Reactivity worth

The analysis has shown that the SRP s with beryllium reflector flooded with lead-bismuth alloy are the most dangerous from the point of view of nuclear safety. The main reasons that can cause Kgfr variation due to a positive reactivity are air voids (porosity) being present in the SRP s cores and the possibility for these voids to be filled with water, as water reactivity worth in the SRP s core is -0.7 Peff / L. Thus it means that about 30 Liters of water have to be accumulated for K ff to be - 1 in the core. 

Comparing calculated and experimentally determined reactivity worth enables verification of the accuracy qf nuclear data and the adequacy of computational methods used. For a meaningful comparison of theory and experiment, it is essential that the perturbation theory expressions used for the calculations apply to exactly the same parameter as that deduced fi-om the experiments, and that these expressions are evaluated accurately. This paper reviews three aspects of accurate determination of reactivity (1) the definition of reactivity, (2) high-order perturbation theory expressions for reactivity, and (3) the accuracy of computational techniques based on the multigroup approximation. 

Reactivity is an integral parameter often met by reactor physicists and engineers. Reactivity worths of control systems and reactivity coefficients are important in the performance and safety of nuclear reactors. Hence, accurate knowledge of such reactivities is essential for reliable and economical design of nuclear reactors. The accuracy of reactivity predictions is... 

If the flux distribution in the perturbed reactor were known, it could have been used in Eq. (8) to give the exact reactivity worth associated with the perturbation. The flux and other distribution-function perturbations are also required for many applications other than reactivity calculations. A few of these applications, in homogeneous and inhomogeneous systems, will be mentioned in the sections to follow. 

The first and most well-known feature is the adequacy of the integral methods for calculating space-dependent flux distribution in heterogeneous geometries. This characteristic can be essential for accurate calculations of reactivity worth of small samples in fast systems [see Foell s monograph (2) and its references]. The heterogeneity is due to the perturbing sample as well as to the inherent structure of the unperturbed reactor. 

Examples of perturbation parameters are reactivity worth, reactivity coefficient, and various sensitivity functions (see Section IV,B). Gandini (39) and Stacey (46) derived GPT formulations for the calculation of reactivity in altered systems. In Section V,F,2 we present Stacey s GPT formulation for calculating the effect of different system alterations on a given reactivity. Also presented is a formulation for calculating the effect of a given system alteration on different reactivities. 

The formulation Stacey derived (41) for reactivity worth in altered systems can be similarly obtained by expressing p in terms of rather than p. ... 

Generalized-function formulations of GPT for homogeneous systems are the source of sensitivity functions for different integral parameters Equation (189) for reactivity worths, and Eq. (162) for ratios of linear and bilinear functionals. The first-order perturbation theory expression for reactivity [Eq. (132)] can also be used for sensitivity studies. 

Second, there are the characteristics that depend on the neutron distribution in the system. These characteristics also have, usually, a direct dependence on the material densities. Examples of characteristics of this type, to be referred to as nucleonic characteristics, are breeding ratio, total power, power shape factor, and reactivity worth. The variation of the functional fiV/], denoting a general nucleonic characteristic, caused by a small but otherwise arbitrary variation 5N in the density distribution of the ith material, is... 

Are these in-group spectral effects responsible for the CWD for fertile and fissile isotopes The simple model results (13S) tend to support this assumption. Results of numerical calculations for realistic problems obtained recently by Kier and Zolotar 139) show, however, that even though spectral fine structure effects are significant in the low energy end of the resolved resonance region, they contribute little to the reactivity worth of a Pu and a sample in the ZPR 6 assembly 7 reactor. These results were obtained from a small number of calculations for two specific perturbations. Further investigation seems necessary before the significance of spectral fine structure effects and their connection with the CWD can be firmly established. 

Spectral effects are probably also important for integral parameters other than material reactivity worth. An example is the Doppler coefficient, which is caused by resonance perturbations. No satisfactory agreement has yet been reached between the calculated and measured Doppler effect of small fissile samples in fast assemblies 23). 

If the perturbation in the space and energy dependence of the flux distribution has important effects on problems such as small-sample reactivity worth, what is the reactivity effects of the perturbation via angular dependent fine structure details This is still an open question. 

E. Greenspan, On the Calculation of Reactivity Worths in Fission Reactors, MATT-944. Princeton Univ. Plasma Phys. Lab. (1972). 

E. A. Fischer, A Method to Calculate Reactivity Worth by Integral Transport Theory, KFK-995. Kemforchungszentrum Karlsruhe (1969). 

W. J. Oosterkamp, The Measurement and Calculation of Reactivity Worth of Samples in a Fast Heterogeneous Zero Power Reactor, KFK-1036. Kernforschungszentrum Karlsruhe (1969). 

The requirements of ANSI/ANS 8.1 specify that calculational methods for away-from-reactor criticality safety analyses be validated against experimental measurements. If credit is to be taken for the reduced reactivity of burned or spent fuel relative to its original fresh composition, it is necessary to benchmark computational methods used in determining such reactivity worth against spent fuel reactivity measurements. This report summarizes a portion of the ongoing effort to benchmark away-from-reactor criticality analysis methods using critical configurations from commercial pressurized- water reactors (PWR). 

