Why Most of the Energy Leaves as Heat

Why this matters

An air compressor is, from the building's point of view, a large electric heater that happens to produce some compressed air on the side. That is not a figure of speech and it is not an efficiency complaint. It is an energy balance: the electricity goes in, the air leaves at roughly the temperature it came in at, so almost everything that went in has to leave as heat. Most plants throw that heat out through a louvre and then run a separate heater in the next room.

The reason this gets missed is that nobody ever writes the balance down. So this article is a sheet with fields on it, and the worked example is the sheet filled in.

The balance that has to close

Over a period of steady running, energy into the package equals energy out of it. Energy in is the electrical input. Energy out has four routes:

1. Heat carried away by whatever cools the package. Cooling air through the enclosure on an air-cooled machine, cooling water on a water-cooled one.
2. Heat radiated and convected off the package skin and the motor into the room.
3. Heat carried out in the compressed air itself, which is whatever the aftercooler did not remove.
4. Energy stored in the air as pressure, which is the only part that is not heat.

Route 4 is the point of the machine and it is the smallest term on the sheet. The compression work that raised the air's temperature is recovered as heat in routes 1 and 3 when that air is cooled back down, which happens in the aftercooler before the air ever leaves the room. What survives to the plant is the pressure, and the pressure energy is small next to the input.

The article on what a compressor is actually doing to the air derives why the temperature rise is so large. This one takes that as given and follows the heat.

The artifact: an air-room energy balance sheet

Nine fields. Fill every one, note whether it was measured or taken from documentation, and check the closure at the bottom.

The sheet only means anything if the machine is in one steady state for the whole set of readings. A machine cycling between loaded and unloaded gives you an average of two different balances and a closure you cannot interpret.

Error basis before any of it is multiplied

Two numbers on this sheet carry error, they carry it on different bases, and they are different kinds of error. Get this wrong and you will report a closure to three significant figures that is worth one.

The temperature rise. Each probe carries a fixed accuracy in degrees from its own data sheet, a fixed count rather than a percent of reading, so it does not shrink as the rise shrinks. Two probes are two independent random spreads, and independent spreads combine in quadrature: two equal terms give the square root of two times one of them, not twice one of them. If you instead use one probe and move it between the two points, its fixed offset cancels in the subtraction entirely and what remains is its repeatability, which is smaller. That is the better method when the process is steady enough to allow it.

The cooling flow. A fan flow off a package data sheet is a percent of reading, and it is a manufacturer's bound, not a spread. Bounds add linearly to whatever they are combined with, and the result is reported as a range, never as a plus-or-minus.

The filled-in sheet

An air-cooled oil-injected rotary screw, running steady and loaded, in a room at 78 F.

• Electrical input, from the controller: 39.5 kW. At 3,412 Btu/h per kW that is 134,800 Btu/h.
• Operating state: loaded, steady, for the full 20 minutes of readings.
• Cooling air flow, from the package data sheet: 1,750 cfm at the enclosure discharge.
• Cooling air inlet: 78 F. Cooling air outlet: 138 F. Rise: 60 F.
• Heat in the cooling stream: 1.08 x 1,750 x 60 = 113,400 Btu/h.
• Aftercooler outlet air: 96 F, which is 18 F above the room.
• Closure: 113,400 / 134,800 = 84.1 percent.

The 1.08 in that line is the sensible-heat constant for standard air at 0.075 lb per cubic foot with a specific heat near 0.24, at sea level. It is not a universal constant. At 6,000 feet the density is roughly a fifth lower and so is the constant, and using 1.08 there overstates the heat by about that much.

Now the bound. The rise of 60 F carries two probes at plus or minus 0.9 F each, independent, so in quadrature that is 0.9 times the square root of two, about 1.3 F, which is 2.1 percent of the 60 F difference. The 1,750 cfm carries the data sheet's plus or minus 10 percent of reading as a bound. Combining a bound with a spread gives a bound: the closure lies roughly between 74 and 94 percent, and it is reported that way.

