Calculation method for uranium-plutonium ratio and isotope ratio of spent fuel assembly of pressurized water reactor

Abstract

The present invention is a method for calculating the uranium-plutonium ratio and isotope ratio of a pressurized water reactor spent fuel assembly, including: determining the burnup depth BU of the spent fuel assembly to be analyzed; according to the uranium-plutonium ratio polynomial calculation formula PUU = a r ×BU 3 +b r ×BU 2 +c r ×BU + d r calculating the uranium-plutonium ratio; according to the uranium isotope ratio polynomial calculation formula U = a u ×BU 3 +b u ×BU 2 +c u ×BU + d u calculating the uranium isotope ratio; according to the plutonium isotope ratio polynomial fitting formula Pu = a pu ×BU 3 +b pu ×BU 2 +c pu ×BU + d pu calculating the plutonium isotope ratio; the uranium-plutonium ratio and isotope ratio values can be directly deduced based on the information of the initial enrichment degree and burnup depth of the spent fuel; after determining each polynomial calculation formula, the calculation results at other burnup points can be obtained, which is fast and convenient.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclide calculation, and particularly relates to a method for calculating the uranium-plutonium ratio and isotope ratio of a pressurized water reactor spent fuel assembly. Background Art

[0002] Currently, the main pressurized water reactors generally use fuel assemblies with uranium dioxide pellets. After the fuel assemblies experience a certain irradiation history in the reactor, they are discharged from the core and become spent fuel. The source term in the spent fuel assembly is an important parameter in reactor physics design and shielding design. The source term of the spent fuel assembly can be calculated using a burnup code for more accurate analysis and research. For actinide nuclides such as uranium and plutonium, a component burnup code for reactor physics design is generally used, and for more fission product nuclides, some common depletion codes can be used for calculation. At the same time, in some estimations of the nuclear fuel cycle, parameters such as the uranium-plutonium ratio, the remaining enrichment of uranium, and the plutonium isotope ratio in the fuel are also concerned. In this application scenario, estimations need to be carried out for a large number of spent fuel assemblies. Therefore, a method for quickly calculating the uranium-plutonium ratio and isotope ratio of a pressurized water reactor spent fuel assembly is required. Summary of the Invention

[0003] Aiming at the defects existing in the prior art, the purpose of the present invention is to provide a method for calculating the uranium-plutonium ratio and isotope ratio of a pressurized water reactor spent fuel assembly.

[0004] To achieve the above object, the technical solution adopted by the present invention is: a method for calculating the uranium-plutonium ratio and isotope ratio of a pressurized water reactor spent fuel assembly, comprising the following steps:

[0005] Determine the burnup depth BU of the spent fuel assembly to be analyzed;

[0006] According to the uranium-plutonium ratio polynomial calculation formula PUU = a r ×BU 3 +b r ×BU 2 +c r ×BU + d r Calculate the uranium-plutonium ratio;

[0007] According to the uranium isotope ratio polynomial calculation formula U = a u ×BU 3 +b u ×BU 2 +c u ×BU + d u Calculate the uranium isotope ratio;

[0008] According to the plutonium isotope ratio polynomial fitting formula Pu = a pu ×BU 3 +b pu ×BU2 +c pu ×BU + d pu The plutonium isotope ratio is calculated;

[0009] where a r , b r , c r and d r are the coefficients of the polynomial calculation formula for the uranium - plutonium ratio respectively, a u , b u , c u and d u are the coefficients of the polynomial calculation formula for the uranium isotope ratio respectively, a pu , b pu , c pu and d pu are the coefficients of the polynomial calculation formula for the plutonium isotope ratio respectively, PUU is the uranium - plutonium ratio, U is the uranium isotope ratio, and Pu is the plutonium isotope ratio.

[0010] Furthermore, to obtain a r , b r , c r and d r specifically includes the following steps:

[0011] Determine the initial enrichment E of the spent fuel assembly to be analyzed;

[0012] According to the coefficient polynomial calculation formula a r a r = a r1 ×E 2 + a r2 ×E + a r3 calculate the value of a r ;

[0013] According to the coefficient polynomial calculation formula b r b r = b r1 ×E 2 + b r2 ×E + b r3 calculate the value of b r ;

[0014] According to the coefficient polynomial calculation formula c r c r = c r1 ×E 2 + c r2 ×E + c r3 calculate the value of c r ;

[0015] According to the coefficient polynomial calculation formula d r d r= d r1 × E 2 + d r2 × E + d r3 Calculate to obtain the value of d r ;

[0016] Among them, a r1 , a r2 and a r3 are respectively the coefficients of the coefficient polynomial calculation formula of a r , b r1 , b r2 and b r3 are respectively the coefficients of the coefficient polynomial calculation formula of b r , c r1 , c r2 and c r3 are respectively the coefficients of the coefficient polynomial calculation formula of c r , d r1 , d r2 and d r3 are respectively the coefficients of the coefficient polynomial calculation formula of d r , and E is the initial enrichment degree.

