I sympathize with your having to do a noise abatement project, having been assigned a few myself over the years. This is driven by OSHA regulations in the USA which require employers to implement engineering controls rather than just administrative controls (earplugs, access control, etc) where-ever practical. Basically you just need to:
1.) Take a plot plan and do a noise survey around the unit to find the highest noise sources. These you attack first because 100dBA + 80dBA = 100dBA. For a "point source" sound falls off with an inverse square relation so if you are reading 100dBA for a source at 10ft, it will contribute to the noise everywhere in that unit. If the noise is coming from a pipe (line source), then the noise is carried by the pipe from the point of generation (such as a control valve).
2.) Decide on a fix for the main contributors starting with the noisiest. For each source you have two basic options: source mitigation or path mitigation.
3.) Source mitigation is elimination of noise generation at the source, and is generally best where applicable. This includes replacing noisy equipment with a quiter design, using staged pressure drops for aerodynamic noise (in pipes and vents to the air), eliminating cavitation (hydrodynamic noise), etc.
4.) Path mitigation is the use of accoustical lagging, doors/walls/screens, or strategically locating equipment to block noise before it gets to the ear. For fans and other rotating equipment it is always best to consider noise in the original installation (i.e. use induced draft finfans, lower speed equipment, etc). After the fact mitigation is usually done by putting lagging on the equipment or walls around it.
The good news is that a few fixes can often make a lot of difference. You usually don't even realize how noisy something was until you visit that area after mitigation- it feels strangly quieter than you were used to.
Best of luck- sshep