Abstract: Horizontal Permeability Anisotropy Developed from the Upscaling of Anisotropic Facies Patterns
R. J. Norris, G. J. Massonnat, D. Gommard
Traditionally, the size and shape of grid blocks owe more to the limitations of numerical simulation procedures than to any consideration of geological heterogeneity. Geological systems, and hence associated permeability and porosity fields, are inherently complex, being characterized by nested levels of heterogeneity. Moreover, for directionally dependent variables, such as permeability, a heterogeneous nature at small scales will lead directly to anisotropy in average (or measured) values at larger scales. The representation of geologically complex volumes as individual horizontal and vertical permeability values has long been recognized as a necessary simplification. Recent advances in stochastic modeling have vastly improved the representation of complex geology in unknown interwe l regions. The high level of detail provided by such models often requires several million grid blocks. This degree of detail cannot, however, be used in flow simulations, and hence, scaling up is necessary.
The difficulties in scaling up of rock-property data are based on the conflicting requirements of significantly reducing the number of grid blocks, while maintaining a reasonable degree of detail in the representation of heterogeneity. To analyze whether grid blocks adequately represent complex heterogeneities we constructed complex, geologically realistic channel-levee complexes, using an object-modeling (Boolean) approach. This approach has the advantage over reservoir, or outcrop, derived data in so much as the 3-D architecture is fully known. The disadvantages are that the realizations are too simplistic, not necessarily geologically realistic, and contain only one scale of heterogeneity. In the present context, however, simplification of both geological and scale-related heteroge eities can be seen as advantageous in the interpretation of the results.
Using known heterogeneous geological systems, constructed by stochastic (Boolean) modeling, the impact of varying the size and shape of up-scaling blocks is investigated. The results are interpreted in terms of the representation of the fine-scale geological heterogeneity by anisotropic permeability (Kx, Ky, and Kz) values. The accurate representation of heterogeneity breaks down at certain scales, with significant detail being lost. Similarly, the shape of the grid blocks is shown to impact the representation of heterogeneity. Indeed, the use of non-square (x, y) grids, aligned to geological anisotropy, can be seen as a criterion for maximizing the efficiency of the gridding; that is, minimizing the number of grid blocks, while guarding the anisotropy of sedimentary bodies. It is ver important to note that the upscaling has not been optimized in terms of the fluid-flow representation, but only in terms of geological anisotropy.
AAPG Search and Discovery Article #90982©1994 AAPG International Conference and Exhibition, Kuala Lumpur, Malaysia, August 21-24, 1994