F.sub.n (n=1 to 8) indicates the values of the change from the asymptotic spectrum of the spectrum at points (indicated by solid black circles) on the boundary of fuel segment A.sub.O of FIG. 2. Equation (7) is one type of approximate analytical solution of equation (4), and has the following desirable features. (1) At the center of the fuel segment the thermal neutron flux approaches the asymptotic value. That is, .delta. .PSI. approaches O. (2) At the mid-point of the side of the fuel segment and at the apex, equation (7) satisfies the asymptotic boundary values given by equations (8) and (9). (3) On the line linking the centers of the two fuel segments that are facing and adjacent each other (indicated by a broken line in FIG. 2), the thermal neutron flux approaches the solution of the one-dimensional diffusion equation on this line. It has been confirmed by numerical experiment that the deviation .delta..PSI.(x,y) of the thermal neutron flux at a fuel rod position (x,y) in a fuel segment and the asymptotic thermal neutron flux F.PHI. shows good agreement with the change of the thermal neutron flux distribution from infinite lattice obtained by heterogeneous calculation. Thus the neutron flux deviation .delta..PSI.(x,y) determined by core neutron diffusion determining means 34 is input to a local power distribution determining means 35 that finds the local power distribution within the fuel segment in question. Local power distribution determining means 35 determines the local power distribution within fuel segment A.sub.O in question, using the neutron flux deviation .delta..PSI.(x,y) and local power distribution P.sub..infin. (x,y) in infinite lattice stored in local power distribution storage area 33B. The local power distribution P.sub..infin. in infinite lattice is indicated by the following equation. EQU P.sub..infin. (x,y)=S.sub.fl .PHI..sub..infin. +S.sub.f2 .PSI..sub..infin.. . . (10) where p is normalized such that its average is 1.0. The subscript .infin. indicates the value in infinite lattice. S.sub.fl indicates the first group fission cross-section and S.sub.f2 indicates the second group fission cross-section. The local power distribution in a system that is subject to the effects of adjacent fuel segments is indicated by the following equation: EQU [P.sub.28 (x,y)+P(x,y)]/(1+.delta.P.sub.av) . . . (11) where Since practically all the contributions to the power distribution are produced by the thermal group, from equation (10): EQU .delta.P(x,y)=S.sub.fz .delta..PSI.(x,y)=[P.sub.28 (x,y)/.PSI..sub.28 (x,y) . . . (12) If this is substituted in equation (11) and second-order terms in .delta. are neglected, ##EQU4## Thus, within the two-dimensional region defined within the core and constituted by fuel segment A.sub.O under consideration and the neighboring fuel segments surrounding it, the local power distribution taking into account the effect of adjacent fuel segments is obtained using the thermal neutron flux deviation .delta..PSI.(x,y) and local power distribution P.sub.28 (x,y) in infinite lattice found by a neutron diffusion calculation in a system obtained by homogenizing these respective fuel segments. The local power distribution within the fuel segment A.sub.O under consideration obtained by local power distribution determining means 35 is input to an R factor correction means 36. R factor correction means 36 finds a corrected R factor from the R factor in infinite lattice and the local power distribution in segment A.sub.O under consideration obtained by local power distribution determining means 35. When the local power in infinite lattice for all the fuel rods of fuel sequent A.sub.O under consideration have been stored in local power distribution storage area 33B in infinite lattice, calculation is made, using equation (2), directly from the local power distribution obtained by local power distribution determining means 35. In contrast, if only the local power in infinite lattice of the several most thermally limiting fuel rods in fuel segment A.sub.O is stored, the solution is found approximately using the following equation, using the value R.sub.O of the R factor in infinite lattice that is stored in R factor storage area 33C and the change of local power of the most thermally limiting fuel rods. EQU R=R.sub.O +A(.differential.R/.differential.P.sub.max).delta.P.sub.max . . . (14) P.sub.max is the local power of the fuel rod that is most thermally limiting. The maximum local power peak of fuel segment A.sub.O can also be substituted for P.sub.max. The maximum local power peak is given as the maximum value of the corrected values determined by local power distribution determining means 35, of the local power in infinite lattice of the several most thermally limiting fuel rods that are stored. Also, the coefficient A in equation (14) is a correction coefficient that depends on the position of generation of P.sub.max in the assembly. The thus-obtained corrected R factor is input to a critical power ratio determining means 37. Critical power ratio determining means 37 determines the critical power ratio based on the corrected R factor obtained from R factor correction means 36. The critical power ratio is output to a reactor core status indicator 38 which produces a representation of the status of each of the fuel segments 21 of the reactor core 30. FIG. 5 shows a display of the reactor core status indicator according to the invention in which the various fuel segments may be represented by a group of pixels, and various critical power ratios can be assigned a corresponding color. The display includes a core map of the reactor core on the left hand portion where the channels, i.e. the fuel assemblies are displayed according to the calculated CPR value. In the lower right corner, ranges of CPR are assigned a particular color (shown by shading in FIG. 5). The ten most limiting channels are listed in the upper right portion of the screen along with their corresponding positions in the core map. In the case where the CPR has fallen below a particular range, control rods (shown by a cross symbol) have been inserted to avoid possible burn-out of the fuel rods. Thus, the status of the reactor core can be instantly and continuously provided to an operator, thereby giving warning of any undesirable conditions of any danger of burn-out of the fuel rods. As shown in FIG. 1, the critical power ratio