At first glance, this equation can seem daunting, but if we just take it one component at a time, it becomes much simpler:

 The first variable we see is “m”, which in our case represents the mass of gasses mixed up inside the pressure vessel. Increasing or decreasing the gas molecules stuffed inside the tank means the more or less work we’ll be able to do as that mass expands through the tool and back into the atmosphere. So, we will multiply the mass of the air by every other component in the equation. 

The second term represents the “internal energy” of the gas, both inside the pressure tank (u_t) and also what it will be once expanded back to the ambient environment (u_a). We’ll be coming back to this one, but for now know that internal energy is a function of gas temperature. We’ll assume isothermal expansion, which I know is only a tad unrealistic, and that our system is like most systems out there with the temperature of the air in the receiver being the same as the temperature outside. With our assumptions, the subtraction of one from the other will bring this entire component of the equation to zero.

The third term represents the “mechanical work” energy available based on the compressed air pressure and the volume occupied both before and after expansion. This component of the equation is what we’re mainly after. Here, we’ll do an algebraic modification by using the ideal gas law (PV=nRT) and definition of mass (m=nM) with ‘air’ as our gas mixture while also reducing the expression since we’ve noted that the temperatures both inside and outside the pressure tank are the same. 

The fourth term represents the loss of energy available associated with thermal disorder as it relates to the thermodynamic principle of “entropy”. Note that this term’s value is subtracted from the overall total energy available. We’ll substitute the form of the change in entropy equation for an ideal gas using pressure and temperature, again the latter of which both values are equal.

The final two terms represent the kinetic and potential energy of the mass in the system. Since we have defined the problem as a static pressure tank holding air at rest, we have no air movement and therefore its velocity is zero. Similarly, there is a negligible change in elevation if expanding air from inside the tank back to atmosphere so z_t can also be assumed to be zero.

Finally, we have a simplified equation to calculate the available work energy in our commonly sized pressure tank. With the ideal gas law, we find the mass of air inside the pressure vessel at the specified conditions and then find our absolute maximum available work energy (Exergy,x_t = 9.06 megajoules), based on ideal conditions and assumptions, stored and ready to be released.

Determining Energy Usage

Now that we understand the maximum energy value of the compressed air to do mechanical work, let’s determine how much energy it took to get the air in that pressure vessel.  Assume that we have installed an air compressor system which would be typical of being paired with the 2,560 gallon air receiver. We select a Rogers K-150-100, a nominal 150 horsepower lubricant injected rotary screw air compressor, with coalescing filter and refrigerated air dryer.

From our calculation above, we already know that the total mass of the air in the tank when it is at pressure is just over 200 pounds, so we’ll use a mass equivalence method to determine how long our air compressor would have to run to fill the tank with this much mass.  Subtracting out the mass already in the vessel while resting at atmospheric pressure, 25.7 pounds of air, we know that we need to add 174.7 pounds of air into the tank.  

Our K-150-100 has a volumetric pumping capacity of 784 ACFM when operating at 100 PSIG.  Because we assume our compressor is optimally located at sea level and standard inlet conditions, the volumetric flow rate here defines the mass flow rate of 784 SCFM, which itself is equivalent to 58.8 pounds of air pushed through the compressor per minute.  Simple division means we’ll need our compressed air system to run for just under 3 minutes to move enough air mass into the system to charge the pressure vessel to the stored mass calculated above.

Not often discussed in detail, but well understood by compressed air professionals industry wide, it is commonplace that air compressor motors run into their service factors by design.  You’ll find some manufacturers out there with 1.25 or even 1.35 service factor motors, the latter of which would allow for a nameplated 75 horsepower motor to turn a shaft requiring 101 brake horsepower, for example.  This particular game we all tend to play, some to more of an extreme than others, allows for higher advertised flow rates relative to lower published nominal power requirements.

At design load, the K-150-100 runs 8.8% into its service factor and includes a 95.8% efficient electric motor.  We need a little power for controls and some extra juice to run the cooling fan, an additional 5 HP, 86.5% efficient motor.  Additionally, we need to power the refrigerated air dryer, selected model being a Zeks 800HSG, which will require an additional 4.8 kW.  All totaled, the compressed air system in this configuration demands 136.5 kW.

Running this air system for the 178.2 seconds it will take to fill the air receiver; we can easily calculate that it will take 24.32 megajoules of electric energy input to have at the ready the maximum available work exergy of 9.06 MJ held in the pressurized air.  Dividing exergy output by energy input, we can see that the absolute maximum theoretical power conversion of this typical compressed air system is something a little over 37% efficient.  

Because of additional supply, transmission and demand losses at every phase of the air’s molecular journey through your production facility and the demanding tool, the actual power efficiency values realized are often much less, possibly even half or less at around 18 to 25% efficient.  

So where did all the rest of that energy go?  The main, best answer to this question is, of course, “to heat.”  

RELATED: 8 WAYS TO INCREASE THE ENERGY EFFICIENCY OF YOUR COMPRESSED AIR SYSTEM

Capturing Heat Lost in the Compression Process

Viewed from a thermodynamic perspective, an air compressor room should really be thought of as a Heater Room.  Even though the heating efficiency of the selected process is a poor 63%, it bests the effective power conversion efficiencies of its compressed air counterpart by more than double.  So, our Heater Room also happens to have a byproduct of compressed air.  

At an energy rate of $0.08 per kwHr, running the K-150-100 compressed air system described above 24/7 will cost over $95,600 a year in energy charges alone.  About $23,000 of that will go to the actual compressed air powering your machinery, while over $60,000 will be spent on generating heat energy.  The remainder is the cost of your being in the utility generation and distribution business, friction losses and the like.