[0017] Furthermore, obtaining the coefficients of each item of the coefficient polynomial calculation formula of a r , the coefficients of each item of the coefficient polynomial calculation formula of b r , the coefficients of each item of the coefficient polynomial calculation formula of c r and the coefficients of each item of the coefficient polynomial calculation formula of d r specifically includes the following steps:

[0018] Use the component burnup program to calculate the multi-group burnup depth BU of the spent fuel assembly, the multi-group initial enrichment degree E, and the corresponding multi-group uranium-plutonium ratio PUU;

[0019] Substitute the multi-group different burnup depths BU and the corresponding multi-group uranium-plutonium ratios PUU into the uranium-plutonium ratio polynomial calculation formula PUU = a r × BU 3 + b r × BU 2 + c r × BU + d r to fit and obtain the coefficients a r , b r , c r and d r ;

[0020] Substitute the multi-group initial enrichment degrees E and the corresponding values of a r into the coefficient polynomial calculation formula of a r a r = a r1 × E2 +a r2 ×E + a r3 to fit and obtain the coefficients a r1 、a r2 and a r3 ;

[0021] Substitute multiple sets of initial enrichment degrees E and the corresponding b r values into the coefficient polynomial calculation formula for b r b r = b r1 ×E 2 + b r2 ×E + b r3 to fit and obtain the coefficients b r1 、b r2 and b r3 ;

[0022] Substitute multiple sets of initial enrichment degrees E and the corresponding c r values into the coefficient polynomial calculation formula for c r c r = c r1 ×E 2 + c r2 ×E + c r3 to fit and obtain the coefficients c r1 、c r2 and c r3 ;

[0023] Substitute multiple sets of initial enrichment degrees E and the corresponding d r values into the coefficient polynomial calculation formula for d r d r = d r1 ×E 2 + d r2 ×E + d r3 to fit and obtain the coefficients d r1 、d r2 and d r3 .

[0024] Furthermore, obtaining a u 、b u 、c u and d u specifically includes the following steps:

[0025] Determine the initial enrichment degree E of the spent fuel assembly to be analyzed;

[0026] According to the coefficient polynomial calculation formula for a u a u = a u2 ×E 2 + a u3 ×E + a u4Calculate to obtain the value of a u ;

[0027] According to b u Coefficient polynomial calculation formula for b u = b u2 ×E 2 + b u3 ×E + b u4 Calculate to obtain the value of b u ;

[0028] According to c u Coefficient polynomial calculation formula for c u = c u1 ×E 3 + c u2 ×E 2 + c u3 ×E + c u4 Calculate to obtain the value of c u ;

[0029] According to d u Coefficient polynomial calculation formula for d u = d u1 ×E + d u2 Calculate to obtain the value of d u ;

[0030] Among them, a u2 , a u3 and a u4 are respectively the coefficients of the coefficient polynomial calculation formula for a u , b u2 , b u3 and b u4 are respectively the coefficients of the coefficient polynomial calculation formula for b u , c u1 , c u2 , c u3 and c u4 are respectively the coefficients of the coefficient polynomial calculation formula for c u , d u1 and d u2 are respectively the coefficients of the coefficient polynomial calculation formula for d u , and E is the initial enrichment degree.

[0031] Furthermore, obtaining the coefficients of each item of the coefficient polynomial calculation formula for a u , the coefficients of each item of the coefficient polynomial calculation formula for b u , the coefficients of each item of the coefficient polynomial calculation formula for c u , and the coefficients of each item of the coefficient polynomial calculation formula for d u specifically includes the following steps:

[0032] The multi-group burnup depth BU, multi-group initial enrichment E, and corresponding multi-group uranium isotope ratios U of spent fuel assemblies are calculated using a component burnup program.

[0033] Substitute the multi-group different burnup depths BU and the corresponding multi-group uranium isotope ratios U into the uranium isotope ratio polynomial calculation formula U = a u ×BU 3 +b u ×BU 2 +c u ×BU + d u to obtain the coefficients a u , b u , c u , and d u fitted.

[0034] Substitute the multi-group initial enrichment E and the corresponding values of a u into the a u coefficient polynomial calculation formula a u = a u2 ×E 2 + a u3 ×E + a u4 to obtain the coefficients a u2 , a u3 , and a u4 fitted.

[0035] Substitute the multi-group initial enrichment E and the corresponding values of b u into the b u coefficient polynomial calculation formula b u = b u2 ×E 2 + b u3 ×E + b u4 to obtain the coefficients b u2 , b u3 , and b u4 fitted.

[0036] Substitute the multi-group initial enrichment E and the corresponding values of c u into the c u coefficient polynomial calculation formula c u = c u1 ×E 3 + c u2 ×E 2 + c u3 ×E + c u4 to obtain the coefficients c u1 , c u2 , c u3 , and c u4 fitted.

