Available online at www.sciencedirect.com annals of NUCLEAR ENERGY Annals of Nuclear Energy 35 (28) 5 55 www.elsevier.com/locate/anucene Evaluation of PBMR control rod worth using full three-dimensional deterministic transport methods Bismark Tyobeka a, Kostadin Ivanov a, *, Andreas Pautz b a Department of Mechanical and Nuclear Engineering, Pennsylvania State University, 23 Reber Building, University Park, State College, PA 682, United States b Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbh, Garching, Germany Received 5 October 27; accepted 6 November 27 Available online 8 January 28 Abstract It is a well known fact that the neutron diffusion theory fails in the vicinity of strongly absorbing media, such as the control rods. This failure is much more pronounced in the PBMR because the location of control rods in the side reflector adds a directional dependence to the flux, and this complicates the problem further. Reactor control and safety can only be ensured if control rod worths are accurately predicted. In this work a thorough evaluation of different control rod models is performed by constructing an approximate two-dimensional (2D) model adopting the so-called grey curtain and this is compared to full 3D deterministic transport model. Both these models are compared to an explicit MCNP model. It is shown in this study that it is possible to have an accurate 2D model of control rods, utilizing appropriate equivalent cross sections and applying them to a control rod grey curtain. Further, this paper also shows that it is possible to obtain reasonably accurate control rod worths using a 3D deterministic transport method with the same fidelity of a Monte Carlo reference calculation, provided that the correct cross sections are used. These results confirm that the deterministic transport models can be successfully used for PBMR transient safety analysis. Ó 27 Elsevier Ltd. All rights reserved.. Introduction The failure of diffusion theory to model highly absorbing regions is well known and numerous methods have been developed to overcome it by using the so-called equivalent diffusion parameters. In the PBMR design, the positioning of these highly absorbing regions in the side reflector, where the leakage out of the core adds a directional dependence to the flux, further complicates the problem. One of these methods is the Method of Equivalent Cross Sections (MECS), which was proposed by (Scherer and Neef, 976). The principle is to model the absorber and its environment in transport theory (S N ) and then extract cross sections and diffusion parameters from the transport solution that will represent the absorber region * Corresponding author. Tel.: + 84 865 4; fax: + 84 865 8499. E-mail address: kni@psu.edu (K. Ivanov). accurately in subsequent 3D diffusion calculations. Another very simplified method available, called the equivalent boron concentration (EBC), consists of adding a certain amount of boron absorber homogeneously into a borated region representing the control rod (Reitsma and Naidoo, 23). The concentration of the boron is adjusted so that the control rod worth is conserved. The method assumes that the rod reactivity worth is known from experiment or from other methods such as MECS. In this work the 3D neutron transport S N code TORT (Johnson, 992), was used with the cross sections generated from MICROX-2 (Mathews et al., 997) to perform control rod worth calculations with control rods accurately and explicitly modeled in three-dimensions. The task here is to first get the accurate control cross sections and to apply them in the neutronics code, while at the same time coming up with the best possible geometric representation of the control rod in TORT. The main objective of these 36-4549/$ - see front matter Ó 27 Elsevier Ltd. All rights reserved. doi:.6/j.anucene.27..8
