In discussing adiabatic efficiency, it is best to first define efficiency. In its broadest terms, efficiency can be defined as the ratio of work output to work input normally expressed as a percentage. With regard to a compression application, one measure of the efficiency of a compressor is the adaibatic efficiency (Volumetric Efficiency being the other). Adiabatic Efficiency is the ratio of the amount of horsepower required just to compress a particular gas (Adiabatic Horsepower) divided by the total brake horsepower required for a praticular type of compressor to accomplish the desired compression. Note that Adiabatic Power is the same regardless of the type of compressor used because it is a function of the physical properties of the gas being compressed, and not the type of compressor doing the work. In other words, it takes a specifc amount of energy to compress a specific volume of gas to a particular pressure and this energy is the same no matter what technology you use to accomplish the compression. Adiabatic HP is the numerator of the equation and is the same no matter what kind of compressor is used.
The denominator of the equation is total brake horsepower (BHP) and it is the total power required for a compressor to accomplish the desirder compression. This will be a larger number as BHP includes adiabatic power plus all the other energy required by the compressor to overcome other losses requiring energy such as drive losses, mechanical friction losses, intake/discharge valve losses, heat exchanger losses, lubrication system power, etc.
Therefore, to answer the question specifically would require information on the specific gas being compressed, flow, pressure, atmospheric conditions, etc. To answer the question in general terms, the rotary vane type compressor will typically have a higher adiabatic efficiency than screw compressors and reciprocating compressors by virtue of the fact that other losses from friction, lube systems, valves, etc. which tend to be significant with screws and recips are not substantial and sometimes not present at all with vane technology. As such, vane compressor total BHP is normally lower than other technologies resulting in higher adiabatic efficiency. Another reason vane machines often have higher adiabatic efficiency is that they are limited to a maximum compression ratio of approximately 4.5 to 1, (depending on the type of gas and the application requirements). As is documented in Marks' Standard Handbook for Mechanical Engineering, as compression ratio increases, both adiabatic efficiency and volumetric efficiency decrease on screws and recips. Therefore, for discharge pressures up to approximately 125 psig, the vane technology, even in a two stage system, will likely be more energy efficient than other compression technologies.
The above is a broad answer to a specific question and the degree to which the efficiency is greater (or not) will vary with the specifics of the application. Adiabatic efficiency is however, a good measure of efficiency and a good indicator of how energy efficient equipment will be once in operation. All the compression technologies mentioned are viable and proven and some are better suited than others depending upon the specifics of the application. For example, as noted above, the vane machine is well suited for relatively high flows and for compression up to about 125 psig. For processes requiring compression above 125 psig discharge pressure, the vane technology is not suitable and screws or recips are likely the more appropriate technologies. Finally, in addition to power cost, buyers should also other factors that impact the cost of ownership such as parts, service, and maintenance requirments when considering compression equipment.
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