Reactivity Effect of Fission and Absorption

Transcription

1 Journal of NUCLEAR SCIENCE and TECHNOLOGY, 1, No. 7, p.246~254 (October, 1964). J. Nucl. Sci. Tech. Space Dependent Reactivity Effect of Fission and Absorption Tohru HAGA* and Iwao KOBAYASHI* Received January 9,1964 The reactivity effect of materials introduced into a critical reactor is generally a result of complex changes given to the system concerned. In this report, the emphasis was put on the space dependent reactivity effect of fuel, and its fission and absorption terms were separately measured. The effect of fuel enrichment on reactivity was also measured by using fuel elements of three different enrichments, 2.6%, 0.71% and 0.28%. The analysis was made by three group perturbation equations and its applicability was carefully checked in comparison with experimental results.. I INTRODUCTION The effect of fuel that contributes to reactivity is generally a function of its location in the core, and it also depends on the geometrical condition of the system concerned. In order to determine such effect, measurement of reactivity change should be made upon the removal or insertion of a small amount of fissionable material at the measuring position in the core. In this experiment, space dependent reactivity effect was first measured on substituting a fuel element located at the position of measurement with an empty fuel tube. Thus, it is possible to obtain the effect of fuel without changing moderator property in the neighborhood of substitution. In the second place, the reactivity was measured on substituting a fuel element with a dummy element which was made of antimony-cadmium-lead (Sb-Cd-Pb) alloy with both its thermal and epithermal absorption cross sections made identical to those of 2.6% enriched UO2 fuel. In this method, the effect of fission neutron birth would be separately obtained. Another type of dummy element was also prepared, which was made of cadmium-lead (Cd-Pb) alloy with only its thermal neutron absorption cross section made identical to that of 2.6% enriched fuel. The difference of reactivity effect between the Sb-Cd-Pb and Cd-Pb dummy elements gives the contribution of epithermal neutron absorption alone, which is also space dependent. All these dummy elements were fabricated to exactly the same dimensions as the fuel. The reactivity effect of varying fuel enrichment was also measured by substituting a regular 2.6% enriched fuel element with others of different enrichment, 0.71% and 0.28%. In this way, the reactivity contributions of 235U and 238U were separately obtained by extrapolation. The self-shielding effect in fuel elements of different enrichment was also taken up because it would be one of the principal causes for nonlinear reactivity effect with increasing fuel enrichment. All these experiments have been conducted by using the core of TCA (Tank-type Critical Assembly) which is a light water-uo2 system. For the analysis, three group perturbation equations have been employed and its applicability was carefully checked in comparison with the experimental results. In order that the experimental results might be well described by the perturbation thoery, the flux disturbance accompanied by the replacement of fuel was measured and found negligibly small. II. THEORETICAL APPROACH The perturbation theory gives the general formula(1) for the reactivity change resulting from the introduction (or removal) of small amounts of materials into a critical reactor, on the assumption that the flux disturbance due to the introduced material is negligibly small: * Japan Atomic Energy Research Institute, Tokaimura, Ibaraki-ken. 26

