Following-on from yesterday's posting about adding iron to the Southern Ocean (SO) to capture CO2, I have done a few sums which I think give some quite insightful results.
(1) How much iron in total? 1800 tonnes of iron added to 400 square miles of ocean. So that's 1800/400 = 4.5 tonnes/sq. mile.
1 sq.mile = 2.59 km^2 and so, we need 4.5/2.59 = 1.74 t/km^2.
The SO has an area of 20 million sq. miles x 2.59 = 51.8 million km^2, x 1.74 = 90.1 million tonnes of iron added altogether.
(2) Algal growth. 3.5 Gt = 3.5 x 10^9 tonnes of CO2 captured to grow it. Multiplying by 12/44 gives 0.95 x 10^9 tonnes of carbon.
If, as an approximation, we base the organic component of the algae on sugar, C6H12O6, we get that 72/180 = 40% is carbon.
Therefore the dry-mass of the algae is 0.95 x 10^9/0.4 = 2.38 x 10^9 tonnes. If we assume that 50% of the living algae is water, then we can double that to give 4.75 x 10^9 tonnes (almost 5 Gt).
If we assume a density of 1 (1 t = 1m^3), the thickness of the algae if it lay on the surface (in reality it will be partly dispersed in the surface ocean layers) would be:
4.75 x 10^9 m^3/(51.8 x 10^6 km^2 x 10^6 m^2/km^2) = 9.17 x 10^-5 m = 92 microns. For comparison, a human hair has a thickness(on average) of 70 microns, so despite the vast mass of the algae at nearly 5 billion tonnes when spread over the huge oceanic area it is not so much.
(3) Turnover rate of iron. The iron acts as a catalyst and can promote maybe hundreds to thousands of carbon-fixing cycles.
However, 0.95 x 10^9 tonnes of C is fixed by adding 9.01 x 10^7 tonnes of iron. Thus each iron atom fixes (0.95 x 10^9/9.01 x 10^7) x 56/12 = 49.2 atoms of carbon; i.e. a relatively low turnover rate of about 50.
Probably this reflects precipitation of iron and its compounds without interacting with algal production, problems of transport into the algal cells, i.e. in the form of iron-porphyrin complexes and other losses, otherwise it would be higher. The amount of added iron chosen is probably determined experimentally and takes-account of these things.
As the iron tends not to stay around in the water for more than a few days, it would presumably need to be added continually and in considerable quantities.