A CoGeneration plant burns raw material inputs in exchange for two process outputs, typically generating electric power and steam for centralized onsite uses.  Take a mental journey through your production facility and imagine the hot water demands being fired by electric or natural gas energy.  Now, imagine the waste heat, over $60,000 of it every year, pouring out of the compressor room’s ducts and wide-open ventilation windows, radiators flush-mounted to the wall to get the heat out and away straight into the atmosphere.  You know that emoji that shows the dollar bills flying away?

Okay, you’re convinced.  But the task seems impossible.  Are we going to run hot glycol/water supply and return lines throughout our facilities alongside the compressed air lines?  Well, maybe?  For greenfield construction when you must run the new air lines anyway, it may absolutely make sense to do exactly that considering the amount of usable energy you receive out of the compressed air stream relative to the over-twice-as-much wasted energy pouring out the window.

Luckily, the very first step is not to re-pipe your building.  Even if you had heat demands at the ready and a distribution system in place, your compressor probably isn’t set up to CoGenerate compressed air and heat.  No, the first step is to pick up the phone, call your compressed air supplier and ask about their options for Dual Cooling.  

A typical lubricated air compressor is cooled by either air OR water, the vast majority by air, but not usually by both.  It is a fairly common option available, though, to add secondary cooling.  Most often, this is done by adding a water-cooled heat exchanger in series downstream of the air-cooled oil-cooler.  Its historical purpose is, in the hot summer months, to augment cooling when the atmospheric air is too warm to keep up with the compressor’s cooling demands.

A thermostatic valve is installed on the water return line and as the temperature probe bathing in the lubricant returning to the air-end heats above its setpoint, that valve opens and cooling water is introduced into the “water-cooled trim-cooler”.  This is a very compressor-centric world view, only considering what the compressor needs to keep spinning while ignoring the needs of the much larger socioeconomic machine of which it is a part.

The next step is the trickiest part to get your CoGen-Aero plant ready to supply energy to its first heat demand.  Ask your supplier to flip around the piping on the arrangement just described and remove the thermostatic water control system altogether.  That’s it. We just want hot lubricant supplied directly from the thermostatic bypass tee into our new exchanger. Not tricky at all.  Even easier than the typical dual-cooling configuration. There will still be a thermostatic control valve in place to maintain proper lubricant temperatures into the air end.

The compressor doesn’t care where the heat goes, only that it goes away.  In fact, if you’ve installed an oil temperature probe and an ASD on your cooling fan motor to help regulate lubricant temperatures, sending all that heat away from the compressor will give you some bonus energy savings at the fan motor when it spins down to adjust for the lower heat load coming in.  

Over at the exchanger, you can even have your supplier leave the water supply and return ports plugged.  After all, this is also how the compressed air outlet arrives on your loading dock, capped for you to connect to as you see fit.  Be sure that the water-cooled exchanger is sized equally to the radiator, each capable of handling the full heat load of the lubricant, and your CoGeneration-Situation is ready.  One compressor supplying two forms of energy which will more than triple the available amount of energy delivered relative to a standard compressor build, all for the cost of a single, properly placed heat exchanger.

You can also recover heat from a two-stage oil-free rotary screw air compressor.  In some ways, the heat available is a bit better quality, what with that compression technology driving higher operating temperatures.  But the simplicity of a single stage absorbing all the heat of compression, widespread popularity and the ROI economics driving a straightforward modification make dual cooling on your next lubricated rotary screw purchase in this manner an obvious choice.  It is a bit of a chicken or an egg scenario.  Do you wait to have a specific heat demand requirement nearby your air compressors before you retrofit the existing machines?  Or do you plant a seed for the future of your facilities’ systemwide power conversion efficiency now with a small capital investment in a unit you’re buying anyway, today.

Next Up — Increasing Air Exergy

One last parting thought in the name of a continued march toward perfect energy conversion and increased compressed air exergy.  Recall our equation and that the Internal Energy (u) component in the exergy calculation is driven by temperature differential, specifically the higher the temperature the air inside the tank, the more energy we have available to do work.  Also recall that we assumed isothermal expansion in our calculations even though real-world work is much more polytropic.  If you’ve gotten this far, you probably can see that these two factors reveal the fact that it would be extra handy if our charge of compressed air were delivered at a higher temperature than ambient.

Turns out there is additional low hanging energy available right in the air stream to just go and grab.  Rogers Machinery Company, in fact, in the 1970’s patented and distributed a “hot lubricant reheater” device with many of its QNW (now known as Rogers K-Series) rotary screw air compressors capitalizing on this very principle.  The refrigerated air dryer had yet to be widely accepted and a side benefit of the reheater was to drive the temperature of the air stream up and away from the pressure dewpoint of the air being delivered to the production floor.  While air dryers have largely solved the problem of condensed moisture contaminating production systems, the core principle of delivering maximum available energy through pressure AND temperature remains.  A quick calculation using reasonable assumptions represent the possibility of an internal energy driven increase from the theoretical maximum 37% to 45% energy conversion efficiency.  Perhaps a hard look at that next time.

For right now, choose to plant a seed by picking up the phone.

Meet the Author

Bryan A. Jensen is a mechanical & aeronautical engineer with over 20 years of application experience in a wide variety of industrial manufacturing processes, focusing on the compressed air & gas industry. Beginning his career as a NASA materials research engineer, he currently heads the Engineered System Solutions team at Rogers.