determining means 37 provides data which is fed back to reactor core monitor and control means 31. In the event that the determined CPR falls below a predetermined value, the power of the reactor core must be reduced to avoid a boiling transition. Upon receipt of a signal indicating that the CPR has fallen below a predetermined threshold, the reactor core monitor and control means 31 then carries out insertion of control rods 25 to reduce the power and thereby avoid a boiling transition. The controller of the monitor and control means 31 activates the moving apparatus to position the appropriate control rods 25 at the required positions. The reactor core monitoring method according to the invention will be described in relation to FIG. 6. In step 60, nuclear constants in infinite lattice, a local power distribution in infinite lattice and R factor in infinite lattice are stored. In step 61, the core state parameters of the reactor core are monitored which are used to determine a global power distribution (step 62). Using the global power distribution and the stored nuclear constants, a deviation between the thermal neutron flux in a fuel rod position in the selected fuel segment and a thermal neutron flux in infinite lattice for the selected fuel segment is determined in step 63. In step 64, a local power distribution of the selected fuel segment is determined based on the thermal neutron flux deviation and the stored local power distribution in infinite lattice. A corrected R factor is determined in step 65 based on the stored R factor in infinite lattice and the local power distribution in the selected fuel segment. In step 66, the CPR is determined based upon the corrected R factor. It is determined in step 67 whether the CPR falls below a predetermined threshold. If the CPR falls below the threshold, the positions of the control rods of the reactor core are adjusted to the appropriate positions to avoid a boiling transition (step 67). Next, as an example, the R factors found by the invention will be compared with the R factors found by a monitoring apparatus which uses an infinite lattice and a monitoring apparatus which finds R factors using a two-dimensional diffusion calculation in four fuel segments. FIG. 7 shows a fuel segment arrangement used in two-dimensional calculation in four fuel segments. The fuel segments are numbered A.sub.1, A.sub.2, . . . A.sub.16, beginning from the bottom leftmost segment. The four fuel segments which will now be considered are fuel segments A.sub.6, A.sub.7, A.sub.10 and A.sub.11 disposed in the middle region. The other fuel segments constitute a boundary layer. FIG. 8 shows the arrangement of fuel types of the respective fuel segments in the fuel segment arrangement shown in FIG. 7. It is assumed that fuel type I is a low enriched fuel of average enrichment 1.3 w/o, fuel type II is a medium enriched fuel of average enrichment 2.4 w/o, and fuel type III is a high enriched fuel of average enrichment 3.3 w/o. All the fuel types have a fuel rod enrichment distribution. It will also be assumed that fuel type II and fuel type III include gadolinia-containing fuel rods. It will further be assumed that the control rod is not inserted. FIG. 9 is a plot showing a comparison of the results of an R-factor determination according to this invention, a two-dimensional diffusion calculation in four fuel segments, and a calculation in infinite lattice, for low enrichment fuel type I, medium enrichment fuel type II, and high enrichment fuel type III. The void fraction is 40% for fuel type I, II, and III. FIG. 10 shows a case where the void fraction of fuel type I is 40%, and the void fraction of fuel types II and III is 70%. In FIG. 9 and FIG. 10, the calculations in infinite lattice are indicated by a triangle symbol, while the two-dimensional diffusion calculation in four fuel segments is indicated by a solid black circle. The R factor of the system according to this invention in which the local power of all the fuel rods is stored is indicated by an open circle, and that when equation (14) is used, in which only the local power in infinite lattice of the several most thermally limiting fuel rods is stored, is indicated by X, respectively. However, in the local power distribution determination according to the invention, the method of equation (7) is employed, in which the power distribution is found analytically for the sight fuel segments adjacent to the fuel segment under consideration. Usually, if the R factor is increased by 0.1, the CPR drops by about 0.25 and the thermal margin is decreased. However, from FIG. 9 and FIG. 10, it can be seen that, due to enrichment mismatch, resulting in spectral mismatch, between the fuel segments, the R factor in the medium enrichment fuel and high enrichment fuel is increased by an amount in the range about 0.02-0.05 from the value in infinite lattice. In contrast, in the system according to the invention, in which the local power of all fuel rods is stored, it can be seen that the R factor can be determined with an error of better than 1%, irrespective of fuel type. Also, even in the case of a system wherein only the local power in infinite lattice of the several most thermally limiting fuel rods is stored, notwithstanding that the error is somewhat larger in the case of the medium enrichment fuel, it can be seen that the R factor can be calculated with an average error of better than 1%. As an example, calculated CPR for a representative BWR core is shown in FIG. 11. FIG. 11 illustrates one quarter of the BWR core where the operating limiting CPR threshold is 1.20. The fuel assemblies here are shown arranged in 15 columns and 15 rows for a BWR core having fuel assemblies arranged in a matrix having 30 columns and 30 rows (and correspond to the core map which is displayed in FIG. 5). As described above, with the reactor core monitoring system according to the invention, the benefit is obtained that the critical power can be determined with high accuracy solely from the results of a single fuel segment nuclear calculation, even when there is a large degree of spectral mismatch between fuel segments. Thus, control of the reactor core 30 is enhanced and an undesirable boiling transition can be avoided by inserting control rods 25 when the CPR falls below a predetermined threshold. Obviously, numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.