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Calculation:
Biological Productivity expressed as GtC sequestered per surface area (km2)

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CARBON SEQUESTRATION CALCULATION - Macro-sedimentation with balanced inorganic nutrient and solid phase surface habitat
(Subject to experimental verification in test plots)

SIZE FACTOR
Pacific Ocean is 96m sq miles
2.59 km2 per square mile 
https://marinedebris.noaa.gov/info/patch.html

GYRES
Indian Ocean Gyre 5000000 km2
North Pacific 20000000 km2
South Pacific 59520000 est
Sum: 84520000 km2

est global 100000000 km2 gyre area for deployment
1.00E+08 km2

According to World Resources Instititute
9.7B tonnes of carbon were emitted into atm in 2012 from fossil fuels and cement
Verified: This is a typical number for the current decade (so far).

CASE I. LOW PRODUCTIVITY FACTOR
100-200 mg as C Avg daily productivity, C exported above steady state
0.054545455 gm/day-m2 C
10e6 m/km2 AREA

19909090.91 this is grams C per year per km2
19909.09091 This is kg
19.90909091 This is metric tons per km2
100000000 This is global gyre area est as above as km2 
1990909091 metric tons for entire gyre surface area
1.99E+09 Gigatons per year

AS PERCENTAGE OF ANTHROPOGENIC CARBON RELEASE
10.00%
20.00%

CASE II. HIGH PRODUCTIVITY FACTOR
2000 mg as C Avg daily productivity, C exported above steady state
0.272727273 gm/day-m2 C

106 m/km2 AREA

99545454.55 this is grams C per year per km2
99545.45455 This is kg
99.54545455 This is metric tons per km2
100000000 This is global gyre area est as above
9954545455 metric tons for entire gyre surface area
9.95x109 Gigatons per year

AS PERCENTAGE OF ANTHROPOGENIC CARBON RELEASE
102.62%
205.25%

Yes, the surface area is very large. Think about the number and cost of nuclear reactors to replace fossil fuels, or the land area of crops replaced by silviculture to sequester an equivalent mass of carbon as CO2. Human geoengineering is occurring on a planetary scale beyond anything bigger that has ever been imagined. So the solutions must be equally heroic. We suspect the true result will be between the low and the high case shown above.
Experimentally, literature summarized at www.climos.com/pubs/2009/Climos_Why_OIF-2009-03-12.pdf
shows a pseudosteady state carbon export of about 290 GtC/gyre surface area/year. But the conditions are not sustained steady state and instead are intermediate bloom kinetics based on use of an immediate release formulation. In contrast, we would use an extended release formulation designed to float in the gyres, capture and sink plastic pieces, and supply habitat for a community of organisms that would release, by sedimentation of fecal matter and detritus, about 100 - 200 GtC/year globally from the atmosphere.
The intent is not to buy more time to continue atmospheric loading of CO2 but instead to minimize the costs of damage caused by climate change while the needed switch to a zero-net carbon emissions economy is pushed through.

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