[0037] Substitute multiple groups of initial enrichment degrees E and the corresponding d u values into d u Coefficient polynomial calculation formula d u = d u1 ×E + d u2 to fit and obtain each coefficient d u1 and d u2 .

[0038] Furthermore, obtain a pu , b pu , c pu and d pu Specifically, it includes the following steps:

[0039] Determine the initial enrichment degree E of the spent fuel assembly to be analyzed;

[0040] According to a pu Coefficient polynomial calculation formula a pu = a pu1 ×E 2 + a pu2 ×E + a pu3 Calculate the value of a pu ;

[0041] According to b pu Coefficient polynomial calculation formula b pu = b pu1 ×E 2 + b pu2 ×E + b pu3 Calculate the value of b pu ;

[0042] According to c pu Coefficient polynomial calculation formula c pu = c pu1 ×E 2 + c pu2 ×E + c pu3 Calculate the value of c pu ;

[0043] According to d pu Coefficient polynomial calculation formula Calculate the value of d pu ;

[0044] Among them, a pu1 , a pu2 and a pu3 are respectively the coefficients of the a pu coefficient polynomial calculation formula, b pu1 , b pu2 and b pu3 are respectively the coefficients of the b pu coefficient polynomial calculation formula, cpu1 and c pu2 and c pu3 are the coefficients of the coefficient polynomial calculation formula for c pu respectively, d pu1 and d pu2 are the coefficients of the coefficient polynomial calculation formula for d pu respectively, and E is the initial enrichment degree.

[0045] Furthermore, obtaining the coefficients of each term of the coefficient polynomial calculation formula for a pu , the coefficients of each term of the coefficient polynomial calculation formula for b pu , the coefficients of each term of the coefficient polynomial calculation formula for c pu , the coefficients of each term of the coefficient polynomial calculation formula for d pu specifically includes the following steps:

[0046] Using the component burnup program to calculate the multi-group burnup depth BU of the spent fuel assembly, the multi-group initial enrichment degree E, and the corresponding multi-group plutonium isotope ratios Pu;

[0047] Substituting the multi-group different burnup depths BU and the corresponding multi-group plutonium isotope ratios Pu into the plutonium isotope ratio polynomial calculation formula Pu = a pu ×BU 3 +b pu ×BU 2 +c pu ×BU + d pu to fit and obtain the coefficients a pu , b pu , c pu and d pu ;

[0048] Substituting the multi-group initial enrichment degrees E and the corresponding values of a pu into the coefficient polynomial calculation formula for a pu a pu = a pu1 ×E 2 +a pu2 ×E + a pu3 to fit and obtain the coefficients a pu1 , a pu2 and a pu3 ;

[0049] Substituting the multi-group initial enrichment degrees E and the corresponding values of b pu into the coefficient polynomial calculation formula for b pu b pu = b pu1 ×E 2 +b pu2 ×E + b pu3 to fit and obtain the coefficients b pu1, b pu2 and b pu3 ;

[0050] Substitute multiple sets of initial enrichment degrees E and the corresponding c pu value into the c pu coefficient polynomial calculation formula c pu = c pu1 ×E 2 + c pu2 ×E + c pu3 to fit and obtain each coefficient c pu1 , c pu2 and c pu3 ;

[0051] Substitute multiple sets of initial enrichment degrees E and the corresponding d pu value into the d pu coefficient polynomial calculation formula to fit and obtain each coefficient d pu1 and d pu2 .

[0052] The method for calculating the uranium - plutonium ratio and isotope ratio of the pressurized water reactor spent fuel assembly provided by the present invention has the beneficial effects as follows:

[0053] First, based on the analysis of the source terms of uranium and plutonium nuclides in the spent fuel assembly, the uranium nuclide decreases with the increase of burn - up depth, and the plutonium nuclide increases with the increase of burn - up depth, showing a certain regularity. Fuel assemblies with different initial enrichment degrees all exhibit such characteristics. Therefore, the uranium - plutonium ratio and isotope ratio values can be directly deduced according to the information of the initial enrichment degree and burn - up depth of the spent fuel;

[0054] Second, after determining each polynomial calculation formula, the calculation results at other burn - up points can be obtained, which is fast and convenient. This method can be coupled into some calculation programs for estimating nuclear fuel cycle parameters to provide a lightweight calculation module. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flowchart of the method for calculating the uranium - plutonium ratio and isotope ratio of the pressurized water reactor spent fuel assembly of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0056] The present invention will be further described below in conjunction with the drawings and specific embodiments.

