Burn biomass (plants) in a power plant to generate electricity, then store the carbon dioxide in empty gas fields. This is called BECCS, Bioenergy with carbon capture and storage [0].
Unfortunately, carbon capture and storage is not economical (yet). Let's hope it will be soon, with EU CO2 prices already reaching 50 euros / ton this week [1].
If I understand this International Energy Agency report[2] correctly, many forms of carbon capture become economical if these price levels subsist in the EU (and other economic blocs impose similar prices on their industry).
Alternative, make charcoal, bury the charcoal, extract whatever useful thing you can from the not-charcol that comes from that process.
Charcoal is pretty much pure carbon and that's what we should be putting into the ground. Putting CO2 into the ground runs into problems because you have to deal with the fact that you are burying a gas (gasses don't like to be contained).
So skip that, and instead focus on burying pure carbon.
This is a good idea, But getting the biomass will be difficult. I dream about large lakes of algae that can be skimmed and then sundried, and cooked in solar ovens to create essentially a solar powered only capture process.
This sort of operation would need a stable cap and trade or carbon tax system to be profitable.
I should also add, I think China or somewhere in the hot parts of Africa would be a a good place for this as it would be a large area operation. Sadly as an Australian we suffer from regulatory capture and a carbon tax won't be back on the cards for some time.
Pretty much the description of all carbon capture. Capturing carbon is inherently difficult.
IMO, barring some breakthrough, biology will be the most efficient mechanism for capture. Millions of years of evolution have made plants and algae pretty good at carbon capture as the carbon levels slowly depleted (until recently).
An appealing benefit of biological carbon capture is the fact that all biology is solar powered. All the non-biological solutions required a pretty hefty energy input from somewhere. I mean, I guess it's nice that you could provide that from solar/wind/or nuclear. But then it's also nice to not require transmission lines for energy input.
I'm hoping someone can find, or mix and match an algae in lab that will have the right mix ofproperties to explosively grow.
Providing food stock will be tricky, either through something very efficient like straight sugar or designing the algae to consume anything which could have other upside benefits.
And like all well meaning engineering the real challenge will be making sure the algae that can grow by eating anything doesn't get out of the pond.
Algae are generally autotrophic, meaning they don't need sugar or food, they create sugars from CO2 and light, and they need nutrients like phosphorus and nitrate and other minerals to do so.
But if you provide too much nutrient, too much algae grow, and when they die and decompose they absorb all the oxygen in the water and kill the whole ecosystem. (That's called eutrophication).
Charcoal is pretty much pure carbon and that's what we should be putting into the ground. Putting CO2 into the ground runs into problems because you have to deal with the fact that you are burying a gas (gasses don't like to be contained).
So skip that, and instead focus on burying pure carbon.