WSRC-MS-99-00313

Updated Critical Mass Estimates for Plutonium-238

Available to the public from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, VA 22161.

Abstract

As part of the standards effort of the American Nuclear Society to establish subcritical mass limits for actinide nuclides other than ²³³U, ²³⁵U, and ²³⁹Pu, updated critical mass estimates are first being calculated for various actinide nuclides. This paper describes updated critical mass estimates for ²³⁸Pu using several combinations of computer codes and nuclear data sets. A brief description of the analytical methods employed is followed by a presentation of the results.

Introduction

ANSI/ANS-8.15-1981, "Nuclear Criticality Control of Special Actinide Elements" is in the process of being revised. For the purpose of this standard, special actinides refer to neutron-fissionable actinides other than the nuclides ²³³U, ²³⁵U, and ²³⁹Pu. These actinide nuclides are typically created by neutron-induced transmutation during the irradiation of nuclear fuels. Several of these nuclides exist in sufficient quantities to be used in nuclear medicine, heat sources, neutron sources, and recycled nuclear fuels. Thus, subcritical limits must be established for the safe handling and use of these nuclides.

One of the nuclides of interest for the update of ANSI/ANS-8.15-1981 is ²³⁸Pu. The relatively sparse experimental data which exists on the measured reactivity coefficient of ²³⁸Pu relative to ²³⁹Pu has been generated by primarily by Stubbins, et. al. [1] and, to a lesser degree, by Byers, et. al. [2] The high heat output (0.557 watts/g) of ²³⁸Pu makes experiments difficult to perform. Therefore, the majority of ²³⁸Pu critical mass estimates are based on the analysis of hypothetical systems using various computer codes and nuclear data sets. Data from hypothetical studies by Clark [3] and Westfall [4] served as the basis for the ²³⁸Pu subcritical limits originally developed for ANSI/ANS-8.15-1981. Since then, improvements have been made to nuclear data sets, more data sets are available, and more computer codes are currently in use as well.

The primary purpose of the present paper is to describe an updated analysis of hypothetical ²³⁸Pu critical systems for use in the revision of ANSI/ANS-8.15-1981. However, a few other calculations of interest related to ²³⁸Pu are included as well. The scope includes:

• single metal and oxide units (bare, water reflected, 304 stainless steel reflected, and carbon steel reflected);
• isotopic mixtures of ²³⁸Pu and ²³⁹Pu oxide, dry or optimally moderated with water, and reflected by water;
• the H/²³⁸Pu ratio for which K_inf = 1.0; and
• K_inf for ²³⁸Pu metal.

The international nuclear community also appears to be interested in the development of a standard dealing with special actinide nuclides. Therefore, the secondary purpose of this paper is to include a representative combination of available computer codes and nuclear data sets such that the results can be of use in the development of an international standard.

Analytical Methods and Data

Critical core radii searches were performed with the following codes and nuclear data sets:

SCALE4.3; KENO-Va with ENDF/B-V, 238 group cross sections [5];

MCNP4b with ENDF/B-V continuous cross sections [6];

MCNP4b with ENDF/B-VI continuous cross sections [6] ;

MCNP4b with JENDL-3.2 continuous cross sections [7];

MONK7B with UKNDL 8220 group cross sections [8,9];

MONK7B with JEF-2.2 13193 group cross sections [8,10];

DANTSYS 3.0 with ENDF/B-V 238 group cross sections [11].

For the monte carlo codes (KENO-Va, MCNP4b, MONK7B), critical radii search results were considered acceptable if the calculated K_eff = 1.0 +/- one standard deviation (< 0.003 when using 100,000 neutron histories). The calculated critical radii and material densities were then used to obtain critical mass estimates. For the DANTSYS 3.0 discrete ordinates transport code, all critical radii searches used S₁₆ quadrature, P₃ scattering, and a convergence criterion of 0.001, or less.

Other data of interest are as follows: a 30 cm. thickness was used for all reflectors: ²³⁸Pu metal density was adjusted relative to 19.84g/cm³ for plutonium containing 95 % ²³⁹Pu and 5% ²⁴⁰Pu; ²³⁸Pu oxide density was adjusted similarly relative to 11.46 g/cm³.

The computer code and data set combinations were validated against the experimental data of Stubbins, et. al. These experimental data show that the ratio of the reactivity worth of ²³⁸Pu/²³⁹Pu for bare metal was 0.99 +/- 0.09 (subcritical measurements) and 1.02 +/- 0.09 (critical measurements). A code and data set combination was considered acceptable if the ²³⁸Pu/²³⁹Pu calculated critical mass ratio for bare metal ranged between 0.9 (i.e., 0.99 - 0.09) to 1.11 (i.e., 1.02 + 0.09). Table 1 presents the calculated bare critical mass of ²³⁸Pu, ²³⁹Pu, and the ²³⁸Pu/²³⁹Pu critical mass ratio. All code and data set combinations met the validation criterion.