[0057] Embodiment 1

[0058] As Figure 1 shown, this embodiment discloses a method for calculating the uranium - plutonium ratio and isotope ratio of a pressurized water reactor spent fuel assembly, including the following steps:

[0059] Determine the burnup depth BU of the spent fuel assembly to be analyzed;

[0060] According to the uranium-plutonium ratio polynomial calculation formula PUU = a r ×BU 3 +b r ×BU 2 +c r ×BU + d, calculate the uranium-plutonium ratio;

[0061] According to the uranium isotope ratio polynomial calculation formula U = a u ×BU 3 +b u ×BU 2 +c u ×BU + d u calculate the uranium isotope ratio;

[0062] According to the plutonium isotope ratio polynomial fitting formula Pu = a pu ×BU 3 +b pu ×BU 2 +c pu ×BU + d pu calculate the plutonium isotope ratio;

[0063] where a r , b r , c r and d r are the coefficients of the uranium-plutonium ratio polynomial calculation formula respectively, a u , b u , c u and d u are the coefficients of the uranium isotope ratio polynomial calculation formula respectively, a pu , b pu , c pu and d pu are the coefficients of the plutonium isotope ratio polynomial calculation formula respectively, PUU is the uranium-plutonium ratio, U is the uranium isotope ratio, and Pu is the plutonium isotope ratio.

[0064] Furthermore, obtaining a r , b r , c r and d r specifically includes the following steps:

[0065] Determine the initial enrichment E of the spent fuel assembly to be analyzed;

[0066] According to the a r coefficient polynomial calculation formula a r = a r1 ×E 2 +a r2 ×E + ar3 Calculate to obtain the value of a r ;

[0067] According to b r Coefficient polynomial calculation formula b r = b r1 ×E 2 + b r2 ×E + b r3 Calculate to obtain the value of b r ;

[0068] According to c r Coefficient polynomial calculation formula c r = c r1 ×E 2 + c r2 ×E + c r3 Calculate to obtain the value of c r ;

[0069] According to d r Coefficient polynomial calculation formula d r = d r1 ×E 2 + d r2 ×E + d r3 Calculate to obtain the value of d r ;

[0070] Among them, a r1 , a r2 and a r3 are respectively the coefficients of the coefficient polynomial calculation formula of a r , b r1 , b r2 and b r3 are respectively the coefficients of the coefficient polynomial calculation formula of b r , c r1 , c r2 and c r3 are respectively the coefficients of the coefficient polynomial calculation formula of c r , d r1 , d r2 and d r3 are respectively the coefficients of the coefficient polynomial calculation formula of d r , and E is the initial enrichment degree.

[0071] Furthermore, obtaining the coefficients of each item of the coefficient polynomial calculation formula of a r , the coefficients of each item of the coefficient polynomial calculation formula of b r , the coefficients of each item of the coefficient polynomial calculation formula of c r , and the coefficients of each item of the coefficient polynomial calculation formula of d r Specifically includes the following steps:

[0072] The multi-group burnup depth BU, multi-group initial enrichment E, and corresponding multi-group uranium-plutonium ratios PUU of the spent fuel assembly are calculated using a component burnup program: In this embodiment, the component burnup program is the CASMO calculation program. Of course, other programs with component burnup calculation functions can also be used.

[0073] Substitute multiple different burnup depths BU and the corresponding multi-group uranium-plutonium ratios PUU into the uranium-plutonium ratio polynomial calculation formula PUU = a r ×BU 3 +b r ×BU 2 +c r ×BU + d r to obtain the coefficients a r , b r , c r and d r ;

[0074] Substitute multiple initial enrichments E and the corresponding values of a r into the a r coefficient polynomial calculation formula a r = a r1 ×E 2 + a r2 ×E + a r3 to obtain the coefficients a r1 , a r2 and a r3 ;

[0075] Substitute multiple initial enrichments E and the corresponding values of b r into the b r coefficient polynomial calculation formula b r = b r1 ×E 2 + b r2 ×E + b r3 to obtain the coefficients b r1 , b r2 and b r3 ;

[0076] Substitute multiple initial enrichments E and the corresponding values of c r into the c r coefficient polynomial calculation formula c r = c r1 ×E 2 + c r2 ×E + c r3 to obtain the coefficients c r1 , c r2 and c r3 ;

[0077] Substitute multiple sets of initial enrichment degrees E and the corresponding d r values into d r coefficient polynomial calculation formula d r = d r1 ×E 2 + d r2 ×E + d r3 to fit and obtain each coefficient d r1 、d r2 and d r3 .