2 Vol.1,No. 7 (Oct. 1964) 247 (1) (3) (4) where the notation follows conventional practice and dsf, dsa, dsg and dd signify the change in each parameter resulting from the introduction or removal of the materials. Although the equation is very complicated, its physical meaning is easy to understand. F is the integral of neutron birth in the core weighted by the fission spectrum averaged importance function ph,(r), P is the change in neutron birth weighted by ph,(r) and integrated over the region R where the variation occurs, A is the change in neutron absorption weighted by the importance function p,(r,e) and integrated over the region R, S is the change in neutron scattering multiplied by the increase of neutron importance caused by scattering and integrated over the region R, and G is the change in neutron current multiplied by the gradient of neutron importance and integrated over the region R. Reducing Eq.(1) into three group one dimensional analysis gives: where i denotes energy group and (dsf)i, (dsa)i, (dsr)i and (dd)i are the changes in group parameters-fission cross section, absorption cross section, removal cross section and diffusion coefficient respectively. The neutron fluxes pi and importance functions pi, obey (2) where the Laplacian D2 is for the cylinder, and BZ2 is the buckling in axial direction, Because the TCA core used in these experiments is a comparatively long cylinder, i.e., about 100 cm active core height against 36 cm diameter, one dimensional treatment will give a fairly good approximation. At present, let us only consider the effect of fissionable materials introduced into the reactor. If the amount of fissionable material presently considered is small enough not to create any flux disturbance in question and if its introduction (or removal) does not change the amount of moderator volume at this location, the last two terms, S and G, in Eq. (2) may be neglected for the following reasons. The term S may be neglected because of the small change in removal cross section due to the fissionable material so far as no change of moderator volume is assumed. As for the term G, while the change in diffusion coefficient D due to the removal of fuel is not of negligible order, when it is multiplied by the product of flux and importance, i.e., gradpi gradpi, the resulting term G may be regarded as negligible compared to the first two terms, P and A in Eq.(2). Thus, it is now possible to separate the reactivity effect of fissionable material into the two major effect, the positive fission term and negative absorption term which are both space dependent. Equation (2) is thus simplified to (5) 27

3 1 248 J. Nucl. Sci, Tech. The purpose of this report is to measure these space dependent reactivity effects for each term, and to check the concept of neutron importance by experiment, as well as to study the applicability of perturbation analysis.. EXPERIMENT III All the experiments have been performed with the TCA cylindrical core, which is a light water moderated -2.6% enriched UO2 system. The fuel element shown in Fig. 1 is in the form of a cylindrical rod of mm outer diameter, sheathed in Al tubing of.76 mm wall thickness, and UO2 fuel is in 0 the form of short cylindrical pellets of 12.5 mm diameter stacked to give 1,441 mm effective fuel height. The system consists of a square lattice with mm pitch to constitute a water to UO2 volume ratio of Fig.2 Reactivity Worth of a 2.6% Fuel Element (Experimental curve) the cube of critical water height. The relation is(2) dr=7.33x106,1/(h+8)3c/cm (6) level change. Fig. 1 Pelletized Type Fuel Rod. Separation of Fission and Absorption Terms The reactivity change was at first measured on substituting a 2.6% fuel element with an empty cladding tube, and measurements were made along the radial direction of the cylindrical core loaded with 292 fuel elements. The use of an empty cladding tube is for avoiding the change in moderator volume accompanying the replacement of fuel and to suppress flux peaking in the neighborhood. The measured reactivity worth of a 2.6% enriched UO2 fuel element is shown in Fig. 2 in terms of space dependent effect. The reactivity worth was obtained from the difference of critical water level of the TCA core which was partly immersed in light water. The differential water eve worth had already been calibrated by period method at various core height, and treated by least square method to assume the form of a simple function inversely proportional to Since the accuracy of water level indication was within mm, it would be negligible as an error source, and average discrepancy of experimental value from the least square fitting was taken as the error source for reactivity determination, which was +-2.4%. As mentioned before, the fuel has both positive fission effect and negative absorption effect, and this property is apparent in Eq. (2). In order to measure these effects separately, a Sb-Cd-Pb(3) alloy dummy element was prepared with its neutron absorption property made identical to that of 2.6% enriched fuel for both thermal and epithermal neutrons. Cross section fitting for epi-thermal neutrons was made with the antimony (Sb) part of the alloy, utilizing very similar resonance characteristics of Sb to 238U(4), and the resonance integral(5) was calculated for Sb to determine the requisite Sb content, while the resonance integral for the fuel element was calculated from the Hellstrand's method(6). On the other hand, the thermal cross section was fitted by calculating the spectra-averaged cross section of Cd, Sb and Pb. 28

