The Future of Energy

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 (Q_t) at any time (t). The production rate (q_t) at any time (t) is the derivative of Q_t with respect to time (t):

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

  (B.1)

Where

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

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

Q_max = 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. ...