# r17_candu_loca_calculations

Document Sample

```					   R17: CANDU LOCA Calculations

B. Rouben
UNENE
Course UN 0802
2010 Jan-Mar

2010 January                      1
Neutron Kinetics
Point-Kinetics Equations
d t                 N
        t    i Ci t 
dt                    i 1

dCi t   i
  t   i Ci t 
dt     
  flux, Ci  concentration of precursor group i (i  1to N ),
 i  group partial fraction, i  group time const.
   But point kinetics inadequate for modern safety
analysis, because different regions of reactor do
not behave uniformly.
   Following slide illustrates important sources of
non-uniformity.
Kinetics Methods
 Coolant voiding not uniform; e.g., 2-loop design of
CANDU-6 heat-transport system [next Figure]; or
inner-core region may void faster than outer core
 Pre-accident asymmetry in power distribution
may in some cases accentuate non-uniformity in
power pulse (e.g., in 2-loop design, if initial power
is higher in the voiding loop)
 Shutdown-system spatial coverage not uniform:
rods are finite + conservative assumptions often
used, e.g., 2 shutoff rods (of 32 in Bruce B) not
functioning  core region with missing rods
 Modern analysis must use spatial kinetics
Side-by-Side Heat-Transport-System Loops in
CANDU 6
Kinetics Methods
Spatial Kinetics: Accounting for 3-d Effects:
Time-Dependent Diffusion Equation
 The CERBERUS module in the RFSP code -
solves equation by Improved Quasi-Static
(IQS) method, which factorizes flux into a
space-independent amplitude function and a
shape function:
                 
 r , t   At  r , t 
Kinetics Methods
   Major time dependence is cast into amplitude.
   Separate, coupled equations are derived for amplitude,
shape function, and precursor concentrations.
   Equation for amplitude is similar to point-kinetics
equations, easy to solve.
   Equation for flux shape is similar to time-independent
   Problem is solved in two-tiered scheme of time
intervals: short for amplitude, much longer (~50-100
ms) for flux shape; reduces computational effort.
Kinetics Methods
   SMOKIN – used until recently at OPG
   Modal method: one-group flux expanded in series
of time-independent flux modes :
                        
 r , t    a j t  j r 
j
   Modes are flux “harmonics” of diffusion equation;
represent 3-d “global” perturbations (see next
Figure).
   Problem is re-cast in terms of small number of
equations in the mode amplitudes; the very small
number of unknowns means very quick solution.
   Advantage of SMOKIN is speed; CERBERUS is
more accurate.
Schematic of Harmonic Flux Shapes
Physics Analysis for Large LOCA
   The main quantitative results of the physics
analysis of a large LOCA are:
 Reactivity transient

 Reactor, channel & bundle powers vs. time

 Time-integrated powers, fuel enthalpy.

   The physics analysis requires assembling complex
models and inputs from various sources, and
making decisions about how to treat assumptions
on the values of different parameters.
   Various considerations which need to be made in
the LOCA analysis are described in the following
slides.
LOE and Best-Estimate Analyses
The two most important regimes of assumptions are
LOE and Best-Estimate Plus Uncertainty.
   LOE analysis: Limit of Operating Envelope
   All parameters set at conservative limiting values, e.g.:
   Set coolant purity to lowest value allowed by license
   Ignore the primary (first) trip signal, use backup signal
   Require 3 logic channels to trip instead of 2
   Assume shutoff rods fall in as slowly as allowable
   Set coolant-void reactivity and detector trip setpoints with
allowance in conservative direction.
   LOE analysis deterministic and simplest to carry out;
but piles conservative assumptions together, cuts into
the apparent safety margin.
LOE and Best-Estimate Analyses
   For this reason, LOE analysis in process of being
replaced with “Best Estimate and Analysis of
Uncertainty” (BEAU) analysis
   BEAU places reactor configuration and other
parameters at their best-estimate values
   Deemed more faithful to real system response
   Variations in parameters according to their distribution
relative to best-estimate values are treated by way of
uncertainty analysis about the mean response
   Requires much more effort than LOE, but is gaining
support as a more realistic picture of real safety
margin.
Neutronics and Thermalhydraulics Models
   Coupled neutronics-thermalhydraulics simulations now
the norm; very detailed core and thermalhydraulics
models used
   Different density transients in critical (downstream-of-
break) and non-critical (upstream) passes
   Thermalhydraulics model uses many channel groups in
critical pass:
   high-power vs. low-power
   elevation in core
   orificed vs. non-orificed
   Voiding transients functions of axial position in channel
   Typical analysis now models 5-20 thermalhydraulics
channel groups (see next Figure)
Example of Thermalhydraulic Channel Grouping for
a LLOCA Calculation
Neutronics and Thermalhydraulics Models

Following Figures show:
   Examples of results for coolant void
fraction and coolant density in various
channel groups
   Typical power pulses for individual fuel
bundle and for core halves with broken and
intact loops.