B. Tyobeka et al. / Annals of Nuclear Energy 35 (28) 5 55 5 studies is to obtain an optimum control rod representation in TORT, and use the differential control rod worth curve resulting from this configuration to evaluate and adjust the 2D control rod approximations (grey curtain) used in diffusion codes. In order to achieve this, it is important to first evaluate the accuracy of the grey curtain representation of control rods by comparing it to the control rod worths obtained using MCNP5 (RSIC Computer Code Collection, 23) as a reference and then proceed to develop an explicit 3D model in TORT and MCNP. The objective of this latter step is to evaluate the grey curtain representation in MCNP against the explicit MCNP control rod representation. 2. Core and control rod models developed In this study, three control rod models were developed and extensively evaluated for accuracy. The first one as mentioned above was the grey curtain representation. The grey curtain was used in DORT (r z geometry) and also used in TORT (r h z geometry) with a dummy theta dimension. This exercise was meant to verify TORT, because using the same cross sections and this dummy theta dimension, the TORT model is the same as the DORT model, hence one expects that the results obtained by the two codes should ideally be the same. This grey curtain model was also developed with MCNP, just for verification purposes. Secondly, an explicit model in MCNP was developed to represent the control rods explicitly, i.e. not as a grey curtain. Thirdly, a TORT model was developed and was made to be as close as possible to the MCNP to accurately model the control rod configuration of the PBMR 268 MW design (Reitsma et al., 24). Before proceeding to the models themselves, it is important to first discuss the PBMR control rod design. The control rods in the PBMR are located in holes in the side reflector. These sleeves are made of graphite and the control rod is an annulus of Boron carbide within a cladding, as shown in Fig.. Control Rod Channel Sleeve He There are 8 control rods and 7 shut down rods filled with small absorber sphere called KLAKS. For purposes of this study, the shut down elements were not modeled as these are not used during normal operation. Inner radius of control rod channel sleeve is 6.5 cm and the outer radius is 7.3 cm. In this study, the control rod can be inserted as far as 85 cm, which is the height of the active core. Again, in the actual PBMR design, control rods are divided into two sets, with nine inserted from the bottom and nine from the top, thereby creating a possibility of control rod overlap. For purposes of this work, all rods are assumed to be inserted from the top and no rod overlap is considered. In both TORT and MCNP, the design data used was obtained from the PBMR (Pty) Ltd Company in South Africa, and this is the same data used for the reactor design. Table gives a summary of the dimensions of the control elements while the number densities and material composition data are given in Table 2. From the data provided, an MCNP model was developed for Case N2 of the PBMR 268 MW Benchmark problem (Reitsma et al., 24). Since this case requires cross sections generated at 9 K and MCNP can perform calculations at room temperatures, further cross section processing was performed with the NJOY code (MacFarlane et al., 999) so as to finally produce the cross section file xsdir for MCNP at 9 K. As mentioned earlier, two MCNP models were developed, namely, MCNP-grey curtain and MCNPexplicit. These models are shown in Figs. 2 4. Table Control element design data Control rod and KLAK channels Other info Outer radius (cm) PCD 375 cm Number of 8 control rods Number of 7 KLAK channels Incoloy inner radius 4. cm Thickness (cm) Control rods Inner incoloy 4.2. B4C 5.5.85 Outer incoloy 5.25 Fig.. PBMR control rod design. Inner Incoloy Outer Incoloy B4C Control Rod Front (Facing Reactor Core) Table 2 Incoloy (Inc8H) material composition of control rods Nuclide Weight percentage C-nat.7 Si-nat. P-3.3 S-32.2 Cr-nat 2. Mn-55.5 Fe-nat 43.38 Co-59. Ni-nat 32.
