injection

injection(im, pc=None, dt=None, inlets=None, outlets=None, maxiter=None, return_sizes=False, return_pressures=True, conn='min', min_size=0, method='qbip')

Performs injection of non-wetting fluid including the effect of gravity and trapping of wetting phase.

Parameters:

• im (ndarray) – A boolean image of the porous media with True values indicating the void space

• pc (ndarray, optional) – Precomputed capillary pressure transform which is used to determine the invadability of each voxel. If not provided then the 2/dt is used, which is equivalent to a surface tension and voxel size of unity, and a contact angle of 180 degrees.

• dt (ndarray (optional)) – The distance transform of im. If not provided it will be calculated, so supplying it saves time.

• inlets (ndarray, optional) – A boolean image with True values indicating the inlet locations. If not provided then the beginning of the x-axis is assumed.

• outlets (ndarray, optional) – A boolean image with True values indicating the outlet locations. If this is provided then trapped voxels of wetting phase are found and all the output images are adjusted accordingly. Note that trapping can be assessed during postprocessing as well.

• return_sizes (bool, default = False) – If True then an array containing the size of the sphere which first overlapped each pixel is returned. This array is not computed by default as computing it increases computation time.

• return_pressures (bool, default = True) – If True then an array containing the capillary pressure at which each pixels was first invaded is returned.

• maxiter (int) – The maximum number of iteration to perform. The default is equal to the number of void pixels in im.

• min_size (int) – Any clusters of trapped voxels smaller than this size will be set to not trapped. This argument is only used if outlets is given. This is useful to prevent small voxels along edges of the void space from being set to trapped. These can appear to be trapped due to the jagged nature of the digital image. The default is 0, meaning this adjustment is not applied, but a value of 3 or 4 is recommended to activate this adjustment.

• conn (str) –

  Controls the shape of the structuring element used to find neighboring voxels. Options are:

  Option	Description
  ’min’	This corresponds to a cross with 4 neighbors in 2D and 6 neighbors in 3D.
  ’max’	This corresponds to a square or cube with 8 neighbors in 2D and 26 neighbors in 3D.

• method (str) –

  Controls the method used perform the simulation. Options are:

  Option	Description
  ’qbip’	Uses ‘queue-based invasion percolation’ [1]. This is the default. It is much faster.
  ’ibip’	Uses ‘image-based invasion percolation’ [2]. This is only provided for completeness since it is the original algorithm.

Returns:

results – A dataclass-like object with the following attributes:

Attribute	Description
im_seq	A numpy array with each voxel value containing the step at which it was invaded. Uninvaded voxels are set to -1.
im_snwp	A numpy array with each voxel value indicating the saturation present in the domain it was invaded. Solids are given 0, and uninvaded regions are given -1.
im_pc	If return_pressures was set to True, then a numpy array with each voxel value indicating the capillary pressure at which it was invaded. Uninvaded voxels have value of np.inf.
im_size	If return_sizes was set to True, then a numpy array with each voxel containing the radius of the sphere, in voxels, that first overlapped it.

Return type:

Results object

References

[1]

Gostick JT, Misaghian N, A Irannezhad, B Zhao. A computationally efficient queue-based algorithm for simulating volume-controlled drainage under the influence of gravity on volumetric images. Advances in Water Resources. 193(11), 104799 (2024)

[2]

Gostick JT, Misaghian N, Yang J, Boek ES. Simulating volume-controlled invasion of a non-wetting fluid in volumetric images using basic image processing tools. Computers and the Geosciences. 158(1), 104978 (2022)

Examples

Click here to view an online example.