SK00ST112
REACTIVITY AND HIGH NEGATIVE SUBCRITICALITY
L.Shishkov. RRC "Kurchatov Institute", Institute of Nuclear Reactors, Russia
ABSTRACT
In the paper the classical notion of core reactivity is discussed, various ways of this notion modifications are shown. Various methods for reactivity measurements are commented. The causes of significant disagreement between the calculation and experimental data on scram system efficiency are given, a suggestion on changing the interpretation of the results of WER startup experiments with scram are made.
The author is of the opinion that the classical notions and determinations introduced by the founders of reactor physics should be kept unchanged. These should be followed not only out of respect to the authorities but rather in order to avoid confusion and K —1 alternative readings. Among these notions ths reactivity p = -~— should be K*ff mentioned, whose introduction into common use was, may be, not very fortunate but which has quite a single meaning.
Indeed, using the generally accepted notation the neutron transport in the reactor can be described using the equations:
*-"* ft _ fTyjyj (i)
If we confine ourselves to the case of linearity OZQTAL operators, a part of equation (1) can be formally separated, forming a new relation:
(2)
447 It has been proved that Eq.(2) has indispensably a single positive solution n>0, (1- p)>0, i.e. at Q and L unchanged the reactivity p, which "physically" characterizes the "proximity" of non-critical reactor to critical state, is unambiguously determined. Strictly speaking, only the "proximity (the degree of proximity) and nothing more. In some cases, using p, one can estimate the rate of change in the full reactor power, but not always.
For the time the reactor physics has existed the notion of reactivity has been continuously used, not always in the same form but this, as a rule, did not result in any negative consequences, as the authors of novations did not go beyond the internal logics of their concepts. Let us consider some modifications of reactivity notion.
Local reactivity. Suppose a physically large reactor is divided into parts, assume that each part receives no neutrons from outside, and determine "in standard way" the reactivity of each part These would be "correct" reactivities, the point is how to use them anyway. It should be noted that, strictly speaking, we always deal only with local reactivities, in the sense, that at an NPP (or on a globe) several reactors are simultaneously in operation, and the reactivity of the whole system is either zero or somewhat positive (provided that at least one reactor has a positive period). Of course, the reactivity of all the reactors is not interesting practically, it is more reasonable to estimate the reactivity of one actually bound system.but taken as a whole. The local properties and effects can be characterized by means of other notions, or "directly", using the codes of spatial dynamics.
Dynamical reactivity. When the composition, state and location of individual parts of the reactor are known, at each moment of time its reactivity is unambiguously determined. If the properties or composition of the reactor change, its reactivity also changes. It is this dynamical reactivity that is mentioned, for example, in [1]. Sometimes the dynamical reactivity is determined as a value obtained reversing the point kinetics equation, when the neutron flux at some point in the reactor or near it is substituted into the equation as power. Sometimes this dynamical reactivity does not coincide with p and can change essentially depending on the point where the neutron flux is fixed.
Reactivity as a parameter determining the change in the integral power of the reactor. If one assumes that the integral power of the reactor is described by point kinetics equations, the reactivity can be determined proceeding from the power change in time. In fact, it is another reactivity: p/t)*p- Even with the system properties remaining unchanged, pi can change in time and will approach p when the neutron flux is becoming asymptotic. Let us briefly consider the specific conditions of the use of high and low reactivity.
The physicists operating the power reactors are mainly interested only in the reactor states which are nearly critical. In this case the reactivity constituting fractions of /?<#• determines directly the dynamical properties of the core: rates of power level rise or reduction. An example of this can be the conditions under which the reactor is found after partial movement of group VI control rods (CR).
44X It is quite another matter when the critical reactor quickly turns into subcritical state with reactivity (-5) + (-20)fitff. At each point of such a reactor the power will reduced by several times for a time of about Jffs+J(T4s. Further decrease in the power will go on at a rate determined by the lifetime of the longest lived group of delayed neutrons. Any precision determination of a high negative reactivity has no sense in itself, it only becomes actual if we feel concern that the negative reactivity would be compensated for a' higher positive reactivity. Thorough knowledge of high negative reactivity is only needed for setting up balance relationships, check of safety assurance after all the effects accompanied by "arising" of positive reactivity manifest themselves. The balance can be set up only for " correct" positive and negative reactivities. The above mentioned "local dynamical reactivities" cannot be summed up in many cases, and this does not "speak well for them".
