Xenon Poisoning: Decay & First Order Diff. Eqns

[morbidwork]

whats the concentration when the reactor is not able to be turned back on without waiting for the xenon to decay and how does this relate to the first order differential equations of the decay of iodine and xenon.

 

[Astronuc]

Is one looking for a qualitative or quantitative answer?

Fission products include Te, I and Xe directly, and then Te decays to I which decacy to Xe, and Xe decays to Cs. Xe-135 has a very high absorption cross-section for thermal neutrons. Half-life of I-135 is 6.58 hrs and the half-life of Xe-135 is 9.14 hrs.

When power reactor or any reactor is operating at steady-state, fission products are present in equilibrium concentrations, i.e. the production rate from fission and decay equals the loss due to decay or neutron absorption.

When a power reactor reduces power, the loss of Xe-135 decreases and so it's concentration increases to a greater level before decaying to a new equilibrium concentration.

Can one find an equation for the Xe concentration in ones text. There should be a source (production) term and decay term. The source term would include a term from fission and one from the decay of I-135.

 

[morbidwork]

Im given two equations one for I and Xe and assume that those are the only chain reactions at the time:

dt(I) + lambda_i*I = 0
dt(Xe) - lambda_i*I + lambda_xe*Xe=0

then I have initial Xe and I concentrations and the lambdas refer to the half life of Xe and I.
If the reacter is turned off right away and no new xenon or I are formed at what point does the concentration of xenon reach too high for the reacter to restart without having to wait for the Xe to break down.

 

[Astronuc]

Does one also assume homogeneous reactor with one-group diffusion theory?

 

[morbidwork]

Nevermind, found a acceptable solution.

Assumed that when xenon concentration was 2.5 times greater then it was then during equilibrium, because 2-3 neutrons are "made" every fission reaction that the reactor would not be able to be restarted which gave a rough estimate of half an hour for a reactor to be able to be turned back on before xenon poisonout.

 

[Homer Simpson]

morbidwork, your assumption right above here is super wrong, but the time is about right.

depends on the mk worth of the Xe poison load and the worth of the adjuster rods in-core. If your adjuster rods in core absorb 5 mk reactivity, when removed will add 5 mk positive. So to turn the Xe curve around, you would need to pull Adjusters to get back to critical before the Xe built up to above their worth.

The Xe transient peak value and rate is determined by the amount of I-135 in core prior to trip, which is proportional to the reactor power pre trip.