Clarification of Question by
f_landry_9-ga
on
25 Apr 2005 06:36 PDT
To: bozo99-ga, who replied on 22 Apr 2005 16:55 PDT
and hedgie-ga, who replied on 25 Apr 2005 00:10 PDT
First of all, thank you both for your thoughtful replies.
> This question is remarkably complicated - I'm tempted to suggest that
> beside banning homework questions GA is not suitable for handling
> large parts of a PhD.
This may be because I have expressed what I am trying to get at
rather poorly. I asked this question here because I knew that
the people I was asking were likely to be very knowledgeable (PhD etc.),
and would indicate what I needed to clarify, etc. I was hoping
the overall intent of the 'model' would come through -- what sort
of simplifications where indicated and which were to be avoided.
My question is largely conceptual, and I am hoping that it can
be seen as such.
> ... when you fission the heavy elements of reactor fuel and produce a
> bunch of elements about half the mass these fission products lie off
> the stable curve and are decidedly radioactive. Hence spent fuel is
> radioactive and a chain of decays (of different types) takes place.
Yes, this is right. As an alternative, let me restate the question
in the terms of the isotope chart. Each nuclear reaction can be thought
of as a mapping on the chart of isotopes, which takes certain isotopes and
transforms them into one or more other isotopes. On this planet, some of
these reactions occur frequently in nature without human assistance and
others are likely to occur only if specific conditions are deliberately
setup. Of those reactions in the latter category, only a specific subset
are used as a part of commercial and/or military application.
Thinking about this as if using graph theory (vertices and arcs) one
can think of the total set of mappings (reactions) from isotopes to
isotopes can (for the purposes of this question) be classified into
three parts as follows:
- 1; those reactions which occur naturally under normal
conditions (in the ground, etc),
- 2; those reactions which require special conditions to occur, and
as a proper subset of this,
- 3; those reactions which require special conditions and which are
currently in active commercial or military usage. Call this "subset 3".
As an idealized scenario, if we were to assume that in some widely
separated location, we had (at T=0) exactly 1kg of each of the
isotopes in the entire table of isotopes. At the moment of its
inception (T=0), call the total radioactivity of the aggregate
sample, in curies, K1. Naturally, some of these samples would
decay into other isotopes (some of which are very stable, and
others much less so), and so the total degree of aggregate
radioactivity would change with increasing time. In effect,
the relative pattern of the proportions of the isotopes would
change.
Over the very long term, I would expect that the total aggregate
degree of radioactivity would decrease. Personally, I do not
know that it would strictly decrease over the short terms as well
(is the degree of radioactivity always monotonically decreasing?),
for perhaps in the short term some less radioactive isotopes would
decay into more radioactive children. In either case, the total
aggregate radioactivity changes with time, and this value could
presumably be graphed for the sample as given, and that it would
have some definite shape. Call this "graph G1".
For the comparison of interest, assume instead that at T plus
epsilon, that all of the 'subset 3' reactions were implemented
(again, idealize this as occurring instantly, in a single moment).
In other words, some of the 1kg isotopes would be specifically
and preemptively transformed into other isotopes (in varying
amounts) in reactions of specific importance to commercial or
military application. Overall, this "moment of human activity"
would change the relative proportions of the isotopes in the
total aggregate in a pattern different than would have occurred
in the undisturbed sample. Given that different pattern of
isotope proportion, the time evolution of the total aggregate
radioactivity (in curies) would also be different. Call this
"graph G2".
A large part of What I am trying to understand is what the difference
between graph G1 and G2 looks like. In other words, what sort of
effects do the 'subset 3' reactions have on the total aggregate
degree of radioactivity in the short term and the long term?
I am aware, however, that even this idealized model has some
significant conceptual limitations, which I was hoping to avoid.
For example, assuming that each isotope type is widely separated
is an attempt to omit the effects of radioactivity of one sample
'catalyzing' the transformations of other samples. However, I
would try to also avoid 'self catalyzing' effects due to the
amount of material involved. Perhaps the model could be made
simpler by assuming that we start with an arbitrarily small
but equivalent amount of each isotope at T=0?
Also, I am aware that, on this planet, not all isotopes occur
equally; some are more common than others. Thus, assuming an
average homogeneous composition similar to this planet would
result in a very different initial configuration pattern of
relative masses in our scenario. This would probably have some
dramatic effect on the shape of G1. Call it "G1 prime".
I also know that the total list of 'subset 3' reactions is varied
and complex. I am not looking for a complete enumeration of this
list. What I am hoping is that at least the most significant ones
(in terms of reaction mass) in commercial or military use are at
least, in summary form, accounted for in both fission and fusion
processes.
Furthermore, given that the available initial relative
concentrations of the various isotopes was different, the
pattern of the concentrations of the isotopes resulting from
the instantaneously completed 'subset 3' reactions would
also be different, and thus this evolution would result in
a different graph for G2. Call it "G2 prime".
In terms of my original question, I am even more interested
in the difference between the shapes of G1 prime vs. G2 prime.
However, I acknowledge that the best I may be able to hope
for is to get some deeper insight into the reality of these
questions; hence this post.
> ... the figures you are looking for depend on (at least)
> - original fuel composition
> - other materials present (how much nickel in that steel ?)
