Resume of PBMR Burnup Analysis

Introduction (to be completed)1. Study by Julian Lebenhaft at MIT (1999)１

In his dissertation at MIT １, Julian Lebenhaft working for the pebble bed modelling using MCNP4B. One of the analysis is the burnup calculation of the pebble-bed reactor, and the procedure is applied in PBMR reactor.

The core and fuel element specification of the 268 MWt PBMR used by Lebenhaft are as follow

Table 1. PBMR Reference Core Specification

Table 2. Reference Specifications for PBMR Fuel Elements

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Figure 1. A Vertical View of the PBMR core

To calculate the burnup of the PBMR Lebenhaft utilize a link between MCNP4B and VSOP94. The fuel management routine in VSOP94 is used to establish the equilibrium core then nuclide atom densities of the depleted fuel resulted from this calculation is transfer to MCNP4B as an input. To handle the data communication between VSOP94 and MCNP4B, Lebenhaft built a program called MCARDS.

VSOP94 Model and AnalysisThe two-dimensional (R-Z geometry) VSOP94 model of the reference PBMR core is shown schematically in Figure 2.

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Figure 2. VSOP94 Model of the PBR

The model include following detail - The reflectors and the borated carbon thermal shields- The reactor pressure vessel, the core barel, and the associated helum

gaps are lumped together in a single annular region.- The control road are modelled by homogenizing the boron carbide

abdorber into the surrounding graphite material.- The various channels for the shutdown system and helium coolant are

modelled by reducing the density of the appropriate graphite regions.- The model of the core comprises of 57 equally sized regions called

layers, each of which contains a mixture of 10 different fuel batches. These batches represent the number of times that the fuel spheres have been through the core, from the first pass (batch =1) to last pass (batch = 10.

- The burnup of each batch is calculated individually using a fission-product chain of 44 isotopes.

- The second member of the chain is a non-saturating fission product chosen by comparisonwith ORIGEN-JUL-II code predictions, which corresponds to low absorbing fission products not modelled explicitly.

- The 43 explicit fission products cover 98.02% of the total-fission product absorptions, while the non-saturating fission product accounts for the remaining 1.98%.

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- Fuel depletion is modelled by means of burnup steps.Approximately every 9 days, each layer and its associated batches are moved down to the position of the next layer. The movement occurs in channels to reproduce the characteristic flow of pebbles within the core vessel.

- The layers at the bottom of the core discharged, and the corresponding batches (with the same number of passes through the core) from different channels are grouped and mixed together. The batches number are the incremented (to initiate additional pass through the core) and then reinserted into the various channels. The oldest batches are discharged from the core, while a tenth of the volume of each top layer is filled with fresh fuel.

- The neutronic calculation is performed using 29 spectral zones, which consist of user-specified grouping of layers. A similar procedure is used for the reflector regions where 25 spectrum zones are defined.

- The temperatures of the specified zones are establish using the thermal-hydraulics module in VSOP94.

MCNP4B Model of the PBMRThe MCNP4B model was based on the 2-D VSOP94 model of the reactor. Key aspect of the VSOP94 model of the PBMR core and structural components were duplicated, including the pebble flow channels and layers (Figure 2.).

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Figure 2. MCNP4B model of the PBMR (vertical view)The control rods, and the shutdown and helium coolant in the side

reflector were modelled explicitly with some exeption that the control rods model using the HTR-10 model (instead of proprietary PBMR design), also the oval shutdown channels which taken from Chinese reactor.

A simple BCC lattice without exclusion zones was used to represent the randomly packed pebble bed. This lattice was subdivided into layers exactly as in the VSOP94 model of the core. The spheres in each layer consisted of the homogenized mix of carbon, silicon, heavy metal dan fission-product nuclides prepared with MCARDS from the corresponding VSOP94 layer-averaged atom densities.

Link Between VSOP94 and MCNP4BAn approximate but direct approach was used by Lebenhaft where the nuclide densities obtained from a whole-core VSOP94 calculation are used directly in an MCNP4B model of the reactor.

