Aplicação do método dos elementos de contorno na simulação dos fenômenos dos cones de água e de gás em poços de petróleo horizontais

This paper presents a study on water and gas coning phenomena in horizontal oil wells. The scope is their two-dimensional numerical modeling using the Boundary Element Method. This text provides a review of these phenomena including their impact on oil industry in order to situate the reader about the motivation for the study of this subject. Two potential flow models, single-phase and two-phase, are used. A third model, single-phase compressible flow is also applied. All the mathematical treatment involved in the deduction of the models’ governing equations is presented. Also present are the mathematical developments of three formulations of the Boundary Element Method. They are the formulation for problems governed by the Laplace equation, the Dual Reciprocity formulation for problems governed by the diffusion equation, and the sub-regions formulation, for problems within a domain which is homogeneous by parts. The details of mathematical development for analytical integration of the influence matrices is shown and used to ensure better performance of the developed simulators. An alternative modeling of horizontal oil wells in two-dimensional domain is proposed, using a set of point sinks to represent its perimeter. This approach allows to satisfactorily analyze the behavior of fluids interface, even after it reaches the well. Implementation of the three simulators is documented to enable the use of this material as reference text for similar implementations. Determination of boundary conditions for the three models, including compatibility and equilibrium at the interface are presented. The proposed simulators were developed and validated in comparison to available analytical results.