In any case, today the NPP personnel and regulatory bodies have already got accustomed to know and to use the scram system efficiency - the value of high subcriticality upon insertion of the scram system. At present the calculation and measurement of the reactor scram system worth (without one most efficient CR) is a mandatory normal operation in the power unit startup. However, as a rule, a significant disagreement between the calculation and measurement results is observed. This disagreement has a principal character and is accounted for by the presence of spatial effects and is practically unavoidable. In order to decrease the discomfort due to the difference in the calculation and measurement data, it is advisable to change the treatment of measurement results on the rate of neutron density decay after the drop of scram rods as it is proposed, for example, at the end of this communication.
Measurement of reactivity. The attempts to measure the reactivity directly, using relation (2) or the equation for a joint function (2') are unsuccessful as there is no method to change the number of secondary neutrons per fission act. The situation may be improved when introducing an external neutron source to the non-critical reactor. If S is a stationary source, the neutron distribution will be represented by the equation: Qn-£n + S = Q (3) Both equations (1) and (2) have the positive solutions 449 (4) However relation (4) is not practically used for two reasons: - at real values of S the absolute values of n are small and do not provide reliable statistics; - formula (4) permits the necessary accuracy to be reached only in measuring n at many spatial points; otherwise the "spatial" effect is unavoidable. Practical measurement of high subcriticality is carried out when the neutron density decreases (falls) from the initial, relatively high level provided by either a pulse neutron source or by the initial critical state of the reactor. Here we shall confine ourselves to the second method which is the normal one when the WER scram system worth is measured. After the scram rods have been inserted into the critical reactor the neutron density there changes according to the equation (1). Considering Eq.(l) together with (2) under the condition of core parameter constancy, we shall obtain the expression determining the constant reactivity value p. d A ;=l 9>J^.6 (5) here A is the time of prompt neutron generation; Equation (5) must be solved taking into account the conditions corresponding to the dn dC, beginning of the process when — = —- = 0. di dt Here, as in the case of stationary case of the reactivity measurement, the change in n at any point of core space must be known for p to be correctly measured. Having obtained the scalar products and solving the inverse equation relative these products, p can be determined. In the actual experiments n is only measured at several points of core space and is substituted into the inverse equation instead of the scalar product over the reactor volume. This, naturally, introduces an error consisting of two components: the error of the first jump of neutron density and the error of its further change in time. The relative 450 contribution of these components is determined by the reactivity magnitude, and for high negative reactivities the former reactivity dominates significantly. It is clear that in this case a more correct result for the determination of p will be obtained if . The -above considerations make it possible to recommend to change the treatment of scram experiment. In the author's opinion, the calculation and experimental values of the initial drop in the neutron flux and their logarithmic derivatives in time should be compared at several spatial points. The agreement between the calculated and measured values of the above fiinctionals can be considered as an evidence of the adequacy of the dynamical reactor model by means of which various transient and accidental processes are modeled. As a compromise settlement, the measurement of the scram system worth can be adopted but with introducing a correction for spatial effects. The correction must be obtained by modeling the experiment using spatial dynamical codes. References 1. GJ.Bell, S.Glasston. Nuclear Reactor Theory. 2. P.Siltanen, E.Kaloinen. Investigations in the interpretation of WER-440 rod drop measurements in the beginning of cycles I and 2 of Loviisa-1. Symposium of VMK, Siofolk, 1990. 3. J.Krell et al. Analysis of rod drop measurements at WER-440 reactor. Annual Meeting on Nuclear Technology, Koln, Germany, 24-27.05.1993. 4. Shishkov LJC et al. Analysis of the measurement results of reactivity with allowance for spatial effects. 7 Symposium of AER, Homhz, Germany, 1997. 5. Shishkov LJC et al. Determination of high negative reactivities in the WER reactors by ex-reactor sensors readings. 8 Symposium of AER, Bystrice, Czech Republic, 1998. 6. AJCereszturi et al. Scram Calculations with the KIKO 3D CODE. 8 Symposium of AER, Bystrice, Czech Republic, 1998 7. J.Svarny, VjCrysl. Rod drop measurement analysis. 8 Symposium of AER, Bystrice, Czech Republic, 1998 8. I.Tinka, Eva Tinkova. Topical results obtained by Helios and DIN 3D/2M(E) codes. 8 Symposium of AER, Bystrice, Czech Republic, 1998 451