Not exactly science, but I need a math formula.

In post linked below, I had to make a table to figure out how long before oil runs out assuming 3% growth. Is there a formula to do this so that I don't have to spend what seems like an eternity making a table?

http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=104&topic_id=3979226&mesg_id=3979816

With almanacs showing total world oil reserves of 1 trillion barrels and daily world consumption of over 80 million barrels, that works out to under 35 years, no matter what the oil optimists say.

Try using current world oil daily consumption of 84 million barrels and the numbers come out even sooner. Some say 120 million barrels per day is coming...

I started 2005 using 80 million barrels with reserves of one trillion barrels. I made each year use 3% more oil. A negative total barrels of oil left appeared in 2028. That is 23 years from now. Of course there is no guarantee that we can or will pump it that fast...

BTW, calculus.net has growth modelling

http://www.calculus.net/ci2/search/?request=category&code=8A&off=0&tag=9200438920658

links. It all comes down to growth limits. A 'steady state' economics, as John Stuart Mill groped for - and many others- Walras, Boulding, etc., predict a 'carrying capacity'. This would go for any limiting factor, oil included.

Mathematicians have guessed that the US reached that limit in 1970, but qualified that by saying our wars have muddied the waters.

2005 29,200 1,000,000
2006 30,076 969,924
2007 30,978 938,946
2008 31,908 907,038
2009 32,865 874,173
2010 33,851 840,322
2011 34,866 805,456
2012 35,912 769,544
2013 36,990 732,554
2014 38,099 694,455
2015 39,242 655,212
2016 40,420 614,793
2017 41,632 573,161
2018 42,881 530,279
2019 44,168 486,112
2020 45,493 440,619
2021 46,857 393,762
2022 48,263 345,498
2023 49,711 295,787
2024 51,202 244,585
2025 52,738 191,847
2026 54,321 137,526
2027 55,950 81,576
2028 57,629 23,947
2029 59,358 -35,411

USGS put reserves at about 1.2T in 2001
DOE quoted about 1.02 T for Jan, 2003, but it's stayed at that level since I started tracking this page in 2001.

Rather than try to wrack out a formula, I just set up a spreadsheet. I've been using 1.018T starting in 2001, with a historical http://www.oilcrisis.com/laherrere/aspoParis.pdf">average annual increase in consumption of 2.5%. Last year, though, it increased 4.3%. The model still puts us at 31.05B bbl/yr, just slightly more than the actual current 84M bbl/day, so it seems to be tracking all right.

If we go back to, say, a conservative 3% for the following years, that would put the theoretical "last barrel" in 2025; if we kept the 4.3%, it would move up to 2023.

That's not what will actually happen, of course. For one thing, there's a top rate that oil can be extracted, and the oil patch boys are saying we're hitting that right about now -- the code phrase is "no spare capacity." But the key thing will be shortfall: how far supply falls behind demand. We could expect a kind of oscillation for a while, as skyrocketing prices reduce demand, which then mitigates prices, which raises demand, etc.

As the dwindling oil gets more and more difficult to extract, the supply situation will be even more constricted. At some point, the depletion curve should kind of smooth out to a long asymptote toward zero.

of the form where if T is the total oil used, A is the amount used in the first year, r the relative proportion of one year to the next, and n the number of years, then:

T = A * (r^n - 1) / (r - 1)

which can be rearranged to

r^n = 1 + ( T * (r - 1) / A)

so that

n = log(1 + T * (r - 1) / A)/log(r)

substituting T=1000000, A=29200, r=1.03, we get n = 23.9