[0078] Furthermore, obtain a u 、b u 、c u and d u Specifically, it includes the following steps:

[0079] Determine the initial enrichment degree E of the spent fuel assembly to be analyzed;

[0080] According to a u coefficient polynomial calculation formula a u = a u2 ×E 2 + a u3 ×E + a u4 calculate the value of a u ;

[0081] According to b u coefficient polynomial calculation formula b u = b u2 ×E 2 + b u3 ×E + b u4 calculate the value of b u ;

[0082] According to c u coefficient polynomial calculation formula c u = c u1 ×E 3 + c u2 ×E 2 + c u3 ×E + c u4 calculate the value of c u ;

[0083] According to d u coefficient polynomial calculation formula d u = d u1 ×E + d u2 calculate the value of d u ;

[0084] Among them, a u2 、a u3 and a u4 are respectively au The coefficient, b, of the coefficient polynomial calculation formula u2 , b u3 and b u4 are respectively the coefficients, c u of the coefficient polynomial calculation formula u1 , c u2 , c u3 and c u4 are respectively the coefficients, d u of the coefficient polynomial calculation formula u1 and d u2 are respectively the coefficients, d u of the coefficient polynomial calculation formula, and E is the initial enrichment degree.

[0085] Furthermore, the coefficients of each term of the a u coefficient polynomial calculation formula, b u coefficient polynomial calculation formula, c u coefficient polynomial calculation formula, and d u coefficient polynomial calculation formula are specifically obtained through the following steps:

[0086] Use the component burnup program to calculate the multi-group burnup depth BU of the spent fuel assembly, the multi-group initial enrichment degree E, and the corresponding multi-group uranium isotope ratios U;

[0087] Substitute the multi-group different burnup depths BU and the corresponding multi-group uranium isotope ratios U into the uranium isotope ratio polynomial calculation formula U = a u ×BU 3 +b u ×BU 2 +c u ×BU + d u to fit and obtain the coefficients a u , b u , c u and d u ;

[0088] Substitute the multi-group initial enrichment degrees E and the corresponding a u values into the a u coefficient polynomial calculation formula a u = a u2 ×E 2 +a u3 ×E + a u4 to fit and obtain the coefficients a u2 , a u3 and a u4 ;

[0089] Substitute the multi-group initial enrichment degrees E and the corresponding b u values into bu Coefficient polynomial calculation formula b u = b u2 ×E 2 + b u3 ×E + b u4 The coefficients b u2 , b u3 and b u4 ;

[0090] Substitute multiple sets of initial enrichments E and the corresponding c u values into the c u Coefficient polynomial calculation formula c u = c u1 ×E 3 + c u2 ×E 2 + c u3 ×E + c u4 The coefficients c u1 , c u2 , c u3 and c u4 ;

[0091] Substitute multiple sets of initial enrichments E and the corresponding d u values into the d u Coefficient polynomial calculation formula d u = d u1 ×E + d u2 The coefficients d u1 and d u2 .

[0092] Furthermore, obtaining a pu , b pu , c pu and d pu Specifically includes the following steps:

[0093] Determine the initial enrichment E of the spent fuel assembly to be analyzed;

[0094] According to the a pu Coefficient polynomial calculation formula a pu = a pu1 ×E 2 + a pu2 ×E + a pu3 Calculate the value of a pu ;

[0095] According to the b pu Coefficient polynomial calculation formula b pu = b pu1 ×E 2 + b pu2 ×E + b pu3 Calculate bpu value;

[0096] According to c pu Coefficient polynomial calculation formula c pu = c pu1 × E 2 + c pu2 × E + c pu3 Calculate to obtain the value of c pu value;

[0097] According to d pu Coefficient polynomial calculation formula Calculate to obtain the value of d pu value;

[0098] where a pu1 , a pu2 and a pu3 are respectively the coefficients of the a pu coefficient polynomial calculation formula, b pu1 , b pu2 and b pu3 are respectively the coefficients of the b pu coefficient polynomial calculation formula, c pu1 , c pu2 and c pu3 are respectively the coefficients of the c pu coefficient polynomial calculation formula, d pu1 and d pu2 are respectively the coefficients of the d pu coefficient polynomial calculation formula, and E is the initial enrichment.

[0099] Furthermore, obtaining the coefficients of each item of the a pu coefficient polynomial calculation formula, b pu coefficient polynomial calculation formula, c pu coefficient polynomial calculation formula, and d pu coefficient polynomial calculation formula specifically includes the following steps:

[0100] Use the component burnup program to calculate the multi-group burnup depth BU, multi-group initial enrichment E, and the corresponding multi-group plutonium isotope ratio Pu of the spent fuel assembly;

[0101] Substitute the multi-group different burnup depths BU and the corresponding multi-group plutonium isotope ratios Pu into the plutonium isotope ratio polynomial calculation formula Pu = a pu × BU 3 + b pu × BU 2 + c pu × BU + d pu to fit and obtain the coefficients a pu , bpu , c pu and d pu ;

[0102] Substitute multiple sets of initial enrichment degrees E and the corresponding values of a pu into the coefficient polynomial calculation formula of a pu a = a pu ×E pu1 + a 2 ×E + a pu2 ×E + a pu3 to fit and obtain the coefficients a pu1 , a pu2 and a pu3 ;

[0103] Substitute multiple sets of initial enrichment degrees E and the corresponding values of b pu into the coefficient polynomial calculation formula of b pu b = b pu ×E pu1 + b 2 ×E + b pu2 ×E + b pu3 to fit and obtain the coefficients b pu1 , b pu2 and b pu3 ;

[0104] Substitute multiple sets of initial enrichment degrees E and the corresponding values of c pu into the coefficient polynomial calculation formula of c pu c = c pu ×E pu1 + c 2 ×E + c pu2 ×E + c pu3 to fit and obtain the coefficients c pu1 , c pu2 and c pu3 ;

[0105] Substitute multiple sets of initial enrichment degrees E and the corresponding values of d pu into the coefficient polynomial calculation formula of d pu to fit and obtain the coefficients d and d pu1 and d pu2 .