4 Vol.1, No. 7 (Oct. 1964) 249 The reactivity change was then measured, along the radial direction of the TCA 292 fuel element loaded core, on substituting a 2.6% fuel element with the Sb-Cd-Pb dummy element made to the same dimensions. For points outside the core, an extra fuel element was loaded in the reflector and then substituted with the Sb-Cd-Pb dummy element. Since there will be almost no change in absorption property caused by this substitution, the reactivity worth obtained in this way gives only the positive fission effect, assuming that the change in scattering property is negligibly small. The worth is and the corresponding experimental results are shown in Fig. 4. (8) (7) Since the denominator of Eq.(7) is an integral covering the whole core region, the space dependend effect is actually determined by the numerator. The results of experiment are shown in Fig. 3 as compared to the calculation of Eq.(7). The subtraction of the above result at each point from the previously obtained net fuel effect shown in Fig. 2 gives only the absorption effect of fuel. It is by theory Fig. 3 Fission Effect on Reactivity by Substitution Method Fig. 4 Absorption Effect on Reactivity by Substitution Method For calculation, a few group one dimensional code ENSIGN was employed. In order that the perturbation theory may well be satisfied, there should be no flux disturbance accompanying the substitution, and to check this effect, thermal neutron flux distribution was also measured before and after the substitution of a fuel element either by an empty cladding tube or a dummy element. The result is shown and discussed in the last section of this report. 2. Contribution of Epithermal Neutron Absorption In order to measure the effect of epithermal neutron absorption alone, another type of dummy element(7) made of Cd-Pb alloy was prepared with its absorption cross section for thermal neutrons alone made identical to that of fuel. The reactivity worth was also measured along the radial direction on substituting a 2.6% fuel element 29

5 250 J. Nucl. Sci. Tech. by this Cd-Pb dummy element. In this case, the substitution causes change of absorption cross section for epi-thermal neutrons as well as for fission cross section. Theoretically, the reactivity change resulting from this substitution is: The measured reactivity worth on substituting a 2.6% fuel element by Cd-Pb dummy element is also shown in terms of space dependent effect in Fig. 3, together with the previous measurement made with Sb-Cd-Pb dummy element. The difference between the two measurements may be regarded as the contribution of the epi-thermal neutron absorption, and it is interesting to note that the two measurements come very close to each other in the neighborhood of core boundary, which apparently shows that the epi-thermal neutron flux sharply decays in that neighborhood. Theoretically, the difference between Eq.(7) and Eq.(9) gives the effect of epi-thermal neutron absorption. It is Fig. 5 Effect of Epi-thermal Neutron Absorption on Reactivity (9) (10) The result of calculation by Eq.(10) is shown in Fig. 5 where it is compared with the experimental data. 3. Reactivity Worth of Fuel in Varying Enrichment In order to measure the reactivity effect of 235U enrichment, two different types of fuel element with identical dimensions were prepared apart from the regular 2.6% enriched UO2 fuel elements, the 235U contents of which were 0.71% and 0.28% respectively. For reactivity worth determination, one of these fuel elements was at first loaded at the position of measurement in the TCA 276 element loaded core and then substituted by an empty fuel cladding tube. The reactivity worth was obtained from the difference of critical water level in just the same way as described before. The measurement was made for each enrichment of fuel element and along the radial direction of the core. The use of an empty fuel cladding tube was again for avoiding change in slowing down property and to suppress flux peaking. The experimental results are shown in Fig. 6 in terms of space dependent effect. It is interesting to note that fuel of lower enrichment acts rather as poison and gives negative reactivity effect as its position approaches to the core center, while at the periphery of the core its effect is positive even with 0.28% depleted UO2 fuel. This fact shows that the effect of absorption is predominant at the central core, while it sharply vanishes on approaching to reflector region. Figure 7 shows the same reactivity effect as Fig. 6 on substituting a fuel element by an empty tube, but plotted against enrichment for each location in the core. The extrapolation of each curve to zero enrichment gives the reactivity worth of 100% 238U UO2, which is apparently negative in all parts of the core. According to the perturbation theory of the first order, the reactivity change us. enrichment would be a straight line, whereas, the experimental data in Fig.7 is somewhat 30