52 B. Tyobeka et al. / Annals of Nuclear Energy 35 (28) 5 55 Control region In developing the TORT model of the PBMR, BOT3P, the preprocessor (and postprocessor) of DORT and TORT was used. This approach was chosen because it would eliminate the possibility of geometrical errors in the model. With BOT3P, the user can actually visualize the geometry of the model and one of the salient features of this tool is that it can make the necessary adjustment in case of simple mistakes like overlaps or mesh size. It also has features that ensure that the volume of the model is preserved in case of some approximations due to small mesh size. The resulting TORT model is shown in Fig. 5. 3. Control rod worth calculations and results Fig. 2. Radial cut of the PBMR 268 MW MCNP model using grey curtain CR representation. Central reflector Mixing zone Fuel region Side Reflector Carbon Insulation Fig. 3. Axial cut of the PBMR 268 MW MCNP model using grey curtain CR representation. Fig. 4. Top view of the PBMR 268 MW MCNP (explicit) model showing positions of control rods. From the developed models above, core calculations were performed with a view of computing control rod worths for each model. Firstly, it was important to verify that with TORT and DORT, using the same cross sections and a dummy theta dimension in TORT, i.e., both using the grey curtain representation of the control region, the results will be the same as expected. Calculations were performed at various insertion depths of the grey curtain with steps of cm. The results obtained are shown in Fig. 6. In this figure, the ratio of rod reactivity worth at a given insertion step to rod reactivity worth when rods are fully inserted is plotted against where x is the insertion step or distance, and H is the height of the active core, in this case 85 cm. From the figure, it is clear that as expected, TORT in two-dimensions completely reproduced the DORT results. This helps to verify TORT for PBMR modeling, as there is no published literature that the authors are aware of in this regard. The same calculations were performed with MCNP using the grey curtain representation of the control region. The results of MCNP were compared with those of DORT and TORT and as shown in Fig. 7, other than the apparent shift as the control rods are inserted deeper into the core, there is a reasonable agreement between these results. Following from the reasonable agreement between the codes while using the grey curtain model of control rod representation, further calculations were performed with MCNP but this time, using the explicit model of control rods. The results were compared to the MCNP results with the grey curtain, to evaluate the accuracy of the grey curtain representation. The results, in Fig. 8, show some differences on the control rod worth between these two models, but the overall result is a reasonable agreement. One of the objectives of performing these calculations is to finally benchmark the DORT-TD code for PBMR and to later couple it with THERMIX-DIREKT. The coupled code will be used for transient analysis and one of the envisaged transient cases to be modeled with the coupled code is the rod ejection incident. It is therefore important that DORT-TD can model rod worth calculations accurately. In two-dimensions, the only feasible way to model control rods is by means of a grey curtain approximation. For this reason, rod worth calculations from DORT-TD
B. Tyobeka et al. / Annals of Nuclear Energy 35 (28) 5 55 53 Control rods Fig. 5. Radial and axial cut of the PBMR 268 MW TORT model showing positions of control rods. are compared with MCNP-explicit model in Fig. 9. It can be concluded from the figure above, that the grey curtain model in DORT-TD agrees excellent with the results of MCNP using explicit representation of control rods for the PBMR 268 MW design. So far, all the results presented above have been obtained from symmetric rod movement, i.e. it is assumed that the whole bank of control rods is moved. It is also important to model an asymmetric movement of control rods and to be able to do that, a three-dimensional deterministic model is necessary. The TORT model presented in Fig. 5 was utilized for this purpose. Using the equivalent boron concentration method, calculations were initially performed with MCNP (explicit model) with all control PBMR 268MWth Control Rod Worth Curve - Grey Curtain Model (DORT-TORT Model Verification).8.6.4 TO RT DO RT-TD.4.6.8 Fig. 6. Control rod worth results using the grey curtain model for DORT and TORT. PBMR 268MWth Control Rod Worth Curve - Grey Curtain Model (MCNP Reference Included).8 MCNP (Grey-Curtain) TORT DORT-TD.6.4.4.6.8 Fig. 7. Control rod worth results comparing grey curtain representation with MCNP reference.
