part4_1_xenon_effects_on_reactor_operation by amUK4tg

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									  Part4_1: Xenon Effects on Reactor Operation


                B. Rouben
             Course UN 0802
              2012 Mar-Apr




2012 March                                1
                       Contents
   We study the reactor-physics effects of Xe-135
    in the operation of nuclear reactors, and their
    importance.




    2012 March                                   2
                  Effects of Xenon Poison

   Saturating fission products are fission products whose
    concentration in fuel operating in a steady flux (i.e., at
    steady power):
      depends on the flux level, and

      comes to an asymptotic, finite limit even for values of

       the steady flux assumed to increase to infinity.
   The most important saturating fission product is 135Xe,
    but other examples are 103Rh, 149Sm and 151Sm. In each
    case the nuclide is a direct fission product, but is also
    produced by the -decay of another fission product.

     2012 March                                            3
                      135Xe   and 135I

    135Xe    is produced directly in fission, and also
    from the beta decay of its precursor 135I (half-life
    6.585 hours).
   It is destroyed in two ways, by its own
    radioactive decay (half-life 9.169 hours), and by
    neutron absorption to 136Xe (which has no
    significant absorption cross section).
   It will be important and instructive to understand
    the relative importance of each production
    pathway and each destruction pathway.
          Figure “135Xe/135I Kinetics” in next slide. 4
    See March
      2012
                       I-135/Xe-135 Kinetics

     Production of 135Xe by beta decay of 135I dominates over its
                     direct production in fission.

                       -(1/2=18 s)
               135Te                   135I             -(1/2=9.169 h)

                                   -(1/2=6.585 h)
                                                      135Xe
Fissions


                                                       Burnout by neutron
                                                       absorption




  2012 March                                                               5
                 “Double-Bathtub” Analogy
                   I Bathtub




Xe Bathtub




    2012 March                              6
                      135Xe   and 135I
 135   Xe has a very important role in the reactor
   It has a very large thermal-neutron absorption
    cross section
   It is a considerable load on the chain reaction
   Its concentration has an impact on power
    distribution, but in turn is affected by the power
    distribution, by movement of reactivity devices,
    and significantly by changes in power.


     2012 March                                      7
                  135Xe    and 135I (cont’d)

   The large absorption cross section of 135Xe plays a
    significant role in the overall neutron balance and
    directly affects system reactivity, both in steady state and
    in transients.
   It also influences the spatial power distribution in the
    reactor.
   Looking ahead, the limiting absorption rate at extremely
    high flux  maximum steady-state reactivity load
    ~ -30 mk.
   In CANDU, the equilibrium load at full power ~ -28 mk
    (more on this later)
     2012 March                                             8
    The Equations for I-135/Xe-135 Kinetics
    First, define symbols:
   Let I and X be the I-135 and Xe-135
    concentrations in the fuel.
   Let I and X be the I-135 and Xe-135
    decay constants, and
   Let I and X be their direct yields in fission
   Let X be the Xe-135 microscopic
    absorption cross section
   Let  be the neutron flux in the fuel, and
   Let f be the fuel fission cross section
2012 March                                            9
Differential Equations for Production and Removal

   I-135 has 1 way to be produced, and 1 way to
    disappear, whereas Xe-135 has 2 ways to be
    produced, and 2 ways to disappear
   The differential equations for the production and
    removal vs. time t can then be written as follows:
    dI
         I  f   I I                            (1)
    dt

    dX
        I I   X  f   X X   X X            ( 2)
    dt

2012 March                                               10
     Let Us First Study the Steady State – Use Subscript ss


    In steady state the derivatives are zero:

   I  f ss  I I ss  0                          (3)


I I ss   X  f ss   X X ss   X X ssss  0   ( 4)



  2012 March                                                11
                                   Steady State

   Solve Eq. (3) for steady-state I-135 concentration Iss:
                 I  f ss
         I ss                        (5)
                    I

   Substitute this in Eq. (4):
             X X ss   X X ssss   I  f ss   X  f ss

   Now solve this for steady-state Xe-135 concentration Xss:
                I   X  f ss
        X ss 
                  X   X ss
     2012 March                                                  12
                 Interactive Discussion/Exercise
   What is the difference in character between the
    equations for the Xe and I steady-state
    concentrations?