That range is the honest answer and it is still enough to decide something. It cannot distinguish 84 from 90, so do not build an argument that needs the difference. It comfortably excludes any conclusion in which most of the input is not heat, which is the conclusion that matters.

The remaining 21,400 Btu/h, which is 15.9 percent of input at the central estimate, leaves by the other three routes: off the package skin and the motor into the room, out in the compressed air at 18 F above ambient, and as the pressure energy that is the reason the machine exists. All three land somewhere, and the first two land in the same building.

What the recovered heat is actually good for

Grade decides the use, and this heat is low grade. A 138 F air stream is useful for space heating in a shop, warehouse or wash bay during the heating season, delivered by ducting the enclosure discharge where the package documentation permits it. It is not useful for anything that needs a high temperature.

On an oil-injected screw the oil circuit runs hotter than the enclosure discharge, and a heat exchanger in that circuit is the route to preheating water. The available temperature, the allowable oil temperature drop and the exchanger arrangement come off the package's own documentation, because taking too much heat out of the oil circuit drives the airend below its condensation limit and puts water in the sump.

The seasonal condition is the whole argument. Ducted heat is worth having when the building is being heated and is a load when it is not, so the duct needs a diverting damper to outdoors and somebody who moves it. A recovery scheme with no summer path does not save heating in winter, it adds cooling in summer.

The hazard your own instruction creates

Ducting the cooling discharge changes the machine's cooling. Every air-cooled package publishes a maximum external static pressure its fan can work against, and a duct that exceeds it reduces cooling flow, raises internal temperature and eventually trips the machine on high temperature or cooks the oil. Size the duct to that published figure and no further, and never fit a screen or filter to the discharge that is not in the manufacturer's scope.

The second-order version is worse because it has no alarm. Heat dumped into the room the compressor breathes raises the intake temperature. A hotter intake means less dense air, so the machine delivers fewer scfm from the same displacement, and each pound of air costs more work because compression work scales with the inlet absolute temperature. The recovery scheme then charges you for the heat it gave you. Duct the discharge out of the room or duct the intake in from outside; do not recirculate.

How to verify you got this right

Repeat the sheet on a cold morning and a hot afternoon in the same week, with the machine in the same loaded steady state both times. The electrical input should barely move. The cooling stream inlet and outlet should both move with the room, and the rise should stay close to constant, because the rise is set by the heat and the flow, not by the ambient. If the rise changed materially between the two sets, either the machine was not in the same state or the flow is not what the data sheet says, and the flow is the field to go after.

Taking these readings. All nine fields come from a display, a probe in an air stream, or an anemometer at a discharge grille, with the package closed. Keep the anemometer and your hands out of the fan path and clear of belt and coupling guards, and never take a reading with a guard removed. Discharge piping, the separator body and the oil cooler burn on contact, so use a non-contact instrument on surfaces and keep sleeves and leads off bare pipe. Read electrical input from the controller rather than a clamp: putting a meter on energized conductors inside a panel is energized work for a qualified person with the arc-rated protection the employer's electrical safety programme assigns under NFPA 70E-2021 in the edition adopted, permitted under 29 CFR 1910.333(b)(2). If any part of the sheet requires opening a pressurised component, stop the machine, isolate and lock its energy sources under 29 CFR 1910.147, vent the sump and receiver, and confirm zero on a gauge before a fastener moves.

References

• 29 CFR 1910.147, control of hazardous energy, for isolation and stored-energy release before opening a package
• 29 CFR 1910.333(b)(2), energized electrical work practices, with NFPA 70E-2021 in the edition and form the employer has adopted
• US Department of Energy, Improving Compressed Air System Performance: A Sourcebook for Industry, for compressor heat recovery as a share of input
• Package manufacturer documentation for maximum external static pressure on cooling discharge ducting and for allowable oil-circuit heat extraction
• See related: What a Compressor Is Actually Doing to the Air; What a Compressed Air System Actually Costs to Run