Upscalling Relative Permeability with gOcad using a strealine-based Approach

@inproceedings{RUNKJRM11,
 abstract = { Upscaling aims at determining equivalent homogeneous parameters at a coarse-scale from a spatially heterogeneous
fine-scale parameter distribution. This homogenization technique is extensively used in reservoir
oil simulators for manipulating a limited number of relatively large grid-blocks on which properties
have been obtained from previous geological or geostatistical studies using well logging and/or seismic
data. This paper proposes to compute the upscaled two-phase relative permeability at a coarse grid from
a spatially fine-scale grid (SGrid) using numerical approximation methods. The propose method consists
in solving the saturation equation using a stream-line approach in order to decouple the resolution of the
continuity equation (Darcy’s law) and the saturation equation. The streamline approach offers substantial
computational efficiency and numerical accuracy compared to traditional finite-element methods because
it transforms a 3D transport problem into several 1D problems.
This method uses a standard homogenization technique to estimate the total mobility by solving
the continuity equation (Darcy’s law) by a finite-element method (Thermass plug-in). Then, at each
step-time, the two-phase saturation equation (black oil model) is solved along the 1D stream-lines. The
mobility is then mapped onto the fine-scale grid and the new streamline field is again estimated till the
block is saturated in water. The up-scaled absolute permeability is then derived together with the relative
permeability versus saturation curve.
This approach has been applied to mono-phase case-studies for validating the methodology. For the
two-phase case, it was validated on simple cases for which solutions are known. },
 author = { Royer, Jean-Jacques AND Voillemont, Jean-Charles AND Thenin, D. },
 booktitle = { 22nd Gocad Meeting },
 chapter = { 0 },
 location = { Nancy },
 month = { "jun" },
 title = { Upscalling Relative Permeability with gOcad using a strealine-based Approach },
 year = { 2002 }
}