Whenever anyone mentions carbon capture there are two opinions - essentially for and against. "For", in service of the carbon-induced global warming/climate change theory and "against" as in "it's pointless" since the impact of using fossil fuels will be attenuated by inevitable cuts in their use according to peak oil, peak gas and a potential peak coal that was recently calculated using a Hubbert Linearization to arrive by 2028. I am not sure about the realities of the "for" case, in terms of how the Earth systems will respond exactly to GW (and nobody will know until the vast experiment is completed in reality) but in regard to the "against" I agree that global warming is the least of our worries in the immediate term, and running short of supplies of oil and gas will launch a cataclysm of social disintegration if we have no alternative - plan B - in place.
The two concepts might be combined however, at least assuming there is enough time, and that the EROEI stacks-up. For the moment, however, let's think positive and assume that it does. Proposals for geoengineering always make me uneasy, including the idea of "seeding the ocean". Principally, my disquiet stems from a feeling that all aspects of nature are interconnected and by messing about with one thing, an unforeseen calamity might ensue elsewhere - the butterfly effect, to use a well-known phrase.
However, if phytoplankton could be caused to bloom, say in the Southern Ocean, 1 Gt (billion tonnes) of carbon could be captured annually. It is claimed that regenerative agriculture might sequester around 3 Gt of carbon each year (although there is some dispute about this), and that by 2050, biochar production could account for another 1 Gt of carbon annually. In principle - and this is where the link comes in - the carbon in the soil can stay there and improve its quality, but if the other kinds of captured carbon could be harvested, it might provide a useful potential source of biomass/fuel. Growing algae on a local level - a "village pond" you might call it - could provide energy to replace fossil fuels for local communities, without impacting on arable land.
Since we emit 7 Gt/year of carbon from fossil fuels, the sum comes out something like (in Gt): 7 - 3 - 1 -1 = 2 Gt left to worry about. A cut in fossil fuel use by 50% through biomass curbs that to 1 Gt. Photosynthesis already absorbs around 3 Gt of carbon/year into oceanic phytoplankton and land-based plants, and if localised algal production cuts emissions from oil by another 1 Gt (assuming that we need 1 Gt less since we have that from algal biomass), the combined scheme is carbon negative by -3 Gt/year.
Hence in 40 years this would have cut 120 Gt of carbon from the atmosphere, which would reduce the concentration of CO2 by around 50 - 60 ppm.
Now this is an extrapolation of sums I have seen done and on paper it looks pretty rosy, implying that we can eke-out our oil, gas, coal and nuclear and at the same time bring down the carbon-content of the atmosphere to pre-industrial levels by the end of this century.
What is rarely mentioned let alone costed-in is the lead-in time, the energy costs, the EROEI, the materials, the engineering and so on... that's when it begins to look less rosy.
For example, while I like the idea of biochar, the stated goal by the International Biochar Initiative (IBI) is that we could have 1 Gt/year of carbon being drawn from the atmosphere by 2050. O.K. let's assume that's 40 years time and that there is currently (in Gt terms) about zero biochar being produced currently. Even if we assume a linear growth in the technology, that "wedge" (if you draw a straight line on a piece of graph paper from 0 - 1 Gt on the y-axis up to 40 years on the x-axis) that only accounts for 20 Gt of carbon, or a reduction of about 10 ppm, which is neither here nor there, and the biomass production and processing would be simply colossal when viewed en mass.
That said, if that level is achieved by, and sustained beyond 2050, 1/7th of all carbon (14%) captured per year is significant, and could be a higher proportion if fossil fuel burning has by then been significantly curbed, either deliberately or because we have less of them available. The main benefit of biochar is likely to be in terms of improving soil quality, if it is employed as a soil-amending agent, and thereby reduces demand on water and nutrients like N and P to grow crops. The latter is likely to be particularly significant in parts of the world where the soil is poor, e.g. Africa and Asia. In the U.K. soil tends to be very rich - too rich sometimes - but even here, the incorporation of biochar into the soil would attenuate problems from run-off waters that contain too much phosphate and nitrate.
Regenerative agriculture is somewhat contested in terms of its carbon capture potential, and there is little evidence that we can "seed" the oceans in a practical fashion, or recover the plankton on any significant scale. Indeed, if massive amounts of phytoplankton were to grow through seeding, the emissions of sulphur compounds (H2S, dimethylsulphide etc.) which are oxidised to particulate "sulphate" matter in the troposphere, would have the effect of further seeding cloud formation. This might help to cool the planet through reflecting more sunlight back into space, which sounds good in GW-terms, but it would surely affect rainfall and how the earth-systems distribute water around the planet.
What I can see is that production of biochar and algae on a local level, as part of a programme of lower-energy living could offer some benefits. There is also (for once) the advantage that there are a lot of people on the planet. Hence if a community of 2000 people could catch and sequester 200 tonnes of biochar per year (100 kg/person), 7 billion of us in total could sequester almost 0.8 Gt/year (close to the IBI projection of 1 Gt/year by 2050). However, it is the curbing of energy use that really counts. Back to the village algae-pond. As a total area, we would need around 3200 km2 of ponds to fuel Britain (more of which could be turned to other purposes than personalised transport through relocalisation), that suggests that each village pond would need to be:
3200 km2 x 100 ha/km2/60 million x 2000 = 10.7 hectares for each 2000 person community. It's big but it doesn't sound impossible when broken down like this. The real problem is how to process the algae either by extraction of its oil/transesterification or bulk thermal gasification. It might be simpler to just grow the algae (and other biomass), dry it out and burn it as a source of thermal energy.
All of the above is going to take an awful lot of engineering, hence energy and time, but let's not depressed about the details, and look at those "happy sums" again.