Transient processes when changing reactor subcriticality degree

1. Transient processes when changing reactor subcriticality degree

2. Transient processes when changing reactor subcriticality degree • Let us use elementary equation of subcritical reactor kinetics as follows: • q— specific power of a neutron source, n/(cm 3•s)

3. In principle, it is already clear that transient process in a subcritical reactor, when changing reactor subcriticality degree from one value to another, • should be a process of transition of neutron density value n(t) from one steady-state value n1corresponding to the initial subcriticality degree dkп1 • to another steady-state value n2 corresponding to another value of subcriticality degree dkп2.

4. We are interested in the nature of this transient process. That is the answer to the question: to what kind of mathematical law is transient process subject.

5. Suppose first the reactor was subcritical at a subcriticality of δkn1, • as a result of which the neutron density was established ny1 = s*l / δkn1. • As the subcriticality increases from δkn1to δkn2, that is, by the amount • ∆δkn=δkn2 - δkn1 • therefore the elementary equation of kinetics for this transient The process will look like • δkn2 = δkn1 + ∆δkn = δkn1 - ∆k

6. Therefore, the elementary equation of kinetics for this transition process will look like: • or: • This equation with separable variables:

7. The expression for the transient process will be according to the value of the effective multiplication factor ke1:

8. The phrase suggests that the transient process in the subcritical reactor when changing the value of effective multiplication factor on the value ∆k • (or what is the same - when changing reactor subcriticality degree) • is exponential.

9. Increasing - when increasing effective multiplication factor by∆k • (or when decreasing reactor subcriticality degree by ∆k) • and decreasing - when decreasing effective multiplication factor by ∆k • (or increasing reactor subcriticality degree by ∆k).

10. Increasing - when increasing effective multiplication factor by ∆k

11. decreasing - when decreasing effective multiplication factor by ∆k

13. Exponent - asymptotic curve: • it reaches its theoretically steady-state value at infinitely large time of the transient process (at t →∞). • Almost (up 1%), any exponent comes to its steady-state value per time equal to four - five of its periods T • (it drew attention even when considering the law of radioactive decay).

14. Therefore, the value of practical time of establishing subcritical neutron density in the reactor is approximately equal to: • .

15. Practical establishment time of subcritical neutron density in the reactor, • as the value of establishing neutron density itself, • is defined by the value of reactor subcriticality degree, which is given to it after the regular moving up of reactivity compensation units.

16. The closer a reactor to the critical state after a regular stage of moving up of reactivity compensation units, • the greater the practical time value of subcritical neutron density establishment in the reactor.

17. After inserting a neutron source to the subcritical core, neutron density increases exponentially, tending to the limit at i→ ∞.

18. This character of the transient process is explained: • by the original density n0source created by the source at the time of its insertion  to the core, • in each multiplication cycle will be added to its neutrons.

19. As a result, when the number of multiplication cycles m tends to infinity, • neutron density in subcritical reactor, where Keff<1, • asymptotically approaches the limit, which is the sum of infinitely decreasing geometric progression

20. The expression is called as subcritical neutron multiplication factor (M) • The steady-state neutron flux in the multiplying medium at Keff <1 and in the presence of an external neutron source:

21. Imagine subcriticality degree δкeffas the sum of the original subcriticality and inserted jump-like perturbation, then we can write down

22. Since δкeffandδкeff0 in the subcritical reacor are negative, and sign кeffв can be different, this equation is often written as

23. minus sign in front of δкeff вmeans insertion of positive reactivity, • plus sign - on the contrary, negative (for a subcritical reactor). • If original neutron density n1, then

24. their ratio • The obtained results show that the greater neutron density increment in case of approaching the critical state, • the smaller remaining subcriticality by the absolute value.

25. Example 1 ∆k = +0.02 К1 = 0,95 ρ1 = - 0,052 ׀ρ1׀ = 0,052 ׀ρВ׀ = 0,02

26. Example 1 ∆k = +0.02 К1 = 0,95 ρ1 = - 0,052 ׀ρ1׀ = 0,052 ׀ρВ׀ = 0,02

27. ∆k = -0.02 К1 = 0,95 ρ1 = - 0,052 ׀ρ1׀ = 0,052 ׀ρВ׀ = 0,02

28. ∆k = -0.02 К1 = 0,95 ρ1 = - 0,052 ׀ρ1׀ = 0,052 ׀ρВ׀ = 0,02

29. Step by step start-up  procedure and nuclear safety • Transient processes in the subcritical reactor at step by step raising of absorbers by the equal size steps in the process of the reactor start-up.

31. At the same time, everything is subject to reasonable caution: • no matter how fast the reactor is brought into a state of instant criticality, having informed him of a large positive reactivity earlier than there is the possibility to confidently control all changes in the neutron flux by the standard means of measuring the neutron density.

32. Caution dictates the following measures: • a) The critical position of the mobile absorbers must be calculated in advance. • The operator must clearly know beforehand how high it is to lift the absorbers from the lower limit switches.