    2012 March                                     13
                      Steady State – Final Equations
                I  f ss
        I ss                                                        (5)
                   I
   The steady-state I-135 concentration is directly proportional to
    the flux value
   Whereas
                I   X  f ss
        X ss                                              ( 6)
                  X   X ss
   Xss is not proportional to the flux, in fact it saturates in high flux:
   In the limit where ss is infinitely large (i.e., very high power):


                                                    I   X  f
       X ss ( steady  state, very high flux )                      (7)
                                                        X
    2012 March                                                             14
        Now Let’s Look at Typical ss Values
    Typical values of the parameters:
   I-135 half-life = 6.585 h  I = 2.92*10-5 s-1
   Xe-135 half-life = 9.169 h  X = 2.10*10-5 s-1
   I = 0.0638
   X = 0.00246 (X depends on the fuel burnup, because the
    Xe-135 yields from U-235 and Pu-239 fission are quite
    different)
   X = 3.20*10-18 cm2 [that’s 3.2 million barns!]
    [X depends on temperature]
   f = 0.002 cm-1, and
   For full power in CANDU, ss,fp = 7.00*1013 n.cm-2s-1
     2012 March                                         15
                                 Values at Steady State
   If we substitute these numbers into Eqs. (5) and (6), we
    find that at steady-state full power:
   Iss,fp = 3.06*1014 nuclides.cm-3                  (8)
   Xss,fp = 3.79*1013 nuclides.cm-3                  (9)
   With these values we note that at steady-state full power
    I I ss , fp  2.92 * 10 5 s 1 * 3.06 * 1014 cm 3  8.93 * 10 9 cm 3.s 1
     X  f ss , fp  0.00246 * 0.002 cm 1 * 7.0 * 1013 cm 2 s 1  3.44 * 10 8 cm 3.s 1

   Therefore at steady-state full power the Xe-135 comes
    very predominantly (96%) from I-135 decay rather than
    directly from fission!

      2012 March                                                                           16
                              Values at Steady State


    Also at steady-state full power
    X X ss , fp  2.1 *105 s 1 * 3.78 *1013 cm 3  7.95 *108 cm 3.s 1
 X X ss , fpss , fp  3.2 *1018 cm 2 * 3.79 *1013 cm 3 * 7.0 *1013 cm 2 .s 1
                   8.48 *109 cm 3.s 1
    Therefore, at steady-state full power, the Xe-135
     disappears very predominantly (91%) from burnout
     (by neutron absorption) rather than from its  decay!



     2012 March                                                                      17
            Values at Steady State with Very High Flux

   In the limit where ss is very large (goes to infinity), we
    find from Eq.(7)
                                   I   X  f
                   X ss ,  
                                       X

                        
                          0.0638  0.00246* 0.002 cm 1
                                        3.2 *1018 cm 2
                         4.11*1013 nuclides.cm 3 (10)
                   Comparing Eq.(8) with this value, we find
                   X ss , fp  0.92 * X ss ,            (11)
                   i.e, we can say that the Xe  135 concentration is
                   92% saturated at full power.

      2012 March                                                        18
              Xe-135 Load (Xe-135 Reactivity Effect) at Full Power
Here we make an estimate of the Xe  135 reactivity at full power :
Xe  135 affects mostly the thermal absorption cross sec tion,  a 2 . The Xe  135 contribution
is a 2, X   X X . We can then get an estimate of the reactivity effect by
                                                       f       12
recalling the 2  group formula for k                                  .
                                                      a2     a1  12
If we apply the change a 2, X to  a 2 ,
              a 2, X               12       
k , X                 * f                a 2, X * k
               a 2 2            a1 12     a2
                                                                         a 2, X
The change in keff would have a similar form : keff , X                          keff
                                                                             a2
Starting from a critical reactor keff  1, and X ss , fp 
              3.2 *1018 * 3.79 *1013                                       k
keff , X                           *1  0.03, and  X , fp   1  1   eff , X  0.03  30 mk
                      0.004                                         k          2
                                                                               keff
                                                                       eff 

This is a first estimate. A more accurate treatment gives  X , fp  28 mk.