As explained before, an MCNP4B model of the PBMR equilibrium core was developed, which uses a regular lattice of spheres with homogenized fuel and graphite interiors. This lattice is subdivided into annular regions that reproduced exactly the core regions of the VSOP94 model. The fuel composition

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used in these regions are batch-aveeraged VSOP94 muclide densities, which are adjusted to allow for the effect of fuel homogenization on resonance absorption in 238U and 240Pu.

In the VSOP94 code,subroutine VORSHU is called before fuel shuffling takes place and work the following jobs

- Reads instructions for the next burnup- Calculates average batch properties- Account for isotope decay during the reshuffling.

this VORSHU subroutine was midified to accommodate new jobs as follow- Calculate the total atom numbers and write the result to FORT.98- Calculate the reaction rates for each isotope per layer and write the

result to FORT.99.- Additional information written to FORT.98 file are

Cycle number Layer number Total number of all nuclides in the given layer The volume of the layer The packing factor.A FORTRAN program MCARDS reads these data and prepares an

MCNP4B material card for each layer. Because a one-to-one mapping does not exist between the nuclides available in the VSOP94 and MCNP4B libraries, is 10B added such that the total absorption reaction rate in each layer is preserved.

With the above hybrid method VSOP94 performs the diffusion calculations on homogenized regions of the core, with self-shielding factors used to correct for double heterogeneity and a diffusion correction to allow for neutron streaming in core voids. Neutron streaming is handled in MCNP4B by modelling explicitly the lattice of spheres.

ResultsPreliminary analysis of the PBMR using the above MCNP4B/VSOP94

calculation method yields an effective multiplication constant at 1.00873 ± 0.00096. The nuclide densities calculated by VSOP94 for each layer is not adjusted, this adjustment is needed to compensate for the approximate MCNP4B representation of fuel-sphere interiors. The effect of this homogenization was shown to decrease the reactivity of the core ~4%dk/k by using an identical MCNP4B model in which the core layers were fully

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homogenized. Two-dimensional VSOP analysis of the PBMR core has established a total temperature reactivity shown in the table 3. Which would reduce the reactivity of the core by ~4%dk/k assuming an average fuel temperature of 950oC. The MCNP4B calculations reported were performed at room temperature, because cross-section libraries at typical HTGR operating temperatures were not available.

The method described in this chapter for obtaining the MCNP input for the composition of fuel spheres in a pebble-bed core with burnup islimited in its accuracy, because of the need to account for the effects of homogenization on resonance absorption. To improve the calculation method, Lebenhaft proposed the following procedure for MCNP-based code system.

Figure 3. Proposed MCNP-bsed Code System for Pebble-Bed Reactors

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with Burnup.2. Study by Brian Boer et.al at TU Delft (2009)2,3

In the paper published 20092, Boer et.at evaluating several pebble loading schemes.The evaluation is based on inner and outer graphite reflector which included in some of current pebble-bed reactor designs with increased thermal power (>300 MW) such as the designs considered in the HTR-PM (China) and 400 MW PBMR (South Africa).

The above annular pebble-bed design can exhibit peaks near this reflectors caused by the local abundance of thermal neutrons. Furthermore, the tall core geometry, adopted for thermal-hydraulic reasons, causes a large difference in the burnup level between top and bottom of the core, resulting in an axial power peak at the top. At the end, this power peaks can results in hig fuel temperatures during normal operating and accident conditions.Thus, optimized loading pattern is needed to improve the power profile which can lead to a reduction of the fuel temperature for a fixed helium outlet temperature.

To evaluate several loading pattern effect on the reactor parameters, Boer et.al developed a new calculation system to be expalained here and applied the procedure to 400MWt PBMR.

Reference Design of 400 MWt PBMRReference design of the 400 MWt PBMR used for the evaluation is as

follow

Figure 2.1 General design and operating characteristic of the PBMR 400

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MWt.

