# POLYTROPIC EFFICIENCY EXPLAINED

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Recently, while attending a conference,I was asked by an audience member, “What is polytropic compression?”It’s not an easy concept but I tried as best as I could to explain that it is a reversible (thus ideal) process which involves both heat and work transfer. Specifically, for polytropic compression processes, one divides the thermodynamic path from suction to discharge pressure and temperature into an infinite number of steps with each of these steps having the same (polytropic) efficiency.

That’s why polytropic efficiency is also sometimes called small-step efficiency.Each polytropic step includes an equal infinitesimally small heat exchange to compensate for temperature increase due to entropy. For example, viscous losses(aka irreversible) in the real compression process are compensated using heat reduction,such that the efficiency for each step remains the same. Importantly, both the isentropic and the polytropic process are ideal processes, and as such reversible.That’s a rather esoteric explanation with little real world meaning.

What does this actually do for me? It’s complex and completely meaningless from a physical perspective. I am yet looking for an engineer in our industry who can properly explain what a “physical” polytropic efficiency actually is. As young engineers many years ago,we mostly used the isentropic compression process as reference, primarily because most of the textbooks use it.

Once I entered the oil and gas industry, I realized that most compressor manufacturers actually did use polytropic efficiency, and because nobody wanted to numerically divide the process into an infinite number of steps, approximate methods for efficiency determination are used.

Isentropic efficiency is seldom mentioned in our industry and the next editions of industry compressor test codes and compressor standards will likely not even include isentropic efficiency. On the other hand, isentropic efficiency is incredibly simple. An isentropic compression process directly relates the amount of energy of compression, such that efficiency is proportional to power required by the compressor.

For example, if the compressor loses3% in isentropic efficiency, the power required by the compressor is 3% higher. It’s that simple. Even the thermodynamic definition of isentropic efficiency is relatively simple: It’s the ratio of the enthalpy (energy per unit mass) difference between an ideal isentropic (no entropy change) versus an actual process.

On the other hand, polytropic efficiency relates to compressor power required via a complex algebraic equation for ideal gases and an iterative process for non-ideal gases.If the polytropic efficiency of a compressor drops by 3%, I have no idea how that affects the compressor power.From a thermodynamic process perspective,the isentropic process is more intuitive, easier to understand, and logical.

Isentropic efficiency relates actual compression with an ideal compression that does not exchange heat with the environment,(adiabatic) and does not create any losses (no viscosity and reversible). Adiabatic and reversible means it is isentropic. Therefore, the isentropic process is the adiabatic process that does the compression with the least amount of work possible.

For aerodynamic comparisons, polytropic head and efficiency appear to have some advantage, at least theoretically. Specifically,in a performance test where the gas used is different from the gas at site,one wants to create a situation where the velocity polygons in all stages are the same for test and site.This can be accomplished if, as a minimum,the actual flow divided by the running speed, the ratio between inlet and discharge flow and some characteristic Mach number are the same.

However, the only way to retain similarity of the velocity polygons is by having exactly the same actual work (divided by the square of the speed) done by each component, and neither the isentropic, nor the polytropic work assure that.

Polytropic work is helpful because it preserves the discharge temperature of the overall compressor and the inlet and exit gas conditions are maintained. However, the polytropic path assumes constant efficiency along the entire compression path while in an actual compressor, each stage, and each sub-component, has a different efficiency.

On the other hand, when we look at the process from the perspective of the people who buy these compressors, polytropic work is irrelevant. For a compression process,we typically define the inlet conditions,and the desired discharge pressure.This is fully defined by the isentropic work, but not by the polytropic work. Yes, polytropic work will provide the actual discharge temperature, but the polytropic work is, like the isentropic work, not equal to the actual work.

Fundamentally the only real value that polytropic efficiency provides is for the compressor designer. Specifically, when quantitatively comparing the aerodynamic performance of multistage compressors it is nice to not have to normalize efficiencies back to an average stage performance or to actually have to compare stage-by-stage performance.

From a holistic compressor performance perspective, especially from the point of view of how much power a compressor driver needs to provide and how much energy will be expended compressing the gas, polytropic efficiency is mostly useless. So why do compressor designers prefer polytropic over isentropic? Polytropic efficiency is always higher than isentropic efficiency and makes their compressors look better. And, yes, it allows comparing the aerodynamic quality of a compressor that has a pressure ratio of 10 for some process,with another compressor, for another process with a pressure ratio of 4.

However, once I compare two compressors for the same process conditions, all I care about is how much power they consume. f course, it’s much nicer to discuss an 85% efficient high-pressure ratio compressor than revealing that the compressor is only 75% energy efficient and 25% is lost to heat generation. The higher the compression ratio the compressor has, the higher the difference between isentropic and polytropic efficiency, and polytropic will always be higher.