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					 Xenon-Induced Spatial Power
Oscillations in the 400MW PBMR




  The Pebble Bed Modular
           Reactor Project
  Gerhard Strydom                HTR2006
          Presentation Overview

Introduction
Spatial Xenon Dynamics
PBMR Xenon Stability Study (General)
Overview of the TINTE code
Inherent Stability Results
100-50-100 Load Follow Results
Conclusions and Future Work
                 Introduction

     Certain fission products poisons (Xe-135 & Sm-149) have
     extremely large thermal neutron absorption cross sections
     (σa>2E06 b for Xe-135).
     Effect compounded by non-trivial fission yields.
     Inclusion of Xe-I spatial dynamics crucial for space & time
     dependent simulations of thermal cores.
     Topics of “Xenon” interest in thermal core designs are:
- Global Xenon override during power load follows.
- Measure and control of spatial power oscillations, which could
  be caused by local variations in the Xenon concentration.
Xenon XS behaviour
Xenon-135 Birth and Death
Xenon-135 Birth and Death -
Simplified
              TINTE Xenon Stability Study of
              400MW PBMR (1)
    PBMR design is tall (active core height ~10 meters) and
    annular. This implies possible Xenon and local Power
    instabilities in the axial dimension.
    Radial Xenon oscillations are not expected, due to small
    annular core radius (85 cm), which is close to neutron
    mean free path length in graphite (~60 cm).
    Azimuthal oscillations are also limited by coupled CR
    bank movements and annular gas flow in core.
    Purpose of TINTE Xenon study:
(1) to determine spatial variations in Xenon, global and local
    power levels during various possible transients.
(2) To determine degree of Xenon stability of current design.
           TINTE Xenon Stability Study of
           400MW PBMR (2)
First section determined the inherent stability of the core,
by analysing „free“ oscillations. („Free“ implies without the
distorting effects of any other parameters changing while
the oscillation is occuring).
Second section analysed realistic PBMR load follow
transients, e.g. 100-50-100 for various durations, and
power levels. (Only selected results presented here).
Stability parameters were calculated for all cases using a
numerical fitting technique on the spatial data.
More than 20 transient cases were included in the study,
with 21 spatial points tracked in the core, at 30 time
steps, for each case. This resulted in ~1000 Excel files,
and ~ 7 GB dataset.
           Presentation Overview

Introduction
Spatial Xenon Dynamics
PBMR Xenon Stability Study (General)

Overview of the TINTE code
Inherent Stability Results
100-50-100 Load Follow Results
Conclusions and Future Work
          Overview of the TINTE code:
          Neutronics
German (FZJ) transient code developed for HTR
applications in mid eighties.
2-D r-z, time-dependent neutron diffusion with finite
difference solver.
1-D Leakage iteration method- transverse leakage
coupling of radial and axial fluxes and currents.
2 Neutron energy groups (3.07 eV).
6 Groups of delayed neutrons.
Local and non-local heat deposition.
Spatial Iodine-Xenon dynamics.
          Overview of the TINTE code:
          Temperatures

2-D r-z, heat transport (diffusion approach).
Gas and solid temperatures calculated seperately in sub-
modules from neutronic power.
FE Surface temperatures from the effective heat
conductivity in pebble-beds. Fuel sphere temperature
profile also calculated in multiple fuel batches.
Fuel element burn-up history supplied by VSOP.
           Presentation Overview

Introduction
Spatial Xenon Dynamics
PBMR Xenon Stability Study (General)
Overview of the TINTE code

Inherent Stability Results
100-50-100 Load Follow Results
Conclusions and Future Work
             PBMR Inherent Xenon Stability
             Results
4 Cases were calculated to determine the inherent stability of
the PBMR core. This was done by inserting the Control Rods 3
meters deeper for 4 hours (for various power levels), and then
returning them to their nominal locations for the specific power
level. No other changes were made for the next 68 hours.


