# A reactor theory question

Hi everybody,I can't understand how a reactor core is sized to be critical.
I'm studing the reactor theory and I've understood how make critical a reactor with simple shapes (spherical,cylindrical,etc.) equating the material and the geometrical buckling.
But it's possible, in a simple way, to understand how a real reactor with a definite amount of nuclear fuel is sized critical?For example, is the single fuel rod critical?Or the total amount of the rods make the core critical?

i'm sorry to be so vague, but I need to make an approximate design calculation of a PWR's core size.

Thank you.

QuantumPion
Gold Member
Hi everybody,I can't understand how a reactor core is sized to be critical.
I'm studing the reactor theory and I've understood how make critical a reactor with simple shapes (spherical,cylindrical,etc.) equating the material and the geometrical buckling.
But it's possible, in a simple way, to understand how a real reactor with a definite amount of nuclear fuel is sized critical?For example, is the single fuel rod critical?Or the total amount of the rods make the core critical?

i'm sorry to be so vague, but I need to make an approximate design calculation of a PWR's core size.

Thank you.
A real reactor is sized to be much greater than critical. This is because excess reactivity is needed to remain critical as fuel is consumed and fission products produced. The excess reactivity is controlled using soluble boron (for a PWR). The k-effective of a freshly refueled PWR with no boron or control rods can be over 1.2.

A single rod cannot be critical, its k-effective would be < 0.3. A single fresh assembly with no burnable poisons, submerged in unborated cold water, might be just critical, depending on its enrichment.

The physical size a power reactor is designed based on thermohydraulic concerns moreso than nuclear. Basically, the maximum power a fuel rod can produce is limited by material properties. Thus to get a desired amount of total power, the reactor has to be a certain size to produce that much power with the allowed power density. If power density were not as limited (e.g. liquid metal cooled reactor), it could be much smaller and produce the same amount of power.

Astronuc
Staff Emeritus
As far as I know, individual fuel assemblies do not have sufficient geometry to be critical. In some shops, fuel assemblies are 'washed' for cleaning before going to packaging.

Reactors are size for power, or rather power density.

Individual assemblies will have burnable absorber rods containing B-10 or gadolinium isotopes in order to reduce the reactivity of fresh fuel.

PWRs use soluble boron in the coolant to control reactivity, and as the cycle progresses the concentration of soluble boron is reduced, almost to nil by EOC. For most PWRs, control rods are fully withdrawn during operation, with the tips sitting just above the core (active fuel zone). Some PWRs use grey rods to allow for rapid power decension or rapin ascension, or for axial or radial power shaping, but this practice is mostly used in Europe, primarily France, and not in the US.

BWRs use control rods (blades) in the core during operation in order to control reactivity, and they can use flow to control voiding (moderator density) in the upper part of the core to also control reactivity. Groups of blades are exchanged or swapped periodically during the cycle.

jim hardy
Gold Member
Dearly Missed
this might help a little, i dont know.

http://www.if.uidaho.edu/~gunner/ME443-543/LectureNotes/ReactorPhysics.pdf

i think but dont know for sure the approach for working it by sliderule is to use "macroscopic" cross sections which account for the real number of atoms per unit volume . One gets the actual amount of fuel, moderator and poison (reactor structural materials) per unit volume and figures each term of the four or six factor formula accordingly. That gets one in the ball park. I'm sure its done nowadays by sophhisticated computer programs but a lot is to be learned by doing it same way as guys in the late 40's must've.

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As far as I know, individual fuel assemblies do not have sufficient geometry to be critical. In some shops, fuel assemblies are 'washed' for cleaning before going to packaging.

Reactors are size for power, or rather power density.

Individual assemblies will have burnable absorber rods containing B-10 or gadolinium isotopes in order to reduce the reactivity of fresh fuel.

PWRs use soluble boron in the coolant to control reactivity, and as the cycle progresses the concentration of soluble boron is reduced, almost to nil by EOC. For most PWRs, control rods are fully withdrawn during operation, with the tips sitting just above the core (active fuel zone). Some PWRs use grey rods to allow for rapid power decension or rapin ascension, or for axial or radial power shaping, but this practice is mostly used in Europe, primarily France, and not in the US.

BWRs use control rods (blades) in the core during operation in order to control reactivity, and they can use flow to control voiding (moderator density) in the upper part of the core to also control reactivity. Groups of blades are exchanged or swapped periodically during the cycle.
Actually, some USA reactors use grey rods for axial/radial power shaping. (B&W) Or at least the one I'm working at does.

Astronuc
Staff Emeritus
Actually, some USA reactors use grey rods for axial/radial power shaping. (B&W) Or at least the one I'm working at does.
I should have pointed out the exception for APSRs. I was thinking more along the lines of load follow and frequency control, however.

A single PWR rod is not critical, nor is a single assembly under any conditions (immersed in water). The number of assemblies is takes to make a critical configuration is very dependent on enrichment. Different corporations use different tools to fuel cycle design - most of these tools would answer much more than you are asking. Simple k-eff calculations can be done with SCALE/KENO of ORNL or MCNP of LANL if you have access to such things. Your back of the envelope buckling calculations will give pretty good rough sizes if you call the core a homogeneous cylinder and don't forget to put boron in the water.

BWRs use control rods (blades) in the core during operation in order to control reactivity [skip]

Groups of blades are exchanged or swapped periodically during the cycle.
I always wondered how exactly it is done, considering that in BWR, blades are driven from the bottom.

It's not like a worker can jump into stopped reactor, detach old blade and attach a new one! Even with fuel unloaded, reactor walls should be very "hot" from activation.

Is there a special tool for this, or what?

Astronuc
Staff Emeritus
I always wondered how exactly it is done, considering that in BWR, blades are driven from the bottom.

It's not like a worker can jump into stopped reactor, detach old blade and attach a new one! Even with fuel unloaded, reactor walls should be very "hot" from activation.

Is there a special tool for this, or what?
During refueling, the reactor core is under water. The surface of the water matches the SFP, since all movement of fuel in the core and from core to SFP is done with the fuel underwater.

If a spent control blade is removed it is also done underwater. The 4 fuel assemblies are removed, the spent control blade is unlatched from the control rod drive, then it is removed to the spent fuel pool. A new blade is installed, and a tool is placed to hold the control blade in place until at least three assemblies are returned to the cell location.

Some plants may do a full core off-load, while others remove discharge and do an in-core shuffle, then load the fresh fuel.

Note that control blade has handle or bails on top, just as the fuel assemblies do. The spent fuel machine can handle CRBs as well as fuel assemblies.

I always wondered how exactly it is done, considering that in BWR, blades are driven from the bottom.

It's not like a worker can jump into stopped reactor, detach old blade and attach a new one! Even with fuel unloaded, reactor walls should be very "hot" from activation.

Is there a special tool for this, or what?
I think we've seen blades in the spent fuel pool so the assumption I've had is that the same sort of processes and equipment that can load and unload fuel from the reactor can also take control blades out and move them to the pool.

edit - oops I was too slow with this post!