Patent Number: 044938101
Section: description

DESCRIPTION OF THE PREFERRED EMBODIMENTS Throughout the following, the term "reflector" material is used to mean a material which partially or totally surrounds the multiplying system being measured. As stated above, effective multiplication constant k.sub.eff of a material is related to the multiplication M of that material by the relationship M.tbd.1/(1-k.sub.eff), where k.sub.eff is the effective multiplication constant of the material. In the method of the invention, the reflector is changed, causing a change in the effective multiplication constant; and this change results in a change in the detected neutron count rate. Referring to the drawing in FIG. 1, a self-interrogation system in its simplest form is shown. The self-interrogation method is based on changing the neutron absorption or reflection in the vicinity of the fuel assembly 8 (which can be for example from a pressurized water reactor, PWR, or boiling water reactor, BWR) and measuring the subsequent change in the neutron signal with the neutron detector 9. The change in the count rate is a result of the reactivity or multiplication of the system changing; the count rate changes when the material 13 external to the system alters the nonleakage probability, P, defined below. A spent-fuel assembly (as well as any neutron-emitting fissile material) can be treated as a multiplying system. As such, the neutron flux N can be approximately written as ##EQU1## where M is the multiplication of the system, k.sub.eff is the effective multiplication constant, and S is a source term. S is the unmultiplied source strength resulting from spontaneous fission of the transuranic isotopes (mostly curium isotopes), (.alpha.,n) neutrons from alpha particle reactions, and induced fissions. The multiplication M of the system depends on the amount of fissionable material, the geometry, the moderator, and the reflector material. The effective multiplication constant k.sub.eff is defined as EQU k.sub.eff =k.sub..infin. P, (2) where k.sub..infin. is the infinite multiplication constant for an infinite system and P is the nonleakage probability. For a first reflector material A, the neutron flux is N.sub.A ; and for a second reflector material B, the neutron flux is N.sub.B. Thus, the change in neutron flux between material A and B is ##EQU2## Therefore, ##EQU3## Equation (3) is the basis for the self-interrogation technique where .DELTA.P is a constant for this system because only the reflector material is changed. The left side of the equation is equal to the count rate change and the right side depends upon the multiplication M.sub.B and change in nonleakage probability (P.sub.A -P.sub.B) of the system. A correlation of Eq. (3) to fissile content (burnup) provides a means of measuring the fuel assembly. In the prior art k.sub.eff was changed by changing k.sub..infin. or may have been changed by changing k.sub..infin. and P, whereas here only P is changed. It is required in the method of the invention that any and all changes in reactivity of the material being assayed arise only from a change in the reflector material which is external to the physical boundary of the material being analyzed, and not from any change in the multiplying system (where the multiplying system was defined above). It is believed that this method has never been done before. Thus, it is required that in the time period during which the first and second measurements (described above) are taken that there be no change in the moderator material or other material that comes in contact with the material being assayed, that there be no change in the geometry of the multiplying system, and that there be no change in any other variable of the multiplying system. The requirement that these variables not change is critical because each of these variables influence the reactivity which is being measured; and it is important that the measurement of the reactivity in the method of the invention depend only upon changing the reflector material external to the multiplying system. In the method and apparatus of the invention, any change in reflector material (which is located externally to the multiplying system of the material to be assayed) can be used, provided that a change in neutron count rates occurs when one reflector material is substituted for another. Therefore, examples of suitable changes in reflector material include but are not by any means limited to (a) making one measurement with water and another with Cd and (b) making one measurement with graphite and another with Cd. After the two measurements of count rates are obtained for a given multiplying system (which must be kept constant for the two measurements), then the difference between the two measurements is obtained. That difference in neutron count rates is then correlated (as described below) to the reactivity (or burnup or multiplication or content of fissile material) of the system being assayed by comparing with a previously determined correlation with standards for which the burnup, fissile content, or multiplication is known. Because burnup, reactivity, and fissile content can each be correlated one with another, these quantities are equivalent. The two measured values of neutron count rates can be correlated to the burnup of the material being measured in any of several possible ways. In one way, the difference between the two rates is divided by the first measured rate (or alternatively, the difference between the rates is divided by the second measured rate), thus providing a normalized value of the change in neutron count rate. This value then can be correlated to burnup or reactivity by comparing with a previously determined calibration of burnup or fissile content or multiplication of known spent fuel assemblies or from calculational techniques that have been experimentally verified. Alternatively, the measurement can be developed in a number of other ways, including a ratio of the two measurements. This value can then be correlated to burnup or reactivity, as described above. In the apparatus of the invention, it is required that there be a means for holding the fissile materials in a reproducible, fixed position and that there be a means for maintaining the reflector materials in a reproducible position. In FIG. 2, an embodiment showing a stationary self-interrogation system is shown and is referred to generally as 10. A nuclear fuel assembly 11, located in water, is lowered into a fuel assembly guide plate 12, through the guide plate 12, and into the boxlike container which is the fuel assembly storage cell 14. The plate 12 and the fuel assembly storage cell 14 provide the means of locating (and supporting) the fuel assembly with respect to the neutron detectors 16 and reflector plates 20. Trestles 18 (which form the stabilizing assembly) support the system. In the first measurement of neutron count rate, with no cadmium next to the fuel assembly, the two rotating neutron reflector plates 20 are in the out position (for example are rotated out on axis A--A' and B--B') so that the plates 20 do not affect the reactivity