[lbo-talk] Was something else, more chem data thoughts

Les Schaffer schaffer at optonline.net
Sun Apr 30 13:42:53 PDT 2006


Chuck Grimes wrote:
> I might be interpreting SWU's wrong. But think about it. SWU is
> separative work units, meaning the amount `work' done to separate a
> given quantity of isotopes. But notice there is no ratio of work units
> to time units.

Chuck: this is all covered in the article i sent you offlist [***]. as i said earlier, i'll be happy to help you run the numbers offlist.

the upshot is this: as first worked out by the physicist Dirac and others, SWU is a thermodynamic quantity applicable to any process that separates isotopes (or different mass species). it can be related to a real work/energy-like quantity for very small enrichment ratios. but it is true that it has no time element in it, as is typical of thermodynamic quantities that depend on end states but not on the path connecting them. the main use of SWU, as it was historically developed by Dirac, is described in section 7 of Appendix A: that is, SWU allows one to calculate the # of centrifuges needed for a system with a given feed, waste, and enrichment desired, independent of the cascade topology.

Dirac then went on to derive the separation rate for an ideal (arbitrary type) centrifuge. it is equation (3) in the paper. it's units are SWU per unit time.

finally, you have to work out the ideal rate for a real implementation. the paper i sent you does that for the concurrent and countercurrent centrifuges in Chapter III, section E, eqn 31, and Chapter III, section G, eqn 42. Here again, these are theoretical values for each process. any given centrifuge could do worse. notice that the Iranian centrifuges 2-3 SWU-kg/year [ as quoted in http://www.armscontrolwonk.com/ ] are less than machines experimented with during the Manhattan Project (approx 4.7 for the gas centrifuges, per Whitley's paper)

then there are power requirements for these devices. it is explained in the paper why the work required in a real separation processor is MUCH greater than any thermodynamically defined measure like an SWU. for example, its takes power to spin up the gas to high speeds, and that power is irretrievably lost in countercurrent devices. This is described in Appendix A, section 6. Appendix A section 7 is better than anything i've seen on the net on cascade calculations.

Whitley also describes a practical limitation to high speed centrifuges which goes unmentioned in net-based reports. that is, there is a limit to the speed of the rotors since the pressure build up in the gas at the outer edges eventually goes above manageable stress levels (this is in addition to centrifugal stresses in the rotors themselves). additionally, the pressure build up reaches a point where you get condensation of the gas on the outer wall, which again leads to centrifuge destruction.

Whitley's paper is so far better than any article found on the web anywhere. Part II, which i haven't read yet, deals with issues of high speed mechanical rotation. The author claims that the review -- written in 1984 -- covers most of the physics available at that date, with subsequent lesser developments being classified by US and European governments.

les schaffer

[***] Review of the gas centrifuge until 1962: Part I: Principles of separation physics. Reviews of Modern Physics, Vol 56, No 1, Jan. 1984

http://prola.aps.org/abstract/RMP/v56/i1/p41_1 http://prola.aps.org/abstract/RMP/v56/i1/p67_1

Of historical interest: Part I includes coverage of work done by Klaus Fuchs on isotope separation.



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