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Investigation of burnable poisons effects in reactor core design
Annals of Nuclear Energy 38 (2011) 2238–2246
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Investigation of burnable poisons effects in reactor core design Amir Hosein Fadaei ⇑ Faculty of Nuclear Engineering & Physics, AmirKabir University of Technology (Tehran Polytechnique), Hafez Street, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 30 November 2010 Received in revised form 28 May 2011 Accepted 6 June 2011 Available online 2 July 2011 Keywords: BAR Chemical shim VVER Core design Burnable poison Reactivity coefficient
a b s t r a c t Burnable absorber rods (BAR) and chemical shim are the main control poisons that are used in the core for improving the reactor behavior and satisfying the safety criteria during the core life time. These poisons have several constraints, criteria, advantages and also disadvantages from the safety and operation points of view; and these characteristics depend on the concentration and distribution of mentioned poisons in the reactor core. Therefore, understanding their effects on the reactor core behavior, especially the mutual interaction between them, is a crucial issue in reactor core design procedure. In this study, the influences of the burnable poisons on the main parameters of the reactor such as multiplication factor, burnup, soluble poison concentration, moderator temperature coefficient and power peaking factor over the reactor life time are investigated. The VVER-1000 reactor was selected for this investigation. The reactor core was modeled by WIMS and CITATION codes. Several different loading patterns based on different distributions and concentrations of BARs were defined. Subsequently, the main parameters of the core for each pattern were calculated by the core model and were investigated to analyze the effects of BAR concentration and distribution on the reactor behavior. The presented results made it possible to analyze and understand the BAR and chemical shims effects on the behavior of the nuclear reactor core. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Two criteria play dominant roles in determining the composition of a power reactor core: Criticality must be maintained over the range of required power levels and over the life of the core as fuel is depleted. Substantial amounts of excess reactivity at the time of reactor startup allow for extended core life before refueling must take place. But, large excess reactivities create challenges in the design of a reactor’s control system. Control rods are the most common means for compensating for excess reactivity (Fadaei et al., 2010). However, in large, neutronically loosely coupled cores great care must be taken to ensure that their presence does not distort the flux distribution to the extent that excessive power peaking results. In pressurized water reactors dissolving a soluble neutron absorber in the coolant and varying the concentration with time serves to compensate for excess reactivity. Burnable poisons embedded in the fuel or other core constituents offer an additional means of limiting excess reactivity as well as mitigating localized power peaking. The design must also allow the thermal energy produced from fission to be transferred out of the core without overheating any ⇑ Tel.: +98 21 88630644; fax: +98 21 88417576. E-mail address: [email protected] 0306-4549/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2011.06.005
of its constituents. Many other considerations also come into play: the mechanical support of the core structure, stability and control of the chain reaction under widely varied circumstances, and so on. In this study, the effects of burnable poisons on main reactor parameters during operating cycle of VVER-1000 nuclear reactor are investigated. For this approach, the different configurations of BAR in the nuclear reactor core with the different boron concentration are considered and the reactor behavior in each state is studied. The effects of BAR concentration in the core are analyzed based on reactor main parameters. Based on desired goal, the definition of BAR and chemical shim is described in Sections 2 and 3, respectively. Main characteristics and the structure of VVER-1000 nuclear reactor core are introduced in Section 4. In Section 5, the conceptual effects of BAR are presented, the problem is defined and the proposed procedure for solving the problem is explained. The results of calculation are shown in Section 6, and finally the conclusion is performed in Section 7. 2. Burnable absorber rod The life time of a given core fuel loading, that is, the period during which the core has sufficient excess reactivity to permit startup and full power operation, is generally determined by the amount of fuel initially loaded into the reactor core. Of course the amount of fuel loaded into the reactor will depend in on the excess reactivity
A.H. Fadaei / Annals of Nuclear Energy 38 (2011) 2238–2246
that can be conveniently compensated for by reactor control elements. In order to increase the allowable initial core fuel loading, it is common to load into the core materials characterized by high neutron absorption cross sections (poison) that compensate for such excess reactivity during the early stages of core by neutron capture into isotopes with low capture cross sections) somewhat faster than fuel burnup, so that later in core life they contribute negligible negative reactivity. Hence these burnable poisons can nearly match the time behavior of the excess fuel reactivity as it decreases over core life, thereby allowing larger initial fuel inventories without a corresponding increase in control requirements. Burnable poisons thus possess a number of advantages. They increase core life time without any decrease in control safety, reduce the amount of mechanical control required, and if distributed in a proper fashion, can also improve core power distributions, for example, by suppressing reactivity in high flux regions, such as near coolant channels. Such burnable poisons are usually fabricated into the initial core loading as either fixed control blades or curtains or mixed into certain fuel pins. For example, in present BWR designs, gadolinium-loaded fuel pins with an initial reactivity worth of 0.12 Dk/k are loaded into the core until an equilibrium fuel cycle is achieved. In PWRs, borosilicate glass tubes are placed in the core in the initial core loading. From this discussion, several desirable characteristics of burnable poisons are apparent. Obviously they should be characterized by absorption cross sections somewhat higher than those of the fuel, since then they will burn out more rapidly than the fuel, leaving minimal poison residue at the end of the fuel cycle. Furthermore the isotopes formed by neutron capture in the poison should have low absorption cross sections. Finally, the burnable poison, as well as its surrounding clad or structural material, should not affect the structural integrity of the core (such as by swelling) (Lewis, 2008).
