Question

World production of crude oil in 2010 was about 3.5 billion tonnes. Assume that we wish to replace 10% of this supply with a transportation fuel derived from biomass. Assume that the energy content of biomass is about 1% of incident solar energy during the growing season. How many hectares of arable land worldwide would be needed to supply this quantity of biomass fuel? What fraction of arable land area worldwide does this represent?

Answer 1

Amount of crude oil = 3.5 * 10¹² kg

Crude oil energy content = 41.868 * 10⁶ J/Kg

So total energy by crude oil = 3.5 * 10¹² kg * 41.868 * 10⁶ J/Kg = 146.538 * 10¹⁸ J

Amount of energy to be replaced = 10 % of 146.538 * 10¹⁸ J = 14.6538 * 10¹⁸ J

Let us assume that the growing season is 180 days long

Energy per unit area per day is approximately 6000 W hr /day-m² = 6000*3600 J/day-m²

Energy in a square meter area in 180 days = 180 * 6000 * 3600 = 3888000000 J/m²

Since biomass is 1% effective, the effective energy per square meter = 38880000 J/m²

So area needed to produce 14.6538 * 10¹⁸ J energy = 14.6538 * 10¹⁸ / 38880000 = 376898148100 m² = 37689814.81 hectares

So area of arable land needed is around 3.8*10⁷ hectare

Total arable land worldwide is approximately 1.386*10⁹ hectare

So fraction of arable land area worldwide this represent = 3.8*10⁷ / 1.386*10⁹ = 0.0274 = 2.74 %

[Note thay there are certain assumptions made and certain data collected from different sources. If you have different values for those values, you might need to change accordingly]