Peak production in an oil depletion model with triangular field profiles

In this paper a model of oil depletion is analyzed in which the shapes of field profiles are triangular and the sizes of successive fields decrease monotonically. It is shown that the curve representing the rate of production for this model is piecewise linear and concave up to a certain point after which it is monotone decreasing. Equations for natural smooth approximating curves having unique maxima are derived. A related model of natural gas depletion with trapezoidal shaped field profiles is also analyzed.

Published in: Accepted in Journal of Interdisciplinary Mathematics
Available from: Queen Mary, University of London