3. Chemical shim Water moderated and cooled reactors can be in part controlled, in addition to control rod systems, by varying the concentration of the boric acid (H3BO3) in the coolant. This is called chemical shim. Because the response to a change in concentration of the solvent is not as quick as obtained by the insertion of control rods, chemical shim cannot be used to control the large reactivity insertions. Thus it is always used in conjunction with the control rod systems. In a reactor with both control systems:
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ments when used in LWRs. Chemical shim does have several disadvantages, however. Since the rate at which one can inject or withdraw appreciable amounts of poison from the coolant is quite small, the reactivity insertion rates are correspondingly small (with maximum insertion rates of almost 3 10 5 s 1). Chemical shim can have a major effect on the moderator void coefficient of reactivity. We will find that in LWRs this void coefficient is usually quite negative, since a decrease in coolant density leads to a higher decrease in neutron moderation than in neutron absorption and hence the reactivity will decrease. However if a soluble poison is present, a decrease in coolant density will also lead to a decrease in poison concentration – a positive reactivity effect. The desire for a negative void coefficient will frequently limit the amount of chemical shim allowed (typically to less than Dq 0.20 Dk/k). We have shown this effect for a modern PWR core design in Fig. 1 (Duderstadt and Hamilton, 1941). 4. VVER-1000 reactor core The VVER-1000 reactor core has hexagonal structure and consists of 163 fuel assembly (FSAR, 2007). The reactor core is shown in Fig. 2. The schematic view of fuel assembly model of the reactor with BAR is illustrated in Fig. 3. There are 18 BAR in each fuel assembly. In VVER-1000 reactor core there are three types of different fuel assemblies with different enrichment and different BAR concentration that are shown in Table 1. 5. BAR effects evaluation Reactors are normally designed to produce a specified amount of power, while with other variables held constant the cost of construction rises dramatically with the core volume. Thus maximizing the ratio Pmax is a central optimization problem of core design. The achievable maximum power density is dependent primarily on materials properties and the temperatures and pressures that can be tolerated by fuel, coolant, and other core constituents. Minimizing the peaking factor falls much more into the domain of reactor physics, for nonuniform distributions of fuel enrichment, the positioning of control rods and other neutron poisons, as well
Control rods are used to provide the reactivity control for fast shutdown and for compensating reactivity variance due to temperature change. Chemical shim is used to keep the reactor critical during xenon transients and to compensate for the depletion of fuel and build-up of fission products during reactor life time.
The use of chemical shim reduces the number of control rods required in a reactor. Since control rod systems are expensive, any reduction in the number of control rods reduces the total cost of the reactor. Chemical shim is almost uniformly distributed in the core and thus perturbs power distribution less as the concentration of the boric acid is changed. Chemical shim in thermal reactors primarily affects the thermal (fuel) utilization factor (Jevremovic, 2009). A suitable soluble poison must be an isotope characterized by a large neutron absorption section which is soluble in the coolant. It should be of a noncorrosive nature and relatively stable so it will not adhere to core components. Boric acid possesses these require-
Fig. 1. The effect of chemical shim on the moderator temperature coefficient in a PWR (Duderstadt and Hamilton, 1941).
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Fig. 2. The VVER-1000 reactor core.
Fig. 3. Fuel assembly model.
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Table 1 All fuel assemblies type with BA in VVER-1000 reactor core. No.
Cell type
Description
1
Fuel 24B20 Fuel 24b36 Fuel 36B36
Fuel assembly of rods with 2.4% enrichment and burnable absorber with 20 kg/m3 density Fuel assembly of rods with 2.4% enrichment and burnable absorber with 36 kg/m3 density Fuel assembly of rods with 3.3% and 3.7% enrichment and burnable absorber with 36 kg/m3 density
2 3
as other neutronic considerations largely determine the value of Fq. The core volume that is ultimately selected also has reactor physics repercussions, most importantly on the core-averaged fuel enrichment and the nonleakage probability. The reactivity effects of fuel depletion must be compensated to maintain criticality over the fuel burnup cycle. The major compensating elements are the control rods, which can be inserted to compensate positive depletion reactivity effects and withdrawn to compensate negative depletion reactivity effects. Adjustment of the concentration of a neutron absorber (e.g., boron in the form of boric acid) in the water coolant is another means used to compensate for fuel-depletion reactivity effects. Chemical shims (Soluble poisons) are used to compensate fuel-depletion reactivity in PWRs but not in BWRs, because of the possibility that they will plate out on boiling surfaces. As, however, PWRs adopt chemical shim, that is the control of reactivity through dissolution of boric acid in the reactor water, the presence of this neutron absorber decreases the safety effectiveness of the moderator temperature coefficient; in fact, if the temperature increases, the amount of boron contained in the reactor water decreases and consequently the reactivity increases. For this reason, when the boron concentration is high (start of life, cold conditions) the overall temperature coefficient of the reactor water may be positive. Additionally, it must be emphasized that, in any case, the power coefficient (which includes the Doppler effect) must be always negative (Petrangeli, 2006). Burnable poisons consist of separate shim rods substituted for a fuel rod in the fuel assembly. These rods may consist of borosilicate glass rods with stainless steel cladding or B4C pellets in an Al2O3 matrix with zircaloy cladding. The shim rods burn out as the fuel depletes, which constitutes a positive reactivity contribution to compensate the negative reactivity contribution of fuel depletion,
Fig. 5. Keff behavior of the reactor for various conditions (Stacey, 2007).
thus reducing the requirement for adjustment of the boric acid concentration (Stacey, 2007). Fig. 4 shows the effect of burnable poison rods on soluble poison requirements; and the multiplication factor behavior of the reactor is shown in Fig. 5 for various conditions. The importance of the burnable poison concentration on the reactor core behavior was described in previous sections. In the next, focus in the reactor core design with emphasis on the burnable absorber effects.
