OAK RIDGE NATIONAL LABORATORY OPERATED BY For Internal Use Only UNION CARBIDE CORPORATION NUCLISION 0 R N L CENTRAL FILES NUMBER OAK RIDGE, TENNESSEE 37831 65-3=-1 DATE: March 3, 1965 COPY NO. é;i SUBJECT: Comparison of Calculations and Uncertainties in the Temperature Coefficients of Reactivity in the MSRE TO: Distribution FROM: B. E. Prince ABSTRACT Several calculated values for the MSRE temperature coefficients of reactivity have been reported in dif- ferent sources. These values are compared and their bases discussed in this memorandum. Calculations based on new experimental data for the temperature coefficient of expansion of the fuel salt are also included. Ranges of uncertainty in the current "best values" of tempera- ture coefficients of reactivity and critical concentra- tion are suggested, and the implication of these un- certainties in the zero power critical experiments are discussed. It is concluded that, with presently planned procedures, the expected uncertainties will not reduce reactor safety below that previously reported in the MSRE safety report. NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use at the Oak Ridge National Laboratory. It is subject to revision or correction and therefore does not represent a final report. The information is not to be abstracted, reprinted or otherwise given public dis- semination without the approval of the ORNL patent branch, Legal and Infor- mation Control Department. INTRODUCTION In the course of obtaining estimates of basic nuclear design para- meters for the MSRE, several values have been reported for the critical concentration and temperature coefficients of reactivity. One should first note that these calculations have had an evolutionary aspect, that is, the more recent calculations are generally considered to be '"better", either in terms of the physical model or the basic nuclear data used in calculating the reported characteristic. In the case of the critical concentration, the most recent computations have been reported in Ref. 1 along with a discussion of the origin of differences from previous calculations. In this memorandum we shall try to achieve some clarification of the second case, that of the temperature coefficients of reactivity. DISCUSSION The earliest reported calculations of the temperature coefficients for the final MSRE core design were those of Nestor.g As indicated in Table 1, two-group bare reactor theory was used, together'With the specific assumptions: | 1. The neutron temperature and the graphite temperature are identical. ~ 2. The effects of changes in reactor size are negligible. 3. The Fermi age is a function only of the graphite density. 4. The resonance escape probabiiity; fast effect, and fi'for U255 were independent of temperature. The fuel salt analyzed by Nestor contained ~0.5 mol % UFM’ 93% enriched in U255, in a carrier salt composition of 70/24/5/1 mol % LiF/BeF2/ZrFu/ThF4. This salt is designated as Fuel A. Subsequent to Nestor's work, it was decided not to include thorium in the first MSRE fuel salt mixture, and to use instead a salt composed of ~0.2 mol % UF) , 9%% enriched in U255, in a carrier salt of 67/29/4 mol % LiF/BeF2/ZrF4. This salt is designated as Fuel B. New calculations of the temperature coefficients were required, and this time use was made of two-group perturbation theory to check the validity of the one-region approximation.3 The remaining assumptions used in the earlier calculations were retained. These results are given 1in Table 1. Comparison of MSRE Temperature Coefficients of Reactivity Temperature Coefficients Temperature Coefficients Fuel Salt of Reactivity of Expansion . Case e o +5 o 1At5 Computational Refer- Composition (Ak/k/°F) x 1072) (20/0/°F) x 10%2) Model noo Fuel Graphite Fuel Graphite 1 A —.8 —6.0 -12.6 —0.4 Mult. const. (k.): Two 2 group, bare reactor theory. Slowing down spectrum: Determined by Fermi age in graphite. Thermal spectrum: Maxwell- Boltzmann approximation. 2 B 4.5 ~7.3 —-12.6 0.4 ke: Two-group perturbation 3 theory. Slowing down and thermal spectrum same as case 1. 3 A —3.0 -3 -11.8 ~1.0 k,: Same as case 1. 6 n B 5.0 —4.9 —11.8 -1.0 Slowing down spectrum: GAM-1 program calcula- < tions. 5 C —3.3 —3.7 -11.8 ~1.0 Thermal spectrum: THERMOS \ program calculations. 