Method of Determining at Least One Technological Uncertainty Factor for Nuclear Fuel Elements, and Corresponding Methods of Designing, Fabricating, and Inspecting Nuclear Fuel Elements

Abstract

The invention relates to a method of determining at least one technological uncertainty factor in respect of nuclear fuel elements ( 23 ) as a function of variations in the production parameters of the elements ( 23 ) in relation to nominal values. The inventive method comprises a step involving the use, for at least one production parameter, of a collective variation in said parameter in relation to the nominal value within a batch of produced elements ( 23 ). The invention can be used, for example, to design, produce and check pellets for light water reactors.

1 - 12 . (canceled) 
   
   
       13 . A method of determining at least one technological uncertainty factor for nuclear fuel elements as a function of variations in fabrication parameters of the nuclear fuel elements about nominal values, the method comprising a step of:
 making use, for at least one fabrication parameter, of collective variation in the at least one fabrication parameter about a nominal value within a batch of fabricated elements.   
   
   
       14 . The method as recited in  claim 13  wherein for the at least one fabrication parameter, in addition to the collective variation, individual variation is used in the at least one fabrication parameter about a nominal value for an individual element. 
   
   
       15 . The method as recited in  claim 13  wherein the technological uncertainty factor is determined for linear power density at a hot point F Q   E . 
   
   
       16 . The method as recited in  claim 13  wherein the technological uncertainty factor is determined for a hot channel F ΔH   E1 . 
   
   
       17 . The method as recited in  claim 13  wherein the collective variation is multiplied by a macroscopic sensitivity coefficient. 
   
   
       18 . The method as recited in  claim 17  wherein an individual variation is multiplied by a microscopic sensitivity coefficient. 
   
   
       19 . The method as recited in  claim 14  wherein the technological uncertainty factor is determined for linear power density at a hot point F Q   E , the collective variation is multiplied by a macroscopic sensitivity coefficient and optionally the individual variation is multiplied by a microscopic sensitivity coefficient, and use is made of a formula of the type: 
     
       
         
           
             
               F 
               Q 
               E 
             
             = 
             
               1 
               + 
               
                 
                   1.645 
                   1.96 
                 
                  
                 
                   
                     
                       ∑ 
                       i 
                     
                      
                     
                       ( 
                       
                         
                           
                             α 
                             i 
                             2 
                           
                            
                           
                             
                               T 
                               i 
                               2 
                             
                             
                               μ 
                               i 
                               2 
                             
                           
                         
                         + 
                         
                           
                             θ 
                             i 
                             2 
                           
                            
                           
                             
                               TL 
                               i 
                               2 
                             
                             
                               μ 
                               i 
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     where T i  and TL i  respectively designate individual and collective variations in a fabrication parameter F i , and α i  and θ i  respectively designate the microscopic and the macroscopic sensitivity coefficients for the fabrication parameter, and where μ i  designates a mean for the fabrication parameter F i . 
   
   
       20 . The method as recited in  claim 14  wherein the technological uncertainty factor is determined for a hot channel F ΔH   E1 , the collective variation is multiplied by a macroscopic sensitivity coefficient and optionally the individual variation is multiplied by a microscopic sensitivity coefficient, and in which use is made of a formula of the type: 
     
       
         
           
             
               F 
               
                 Δ 
                  
                 
                     
                 
                  
                 H 
               
               
                 E 
                  
                 
                     
                 
                  
                 1 
               
             
             = 
             
               1 
               + 
               
                 
                   1.645 
                   1.96 
                 
                  
                 
                   
                     
                       ∑ 
                       i 
                     
                      
                     
                       ( 
                       
                         
                           
                             α 
                             i 
                             2 
                           
                            
                           
                             
                               TL 
                               i 
                               2 
                             
                             
                               μ 
                               i 
                               2 
                             
                           
                         
                         + 
                         
                           
                             θ 
                             i 
                             2 
                           
                            
                           
                             
                               TL 
                               i 
                               2 
                             
                             
                               μ 
                               i 
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     where TL i  designates the collective variation in a fabrication parameter F i , where α i  and θ i  designate respectively the microscopic and the macroscopic sensitivity coefficients in the fabrication parameter, and where μ i  designates a mean for the fabrication parameter F i . 
   
   
       21 . The method as recited in  claim 13  wherein the collective variation is a collective tolerance, a deviation between a mean of the real values for the fabrication parameter within a batch of elements and the nominal value being required to comply with the collective tolerance. 
   
   
       22 . The method as recited in  claim 21  wherein an individual variation is an individual tolerance, a deviation between a real value of the fabrication parameter for an individual element and a nominal value needing to comply with the individual tolerance. 
   
   
       23 . A method of designing a nuclear fuel element including a step of using a method of determining at least one technological uncertainty factor as recited in  claim 13 . 
   
   
       24 . The design method as recited in  claim 21  wherein the nuclear fuel element is required to comply with a limit value for at least one technological uncertainty factor, the method comprising the steps of:
 defining a collective fabrication tolerance at least for the fabrication parameter, a deviation between a mean of real values of the fabrication parameter in the batch of fabricated elements and the nominal value of the fabrication parameter being required to comply with the collective fabrication tolerance;   optionally defining an individual fabrication tolerance at least for the fabrication parameter, an individual deviation between a real value of the fabrication parameter for an individual element and a nominal value of the fabrication parameter for a fabricated element and the nominal value for said parameter being required to comply with the individual tolerance; and   determining a value of the technological uncertainty factor using a method as recited in  claim 13  using as collective variation the defined collective fabrication tolerance, and optionally as individual variation the defined individual tolerance; and   comparing the determined value of the technological uncertainty factor with a limit value for validating the defined fabrication tolerances.   
   
   
       25 . A method of fabricating nuclear fuel elements designed by a method as recited in  claim 20 . 
   
   
       26 . A method of inspecting fabricated nuclear fuel elements, the method comprising the steps of:
 using a method as recited in  claim 13  for determining a value of at least one technological uncertainty factor for the fabricated nuclear fuel elements, using as the collective variation a deviation between a mean of real values of the fabrication parameter as measured in a batch of fabricated elements and the nominal value of the fabrication parameter, and optionally as individual variation a deviation between a real value actually measured on a fabricated element and the nominal value of the fabrication parameter; and   making a comparison with a limiting value for the technological uncertainty factor that the nuclear fuel elements are required to comply with in order to make a decision about the fabricated nuclear fuel elements.