      2012 March                                                                              19
                        Xe-135 Load in Various Conditions
   The most accurate value for the steady-state Xe-135 load
    in CANDU at full power is X,fp = -28 mk            (12)
   In any other condition, when the Xe-135 concentration is
    different from the steady-state full-power value (e.g., in a
    transient), since the reactivity effect is proportional to the
    Xe-135 cross section, and therefore to X, we can
    determine the Xe-135 load by using the ratio of the
    instantaneous value of X to Xss,fp:
              X                                   X                            X
     X                *  X , fp  28 mk *                28 mk *          13  3
                                                                                       (13)
            X ss , fp                           X ss , fp              3.79 * 10 cm
   The concentration X would of course have to be known,
    say, by solving the Xe/I kinetics equations (1)-(2).
      2012 March                                                                              20
                               “Excess” Xe-135 Load

   We may sometimes like to quote not the absolute
    Xe-135 load, but instead the “excess” xenon load,
    i.e., the difference from its reference full-power
    value (-28 mk),
    Using Eq.(13) in the previous slide:

    Excess or "Additional" Xe  135 Load
                                                 X         
                   X   X , fp     28*              1 mk   (14)
                                             3.79 *10      
                                                      13




    2012 March                                                            21
         Xenon Load at Various Power Levels




             Figure Credit: “Nuclear Reactor Kinetics”, by D. Rozon,
                      Polytechnic International Press, 1998.
2012 March   Note: The Xenon Load should really have a minus sign.     22
         Effects of 135Xe on Power Distribution
   In the figure on the previous slide, the power on
    the horizontal axis can be taken as “relative”
    rather than as an absolute value, i.e., the figure
    can tell us the relative local xenon concentration
    as a function of the local power:
    High-power bundles have a higher Xe-135
    concentration, i.e., a higher xenon load, therefore
    a lower local reactivity  xenon flattens the
    power distribution
   In steady state, 135Xe reduces maximum bundle
    and channel powers by ~ 5% and 3% respectively.
      2012 March                                       23
            Saturating-Fission-Product-Free Fuel

   In fresh bundles entering the reactor, 135Xe and
    other saturating fission products will build up
    (see Figure on next slide).
   The reactivity of fresh bundles drops in the first
    few days, as saturating fission products build in.
   “Saturating-fission-product-free fuel” will have
    higher power for the first hours in the first couple
    of days than later – the effect may range up to
    ~10% on bundle power, and ~5% on channel
    power.
     2012 March                                      24
              Build-up of 135Xe in Fresh Fuel




             Figure Credit: “Nuclear Reactor Kinetics”, by D. Rozon,
                      Polytechnic International Press, 1998
2012 March                                                             25
           Saturating-Fission-Product-Free Fuel

   For an accurate assessment of powers after
    refuelling, calculations of the nuclear properties
    need to be performed at close intervals (a few
    hours) to capture the build-up of saturaring
    fission products, or else a “phenomenological”
    correction of the properties of fresh bundles
    needs to be made.


    2012 March                                      26
        Effect of Power Decrease on 135Xe Concentration

   The Xe-135 concentration changes significantly in
    power changes, and this has very strong effects on the
    system reactivity.
   When power is reduced from a steady level:
       The burnout rate of 135Xe is decreased in the reduced flux, but
        135Xe is still produced by the decay of 135I
         the 135Xe concentration increases at first
   But the 135I production rate is decreased in the lower
    flux, therefore the 135I inventory starts to decrease
   The 135I decay rate decreases correspondingly
     the 135Xe concentration reaches a peak, then starts to
    decrease - see Figure.
   The net result is that there is an initial decrease in core
    reactivity; the reactivity starts to turn around after the
    xenon reaches its peak.
     2012 March                                                     27
     Xenon Reactivity Transients Following Setback to
                                Various Power Levels
                           Xe Reactivity (mk) vs. Time (h):
                           Step Change from FP to 80% FP
             0   10   20   30    40   50   60   70   80   90   100   110   120   130
     -27.0




