Application of Logistic Mathematical Model to Simulate the Consumption of Natural Gas in Brazil Until 2020

Abstract

Over the next two decades Brazil expects to see an increasing share of energy provided by natural gas. Natural gas use in 2010 was 10.2% of the total energy consumption and comprised 73 million cubic meter per day. Natural gas is considered one of the main energy sources which contributes and will contribute to the development of the country by providing economic, social and environmental benefits. This work uses population dynamics mathematical model (Verhulst) in order to analyze the evolution of natural gas consumption in Brazil within a forecast until 2020. The Verhulst model, also known as “logistic”, has been advanced in its application and shows that the population dynamics mathematical models, within their basic assumptions, may allow estimating the growth of a population or other variable with the same characteristic. The calculation to solve the differential equations, linear regression, method of least squares and graphics were performed using the MatLab software. Through simulations it was found that the mathematical model can be applied to natural gas consumption in Brazil. Simulations using the proposed model show a tendency of saturation in the consumption between 70 and 90 million cubic meters per day. These numbers are below the projected numbers until 2020 according to forecast presented in the energy plan. The results of this study indicate that the growth of natural gas consumption is stable and is within the limit of saturation related to the Brazilian market.