The Hubbert diffusion process: Estimation via simulated annealing and variable neighborhood search procedures—application to forecasting peak oil production

Abstract

Accurately charting the progress of oil production is a problem of great current interest. Oil production is widely known to be cyclical: in any given system, after it reaches its peak, a decline will begin. With this in mind, Marion King Hubbert developed his peak theory in 1956 based on the bell-shaped curve that bears his name. In the present work, we consider a stochastic model based on the theory of diffusion processes and associated with the Hubbert curve. The problem of the maximum likelihood estimation of the parameters for this process is also considered. Since a complex system of equations appears, with a solution that cannot be guaranteed by classical numerical procedures, we suggest the use of metaheuristic optimization algorithms such as simulated annealing and variable neighborhood search. Some strategies are suggested for bounding the space of solutions, and a description is provided for the application of the algorithms selected. In the case of the variable neighborhood search algorithm, a hybrid method is proposed in which it is combined with simulated annealing. In order to validate the theory developed here, we also carry out some studies based on simulated data and consider 2 real crude oil production scenarios from Norway and Kazakhstan.

Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean

“…In recent years it has been widely used in the context of estimation in diffusion processes (see, for example Luz Sant’Ana et al. ( 2018 ) and Román-Román and Torres-Ruiz ( 2015 )).…”

“…We recall that the S.A. is successful because it avoids local minima. In recent years it has been widely used in the context of estimation in diffusion processes (see, for example Luz Sant'Ana et al (2018) [21] and Román-Román and Torres-Ruiz (2015) [30]). In this context, the algorithm works in the following way.…”

Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors

“…These algorithms are often more appropriate than classical numerical methods since they impose fewer restrictions on the space of solutions and on the analytical properties of the function to be optimized. Some examples of the application of these procedures in the context of diffusion processes can be seen in [19,21,23,25].…”

“…In any case, the exact distribution of the estimators cannot be obtained. Recently, the asymptotic distribution of the MLestimators and delta method have been used in order to obtain estimation errors, as well as confidence intervals, for the parameters and parametric functions in the context of the Hubbert diffusion model [25].…”

Influencing Factors of New Energy Development in China: Based on ARDL Cointegration and Granger Causality Analysis

“…In the past 10 years, the international oil giants have been exhausted only by maintaining production. The peak oil (Ghosh and Prelas, 2009;da Luz Sant'Ana et al, 2018) has not yet come, but it is approaching quickly. China has a vast territory and abundant resources.…”