According to

this site,

hydrogen has 50,000 Btu's per pound whereas Brown's gas has about 66,000 Btus per pound. So, that means it would (presumably) be 32% more energetic

(66 000 - 50 000 = 16 000 / 50 000 = 0,32 x 100 = 32 )

If so, than it would have 0,00396 kWh/l

(0,003 kWh for hydrogen x 1,32 = 0,00396 )

The same site also mentioned that you could generate 340 litres of Brown's gas (13.6 cu. ft.) per kilowatt-hour. If so, than the amount of energy you could generate per 1 kWh battery would be 1,3464 kWh

(340l x 0,00396 kWh/l) so that would be even more energy than the energy in the battery itself.

This doesn't seem right. I guess there are probably some incorrect figures here, so let's calculate it out another way.

At wikipedia we read at the Brown's gas page:

"Theoretically, a ratio of 2:1 hydrogen/oxygen is enough to achieve maximum efficiency; in practice a ratio 4:1 or 5:1 is needed to avoid an oxidizing flame."

So if we consider that oxygen does not add any energy, and only the hydrogen in the HHO adds energy, then HHO could be

- 50% less energetic then hydrogen (2:1 H2-02 ratio)

- 25% or 20% less energetic then hydrogen (4:1 or 5:1 H2-02 ratio)

Depending on this, it could have:

- 0,0015 kWh/l

(0,003 kWh for hydrogen x 0,5 = 0,0015 )

- 0,00225 kWh/l or 0,0024 kWh/l

(0,003 x 0,75 = 00225 ; 0,003 x 0,8 = 0,0024 )

Regarding the amount of energy you could generate with it:

I could not find any data on the efficiency of HHO electrolysers, but there is

data of the efficiency of hydrogen electrolysers (which granted, work at a different way). But still, it gives an idea. Anyway, PEM electrolysers are 94% efficient, alkaline electrolysers are 43-67% efficient. So let's say the HHo electrolysers are 50% efficient. Then how much liter of gas could they generate ?

Calculation:

A 1 kWh battery could then generate 0,5 kWh on HHO gas.

The HHO gas has an energy of (and now we use a range of found data above): 0,00396 kWh/l or 0,0015 kWh/l or 0,00225 kWh/l or 0,0024 kWh/l

So:

0,5 kWh /0,00396 kWh/l = 126 liter

0,5 kWh /0,0015 kWh/l = 333 liter

0,5 kWh /0,00225 kWh/l = 222 liter

0,5 kWh /0,0024 kWh/l = 208 liter