Towards the application of Stokes' viscous flow equations to structural restoration simulations

Melchior Schuh-senlis and Cedric Thieulot and Guillaume Caumon and Paul Cupillard. ( 2019 )
in: 2019 Ring Meeting, ASGA

Abstract

Modelling the mechanical behavior of the subsurface at various spatial and temporal scales may be achieved using different rheologies and mechanical parameters in the same model. However, most numerical techniques face major difficulties in handling different rheologies because of the huge computation cost resulting from the simultaneous application of different mechanical laws. As a consequence, (possibly strong) assumptions on rock behaviour are often made to alleviate the modelling and ease the simulations. In geomechanical restoration, numerical methods to date rely on considering the rock properties as fully elastic and applying boundary conditions, along with restoring faults using geometric frictionless contact methods. However, salt rock in particular has been proven to behave as a Stokes viscous fluid in geomechanics, and faults appear in rocks reaching a plastic limit inside a shear zone. In order to take these behaviours into account while reducing the computation cost of mechanical simulations, we study here the possibility of using Stokes equations in a geomechanical restoration scheme. Such a strategy seems reasonable since rocks have been found to be mainly ductile in large deformations under long time periods (10^5 to 10^9 years). Moreover, the resolution of Stokes' equations for the velocity is computed at each time step only from the current state of boundary conditions and inside rheology. This led us to a new restoration method based on applying a movement proportional to but in the inverse direction of the forwardly computed velocity. It has been tested on simple models and shows a great potential for restoration using only mechanical and not geometrical conditions. Benchmarks were also implemented with his code to validate the results of its simulations.

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BibTeX Reference

@INPROCEEDINGS{SchuhSenlisRM2019,
    author = { Schuh-senlis, Melchior and Thieulot, Cedric and Caumon, Guillaume and Cupillard, Paul },
     title = { Towards the application of Stokes' viscous flow equations to structural restoration simulations },
 booktitle = { 2019 Ring Meeting },
      year = { 2019 },
 publisher = { ASGA },
  abstract = { Modelling the mechanical behavior of the subsurface at various spatial and temporal scales may be achieved using different rheologies and mechanical parameters in the same model. However, most numerical techniques face major difficulties in handling different rheologies because of the huge computation cost resulting from the simultaneous application of different mechanical laws. As a consequence, (possibly strong) assumptions on rock behaviour are often made to alleviate the modelling and ease the simulations. In geomechanical restoration, numerical methods to date rely on considering the rock properties as fully elastic and applying boundary conditions, along with restoring faults using geometric frictionless contact methods. However, salt rock in particular has been proven to behave as a Stokes viscous fluid in geomechanics, and faults appear in rocks reaching a plastic limit inside a shear zone. In order to take these behaviours into account while reducing the computation cost of mechanical simulations, we study here the possibility of using Stokes equations in a geomechanical restoration scheme. Such a strategy seems reasonable since rocks have been found to be mainly ductile in large deformations under long time periods (10^5 to 10^9 years). Moreover, the resolution of Stokes' equations for the velocity is computed at each time step only from the current state of boundary conditions and inside rheology. This led us to a new restoration method based on applying a movement proportional to but in the inverse direction of the forwardly computed velocity. It has been tested on simple models and shows a great potential for restoration using only mechanical and not geometrical conditions. Benchmarks were also implemented with his code to validate the results of its simulations. }
}