     Case # and           Steady-state CR        Inserted CR
      description            depth (cm)            depth (cm)

1: 100% power            200                   500

2: 80% power             230                   530
3: 50% power             280                   580
4: 20% power             380                   680
                                      CR variations: Cases 1-4

                  7.00

                  6.60
                                          Case 4
                  6.20
                             Case 3
                  5.80
                             Case 2
                  5.40

                  5.00
CR location (m)




                             Case 1
                  4.60

                  4.20

                  3.80

                  3.40

                  3.00

                  2.60

                  2.20

                  1.80
                         0   2        4     6      8   10      12        14   16   18   20   22   24
                                                            Time (hrs)
                                                            CR and Xenon variations: Cases 1-4

                                             2.50

                                             2.40

                                             2.30
                                                                                                      Case 1
Core average Xenon absorption (% of total)




                                             2.20

                                             2.10

                                             2.00
                                                                                                      Case 2
                                             1.90

                                             1.80
                                                                                                      Case 3
                                             1.70

                                             1.60

                                             1.50

                                             1.40
                                                                                                      Case 4
                                             1.30

                                             1.20

                                             1.10

                                             1.00
                                                    0   4   8   12   16   20      24        28   32        36   40   44   48
                                                                               Time (hrs)
                                                                   Normalized power density: Case 1

                                  3.5




                                   3                    Bottom of core – power
                                                           density increases
Normalised Heat Sources [W/cm3]




                                  2.5




                                   2

                                                                    Free oscillations start

                                  1.5

                                                                                                                                 Free oscillations damped out
                                   1




                                  0.5




                                   0
                                        0   4   8          12      16        20        24      28          32     36        40     44       48    52      56      60        64         68   72

                                                                                                                Time [h]

                                                    ( 105; 100 )        ( 105; 250 )        ( 105; 400 )         ( 105; 550 )      ( 105; 700 )    ( 105; 850 )        ( 105; 1000 )
                                                                Normalized power density detail:
                                                                Case 1
                                  1.2



                                                                           Top of core
                                  1.1
Normalised Heat Sources [W/cm3]




                                   1




                                  0.9




                                  0.8



                                                                                 Bottom of core
                                  0.7
                                        8   12          16        20              24           28       32            36            40      44           48            52     56

                                                                                                      Time [h]

                                                 ( 105; 100 )     ( 105; 250 )         ( 105; 400 )    ( 105; 550 )        ( 105; 700 )   ( 105; 850 )        ( 105; 1000 )
                                                                         Case 1 Axial fast flux difference cuts at
                                                                         r=105 cm
                                       25


                                       20


                                       15


                                       10
                       12*n/(s.cm2))




                                        5
Fast flux difference(1E




                                        0


                                        -5


                                       -10


                                       -15


                                       -20
                                             50   100   150      200      250   300       350    400     450   500      550      600     650    700   750    800     850   900   950      1000
                                                                                                                    z (cm)

                                              10 hrs    12 hrs         14 hrs    16 hrs         18 hrs     20 hrs       22 hrs         24 hrs    26 hrs     28 hrs     30 hrs    32 hrs
                                              34 hrs    36 hrs         40 hrs    44 hrs         48 hrs     52 hrs       56 hrs         60 hrs    65 hrs     70 hrs
                                             Case 1 Normalized Radial fast flux

                              2.80
                              2.60
                              2.40
                              2.20
                                                 No variation in time in radial
                              2.00
                                                    fast flux values
N o rm a lised F a st flu x




                              1.80
                              1.60
                              1.40
                              1.20
                              1.00
                              0.80
                              0.60
                              0.40
                              0.20
                              0.00
                                     0   4   8   12          16      20         24       28         32       36     40   44   48
                                                                            Time (hrs)

                                                      r=105, z=250   r=180, z=250    r=105, z=800    r=180, z=800
                                                                   Case 1 Power density difference radial cuts

                                   0.1


                                     0
Heat Sources Difference [W/cm^3]




                                   -0.1


                                   -0.2


                                   -0.3


                                   -0.4


                                   -0.5


                                   -0.6


                                   -0.7
                                          100          110          120         130          140            150          160         170         180

                                                                                                  R [cm]

