2.1. Overview of MOCBurn

The MOCBurn code was developed using the Object Oriented Programming (OOP) ^[20,21] technology under the MATLAB platform based on MCNP and ORIGEN2. In running the MOCBurn, the one-group cross-section of selected nuclides and neutron flux of burnup cells are transferred from MCNP to ORIGEN2, and the resulting material inventory after irradiation and/or decay are transferred from ORIGEN2 back to MCNP.

The flow diagram of MOCBurn is showed in Fig. 1. The burnup predictor-corrector algorithm ^[10,12] is implemented in this code system to improve the precision, as it is implemented in Monteburns, MCBurn and some other codes. In an MSR, the fuel mixture is carried out after every bunrup time step or decay time step. First, initialize the code system with the user input file. Next, for a first run case, the MCNP is run to get the initial K_eff, neutron flux distribution and the problem-dependent neutron-spectrum-weighted cross-section. For a continue-run case, the code system is initialized with the output file from last run. Then, the code system gets into the burnup steps run until all the steps are finished. In each burnup step, the predictor-corrector algorithm is implemented first to obtain K_eff, neutron flux and the problem-dependent neutron-spectrum-weighted cross-section for the current time step, and the point burnup calculation of every burnup-cell is then carried out using ORIGEN2 code. After that, the MCNP calculation is performed to obtain parameters for the next time step calculation. The detailed calculation procedure for molten salt reactor is described in the Fig. 2.

Fig.1.Full-screen View

Flowchart of the MOCBurn code system.

Fig.2.Full-screen View

Calculation procedure for a molten salt reactor case.

2.2. Characteristics of MOCBurn

The MOCBurn code is designed with new characteristics and arrangements for MSR analysis, specifically.

(1) Treatment of the fuel mixture due to the molten salt motion

In an MSR, the fuel salt moves all the time through the primary loop, and fuel mixing occurs in the convection and diffusion of molten salt. This is the most critical difference between an MSR and a solid fuel reactor. The fuel mixing needs additional calculation and consideration in a burnup analysis code. The MOCBurn code calculates the fuel mixing after each burnup time step, if necessary, during the MSR analysis.

(2) Treatment of repeat structures

Repeat structures are widely used in modern nuclear reactors. The MOCBurn code can model repeat structures of complex geometry.

(3) Simulation of refueling and processing online

In an MSR, the fuel can be added online, and processed online or offline. The MOCBurn code can simulate the online and offline fuel adding and processing.

(4) Easy to modify and update

The MOCBurn code under OOP technology is easy to modify or update. In the MOCBurn, two abstract classes, NeutronTransport and PointBurnup, are defined. The class Mcnp is inherited from class NeutronTransport, packaging the Monte Carlo neutron transport code MCNP. The class Origen is inherited from class PointBurnup, packaging the ORIGEN2 code. The code system can be modified or updated by just replacing the class Mcnp and class Origen. One can alternate the class Mcnp by other class inherited from class NeutronTransport packaged other neutron transport or neutron diffusion code. Also, one can alternate the class Origen by other class inherited from class PointBurnup packaged other burnup code, such as multi-group burnup code.

(5) Easy to be cross platform

The MOCBurn code can run on either Windows or Linux operating systems.

3.1. Description of the high burnup PWR UO₂ lattice benchmark

This benchmark is a high burnup UO₂ lattice problem ^[22], which employed a single pin cell model of a standard Westinghouse 17×17 PWR assembly. The geometry model is shown in Fig. 3, the detailed pin cell model parameters are listed in Table 1 and the initial material compositions are given in Table 2. Reflecting boundary is used for the unit cell. This model represents cross section of the fuel pin while axial dependence is ignored, so the top and bottom boundary conditions are set to reflecting boundaries. The ENDF/B-VII evaluated nuclear data libraries are used to generate ACE formatted libraries for MCNP. The temperature is 300 K, the fuel is uranium dioxide with 9.75 w/o ²³⁵U enrichment which can burn to a high burnup (about 100 MWd/kg).

Fig.3.Full-screen View

Pin cell model

3.2. Results and Analysis

The CASMO-4^[23] results from the benchmark are used as references. The CASMO-4 uses neutron cross-section libraries processed from JEF-2.2 and ENDF/B-VI, the MCODE uses the libraries based on ENDF/B-VI library data, and our MOCBurn code system uses the cross-section libraries processed from the ENDF/B-VII library data.

In Fig. 4(a), the eigenvalue histories are compared among MOCBurn, CASMO-4 and MCODE, as a function of burnup, and the eigenvalue differences of MCODE and MOCburn from CASMO-4 are shown in Fig. 4(b). It can be seen that MOCBurn-CASMO-4 difference is less than the MCODE-CASMO-4 difference. Especially, at the high burnup of >60 MWd/kg, the MOCBurn is apparently better than MCODE in agreeing with CASMO-4. This means the MOCBurn code is more suitable for the high burnup problems than the MCODE.

Fig.4.Full-screen View

Eigenvalues by CASMO-4, MCODE and MOCBurn (a), and the differences from CASMO-4(b), as a function of burnup.

In Table 3, the nuclide compositions at 100MWd/kg obtained by CASMO-4 are given, and the MCODE and MOCBurn results are compared in fractional differences of nuclide composition from those by CASMO-4. It can be seen that, the fractional difference of all actinides are less than 10% except ²⁴³Am. For the fission products, all the fractional differences are less than 30%, and most of them are less than 10% except the Sm isotopes, ¹⁰⁹Ag and ¹⁵³Eu. It can be found that there is more ²³⁵U consumed and more ²³⁹Pu produced. At the last steps of burnup calculation, there is less ²³⁵U, which means less fission product of Sm, and more ²³⁹Pu, which means more Am. Considering the high burnup condition, the differences are mostly acceptable. It shows that the MOCBurn’s material composition predictions are acceptable in high burnup problems.

The benchmarking results of this high burnup UO₂ lattice problem indicate that MOCBurn is suitable for the bunrup analysis, even for high burnup cases.

4.1. Molten salt channel cell case description

This case employs a molten salt channel cell model moderated by hexagon graphite. The geometry model is shown in Fig. 5, the model parameters are listed in Table 4, and initial compositions of molten salt are given in Table 5. Reflecting boundary condition is used for the cell. The ENDF/B-VII evaluated nuclear data libraries are used to generate ACE formatted libraries for MCNP. The temperature is 900 K, the fuel is LiF-BeF₂-ZrF₄-UF₄, and the given radiation power is 1 MW.

Fig.5.Full-screen View

Molten salt channel cell model.

This study compared the eigenvalue history and the heavy metal mass separately for the fuel mixing case, which resembles the process in an MSR; and for the non-fuel-mixing case, i.e. the case of a solid fuel reactor.

4.2. Results and Analysis

Figure 6 shows comparisons of eigenvalue history and heavy metal mass history, between considering and non-considering the fuel mixing. It can be seen that fuel mixing increases the fuel efficiency, leading to the growth of eigenvalue at the first several steps. At the same time, the fuel mixing increases the depletion rate of heavy metals, which decreases the rate of eigenvalue.

Fig.6Full-screen View

Comparisons of the eigenvalue (a) and heavy metal mass (b), between fuel-mixing and non-fuel–mixing.