Compressed Air Storage Calculations
Contents
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
Vane vs Piston
- Vane motors have shorter life and less efficiency than piston motors - [29]
Specific Cases of Motor Power
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
