Old calculations

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(1) LPG has a typical specific calorific value of 46.1 MJ/kg or 12.8kWh, but the usable energy is not that; for instance, a heating appliance might be 80-90% efficient, while an internal combustion engine might only be 20-30% efficient. If we ASSUME that the conversion efficiency for H2 combustion is similar, then it is ok to use 46.1MH/kg. (2) Density of LPG is typically between 500 to 580 kg/m³ when stored under moderate pressure to keep it in liquid form. Let’s take 540g/L (average)

(3) Liquid LPG is much more dense than liquid hydrogen, hence even though the energy density of hydrogen is bigger than LPG, for the same volume, liquid LPG stores slightly more energy. The density of liquid hydrogen is 70.85 g/L, while the energy density of liquid hydrogen is 120MJ/kg or 33.33kWh/kg (4) 1 kg of hydrogen gas occupies a volume of approximately 11,207 liters at STP. So in 6L there is a mass of hydrogen = 6L/11207L*1kg = 0.535g

  • Hydrogen has nearly three times the energy content of gasoline—120 MJ/kg for hydrogen versus 44 MJ/kg for gasoline. On a volume basis, however, the situation is reversed; liquid hydrogen has a density of 8 MJ/L whereas gasoline has a density of 32 MJ/L, as shown in the figure comparing energy densities of fuels based on lower heating values. Onboard hydrogen storage capacities of 5–13 kg hydrogen will be required to meet the driving range for the full range of light-duty vehicle platforms (from here)

MASS of H2 in the 6L canister at this pressure and ambient temperature

Avagadro's Law:

Note: the volume of 1 mole of any ideal gas at STP (Standard Temperature and Pressure = 0 °C, 1 atm) is 22.41 L/mol at STP. 

The volume of 1 mole of any (ideal) gas = 22.4 liters. 
Mass of 1 mole hydrogen gas (H2) = 2 grams, so the mass of 22.4 liters (stp) is 2 g.
One litre of hydrogen under standard conditions weighs: 2/22.4 =  0.0896 g 
If pressure multiplies by 2.4 (car tire), this just means 0.0896*2.4 = 0.215g per litre, and in 6L it’s just six times that:
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Mass of compressed H2 in a 6L canister is about 1.26 grams (at 1bar) At 17.5 bars (typical LPG canister) this means: 1.26/2.4*17.5 = 9 grams (17.5bars)

VOLUME in the ballon (before compression):

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The volume (V2) of H2 that needs to be produced by electrolysis and at sea level (before compression) is:

P1.V1 = P2.V2 ⇒ V2 = 2.4atm * 6L / 1atm = 2.6*6 = 15.6 L

STORED ENERGY:

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Since the heat value of H2 (per kg) is about 140MJ/kg, the stored energy would be: 140MJ/1000*1.26 = 0.176MJ or 0.053kWh (1MJ is 0.277778 kWh)

Since a 3KG LPG canister stores 50.7MJ, this means the equivalent of ONE LPG canister in compressed (2.4bars) H2 canisters is:

  • 50.7MJ / 0.176MJ = 288 canisters filled with gaseous H2 (of 6L and at tire pressure)
  • Or equivalent volume at ambient temperature and sea level of: 288*15L = 4320L
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1 LPG canister At 2.4 bars: ↔ 288 H2 manually compressed canisters, or about 4 cubic meters of H2 at ambient temperature At 17.5 bars:

Note: A volume of around 11 m3 (which is the volume of the trunk of a large utility or commercial vehicle) is needed to store just 1 kg of hydrogen, which is the quantity needed to drive 100 km.

Enapter_Datasheet_EL40_EN.pdf1215.8KB
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B) STORAGE (at ambient temperature):

Ambient pressure:

  • 1kg of H2 occupies 11m3. Therefore we would need 1.45 x 11m3 = 16 m3 or 16000L to store all the hydrogen for a month in STP. This is a cube of 2.22meters side! not that large (lipo batteries are also big, and need refrigeration)
  • Number of tire-pressurized (3.2 bar) H2 canister (6L): 16000/6/3.2 = 888 standard green canisters per month
  • Green balloons (75cm diameter) have a volume of V = 4/3 π r³ = 4/3*3.1415*(0.75/2)^3 = 0.22 m3 or 220 liters. That means we would need 16000/220 = 72 balloons.
  • Per day, in balloons: 72/30 = 2.4 balloons (220*2.4 = 528L)
  • At 35 bars, this is a volume of 528/35 = 15L
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Pressurized:

  • Scuba diving tanks: If we use a big diving tank (18L, 300 bar) instead, we need 16000/18/300 = 3 tanks. Of course this needs a compressor. How much energy for that? (to do, assuming adiabatic compression). The compressor could be powered by a battery charged all day by excess solar energy or human powered - bicycles/gym)
  • The commercial electrolysis EL 4.0 (this) already produces H2 already at 35bars. Scuba tanks sustain this pressure without problem. Using 10L tanks e can store the energy for a month in 16000/10/35 = 17 tanks.

Notes:

  • Cylinders used for scuba typically have an internal volume (known as water capacity) of between 3 and 18 litres (0.11 and 0.64 cu ft) and a maximum working pressure rating from 184 to 300 bars (2,670 to 4,350 psi).

C) And what about producing just for day consumption without the need of storage?

  • 21 balloons per month means less than one balloon per day / household (exactly 21/30 = 0.7 balloons). This means that much less efficient electrolysers can be used (DIY?), but more importantly, that pressurized hydrogen is not needed at all. If the production of H2 is faster, then that excess can be compressed.