5.1. Problem definition Based on mentioned cases, obtaining of BAR effects on the reactor core behavior, especially with spotting the interaction with soluble poison, is very important issue in reactor core design procedure. In this study, the influences of the burnable poisons on the main parameters of the reactor such as multiplication factor, burnup, soluble poison concentration, moderator temperature coefficient and power peaking factor over the reactor life time are
Fig. 4. Boron concentration versus first cycle burnup with and without burnable poison rods (Stacey, 2007).
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investigated. VVER-1000 reactor was selected for this survey. The procedure of this research is described in the next subsection. 5.2. Procedure In order to mentioned subject, the analysis of burnable poison’ effects on the reactor core behavior is aimed in this study. For obtaining the demand results, several different configurations consist of different loading patterns and different concentrations of the burnable poisons in the VVER-1000 reactor core are considered, and neutronic core calculation are performed for each configuration to gain the main parameters of the core. The reactor core configuration of VVER-1000 that is proposed by designer is shown in Fig. 6, for reaching to the ability of BAR effects analysis, several different configurations are proposed with different characteristics. The patterns of these cases are shown in Fig. 7. Eight different core configurations were illustrated to investigate the effects of burnable poisons in the nuclear reactor core behavior. In this study, the main neutronic parameters of the core are calculated for the mentioned configurations and finally the effect of burnable poison concentration on the core behavior are deduced based on them. For performing neutron calculation in the reactor core, reactor simulation is necessary. In this study, as before mentioned, two steps have been used for reactor simulation. First step is cell calculation that simulates fuel assemblies in reactor core and second step is core calculation that simulates reactor core. In the first step, cell calculations, macroscopic cross sections for all different types of fuel assemblies (Table 2) calculate for using in the next step, core calculation (Fig. 8), which performs for calculating neutronic parameters (Faghihi et al., 2007; Fadaei and Setayeshi, 2008). For simulating of fuel assembly WIMS code (Winfrith, 1982) has been used. WIMS-D5 is a general lattice cell program, which uses transport theory to calculate flux as a function of energy and position in the cell. This code first calculates spectra for a few spatial regions in the full number of energy groups of its library, and uses these spectra to condense the basic cross sections into few groups. A few group calculations are then carried out using a much more detailed spatial representation. The resulting fluxes are then expanded using the spectra of the previous calculation, so that the
Fig. 6. VVER-1000 core configuration proposed by designer.
reaction rates at each spatial point can be calculated in the library group structure. As an example, the cell models of FA’s that are containing BAR are performed based on Fig. 3 simulation; the BAR that are made of B4C are defined depend on their concentration and distribution in FA’s cell model, and then the group constant of simulated cell are obtained by running provided model by WIMS. Reactor core is simulated by CITATION code (Oak Ridge National Labratory, 1972). This code was designed to solve problems involving the finite-difference representation of diffusion theory treating up to three space dimensions with arbitrary group-to-group scattering. Explicit, finite-difference approximation in space and time has been implemented. The neutron-flux-eigenvalue problems are solved by direct iteration to determine the multiplication factor or the nuclide densities required for a critical system. More details about the simulation can be gained by respect to ‘‘Fadaei and Setayeshi (2009)’’ that is mentioned in References. Briefly, first fuel assembly’s group constants prepared by WIMS D-5 code which are functions of temperature, burnup and power. The results are used in input file of CITATION code for simulating reactor core (Faghihi et al., 2007; Fadaei and Setayeshi, 2008). The main neutronic parameters of each proposed configuration over the whole of cycle length are needed to assess the quality and quantity of core behavior variation. Therefore, dynamic software by FORTRAN was prepared to simulate the core in the cycle and dependent on time, that uses WIMS and CITATION codes in a serial manner for performing the large volume of required calculation to obtain main reactor parameters. To investigate the effects of burnable poison in core behavior, the effects of control rods are neglected. The acid boric concentration value for criticality condition is calculated to assess the moderator temperature coefficient variable in the core. Also, Treatment of Radial Power peaking factor over the cycle length in the point of safety view and the life time of the core in order to economic considerations are calculated to evaluate the efficacy analysis.
6. Result In this study, based on mentioned cases, analysis of burnable absorber concentration’ effects on nuclear core behavior is aimed. In order to the defined procedure for problem solving, the reactor core was modeled by preparing the FORTRAN coupling program between WIMS and CITATION codes. To verify and validate the proposed simulation model, moderator temperature coefficient was calculated versus burnup along the first cycle for designer configuration and then compared with the reference data that are presented in FSAR, (2007). Fig. 9 shows good agreement between the model and references data specially after fixing the power level on 3000 Mw that is occurred at 80th day (there are some error before fixing the power because of the variation in power level and the manner of disceretizing the time that are described in Faghihi et al. (2007) and therefore the presented model can be used to simulate a reactor core behavior with accepted precision. At the next step, several different patterns, which the burnable absorber concentration is the main choppy variable, were proposed to analyze the variations effects. For evaluating the effect of BAR concentration on the core, neutronic calculations were performed for all proposed pattern, and the main core parameters obtained. In Fig. 10 the behavior of boric acid concentration in the core to achieve the criticality state in each pattern are shown. It is obvious that the required boric acid concentration for reaching the criticality state along the core cycle is higher for the pattern which is without BAR, and also, with increasing the BAR concentration required boric acid decrease. The importance of mentioned issue
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Fig. 7. Different considered core configuration for analysis (a) pattern 1, (b) pattern 2, (c) pattern 3, (d) pattern 4, (e) pattern 5, (f) pattern 6, (g) pattern 7, and (h) pattern 8.
is denoted while the moderator temperature coefficient pursued. It is clear that the moderator temperature coefficient because of safety consideration should be placed in the acceptable margin;
and the ideal acceptable margin enforces to be sitting in the negative values. Based on significance of inherent safety in nuclear reactor design, the moderator temperature coefficient (MTC) act as a
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Table 2 All cell types (fuel assemblies and reflectors) in VVER-1000 reactor core. No.