54 B. Tyobeka et al. / Annals of Nuclear Energy 35 (28) 5 55 PBMR 268MWth Control Rod Worth Curve (Grey-Curtain v/s Explicit Models).8 MCNP (Explicit) MCNP (Grey-Curtain) rho (x)/rho(h).6.4.4.6.8 Fig. 8. Control rod worth results evaluating the accuracy of the grey curtain representation. PBMR 268MWth Control Rod Worth Curve (Explicit v/s Grey Curtain Models).8 MCNP (Explicit) DORT-TD.6.4.4.6.8 Fig. 9. Control rod worth results evaluating the accuracy of the DORT-TD grey curtain. rods inserted in the core and the resulting eigenvalue was noted. Subsequently, an iterative series of calculations was performed between MICROX, GIP and TORT, the goal being to find the eigenvalue in TORT which is reasonably close to the MCNP value. The Boron number density in MICROX was adjusted accordingly and cross sections were generated and arranged into a format readable by GIP. GIP was used to process the cross sections into the FIDO format used by TORT and core calculations were then performed in TORT. This process was repeated until the target k eff value was obtained in TORT. With the final cross sections obtained, the calculation is repeated with all rods withdrawn and the comparison between TORT and MCNP yielded good agreement. Finally, a series of calculations in both TORT and MCNP was performed where, a single rod and subsequently a combination of rods in an asymmetric arrangement were inserted whilst the rest were fully withdrawn and the corresponding reactivity worth was calculated. The results are shown in Table 3 and Table 3 Reactivity worth of a combination of control rods Combination MCNP (dk/k) TORT (dk/k) % Difference CR+CR4+CR7.292.2239 2.637 CR+CR5+CR.2458.2458.256 CR+CR.67.66 2.6339 CR+CR3+CR7.29.24 2495
B. Tyobeka et al. / Annals of Nuclear Energy 35 (28) 5 55 55 PBMR 268MWth Single Rod Worth Calculations (CR).8 MCNP TORT.6.4.4.6.8 Fig.. PBMR 268 MW single rod worth calculations for CR. Fig.. The results show a good agreement between TORT and MCNP for both single rod movement and for the case where a cluster of control rods moves in one part of the core. This demonstrates that deterministic transport methods when applied with the correctly computed cross sections can reproduce Monte Carlo results. 4. Conclusions Accurate prediction of control rod worths is imperative for the safety of all reactor types, especially for new designs where there exists little or no experimental or plant data, like the PBMR design. With the failure of diffusion theory in carrying out this task, it is traditional to make use of Monte Carlo calculations, or use approximations such as the Method of Equivalent Cross Sections or the EBC. In this work, it was shown that deterministic transport codes, which are readily available, can actually be used for this purpose with almost the same fidelity as the Monte Carlo calculations. It was shown, however, that these methods can only be useful if proper cross section generation tools are used. Furthermore, results from these models can be used to evaluate approximate models like the MECS and the grey curtain model of control rods, which in this case have shown to be quite accurate when compared to both MCNP and TORT. More importantly, the comparative analysis performed in the reported study given in this paper has indicated that the neutron transport models can be successfully utilized for both PBMR control rod worth calculation and transient safety analysis involving control rod movements. References Johnson, J.O., 992. A users manual for Mash., a Monte Carlo Adjoint Shielding Code System (Contains the documentation for DORT), Oak Ridge National Laboratory Report ORNL/TM-778. MacFarlane, R.E., NJOY 99.8, 999. Code system for producing pointwise and multi-group neutron and photon cross sections from ENDF/ B data, Los Alamos, New Mexico. Mathews, D., 997. An Improved Version of the MICROX-2 Code, Paul Scherrer Institute, Switzerland, PSI Bericht Nr. 97-. Reitsma, F., Naidoo, D., 23. Evaluating the control rod modeling approach used in the South African PBMR: comparison of VSOP calculations with ASTRA experiments. Nuclear Engineering and Design 222 (2 3), 47 59. Reitsma, F., de Haas, J.B., Tyobeka, B., Ivanov, K., De Cruz, F., 24. PBMR steady state and coupled kinetics core thermal-hydraulics test problems, in: Transactions of the ANS National Meeting, Pittsburg, PA, USA. RSIC Computer Code Collection, April 23, MCNP5 Monte Carlo N- Particle Transport Code System, Oak Ridge National Laboratory. Scherer, W., Neef, H.J., 976. Determination of equivalent cross sections for representation of control rod regions in diffusion calculations, July- 3.