Modeling oil production and its peak by means of a stochastic diffusion process based on the Hubbert curve

Abstract The present paper introduces a new diffusion process for the purpose of modeling a Hubbert-type behavior pattern. The main features of the process will be analyzed and the maximum likelihood estimation of the parameters will be carried out through discrete sampling. To this end, a complex system of equations must be solved through numerical procedures, requiring the search for an appropriate initial solution. To this end, we propose three search procedures. The estimation of peak time (and consequently peak value) is approached from two perspectives: one, by obtaining the maximum likelihood point estimation of the two values (both of them can be expressed as parametric functions); the other, by formulating the peak-time as a first-passage-time problem. Finally, in order to validate the methodology developed, we carry out some studies based on simulated data, and then we consider some real-world applications to crude oil production data for Norway and Kazakhstan.

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