Further Enrichment of Salehi’s Statement

Some readers noted errors in my previously posted calculations (Enriching Salehi’s Statement, 25 June 2010). My assumptions were quite wrong. I’ve now, finally, found some time to sit down and revisit my numbers. And as it happens, on the same day as Mr. Ali Akbar Salehi, the head of the AEOI, have announced that his outfit has now produced about 20 kilograms of ‘higher enriched uranium’.

Again, according to the latest IAEA report on Iran:

• One cascade is presently enriching uranium to ‘higher grade’. This cascade comprises 164 IR-1 machines.

• Between 9 February 2010 and 21 May 2010 (that is, for 101 days), a total of approximately 172 kg of low enriched UF6 was fed into the first cascade. This gives as approximate feed rate of 1.703 kg/day.

• On 7 April 2010 (after 57 days), Iran withdrew 5.7 kilograms hexafluoride gas enriched to 19.7 per cent U-235 (the Agency assay indicates an enrichment level of 19.3 per cent). This gives us an approximate product rate of 100 grams per day.

• The tails are set to 2.0 wt% U-235 (and not 0.2 wt% as assumed in the previous post). Iran intends, by connecting the second cascade, to bring the tails down to 0.7 wt% (that is natural uranium).

Under these parameters, a feed of 172 kilograms of 3.5 per cent enriched hexafluoride gas should equal about 14.54 kilograms of 19.7 per cent enriched material. As noted above, Iran withdrew much less than half of this on 7 April 2010. In order to make approximate sense of that numbers, the tails setting must be close to 2.5 wt% (this assuming that material were fed at a constant rate from 9 February to 7 April). Also, under that assumption, the machines operated at about 0.63 SWU/machine and year, not by any means an impressive figure.

However, the numbers make more sense in the aggregate. I ran the known average feed and product per day through statistical software, and came up with some interesting numbers, but only after making two assumptions. First, in order to produce 20 kilograms of enriched gas, the total feed for the period would need to be 236.7 kilograms. Second, I had to assume that the additional material has been fed into the cascades after 20 May 2010. This actually leads to a drop in the feed rate (down to 1.2207 kilograms per day). I’ve put it all in a graph.

Running all 156 data points leads to some interesting conclusions. The mean feed flow rate, under all these assumptions, becomes about 1.536 kilograms per day (with a sigma of about 230 grams and a deviation of 218 grams). The mean product flow rate becomes about 129 grams, with a sigma of about 22 grams and a deviation of about 21 grams).

Extrapolating the mean value over a year gives a feed of 560.64 kg yield a product of about 47.09 kg. All things being equal, this would require a tails setting of 2 wt%, which is precisely what Iran has declared. The total separative investment would be 154.4 SWU/year. This would mean that the machines are running at 0.94 SWU/machine/year.

The cascade solution would look something like this:

So, to sum up, I can draw three conclusions:

First, I was definitely wrong in accusing Mr. Salehi of misleading us;

Second, in fact, his figures may well be right; and

Third, playing around with these figures are inherently dangerous, since there are many assumptions that have to be made, especially regarding tails enrichment.