If it is economic to capture CO2 from the atmosphere then there are a few advantages.

• There is no need to pipe the CO₂ from the source to the storage area.
• And it should be possible to capture past emissions and repair climate change.

The challenge is that CO2 is 400 ppm, i.e. only one molecule to 2,500 air molecules.

Artificial trees.  National Geographic

Oxy-burning biomass

The most obvious way to capture CO₂ from the atmosphere is to:

1. grow plants,
2. Use the biomass, 
3. burn the used biomass with oxygen,
4. bury the CO₂ given off.

It would take many generations to repair the damage done by this one.

It is also referred to as "Bio-energy with carbon capture and storage", or BECCS

Compressing CO₂ will take 7-10% of the energy generated by the power station. Source

Firing with pure oxygen would result in too high a flame temperature, so the mixture is diluted by mixing with recycled flue gas,

Sounds simple, but as usual, there are technical details .

Cost is estimated to be AU$75-150 /Tonne of CO2. Source  Source2

That is AU$225-450 /T of coal.

Ethanol

When ethanol is made by fermentation of sugar, 50% of the sugar becomes ethanol, and 50% becomes CO₂. If this is buried, then it is removed from the atmosphere.

Bio-char

Use pyrolysis to convert biomass to biochar and bury it.

See page on biochar

Chemical absorption

There are processes using CO₂ absorbers:

• Sodium hydroxide
• Calcium hydroxide
• Lithium oxide
• Amines
• Ion exchange resins

One idea is to react the absorbent in a solar updraft tower.

The challenge is to find a substance to absorb the CO2, then to release it again with a minium of energy.

For example: NaOH binds the CO₂ with ten times the energy needed, and this is how much energy is needed to release the CO₂ and recycle the absorbent.

Amine estimated cost: US$15-50/T CO₂ (US$45-150/T of coal) This depends on how long the amine surfaces last.

Lithium carbonate and oxide

Lithium oxide dissolved in molten lithium carbonate, will combine with carbon dioxide in the air, forming lithium carbonate. A voltage across the molten carbonate, produces lithium oxide, (which is recycled) oxygen, carbon. The carbon can be produced as a variety of different carbon nanofibres. This depends on the conditions of the electrolysis. 

Li₂O + CO₂ → Li₂CO₃

Li₂CO₃    → Li₂O + C + O₂

Researcher: Stuart Licht, professor of chemistry at George Washington University_.

The researchers claim one million square KM would be enough to repair our carbon dioxide levels.

MIT Technology review August 19, 2015

Absorption by ion exchange fibres

Wind can drive air into a funnel and over fibres to absorb the CO₂. The energy cost of collection depends on the amount of CO₂ captured, rather than with the volume of air processed. It is most economical if only half the CO₂ is collected.

A process being developed by Klaus Lackner of Columbia University NY traps CO₂ on ion exchange membrane and then releases it with water or moist air at 45^oC..

The ion exchange resin similar to Dow Chemicals Marathon A , absorbs CO2 with much less binding energy than NaOH.

A collection unit with one square meter face area can keep up with one person’s CO2 emissions.

A shipping container sized collector should be able to collect one Tonne of CO2 per day, As much as a hectare of crops.

http://www.skyscrubber.com

NaOH  +  CO₂  →  Na₂CO₃

A rough estimate cost would be at first $200/T CO_2, but with large scale manufacture, theat may drop to US$30/T of CO₂, or US$600-90/T of coal burned.

It would take about 25% of a power stations output to collect the CO₂.

At a speed of 6 m/s, which is typical for a windmill location, the kinetic energy density in air is approximately 20 J/m³. This comparison suggests that windmills successfully extract from the air a value which in energy terms is five hundred times more dilute than the CO2 captured in an air collector. Therefore, a well-designed CO2 collector that keeps up with the emissions of a fossil energy source could be two orders of magnitude smaller in its wind-facing cross section than a windmill that replaces the same energy source.  Source: Lackner

Area need​ed

With a flow of 3 m/s through some filter system collecting half the CO₂ , then 0.75 square metre can collect the CO₂ output from one person.   more

Nano tubes

Nano tubes made mainly of carbon, can absorb CO₂. It is released again simply by heating.   More