33. b) The sequence and rate of lifting of groups of absorbers is set by a special program of safe lifting them at start-up. • The essence of this program is that the lifting of the absorbers to the critical position is performed with cautious steps. • In addition, time pauses larger than the stabilization time of the subcritical neutron density in real conditions of start-up should be maintained between the steps.

34. In the initial stage of the uptake of absorbers, when the reactor is deeply subcritical, changes in the neutron density with each step of the absorbers are relatively small. • In such conditions, it is possible not to pause at all between steps, that is, to carry out the lifting of the absorbers almost continuously: this can save considerable time during start-up. • At the second stage of the start, active precautions begin: between the steps, temporary pauses of 1 minute are maintained.

35. At the third and final stage of the start-up, the pauses between the steps increase to 3 minutes, and in some cases the single step steps are limited to 0.1 $, • since the neutron density stabilization time under such conditions is of the same order of magnitude, and the values of the established neutron densities themselves become large enough that they can be fixed by a regular neutron density monitoring system.

36. Stabilization time of neutron density in the subcritical reactor increases as reactor approach to criticality. • It leaves its mark on the organization of the reactor start-up procedure, • especially if the initial raise stage of reactivity compensation units due to the limited sensitivity of the start-up equipment for neutron flux monitoring in the reactor is performed "blindly".

37. Inverse multiplication method • Introduce the notion of Yineutron multiplication factor for the reactor state «i» as the ratio of the number of neutrons in the reactor in the state «i» -Ni • to the number of neutrons without multiplication N0 • (or a minimum starting multiplication) Yi= Ni/ N0

38. In reality, of course we do not know the true number of neutrons in the reactor, • but only assess it by the rate of detector readings or current of ionization chambers Ii, • which are related to the number of neutrons through the efficiency of these detectors () as • Ii= * Ni

39. Then we can conditionally take: • Yi= Ii /I0 • Fundamental fact is that at Keff1.

40. After defining the concept of multiplication, the concept of "inverse multiplication" • ОY = 1 / Y • is introduced and on the basis of the ratio inverse multiplication formula is written. • It is in this relation "inverse multiplication method" is formulated, allowing to experimentally measure reactivity (or criticality) of the reactor and reactivity of inserted perturbations.

41. Measurement of any changes of reactor reactivity is based on the method of inverse multiplication. • The fundamental conclusion is that the change of reactivity in the reactor transition from state "1" state "2" is equal to: • 21=2 -1 =1/Y1 – 1/Y2 = • =ОY1-ОY2= - OY

42. Determination ofthe full effectiveness of rods in the subcritical states is also based on this method, • i.e. determination of  the reactor reactivity change when moving rods from the lower to the upper position (or vice versa). • The same method is used to obtain integral and differential calibration characteristics of the regulating unit by measuring the weight of rod parts.

43. On the contrary, in the critical reactor states any measurements of rod characteristics are possible only by the "compensation" method of the measured reactivity by other known reactivity.

44. Note that IY method gives a relative "weight". • In this case, as well as during fuel loading (FA), the "weight" of rod is expressed in units OY. • We can convert it into absolute units (i.e. to produce absolute calibration)by measuring the same portion of any reactivity fraction (rod weight) by any method of absolute measurement of reactivity and by OY.

45. For this purpose, asymptotic period method (which gives the relation of reactivity in beta with period) • Tасper s: /= 1/(1+Тас) • or method of "rod insertion" will be suitable. • Method of safe achievement of the critical state when loading a reactor is based on the inverse multiplication method.

46. It should be noted that inverse multiplication method - static. • Therefore, when measuring rates of detector readings, exposure after any perturbations (1-3 minutes) should be done to eliminate transient processes.

47. Reactor start-up method • Start-up method secures nuclear safety in the process of start-up

48. Start-up method secures nuclear safety in the process of start-up • and in the process of loading it comes to the construction of inverse multiplication dependence (OY = 1/M) on characteristics of the reactor changing the parameter of its criticality • (e.g., in this case- on the number of fuel assemblies FA (n) loaded into the reactor, • in other situations - on the  moderator level H, • boric acid concentration C, • position of the compensating units and so on).

49. In general, the procedure is as follows. • One establishes "zero" or "reference" state of the reactor; it records all parameters (temperature, flow, position of all control units). • Current of the ionization chamber (IC) is measured - it is I0, Y0=1 and OY0=1, respectively. • Value of OY0= 1 is plotted on the IM dependence graph from the number of loaded fuel assemblies (nFA).

50. Then a safe number is loaded - FA portion (nFA) and IC current is measured - InorIi. • Y and OYnare calculated. • OYnvalues are plotted on the graph of IM dependence on the number of nfa. • Through these two points, a straight line is drawn, and one it is extrapolated to the intersection with nFA axis. • This is the first extrapolated value of the critical state n1extr.