Role of reactivity in nuclear reactors

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Lisa!
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Could you please explain about the role of reactivity in reactors?
 

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Lisa! said:
Could you please explain about the role of reactivity in reactors?

Lisa,

Reactivity is the term given to the quantity that tells you how much the
neutron economy is out of balance.

If a reactor is exactly critical - that is, the neutron production is exactly
equal to neutron destruction - then the reactivity is zero.

If the reactivity is positive - then the reactor is supercritical. If the
reactivity is negative - then the reactor is sub-critical.

The Reactivity is defined as the ratio of an adjoint weighted average
of the excess neutron production divided by an adjoint weighted average
of the fission production.

The quantity "reactivity" is one of the terms in the "Point Kinetics"
equations, which is a zero-dimensional set of equations that describe the
transient behavior of a reactor.

Look up "point kinetics equations" in a reactor physics text.

Dr. Gregory Greenman
Physicist
 
Morbius said:
Lisa,

Reactivity is the term given to the quantity that tells you how much the
neutron economy is out of balance.

If a reactor is exactly critical - that is, the neutron production is exactly
equal to neutron destruction - then the reactivity is zero.

If the reactivity is positive - then the reactor is supercritical. If the
reactivity is negative - then the reactor is sub-critical.

The Reactivity is defined as the ratio of an adjoint weighted average
of the excess neutron production divided by an adjoint weighted average
of the fission production.

The quantity "reactivity" is one of the terms in the "Point Kinetics"
equations, which is a zero-dimensional set of equations that describe the
transient behavior of a reactor.

Look up "point kinetics equations" in a reactor physics text.

Dr. Gregory Greenman
Physicist
Thanks a million you Dr. Greenman.
You know I've asked some of nuclear engineers my question and well I didn't get a good response.And whenever I ask them a question about reactor physics,they just say that refers to reactivity.sounds kind of catch-22.I can't understand what's reactivity is if I don't know all about reactor physics and I can't understand reactor physics if I don't know what's reactivity.Anyway I try to find a suitable article and I may understand it coz you made it more understandable.
 
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Thanks for posting that, Astronuc. I wish the book I had used provided some examples, I was lost most of the time for problems. I guess the author wanted students to understand the concept and not "plug and chug" problems with an equation.
 
theCandyman said:
Thanks for posting that, Astronuc. I wish the book I had used provided some examples, I was lost most of the time for problems. I guess the author wanted students to understand the concept and not "plug and chug" problems with an equation.

Candyman,

I did a google search and found a nice derivation of the point kinetics
equations:

http://canteach.candu.org/library/20043611.pdf

and then discovered that the author was Jean Koclas, who was one of my
contemporaries when I was a graduate student at M.I.T.

Dr. Gregory Greenman
Physicist
 
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Lisa! said:
.Anyway I try to find a suitable article and I may understand it coz you made it more understandable.

Lisa,

See the online derivation of the point kinetics equations that Jean Koclas
wrote - referenced in my post above in response to Candyman.

The definition of reactivity is Equation 78 on page 111 of the paper -
page 5 of the PDF file.

The basic physics can be seen in Equation 79, which is an equation for the
amplitude "T" of the neutron population.

The rate of change of the amplitude is given by how "unbalanced" the
neutron population equation is, plus the contribution due to delayed
neutrons.

The first term on the right side of Eq. 79 is the reactivity minus the
delayed neutron fraction, quantity; divided by the mean neutron lifetime.

You subtract off the delayed neutron fraction "beta" because the result
gives you what the prompt neutrons alone are doing. They can "ramp-up"
in magnitude with a time constant "lambda".


Dr. Gregory Greenman
Physicist
 
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Candyman, what text have you been using?

I used J. R. Lamarsh, Nuclear Reactor Theory, as an undergrad.

Graduates used Duderstadt and Hamilton, Nuclear Reactor Analysis.

Try also - http://engphys.mcmaster.ca/~garlandw/ep4d3/text/10-kinetics-r1.pdf

from - http://engphys.mcmaster.ca/~garlandw/ep4d3/ep4d3home.htm
 
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I was comparing it to my introduction class text, Raymond L. Murray's Nuclear Energy which I probably should not have because it really is not the same subject. I am going to take fundamentals in the fall, using the same book as you used, third edition. I actually found it in the library, it is a bit difficult for me to decipher, but I figure if I keep breaking it down it should make sense eventually.

Morbius, those equations look really daunting, mostly because I do not recognize many of the symbols . What does the last statement in that paper mean? ("Because of all this, the analytic solution of the point kinetics equations constitutes a method which is too costly and difficult to be considered practical.") Are these equations not used or is this referring to approximations?
 