Cell type
Description
1 2 3 4
Fuel 16 Fuel 24 Fuel 36 Fuel 24B20 Fuel 24b36 Fuel 36B36
Fuel assembly of rods with 1.6% enrichment Fuel assembly of rods with 2.4% enrichment Fuel assembly of rods with 3.3% and 3.7% enrichment Fuel assembly of rods with 2.4% enrichment and burnable absorber with 20 kg/m3 density Fuel assembly of rods with 2.4% enrichment and burnable absorber with 36 kg/m3 density Fuel assembly of rods with 3.3% and 3.7% enrichment and burnable absorber with 36 kg/m3 density
5 6
suitable feedback to increase the inherent safety features. Two different parameters affect the MTC behaviors, which are moderator temperature and boric acid concentration. To understand the MTC behavior in the core and its relationship with two mentioned parameters, some efforts were done. The neutronic analysis of the reactor core in the different conditions of moderator temperature and boric acid concentration were performed. Fig. 11 shows the treatment of MTC in VVER-1000 reactor by considering the proposed pattern by designer. It is clear that the given data in this figure should be used to design the core in order to satisfy the safety consideration; these quantities can help to define the maximum licensable value of boric acid concentration. The other important parameter in core design is radial power peaking factor. Needless to say that, the boric acid concentration value, BAR concentration and also its pattern distribution in the core can be affect this parameter. Radial power peaking factor could be increase the safety margin of the reactor especially in the accident conditions, therefore it is desired to decrease its value. In Fig. 12, the behavior of the radial power peaking factor parameter, during the cycle length and for different mentioned patterns are illustrated.
Fig. 9. Moderator temperature coefficient versus burnup.
Based on presented results for different patterns and for different conditions, the effect of BAR concentration can be concluded and used to design the reactor core in order to designer’s request and cost. 7. Conclusion In this paper, the effects of control poisons in the function of nuclear reactor core are investigated. BAR and chemical shim are the main poisons that are exploited in the core. BAR are used to compensate the initial excess reactivity of loaded fuel, uniform the power distribution and decrease the required chemical shim for avoiding the positive moderator temperature coefficient. Placement of BAR in the core and its concentration are two keys subject
Fig. 8. VVER-1000 core model is prepared for core calculation.
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Fig. 10. Acid boric concentration variation for different pattern during first cycle length.
Fig. 11. Moderator temperature coefficient versus acid boric concentration and coolant temperature.
in designing procedure. In this study, some efforts were performed to specify the role of these subjects in the reactor behavior. Several different patterns with regards to the concentration and distribution of BAR are defined and analyzed for investigating the quality and quantity of BAR effects. It can be concluded that the moderator temperature coefficient goes to positive by increasing the acid boric concentration in the coolant, so the minimum worth of BAR are needed to avoid much acid boric concentration. Power peaking factor is dependent on the BAR distribution; the different presented patterns show the effect of BAR placement on this
parameter. It is very interesting that the relative behavior of power peaking factor parameter for different patterns is not uniform during a cycle. It means that in some times this parameter for one pattern is larger than the other while in the other times this relation is inverse. So, analyzing this behavior is complex and needs careful investigation for design. Fig. 10 shows the required acid boric concentration for reaching the criticality sate for different proposed patterns; needless to say that by increasing the BAR concentration in the core, the required acid boric is decreased.
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Fig. 12. Radial power peaking factor for different patterns during first cycle.
Based on the performed research, the mutual effects of chemical shim and BAR in the core can be realized and used by designers to find the optimum values and distributions of burnable poison in the reactor core for obtaining the desired goal. References Duderstadt, J.J., Hamilton, L.J., 1941. Nuclear Reactor Analysis. Department of Nuclear Engineering, The University of Michigan. Fadaei, A.H., Fadaei, M.M., Lia, Sh., Setayeshi, S., 2010. Core design improvement by optimizing the control and protection system elements distribution. Annals of Nuclear Energy 37, 1640–1648. Fadaei, A.H., Setayeshi, S., 2008. LONSA, as a tool for loading pattern optimization using synergy of neural network and simulated annealing for VVER-1000. Annals of Nuclear Energy 35 (10), 1968–1973.
