Oil production

There are two things that are clear about crude oil. One is that we use a lot of it. The world consumption of crude oil is approximately 80 million barrels per day, and world consumption grew by 3.4% in 20041. The other is that the Earths oil reserves are finite. The processes that created the crude oil that we use today are fairly well understood. There may be significant deposits of crude oil yet to be discovered, but it is a limited resource. Governments, economists, and scientists argue endlessly about almost every other aspect of oil production. Exactly how much oil is left in the earth and what fraction of that oil can or will ever be removed is difficult to estimate and has significant financial ramifications. Substantial disagreement on oil policy is not surprising. Predictions of the decline in production are notoriously difficult, and it is easy to find exam- ples of such predictions that ended up being absurdly wrong2. On the other hand, sometimes predictions of decline in production are accurate. In Hubberts Peak3, Kenneth Deffeyes recounts the work of geologist M. King Hubbert. Hubbert fit a logistic model, to the production data for crude oil in the United States. Using production data up to the mid 1950s along with approximations of the total amount of recoverable crude oil, Hubbert predicted that production would peak in the U.S. in the 1970s. He was right. In this lab we model the U.S. and world crude oil production using a logistic model, where the carrying capacity represents the total possible recoverable crude oil.

This model is of the form: Q(t) = k 1 Q(t) Q(t) N where k is the growth rate, N is the carrying capacity, and Q is a function describing the amount of crude oil at time t. Your report should address the following items:

b) Predicting both the growth rate and the total amount of recoverable crude oil 2 from the data is difficult. Model the crude oil production of the U.S. assuming the total amount of recoverable crude oil in the U.S. is 200 billion barrels. (This assumption includes what has already been recovered and serves the role of the carrying capacity in the logistic model.)

Year U.S. Oil World Oil |Year U.S. Oil World Oil 1920-24 1925-29 4.2 1930-34 4.3 1935-39 1940-44 7.5 1945-49 9.2 1950-5411.2 1955-5912.7 1960-6413.4 4.3 6.2 7.0 9.6 11.3 15.2 22.4 31.9 44.6 2.9 1965-6915.8 1970-74 17.0 1975-7915.3 1980-8415.8 1985-8915.2 1990-9412.9 1995-9911.5 2000-0410.4 2005-08 7.4 65.4 93.9 107 101 104 110 118 126 107 5.8 Figure 1: Oil production per five year periods in billions of barrels Year U.S. Oil World Oil |Year U.S. Oil World Oil 1920-24 1925-29 4.2 1930-34 4.3 1935-39 1940-44 7.5 1945-49 9.2 1950-5411.2 1955-5912.7 1960-6413.4 4.3 6.2 7.0 9.6 11.3 15.2 22.4 31.9 44.6 2.9 1965-6915.8 1970-74 17.0 1975-7915.3 1980-8415.8 1985-8915.2 1990-9412.9 1995-9911.5 2000-0410.4 2005-08 7.4 65.4 93.9 107 101 104 110 118 126 107 5.8 Figure 1: Oil production per five year periods in billions of barrels