Examples of Coolant Void Fractions Calculated for
Various Channel Groups
Examples of Coolant Densities Calculated for
Various Channel Groups
Examples of Power Pulses Calculated for the
CANDU-6 for an Individual Bundle and Core Halves
Uncertainty in Coolant-Void Reactivity
   Lattice parameters change with time in regions of
voiding, cause insertion of positive reactivity
   Difference between cell-code void reactivity and
measured value is taken into account by
incorporating an “uncertainty allowance” in cell
code
   The allowance may be made by “renormalizing” a
nuclear cross section, or by changing some lattice
parameter (e.g., coolant purity) to artificially change
void reactivity by the postulated amount
Pre-Accident Configuration
Moderator Poison
   Moderator poison (B, Gd) used to suppress excess
reactivity increases void reactivity because flux
redistribution in cell on voiding reduces neutron
absorption by poison
   Must be modelled if present, especially when
concentration high, e.g.:
   in “young” reactor core, to first refuelling (excess
reactivity and B concentration highest at plutonium peak)
   after long shutdown (Xe-135, other sfp decayed)
   in periods of intentional overfuelling
   Configuration after long shutdown from plutonium
peak assumed in many LOE analyses for CANDU 6.
Cont’d
Pre-Accident Configuration
Flux Tilts
   Flux tilts may increase power pulse: e.g., in
CANDU 6, pre-existing side-to-side flux tilt
increases neutronic importance of void when
LOCA is on high-flux side.

   Pressure-Tube Creep
   One effect of reactor aging. Increased pressure-
tube radius results in greater volume of coolant
lost in LOCA. Accounted for in analysis for
aging reactors.
Cont’d
Pre-Accident Configuration
Fuel-String Relocation
   Axial creep  elongation of pressure tube, fuel
string pushed to coolant-outlet end
   In RIH break, fuel string pushed back into the
core (“fuel-string relocation”)
   If axial refuelling scheme is against direction of
coolant flow (e.g., Bruce), irradiation distribution
in channel is such that fuel-string relocation
introduces positive reactivity in addition to the
void reactivity.
   Magnitude of effect depends on gap length,
pressure-tube age.
Fuel-String Relocation Effect in Fuelling Against Flow

Flow 
13   12   11   10    9    8   7   6        5    4      3   2   1

 Fuelling

Flow 
13   12   11   10    9    8   7   6        5    4      3   2   1

 Fuelling

High-                                                                             Low-Burnup
Burnup Fuel                       Flow                                                 Fuel
13   12   11   10    9    8   7       6    5    4      3   2       1

 Fuelling

Reactor Core
Protection-System Modelling
Data Required
   Positions of NOP detectors and ion chambers
   Channelization of detectors and ion chambers
   Delayed-response characteristics of in-core
detectors
   Electronic components (amplifiers, compensators,
etc.) of protection system
   Trip setpoints of detectors:
   High-flux setpoint for in-core detectors
   High log rate for ion chambers
cont’d
Shutdown-System Configuration
Conservative assumptions in LOE analysis
   For SDS-1, two missing rods - selected so
remaining rod configuration is least effective;
missing rods usually adjacent (see next Figure),
leaving core region uncovered
   Use conservative speed of insertion for shutoff
rods - e.g., base “insertion characteristic” on
actual tests of shutoff-rod speed, slowed down by
   For SDS-2, make conservative assumptions re
pressure in injection tanks and poison
concentration; also assume one (of 8) poison tanks
non-functional
Schematic Top View of Reactor Showing
Location of Shutoff-Rod Pair Assumed Missing
Decay Heat
   Power produced in reactor has two components:
   “prompt”, or neutronic, component - appears very
quickly following fission, and
   decay heat, produced in the decay of fission products -
appears with delay (seconds/minutes to weeks/months)
following fission
   In steady state, decay heat is approximately 7% of
the total thermal energy
   In transient, time variation of decay power very
different from that of prompt power: prompt
power increases quickly and is reduced quickly
(within seconds), while decay power decreases
very slowly (see next Figure).
Time Variation of Neutronic Power and Decay Power
Fuel Enthalpy
   Final output of physics analysis for LOCA is the
element fuel enthalpy
   Intra-bundle power distribution required to
calculate element powers.
   Fuel enthalpy evaluated by adding integral of
(prompt + decay) power to initial enthalpy
(corresponding to initial fuel temperature)
   In LOE analysis, may consider “hot” element in
bundle initially at license limit, or initially at
historically maximum power corresponding to
location.
Summary - Core Physics in Safety Analysis
   Physics analysis essential to quantitative understanding
of core behaviour before and following hypothetical
accident.
   Physics not done in isolation from other disciplines.
   Central concern of physics analysis is reactivity and
power distribution and their evolution
   Loss of coolant in CANDU introduces positive
reactivity; LLOCA presents greatest challenge to
CANDU SDS in terms of rate of positive reactivity
insertion.
   Many conservative assumptions are made in LOE
methodology; latter will gradually give way to Best
Estimate And Uncertainty (BEAU) method.
END

2010 January         30

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 3 posted: 4/13/2011 language: Galician pages: 30
How are you planning on using Docstoc?