Fadaei, A.H., Setayeshi, S., 2009. Control rod worth calculation for VVER-1000 nuclear reactor using WIMS and CITATION codes. Progress in Nuclear Energy 51, 184–191. Faghihi, F., Fadaie, A.H., Sayareh, R., 2007. Reactivity coefficients simulation of the Iranian VVER-1000 nuclear reactor using WIMS and CITATION codes. Progress in Nuclear Energy 49 (1), 68–78. Final Safety Analysis Report. Bushehr Nuclear Power Plant (NPP), 2007. Jevremovic, T., 2009. Nuclear Principles in Engineering. Springer Science, New York. Lewis, E.E., 2008. Fundamentals of Nuclear Reactor Physics. Academic Press. Oak Ridge National Laboratory, 1972. CITATION-LDI2 Code. Petrangeli, G., 2006. Nuclear Safety. Published by Elsevier Butterworth-Heinemann. Stacey, M., 2007. Nuclear Reactor Physics. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim. Winfrith, 1982. LWR-WIMS, A Computer Code for Light Water Reactor Calculations. UK: AEE, AEEW-R 1498.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Investigation of burnable poisons effects in reactor core design Amir Hosein Fadaei ⇑ Faculty of Nuclear Engineering & Physics, AmirKabir University of Technology (Tehran Polytechnique), Hafez Street, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 30 November 2010 Received in revised form 28 May 2011 Accepted 6 June 2011 Available online 2 July 2011 Keywords: BAR Chemical shim VVER Core design Burnable poison Reactivity coefficient
a b s t r a c t Burnable absorber rods (BAR) and chemical shim are the main control poisons that are used in the core for improving the reactor behavior and satisfying the safety criteria during the core life time. These poisons have several constraints, criteria, advantages and also disadvantages from the safety and operation points of view; and these characteristics depend on the concentration and distribution of mentioned poisons in the reactor core. Therefore, understanding their effects on the reactor core behavior, especially the mutual interaction between them, is a crucial issue in reactor core design procedure. In this study, the influences of the burnable poisons on the main parameters of the reactor such as multiplication factor, burnup, soluble poison concentration, moderator temperature coefficient and power peaking factor over the reactor life time are investigated. The VVER-1000 reactor was selected for this investigation. The reactor core was modeled by WIMS and CITATION codes. Several different loading patterns based on different distributions and concentrations of BARs were defined. Subsequently, the main parameters of the core for each pattern were calculated by the core model and were investigated to analyze the effects of BAR concentration and distribution on the reactor behavior. The presented results made it possible to analyze and understand the BAR and chemical shims effects on the behavior of the nuclear reactor core. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Two criteria play dominant roles in determining the composition of a power reactor core: Criticality must be maintained over the range of required power levels and over the life of the core as fuel is depleted. Substantial amounts of excess reactivity at the time of reactor startup allow for extended core life before refueling must take place. But, large excess reactivities create challenges in the design of a reactor’s control system. Control rods are the most common means for compensating for excess reactivity (Fadaei et al., 2010). However, in large, neutronically loosely coupled cores great care must be taken to ensure that their presence does not distort the flux distribution to the extent that excessive power peaking results. In pressurized water reactors dissolving a soluble neutron absorber in the coolant and varying the concentration with time serves to compensate for excess reactivity. Burnable poisons embedded in the fuel or other core constituents offer an additional means of limiting excess reactivity as well as mitigating localized power peaking. The design must also allow the thermal energy produced from fission to be transferred out of the core without overheating any ⇑ Tel.: +98 21 88630644; fax: +98 21 88417576. E-mail address: [email protected] 0306-4549/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2011.06.005
of its constituents. Many other considerations also come into play: the mechanical support of the core structure, stability and control of the chain reaction under widely varied circumstances, and so on. In this study, the effects of burnable poisons on main reactor parameters during operating cycle of VVER-1000 nuclear reactor are investigated. For this approach, the different configurations of BAR in the nuclear reactor core with the different boron concentration are considered and the reactor behavior in each state is studied. The effects of BAR concentration in the core are analyzed based on reactor main parameters. Based on desired goal, the definition of BAR and chemical shim is described in Sections 2 and 3, respectively. Main characteristics and the structure of VVER-1000 nuclear reactor core are introduced in Section 4. In Section 5, the conceptual effects of BAR are presented, the problem is defined and the proposed procedure for solving the problem is explained. The results of calculation are shown in Section 6, and finally the conclusion is performed in Section 7. 2. Burnable absorber rod The life time of a given core fuel loading, that is, the period during which the core has sufficient excess reactivity to permit startup and full power operation, is generally determined by the amount of fuel initially loaded into the reactor core. Of course the amount of fuel loaded into the reactor will depend in on the excess reactivity
A.H. Fadaei / Annals of Nuclear Energy 38 (2011) 2238–2246
that can be conveniently compensated for by reactor control elements. In order to increase the allowable initial core fuel loading, it is common to load into the core materials characterized by high neutron absorption cross sections (poison) that compensate for such excess reactivity during the early stages of core by neutron capture into isotopes with low capture cross sections) somewhat faster than fuel burnup, so that later in core life they contribute negligible negative reactivity. Hence these burnable poisons can nearly match the time behavior of the excess fuel reactivity as it decreases over core life, thereby allowing larger initial fuel inventories without a corresponding increase in control requirements. Burnable poisons thus possess a number of advantages. They increase core life time without any decrease in control safety, reduce the amount of mechanical control required, and if distributed in a proper fashion, can also improve core power distributions, for example, by suppressing reactivity in high flux regions, such as near coolant channels. Such burnable poisons are usually fabricated into the initial core loading as either fixed control blades or curtains or mixed into certain fuel pins. For example, in present BWR designs, gadolinium-loaded fuel pins with an initial reactivity worth of 0.12 Dk/k are loaded into the core until an equilibrium fuel cycle is achieved. In PWRs, borosilicate glass tubes are placed in the core in the initial core loading. From this discussion, several desirable characteristics of burnable poisons are apparent. Obviously they should be characterized by absorption cross sections somewhat higher than those of the fuel, since then they will burn out more rapidly than the fuel, leaving minimal poison residue at the end of the fuel cycle. Furthermore the isotopes formed by neutron capture in the poison should have low absorption cross sections. Finally, the burnable poison, as well as its surrounding clad or structural material, should not affect the structural integrity of the core (such as by swelling) (Lewis, 2008).