     -28.0




                                Note: this is just the Xe-135
     -29.0




     -30.0
                                reactivity. If the reactor is to
                                continue operating at this power,
     -31.0
                                the change in Xe-135 reactivity
                                must be compensated by some
     -32.0                      other change in reactivity, i.e., by
                                moving control rods (zone
     -33.0                      controllers, adjusters)
2012 March                                                                             28
     Xenon Reactivity Transients Following Setback to
                                Various Power Levels
                           Xe Reactivity (mk) vs. Time (h):
                           Step Change from FP to 60% FP
             0   10   20   30   40   50   60   70   80   90   100   110   120   130   140
       -26



       -28



       -30
                                          Note: the final Xe-135
       -32                                reactivity is less negative
       -34
                                          than the starting value, as
                                          is to be expected on
       -36                                account of the lower
                                          steady-state power.
       -38



       -40



2012 March                                                                                  29
     Xenon Reactivity Transients Following Setback to
                                Various Power Levels
                           Xe Reactivity (mk) vs. Time (h):
                           Step Change from FP to 40% FP
             0   10   20   30    40   50   60   70   80   90   100   110   120   130


     -22.0



     -27.0



     -32.0


                                      Note: It is unlikely that a
                                      reduction from full power to
     -37.0



     -42.0
                                      50%FP or lower can be
                                      sustained, because the change
     -47.0                            in Xe-135 reactivity is too large
                                      to be compensated by
                                      adjuster-rod withdrawal.
     -52.0




2012 March                                                                             30
       Xenon Transient Following a Shutdown

     A reactor shutdown presents the same scenario in an
      extreme version: there is a very large initial increase
      in 135Xe concentration and decrease in core
      reactivity.
     If the reactor is required to be started up shortly after
      shutdown, extra positive reactivity must be supplied,
      if possible, by the Reactor Regulating System.
     The 135Xe growth and decay following a shutdown in
      a typical CANDU is shown in the next Figure.



    2012 March                                              31
                  Xenon Reactivity Transients Following
                            a Shutdown from Full Power
                              Xe Reactivity (mk) vs. Time (h):
                                Shutdown from Full Power
              0   10   20    30   40   50   60   70   80   90    100   110   120   130
        0.0

      -10.0

      -20.0

      -30.0

      -40.0

      -50.0

      -60.0

      -70.0

      -80.0

      -90.0

     -100.0

     -110.0

     -120.0


2012 March                                                                               32
         Xenon Transient Following a Shutdown
   It can be seen that, at about 10 hours after shutdown, the
    (negative) reactivity worth of 135Xe has increased to
    several times its equilibrium full-power value.
   At ~35-40 hours the 135Xe has decayed back to its pre-
    shutdown level. Beyond that time it will go to 0.
   If it were not possible to add positive reactivity during this
    period, the reactor would go into “poison-out” and the
    shutdown would necessarily last some 40 hours, when the
    reactor would again reach criticality.
   In “poison-out”, the reactor must be put into “guaranteed
    shutdown” (overpoisoned with B or Gd), to ensure that the
    reactor cannot go critical when the Xe-135 has decayed
    away, until a conscious decision is made to restart.
      2012 March                                             33
                      Xenon Override
   To achieve xenon “override” and permit power
    recovery following a shutdown (or reduction in reactor
    power), positive reactivity must be supplied to
    “override” xenon growth; e.g., the adjuster rods can be
    withdrawn to provide positive reactivity.
   It is not possible to provide “complete” xenon
    override capability; this would require > 100 mk of
    positive reactivity.
   The CANDU-6 adjuster rods provide approximately
    15 milli-k of reactivity, which is sufficient for about
    30-35 minutes of xenon override following a
    shutdown.
    2012 March                                           34
                  Case of Power Increase

   Conversely to the situation in a power reduction,
    when power is increased the 135Xe concentration
    will first decrease, and then go through a
    minimum.
   Then it will rise again to a new saturated level (if
    power is held constant at the reduced value).
   However, one point to remember is that Xe-135
    changes following power changes provide
    positive feedback.
   Large reactors may be unstable with respect to
    xenon changes above a certain power level.
     2012 March                                      35
    Solution of Xe-I Kinetics After a Shutdown

