Effective transmissibilities of a gridblock by upscaling - why use renormalization?

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:468141

Peaceman, D W

Previous methods for upscaling fine-scale permeability data for use in reservoir simulation produce effective permeabilities for each simulator gridblock. Since transmissibilities between neighboring gridblocks are required by the simulator, it is better to determine six {open_quotes}half-block transmissibilities{close_quotes} for each gridblock. These can be calculated directly by solving the finite-difference equations for pressure in each of six half-blocks, wherein uniform pressures are applied at two opposite faces and no-flow conditions are applied at the other four faces. Alternatively, in order to reduce computation time, renormalization has been proposed for calculating effective permeabilities of the gridblocks. These previous proposals ignore anisotropy and require that the elemental blocks and each coarse block be rectangular. In this paper, renormalization is modified to avoid these disadvantages. While it might be expected to be faster than the direct pressure solution, renormalization is inherently less accurate. Furthermore, renormalization is not easily implemented unless there are N x N x N elemental blocks within each coarse block, where N is a power of 2. However, the direct method is much more flexible with regard to the number of elemental blocks in each direction. Comparison of running times shows that a highly efficient iterative solver for the direct method is just as fast as renormalization.

• OSTI ID: 468141
• Report Number(s): CONF-961003--
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
58 GEOSCIENCES
99 GENERAL AND MISCELLANEOUS
COMPUTERIZED SIMULATION
GEOLOGIC MODELS
KRIGING
PERMEABILITY
PETROLEUM DEPOSITS
RENORMALIZATION
RESERVOIR ROCK