An {U}pscaling {T}echnique for {G}eomechanical {P}roperties

in: X {E}uropean {C}onference on the {M}athematics of {O}il {P}roceedings, European {A}ssociation of {G}eoscientist and {E}ngineers

Abstract

Fine levels of details for mechanical rock properties can be simulated at the reservoir modeling stages thanks to the impressive growing in computer power efficiency. However, It is sometimes necessary to model large scale reservoirs with large cells, while rock properties are determined at smaller scales. Then, the challenge is to determine the equivalent properties of heterogenous elastic but transversely isotropic materials at an intermediate scale of the reservoir and not only at the laboratory sample scale. This work presents a new technique in Upscaling for mechanical rock properties. It implies a Finite-Element approach and a least-square approximation. Each coarse cell is composed of several fine-scale cells. Each of the small cells is supposed to have isotropic elastic mechanical properties. The main point of this work is to assume that the coarse cells are transversely isotropic. Then, it is possible to build a local equivalent compliance tensor on a coarse cell from three "numerical mechanical" experiments (two odoemetric tests, and one pure shear) using Finite Elements Analysis. This methodology was proposed by (Royer, 2005; Mallet, 2005) for permeability upscaling, which is suggested here to be extended to geomechanical problems.

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    BibTeX Reference

    @INPROCEEDINGS{titeuxetal2006ECMOR,
        author = { Titeux, Marc-Olivier and Mallet, Jean-Laurent and Royer, Jean-Jacques },
         title = { An {U}pscaling {T}echnique for {G}eomechanical {P}roperties },
         month = { September },
     booktitle = { X {E}uropean {C}onference on the {M}athematics of {O}il {P}roceedings },
          year = { 2006 },
    organization = { European {A}ssociation of {G}eoscientist and {E}ngineers },
       address = { Amsterdam, {T}he {N}etherlands },
      abstract = { Fine levels of details for mechanical rock properties can be simulated at the reservoir modeling stages thanks to the impressive growing in computer power efficiency. However, It is sometimes necessary to model large scale reservoirs with large cells, while rock properties are determined at smaller scales. Then, the challenge is to determine the equivalent properties of heterogenous elastic but transversely isotropic materials at an intermediate scale of the reservoir and not only at the laboratory sample scale. This work presents a new technique in Upscaling for mechanical rock properties. It implies a Finite-Element approach and a least-square approximation. Each coarse cell is composed of several fine-scale cells. Each of the small cells is supposed to have isotropic elastic mechanical properties. The main point of this work is to assume that the coarse cells are transversely isotropic. Then, it is possible to build a local equivalent compliance tensor on a coarse cell from three "numerical mechanical" experiments (two odoemetric tests, and one pure shear) using Finite Elements Analysis. This methodology was proposed by (Royer, 2005; Mallet, 2005) for permeability upscaling, which is suggested here to be extended to geomechanical problems. }
    }