Direct Air Capture (DAC) of $CO_2$: Would a DAC mechanism run out of local $CO_2$ to convert? Per Carbon Engineering's Website: Direct Air Capture (DAC). 
They claim to be able to remove 1 million tons of CO$_2$ per year with a single plant. My question is whether they needed to account for the fact that by running a DAC plant, they would decrease local CO$_2$ concentrations. Is this a factor? Or does the air in the atmosphere circulate quickly enough that they didn't need to account for changing levels of CO$_2$ in the area?
 A: Direct capture of CO2 from gas streams is known technology. It is one of standard industrial methods to produce CO2 of very high purity (i.e. 99.995% pure).
However those processes use exhaust gas streams which are rich in CO2 - i.e. concentrations of the order of 10% to 50%, not 400ppm as in the general atmosphere.
Carbon Engineering's claim is just that, a claim. If you browse the site, they have "plans" to build a first operating plant starting in 2021, and "plan" that it will be operational by 2023.
Ignoring the issue of processing the same air repeatedly, and assuming the process is 100% efficient at capturing the CO2, it is easy enough to work out how much air needs to pass through their extraction plant.
Working to one significant figure, one year is 30 million seconds. So to extract 1 million tons of CO2 per year, they need to extract about 30 kg per second.
The mass of CO2 in air is about 0.07 kg/liter, so they need to process about 400 liters of air per second.
To get some idea of what that means "in real life," the air flow through a large jet engine at full power is of the order of 1000 liters per second.
Large gas turbine engines (based on aircraft engines) used in natural gas pumping run continuously for months on end without any issues depleting the local atmospheric oxygen content, so an isolated plant of this size probably won't have problems with processing recycled air either.
So on the face of it the claim is not obviously impossible to achieve, though time will tell.
However, one such plant would extract about 1 millionth of the total CO2 in the atmosphere in about 3 years of operation. To restore a "pre-industrial" CO2 concentration, requires removal of about 30% of the global CO2, or about 1 million "plant-years" of this type of device.
Draw your own conclusions whether this is a realistic technical solution to the problem, or simply a way to make money from concerned investors.