                                           0h    12h         13h    14h   15h         16h   17h       18h    19h   20h         21h   22h   23h         24h
                                           25h   26h         27h    28h   29h         30h   31h       32h    33h   34h         35h   36h   37h         38h
                                           39h   40h         41h    42h   43h         44h   45h       46h    47h   48h         49h   50h   51h         52h
                                           53h   54h         55h    56h   57h         58h   59h       60h    61h   62h         63h   64h   65h         66h
                                           67h   68h         69h    70h   71h         72h
            PBMR Inherent Xenon Stability Results

  The least-squares fit is applied to the general damped
  oscillation equation

        N Xe (t ) = N Xe (t 0 ) e b t sin (C t + D) + E
where

b = damping constant of the system, or a measure of the
  energy dissipated in one cycle of free oscillation.

Visual and statistical comparisons are made on the quality
  of the fits.
                                                                            Case 1 Normalized power density: LS Fits

                                  1.16
                                  1.14
                                  1.12
                                   1.1
                                  1.08
                                  1.06
Normalised Heat Sources [W/cm3]




                                  1.04
                                  1.02
                                     1
                                  0.98
                                  0.96
                                  0.94
                                  0.92
                                   0.9
                                  0.88
                                  0.86
                                  0.84
                                  0.82
                                   0.8
                                  0.78
                                  0.76
                                  0.74
                                  0.72
                                   0.7
                                         8                     12           16            20                    24             28          32                    36               40          44                   48

                                                                                                                          Time [h]

                                             ( 105; 100 )           Fit to ( 105; 100 )   ( 105; 250 )               Fit to ( 105; 250 )   ( 105; 400 )               Fit to ( 105; 400 )   ( 105; 550 )
                                             Fit to ( 105; 550 )    ( 105; 700 )          Fit to ( 105; 700 )        ( 105; 850 )          Fit to ( 105; 850 )        ( 105; 1000 )         Fit to ( 105; 1000 )
                                                       Case 1 Normalized Xenon concentration:
                                                       LS Fits
                                 2.1
                                  2
                                 1.9
                                 1.8
Normalised Xenon Concentration




                                 1.7
                                 1.6
                                 1.5
                                 1.4
                                 1.3
                                 1.2
                                 1.1
                                  1
                                 0.9
                                 0.8
                                 0.7
                                 0.6
                                       0   4       8                 12      16                 20      24             28     32              36     40              44   48
                                                                                                     Time (h)
                                               ( 105; 100 )               Fit to ( 105; 100 )        ( 105; 250 )           Fit to ( 105; 250 )    ( 105; 400 )
                                               Fit to ( 105; 400 )        ( 105; 550 )               Fit to ( 105; 550 )    ( 105; 700 )           Fit to ( 105; 700 )
                                               ( 105; 850 )               Fit to ( 105; 850 )        ( 105; 1000 )          Fit to ( 105; 1000 )
                PBMR Inherent Xenon Stability:
                Power and Xenon Damping Results

                     Power density          Xenon
    Spatial
   Coordinate
                      b          T      b            T

( 105; 250 )        -0.140     48.1   -0.154        44.5

( 105; 400 )        -0.121     53.7   -0.146        55.0

( 105; 550 )        -0.159     39.6   -0.173        42.9

( 105; 700 )        -0.139     47.3   -0.150        46.2

( 105;1000)         -0.126     52.7   -0.119        56.1
             PBMR 100-50-100% Load Follow
             Results

Several Load Follow (LF) Cases were calculated, with and
without Control Rod movements. A sample 100-50-100% LF
case is included here.
100-50-100% LF was done by reducing the power, mass flow
rate and pressures to 50% over 5 minutes, and then remaining
there for 6 hours.
After 6 hours, the power and mass flow rate was returned to
nominal values.
The Control Rods were moved over the duration of the 72 hour
transient, to keep the core critical.
                                                                CR and Xenon variations: 100-50-
                                                                100% LF with and without CR’s
                                             2.85                                                                                             2.8

                                                                                                                                              2.6
                                             2.75
                                                                                                                                              2.4
Core average Xenon absorption (% of total)




                                             2.65                                                                                             2.2

                                             2.55                                                                                             2.0