6 C 5.6 —4.0 -18.6 ~1.0 k,: Same as case 1. This : . memo - Slowing down spectrum: randum GAM-2 program calcula- tions. Thermal spectrum: THERMOS calculations. line 2 of Table 1. Together with the perturbation theory calculations, estimates based on a one-region homogeneous model were alSo made for fuel B. The resulting coefficients were found to compare within 5 to 10%, indicating that the detailed description of the external regions of the core (downcomer, top and bottom heads, etc.) did not significantly in- fluence the reactivity coefficients. Note, however, that the magnitude of the temperature coefficients differs from the earlier calculations primarily because of the change in fuel salt composition. With fuel B the reactor neutron spectrum is more thermalizéd and the effect of salt density changes on the leakage factors is proportionally larger. A further request was made to examine the possibility of increasing the total uranium content of the salt to the range of 0.8-0.9 mol % UFA («55% enriched for criticality, designated fuel C). About this same time, two new computer programs were acquired by use of which detailed calcula- tions of the slowing down and thermal spectra could be made. ©Specifically, the GAM-1 programLL 1s based on consistent P-1 theory for calculation of the slowing down spectrum in finite, homogeneous mixtures. The THERMOS programj numerically solves the Boltzmann equation fdr the thermal spectrum in a one-dimensional lattice cell, and thus allows the temperature of the fuel salt and graphite to be independently varied. A minor complication in the GAM-1 calculation for the MSRE spectrum was that the then-available 7, and Fl9. The other advantages of the GAM-1 calculation were considered sufficient, 6 version of the cross section library did not include Li , Li however, to warrant simulating the slowing down effect of the lithium and fluorine by an equivalent amount of oxygen, which was included in the GAM-1 cross section library. With these programs available, it was decided to recalculate the temperature reactivity coefficients for all three fuels under consideration, and to further examine the validity of some of the assumptions underlying previous calculations. The results are summarized in lines 3, 4, and 5 of Table 1. The major difference in these results and previously reported values is in the graphite temperature coefficilent. This difference arises primarily in the temperature dependence of the thermal spectrum. For the MSRE lattice, (a) the thermal spectrum is not determined by the graphite temperature (assumption 1, above) but depends on the temperature of the fuel channel as well, and (b) the Maxwell- Boltzmann approximation predicts too large a change in the thermal dif- fusion length as the temperature is varied. Other differences are also reflected in the values given in lines 3, L, and 5 of Table 1. These include the modified estimate of the graphite expansion coefficient, based on an average of longitudinal and transverse expansions, and changes due to explicit treatment of the temperature de- pendence of resonance absorption (assumption b, above). In general, these differences were smaller than that due to the spectrum effect discussed above. Very recently, new experimental data has become available for the density and temperature coefficient of expansion of fuel salt C.7 These new data indicate that the expansion coefficient is nearly 60% larger in magnitude than assumed in the preceding calculations. The previous values had been based on estimated temperature variations in the molar volumes of the salt constituents.8 Also subsequent to the last reported calculations, acquisition was made of the GAM-2 program, an improved version of GAM-1l, described above. By means of this new program, the slowing down effects in lithium and fluorine could be treated explicitly. The program has already been used to revise estimates of critical concentration and control rod worth,9 and a set of temperature coefficients of reactivity for fuel C was also re- calculated based on the new density data and the GAM-2 program. These results are summarized in line 6 of Table 1. As may be expected, the new expansion coefficlent causes a significant increase in the fuel tempera- ture coefficient of reactivity. Also, the explicit treatment of the slowing down by lithium and fluorine, particularly the inelastic scat- tering of fluorine, has the effect of further thermalizing the reactor spectrum. Hence both fuel and graphite reactivity coefficients are in- creased. Most of the changes summarized in Table 1 have had the effect of making the fuel, or prompt temperature coefficient of reactivity more negative. In turn, the changes appear to improve the safety and stability margins for reactor operation.lo The question still remains, however, as to the absolute uncertainties in these parameters. A method is presently being investigated by which the uncertainty in the-basic library of nuclear cross section data and densities cah be related to the un- certainties in the nuclear design parameters (critical concentration, etc.). The basic notion is that of relating the standard deviation in the cal- culated parameter to the standard deviations in the cross sections and densities. This method would indicate the sensitivity in the parameters To uncertainties in all basic data used in calculation, and would be use- ful in later evaluation of results from the reactor critical experiments. This 1s not complete at the date of this writing and could not be included. However, since the