Numerical Simulation of Fluid Flows in Petroleum Reservoirs Using a Cell Centered Non-Linear Finite Volume Method in Unstructured Polygonal Meshes

Fernando Contreras¹; Marcio Souza¹; Paulo Lyra¹; Darlan Carvalho¹

¹ Universidade Federal de Pernambuco

doi:10.20906/CPS/CILAMCE2015-0630

Resumo

The numerical approximation of the equations that describe the incompressible fluid flow in petroleum reservoirs represents a great challenge from a numerical point of view. In fact, for the elliptic pressure equation the permeability tensor can be highly anisotropic, and, as far as the authors know, no linear convergent scheme can guarantee monotone solutions for any polygonal mesh or high anisotropy ratio, producing spurious oscillations for the pressure variable. Besides, the non-linear hyperbolic character of the saturation equation may lead to the formation of saturation shocks even when the initial saturation distribution is smooth throughout the reservoir. In general, the system of equations that describes the fluid flow in petroleum reservoirs can be solved by an IMPES (Implicit Pressure Explicit Saturation) procedure, in which the pressure field is solved implicitly and the saturation field is computed explicitly. In the present work, to solve the pressure equation, we use a Non-Linear Finite Volume method that honors the Linearity-Preserving (LP) criterion and produces monotone solution on any star-shaped polygonal meshes and arbitrary anisotropic permeability tensors. To solve the saturation equation, we use a multidimensional 2ndorder MUSCL-Type finite volume method to reduce the artificial numerical diffusion and the Grid Orientation Effect (GOE). To show the potential of our finite volume formulation, we solve some benchmark problems found in literature.

Palavras-chave: Oil-Water Displacements; Numerical Simulation; Non-Linear Monotone Finite Volume; MUSCL