Burnup Calculation - Analysis and Evaluation of the Dual Fluid Reactor Concept

Chapter 8 Introduction

One of the important dierences between the DFR and conventional, thermal LWRs is its fast neutron spectrum. This spectrum allows the FR to eciently breed fuel and ssion minor actinides. Therefore, the study of the burn-up process in the DFR will focus on the online fuel processing capability, the development of the specic nuclide inventory during the burn-up, and the determination of its breeding gain and breeding ratio. In this thesis fuel re-processing is only mentioned in specic contexts, but no detailed study is oered.

Prior to performing the burn-up calculations, the discretization of the ssion zone into dierent depletion sections, not only in the radial but also in the axial direction, was considered. In the end, such a rened nodalization it was not adopted, because, for a reactor with a liquid fuel salt core, as is the case of the DFR, the fuel salt is distributed from a common well mixed source into the fuel tubes into the ssion zone and, in a few seconds, the fuel salt ows out of the zone and is mixed in the outlet plenum. Therefore, inside of the ssion zone there are no regions with dierent burn-ups.

Burn-up with and without online processing involving various nuclear fuel types is studied in this Chapter, without regard to the details on how the ssion products and other nuclides are extracted from the owing salt. In each case general information about the fuel salt composition and the reactor conguration are given, and the results obtained for the evolution of k_e and the salt inventory are presented and analyzed. Finally, the breeding characteristics of each case are discussed.

The following section oers a complete discussion on the topic of the calculation options. Since a burn-up calculation involves many nuclides and materials, it needs important calculation resources. Based on the resources available at the time of this thesis work, adequate parameters for the calculations should be carefully selected, so that they are performed as accurate and eciently as possible. The study presented in Sec. 8.1 assesses dierent combinations and obtains the proper parameters for an ecient burn-up calculation of the DFR reactor. The results reported in sub-sequent sections are based on calculations following the conclusions reached in this rst section.

82 CHAPTER 8. INTRODUCTION

Figure 8.1: Optimization mode

8.1 Calculation options

The code SERPENT provides various calculation and optimization modes for specic needs. Because the burn-up calculation always consumes a large amount of time and computer memory, rst, an assessment of the results generated by dierent calcula-tion opcalcula-tions is carried out, in order to achieve a balance between time, calculacalcula-tion resources and precision of the results.

8.1.1 Parameters

The assessment has investigated the eect of the following parameters depletion calculation:

1. bumode gives the probability to choose the method for solving the Bateman equations from Transmutation Trajectory Analysis [Iso13] (TTA), Chebyshev Rational Approximation Method [PL12] (CRAM) or the variation TTA.

2. egrid denes the energy grid used for the reconstruction of the continuous-energy cross sections to accelerate the calculation. By changing the fractional reconstruction tolerance, the total allocated memory is changed. Because of some loss of data, the consequence due to the reduction of the grid on the results is not signicant until the tolerance is raised above×10⁻² [Lep13, pp.25].

3. dix means double-indexing mode, which is not available in SERPENT 2, but only functional in SERPENT 1.

4. opti provides 4 dierent modes to balance the memory usage and the calcula-tion time, while maintaining the quality of the results. A detailed optimizacalcula-tion description can also be found in Fig. 8.1 [LI12].

5. pcc balances the calculation time and the accuracy of the estimation of iso-topic changes during each burn-up step by activating the predictor-corrector

8.1. CALCULATION OPTIONS 83

ref bumode dix1 3 4 egrid3 2 1 2opti3 4 pcc xscalc1

bumode1 × × × × × × × × × × × ×

bumode2 + × × + + + + + + + + + +

bumode3 × × × × × × × × × × × ×

dix × × × × × × × × × × × ×

egrid5 + + + + × × × + + + + + +

egrid4 × × × × × × × × × × × ×

egrid3 × × × × × × × × × × × ×

egrid2 × × × × × × × × × × × ×

opti1 × × × × × × × × × × × ×

opti2 × × × × × × × × × × × ×

opti3 × × × × × × × × × × × ×

opti4 + + + + + + + × × × + +

pcc × × × × × × × × × × × ×

xscalc1 × × × × × × × × × × × ×

xscalc2 + + + + + + + + + + + + ×

Table 8.1: Optimization Options

calculation [DKSL13]. Although this is not really an optimization mode, the activation of the option will double the number of transport runs and, therefore, increase the running time and the desired precision.

6. xscalc provides two modes to deal with the one-group transmutation cross sections during the transport cycle. The default value in the reference is ex-pected to reduce the time by a factor up to 4, but aect the statistical accuracy compared to a direct calculation of the cross section [Lep13, pp.113].

All the calculations were carried out with 10 threads on Intel^R Xeon^R L7555 1.87 GHz processors. Moreover, it is worthy to note that the results depend sig-nicantly on the number of burnable materials considered, which is set in the cut-o option.

8.1.2 Results

A burn-up case with U-Pu fuel salt was selected to be used in the test calculations.

This case has 23 burn-up steps and a neutron population of 100,000 in 50 active and 50 inactive cycles. A total of 292 nuclides were considered in each step of the burn-up calculation.

The reference calculation adopted the default optimization options, which are listed and compared with other test calculations in Table 8.1. In the table the symbol means that this parameter was assigned the corresponding value or that this option was activated, while × means there was not such a parameter or option in this case or it was deactivated, and + means default parameter values or values assigned by the program automatically, if they are not specied.

