Axial void fraction distribution measurement method and neutron multiplication factor evaluating method

Abstract

A first intensity A z expressed as A z =a z ×E α , a first reference intensity A o expressed as A o =a o ×E α , a second intensity B z expressed as B z =b z ×E, and a second reference intensity B o =b o ×E, are evaluated. The first intensity and the first reference intensity are of radioactive nuclides generated by a neutron capture reaction of a heavy nuclide or a fission product nuclide. The second intensity and the second reference intensity are of radioactive fission product nuclides except nuclides generated by a neutron capture reaction. The reference intensities are measured where the void fraction is known. Also a correlation curve of (a z /a o ) and a void fraction is evaluated. Finally an axial void fraction distribution is evaluated based on the value of (a z /a o ) and the correlation curve.

1 . A method for evaluating an axial void fraction distribution of a fuel irradiated in a nuclear reactor, the method comprising: 
 measuring a first intensity A z  of a type of radioactive ray emitted from a nuclide of a first group at an axial position of the fuel, the first group consisting of radioactive nuclides generated by a neutron capture reaction of a heavy nuclide or a fission product nuclide;    measuring a second intensity B z  of a type of radioactive ray emitted from a nuclide of a second group at an axial position of the fuel, the second group consisting of radioactive fission product nuclides except nuclides generated by a neutron capture reaction;    measuring a first reference intensity A o  of the same type of radioactive rays of the first intensity at an axial reference position of the fuel at which a void fraction of the fuel can be evaluated;    measuring a second reference intensity B o  of the same type of radioactive rays of the second intensity at the axial reference position;    calculating an exponent constant a used in an expression of A z =a z ×E α  and A o =a o ×E α  where E is an exposure of the fuel, a z  and a o  are proportionality constants;    evaluating a value of (a z /a o ) by an equation of (a z /a o )=(A z /A o )(B o /B z ) α (b z /b o ) α , where b z  is a value used in an expression of B z =b z ×E as a proportionality constant, b o  is a value used in an expression of B o =b o ×E as a proportionality constant;    evaluating a correlation curve of (a z /a o ) and a void fraction; and    evaluating the axial void fraction distribution based on the value of (a z /a o ) and the correlation curve.    
   
   
       2 . The method of  claim 1 , wherein the first intensity and the first reference intensity are neutron emission rates, and the second intensity and the second reference intensity are gamma ray intensities of a fission product that is proportional to the exposure within a certain exposure range.  
   
   
       3 . The method of  claim 2 , wherein the neutron emission rates include rates of neutron emission of nuclides except curium 242, and the gamma ray intensities include a gamma ray intensity of cesium 137.  
   
   
       4 . The method of  claim 2 , wherein the neutron emission rates include rates of neutrons emission of curium 244, and the gamma ray intensities include a gamma ray intensity of cesium 137 or cerium 144.  
   
   
       5 . The method of  claim 2 , wherein the neutron emission rates include rates of neutrons emission of curium 242, and the gamma ray intensities include a gamma ray intensity of cesium 137 or cerium 144.  
   
   
       6 . The method of  claim 2 , wherein the neutron emission rates are neutron emission rates. except for curium 242 and curium 244, and the gamma ray intensities include a gamma ray intensity of cesium 137 or cerium 144.  
   
   
       7 . The method of  claim 2 , further comprising: 
 evaluating a neutron multiplication factor k z  at a plurality of axial position of the fuel assembly, and a neutron multiplication factor ko at the reference position;    wherein the step of evaluating a value of (a z /a o ) includes: 
 measuring a neutron flux or a neutron counting rate φ z ;  
 measuring a neutron flux or a neutron counting rate φ o  at the reference position;  
 calculating a ratio of the neutron emission rate to that at the reference position, S z /S o , by an equation of S z /S o =(φ z /φ o )(1−k z )/(1−k o ); and  
 assuming A z /A o  equal to S z /S o .  
   
   
   
       8 . The method of  claim 2 , further comprising: 
 calculating an axial exposure distribution based on an assembly-averaged fuel exposure and an axial distribution of an intensity of gamma ray, by assuming the axial exposure distribution equal to the axial distribution of an intensity of gamma ray; and,    evaluating a conversion factor from an infinite multiplication factor to a neutron multiplication factor by a neutron transport diffusion calculation according to a condition of the measurement;    wherein the step of evaluating the axial void fraction distribution includes evaluating the axial void fraction distribution by repeating following (i) to (vii) steps until a convergence of the axial void fraction distribution, assuming an infinite multiplication factor can be expressed as a quadratic function of the exposure where parameters of the function depends on the void fraction: 
 (i) assuming an axial void fraction distribution as appropriate one for an initial calculation, or an axial void fraction distribution calculated at the step of (vii) of a previous loop for a calculation except the initial calculation;  
 (ii) calculating an infinite multiplication factor based on the assumed axial void fraction distribution;  
 (iii) calculating an neutron multiplication factor k z  and k o  by using the conversion factor and the multiplication factor;  
 (iv) calculating a ratio of neutron emission rate to that at the reference position S z /S o  based on the neutron multiplication factor k z  and k o ;  
 (v) calculating a z /a o  based on S z /S o ;  
 (vi) evaluating the axial void fraction distribution based on a z /a o  and the correlation curve; and  
 (vii) terminating if a convergence of the axial void fraction distribution is achieved, or returning to the step of (i), if not.  
   
