How do amines react with flue gases to absorb CO₂?

I'm reading [this](https://www.netl.doe.gov/technologies/carbon_seq/refshelf/project%20portfolio/2009/Overview/Selected%20CS%20Program%20Papers/2008%20Jan%20Advances%20in%20CO2%20Capture%20IJGGC.pdf) article about carbon capture from the combustion of fossil fuels. In this article, it says that amines are used as a chemical absorbent to capture the $\ce{CO2}$ from the exhaust of the combustion. 


In particular, I have read that N-Methyl diethanolamine (MDEA) is used (a  [reference](http://training.swpartnership.org/CCSclass/CCS_Module_files/co2_capture_sept_2012.pdf)  lists the formula as $\ce{CH3N (C2H4OH)2}$). I am curious if anyone can explain what happens during the reaction with $\ce{CO2}$ and how it absorbs the $\ce{CO2}$ from the flue gas. 




In addition to the reaction in permeakra's answer, some amines may react with $\ce{CO2}$ in absence of water also. This type of reaction is a Lewis acid-base reaction forming a zwitterionic complex: $\ce{R3N + CO2 -> R3NCO2}$.


![enter image description here](https://i.stack.imgur.com/CAPWK.png) 


MDEA adds some stability to this complex. The alcohol groups can stabilize the carboxylate group through hydrogen bonding.


![enter image description here](https://i.stack.imgur.com/G2JY8.png)


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All amines are proton bases. $\ce{CO2}$ in water containing solutions acts as a weak acid. An overall reaction is $\ce{NR3 + H2O + CO2 -> [NHR3][HCO3]}$ and is possible for all amines. Aminoalcohols are cheap as they are produced from easily available oxirane (ethylene oxide) and have a high boiling point, so for them this reaction can be reversed by heating, with the regeneration of working solution. 


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