Hydrogen from Sugar - The Math.

I have mentioned before that the B.B.C. are running a four part series on Radio 4, entitled "Driven by Oil", which is broadcast on Monday mornings at 9.00. Today's programme (part 3) was concerned with the likelihood and consequences of terrorist attacks on oil installations, particularly in the Middle East. In the catastrophic event that the output from Saudi were curtailed, some 9 million barrels per day would be struck from the world market, or around 10%, causing an economic catastrophe. The entire Saudi oil production depends on a single processing plant and two tanker terminals. The tankers themselves are sitting-ducks for a "9/11" type strike at sea. Interestingly, it was pointed out that Houston, which has the second largest oil-refining complex after Rotterdam, would be a highly sensitive target, and a strike there would hurt the entire U.S. I mention this because, in upshot, the message is that it is mandatory to break the dependence of the West on oil, especially as imported from the Middle East.
Of the possible energy sources to run transportation as an alternative to oil, hydrogen is often talked about. As I have stressed before, hydrogen is not a fuel, but an energy carrier, and it needs to be produced from a primary fuel such as natural gas, or by electrolysing water using electricity generated from primary fuels, or when that utopia arrives, renewables. Therefore, the prospect of "bio-hydrogen" is very attractive. In order to check the "math", I have worked out what would be required to substitute for the current 54 million tonnes of oil (equivalent) used annually in the U.K. for transportation, nearly a quarter (12 million tonnes) being used by the aviation industry. One method of producing hydrogen is by fermentation of sugars. In the following I shall work in terms of a general formula C6H12O6 (i.e. a sugar such as glucose), bearing in mind that more complex sugars such as sucrose can be broken down to this simpler form. There are two principal fermentation reactions that occur to produce hydrogen:

(a) C6H12O6 + 2H2O --> 2C2H4O2 + 2CO2 + 4H2
(b) C6H12O6 --> C4H8O2 + 2CO2 + 2H2

1 kg of C6H12O6 = 1000/180 = 5.56 moles, and hence 1 kg of C6H12O6 reacting by step (a) yields 5.56 x 4 x 22.5 = 500.4 litres = 0.50 cubic metres (m*3) of hydrogen, H2.

1 kg of C6H12O6 reacting by step (b) yields 5.56 x 2 x 22.5/1000 = 0.25 m*3 of H2. This assumes a yield of 100% for each process.

The actual reaction yields 0.18 m*3 of H2/ kg of C6H12O6. In one study from the University of Glamorgan the ratio of butyric acid/acetic acid is quoted as 1700/780 mg/l, which gives a molar ratio of:

(1700/88)/(780/60) - dividing by the molecular weights - and hence the ratio of reaction (a)/(b) = (780/60 x 2)/(1700/88) = 0.336.

So, 0.18 m*3 of H2 is the product of processes (a) and (b) acting in the proportion: 3 of (a) + 1 of (b) (near enough, it is actually: 2.98 + 1). hence we can assume that 0.75 kg of C6H12O6 reacts by (b) and 0.25 kg of C6H12O6 reacts by (a).

For a 100% yield from the two processes, we expect 0.1875 m*3 of H2 from (b) + 0.125 m*3 from (a) = 0.3125 m*3. Therefore the efficiency of the process is 0.18/0.3125 x 100 = 58%. It is important to note that this efficiency is only attained if the H2 is continually swept from the fermentation vessel, otherwise it falls to 32%, giving a yield of H2 of just 0.1 m*3.

1 tonne oil (equivalent) provides 42 GJ of energy = 42 x 10*9 Joules (J).
Therefore 54 million tonnes would provide 54 x 10*6 x 42 x 10*9 = 2.268 x 10*18 J.
One mole of H2 produces 285.83 kJ/mol when burned (heat of combustion), and so the amount of H2 required is 2.268 x 10*18/285.83 x 1000 J/mol = 7.935 x 10*12 moles of H2 = 1.79 x 10*11 m*3 of H2 (multiplying by the volume of one mole taken as 22.5 litres).

If 1 kg of C6H12O6 produces 0.18 m*3 of H2, we need 1.79 x 10*11/0.18 = 9.94 x 10*11 kg = 9.94 x 10*8 tonnes of C6H12O6.

Sugar cane yields are reported at a maximum of 87 tonnes/hectare (ha) and the crop yields 19% of sucrose, making 16.53 tonnes per hectare.

So we need 9.94 x 10*8/16.53 = 6.01 x 10*7 ha = 6.01 x 10*5 km*2 (square kilometers), or roughly 600,000 km*2. This is to be compared with the entire area of the U.K. mainland of about 244,000 km*2 (of which just 65,000 km*2 is arable). [Sugar beet would be slightly richer as a crop since it produces 19.1 tonnes/ha of sucrose, but we still need just over twice the land area of the U.K.!].

So we need about 250% (two and a half times) the total land area of the U.K. or almost ten-times the amount of arable land there is! Put another way, if we grew no food at all, we could still only supply 10% of our transportation fuel equivalent (or maybe 40% if we managed to "seed" everywhere). On the large scale, this is a non-starter.

Out of interest, let's just consider the total volume of the fermentation vessels. If 0.75 kg of C6H12O6 produces (at 58% yield) (88/180) x 0.75 x 1000 = 213 g butyric acid. Since the butyric acid concentration was quoted at 1700 mg/l (1.7 g/l), the volume of the reactor = 213/1.7 = 125 litres to ferment 1 kg (total, because 0.25 kg reacts by step (a)) of C6H12O6.

Hence, to ferment 9.94 x 10*8 tonnes would require 125 x 1000 kg x 9.94 x 10*8 = 1.243 x 10*14 litres = 1.243 x 10*11 m*3 = 124.3 km*3 (cubic kilometers, since 1 km*3 = 1 x 10*9 m*3). This is to be compared with the entire available freshwater in the U.K. of 148 km*3. So, we could just about match this assuming we had no other need for water (i.e. washing and drinking), and water is already in short supply for even these basic purposes.

Hence on grounds both of providing sufficient land to grow the necessary sugar crop and supplying enough water to fill the fermentation vessels, the prospect is a complete non-starter! I conclude, therefore that biohydrogen is not going to permit us to break our dependency on imported oil from the Middle East.