Name: Raphael Laquini
Type: MSc dissertation
Publication date: 02/12/2016

Namesort descending Role
Carlos Friedrich Loeffler Neto Advisor *

Examining board:

Namesort descending Role
Adenilcia Fernanda Grobério Calenzani External Alternate *
Antonio Manoel Ferreira Frasson External Examiner *
Carlos Friedrich Loeffler Neto Advisor *

Summary: Notwithstanding the most realistic rheological models are based on continuum
mechanics, research involving oil extraction in rocks has emphasized a simpler approach using hydraulic diffusivity models, based on Darcy’s Equation to simulation of the fluid flow. The constitutive medium, in turn, besides a number of important properties, is presented as a non-isotropic material. Thus, the governing equation in these conditions can be given as a special case of the Generalized Scalar Field Equation. On the other hand, the Boundary Element Method (BEM) is a technique that adapts easily to non regular regions and has a
high accuracy in simulation problems in which the mathematical field is scalar,
particularly models involving the Darcy’s Equation. However, the non-isotropic
BEM model has not found highlighting in oil extraction applications, so as to be
normally restricted to a limited set of applications in dams. The BEM should be
used more ostensibly, since it is particularly suitable to model non regular
domains. In view of future applications in reservoir engineering, this paper
presents the mathematical modelling and the implementation of the BEM in
orthotropic problems with the classical formulation that uses a correlate nonisotropic
fundamental solution. Numerical tests are implemented in problems with
known analytical solution and their results are also compared with solutions
achieved by the Finite Element Method (FEM), for a better performance

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