Print this pageForecasting Petroleum Production with a Model Based from Discharge Process
This work deals with a mathematical model to forecast the production of oil and gas at both national and worldwide scales, by having as input the historical production series and the estimated ultimate resource (EUR). This volume is defined as the sum of three factors, namely, the reserves, the cumulative production and the estimate of undiscovered resource potential.
The proposed model consists of representing the depletion of a finite resource at a variable rate through time. Therefore the model allows the evolution of an increasing production up to a peak followed by a decline down to the resource exhaustion.
The graph of the proposed model is similar to a unimodal probability density function, with variable asymmetry, either negative (longer tail at initial, past years) or positive (longer tail at future years). The functional shape is a consequence of the uncountable possibilities of parameter value combinations. Symmetry, like in the logistic function, is just a very special instance, unlikely to occur.
The parameters of the model are the estimated ultimate volume (EUR), the initial production and the initial rate of decline. Fitting the model to historical time series of production may be constrained by hypotheses about future demand and rate of decline.
For the sake of comparison, both the logistic function and the proposed model were fitted to the historical series of American petroleum annual production, using data published by the USGS (US Geological Survey) and the DOE/EIA (US Department of Energy/Energy Information Administration), from which three quantile estimates of EUR were taken, to quantify the uncertainty.
From a statistical perspective, the proposed model works better than the logistic function, when both are fitted to the historical data, with or without restrictions on the parameters. The logistic function underestimates the observed values after 1990, while the proposed model remains adherent, following the positively asymmetric trend shown by the historical series over the past two decades. Therefore the proposed model is more flexible than the logistic, which is constrained to the symmetrical bell shape. The model was further applied to forecast the World Oil and Gas Production.
AAPG Search and Discover Article #90100©2009 AAPG International Conference and Exhibition 15-18 November 2009, Rio de Janeiro, Brazil