I think Koclas means that we use digital computation (computer models) rather than analytical models.

The lastest technology is 3D-spatial kinetics models used in the core simulators like Studsvik's SIMULATE-3K or EPRI's ARROTA codes. The fuel vendors like BNFL, GE and AREVA have their own proprietary codes.

IIRC, Murray is an introductory text in nuclear engineering, so there will be limited information on reactivity. Koclas's notes go deeper into reactor (neutron) kinetics which involves delayed neutrons, i.e. neutrons originating not from the fission process, but from some of radionuclides produced by fission. This slight delay allows for the control of a nuclear reactor.
 
Astronuc said:
I think Koclas means that we use digital computation (computer models) rather than analytical models.

The lastest technology is 3D-spatial kinetics models used in the core simulators like Studsvik's SIMULATE-3K ...

Astronuc,

That brings another one of my contemporaries at M.I.T. into the picture;
Kord Smith. Kord works for Studsvik Scandpower - and has been the
"developer in chief" for Studsvik's reactor analysis codes like SIMULATE-3K.

Jean Koclas, Kord Smith, and I were all students of the late Prof. A. F. Henry,
of the M.I.T. Nuclear Engineering Department. Our research was in the
field of what are called "nodal methods" - coarse mesh methods.

For many years, transient reactor analysis was done using the point
kinetics equations - which are a zero dimensional approximation to
the time-dependent behavior of a reactor. If spatial effects are not
important, and the spatial shape of the neutron distribution in the
reactor is fairly constant - then the point kinetics equations are a
good approximation.

Astronuc is correct that even a very simple model like the point kinetics
equations are too complex to solve analytically; one solves them
numerically with the use of computers.

One could also solve the time and spatial-dependent neutron transport
and diffusion equations numerically also. However, the short mean-free
paths of low energy thermal neutrons in a reactor [ about 1/4 of a
centimeter ] means that if conventional finite difference or finite element
techniques are used - one needs an awful lot of mesh cells.

The core of a commercial reactor is a 12 foot "square cylinder" - that
is it is a cylinder 12 feet in diameter and 12 feet high - or 365.76 cm in
each dimension. That is 1463 mean free paths in each direction. So if
you want to model the core with finite difference or finite elements -
you are looking at about a BILLION points.

The mean neutron lifetime in a thermal reactor is about 0.1 millisecond
or 0.0001 seconds. If a transient model uses finite difference in time -
then you need 10,000 time steps per second of time modeled; each of
these time steps requires the computation of a BILLION quantities per
energy group.

A reactor transient calculation could really choke even the most
powerful computers of today; let alone those of about 30 years ago.

Therefore, Prof. Henry and his students worked on methods that could
make these types of problems more tractible for computation. Some
similar techniques were explored at the University of Illinois, and the
University of Michigan.

Studsvik's SIMULATE embodies a lot of these advanced concepts - and
that's why it is one of the most used reactor analysis codes. Graduate
students in nuclear engineering are often taught how to use SIMULATE.

Dr. Gregory Greenman
Physicist
 
That brings another one of my contemporaries at M.I.T. into the picture;
Kord Smith. Kord works for Studsvik Scandpower - and has been the
"developer in chief" for Studsvik's reactor analysis codes like SIMULATE-3K.
The nuclear industry is small world. I know of Kord Smith, but I have not had the pleasure of meeting him. IIRC, he is married to a friend's cousin. My friend also trained with me in Nuclear Engineering.

I have had several interactions with Studsvik since I have had the need to generate very detailed fuel rod (pin) power histories which involved the CASMO/SIMULATE package.

BTW Greg, Fred said - Hi! Too bad you couldn't make it to the conference.
 
Astronuc said:
BTW Greg, Fred said - Hi! Too bad you couldn't make it to the conference.

Astronuc,

You mean he sends his "Best"? :smile:

Thank you. I trust you had a nice conference.

Dr. Gregory Greenman
Physicist
 
theCandyman said:
Morbius, those equations look really daunting, mostly because I do not recognize many of the symbols .

Candyman,

The quantities in "[ ]" are G X G matrices - where "G" is the number of
energy groups. It is convenient to represent the energy dependece of the
equations in this manner. Energy is divided up into a number of groups -
each of which has it's own equation, which is coupled to the others. Matrix
notation is a convenient way to write those equations.

The "< >" is Dirac-notation for an integral. When you see those "< >",
you should integrate over whatever quantities required. It may be
necessary to use the context of the equation to know what is being integrated
over.

Dr. Gregory Greenman
Physicist