Modelagem matemática e computacional da injeção de polímeros em reservatórios de petróleo

Abstract

This final project addresses a mathematical and computational modeling of polymer flooding in oil reservoirs. Polymer flooding is an EOR method used primarily in projects in which water flooding is inefficient due to its high mobility in the porous medium. The objective of this work is to derivate a mathematical modeling for the problem of polymer flooding and then a computational modeling, obtaining a simple and robust 1D simulator. First, the equations governing the mass transport in porous media are obtained considering the laws of mass conservation. The equations obtained are non-linear hyperbolic partial differential equations. From the mathematical models derivated, analytical solutions are developed. Then the discretization of the mathematical models is obtained following the method of finite volumes proposed by Kurganov and Tadmor (2000). Subsequently and considering the discretized equations, the implementation of the method in programming language FORTRAN 90 is conducted. Finally, numerical simulations are conducted for the cases of water flooding and polymer flooding, in order to validate the implementation of the method and to analyze several cases. The Numerical results obtained were accurate and showed low numerical diffusion, restating the features of the method used.