The transient reactor test facility (TREAT), a graphite moderated experimental reactor, is scheduled to restart in late 2017. There is now renewed interest in development of capabilities to model and simulate the TREAT transients using three-dimensional coupled physics. To validate existing transient analysis tools as well as those under development, several temperature-limited transients have been modeled and analyzed. These transients are from the M8 calibration (M8CAL) experiment series, a set of experiments performed to calibrate the reactor detectors for the planned M8 series of fuel tests. Detailed reactor models were prepared that were then used to calculate the pretransient and post-transient keff values as well as corresponding reactivity insertions. Alterations to modeled values of shutdown and initial transient rod insertion depths were made to better match the reported experimental values of reactivity insertions assuming just critical pretransient states. It was found that two of the altered media inputs, fuel and Zircaloy-3 cladding, had significant effects on the keff. In addition, increasing shutdown rod insertion by 3–5 cm and decreasing initial transient rod insertion by 1–2 cm gave perfect pretransient keff and total reactivity insertion values. However, the revised positions are as much as a factor of 3–20 different from reported uncertainty of 0.762 cm. This suggests that boron concentration uncertainties may play a significant role in accurately modeling the TREAT transients and should be investigated thoroughly.
The transient reactor test facility (TREAT) is a graphite-moderated experimental reactor, designed to enable a short high-energy neutron pulse leading to rapid energy deposition within mockups of reactor fuel elements under controlled conditions without harm to the reactor itself, allowing the ability to examine the behavior of fuel materials in accidental supercritical events. TREAT has been on cold standby since 1994 . Recently, interest in novel heat-resistant fuel and cladding types has increased . The TREAT reactor is scheduled to be returned to operation with a target date of November 2017.
The TREAT core is made up of square fuel elements with chamfered corners that form square channels for airflow through the axial length of the core. The core's time-dependent behavior is difficult to model with traditional methods due to these unique air channels. Traditional methods typically involve the deterministic solution of discretized meshes over a reactor. The viewports and air holes, which allow some neutrons a path to escape the reactor while passing through very little graphite and fuel, result in a highly anisotropic flux. This requires the cross sections to be corrected to account for those streaming paths for accurate solutions. Monte Carlo calculations are an alternative for determination of the correct time-dependent fluxes and do not require any cross section corrections.
In this study, three experiments from the M8 calibration (M8CAL) series , referred to as temperature-limited transients, were modeled and analyzed with KENO codes [4,5]. The geometry of the reactor used for these experiments, and the corresponding KENO models, are described in the following sections.
The TREAT fuel elements are made of graphite with highly enriched (93.1%) UO2 dispersed homogeneously within the element, with graphite to uranium ratio of 10,000:1. The fuel elements are 10.06 cm square with 1.59 cm chamfered corners for air coolant flow, as can be seen on the right side of Fig. 1. The active fuel length is 122.24 cm and the total fuel element length is 247.65 cm. Each of these elements is surrounded by a vacuum layer and a layer of Zircaloy-3 cladding. On either axial end are octagonal graphite blocks, clad to the same outer dimensions with aluminum. The innermost 9 cm of graphite on either side forms unchamfered rectangular prisms with smaller radial edges, to make room for small flaps of Zircaloy-3 used to fasten the fuel segments to the reflector blocks. These fuel and reflector segments form single elements, which are arranged in a square lattice with a pitch of 10.16 cm. The spacing between the elements and the chamfered corner areas are used for air entry for cooling the reactor between experiments. In the center of the reactor, experimental fuel or calibration fission wire may be placed in a containment vessel for testing.
