Since oxygen is active reactor with H2S , is there a way that we can enhance the reaction? What is the condition if reaction needed? Like flow or pressure in order to get red of H2S ?
Fire works nicely. Some convert the H2S in the air to SO2 first, then absorb it. Instead of a sodium sulphide disposal problem, they can end up with saleable sodium sulphite solution if they do it right.
In alkaline water solution though, the reaction with dissolved oxygen is slow, and the saturation pressure of oxygen is low. Pressure and temperature both help, but also cost money (capital and operating). Materials selection gets harder and more expensive as temperature and pressure increase.
Peroxide and ozone also both work. So does bleach. All at room temperature and atmospheric pressure, without the materials concerns (if you use nonmetallics in your scrubber). But again, those oxidants cost more money than compressed air. So it's all a balance.
In biogas plants, H2S is biologically oxidized to H2SO4 and elementary sulphur, by blowing small amounts of air into the fermenters. H2S < 200ppm are achievable, some plants manage <1 ppm
The bacteria are ubiquitous but need surfaces for habitation and nutrients. Biofilters should work.
In the biogas field, biological desulph by blowing a small amount of air into the tanks is industry standard. At least 2 out 3 of Germanys 7000 biogas plants use this system, and almost all plants my employer has built. The bacteria are ubiquitous, they grow everywhere. The biological process and feedstock provides nutrients for the bacteria.
Providing ample moisture, oxygen nutrients and a surface for the bacteria to dwell on will greatly reduce your H2S but will not guarantee a treshold.
Another solution is to have a packed column and a aquauos solution of the nutrients the bacteria need taht is circulated over the column. TS Umweltanlagenbau in Germany and DMT technologies in the Netherlands offer such systems.
However, since I don't know your appliocation and the amounts of H2S I can't really tell if a biological system is appropriate - since you wrote "... removal from air" I assumed oxygen to be present.