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.
  • This is an inefficient adiabatic system - could be much better if we use isothermal process

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. Thus: a system where we heat the air for an air engine (heat added to keep it isothermal) - 1.5kWhr is the available energy. A 33% effcient air engine gets us 500Whr. This is not bad, worth pursuing. Essentially: 1/2kWhr of storage for a $300 tank cost. This paper shows 70% efficient engines. [1] - implying that we can get 1kWhr power output from a single cylinder of high pressure air.

Rough Calculations

• Air tools require 30 cfm for 1 hp [2]
• 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 - [3]
• 0,75 hp $200 30 cfm [4]
• Rotary vane, 1.8 hp $200 [5]
• Radial Piston Motor - 20x more efficient at full load than rotary! [6]
• Radial vs axial piston motors - [7]
• Data curve - 25 cu ft/min for 0.8 hp at 100 psi [8]. 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 [9]
• 250 cf - $285 [10]
• 250 cf = $330 [11] K size?
• T-size 300 cf - [12]
• T goes up to 390 cf - [13]

Compressor

• Scuba compressor - $243, 1800W - [14]

Technical

• Compressed Air Index - [15]
• Energy stored in a cubic meter of volume at 70 bar is 6.3 kWhr. [16]. 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 [17] checks with online calculator [18].

3D Printed

• Diaphragm air-tight engine seems to work reasonably well [19]

• Tech used: diaphragm and bump valve without spring. Diaphragm acts as spring.
• 5x bigger version - [20]

Efficiencies

• Piston engine - 13% at 5 bar [21]
• 50 Whr/l at 300 bar [22]
• This with 50 kwHr/cubic meter. Does not match 6.4 kwhr at 70 bar [23]? Possibly, though simple multiplication yields 25 kWhr/cu m.
• Harmonic motor 60% efficient? [24]. You can license it form LLN, where you can Pay for the Results Twice.

Air Drill

• 1 hp - [25]. 30 CFM at 1 hp [26]
• 0.5 hp - [27]. 19 cfm. [28]

Vane vs Piston

• Vane motors have shorter life and less efficiency than piston motors - [29]

Specific Cases of Motor Power

edit

Low Velocity Air Motors

• Ex [30] - any rpm, any power from low to high
• 100W example - 10 cfm on page 4. [31]
• 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 [32]
• 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. [33]

Turbines

• 75-95% motorbike turbine efficiency - [34] ? No, paper seems bogus. The high percentage is the closeness to which reality matches theory, but the actual efficiency is unstated. This is describing a vane type motor, with likelu 30% efficiencies.
• Smaller turbines in industry can be geared down - [35]
• See 3D Printed Rotary Tool

Links

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