In the current core configuration, there are a total of 20 control elements, which are fuel elements with a central cylindrical hole to accommodate control rods. The control rods have a 152.4 cm active absorber length with a graphite follower. These 20 control elements are grouped into three banks: four compensation rods, eight control/shutdown rods, and eight transient rods. During transient operation, the compensation rods are used at the end of the transient to shut down the reactor. The control/shutdown rods are used to maintain the reactivity of the core during transient operation. The transient rods are the rods that are maneuvered to initiate transient conditions during transient operation. Control rod consists of mobile cylindrical rods moved through a central cylindrical hole in otherwise standard fuel elements, with a cylinder containing B4C at the top, and with a graphite follower attached below this cylinder. The graphite follower sets on top of a steel rod, which extends down into the subpile room. The boron carbide section and lower graphite section are clad in mild steel, and the upper graphite plug in Zircaloy-3, and the whole rod travels through an aluminum tube inside the fuel element. Fuel elements containing these rods are placed throughout the reactor in a roughly circular fashion midway from the center. Elements are generally arranged in a symmetric fashion around a central experimental vehicle containing fuel or fission wire.
The array of elements is surrounded laterally by a large number of contiguous graphite blocks, with a small number of holes and slots functioning as visual or radiation viewports and air holes for air entry. This graphite is surrounded axially and radially by machinery and shielding, as shown in Fig. 2. The elements can be removed or replaced with dummy elements between experimental procedures, allowing for highly varied reactor geometries.
M8 Calibration Core Layout.
The experiments modeled here are three similar temperature-limited transients from the final experimental series identified as M8CAL experiments. The M8CAL experiments were a series of 23 tests for the purpose of determining the correlation of the power generated in a test sample to the TREAT reactor power . The intent of these tests was to calibrate the core detectors to the test environment in preparation for a series of fuel failure tests called the M8 tests. The M8 test series was never performed due to the decision to place the core in standby mode. However, due to the relatively large amount of available information on the geometry and energy output for each transient, the M8CAL test series is generally considered the best source of information on reactor performance, and reflects the current configuration of the core.
In this series of experiments, the reactor was arranged to have a 19 × 19 element lattice. Dummy elements were placed in the three positions nearest each corner; these elements contained unfueled graphite throughout the entire axial length. In the middle, the three element locations nearest the center contain the experimental vessel of a size of roughly 1 × 2 elements, in this case containing a neutronic mockup of a pumped sodium loop. In the outer sides of this can were two “half block” dummy elements, filling up the rest of these outer spaces. The lower half block was a half-width graphite block, while the upper half block and all full blocks above it were instead equivalent to normal fuel elements with the fuel removed. A scheme showing this is given in Fig. 3. In this figure, the numbers represent the unit numbers, which are building blocks for defining the geometry for modeling and simulating the system using the Monte Carlo method. A 10.16 cm hole across the outer graphite area edge provided a viewport through which motion within an experiment could be observed via fast neutron detectors , shown in purple in Fig. 3. The assembled bank of fast neutron detectors is known as a hodoscope. Although this device was not used for M8CAL measurements, the air gap between the experiment location and the hodoscope was still present. Figure 4 shows a three-dimensional model of the core center, with one quarter cut away for better viewing.
The eight shutdown rods were partially inserted during experiments to achieve exact criticality in the pretransient state. The four compensation rods, located near the center of the core, were used to shut down transients completely at the end of each experiment, but remained fully withdrawn during each transient experiment. Neither of these types of rods moved during the experiments modeled in this paper. Finally, the eight transient rods were partially inserted at positions that would result in a prescribed Δk when fully withdrawn. To initiate a transient, the transient rods were rapidly (∼0.1 s) removed from the core to produce supercritical transients in the reactor. The axial heights of the shutdown and transient rods were varied to change the period of the reactor excursion. The period would in turn drive the amount of energy deposited in the target materials. In Fig. 3, elements with shutdown rods are depicted in yellow and labeled with numbers ending in 53 or 72, compensation in orange and labeled with numbers ending in 57, and transient in green, labeled with numbers ending in 27 or 35.
In this paper, we investigate models of three specific M8CAL transients, which were temperature-limited and lasted for 60 s each. These tests, which are identified in operations records as transient tests 2855, 2856, and 2857, have enough recorded data available that they can be used to perform detailed analyses. The reactor configurations for these experiments were identical in all aspects except the rod insertion depth. In order to prevent inconsistencies, a Fortran program was developed to prepare model inputs for the Monte Carlo transport code KENO. This allowed quick generation of various inputs corresponding to varying rod insertion values.