                                                                                                                                              1.8




                                                                                                                                                    CR Location (m)
                                             2.45
                                                                                                                                              1.6

                                             2.35                                                                                             1.4

                                                                                                                                              1.2
                                             2.25
                                                                                                                                              1.0
                                             2.15                                                                                             0.8

                                             2.05                                                                                             0.6

                                                                                                                                              0.4
                                             1.95
                                                                                                                                              0.2

                                             1.85                                                                                             0.0
                                                    0   4   8     12   16      20       24       28       32   36         40   44   48   52
                                                                                        Time (hrs)

                                                                       Xenon - Case 5        Xenon - Case 6    CR depth
                                                                               Normalized power density: 100-50-
                                                                               100% LF with CR movement
                                                     1.80
                                                                                  Power returned to 100%
Pow er density (normalised to steady-state values)




                                                     1.60


                                                     1.40                                              Spatial oscillation at
                                                                                                          constant power starts
                                                     1.20


                                                     1.00


                                                     0.80


                                                     0.60


                                                     0.40


                                                     0.20
                                                            0   4          8       12        16      20         24          28     32            36       40        44          48     52
                                                                                                                 Time (hrs)

                                                                    P(105/ 100)    P(105/ 200)    P(105/ 300)        P(105/ 400)   P(105/ 500)        P(105/ 600)        P(105/ 700)
                                                                    P(105/ 800)    P(105/ 850)    P(105/ 900)        P(105/1000)
                                                                                Axial cuts of Normalized power density:
                                                                                100-50-100% LF with CR movement
                                                       1.40
P ow er density (norm alised to steady-state values)




                                                       1.30


                                                       1.20


                                                       1.10


                                                       1.00


                                                       0.90


                                                                                             Axial nodal point
                                                       0.80


                                                       0.70


                                                       0.60
                                                           100       200        300         400        500         600          700        800        900        1000     1100
                                                                                                                  z (cm)

                                                                 0   10    14     18   22         26   30    34      38    42         46   50    54    58   62      66   72
                                                          Fuel temperature: 100-50-100% LF with CR
                                                          movement
                             1350

                             1300

                             1250

                             1200
Fuel tem perature (Kelvin)




                             1150

                             1100

                             1050

                             1000

                             950
                                                                    Spatial oscillation at
                             900
                                                                       constant power starts
                             850

                             800
                                    0   4             8        12       16        20       24         28            32       36        40        44       48        52
                                                                                             Time (hrs)

                                        P(105/ 100)       P(105/ 200)   P(105/ 300)    P(105/ 400)        P(105/ 500)    P(105/ 600)   P(105/ 700)    P(105/ 800)
                                        P(105/ 900)       P(105/1000)
              PBMR 100-50-100% LF Xenon Stability:
              Power and Xenon Damping Results

Spatial          Without CR         With CR
Coordinate       b         T        b         T
(105; 100)       -0.132    50.0     -0.116    47.6
(105; 250        -0.132    56.5     -0.108    47.0
(105; 400)       -0.129    66.6     -0.071    57.1
(105; 550)       -0.136    39.3     -0.121    49.1
(105; 700)       -0.135    53.6     -0.110    46.7
(105; 850)       -0.131    57.7     -0.105    46.2
(105; 1000)      -0.129    59.7     -0.102    46.1
              Conclusions and Future Work
PBMR Xenon stability study have shown well-damped axial
oscillations for all cases analysed. No radial oscillations were
observed.
Stability of load-follow cases (limited set presented here)
similar to the inherent core stability, although the continuous
movement of Control Rods did decrease the damping of
power/Xenon oscillations slightly.
PBMR design does not need an active Xenon oscillation
control system, but an accurate flux mapping capability would
still be very useful to confirm stability under various
operational conditions.
Main outstanding issue: PBMR azimuthal power/Xenon
oscillations (3D CITATION).
Future work (thesis) will investigate hypothetical PBMR
designs, to obtain transition point to instability. Examples are
a 20 meters tall 2000MW core; a cylindrical core with radius 4
meters; and a 400MW core with a core delta of 50C.
  END
The Pebble Bed Modular
    Reactor Project

				
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