Table I.  Code and Data Set Validation

Results and Conclusions

²³⁸Pu Metal and Dry Oxide Systems, Bare and Reflected

Calculated critical masses for ²³⁸Pu metal and dry oxide systems, bare and reflected in each case, are given in Table II and III, respectively. ²³⁸Pu is dependent on fast neutrons for criticality. Of the three reflectors chosen for study, 304 stainless steel has the greatest reflector worth, reducing critical mass by 47 - 50% of the values for the unreflected metal system and by 50 - 57% of the critical values for the unreflected oxide system. Carbon steel has somewhat less reflector worth than 304 stainless steel. A water reflector has the least reflector worth and only reduces the critical mass by approximately 17 - 24% compared to the unreflected values for either the metal or oxide system. Table II also includes the earlier Clark [3] and Westfall [4] results for the purpose of comparison.

Table II.  Calculated Critical Masses for ²³⁸Pu Metal Systems

^aType 304 stainless steel; density = 7.9 g/cm³; number densities (atoms/barn-cm): C = 3.1691-4, Cr = 1.6471-2, Mn = 1.7321-3, Fe = 6.036-2, Ni = 6.4834-3, Si = 1.694-3 as contained in the SCALE/KENO-Va data library.

^bCarbon steel; density = 7.82 g/cm^3; number densities (atoms/barn-cm): C = 3.921-3, Fe = 8.3491-2 as contained in the SCALE/KENO-Va data library.

Table III.  Calculated Critical Masses for ²³⁸Pu Oxide Systems

Mixtures of Dry and Optimally Moderated ²³⁸Pu and ²³⁹Pu Oxide, Reflected by Water

Mixtures of ²³⁸Pu and ²³⁹Pu are of interest in preparing heat sources. Generally, such mixtures contain approximately two thirds ²³⁸Pu and one-third ²³⁹Pu. The processing of this type of material typically involves the handling of both dry oxide and oxide mixed with water, with the potential for water reflection in either case. However, depending on the isotopic mix, either the dry oxide reflected by water, or a water-oxide mixture reflected by water, may result in the limiting critical mass. For ease of operations, it is useful to determine the isotopic mix for which the Pu mass and limiting value for K_eff of the dry oxide reflected by water is the same as that for a water-oxide mixture reflected by water. Due to uncertainties in the ²³⁸Pu cross sections, Clark [3] suggested during the original preparation of ANSI/ANS-8.15-1981 a limiting value of K_eff = 0.9 as adequate to ensure subcriticality. Clark calculated that a total Pu mass of 8.15 kg , with an isotopic mix containing 67 wt. % ²³⁸Pu/ 33 wt. % ²³⁹Pu, would result in K_eff = 0.9 for both dry Pu oxide reflected by water and a water-Pu oxide mixture reflected by water. Although updated nuclear data sets are available, uncertainties in the ²³⁸Pu cross sections remain and no experimental data exists for such systems. Therefore, a limiting value of K_eff = 0.9 is maintained as a suitable subcritical value for this paper. Table IV gives the calculated total Pu mass and isotopic mix, for dry Pu oxide reflected by water or for a water-Pu oxide mixture reflected by water, for a limiting value of K_eff = 0.9 for three of the code/data set combinations.

Table IV.  Total Pu Mass and Isotopic Mix, as Dry Pu Oxide Reflected by Water, or an Aqueous Mixture of Pu Oxide Reflected by Water, for K_eff = 0.9

H/²³⁸Pu Ratio for K_inf = 1.0

The thermal neutron fission cross section is higher than the fast neutron fission cross section for ²³⁸Pu. However, the corresponding capture cross section is such that the probability of fission is much higher for fast neutrons. Therefore, it is of interest to determine the minimum H/²³⁸Pu ratio for ²³⁸Pu metal-water mixtures for which K_inf = 1.0. This ratio is useful for developing a subcritical concentration limit for ²³⁸Pu. Clayton and Bierman [12] previously published a value for the minimum H/²³⁸Pu ratio of 3.8 for K_inf = 1.0 for metal-water mixtures using cross section data from the late 1960's. Table V give the minimum H/²³⁸Pu ratio, and equivalent ²³⁸Pu concentration, for K_inf = 1.0 for each of the code and data set combinations used in this paper.

Table V.  H/²³⁸Pu Ratio and Equivalent ²³⁸Pu Concentration for K_inf = 1.0

K_inf for ²³⁸Pu Metal

The final parameter of interest related to ²³⁸Pu which was calculated as part of this paper is K_inf of the metal. Srinavasan, et. al.[13] have previously published K_inf = 2.884 for ²³⁸Pu metal. Table VI gives K_inf for five of the code and data set combinations used in this paper.

TABLE VI.  K_inf for ²³⁸Pu Metal

Summary and Conclusions

In summary, this paper has examined several systems of interest related to ²³⁸Pu. Critical masses were calculated for ²³⁸Pu metal and oxide (bare, water reflected, 304 stainless steel reflected, and carbon steel reflected). The subcritical limit was calculated for isotopic mixtures of ²³⁸Pu and ²³⁹Pu oxide, dry or optimally moderated with water. The H/²³⁸Pu ratio for which K_inf = 1.0 and K_inf for ²³⁸Pu metal were also calculated. The analyses have demonstrated the:

• general agreement of current code and data set combinations to previous experimental measurements of the reactivity worth of bare ²³⁸Pu relative to bare ²³⁹Pu;
• sensitivity of the results to the various code and data set combinations;
• increase in critical mass estimates compared to earlier results.

References

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