3. Chemical shim Water moderated and cooled reactors can be in part controlled, in addition to control rod systems, by varying the concentration of the boric acid (H3BO3) in the coolant. This is called chemical shim. Because the response to a change in concentration of the solvent is not as quick as obtained by the insertion of control rods, chemical shim cannot be used to control the large reactivity insertions. Thus it is always used in conjunction with the control rod systems. In a reactor with both control systems:
2239
ments when used in LWRs. Chemical shim does have several disadvantages, however. Since the rate at which one can inject or withdraw appreciable amounts of poison from the coolant is quite small, the reactivity insertion rates are correspondingly small (with maximum insertion rates of almost 3 10 5 s 1). Chemical shim can have a major effect on the moderator void coefficient of reactivity. We will find that in LWRs this void coefficient is usually quite negative, since a decrease in coolant density leads to a higher decrease in neutron moderation than in neutron absorption and hence the reactivity will decrease. However if a soluble poison is present, a decrease in coolant density will also lead to a decrease in poison concentration – a positive reactivity effect. The desire for a negative void coefficient will frequently limit the amount of chemical shim allowed (typically to less than Dq 0.20 Dk/k). We have shown this effect for a modern PWR core design in Fig. 1 (Duderstadt and Hamilton, 1941). 4. VVER-1000 reactor core The VVER-1000 reactor core has hexagonal structure and consists of 163 fuel assembly (FSAR, 2007). The reactor core is shown in Fig. 2. The schematic view of fuel assembly model of the reactor with BAR is illustrated in Fig. 3. There are 18 BAR in each fuel assembly. In VVER-1000 reactor core there are three types of different fuel assemblies with different enrichment and different BAR concentration that are shown in Table 1. 5. BAR effects evaluation Reactors are normally designed to produce a specified amount of power, while with other variables held constant the cost of construction rises dramatically with the core volume. Thus maximizing the ratio Pmax is a central optimization problem of core design. The achievable maximum power density is dependent primarily on materials properties and the temperatures and pressures that can be tolerated by fuel, coolant, and other core constituents. Minimizing the peaking factor falls much more into the domain of reactor physics, for nonuniform distributions of fuel enrichment, the positioning of control rods and other neutron poisons, as well
Control rods are used to provide the reactivity control for fast shutdown and for compensating reactivity variance due to temperature change. Chemical shim is used to keep the reactor critical during xenon transients and to compensate for the depletion of fuel and build-up of fission products during reactor life time.
The use of chemical shim reduces the number of control rods required in a reactor. Since control rod systems are expensive, any reduction in the number of control rods reduces the total cost of the reactor. Chemical shim is almost uniformly distributed in the core and thus perturbs power distribution less as the concentration of the boric acid is changed. Chemical shim in thermal reactors primarily affects the thermal (fuel) utilization factor (Jevremovic, 2009). A suitable soluble poison must be an isotope characterized by a large neutron absorption section which is soluble in the coolant. It should be of a noncorrosive nature and relatively stable so it will not adhere to core components. Boric acid possesses these require-
Fig. 1. The effect of chemical shim on the moderator temperature coefficient in a PWR (Duderstadt and Hamilton, 1941).
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Fig. 2. The VVER-1000 reactor core.
Fig. 3. Fuel assembly model.
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Table 1 All fuel assemblies type with BA in VVER-1000 reactor core. No.
Cell type
Description
1
Fuel 24B20 Fuel 24b36 Fuel 36B36
Fuel assembly of rods with 2.4% enrichment and burnable absorber with 20 kg/m3 density Fuel assembly of rods with 2.4% enrichment and burnable absorber with 36 kg/m3 density Fuel assembly of rods with 3.3% and 3.7% enrichment and burnable absorber with 36 kg/m3 density
2 3
as other neutronic considerations largely determine the value of Fq. The core volume that is ultimately selected also has reactor physics repercussions, most importantly on the core-averaged fuel enrichment and the nonleakage probability. The reactivity effects of fuel depletion must be compensated to maintain criticality over the fuel burnup cycle. The major compensating elements are the control rods, which can be inserted to compensate positive depletion reactivity effects and withdrawn to compensate negative depletion reactivity effects. Adjustment of the concentration of a neutron absorber (e.g., boron in the form of boric acid) in the water coolant is another means used to compensate for fuel-depletion reactivity effects. Chemical shims (Soluble poisons) are used to compensate fuel-depletion reactivity in PWRs but not in BWRs, because of the possibility that they will plate out on boiling surfaces. As, however, PWRs adopt chemical shim, that is the control of reactivity through dissolution of boric acid in the reactor water, the presence of this neutron absorber decreases the safety effectiveness of the moderator temperature coefficient; in fact, if the temperature increases, the amount of boron contained in the reactor water decreases and consequently the reactivity increases. For this reason, when the boron concentration is high (start of life, cold conditions) the overall temperature coefficient of the reactor water may be positive. Additionally, it must be emphasized that, in any case, the power coefficient (which includes the Doppler effect) must be always negative (Petrangeli, 2006). Burnable poisons consist of separate shim rods substituted for a fuel rod in the fuel assembly. These rods may consist of borosilicate glass rods with stainless steel cladding or B4C pellets in an Al2O3 matrix with zircaloy cladding. The shim rods burn out as the fuel depletes, which constitutes a positive reactivity contribution to compensate the negative reactivity contribution of fuel depletion,
Fig. 5. Keff behavior of the reactor for various conditions (Stacey, 2007).
thus reducing the requirement for adjustment of the boric acid concentration (Stacey, 2007). Fig. 4 shows the effect of burnable poison rods on soluble poison requirements; and the multiplication factor behavior of the reactor is shown in Fig. 5 for various conditions. The importance of the burnable poison concentration on the reactor core behavior was described in previous sections. In the next, focus in the reactor core design with emphasis on the burnable absorber effects.
