Question

Assume 1000 acres of land is available for switchgrass to produce cellulosic ethanol. The yield of switchgrass is 5 tons/acre each year. 5% of the switchgrass mass is lost in the harvesting and grinding processes. 40% of the remaining mass is lost in converting cellulosic material to sugars using temperature, pressure, acids and enzymes. The fermentation process (conversion of sugar to ethanol) efficiency is 50% by mass. Switchgrass has an energy density of 6500 Btu/lb. Ethanol has a volumetric density of 6.8 lb/gallon and an energy density of 25 MJ/liter. Calculate how much ethanol (gallons) can be produced by the switchgrass grown on this land in a year?

Answer 1

1000acres land

total yield= 5tons/acre *1000acre=5000tons

5% lost in harvesting and grinding

thus remaining= 4750tons

40%of remaining lost

thus remaining= 2850tons

the efficiency of fermentation process=50%

now remaining=1425tons

using conservation of energy, the energy of switchgrass=energy of ethanol

energy density of switchgrass = 6500Btu/Lb = 1.5119e+7J/Kg = 15.119MJ/Kg

energy density of ethanol=25MJ/Litre

also density of ethanol=6.8lb/gallon

6.8lb/gallon = 0.8148Kg/L

energy density of ethanol in Joule/Kg=25MJ/Litre /0.8148Kg/L = 30.68MJoule/Kg

mass of ethanol produced=15.119*1425/30.68 tons=702.235ton

volume=702.235(ton)*907(Kg/ton) / 0.8148(Kg/L) =7.817e5Litre

volume in gallons = 7.817e5Litre * 0.2641gallon/L=2.065e5gallon