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I wonder if a combustion process with air as oxidant can benefit by oxygen enriching the air intake? By benefit I mean if the net energy output would be positive, or negative, since the enrichment process will consume some of the energy released in combustion.

A general answer is sufficient, or an answer based on a modern motor vehicle combustion engine.

Actually a practical answer would also do. A car with variable valve timing would automatically adjust the engine compression ratio based on the oxygen level detected by the oxygen sensor. (If oxygen levels increase, variable valve timing close the intake valves earlier.)

One way of answering this question is to show the efficiency of increasing oxygen content in the intake and combine that with the energy needed to do the oxygen enrichment from air.

Some clues can be had from

Engineering Science and Technology, Volume 19, Issue 1, March 2016, Pages 438-443 Effects of oxygen enriched combustion on pollution and performance characteristics of a diesel engine P.Baskar, A.Senthilkumar

THE EFFECT OF OXYGEN-ENRICHED AIR ON THE PERFORMANCE AND EXHAUST EMISSIONS OF INTERNAL COMBUSTION ENGINES ,VARADARAJA SETTY, B.E. MASTER THESIS IN MECHANICAL ENGINEERING , Texas Tech University

Reports like the following are less interesting, since spark timing is the regulating mechanism with increased oxygen levels.

J.X. Zhou, B. Moreau, Christine Mounaïm-Rousselle, Fabrice Foucher. Combustion, Performance and Emission Analysis of an Oxygen-Controlling Downsized SI Engine. Oil & Gas Science and Technology - Revue d’IFP Energies nouvelles, Institut Français du Pétrole, 2016, 71 (4), pp.49. ff10.2516/ogst/2015035ff. ffhal-01597165f

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    $\begingroup$ Let me get this straight: you want to know the relative efficiency of 1) combustion with air as oxidizer and 2) combustion with oxygen-enriched air, with the energy cost of the oxygen enrichment process taken into account, i.e., not just ignored? If my understanding is correct, then it comes down to doing some detailed energy cost accounting. I have no expertise in that, but maybe someone here does. I hope you get a helpful answer. $\endgroup$ – Ed V Jun 26 at 19:55
  • $\begingroup$ If you like cars, check out turbo charger $\endgroup$ – Karsten Theis Jun 26 at 21:58
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What does "energy efficienct" mean?

It depends on what you mean by "efficient".

For combustion reactions that involve engines, if "efficiency" means how much work (the "good" type of energy) that comes out of the engine per unit input of fuel, then yes oxygen-enriched mixtures would be more efficient than regular old air.

If instead "efficiency" means how much of the fuel is combusted all the way to $\ce{CO2}$, the answer is also probably yes, but for different reasons.

The efficiency of engines

To understand why, keep in mind that no engine can ever be more efficient than an ideal Carnot engine. The efficiency of a Carnot engine is $\frac{T_H - T_C}{T_H} = 1 - \frac{T_C}{T_H}$, where $T_C$ is the temperature of a cold reservoir (e.g. our everyday environment) in Kelvins and $T_H$ is the temperature in Kelvins of a hot reservoir.

Thus, the hotter you can get the "hot" side of Carnot engine, the better. In a car engine or other Otto engines, this would correspond to the maximum temperature of the combusted air (or oxygen)-fuel mixture just before the expansion stroke.

Adiabatic flame temperature

With air instead of pure oxygen as the oxidizer, some of the energy of combustion goes into heating up inert components of the air, mostly nitrogen. This lowers the maximum temperature of the air-fuel mixture and decreases theoretically attainable efficiency.

The adiabatic flame temperature is a quantitative number behind this idea. Wikipedia lists the adiabatic flame temperature, the maximum temperature attainable in the combustion of certain fuels, and the values for fuels burning in air are a bit less than the same fuels burning in oxygen.

Limits of this analysis

Of course, there are many factors that make real engine performance different than ideal engine performance. In fact, designing engines that can operate with at the extremely high temperatures that would maximize efficiency is tough because of materials problems. (The adiabatic flame temperature of gasoline in pure oxygen is somewhere around 3800 K, far higher than the melting temperature of steel, for example.). So whether a given real engine designed to work under particular sets of conditions will necessarily do better with pure oxygen instead of air is less clear. Probably yes? And for sure an engine designed appropriately for use with pure oxygen would be more efficient than an equivalent one designed for us with air.

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With respect to your question "if a combustion process with air as oxidant can benefit by oxygen enriching the air intake?", the answer is possibly yes, as to quote from Wikipedia on gas mixes associated with the fuel gas hydrogen, as an example:

The flame temperature is high, about 2,000 °C for hydrogen gas in air at atmospheric pressure, and up to 2800 °C when pre-mixed in a 2:1 ratio with pure oxygen (oxyhydrogen). Hydrogen is not used for welding steels and other ferrous materials, because it causes hydrogen embrittlement.

where one could claim that obtaining a higher combustion temperature is likely consistent with achieving an increase in energy efficiency. Note, with respect to 'net' accounting of total energy employed to achieve the elevated temperature, that is likely a technology-specific based answer (see, for example, here) on how, for example, was oxygen concentration achieved.

Interestingly, one can expand beyond the conceptional use of pure oxygen also as noted in this application employing the fuel gas acetylene:

Air/acetylene and nitrous-oxide/acetylene are the gas mixtures used as a fuel source in Flame Atomic Absorption (FLAA).

where NH3/air/catalyst is a possible path to NO (as derived from air). With respect to FLAA, it has been described, per a reference, as:

Flame Atomic Absorption is a very common technique for detecting metals present in samples. The technique is based on the principle that ground state metals absorb light at a specific wavelength. Metal ions in a solution are converted to atomic state by means of a flame.

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  • $\begingroup$ Note that pure oxygen is used in iron production, as net energy gain is positive, More energy is saved than spent by oxygen separation. $\endgroup$ – Poutnik Jun 28 at 7:26
  • $\begingroup$ Poutnik: Thanks for your cited example, as my 'net' energy accounting qualification may imply that any positive net energy gain cases may not actually exist in practice. $\endgroup$ – AJKOER Jun 28 at 20:32

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