6 Vol.1, No. 7 (Oct. 1964) 251 curved. The major reasons for this result could be that; firstly the fission rate will not change linearly with the increase of enrichment because of the self-shielding effect, and secondly, possible flux disturbance accompanies fuel substitution. In order to check these points, thermal neutron flux distribution was measured both from microscopic and macroscopic point of view for each enrichment by irradiating small Dy foils. The result is shown and discussed in the last section of this report. Figure 8 shows the reactivity change on replacing a 2.6% enriched regular element with 0.71% and 0.28% fuel elements at each location. The data shown in Fig. 8 is again the same in principle as that of Fig. 7, but the extrapolation of the curves to zero enrichment gives the reactivity effect contributed only by the 235U contained in 2.6% fuel. Fig. 6 Reactivity Worth of Different Enrichment (Experimental curve) Fig.8 Reactivity Change on Replacing a 2.6% UO2 Fuel to 0.71% and 28% UO2 Fuel Element 0. (Experimental curve) IV. SUPPLEMENTARY EXPERIMENTS AND DISCUSSIONS Fig. 7 Reactivity Worth us. Enrichment (Experimental curve) 1. Thermal Neutron Flux Disturbance In order to well satisfy the perturbation theory, neutron fluxes must not be disturbed by the substitution made in the reactor. However, any small substitution may actually cause flux disturbance to some extent, and especially thermal neutron flux. If the substitutions made in the experiments of the previous section result in large flux disturbance, calculations by perturbation theory and comparison of the results with experiment will not make sense. For this reason, thermal neutron flux distribution was first measured along the radial direction of the 2.6%

7 252 J. Nucl. Sci. Tech. element core before and after substituting one of the fuel elements at the core center with a dummy element, with a fuel element of lower enrichment and with an empty fuel cladding tube. For measurement, small Dy foils, 2 mm diam., 0.5 mm thick, each containing approximately 2 mg of Dy2O3, were irradiated. The measured flux distribution was normalized against each other at several points along the core periphery. The results are given in Fig. 9, which shows that there is no detectable amount of flux disturbance within the accuracy of experiment, except in the case of substitution with a cladding tube. However, it shows that the effect of flux disturbance around an empty cladding tube can not be ignored, and the authors are planning to make more accurate experiments on the relation between reactivity and flux disturbance. Element Disadvantage Factor 2.6%UO %UO %UO Sb-Cd-Pb dummy 1.19 Cd-Pb dummy 1.16 The experimental error in the above data was not definitely known, but it was estimated to be 3~5% from the ambiguity of the flux contour maps. The absence of difference between the measurements on the 0.71% and 0.28% fuel elements is due to experimental error. However, the disadvantage factors of 2.6% UO2 fuel and the Sb-Cd-Pb dummy element agreed within the experimental error, which can be considered a proof that the dummy element was properly made. Fig.10 Fine Stucture of Thermal Neutron Flux Fig.9 Thermal Neutron Flux Distribution 2. Fine Structure of Thermal Neutron Flux The fine structure of thermal neutron flux was also measured in a unit cell at the core center around each of the dummy and the fuel elements, by arranging small Dy foils as shown in Fig. 10. The disadvantage factor for each element was then obtained pm/pf by drawing flux contour maps and the results were as follows. 3. Preparation of Dummy Elements It should be noted that the difference in reactivity worth between the Sb-Cd-Pb and Cd-Pb dummy elements almost vanishes on entering the reflector. This would again be a proof that for thermal neutron absorption the dummy elements are almost identical each other, and the difference between the two measurements may confidently be taken to represent the effect of epi-thermal neutron absorption. For making the thermal neutron absorption of dummy elements identical to that of 2.6% UO2 fuel, B should serve better than Cd for its 1/v characteristics. However, the authors considered the difficulty of preparing a uniform mixture of B and Sb, and employed 32