[0106] Next, a set of fitting formulas and their coefficients obtained from irradiated spent fuel assemblies of a typical pressurized water reactor composed of 157 quadrilateral assemblies under normal core operating conditions are as follows:

[0107] 1) For the plutonium - uranium ratio Pu / U, its fitting formula with burnup depth is PUU = a r ×BU 3 + b r ×BU2 +c r ×BU + d r

[0108] where:

[0109] a r = 3.049×10 -18 ×E 2 - 3.867×10 -17 ×E + 1.489×10 -16

[0110] b r = - 2.387×10 -13 ×E 2 + 3.442×10 -12 ×E - 1.685×10 -11

[0111] c r = 4.032×10 -9 ×E 2 - 6.718×10 -8 ×E + 6.965×10 -7

[0112] d r = 1.971×10 -5 ×E 2 - 1.836×10 -4 ×E + 4.709×10 -4

[0113] 2) For the uranium isotope ratio, taking U - 235 / U as an example, its fitting formula with burnup depth is U = a u ×BU 3 + b u ×BU 2 + c u ×BU + d u

[0114] where:

[0115] a u = - 7.389×10 -18 ×E 2 + 8.387×10 -17 ×E - 2.658×10 -16

[0116] b u = 2.124×10 -13 ×E 2 - 4.619×10 -12 ×E + 2.671×10 -11

[0117] c u =-8.793×10 -9 ×E 3 +1.131×10 -7 ×E 2 -5.0×10 -7 ×E - 3.542×10 -7

[0118] d u =1.018×10 -2 ×E - 2.787×10 -4

[0119] 3) For the plutonium isotope ratio, taking Pu - 240 / Pu as an example, its fitting formula with the burnup depth is Pu = a pu ×BU 3 +b pu ×BU 2 +c pu ×BU + d pu

[0120] Where:

[0121] a pu =2.911×10 -16 ×E 2 -2.836×10 -15 ×E + 8.767×10 -15

[0122] b pu =-2.681×10 -11 ×E 2 +2.767×10 -10 ×E - 9.438×10 -10

[0123] c pu =5.446×10 -7 ×E 2 -6.47×10 -6 ×E + 2.973×10 -5

[0124] d pu =0.0328×E -1.056

[0125] Using the above fitting formulas, the nuclide composition ratios of spent fuel with different core types and states were calculated and compared with the calculated values obtained from the assembly burnup code CASMO, as shown in Tables 1 - 4.

[0126] Table 1 Calculated values of nuclide composition ratios of a spent fuel assembly calculated by the fitting formula

[0127]

[0128]

[0129] Table 2 Calculated values of nuclide composition ratios of a spent fuel assembly calculated by the fitting formula

[0130]

[0131] Table 3 Calculated values of nuclide composition ratios of a spent fuel assembly calculated by the fitting formula

[0132]

[0133]

[0134] Table 4 Calculated values of nuclide composition ratios of a spent fuel assembly calculated by the fitting formula

[0135]

[0136] It can be seen from the above calculation results that for the calculated values under the same operating parameter conditions, the fitting formula and the program calculation are in good agreement. The ratio difference of uranium isotopes is less than 1%, and the ratios of plutonium isotopes and plutonium-uranium ratio are basically less than 5%. For different reactor types, different operating irradiation histories and some different parameters of the assembly, such as the case of containing neutron poisons, the difference between the calculated values obtained by the fitting formula and the program calculated values is also acceptable. Using the method of the present invention, corresponding formula fitting can also be carried out for similar calculation conditions, which can make the results of the fitting formula more consistent with the results of the program calculation.

[0137] Those skilled in the art should understand that the method and system of the present invention are not limited to the embodiments in the specific implementation manners. The above specific description is only for explaining the purpose of the present invention and is not used to limit the present invention. Other implementation manners obtained by those skilled in the art according to the technical solution of the present invention also belong to the scope of technical innovation of the present invention. The protection scope of the present invention is defined by the claims and their equivalents.

