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We look at the more basic bits of information one will need when looking at replacing conventional fossil fuels with hydrogen
For now, we will concentrate on gaseous hydrogen; but in future articles we will include such things as liquid hydrogen and even metal hydrides.
A very common question from many is “How do you measure hydrogen volume and energy content relative to gasoline or diesel fuel?” Most people think in terms of miles per gallon and we feel comfortable filling up and expecting to drive a certain number of miles. But when it comes to hydrogen, we feel less confident. After completing this lesson, you will have a better understanding of where and how to begin your calculations.
First we need to know that hydrogen is the lightest element in the universe. In terms of energy density or the amount of usable energy for a given weight it is better than any other fuel. In terms of energy density for a given cubic foot or cubic meter or other measures of volume -- hydrogen has a low density. Therefore we either need a very large tank at atmospheric pressure (or as it is known in engineering terms 1 bar) or we have to compress it to get more fuel in a smaller space.
To make our calculations easier we will use a common unit of energy measurement for all of our fuel comparisons. Thanks to the 18th century British who had to deliver coal to steam engines and allow designers a method of measuring how much useful work a given ton of coal could perform -- we have what is known as a BTU or British Thermal Unit. This measurement is defined as the amount of energy needed to raise one pound of water one degree Fahrenheit.
Gasoline contains approximately 127,000 BTU’s per gallon. Diesel fuel does better at about 134,000 per gallon. Hydrogen in its gaseous form contains about 54,000 BTU’s per pound.
Okay now I can hear the groaning as you try to compare gallons to pounds. First let’s look at what gasoline and diesel weigh per gallon. That would be about 6.4 pounds. At room temperature and 1 bar (remember that represents pressure at sea level or 14.41 pounds per square inch) hydrogen weighs about .52 pounds per cubic foot. or .520 pounds per hundred cubic feet.
So now what shall we do with this information in terms of calculating the size of tank we will need for a vehicle? First let us convert our hydrogen to a unit of measure that is approximately equivalent to a gallon of gasoline.
What we need here is a ratio we can work with. Since 100 cubic feet of hydrogen has about 37,000 BTU’s and gasoline has about 127,000 BTU’s per gallon -- if we divide the gasoline by the hydrogen or 127,0000/37,000 we come up with 3.43. We would need 3.4 x 100 cubic feet or 343 cubic feet of hydrogen to equal one gallon of gasoline. At just over a half pound per hundred cubic feet hydrogen would weigh just over one and three quarter pounds compared to a gallon of gasoline at 6.4 lbs per gallon. These are just the rough figures (actual engineering terms are far more precise) but, this will give us something to work with without getting too technical.
The weight difference may seem like a big advantage for hydrogen but not in reality. The gallon of gasoline can be contained in a very light weight tank since it is not pressurized and the small volume is very energy dense. So now what do we do with the hydrogen? Let’s assume we wanted to haul our 343 cubic feet of hydrogen at the same pressure as gasoline. Let’s build a rectangular tank and see what we have. If our tank is as long as the car at maybe 12 feet and just as wide at maybe 5 feet and we made it 2 feet tall we could haul about 120 cubic feet. That is less than half of what we need. So let’s make the tank 6 feet tall. We are still short of our 343 cubic feet needed to equal a gallon of gasoline.
When the tank needed to haul the equivalent of one gallon of gasoline is bigger than the entire car, it can be seen that this is not very practical.
One solution? Compress the hydrogen. Let’s assume we want to carry about 15 gallons of gasoline equivalent which is about average in most vehicles. That means we will need about 5145 cubic feet of hydrogen or 343 cubic feet times 15.
We know the cubic volume needed and we can assume 3600 psi for now. These tanks are commercially available and won’t break most budgets. So let’s pick a tank. To keep it simple we will use a tank that can hold at least 15 gallons. Most engineers don’t like to complicate design process any more than the average person, so they have developed what are known as constants. These are used in many mathematical equations to help reduce complexity. Lucky for us we have a constant we can use that allows us to calculate our cubic volume of hydrogen when only gallons and pressure are known elements. Volume as gallons times pressure in bars multiplied times the constant .1337 will give us a close approximation of the amount of hydrogen or other gases contained in our tank. The word bar described in the equation is just another constant that represents one atmosphere of pressure at sea level or 14.41 psi.
Now we simply need to divide our required pressure of 3600 psi by 14.41 to obtain our number of bars or in rounded numbers 250 bar. We had estimated our needs at 5145 cubic feet so let us see if a 15 gallon tank is large enough. Fifteen gallons times 250 bar times .1337 calculates out to approximately five hundred and one cubic feet. This falls short of our required capacity by a factor of ten. These numbers are approximations since increasing temperatures encountered when filling high pressure tanks plays a role in our total capacity.
But it does reveal something that is all too obvious to hydrogen systems designers. Storing energy in the form of hydrogen relative to what we all take for granted when dealing with gasoline is a challenge. That does not mean that these challenges cannot be overcome. In later articles we will look at many forms of hydrogen storage that present additional challenges but also possible great opportunities such as metal hydrides, liquid hydrogen and beyond.
So in review we see that hydrogen cannot be practically transported without compression or other means of concentration. We now have a handy unit called BTU’s to describe energy content or quantity so our conversion from one fuel to another is no longer rocket science and we have completed the first of many steps needed to convert your current vehicle over to hydrogen. Hope this helps.