   
   
       9 . The method of  claim 8 , further comprising: 
 evaluating an exposure at the reference position by a neutron emission rate technique.    
   
   
       10 . The method of  claim 1 , wherein the first group includes gamma ray emitting nuclides transmuted by neutron capture reactions after generation by fission, and the second group includes gamma ray emitting nuclides that is not subjected to a neutron reaction and emit gamma ray proportional to the exposure within a definite range.  
   
   
       11 . The method of  claim 10 , wherein the first group includes cesium 134 or europium 154, and the second group includes cesium 137 or cerium 144.  
   
   
       12 . A method for evaluating an axial void fraction distribution of a fuel irradiated in a nuclear reactor, the method comprising: 
 measuring a first intensity A z  of gamma ray emitted from cesium 134 or europium 154 at an axial position of the fuel;    measuring a first reference intensity A o  of a same type of radioactive rays of the first intensity at an axial reference position of the fuel at which a void fraction of the fuel can be evaluated;    measuring a second intensity B z  of gamma ray emitted from cesium 137 or cerium 144 at an axial position of the fuel;    measuring a second reference intensity B o  of a same type of radioactive rays of the first intensity at the axial reference position;    calculating G z /G o =(A z /B z )/(A o /B o );    evaluating a correlation curve of (G z /G o ) and a void fraction; and    evaluating the axial void fraction distribution based on the value of (G z /G o ) and the correlation curve.    
   
   
       13 . A method for evaluating an axial void fraction distribution of a fuel irradiated in a nuclear reactor, the method comprising: 
 measuring a radiation ray intensity of radioactive rays emitted from nuclides at an axial position of the fuel for at least twice with a definite interval, the nuclides generated by a neutron capture reaction of a heavy nuclide or a fission product nuclide;    measuring a radiation ray reference intensity of a same type of radioactive rays of the radioactive ray intensity at a reference position for at least twice with a definite interval, the axial reference position of the fuel at which a void fraction of the fuel can be evaluated;    dividing the radiation ray intensity into that of a first neutron emission rate A z  from curium 242 and that of a second neutron emission rate B z  from nuclides except curium 242;    dividing the radiation ray reference intensity into that of a first reference neutron emission rate A o  from curium 242 and that of a second reference neutron emission rate B o  from nuclides except curium 242;    calculating α of an exponent constant expressed in equations of A z =a z ×E α , A o =a o ×E α  by using the exposure E, and proportionality constants a z  and a o ;    calculating β of an exponent constant expressed in equations of B z =b z ×E β , B o =b o ×E β  by using the exposure E, and proportionality constants b z  and b o ;    calculating (a z /a o ) α (b o /b z ) β by an equation of     ( a   z   /a   o ) α ( b   o   /b   z ) β =( A   z   /A   o ) α ( B   o   /B   z )  β ;   evaluating a correlation curve of (a z /a o ) α (b o /b z ) β  and a void fraction; and    evaluating the axial void fraction distribution based on the value of (a z /a o ) α (b o /b z ) β  and the correlation curve.    
   
   
       14 . A method for evaluating a neutron multiplication factor of a fuel assembly irradiated in a nuclear reactor, the method comprising: 
 measuring a neutron counting rate φ o  at a reference position of the fuel assembly where a void fraction is known, and evaluating a neutron multiplication factor k o ;    measuring a neutron counting rate φ z  at a multiplication factor evaluation point of the fuel assembly;    calculating φ o /φ z ;    measuring a gross gamma intensity ratio (y g /y go ) at the multiplication factor evaluation point and the reference position;    evaluating a relationship between the gross gamma intensity ratio and an exposure of the fuel assembly;    evaluating an exposure ratio (E z /E o ) at the multiplication factor evaluation point and the reference position based on the relationship between the gross gamma intensity ratio and an exposure of the fuel assembly;    calculating (E z /E o ) α  based on a value of calculated a;    evaluating a relationship between (a z /a o ) and a void fraction;    evaluating an axial void fraction distribution;    evaluating the value of (a z /a o ) based on the axial void fraction distribution and the relationship between (a z /a o ) and a void fraction; and    calculating the neutron multiplication factor k as k=1−(1−k o )(φ o /φ z )(E z /E o ) α (a z /a o ).