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Considering our problematic issues,

This is an area of concern where it's worth asking some stupid questions.

What would happen if a hose was attached to the core/hot nozzle of a turbofan, diverted to storage on the body? Could it still be efficient 'enough' (assuming a highest possible bypass ratio) to compress and carry some of that carbon dioxide to the next airport?

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    $\begingroup$ @PerlDuck You don't need to capture all the air. You only need to capture the CO2. Assuming the jet fuel is 100% ethanol, C2H5OH + 3O2 = 2CO2 + 3H2O, that's a ratio of 1.7 CO2 to fuel, in terms of weight. Liquid CO2 actually has a higher density than jet fuel at room temperature. So still a hefty and unrealistic proposition, but not as crazy as initially believed. $\endgroup$ – Jimmy Jul 29 at 6:15
  • $\begingroup$ @Jimmy Not sure if I can follow. This post says a B737-800 uses about 2,500 kg/hr of fuel (=1,250 per engine) during cruise. Does your calculation mean it emits 1.7 times 2,500 kg = 4,250 kg CO2 per hour? $\endgroup$ – PerlDuck Jul 29 at 11:34
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    $\begingroup$ @PerlDuck There's a set amount of fuel per aircraft. And yes, the aircraft would get heavier if we capture all the CO2 released. If we burn all the fuel stoichiometrically and assume a very optimistic fuel of 100% ethanol, the airplane will gain the weight of 1.7 times the fuel. $\endgroup$ – Jimmy Jul 29 at 13:27
  • $\begingroup$ Context: "Globally, the team estimated that about 8,000 deaths a year result from pollution from planes at cruising altitude—about 35,000 feet (10,668 meters)—whereas about 2,000 deaths result from pollution emitted during takeoffs and landings." and "Emissions from ships, for instance, kill an estimated 60,000 people a year, according to a 2007 study also published in Environmental Science & Technology." CDC in US says "Cigarette smoking is responsible for more than 480,000 deaths per year in the United States, including more than 41,000 deaths resulting from secondhand smoke exposure." $\endgroup$ – CrossRoads Jul 29 at 13:33
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    $\begingroup$ "Nearly 1.25 million people die in road crashes each year, on average 3,287 deaths a day." So sink all the ships, kill all the tobacco plants, and reduce the number of cars on the road - low hanging fruit vs trying to improve plane engines. $\endgroup$ – CrossRoads Jul 29 at 13:37
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There's a fundamental problem. A jet engine performs work by expansion of the combustion products. Compressing the combustion products would require at least as much work as was provided by the expansion of the combustion products. Only an external combustion engine (for example, a steam engine) would work in this case.

A second problem is that the mass flow of the CO2 is more than three times higher than the mass flow of the fuel. Your plane would get heavier as you fly, and since the max landing weight of a typical plane is lower than the max takeoff weight, this will severely limit the aircraft range.

All in all, you can probably manage to make a purpose-built plane that fits the bill but I highly doubt it will have much usable payload if any at all.

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This answer suggests the typical air mass flow of an airliner during cruise is around 100 kg per second per engine. Given a moderate bypass ratio of 8 this would yield 12.5 kg per second per engine. I'd assume the fuselage would simply blow up. Or, if some device was capable of compressing that amount of hot air within a second, the aircraft would gain weight at the same rate. That's 45 tons every hour. But maybe my calculation is too naive.

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    $\begingroup$ More impressive numbers considering 2 GE90s. $\endgroup$ – ymb1 Jul 29 at 11:29
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    $\begingroup$ As mentioned in the comment section in OP, you don't need to capture all the air, just the CO2. Assuming the jet fuel is 100% ethanol, C2H5OH + 3O2 = 2CO2 + 3H2O, that's a ratio of 1.7 CO2 to fuel, in terms of weight. That is, if we burn stoichiometrically all the fuel (assuming ethanol), the plane will gain 0.7 times the weight of the fuel. Liquid CO2 actually has a higher density than jet fuel at room temperature. Obviously, this is still an impractical and uneconomical proposition, but not aphysical. $\endgroup$ – Jimmy Jul 29 at 15:28
  • $\begingroup$ @PerlDuck, Even of these 12.5 kg, not everything is burned: jet engines burn a very lean mixture (due to temperature constraints), even if we consider just the core. It's better to calculate from fuel rather than air. $\endgroup$ – Zeus Jul 30 at 1:16

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