Claims

1. A method for calculating the uranium-plutonium ratio and isotope ratios of a pressurized water reactor spent fuel assembly, characterized in that, it includes the following steps: Determine the burnup depth BU of the spent fuel assembly to be analyzed; According to the uranium-plutonium ratio polynomial calculation formula PUU = a r × BU 3 + b r × BU 2 + c r × BU + d r The uranium-plutonium ratio is calculated; According to the polynomial calculation formula of uranium isotope ratio U = a u × BU 3 + b u × BU 2 + c u × BU+d u The uranium isotope ratio is calculated; According to the polynomial fitting formula for plutonium isotope ratio Pu = a pu × BU 3 + b pu × BU 2 + c pu × BU + d pu the plutonium isotope ratio is calculated; where a r , b r , c r and d r are the coefficients of the polynomial calculation formula for the uranium-plutonium ratio, respectively. a u 、b u 、c u and d u are the coefficients of the polynomial calculation formula for uranium isotope ratio, a pu 、b pu 、c pu and d pu are the coefficients of the polynomial calculation formula for plutonium isotope ratio, PUU is the uranium-plutonium ratio, U is the uranium isotope ratio, and Pu is the plutonium isotope ratio; Obtain a r , b r , c r and d r Specifically, it includes the following steps: Determine the initial enrichment E of the spent fuel assembly to be analyzed; According to a r Coefficient polynomial calculation formula a r = a r1 × E 2 + a r2 × E + a r3 Calculate to obtain a r value; According to b r Coefficient polynomial calculation formula b r = b r1 × E 2 + b r2 × E + b r3 Calculate to obtain the value of b r ; According to c r Coefficient polynomial calculation formula c r = c r1 × E 2 + c r2 × E + c r3 Calculate to obtain c r value; According to d r Coefficient polynomial calculation formula d r = d r1 × E 2 + d r2 × E + d r3 Calculate to obtain the value of d r ; Among them, a r1 , a r2 and a r3 are the coefficients of the coefficient polynomial calculation formula of a r respectively; b r1 , b r2 and b r3 are the coefficients of the coefficient polynomial calculation formula of b r respectively; c r1 , c r2 and c r3 are the coefficients of the coefficient polynomial calculation formula of c r respectively; d r1 , d r2 and d r3 are the coefficients of the coefficient polynomial calculation formula of d r respectively; E is the initial enrichment degree. Obtain a r The coefficients of each term in the coefficient polynomial calculation formula, b r The coefficients of each term in the coefficient polynomial calculation formula, c r The coefficients of each term in the coefficient polynomial calculation formula, and d r The specific steps for the coefficients of each term in the coefficient polynomial calculation formula are as follows: Use the assembly burnup program to calculate the multi-group burnup depth BU, multi-group initial enrichment E and the corresponding multi-group uranium-plutonium ratio PUU of the spent fuel assembly; Substitute multiple different burnup depths BU and corresponding multiple plutonium-uranium ratios PUU into the plutonium-uranium ratio polynomial calculation formula PUU = a r ×BU 3 +b r ×BU 2 +c r ×BU + d r to obtain the coefficients a r 、b r 、c r and d r ; Substitute multiple groups of initial enrichment degrees E and the corresponding values of a r into the a r coefficient polynomial calculation formula a r = a r1 ×E 2 + a r2 ×E + a r3 to fit and obtain the coefficients a r1 , a r2 and a r3 ; Substitute multiple sets of initial enrichment degrees E and the corresponding b r values into b r coefficient polynomial calculation formula b r = b r1 × E 2 + b r2 × E + b r3 to fit and obtain each coefficient b r1 、b r2 and b r3 ; Substitute multiple sets of initial enrichment degrees E and the corresponding c r values into c r Coefficient polynomial calculation formula c r = c r1 × E 2 + c r2 × E + c r3 to fit and obtain each coefficient c r1 、c r2 and c r3 ; Substitute multiple sets of initial enrichment degrees E and the corresponding d r values into d r Coefficient polynomial calculation formula d r = d r1 ×E 2 + d r2 ×E + d r3 to obtain each coefficient d r1 、d r2 and d r3 ; Obtain a u , b u , c u and d u Specifically, it includes the following steps: Determine the initial enrichment E of the spent fuel assembly to be analyzed; According to a u Coefficient polynomial calculation formula a u = a u2 × E 2 + a u3 × E + a u4 Calculate to obtain a u value; According to b u Coefficient polynomial calculation formula b u = b u2 × E 2 + b u3 × E + b u4 Calculate to obtain the value of b u ; According to c u Coefficient polynomial calculation formula c u = c u1 × E 3 + c u2 × E 2 + c u3 × E + c u4 Calculate to obtain the value of c u ; According to d u Coefficient polynomial calculation formula d u = d u1 × E + d u2 Calculate to obtain d u value; Among them, a u2 , a u3 and a u4 are the coefficients of the coefficient polynomial calculation formula of a u respectively. b u2 , b u3 and b u4 are the coefficients of the coefficient polynomial calculation