The TREAT geometry was modeled with fine detail, up to the exterior of the outer graphite elements. However, uncertainties exist regarding the exact contents of the reactor, and these unknown differences may have significant effects on the outcomes of the model, as will be discussed below. In all models, ENDF/B-VII.0-based 238 group SCALE multigroup cross section libraries were used. All KENO models used at least 8800 active generations with at least 10,000 particles per generation. Although eigenvalue calculations with the Monte Carlo codes typically converge within the first 100 generations (except for high dominance ratio systems of which TREAT is not), in each case the first 1200 generations were skipped.
Due to a lack of chemical analysis or accurate manufacturing data about whether nominally identical materials in different parts of the reactor that contain fuel were produced with the same impurities, it is difficult to accurately determine the number densities (atoms/barn/cm) of fuel containing reactor materials contributing to the uncertainty about the isotopic compositions of a number of the materials.
The two materials with the highest impact on the k-eff are naturally the fuel and the Zircaloy clad due to their large uncertainties and impurities. No complete chemical analysis of TREAT fuel has been found, and quantities such as impurity content and graphitization of the carbon surrounding the fuel are only estimated. It is believed that fuel is roughly 59% graphitized . Furthermore, during manufacturing of the fuel, borated steel divider plates were used in the baking crucibles. Although the material blocks used to construct the fuel only had a boron content very close to 1 ppm, later analyses of the fuel blocks showed varying quantities of boron with an average of 5.90 ± 0.35 ppm  due to unexpected diffusion of boron from these borated steel dividers. The only solution for this problem is to replace the fuel, which will not happen with a highly enriched uranium core. A potential conversion to low enriched uranium fuel, however, would alleviate the problem.
Graphite, Aluminum 6063, Aluminum 1100, control rod poison, mild steel, and SS-304 definitions used in the models were based on definitions from Tables 3.5, 3.17, 3.15, 3.21, 3.18, and 3.19 of , respectively.
Alterations to modeled values of shutdown and initial transient rod insertion depths were made to better match the reported experimental values of reactivity insertions assuming just critical pretransient states. This was accomplished by first establishing the initial values with the reported rod positions. The pretransient transient rod positions were then adjusted within the specified uncertainty and even beyond the given uncertainty to see if reported reactivity values can be obtained. Finally, shutdown rod positions were modified to obtain keff = 1.0 with the original transient rod positions and the transient rod positions were modified to obtain the reported reactivity values since one would expect to have the correct power trace only if the total reactivity insertion is calculated correctly barring cancellation of errors. It was assumed that the fission source was sufficiently converged for the purpose of eigenvalue calculations in this study. All KENO simulations with the original rod positions were performed with 125 × 106 total active histories. KENO simulations with revised rod positions were performed with 1.21 × 109 total active histories to achieve as precise values as possible.
Calculations With Original Pre- and Post-Transient Rod Positions.
The rod insertion and withdrawal positions found in Ref.  are shown in Table 1. In this study, “withdrawal point” values are the maximum withdrawal of the rods, determined by the distance from the lowest reach of the poison to the axial center of the fuel. Insertion values are the distance below the withdrawal point to which the rod extends at the start of the transient. Table 1 lists best known values, but there is a 95% confidence error estimate of ±0.762 cm .