8 Vol.1, No. 7 (Oct. 1964) 253 Cd instead which is easy to alloy with Sb. For reference, the weight contents of the dummy elements are given below(3). Sb-Cd-Pb element: Sb 48%, Cb 0.184%, Pb 51.8% Cd-Pb element: Sb 0%, Cd 0.181% Pb 99.8% 4. Measurement of Effective Delayed Neutron Fraction The measurement of reactivity worth on substituting 2.6% UO2 fuel elements by Sb- Cd-Pb dummy elements throughout the core also gives the value of effective delayed neutron fraction beff. This is generally known as the "substitution method"(8). Accordingly, the authors simply extended the substitution experiment described in Sec. III.1 to cover the whole of the 1/8 symmetrical core region, and obtained the total reactivity worth Score(dr)= $125.2 from which the effective delayed neutron fraction was determined to be beff=1/125.2 = This value is very close to the calculation of Barth(9), that is, beff = Applicability of Perturbation Analysis Looking through the experimental results of this report, it is seen that the relative space dependent effect of fission and absorption is fairly well described by perturbation theory provided there is no flux disturbance of importance. However, it is dangerous to belive too simply in the absolute value of reactivity worth given by the perturbation analysis because of the following reasons. (1) In perturbation analysis, the reactivity effect is to be calculated about each elementary cause accounted for in Eq.(1), and each term includes a certain amount of error originating from the uncertainties in such data as cross sections, fluxes and importance functions. When these terms were separately calculated, the amount of error may not be so serious. However, when overall reactivity worth is calculated by, for instance, the subtraction of absorption term from fission term, i.e., P-A, the amount of error would sometimes become serious because fission term and absorption term are in most cases of comparable value, so that the relative error will be greatly magnified in the final result. This is especially true in the case of fissionable materials taken into or out of the core. For this reason, as much care should be taken in the determination of nuclear parameters for perturbation analysis as be taken in concerning flux disturbance, otherwise the overall calculation of reactivity will become senseless. (2) Even if there was no detectable amount of flux disturbance in the neighborhood of substitution, the effect of self-shielding in the given materials must not be neglected. In many cases, perturbation analysis is made on the assumption that reactivity changes linearly with the nuclear parameters. However, the experimental curves given in Fig. 7, for reactivity worth us. enrichment, is clearly not a straight line. This fact shows that, to calculate the perturbation equations, one must always be aware of the range in which the linear relation is satisfied. For the reasons mentioned above, it was concluded that in so far as relative space dependent properties were concerned the perturbation theory could be effectively used to understand the reactivity effect for the materials introduced into the reactor. Accordingly, if one knows by experiment the reactivity worth of a test sample small enough not to create flux disturbance, its reactivity worth at different positions in the core may be reliably calculated by perturbation theory. However, when making such analysis of reactivity worth for positions where the neutron flux gradient is large, such as in the core reflector boundary, one must be careful about whether the term resulting from the change in diffusion coefficent, the third term in Eq. (2), is of negligible order or not, otherwise it would introduce uncertainties in the calculations. ACKNOWLEDGEMENT The authors express thier obligation to Mr. H. Mizuta of Nippon Atomic Industrial Group for his help in the calculation of the resonance integral of Sb alloy, to Mr. M. Ueda of the same firm for his help in the use of the diffusion code ENSIGN, to Mr. H. Okashita 33

9 254 J. Nucl. Sci. Tech. for his help in chemical analysis of Cd content in the dummy elements and to Mr. M. Hashimoto of Japan Atomic Energy Research Institute for his help in operating the critical assembly. REFERENCES (1) HURWITZ, H.,Jr. : Note on the Theory of Danger Coefficient, Rept. KAPL-98, (Sep.1948). (2) HAGA, T., et al.: TCA-2 Critical Approach and Characteristics, TCA Memo, '63-022, (Oct. 1963). (3) HAGA, T., et al,: JAERI Memo, to be published. (4) HUGHES, D.J., SCHWARTZ, R.B.: BNL-325, (July 1958), (5) MIZUTA,H.: Private communication. (6) HELLSTRAND, E.: J.Appl. Phys.,28, 12 (1957). (7) HAGA,T., et al,: JAERI Memo, to be published. (8) MURRAY, R.L.: Lecture Note given at JAERI, ibid., (1963). (9) BARTH, N.H.: JPDR Physics Startup Report. GECR-4276, (June 1963). 34