formula of b u respectively. c u1 , c u2 , c u3 and c u4 are the coefficients of the coefficient polynomial calculation formula of c u respectively. d u1 and d u2 are the coefficients of the coefficient polynomial calculation formula of d u respectively. E is the initial enrichment degree; Obtain a u The coefficients of each term in the coefficient polynomial calculation formula, b u The coefficients of each term in the coefficient polynomial calculation formula, c u The coefficients of each term in the coefficient polynomial calculation formula, and d u The specific steps for the coefficients of each term in the coefficient polynomial calculation formula are as follows: Use the assembly burnup program to calculate the multi-group burnup depth BU, multi-group initial enrichment E and the corresponding multi-group uranium isotope ratios U of the spent fuel assembly; Substitute multiple different burnup depths BU and the corresponding multiple sets of uranium isotope ratios U into the uranium isotope ratio polynomial calculation formula U = a u ×BU 3 +b u ×BU 2 +c u ×BU + d u to obtain the coefficients a u 、b u 、c u and d u ; Substitute multiple sets of initial enrichment degrees E and the corresponding values of a u into a u coefficient polynomial calculation formula a u = a u2 ×E 2 + a u3 ×E + a u4 to fit and obtain each coefficient a u2 , a u3 and a u4 ; Substitute multiple sets of initial enrichment degrees E and the corresponding b u values into b u coefficient polynomial calculation formula b u =b u2 ×E 2 +b u3 ×E + b u4 to fit and obtain each coefficient b u2 , b u3 and b u4 ; Substitute multiple groups of initial enrichment degrees E and the corresponding c u values into c u Coefficient polynomial calculation formula c u = c u1 × E 3 + c u2 × E 2 + c u3 × E + c u4 to obtain each coefficient c u1 , c u2 , c u3 and c u4 ; Substitute multiple sets of initial enrichment degrees E and the corresponding d u values into d u Coefficient polynomial calculation formula d u = d u1 × E + d u2 to fit and obtain each coefficient d u1 and d u2 ; Obtain a pu , b pu , c pu and d pu Specifically, it includes the following steps: Determine the initial enrichment E of the spent fuel assembly to be analyzed; According to a pu Coefficient polynomial calculation formula a pu = a pu1 × E 2 + a pu2 × E + a pu3 Calculate to obtain a pu value; According to b pu Coefficient polynomial calculation formula b pu = b pu1 × E 2 + b pu2 × E + b pu3 Calculate to obtain the value of b pu ; According to c ou Coefficient polynomial calculation formula c ou = c ou1 × E 2 + c pu2 × E + c pu3 Calculate to obtain c pu value; According to d pu Coefficient polynomial calculation formula Calculate to obtain d pu value; Among them, a pu1 , a pu2 and a pu3 are the coefficients of the coefficient polynomial calculation formula of a pu respectively, b pu1 , b pu2 and b pu3 are the coefficients of the coefficient polynomial calculation formula of b pu respectively, c pu1 , c pu2 and c pu3 are the coefficients of the coefficient polynomial calculation formula of c pu respectively, d pu1 and d pu2 are the coefficients of the coefficient polynomial calculation formula of d pu respectively, and E is the initial enrichment degree; Obtain a pu The coefficients of each term in the coefficient polynomial calculation formula, b pu The coefficients of each term in the coefficient polynomial calculation formula, c pu The coefficients of each term in the coefficient polynomial calculation formula, and d pu The specific steps for the coefficients of each term in the coefficient polynomial calculation formula are as follows: Use the assembly burnup program to calculate the multi-group burnup depth BU, multi-group initial enrichment E and the corresponding multi-group plutonium isotope ratios Pu of the spent fuel assembly; Substitute multiple different burnup depths BU and the corresponding multiple sets of plutonium isotope ratios Pu into the plutonium isotope ratio polynomial calculation formula Pu = a pu ×BU 3 +b pu ×BU 2 +c pu ×BU + d pu to obtain the coefficients a pu 、b pu 、c pu and d pu ; Substitute multiple groups of initial enrichment degrees E and the corresponding values of a pu into the a pu coefficient polynomial calculation formula a pu = a pu1 ×E 2 + a pu2 ×E + a pu3 to obtain each coefficient a pu1 , a pu2 and a pu3 ; Substitute multiple sets of initial enrichment degrees E and the corresponding b pu values into b pu in the coefficient polynomial calculation formula b pu = b pu1 × E 2 + b pu2 × E + b pu3 to obtain each coefficient b pu1 , b pu2 and b pu3 ; Substitute multiple groups of initial enrichment degrees E and the corresponding c pu values into c pu Coefficient polynomial calculation formula c pu = c pu1 ×E 2 + c pu2 ×E + c pu3 to fit and obtain each coefficient c pu1 、c pu2 and c pu3 ; Substitute multiple groups of initial enrichment degrees E and the corresponding d pu values into d pu Coefficient polynomial calculation formula to fit and obtain each coefficient d pu1 and d pu2 .

Images