Estimation of Natural Gas Production, Import and Consumption in Brazil Based on Three Mathematical Models

Abstract

A mathematical model capable of providing a forecast of future consumption and import of natural gas is essential for the planning of the Brazilian energy matrix. The aim of this study is to compare three mathematical models, logistic model or model of Verhulst, exponential model or the model of Malthus and the model of von Bertalanffy to analyze the possibilities of these models to describe the evolution of production, import and consumption of natural gas in Bra-zil, from data provided by the energy balance of the Ministry of Mines and Energy (MME) from 1970 to 2009. A projection of the production and the import of natural gas up to 2017 is made with the models studied in this article and compared with the Brazilian Ten-Year Plan for Expansion of Energy (PDE). At the end of this paper a comparison with the Hubbert model for Brazilian natural gas production is made. These data were adjusted to use the differential equations which describe the models of population growth. All the computer work used in this article: graphics, resolution of differential equations, calculations of linearization and the least squares fitting was prepared in the software MatLab. The results obtained by means of graphs show that the population dynamics models (logistic, exponential and von Ber-talanffy) can be applied in modeling the production, import and consumption of natural gas in Brazil.