Using the rod withdrawal and insertion values listed in Table 1, a series of eigenvalue calculations were performed for transients 2855, 2856, and 2857 for pre- and post-transient states. The resulting values of keff and Δk/k computed by KENO-VI are shown in Table 2. In all tables, “Pre”, “Post,” and “Δk/k” refer to the calculated pretransient keff, post-transient keff, and the corresponding reactivity values, respectively. For all three transients, the initial keff values are within 0.25% of the experimentally measured values. Note that none of the documentations on these experiments state the actual multiplication of the system. Rather, it is stated that the system is critical at low power (10 W), meaning the multiplication factor of the system is slightly over 1.0 to result in positive period. For all practical purposes, it can be assumed that the initial keff of the system is 1.0. The calculated post-transient values for transients 2855, 2856, and 2857 are 0.35, 0.41, and 0.50% higher, respectively, than the experimentally measured values, indicating that the reactivity insertion as a result of corresponding transient rod movements will be higher (overestimated) than stated. This could be due to problems with the reported values (and reference positions) or with the code. However, unless there are problems with the post-transient geometry, one would expect similar overestimation of the post and pretransient keff values. As seen by the Δk/k values, the calculated reactivity insertions are more than 5% higher in all three cases. With such higher estimated reactivity insertions, the peak and total powers calculated by transient analyses tools utilizing the same set of cross sections and KENO would also be higher.
Calculations With Revised Pretransient Rod Positions.
As stated above, uncertainties of 0.762 cm exist in the initial transient rod insertions in the M8CAL experiments. Due to the differences in Δk/k between the values found in Table 2 and the experimental values, rod positions were revised to test whether models with rod insertion within these uncertainties could have experimental values of Δk/k. Since the initial rod positions gave slightly larger keff values, the initial rod positions were changed to result in smallest amount of rod insertions therefore smallest amount of reactivity insertions. This was expected to have better Δk/k agreement with the experimental values than did those in Table 2. The calculated pretransient, post-transient and estimated reactivity values are shown in Table 3. Since the post-transient positions have not been altered, the post-transient values in Table 3 are the same as those listed in Table 2. Note that the initial keff is slightly farther above 1 than in Table 2, but the difference from experimental values in Δk/k is lower with transient 2855 showing the largest improvement than transients 2856 and 2857. However, the agreement on Δk/k is still not as good as desired. In this study, a good agreement on Δk/k is arbitrarily defined as less than 0.1% difference.
Since changing the pretransient rod positions did not result in good agreement, the pretransient rod positions were further revised to improve the agreement. However, this resulted in initial positions that are not within experimentally reported positions. The resulting pretransient rod insertion values are shown in Table 4, with the calculated pretransient keff values and reactivity data given in Table 5. With the rod positions given in Table 4, the estimated reactivity insertions for all three transients are within less than 0.1% of the reported values.
Calculations With Revised Shutdown and Transient Rod Positions.
Finally, shutdown rod insertion values were revised to calculate an initial keff of 1 using the original pretransient rod values. The initial and final keff were calculated, and the post-transient rod insertion was altered to find the Δk/k values that matched the experimentally reported reactivity values. The final rod insertion values, which resulted in both experimentally reported Δk/k and initial keff values, are shown in Table 6. The corresponding calculated pre- and post-transient keff values as well as Δk/k values are listed in Table 7. All estimated Δk/k values are within 0.1% of the reported values with initial calculated keff values within 0.01% of the initially just critical systems (keff = 1.0).
Although the initial model of the TREAT reactor behaved similarly to experimental results, the agreement between calculated and reported values was not as good as desired. The shutdown and transient rod positions were altered in order to increase agreement with reported values from Refs.  and . Final calculated values for pre- and post-transient keff and Δk/k values indicate that transient analyses using the revised shutdown and transient rod positions should result in more accurate calculation of peak and total powers for the temperature-limited transients 2855, 2856, and 2857 analyzed in this study. However, the revised positions are as much as a factor of 3 to 20 different from reported uncertainty of 0.762 cm. This suggests that boron concentration uncertainties may play a significant role in accurately modeling TREAT transients due to the high absorption cross section of boron in the thermal energy range. Since chemical analysis of existing fuel elements is not possible without damaging the fuel, the effect of boron concentration uncertainties should be investigated thoroughly with detailed computational models. However, other uncertainties in the transient state are also known to bias the transient solution. The spatial temperature distribution in the core is not known and could introduce significant error in feedback calculations .
Idaho National Laboratory (Grant No. 156392).