> - time, power, burn up
> - spectrum
> - geometry
> - elapsed time after shutdown.
These are the sorts of details I was specifically hoping to avoid
and/or simplify away. I acknowledge that any real or practical
consideration might have to include these factors, but I am hoping
to keep this on a fairly conceptual level by using (admittedly
unrealistic) idealized models.
> As a result I think only a _very_ rough estimate would be
> appropriate for your question.
Agreed.
> What's more, the uniform dispersal of waste is unrealistic.
I know this; I was attempting to indicate the kinds of drastic
conceptual simplifications I would allow in thinking about this.
I was also trying to show what sort of simplifications often
made that I wanted to specifically avoid; particularly things
relating to the conservation of mass of things, piping, vessels
etc., that were 'made radioactive' as a side effect.
The notion of 'perfectly uniform dispersal' is an account for
two aspects of this question: 1) the difference in the notion
of 'total radioactivity' (curies) as distributed through some
cubic volume of mass, and the notion of measured radioactivity
at some surface of this cube, and 2) the potential absorbency
effects that the non-radioactive isotopes (as a percentage of
the total volume) would have on the measured degree of surface
radioactivity.
> Assuming a certain composition at defuelling it is in principle
> simple to track that over time (but will require a lot of decay
> data).
Yes, this is exactly right. This is, in part, what I am trying to
get at, but without having (either myself or someone else) do all
of the math. I am trying to get a 'overall summary' of the decay,
as averaged across multiple types of nuclear process, somehow
weighted in relative proportion to the frequency of their usage,
and to see how this resulting decay profile compares to what it
would have been if things had simply been left alone.
~ ~ ~
> There are aspect which perhaps can be reformulated to make sense:
> - the 'background' level of (natural) radioactivity 'the M1'
> is known.
> - R1; amount of ore (which can be converted to nuclear fuel)
> present in Earth can be estimated.
> - the total of radioactive product mass (resulting from nuclear
> power generation) (the 'waste') "R2" can be estimated for a
> PARTICULAR process.
Correct; although I do not have this particular data at hand.
I am not so interested in the specific data, so much as I am
interested in a reasoned "expert opinion" on what this data,
overall, means. Which is, in part, why I ask this question here,
where I am sure that I will get an intelligent response.
> But, there are problems with the question which cannot be cured:
>
> For example:
>
> Q1: How would 'background' level of radioactivity increase if all
> waste product of process X were uniformly spread through Earth - this
> new level is 'M2'
Correction; I did not mean through the whole planet; I meant only
through the exact same volume of the original arbitrary dirt from
the "raw materials" were themselves extracted. That the "stuff taken
out" was replaced with other "stuff put back", and to somehow
estimate the total difference in inherent radioactivity (the total
curies) that this caused. However, the question was expressed in
that particular way as I wished to account for the total degree to
which this change might (or might not) matter on the surface. Perhaps
the radiation is of such a type (Alpha or Beta) that the adsorbent
properties of the remainder of the "non involved" material made the
difference on the surface negligible. If this was so, I want to
know it.
> Problem 1 Through volume of the whole of Earth or
> just some layer (SiaAl crust) ?
As a clarification, I am assuming an 'average portion' of the
crust, somewhere near the surface, say around Nevada (US) where
such things tend to happen. I know that many places have
relatively few of the required isotopes for commercial application.
> problem 2 (both fission and fusion)
Yes; although if forced to make a choice, I would assert that
fission is of somewhat more interest than fusion.
> Problem 3 how these ratios vary,
With time; yes.
> > ... multiple curves, each for various nuclear process types ...
> You want a curve for each process, like reactor type?
> which shows a natural decay of radioactive waste?
I honestly did not expect that I would get such a detailed answer
(although one can always dream!), unless by some chance that someone,
somewhere had asked something similar to this before, and thus the
information could be provided thereby. I certainly do not expect
anyone to do so much calculation from scratch for a mere $35!.
If someone _has_ done something like this before (as part of a PhD
thesis (grin)), I would want to know about it. BTW; I am not currently
in school, and am not asking this for any sort of credit; it is for
my own interest, and so that I am properly informed when making certain
types of (low impact) long term personal policy decisions.
> Main issue is that the technology is evolving.
> People (scientists) are working on new type of rectors which will
> re-use the waste and burn it better.
> There are breeder reactors (which some people (politicians) want to
> ban because of proliferation issues)
> and fusion is still subject of active research. No one knows amount of waste.
Agreed; I know this. Again, I am trying to keep this conceptual as
best as possible. For simplicity sake, it is valid to assume only those
reaction types as is currently 'state of the art', and thus ignore the
effects of any future invention.
> Also, this mixing of waste into bulk of Earth is dubious comparison, as
> Earth is an active stock-pile, generating heat by burning fuel - so
> surface background is not related to bulk content.
True, but how else could I ask this and still get at what I am trying
to get at? Suggestions are welcome.
I hope that all of these comments are as helpful as yours have been.
Again, what I am looking for are the methods of thinking involved and
for some sort of ultimately objective, informed and unbiased,
reasonable conclusions that truly match the question that I am asking.
Again, thank you very much for your time!
