Polygonal Mesh Generation from Equipotentials Accounting for Geostatistical Heterogeneities.

Caroline Godefroy and Guillaume Caumon and Christophe Antoine. ( 2009 )
in: Proc. 29th Gocad Meeting, Nancy

Abstract

In reservoir modeling practice, it is common to upscale fine-scale petrophysical grids to perform efficient flow simulation. Because twisted cells are not accepted by every flow simulators, it is important for the upscaled grid cells to be as much orthogonal as possible. Moreover, upscaling should not only compute equivalent properties on a given 3D coarse block geometry, but also strive to optimize the control volume shape to conform to heterogeneities and well layouts. In this paper, we present some preliminary results to achieve this goal by generating a polygonal mesh which conforms to the main heterogeneities described by the fine-scale petrophysical models. The resulting mesh should fit with the sedimentary objects such as channels, but also be adapted to the heterogeneity variations. Indeed, the mesh should be coarser on zones where the geostatistical property is homogeneous, but finer where high heterogeneities occur or where the flow rate is high. Cartesian grids containing the geostatistical property are used for generating such a mesh. They are divided into slices to allow surface treatments. The level sets of the geostatistical property are then established using a tracking algorithm. Orthogonal crossing lines are obtained by computing the streamlines in the current Cartesian grid section using Pollock’s method. On each current slice, the level sets and the streamlines define by construction a sub-orthogonal mesh which follows the geostatistical property heterogeneities.

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BibTeX Reference

@INPROCEEDINGS{GodefroyGM2009,
    author = { Godefroy, Caroline and Caumon, Guillaume and Antoine, Christophe },
     title = { Polygonal Mesh Generation from Equipotentials Accounting for Geostatistical Heterogeneities. },
 booktitle = { Proc. 29th Gocad Meeting, Nancy },
      year = { 2009 },
  abstract = { In reservoir modeling practice, it is common to upscale fine-scale petrophysical grids to perform efficient flow simulation. Because twisted cells are not accepted by every flow simulators, it is important for the upscaled grid cells to be as much orthogonal as possible. Moreover, upscaling should not only compute equivalent properties on a given 3D coarse block geometry, but also strive to optimize the control volume shape to conform to heterogeneities and well layouts. In this paper, we present some preliminary results to achieve this goal by generating a polygonal mesh which conforms to the main heterogeneities described by the fine-scale petrophysical models. The resulting mesh should fit with the sedimentary objects such as channels, but also be adapted to the heterogeneity variations. Indeed, the mesh should be coarser on zones where the geostatistical property is homogeneous, but finer where high heterogeneities occur or where the flow rate is high. Cartesian grids containing the geostatistical property are used for generating such a mesh. They are divided into slices to allow surface treatments. The level sets of the geostatistical property are then established using a tracking algorithm. Orthogonal crossing lines are obtained by computing the streamlines in the current Cartesian grid section using Pollock’s method. On each current slice, the level sets and the streamlines define by construction a sub-orthogonal mesh which follows the geostatistical property heterogeneities. }
}