Koster4 give a schematic picture of the core design as follow

Figure 2.2 Core configurationCalculation ProcedureIn the calculation it is assumed that the equilibrium core is already achieved so that the neutron flux profile does not change in time. Also assuming that the pebble is irradiated wih a fixed flux level during a certain time interval, when it moves from one point in the core to the next.The general equation for fuel depletion, including fuel movement is as follows

dN idt

=∑j≠1

(φγ jiσ aj+α ji λ j )N j−(φσai+ λ j )N iWhere dN idt = Material derivative of nuclide i

Ni = Atomic concentration of atom iφ = Neutron fluxγ ji = Probability that neutron interaction with nuclide j will yield nuclide i

α ji = Probability that the decay of nuclide j will yield nuclide i

λ j = Decay constant for nuclide j

σ aj = Absorption cross section of nuclide j

The outline of the calculation method id depicted in figure 2.2 as follow

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Figure 2.2 Flow scheme of calculation procedure for the calculation of the power profile in the core.

The above procedure involving several codes. The codes are used iteratively unti convergence is reached on both the inner and the outer iteration. The criterion for the inner loop is the change in the neutron flux, while convergence in outer loop is determined by the deviation from a preset kdes value. The final burnup level of the pebbles, Bufin, id modified to meet this criterion.The total residence time T that the pebbles reamin in the core is modified in turn to reach this burnup level.The inner loop consist of the following step :1. Depletion calculation.

- Provided the flux profile in the core is known the fuel in the pebble during its lifetime can be calculated.

- The core is divided into several discrete radial and axial zones - Depletion calculation is performed using the ORIGEN module from

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SCALE-5.- Between burnup steps the cross sections are updated using successive

1D transport calculations for the TRISO coated particle and pebble geometry.

- 172 energy group XMAS library is used based on the JEFF3.1 libarary.- Results of this step is the nuclide distribution over the core of each

burnup interval, N(r,z).2. Neutron cross section calculation

- Zone averaged nuclide concentrations N(r,z) are used for generating neutron cross section for the entire reactor.

- Double heterogeneity of the fuel is taken into account by performing a cell weighting of a fuel particle in moderator material using a Dancoff factor calculated according to the method developed by Bende5.

- Resonance treatmen of the unresolved resonance is performed by Bondanrenko method, While the resolved method using the Nordheim Integral Method.

- Then followed by a 1-D transport calculation of a pebble geometry including the surrounding helium. Radial and axial (1-D) transport calculations are used to calculate zone weighted cross section for the entire reactor.

- Result of this step is a two dimensional cross section library (Σ(r,z)).3. Neutron flux calculation

- The above neutron cross sections are used to calculate the 2-D multigroup flux profile φ (r,z) with the neutron diffusion code DALTON.

- Average fluxes are generated for each depletion zone and scaled to the desired reactor power.

- K-eff of the reactor is calculated- Using the nuclide distribution over the core and the cross sections are

generated for several temperatures of the fuel and moderator, the temperature dependent cross section library is generated.

- The library can be used in coupled neutronic and thermal hydraulic calculations using the DALTON-THERMIX code system. The results is a temperature corrected power profile.

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References :1. Lebenhaft JR, 1999, “MCNP4B Modelling of Pebble Bed Reactor”, MIT

Dissertation.2. Boer B, Kloosterman J.L, lathouwers D, van Der Hagen T.H.J.J, 2009, “In-core

fuel management optimization of pebble-bed reactors”, Annals of Nuclear Energy 36 (2009) 1049 – 1058

3. Boer B, 2009, “Optimized Core Design and Fuel Management of a Pebble-Bed Type Nuclear Reactor”, TU Delft Dissertation.

4. Koster A, Matzner H.D,NIcholsi D.R, 2003, “PBMR Design for the Future”, Nuclear Energy and Design 222 (2003) 231 – 245

5. Bende E.E,1999,”Pebble Bed Burning in a Pebble Bed Type High Temperature Nuclear Reactor”, TU Delft Dissertation.

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