摘要
The fundamental equation of mineral production allows to model and design the dynamics of mineral production, however complex they are or could be. It considers not only the case of a constant production to reserves ratio for given intervals of time, but with a piecewise approach, it is also enabled to account the variation on time of this ratio. With a constant production to reserves ratio, the limit expression of the fundamental equation takes the form of an Erlang distribution with a fixed shape parameter. The rate parameter equals the scale factor. The discrete piecewise version, instead of considering the reserves and the production to reserves ratio being constant through certain intervals of time, updates both variables by units of time. This version, using either lineal or non lineal functions for the variables involved, let to model known production profiles or to forecast them by experimental design. The Hubbert’s linearization updated with recent data and the p-box method applied to determine ultimate recovery of U.S. crude oil reserves indicate official accounts underestimate them. The analysis of the ideal model of production based on Hubbert’s linearization and curve, can be made by decomposing it in the distribution with time of the reserves and of the production to reserves ratio. The distribution of reserves with time is synchronized for both the ideal Hubbert’s curve and real profiles, disregarding whether they match or not. The departure of real profiles from the ideal Hubbert’s curve lies on the differences or correspondences of the distribution with time of the production to reserves ratio. The MonteCarlo simulation applied to forecast US crude oil production for the next five years points to a slow decline, with average annual yields presenting a difference lower than 10% between the start and the end of the simulation.
The fundamental equation of mineral production allows to model and design the dynamics of mineral production, however complex they are or could be. It considers not only the case of a constant production to reserves ratio for given intervals of time, but with a piecewise approach, it is also enabled to account the variation on time of this ratio. With a constant production to reserves ratio, the limit expression of the fundamental equation takes the form of an Erlang distribution with a fixed shape parameter. The rate parameter equals the scale factor. The discrete piecewise version, instead of considering the reserves and the production to reserves ratio being constant through certain intervals of time, updates both variables by units of time. This version, using either lineal or non lineal functions for the variables involved, let to model known production profiles or to forecast them by experimental design. The Hubbert’s linearization updated with recent data and the p-box method applied to determine ultimate recovery of U.S. crude oil reserves indicate official accounts underestimate them. The analysis of the ideal model of production based on Hubbert’s linearization and curve, can be made by decomposing it in the distribution with time of the reserves and of the production to reserves ratio. The distribution of reserves with time is synchronized for both the ideal Hubbert’s curve and real profiles, disregarding whether they match or not. The departure of real profiles from the ideal Hubbert’s curve lies on the differences or correspondences of the distribution with time of the production to reserves ratio. The MonteCarlo simulation applied to forecast US crude oil production for the next five years points to a slow decline, with average annual yields presenting a difference lower than 10% between the start and the end of the simulation.