of the fuel assembly (i.e., angle .theta. is at least 90.degree. and is preferably 135.degree., which is the least reactive condition). Then, the plates 20 are positioned as shown in FIG. 2, and the second measurement is taken. Alternatively, the pivot points could be located at other positions other than along the diagonals of the fuel assembly, for example along C--C', although this is not preferred. Alternatively, the first measurement could be taken with the plates 20 in place as shown in FIG. 2; and the second measurement would then be taken with the plates 20 rotated out. The neutron detectors 16 (numbering 1, 2, or more preferably on each of two opposite faces as shown) are preferably located within guide tubes 17 on opposite faces of the fuel assembly storage cell 14 and are parallel to the face of the fuel assembly and are fixed in their positions. The rotating plates 20 are preferably on opposite faces of the fuel assembly storage cell 14. Motor and gear assembly 22 preferably located as shown is preferably used to rotate plates 12, although manual operation is alternatively possible. In FIG. 3, an embodiment showing a scanning self-interrogation system is shown and referred to generally as 30. The system is located in water and has many of the same items which were shown in FIG. 2, including two detector tubes which are like those shown in FIG. 2, except that they are spaced apart from the fuel assembly. A slidable sheath 32 is slidably positioned between the guide tubes 17 housing the detectors and the fuel assembly storage cell 14. The slidable sheath 32 is preferably driven along guide tube 17 by ball screw 34 by any suitable driver means, for example a motor and gear assembly 22. Sheath 32 surrounds the fuel on four sides, thus giving a high change in reactivity for a given area of sheath 32. Sheath 32 is made of the second reflector material (e.g., graphite, cadmium, or any material which will change the reactivity, either increasing or decreasing it, although for safety purposes a material which decreases the reactivity may be preferred for use). Sheath 32 need not be a solid. For example, it could be a container housing deuterated water. The number of measurements of a fuel assembly which would need to be made with a given sheath 32 depends upon the dimensions of the sheath. The entire length of the fuel assembly would need to be covered once by the sheath. As the sheath is raised or lowered, the area that it formerly covered is now uncovered; and the uncovered and covered portions can be measured simultaneously. The amount of time of the measurments equals the length of the fuel assembly divided by the vertical height of sheath plus the time needed for moving the sheath. A profile of the local multiplication at each point is obtained; and this can be averaged, if desired. EXAMPLE The following experiment was carried out. A series of calculations of the magnitude of change in the multiplication constant for a change in the reflector material and experimental verifications of those calculations were done. Two detectors were used, a thermal neutron detector and an epithermal neutron detector. A 15.times.15 rod PWR assembly with 3.2% enrichment was computer modeled for the calculation of k.sub.eff and .DELTA.k.sub.eff. The Los Alamos National Laboratory Monte Carlo neutron transport code (MCNP), Los Alamos National Laboratory Report LA-7396, Los Alamos National Laboratory Group X-6, "MCNP-A General Monte Carlo Code for Neutron and Photon Transport," (June 1978), was used in the calculation of k.sub.eff. The initial reflector material was water and the calculation of k.sub.eff was carried out for cadmium placed on one or more sides. The results are shown in FIG. 4. As expected, the multiplication constant decreased when cadmium was added. Substitution of the calculated k.sub.eff into Eq. (3) (see above) reveals that count rate changes up to 40% possible. The experimental setup is shown in FIG. 5. Although neither the experimental configuration shown in FIG. 2 nor FIG. 3 was used in the experimental verification, the configuration in FIG. 5 is conceptually identical to the configurations in FIGS. 2 and 3. The measurements made with the prototype had an aluminum frame on which cadmium sheets could be slid in and out. The experimental tests consisted of placing the PWR fuel assembly in water in a 200 liter barrel 51 and inserting a .sup.252 Cf isotopic neutron source (3.times.10.sup.4 n/s) into the assembly to simulate the normal neutron emissions from spent fuel. The thermal neutron detector 50 and epithermal neutron detector 52 measured the detection sensitivity for two different detection thresholds. Measurements were first made with distilled water 54 surrounding the PWR fuel assembly 56 and then with cadmium sheet(s) 58 placed in close proximity to one or more sides. The results of the measurements are shown in Table I. The calculated quantities were obtained by using Eq. (3) and the values of k.sub.eff found in FIG. 4. For the epithermal detection system the calculated and experimental values show good agreement, indicating that Eq. (3) is a satisfactory approximation for an epithermal system. However, with thermal detection, the measured count-rate changes consistently underestimated the calculated quantities. Extending these results to spent fuel of higher burnup was accomplished by substituting the burnup-dependent multiplication constant into Eq. (3). The burnup-dependent multiplication constant is shown in FIG. 6 (obtained from G. Schulze, H. Wurz, "Nondestructive Assay of Spent Fuel Elements." Internat. Meeting on Monitoring of Pu Contaminated Waste, Sept. 1979, ISPRA). This reference is hereby incorporated herein by reference. The estimated count-rate change for different burnups is shown in FIG. 7. This figure shows that at 35,000 MWd/tU, a precision of 2.4% on the count rate change is required for a 1000 MWd/tU precision on burnup. Repeat measurements have shown that this level of precision is possible. FIG. 7 shows clearly that a reactivity change produced by a reflector change alone is an effective means of measuring burnup in spent fuel assemblies. This figure demonstrates the measurement method and apparatus of the invention. The significant advantages of this technique used in this example are (1) no external isotopic neutron source is required, (2) the measurement can be performed at any cooling time, irrespective of the passive neutron rate, and (3) it is possible to do the measurement without any complex scanning system. TABLE I ______________________________________ CALCULATED AND EXPERIMENTAL AVERAGE COUNT-RATE CHANGES Experimental No. of Sides Covered With Cd Epithermal Thermal Calculated ______________________________________ 1 0.19 0.08 0.17 2 0.26 0.17 0.28 3 0.34 0.27 0.35 4 0.38 0.38 ______________________________________ The foregoing description of the preferred embodiments of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best utilize the invention in various embodiments and with various modifications as are suited to the particular uses contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.