from CR4 thread:
here:
CR4 - Thread: Browns Gas for Increased Fuel Efficiency, True?
So-called Brown's Gas is a mixture of hydrogen and oxygen gas prepared by electrolyzing water. Generators which prepare Brown's Gas are sold for welding. Brown's Gas has also been proposed as a fuel for internal combustion engines and as an input gas for fuel cells. Here I propose to examine the energetics of Brown's Gas and the practicality of these latter applications.
All calculations are made in metric units with occasional translations. I shall also refer mainly to the mass of the gas since using volumes requires specifying the temperature and pressure. For illustration some masses will be translated into volumes at one atmosphere pressure and room temperature (75 F).
In electrolysis the output rate is a function of the molecular weight of the product, its valency and the total current passing through the electrolytic cell. One Faraday is that amount of current which will produce one gram.mole of a product with a valency of one. To split water, H2O, into H2 and O2 takes two Faradays per mole, that is two Faradays will convert 18 grams (about 0.635 oz) of water into Brown's Gas.
Two Faradays is equivalent to 193038 Coulombs. This equals the product of the current through the cell in amps and the time in seconds for which it passes. For example, if 5 amps pass through the cell it will take 193038/5 seconds or 10.72 hours to electrolyze 18 grams of water. Thus the output of a Brown's Gas generator operating at 5 amps would be 1.678 grams of gas per hour. At 500 amps the output would be 167.8 grams per hour and so on.
A cell running at 500 amps would produce 364 liters of Brown's Gas at atmospheric pressure every hour. (A liter of gas is about as much as a quart milk carton will hold.) My guess is that a welding torch uses some tens of liters of gas a minute. A practical Brown's Gas welder thus either has to operate at currents higher than 500 amps or must be operated in bursts.
Normally the current passing through the cell comes from a step-down transformer. At DC it takes some 1.7 volts to cause an electrolytic cell to operate. That is, our 500 amp cell is operating with a continuous power input of 850 watts. The AC input will be somewhat higher than this, depending on the details of the construction of the generator. Let's assume 1000 watts. That is, to generate 168 grams of gas requires one kilowatt.hour of electrical input or about 10 cents worth of electricity.
Suppose we wanted to run an internal combustion engine on this gas. How much energy would we get out? If we burn Brown's Gas we get pure water vapor. Burning 18 grams releases 242000 Joules of heat energy or 229.5 btu. (Allowing the vapor to condense would yield an additional 44500 joules, 42.4 btu, but in any conventional engine this output would only appear as waste heat and will be ignored.)
Thus if we drove an engine with 168 grams of gas per hour we would be putting 2.26 million joules per hour of heat energy into it. Operating at a plausible combustion temperature the thermal efficiency might be as high as 50% so we would get out 1.13 million joules per hour or 314 joules per second, that is 314 watts.
The bottom line is that we have put in about a kilowatt of electrical energy to get out under a third as much in mechanical energy. Considering that the efficiency of an electric motor would be over 85% there is no justification at all for using a Brown's Gas generator and an internal combustion engine. An electric motor would do better at less cost and with far greater reliability.
It has also been proposed to use Brown's Gas in a fuel cell. Unless it is proposed to store the Brown's Gas, this is an inherently absurd idea. A fuel cell is fundamentally an electrolysis cell run backwards. That is, the same relationship between current passing and mass of input and output gas applies, less inevitable losses. If the oxygen and the hydrogen were generated separately, which they are not, an ideal fuel cell would generate a given current using exactly the same input gas flow as would be supplied by electrolyzing water with the same current. Unfortunately, the electrolysis cell requires an input voltage of around 1.7 volts while a practical hydrogen/oxygen fuel cell generates 1.23 volts in theory and perhaps 0.7 volts in practice. Thus the ratio of output electrical power to input electrical power would be roughly 42%. Operating such a system has no conceivable utility.
The only justification for such a double conversion would be if Brown's Gas could be stored in large quantities. Since Brown's Gas is an explosive mixture it would be hazardous to store any quantity of it at atmospheric pressure. To compress it for storage would be criminally stupid.
A standard cylinder used for storing hydrogen contains just over a cubic foot of gas under about 150 atmospheres pressure. At that pressure it would contain the equivalent of about 5380 liters of Brown's Gas. That is 2880 grams or 160 moles. At 242000 joules per mole a cylinder contains almost 39 million joules or 36700 btu.
There are two ways of looking at this. One is that the cylinder is a poor storage device since, for all its size and weight, it contains about as much energy as two pints of gasoline. The other is that each cylinder is the equivalent of 21 pounds of TNT in a steel tube. This is not something I'd want to have around!