84 CHAPTER 8. INTRODUCTION

Average Time Per Burnup Step (min)

TOT_CPU_TIME

BATEMAN_SOLUTION_TIME Average Time Per Burnup Step (min) Other Average Time Per Burnup Step (min)

Parameters Other Time Terms

INIT_TIME PROCESS_TIME BURNUP_CYCLE_TIME BATEMAN_SOLUTION_TIME

Figure 8.2: Time comparison between parameters

It has to be mentioned that for the parameter egrid, in the table the number behind the name means the power of 10 of the tolerance. For example, egrid5 means a tolerance of10⁻⁵ and so on. In the optimization mode opi 3 overrides the energy grid thinning with the thinning tolerance set to 0.

It needs to be remarked that the results shown are exclusively valid for the case, for which the calculation was performed. For other dierent cases the results may vary. The results are classied into parameter groups: referenced with parameter bumode; referenced with parameter egrid; referenced with parameter opti and referenced with other parameters.

8.1.2.1 Balance of Time and Memory 1. Time

The time comparison between parameters is shown in Fig. 8.2. For the burn-up calculation the total time, following the calculation sequence, can be di-vided into Initial time (INIT_TIME), Process time (PROCESS_TIME), Transport time (TRANSPORT_CYCLE_ TIME) and Burn-up time (BUR-NUP_CYCLE_TIME).

The top gure shows the comparison of the Total CPU Time, which uses TOT_CPU_TIME to calculate the average CPU time used for each

burn-8.1. CALCULATION OPTIONS 85

Figure 8.3: Memory comparison between parameters

up step. Since each calculation is OMP [omp15] parallelized with 10 threads, TOT_CPU_TIME is the product of the real running clock time (RUNNING_TIME) and the real CPU usage (CPU_USAGE). The middle gure reveals the The Transport Time, the time used for the transport cycle. The bottom one sum-marizes four other time terms. The time used for solving the Bateman equa-tions, displayed as red dots, refers to the right axis, and the other three terms as columns refers to the left axis.

It can be clearly observed that, even though the change of the egrid value has an obvious trend in the other time terms, the most important Transport Time only aects the calculation time when the tolerance is set to10⁻². The time used between the optis depends on the corresponding purposes as shown in Fig. 8.1. Setting pcc to 0 causes a time reduction of almost half of the total time for the calculation compared to other parameters. And the default xscalc setting reduces the total CPU time, as well as, the transport cycle time. Nonetheless, for other time terms the dierence is not signicant.

2. Memory Requirements

The memory usage in SERPENT consists of several terms: memory used for material (MAT_MEMSIZE), memory used for cross section (XS_MEMSIZE), other memory consumption (MISC_MEMSIZE) and terms that not be grouped (REST_MEMSIZE).

Figure 8.3 (upper plot) shows that in this case only some parameters (egrid and opti) have eect on the memory usage of the SERPENT depletion cal-culation. The amount of memory needed for other parameters almost does not change. Since in the reference (ref) calculation the egrid adopts the frac-tional reconstruction tolerance of 10⁻⁵, the tolerance level on 10⁻⁴ reduces the memory usage dramatically from nearly 30GB to around 15GB, while the tolerance level on 10⁻³ and on 10⁻² reduces this usage less, which result in

86 CHAPTER 8. INTRODUCTION

ref dix egrid4 egrid3 egrid2 opti1

opti3 opti4 bumode1 pcc0 xcalc

-250

ref dix egrid4 egrid3 egrid2 opti1 opti3 opti4 bumode1 pcc0 xcalc

Figure 8.4: k_e comparison between parameters

a memory usage of 10 GB and 9 GB respectively. The parameter egrid de-scribes the minimum relative dierence between two grid points, below which both points are combined into a single one. THus, the higher the tolerance, the less memory is needed to store the energy grids.

The optimization mode opti has also a noticeable impact on memory usage.

The option opti 1 requires a minimum of memory, around 3GB, whereas the other options consumes increasingly more, until the option opti 4 stabilizes the memory requirements.

On the other memory terms, the comparison of which are showed in the lower gure, egrid series also have signicant impacts on the memory usage. The memory usage of the cross section generation of opti1 and opti2 are nearly none.

8.1.2.2 Evolution of k_e

In this subsection, thek_e calculated with dierent combinations of computational parameters are compared and discussed. Figure 8.4 shows the relative dierences with respect to the reference settings. The depletion calculated in this evaluation is expected to be as long as possible in order to investigate the accumulated dierences caused by the options used. Therefore, a total depletion of 630 GWd was chosen.

With the ref results (red line and rst column in Table 8.1) are taken as a reference, most of thek_evalues spread in a range between -200pcm and 150pcm, which can be considered acceptable for general evaluations. The k_e for the case pcc0, however, begins to diverge at about 200GWd/MTHMf uel. The ∆k_e of this case reaches the boundary of the variations of the other cases at about 520GWd/MTHMf ueland exceeds it at 550GWd/MTHMf uel.

8.1.2.3 Material Inventory

In order to evaluate the dierences introduced by the material inventory, the nuclides

238U , ²³⁹Pu and ²⁴¹Pu were selected for comparison. Figure 8.5 shows that the material inventories in the burn-up region of interest are consistent except for the combination of parameters labeled dix with the double indexing mode.

8.1. CALCULATION OPTIONS 87