Compressed Air Storage Calculations

Calculations for a 1kWhr System

• From Compressed Air Energy Storage results, it takes 170 cubic meters of air to deliver 1kWhr of usable stored energy.

Calculator

See https://www.tribology-abc.com/abc/thermodynamics.htm

According to the calculator, a 50 l tank of air at 3000 psi will release about 0.5kWhr via adiabatic expansion, and 2.5x this with isothermal expansion.

Rough Calculations

• Air tools require 30 cfm for 1 hp [1]
• A 300 cuf tank thus gives 10 minutes, about, of 1 hp power. With radial piston motor - at 10-20 the efficiency, easily gives 1 hp hr. Let's get specifics.
• 6 cylinders would thus give 1 hp hr. Not great, but we can get much better efficiencies from a better air engine.

Air Engine

• Rotary air engine - [2]
• 0,75 hp $200 30 cfm [3]
• Rotary vane, 1.8 hp $200 [4]
• Radial Piston Motor - 20x more efficient at full load than rotary! [5]
• Radial vs axial piston motors - [6]
• Data curve - 25 cu ft/min for 0.8 hp at 100 psi [7]. Thus, 12 minutes on 1 tank of 300 cu ft. Get 5 tanks for 1 hp hr, at cost of $1500. The good part is that the metal tanks will last for ever.

Cylinder Sourcing

• Firefighter supply - 300 cf $300 [8]
• 250 cf - $285 [9]
• 250 cf = $330 [10] K size?
• T-size 300 cf - [11]
• T goes up to 390 cf - [12]

Compressor

• Scuba compressor - $243, 1800W - [13]

Technical

• Compressed Air Index - [14]
• Energy stored in a cubic meter of volume at 70 bar is 6.3 kWhr. [15]. Compare to 300 cu ft - which correcponds to 42l volume inside - 0.04 cu meter - but equiv to 0.1 of the above if done at 200 bar - then energy stored in the gas cylinder is 0.6 kWhr. And before, we said we have 12 minutes of 0.75 kW. Yes, figures match assuming around 20% efficiency of air motor.
• One k type cylinder, 50 l volume, gives 5300 kJ or 1.4kWhr of stored energy under isothermal expansion. Thus, Wikipedia [16] checks with online calculator [17].

3D Printed

• Diaphragm air-tight engine seems to work reasonably well [18]

• Tech used: diaphragm and bump valve without spring. Diaphragm acts as spring.
• 5x bigger version - [19]

Efficiencies

• Piston engine - 13% at 5 bar [20]
• 50 Whr/l at 300 bar [21]
• This with 50 kwHr/cubic meter. Does not match 6.4 kwhr at 70 bar [22]? Possibly, though simple multiplication yields 25 kWhr/cu m.
• Harmonic motor 60% efficient? [23]. You can license it form LLN, where you can Pay for the Results Twice.

Air Drill

• 1 hp - [24]. 30 CFM at 1 hp [25]
• 0.5 hp - [26]. 19 cfm. [27]

Vane vs Piston

• Vane motors have shorter life and less efficiency than piston motors - [28]

Specific Cases of Motor Power

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Low Velocity Air Motors

• Ex [29] - any rpm, any power from low to high
• 100W example - 10 cfm on page 4. [30]
• This is hugely inefficient, as 30 CFM gets you 1 hp, or 3.5 cfm for 100W from piston motors.
• But,

About Standard Vane Motors

• See [31]
• 2000 hour life of lubricated, 1000 for unlubed motors
• Note piston motors last longer.
• Hard to find efficiency of vane motor
• Turbines are 75% efficient. [32]

Turbines

• 75-95% motorbike turbine efficiency - [33]
• 3000 RPM! How?

Links

• Compressed Air Energy Storage
• Low Tech Magazine on Compressed Air Storage
• Gas Cylinders.
• Radial Piston Motor