The 4S FR concept was proposed and developed by CRIEPI — Toshiba (Japan). Tlie main features of reactor design are a tall thin reactor core (an equivalent diameter 90 cm, length 4 m) and axially moveable radial reflector for compensation of bumup reactivity. Its reference design of 50 MW(e) was for 10 years of electric power output without refuelling and without the use of the safety rod for bum up reactivity control. Now, the CRIEPI — Toshiba team has proposed a new design variant for 24 years of full power operation without refuelling. It uses part of the reactivity worth of the safety-rod in addition to the radial reflector segments for bumup reactivity control. 

In the shutdown mode, the reactor vessel is fully pressurized or, at different times, in various stages of depressurization. Afterheat from fission product decay is generated at rates of up to about 7 percent of the core power level prior to shutdown, depending on the time interval since shutdown. The core decay heat is removed by the HTS. When the HTS is not available, the heat is removed by the Shutdown Cooling System (SCS). The outer control rods are normally fully Inserted during shutdown, and meet the required shutdown margin, with due allowances for uncertainties, even if the maximvim reactivity worth rod remains fully withdrawn. For cold shutdown, the control rods in the inner reflector are also Inserted and for this case, the maximum reactivity worth control rod is in the inner reflector. The neutron flux level is continuously monitored by the source range detectors. 

Nominal Reactivity Control Worths The calculation of control rod and reserve shutdown control (RSC) worths under both hot and cold conditions have been performed for both the initial cycle BOG conditions and the equilibrium cycle EOC condition. In addition, the worth of all 30 control rods has been calculated for other times in cycle for both the initial core and an equilibrium reload cycle to determine how the total control rod bank worth is expected to change over the cycle. Other specific rod pattern control worths for hot conditions for the selected withdrawal of groups of three rods each in the outer bank of control rods were analyzed to define the maximum group worth for use in the transients analyzed in Chapter 15. These calculations were only performed for the EOC equilibrium core loading since that cycle condition yields the minimum temperature coefficient of reactivity and the maximum rod group reactivity worth for a rod group withdrawal transient. No reduction in control rod poison worth due to burnup has been assumed in this or other EOC rod worth calculations discussed below, although this effect would be minimal. 

A summary of the calculated control reactivity worths for both hot and cold conditions is given in Table 4.2-6 for the end-of-equilibrium cycle conditions. The eight groups of three rods each which make up the outer bank of rods were analyzed under hot conditions for several withdrawal sequences. The minimum group reactivity worth was for the first group withdrawn and was worth 0.9 percent A p- The maximum group worth was found to be 2.1 percent and 20 percent uncertainty was assumed for the Chapter 15 rod withdrawal transients in which a value of 2.5 percent AP was assumed. The total worth of the trip of the outer rod bank is 12.7 percent AP hot, but this worth was reduced to 9 percent A Pfor all Chapter 15 transients involving a trip. 

The se results show that hot control reactivity worths are typically 15 to 20 percent higher than the cold worths. The nominal cold reactivity worth of all 30 control rods is 20.2 percent Ap which is significantly larger... 

Reserve Shutdown Requirements and Reactivity Worths The primary reactivity requirement for the reserve shutdown control (RSC) is to maintain shutdown (k < 0.99) indefinitely at or below the refueling temperature 192 C (377 F). Any partially inserted control rods or other fully withdrawn control rods are assumed not to be inserted in determining the RSC capability to meet this requirement, i.e., the maximum core operating excess reactivity is assumed to be held down by control rods and this excess reactivity is not a component of the requirement for the RSC. The reserve shutdown control equipment (RSCE) is also required to trip following the trip of the outer bank of control rods, and after some delay, for transients initiated by moisture ingress during power operation. 

Table 4.2-11 gives the reactivity control requirement and the estimated RSC reactivity worth for the beginning, middle, and end of cycle. The... 

BOIC) cold reactivity worth of 12 RSC alone is 10.1 percent Ap and the worth of 24 outer rods alone is worth 8.1 percent AP while the worth of 12 RSC and 24 outer rods is worth 28.4 percent A p. Therefore, the worth of 12 RSC in the presence of 24 outer rods is 28.4 percent Ap - 8.1 percent AP 20.3... 

The reactivity worth of the outer control rods is increased, and the worth of the inner control rods is decreased. This ensures earlier withdrawal of the inner rods. 

MOC, and EOC conditions. Nominal calculated values of the components of the control requirements at each cycle condition were used and these preliminary estimates of critical rod positions do not include either requirements uncertainties or rod group reactivity worth uncertainties. 

The data shown Includes the estimated hot-unrodded kgff, cold shutdown kg , cold critical rod patterns, hot 25 percent power rod patterns and hot 100 percent power rod patterns expected for each cycle condition. Critical rod "positions" are expressed as the expected percentage of the rod group reactivity worth that is withdrawn at the indicated condition. A range of critical rod "positions" at the indicated power level is shown and corresponds to position changes expected as xenon buildup takes place at the indicated power level. 

Assumes maximum reactivity worth stuck rod reduces calculated rod bank worth by 2%Ap for all cycle conditions. 

Percent withdrawal represents the percentage of the critical rod bank total reactivity worth that is withdrawn at the indicated condition. 

One can see the validity of the recommended method (errors in the last column) but also the inadequacy of simpler methods (homogenisation by volume or by flux) for the determination of the control rod worth. The control and shutdown systems have been measured under different situations and their control rod reactivity worth have been calculated with the current scheme. The results are given in Table 4. 

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