Generation and application of Voronoi grid to model flow in heterogeneous reservoirs

A new gridding technique is proposed to simulate fluid flow in heterogeneous petroleum reservoirs with a flexible grid known as Voronoi grid. Several aspects of the gridding technique are investigated in detail: grid generation, assignment and averaging of physical properties, treatment of wells and practical applications. The grid system is generated in the domain by the combination of modules of simple geometry (Cartesian, cylindrical and hexagonal). Each module can be located, scaled and rotated in the physical domain such that the grid geometry conforms to major directions of flow around wells and geologic features. Because each gridpoint can be located independently, the modules can be used, for instance, to conform exactly and simultaneously to the location of a vertical well and the longitudinal direction of a horizontal well.; It is proposed that the specification of the physical properties of the reservoir be decoupled from the specification of the grid geometry. This procedure allowed the development of a technique to compute exact well indices in heterogeneous reservoirs by comparing numerical results obtained with fine and coarse grids. A new simplified well model for heterogeneous reservoirs is also proposed and tested. Homogeneous reservoirs can be treated as a special case of this general well model. Additionally, the decoupling between reservoir description and grid geometry allowed the development of a new upscaling procedure to compute effective permeability of the connections of a flexible grid as the power law average of permeability values at locations close to the connection.; The use a cylindrical module around the injection well significantly minimizes the grid orientation effect for "piston-like", unfavorable mobility displacements in a five-spot pattern. Although the results are almost insensitive to the orientation of the grid, they do not converge as the grid is refined.; Besides the aspects related to the grid system, a new dual timestepping technique is also presented to simulate flow of tracer components in multipurpose simulators with flexible grids. The main system of equations is solved implicitly with a major timestep, which is automatically divided into smaller and stable minor timesteps to march explicitly the tracer concentration in time.