5.1. Problem definition Based on mentioned cases, obtaining of BAR effects on the reactor core behavior, especially with spotting the interaction with soluble poison, is very important issue in reactor core design procedure. In this study, the influences of the burnable poisons on the main parameters of the reactor such as multiplication factor, burnup, soluble poison concentration, moderator temperature coefficient and power peaking factor over the reactor life time are
Fig. 4. Boron concentration versus first cycle burnup with and without burnable poison rods (Stacey, 2007).
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investigated. VVER-1000 reactor was selected for this survey. The procedure of this research is described in the next subsection. 5.2. Procedure In order to mentioned subject, the analysis of burnable poison’ effects on the reactor core behavior is aimed in this study. For obtaining the demand results, several different configurations consist of different loading patterns and different concentrations of the burnable poisons in the VVER-1000 reactor core are considered, and neutronic core calculation are performed for each configuration to gain the main parameters of the core. The reactor core configuration of VVER-1000 that is proposed by designer is shown in Fig. 6, for reaching to the ability of BAR effects analysis, several different configurations are proposed with different characteristics. The patterns of these cases are shown in Fig. 7. Eight different core configurations were illustrated to investigate the effects of burnable poisons in the nuclear reactor core behavior. In this study, the main neutronic parameters of the core are calculated for the mentioned configurations and finally the effect of burnable poison concentration on the core behavior are deduced based on them. For performing neutron calculation in the reactor core, reactor simulation is necessary. In this study, as before mentioned, two steps have been used for reactor simulation. First step is cell calculation that simulates fuel assemblies in reactor core and second step is core calculation that simulates reactor core. In the first step, cell calculations, macroscopic cross sections for all different types of fuel assemblies (Table 2) calculate for using in the next step, core calculation (Fig. 8), which performs for calculating neutronic parameters (Faghihi et al., 2007; Fadaei and Setayeshi, 2008). For simulating of fuel assembly WIMS code (Winfrith, 1982) has been used. WIMS-D5 is a general lattice cell program, which uses transport theory to calculate flux as a function of energy and position in the cell. This code first calculates spectra for a few spatial regions in the full number of energy groups of its library, and uses these spectra to condense the basic cross sections into few groups. A few group calculations are then carried out using a much more detailed spatial representation. The resulting fluxes are then expanded using the spectra of the previous calculation, so that the
Fig. 6. VVER-1000 core configuration proposed by designer.
reaction rates at each spatial point can be calculated in the library group structure. As an example, the cell models of FA’s that are containing BAR are performed based on Fig. 3 simulation; the BAR that are made of B4C are defined depend on their concentration and distribution in FA’s cell model, and then the group constant of simulated cell are obtained by running provided model by WIMS. Reactor core is simulated by CITATION code (Oak Ridge National Labratory, 1972). This code was designed to solve problems involving the finite-difference representation of diffusion theory treating up to three space dimensions with arbitrary group-to-group scattering. Explicit, finite-difference approximation in space and time has been implemented. The neutron-flux-eigenvalue problems are solved by direct iteration to determine the multiplication factor or the nuclide densities required for a critical system. More details about the simulation can be gained by respect to ‘‘Fadaei and Setayeshi (2009)’’ that is mentioned in References. Briefly, first fuel assembly’s group constants prepared by WIMS D-5 code which are functions of temperature, burnup and power. The results are used in input file of CITATION code for simulating reactor core (Faghihi et al., 2007; Fadaei and Setayeshi, 2008). The main neutronic parameters of each proposed configuration over the whole of cycle length are needed to assess the quality and quantity of core behavior variation. Therefore, dynamic software by FORTRAN was prepared to simulate the core in the cycle and dependent on time, that uses WIMS and CITATION codes in a serial manner for performing the large volume of required calculation to obtain main reactor parameters. To investigate the effects of burnable poison in core behavior, the effects of control rods are neglected. The acid boric concentration value for criticality condition is calculated to assess the moderator temperature coefficient variable in the core. Also, Treatment of Radial Power peaking factor over the cycle length in the point of safety view and the life time of the core in order to economic considerations are calculated to evaluate the efficacy analysis.
6. Result In this study, based on mentioned cases, analysis of burnable absorber concentration’ effects on nuclear core behavior is aimed. In order to the defined procedure for problem solving, the reactor core was modeled by preparing the FORTRAN coupling program between WIMS and CITATION codes. To verify and validate the proposed simulation model, moderator temperature coefficient was calculated versus burnup along the first cycle for designer configuration and then compared with the reference data that are presented in FSAR, (2007). Fig. 9 shows good agreement between the model and references data specially after fixing the power level on 3000 Mw that is occurred at 80th day (there are some error before fixing the power because of the variation in power level and the manner of disceretizing the time that are described in Faghihi et al. (2007) and therefore the presented model can be used to simulate a reactor core behavior with accepted precision. At the next step, several different patterns, which the burnable absorber concentration is the main choppy variable, were proposed to analyze the variations effects. For evaluating the effect of BAR concentration on the core, neutronic calculations were performed for all proposed pattern, and the main core parameters obtained. In Fig. 10 the behavior of boric acid concentration in the core to achieve the criticality state in each pattern are shown. It is obvious that the required boric acid concentration for reaching the criticality state along the core cycle is higher for the pattern which is without BAR, and also, with increasing the BAR concentration required boric acid decrease. The importance of mentioned issue
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Fig. 7. Different considered core configuration for analysis (a) pattern 1, (b) pattern 2, (c) pattern 3, (d) pattern 4, (e) pattern 5, (f) pattern 6, (g) pattern 7, and (h) pattern 8.
is denoted while the moderator temperature coefficient pursued. It is clear that the moderator temperature coefficient because of safety consideration should be placed in the acceptable margin;
and the ideal acceptable margin enforces to be sitting in the negative values. Based on significance of inherent safety in nuclear reactor design, the moderator temperature coefficient (MTC) act as a
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Table 2 All cell types (fuel assemblies and reflectors) in VVER-1000 reactor core. No.
