SPE11 Geometry Files

This folder contains geometry files for the SPE11 variants in the gmsh geometry format. Note: all files have been tested with gmsh version 4.11.1. In case you experience issues, consider upgrading your gmsh version. This may be required, in particular, for the Python scripts using the gmsh API (see below).

You can open the geometry files with gmsh, or let it create a mesh directly via the command line with

gmsh -2 FILENAME.geo  # creates a 2d mesh in the file FILENAME.msh
gmsh -3 FILENAME.geo  # creates a 3d mesh in the file FILENAME.msh

This produces the gmsh file format (.msh), however, gmsh can export the mesh into a variety of different formats. The easiest way to achieve this is by opening the .msh file with gmsh, and then clicking file > export. This lets you choose from a list of supported file formats. Note that you can also open the geometry in gmsh and export that into different geometry formats, if needed. For instance, in order to use a different meshing tool.

Note that the geometry files contain information about which facies the individual geometries belong to. This information also ends up in the .msh files such that for each element of the discretization, a corresponding facies index can be retrieved. In gmsh this is done via the mechanism of "physical indices". When you export into a different geometry or mesh file format, you will have to check if or how this information is forwarded.

SPE11-A (spe11a.geo)

Important: the geometry is defined in the x-y plane, that is, all point coordinates are given in the form of (x, y, 0.0). The description defines the geometry in the x-z plane (to be in agreement with variant C), however, we have chosen the x-y plane here in order to facilitate the parsing of two-dimensional meshes created with this geometry file.

This file contains the geometry of the SPE11 variant A. At the beginning of the file you can see a large list of mesh size definitions around individual points of the geometry. You can modify these individually to achieve the desired mesh, or, you can conveniently scale all mesh sizes with the provided command-line argument refinement_factor. That is, in order to generate a mesh with a characteristic mesh size twice as coarse as the default, you may invoke gmsh as follows:

# produces spe11a.msh with mesh sizes twice as coarse as the default
gmsh -2 spe11a.geo -setnumber refinement_factor 2.0

Besides this, you can use the with_facies_7 option (default: 1), to remove all elements in facies 7:

# produces spe11a.msh with all elements in facies 7 removed
gmsh -2 spe11a.geo -setnumber with_facies_7 0

SPE11-B (spe11b.geo)

Important: as for variant A, the geometry is defined in the x-y plane, while the description defines the geometry in the x-z plane in order to be in agreement with variant C. See the above section for more details.

This file contains the geometry of the SPE11 variant B. Internally, it reuses spe11a.geo and scales it to the required dimensions. The default mesh sizes of spe11a.geo are also scaled in order to fit to the extended domain sizes. However, you can still scale the default mesh size with a runtime argument:

# produces spe11b.msh with mesh sizes twice as coarse as the default for variant B
gmsh -2 spe11b.geo -setnumber refinement_factor 2.0

You can also again decide to remove all elements inside facies 7:

# produces spe11b.msh with all elements in facies 7 removed
gmsh -2 spe11b.geo -setnumber with_facies_7 0

SPE11-C (make_spe11c.py)

This is a generator script for producing the geometry of the SPE11 variant C. It makes use of the Python API of gmsh, and thus, you need to have python and the gmsh Python package available. The latter can simply be installed via pip with pip install gmsh.

The script takes the spe11b.geo file and rotates and extrudes the geometry according to the description of variant C. After successful execution, the script produces the file spe11c.geo (and spe11c.brep, which is included internally). The script also takes a runtime argument mesh-size that controls the mesh size to be used at all points of the resulting geometry:

# generates spe11c.geo with a characteristic mesh size of 250m to be used around all points
python3 make_spe11c_geo.py --mesh-size 250

Structured grid generation (make_structured_mesh.py)

Important: for the variants A & B, keep in mind that the geometries are defined in the x-y plane instead of the x-z plane used in the description. See the above sections for more details.

If you need a structured mesh for your simulator, you may use this script to generate a .msh file containing a structured mesh including the facies indices that all elements of the mesh belong to. The script takes the SPE variant and the resolution as runtime arguments. That is, to generate structured meshes for all three variants, you can use the script in the following way:

# generate a 200x200 mesh for variant A in the file spe11a_structured.msh
python3 make_structured_mesh.py --variant A -nx 200 -ny 200
# generate a 200x200 mesh for variant B in the file spe11b_structured.msh
python3 make_structured_mesh.py --variant B -nx 200 -ny 200
# generate a 200x200x200 mesh for variant C in the file spe11c_structured.msh
python3 make_structured_mesh.py --variant C -nx 200 -ny 200 -nz 200

Note that this script also requires the Python API of gmsh. Furthermore, passing the flag --remove-cells-in-facies-7 creates mesh files in which the cells in all regions of facies 7 are removed.

Extrusion of 2D meshes to one cell thick 3D meshes

The script extrude_and_rotate.py can be used to extrude 2D generated meshes to one cell thick 3D vtk versions for simulators that are not accepting such 2D meshes, .

Leveraging vtk, it reads from a gmsh generated vtk mesh, extrudes it with one cell in the 3rd dimension and rotates it in the x-z plane.

Important: The script is not detecting either if it is a structured mesh (based on quads) or unstructured (based on triangles), so we have to provide it with the explicit option --quad or --tri.

The full procedure is then, for instance for spe11-a:

gmsh -2 spe11a.geo -format vtk
python3 extrude_and_rotate.py --tri --spe a spe11a.vtk
#optionally some clean up
rm -iv spe11a.vtk

This should produce a file spe11a_extruded.vtu that can be inspected with paraview or another vtk enabled 3D reader. The cell data of porosity and permeability are tagged as PORO and PERM in this output. The facies labels are registered under attribute.

An additional option exists for applying pore-volume modification for case spe11-b. Then the altered procedure, starting this time from a structured mesh is:

python3 make_structured_mesh.py --variant B -nx 300 -ny 100
meshio convert spe11b_structured.msh spe11b_structured.vtu
python3 extrude_and_rotate.py --quad --poromult --spe b spe11b_structured.vtu
#optionally some clean up
rm -iv spe11b_structured.vtu spe11b_structured.msh

Note: In this last case we use meshio to convert to vtu format (not vtk).

Note: Though valid, the option --poromult will have no effect on spe11-a case.

The file spe11b_structured_extruded.vtu should be produced and can be inspected using paraview or another vtk enabled 3D reader.