porespy.filters.satn_to_time

porespy.filters.satn_to_time(satn, im, flow_rate, voxel_size=1.0, mode='drainage')

Converts a saturation map to a time-of-invasion map for a constant flow-rate injection.

Parameters:

• satn (ndarray) – The saturation map produced by an invasion simulation. Each void voxel holds the global saturation at the moment it was invaded (in the convention used by seq_to_satn and pc_to_satn: invading-phase saturation for drainage, defending-phase saturation for imbibition). Solid voxels should be 0 and trapped (never-invaded) voxels -1.

• im (ndarray) – A boolean image of the porous medium, with True indicating the void space and False indicating the solid phase.

• flow_rate (scalar) – The volumetric injection rate of the displacing fluid, in units of [length]^ndim / [time] consistent with voxel_size.

• voxel_size (scalar) – The physical size of a voxel side, in [length] units consistent with flow_rate. Default is 1.0, in which case the returned times are in units of voxels^ndim / flow_rate.

• mode (str) –

  Controls how the saturation is interpreted. Options are:

  mode	Description
  ’drainage’	satn is the invading-phase saturation; it increases over time. t = satn * V_void / flow_rate.
  ’imbibition’	satn is the defending-phase saturation; it decreases over time. t = (1 - satn) * V_void / flow_rate.

Returns:

time – An ndarray the same shape as satn. Each void voxel holds the time at which it was invaded. Solid voxels are 0 and trapped voxels are -1.

Return type:

ndarray

Notes

V_void = im.sum() * voxel_size**im.ndim is the total void volume. The underlying assumption is constant volumetric flow rate, so injected volume grows linearly with time and saturation maps directly to time. Residual voxels (already-invaded at $t=0$) end up at a small positive time equal to the time it would take to inject the residual volume.

Examples

Click here to view online example.