Cell type
Description
1 2 3 4
Fuel 16 Fuel 24 Fuel 36 Fuel 24B20 Fuel 24b36 Fuel 36B36
Fuel assembly of rods with 1.6% enrichment Fuel assembly of rods with 2.4% enrichment Fuel assembly of rods with 3.3% and 3.7% enrichment Fuel assembly of rods with 2.4% enrichment and burnable absorber with 20 kg/m3 density Fuel assembly of rods with 2.4% enrichment and burnable absorber with 36 kg/m3 density Fuel assembly of rods with 3.3% and 3.7% enrichment and burnable absorber with 36 kg/m3 density
5 6
suitable feedback to increase the inherent safety features. Two different parameters affect the MTC behaviors, which are moderator temperature and boric acid concentration. To understand the MTC behavior in the core and its relationship with two mentioned parameters, some efforts were done. The neutronic analysis of the reactor core in the different conditions of moderator temperature and boric acid concentration were performed. Fig. 11 shows the treatment of MTC in VVER-1000 reactor by considering the proposed pattern by designer. It is clear that the given data in this figure should be used to design the core in order to satisfy the safety consideration; these quantities can help to define the maximum licensable value of boric acid concentration. The other important parameter in core design is radial power peaking factor. Needless to say that, the boric acid concentration value, BAR concentration and also its pattern distribution in the core can be affect this parameter. Radial power peaking factor could be increase the safety margin of the reactor especially in the accident conditions, therefore it is desired to decrease its value. In Fig. 12, the behavior of the radial power peaking factor parameter, during the cycle length and for different mentioned patterns are illustrated.
Fig. 9. Moderator temperature coefficient versus burnup.
Based on presented results for different patterns and for different conditions, the effect of BAR concentration can be concluded and used to design the reactor core in order to designer’s request and cost. 7. Conclusion In this paper, the effects of control poisons in the function of nuclear reactor core are investigated. BAR and chemical shim are the main poisons that are exploited in the core. BAR are used to compensate the initial excess reactivity of loaded fuel, uniform the power distribution and decrease the required chemical shim for avoiding the positive moderator temperature coefficient. Placement of BAR in the core and its concentration are two keys subject
Fig. 8. VVER-1000 core model is prepared for core calculation.
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Fig. 10. Acid boric concentration variation for different pattern during first cycle length.
Fig. 11. Moderator temperature coefficient versus acid boric concentration and coolant temperature.
in designing procedure. In this study, some efforts were performed to specify the role of these subjects in the reactor behavior. Several different patterns with regards to the concentration and distribution of BAR are defined and analyzed for investigating the quality and quantity of BAR effects. It can be concluded that the moderator temperature coefficient goes to positive by increasing the acid boric concentration in the coolant, so the minimum worth of BAR are needed to avoid much acid boric concentration. Power peaking factor is dependent on the BAR distribution; the different presented patterns show the effect of BAR placement on this
parameter. It is very interesting that the relative behavior of power peaking factor parameter for different patterns is not uniform during a cycle. It means that in some times this parameter for one pattern is larger than the other while in the other times this relation is inverse. So, analyzing this behavior is complex and needs careful investigation for design. Fig. 10 shows the required acid boric concentration for reaching the criticality sate for different proposed patterns; needless to say that by increasing the BAR concentration in the core, the required acid boric is decreased.
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Fig. 12. Radial power peaking factor for different patterns during first cycle.
Based on the performed research, the mutual effects of chemical shim and BAR in the core can be realized and used by designers to find the optimum values and distributions of burnable poison in the reactor core for obtaining the desired goal. References Duderstadt, J.J., Hamilton, L.J., 1941. Nuclear Reactor Analysis. Department of Nuclear Engineering, The University of Michigan. Fadaei, A.H., Fadaei, M.M., Lia, Sh., Setayeshi, S., 2010. Core design improvement by optimizing the control and protection system elements distribution. Annals of Nuclear Energy 37, 1640–1648. Fadaei, A.H., Setayeshi, S., 2008. LONSA, as a tool for loading pattern optimization using synergy of neural network and simulated annealing for VVER-1000. Annals of Nuclear Energy 35 (10), 1968–1973.
Fadaei, A.H., Setayeshi, S., 2009. Control rod worth calculation for VVER-1000 nuclear reactor using WIMS and CITATION codes. Progress in Nuclear Energy 51, 184–191. Faghihi, F., Fadaie, A.H., Sayareh, R., 2007. Reactivity coefficients simulation of the Iranian VVER-1000 nuclear reactor using WIMS and CITATION codes. Progress in Nuclear Energy 49 (1), 68–78. Final Safety Analysis Report. Bushehr Nuclear Power Plant (NPP), 2007. Jevremovic, T., 2009. Nuclear Principles in Engineering. Springer Science, New York. Lewis, E.E., 2008. Fundamentals of Nuclear Reactor Physics. Academic Press. Oak Ridge National Laboratory, 1972. CITATION-LDI2 Code. Petrangeli, G., 2006. Nuclear Safety. Published by Elsevier Butterworth-Heinemann. Stacey, M., 2007. Nuclear Reactor Physics. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim. Winfrith, 1982. LWR-WIMS, A Computer Code for Light Water Reactor Calculations. UK: AEE, AEEW-R 1498.