Influencia de la permeabilidad vertical en el flujo de petroleo hacia un pozo productor

The two dimensional flow of oil through an heterogeneous porous media is described using a parabolic partial differential equation, which is an extension of the diffusivity equation. This model has practical interest in reservoir engineering: it is used to predict the production of an oil well and also in well test analysis. The numerical solution is obtained by applying a family of finite difference schemes which depend on one parameter. A technique based on Taylor Series of Matrix Functions (TSMF) is used to solve the resulting system of linear equations. The numerical simulator is applied to study the behavior of two-layer reservoirs with vertical permeability less or equal than horizontal permeability. Specifically, the influence of vertical permeability is analyzed for an oil well producing at constant rate. We deduce that vertical permeability affects pressure and flow rate response at low and intermediate times, therefore is has to be considered in the design and interpretation of pressure transient tests