 The differential equations for Xe-135/I-135
  kinetics are:
 dI
       I  f   I I                        (15)
  dt
 dX
      I I   X  f   X X   X X        (16)
  dt
 In a transient (non-steady-state) situation,
  these equations can be numerically integrated
  to find the evolution of I and X, starting from
  known initial conditions I0 and X0.
    2012 March                                   36
            Case of an Instantaneous Shutdown
   If the reactor is subjected to an “instantaneous”
    shutdown, we can solve Eqs. (15) and (16) analytically.
   If the flux 0 at t = 0, the terms containing 
    disappear, and the equations simplify to:
     dI
          I I                                (17)
     dt
     dX
          I I   X X                         (18)
     dt
   The solution of Eq. (17) is immediate: I decays
    according to the exponential-decay law:
     I  I 0 e  I t                           (19 )
     2012 March                                         37
          Instantaneous Shutdown – Solving for X
   Eq.(18) for X becomes
    dX
         I I 0 e I t   X X                           (19)
     dt
    The terms in e I t and  X X suggest that the solution for X
    may contain exp onentials of the form e I I and e  X X . So try
    X  AeI t  BeX t                                                   ( 20)
    Substituting the form 10 int o Eq.(19) yields
                                                                       
     AI e I t  B X e  X t  I I 0e I t   X AeI t  Be X t ( 21)
    In order for this to be a n equality for all t , the terms in
    e I t and e   X t must balance out separately.

     2012 March                                                                     38
      Instantaneous Shutdown – Solving for X
 Balancing the e  I t , we get
                                  I I 0
  AI  I I 0   X A  A                                ( 9)
                                 X  I
 The terms in e  X t already balance,  no inf ormation on B.
 To det er min e B, we resort to Eq.(7) and the initial condition :
 X t  0  X 0  A  B
                            I I 0
  B  X0  A  X0                                       (10)
                           X  I
 Therefore we have the full solution :
  I  I 0 e I t                                          (5)
       I I 0   t       I I 0       X t
  X          e   X0 
                    
                    I
                                      e
                                                         (11)
      X  I            X  I     
 [ I leave it to you to verify that these indeed satisfy Eqs.(17)  (18)!]
2012 March                                                                   39
         Instantaneous Shutdown - Numerics
   It will be left as an exercise to evaluate I and
    X, and the corresponding reactivity effect, for
    a time period following a reactor shutdown,
    using the initial conditions of a steady state at
    various powers.




    2012 March                                      40
                      Xenon Oscillations

   Xenon oscillations are an extremely important scenario
    to guard against in reactor design and operation.
   Imagine that power rises in part of the reactor (say one
    half), but the regulating system keeps the total power
    constant (i.e., the assumption is that bulk control is
    active, but spatial control is lost)
   Therefore the power must decrease in the other half of
    the reactor.
   The changes in power in different directions in the two
    halves of the reactor will set off changes in 135Xe
    concentration, but in different directions, in the two
    reactor halves.                                     cont’d


     2012 March                                             41
                 Xenon Oscillations (cont’d)

   The 135Xe concentration will increase in the
    reactor half where the power is decreasing.
   It will decrease in the half where the power is
    increasing.
   These changes will induce positive-feedback
    reactivity changes (why?).
   Thus, the Xe and power changes will be
    amplified (at first) by this positive feedback!
                                          cont’d

    2012 March                                        42
                  Xenon Oscillations (cont’d)

   If not controlled, the effects will reverse after many
    hours (just as we have seen in the xenon transients in the
    earlier slides).
   Xenon oscillations may ensue, with a period
    of ~20-30 h.
   These may be growing oscillations – the amplitude will
    increase!
   [Are xenon oscillations completely hypothetical, or can
    they really happen? What daily perturbation can set off
    such transients?]
                                                      cont’d


     2012 March                                                43
                  Xenon Oscillations (cont’d)

   Large reactors, at high power (where 135Xe
    reactivity is important) are unstable with respect
    to xenon!
   This is exacerbated in cores which are more
    decoupled (as in CANDU).
   It’s the zone controllers which dampen/remove
    these oscillations – that’s one of their big jobs
    (spatial control)!


     2012 March                                     44
             END


2012 March         45

								
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