validity of most of the main assumptions in the computa- tion have been checked, it appears reasonable to assign a confidence in- terval of +10% to the critical concentration and +25% to the temperature coefficients of reactivity. Because of the "slope-like" nature of the latter quantity, it is expected to be the more sensitive of the two to errors in data and computational methods. For all of the conceivable incidents previously analyzed which could result in significant additions of reactivity,ll only the so-called cold slug accident would lead to a more severe transient if the fuel temperature coefficient of reactivity were more negative. This incident is not ex- pected to lead to dangerous or damaging conditions, and in addition, precaution will be taken not to start fuel circulation unless the control rods are inserted in the core. Thus, safe operation should be insured for all values of the fuel reactivity coefficients indicated in Table 1. The procedure; of the initial critical experiments will be designed12~ to allow greater uncertainty in the clean critical concentration than the 10% margin suggested above. The initial addition of uranium to the salt in the drain tanks will be ~65% of that predicted for criticality at zero power with all rods withdrawn from the core. The second addition is anticipated to be that amount to bring the salt within 87% of the critical mass. From this point on, the amount in each addition will be determined by inverse count rate measurements. Even if the minimum critical mass were exceeded, this would only mean that criticality would be achieved with the rods slightly inserted and would not require other special procedures. (Y The uncertainty in the temperature coefficients of reactivity has no effect on procedures in the zero power critical experiments. The coef- ficients will be measured along with the rod calibration experiments, and any large discrepancy between measured and calculated coefficients will be taken into consideration in the planning and operation of experiments at higher power levels. REFERENCES 1. "MSRP Semiann. Prog. Rep. Jan. 31, 196L4," USAEC Report ORNL-3626, p. 53-5k. 2. "MSRP Semiann. Prog. Rep. Aug. 31, 1961," USAEC Report ORNL-3215, p. 83. | 5. B. E. Prince and J. R. Engel, "Temperature and Reactivity Coef- ficient Averaging in the MSRE," USAEC Report ORNL-TM-379, Oak Ridge National Laboratory, October 15, 1962. L. G. D. Joanou and J. S. Dudek, "GAM-I: A Consistent P-1 Multi- group Code for the Calculation of Fast Neutron Spectra and Multigroup Constants," USAEC Report GA-1850, General Atomic, June 28, 1961. 5. H. C. Honeck, "THERMOS: A Thermalization Transport Theory Code for Reactor Lattice Calculations," USAEC Report BNL-5826, Brookhaven National Laboratory, September 1961. 6. P. N. Haubenreich, et al., "MSRE Design and Operations Report - Part III, Nuclear Analysis," USAEC Report ORNL-TM-730, p. 37—47, Feb. 3, 196k. 7. B. J. Sturm, Reactor Chemistry Division (report in preparation). 8. 8. Cantor, "Reactor Chem. Div. Ann. Prog. Rep. Jan. 31, 1962," USAEC Report ORNL-3262, p. 38. | 9. "MSRP Semiann. Prog. Rep. July 31, 196L4," USAEC Report ORNL-3708, p. 95-96. | 10. S. J. Ball and T. W. Kerlin, "MSRE Stability Analysis, USAEC Report ORNL-TM-1070 (in preparation). 1l1. S. E. Beall, et al., "MSRE Design and Operations Report - Part IV, Reactor Safety Analysis Report," USAEC Report ORNL-TM-732, Oak Ridge National Laboratory, p. 196231, August 196kL. 12. P. N. Haubenreich, private communication (part of summary of test program, in preparation). 10 INTERNAL DISTRIBUTION 1. MSRP Director's Office 28. R. L. Moore Rm. 219, 9204-1 29. E. A. Nephew 2. S. J. Ball 50. R. C. Olson 5. H. F. Bauman 51. A. M. Perry L. 8. E. Beall 32. P. H. Pitkanen 5. L. L. Bennett 5%5. C. M. Podeweltz 6. E. S. Bettis 34. C. A. Preskitt (. F. F. Blankenship 55-39. B. E. Prince 8. 8. Cantor 40. M. Richardson 9. R. S. Carlsmith 41. M. W. Rosenthal 10. R. D. Cheverton 2. D. Scott 1l1. H. C. Claiborne 43. M. J. Skinner l2. C. W. Craven, Jr. LL. 0. L. Smith 13. J. G. Delene 45. J. R. Tallackson 14. J. R. Engel 46. R. E. Thoma 15. T. B. Fowler 47. W. E. Thomas 16. C. H. Gabbard 4L8. M. L. Tobias 17. J. J. Geist 49. M. E. Tasgaris 18. E. H. Gift 50. R. Van Winkle 19. W. R. Grimes 51. D. R. Vondy 20. R. H. Guymon 52. F. G. Welfare 21. P. N. Haubenreich 55. J. V. Wilson 22. A. Houtzeel 54. K. J. Yost 23. L. Jung 55-56. Central Research Library 24. T. W. Kerlin 57-58. Document Reference Section 25. H. G. MacPherson 59-60. Reactor Division Library 26. W. B. McDonald 61-63. Laboratory Records 27. H. F. McDuffie 64. ORNL-RC EXTERNAL DISTRIBUTION 65. S. K. Breslauer, AEC, Washington 66-67. D. F. Cope, Reactor Division, AEC, ORO 68. R. W. Garrison, AEC, Washington 69. H. M. Roth, Division of Research and Development, AEC, ORO 7Q. W. L. Smalley, Reactor Division, AEC, ORO 7L. M. J. Whitman, AEC, Washington 2. J. B. Lingerfelt, AEC, ORO