A RESERVOIR SIMULATOR BASED ON FORMULATIONS OF ISOGEOMETRIC BOUNDARY ELEMENTS

Resumo

The development of the reservoir simulator for the study of water and gas cone phenomena
in the producer well (represented by a sink) is obtained by combining the Boundary Element Method
(BEM) and the Isogeometric Formulation using the NURBS (Non Uniform Rational B-Spline) as
shape functions. Through the Isogeometric Formulation, the discretization of the geometric model
(mesh generation), which is the step of the numerical analysis that requires more time for the engineer,
is no longer necessary, since the same functions that describe the geometry can also approximate the
field variables in the BEM, making it a great advantage in its use. The same discretization used in the
geometric model, generated in CAD (Computer Aided Design) modeling programs, can also be used
by the BEM. From the modeling of the potential flow, i.e. the study of multiphase flow in porous
media from the Laplace Equation, the isogeometric formulation can be coupled to the problem and,
therefore, to obtain the reservoir simulator for the single phase case. The determination of the
boundary conditions for the model, including the analysis of fluids interface movement, is also
presented. The final code is able to present itself as an efficient tool for the analysis of oil extraction in
reservoirs in the presence of undesirable fluid production. Validation of the results is carried out by
comparing to the conventional Boundary Element Method.