A PWR has operating characteristics given below for Beginning Of Cycle 1 (BOC) (i.e. no Xe or Sm) where the
reactivity parameters are referenced to Hot Zero Power (HZP). The control rods are in four banks and insert
reactivity linearly with position as they move out, i.e. at “full out” they insert zero reactivity and at “full in” they
insert their full worth. The control rods move in steps, with a 100 step overlap and 228 steps corresponding to full
out. You can assume the banks move out in order A, B, C, D, and insert in reverse order, i.e. D, C, B, A.
Problem Parameters
BOC
Core Excess Reactivity (Not including Fix BP’s)
Fixed Burnable Poison Worth
Moderator Temperature Coefficient
Doppler Only Power Coefficient
Equilibrium Xenon Worth
Equilibrium Samarium Worth
Soluble Boron Coefficient
Control Bank A Worth
Control Bank B Worth
Control Bank C Worth
Control Bank D Worth
15,334
-5600
-11.8
-9.8
-2653
-463
-7
582
973
1171
893
pcm
pcm
pcm/F
pcm/% Power
pcm
pcm
pcm/ppm
pcm
pcm
pcm
pcm
You can assume the moderator temperature as a function of power is given by
Tave =560 + 30×(Rx Pwr) REL
a) Determine the necessary boron concentration for the reactor to be critical at 100% power, BOC with All Rods
Out (ARO), prior to Xe and Sm build up.
b) Xenon reaches its equilibrium value in about 40 hours. At this same time, Samarium has reached 7.5% of its
equilibrium value. What would be the new critical boron concentration at the HFP, ARO condition?
SOLUTION
a) The general reactivity balance is
  0   FBP   B   Xe   Sm   MOD   RX  CR
For the reactor to be critical at the given conditions:
 0
0  15334 pcm
 FBP  5600 pcm
 B   B  CB
 Xe  0 pcm
 Sm  0 pcm
 MOD   MOD TMOD  11.8  30  354 pcm
 RX   RX (%RxPwr )  9.8 100  980 pcm
CR  0
 B  ( 0   FBP   MOD   RX )
 (15334  5600  354  980)
 8400 pcm
CB 
 B 8400

 1200 ppm
7
B
b) The general reactivity balance is
  0   FBP   B   Xe   Sm   MOD   RX  CR
For the reactor to be critical at the given conditions:
 0
0  15334 pcm
 FBP  5600 pcm
 B   B  CB
 Xe  2653 pcm
 Sm  0.075  463  34.72 pcm
 MOD   MOD TMOD  11.8  30  354 pcm
 RX   RX (%RxPwr )  9.8 100  980 pcm
CR  0
 B  ( 0   FBP   Xe   Sm   MOD   RX )
 (15334  5600  2653  34.72  354  980)
 5712.3 pcm
CB 
 B 5712.3

 816 ppm
7
B