Bio-mass energy Problem

We worked part of this in today's quiz. The question is this: what percentage of the land mass of the U.S. would be required to grow biomass to meet the gasoline needs of the U.S. We started with corn based ethanol, and determined that an acre of corn yields on average, 375 gallons of ethanol. We used the average corn yield of 150 bushels per acre, and 2.5 gallons of ethanol per bushel. While a few corn-belt counties yield up to 400 bushels per acre, 150 is the nationwide average.

Now, to grow corn, one must have farmland. We can only use so much farmland for fuel production before we starve! So lets imagine using cellulosic biomass, harvested from semi-arid, non-farmed land. You hear ignorant politicians telling us bio is the way out of the mess we are in, all the time.

Using switchgrass as an example, the average biomass yield has been estimated to be 4 tons per acre per year. Using Bio-Engineering Resources process (which converts biomass to synthesis gas, and ferments the syn gas to ethanol) a yield of 100 gallons per ton is achieved. The land mass of the lower 48 states is 1.89 billion acres, the current daily consumption of gasoline is 390 million gallons, and 1 gallon of ethanol replaces 0.67 gallons of gasoline. You now have all the information needed to answer the question, using your skill at setting up conversions. Lets do the problem in pieces.

Annual demand for ethanol if 100% of gasoline were to be replaced (note E6 means 10 to the 6th - I haven't found superscripts in google yet):

390 x E6 gal/day X (365 days/1 year) x (1 gal EtOH/0.67 gal Gas) = 2.12 x E11 gal EtOH/yr

or 212 billion gallons per year

The yield of ethanol per acre per year is

4 tons biomass/acre/year x (100 gal EtOH/ton) = 400 gallons/acre/year

Now we set up our final conversion, multiplying demand by 1 over yield:

(2.12 E11 gal/yr) x (1/400 gal/acre/yr) which, remembering how to deal with fractions is

(2.12 E11 gal/yr) x (1 acre-year/400 gal) = 5.3 E8 acres or 0.53 billion acres

0.53 billion acres/1.89 billion acres = 0.28 or 28% of all the land mass of the lower 48

This assumes that no energy is required to grow and harvest. In the case of corn, about 75% of the energy produced in the form of ethanol is consumed in farming, collection, and production. If this were the case for cellulosic biomass, you'd need 28%/0.25 or 112% of the land mass of the lower 48 states.

You all can do this - it was a long series of simple conversions that you know how to do. Stringing it all together might be tough for some of you, but you won't have to with such a long sequence in any of my exams ----- I Promise!

Doc Hilton