Appendix B

# Hubbert’s Peak Oil Theory from Chapter 5

## Hubbert’s Model for World Oil Production

The equations Hubbert used to model world oil production start with the equation for the cumulative production (Qt) at any time (t). The production rate (qt) at any time (t) is the derivative of Qt with respect to time (t):

${\mathit{Q}}_{\mathit{t}}=\frac{{\mathit{Q}}_{\text{max}}}{1+\mathit{a}{\mathit{e}}^{-\mathit{bt}}}$

(B.1)

Where

Qt = cumulative production at time (t), usually in barrels.

qt = production rate at time (t) usually in barrels/day.

Qmax = ultimate cumulative production, usually in barrels.

a = growth or decline coefficient, dimensionless.

b = growth or decline exponent where dimensions are the reciprocal of time, such as 1 per day. ...

Get The Future of Energy now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.