satn_profile

Computes the saturation profiles in an invasion image

import matplotlib.pyplot as plt
import numpy as np
import porespy as ps
ps.visualization.set_mpl_style()

[01:04:21] ERROR    PARDISO solver not installed, run `pip install pypardiso`. Otherwise,          _workspace.py:56
                    simulations will be slow. Apple M chips not supported.

Start by performing a basic invasion simulation:

np.random.seed(1)
im = ps.generators.blobs(shape=[150, 150], porosity=0.6, blobiness=1)
pc = ps.filters.capillary_transform(im=im, sigma=0.01, theta=180, g=0)
inlets = np.zeros_like(im)
inlets[0, :] = True
inv = ps.simulations.drainage(im=im, pc=pc, inlets=inlets)

fig, ax = plt.subplots(1, 2, figsize=[12, 6])
ax[0].imshow(inv.im_satn/im, interpolation='none', origin='lower')
ax[0].axis(False)
ax[0].set_title('Saturation map')
ax[1].imshow((inv.im_satn < 0.6)*(inv.im_satn > 0)/im, interpolation='none', origin='lower')
ax[1].axis(False)
ax[1].set_title('Fluid distribution at saturation = 0.6');
../../../_images/12269657619e250766f0ed73cb4af91f368b36e72bf7678b1e32545c2bf3599a.png

satn

This is the output of the invasion function, converted to saturation if needed:

s_prof = ps.metrics.satn_profile(satn=inv.im_satn, s=0.6)
plt.plot(s_prof.position, s_prof.saturation, 'b-o')
plt.xlabel("distance from injection face")
plt.ylabel("non-wetting phase saturation");
../../../_images/bc337d5296508acbe5f6a15805118458e8e8addd875e5bdbcf8ab039d3e2fcea.png

s

The global saturation for which the profile should be obtained:

s = 0.6
s_prof1 = ps.metrics.satn_profile(satn=inv.im_satn, s=s)
plt.plot(s_prof1.position, s_prof1.saturation, 'b-o', label=s)

s = 0.4
s_prof2 = ps.metrics.satn_profile(satn=inv.im_satn, s=s)
plt.plot(s_prof2.position, s_prof2.saturation, 'r-o', label=s)

s = 0.1
s_prof3 = ps.metrics.satn_profile(satn=inv.im_satn, s=s)
plt.plot(s_prof3.position, s_prof3.saturation, 'g-o', label=s)

plt.xlabel("distance from injection face")
plt.ylabel("non-wetting phase saturation")
plt.legend();
../../../_images/0688c7edaf8e76e7278462dda8aa7d11720eb45ebae48e0bc52b81f418e0c712.png

span

The width of the slice over which the saturation is computed. The default is 10 voxels. A higher number makes the curve smoother, but risks losing features like dips and spikes:

s = 5
s_prof1 = ps.metrics.satn_profile(satn=inv.im_satn, s=0.6, span=s)
plt.plot(s_prof1.position, s_prof1.saturation, 'b-o', label=s)

s = 10
s_prof2 = ps.metrics.satn_profile(satn=inv.im_satn, s=0.6, span=s)
plt.plot(s_prof2.position, s_prof2.saturation, 'r-o', label=s)

s = 30
s_prof3 = ps.metrics.satn_profile(satn=inv.im_satn, s=0.6, span=s)
plt.plot(s_prof3.position, s_prof3.saturation, 'g-o', label=s)

plt.xlabel("distance from injection face")
plt.ylabel("non-wetting phase saturation")
plt.legend();
../../../_images/5e67eca62c6abb042543104ba851254e110c62a5b138751e882f341f0fbe7527.png

mode

How the averaging window moves, either by sliding or by tiling.

s_prof1 = ps.metrics.satn_profile(satn=inv.im_satn, s=0.6, mode='slide')
plt.plot(s_prof1.position, s_prof1.saturation, 'b-o', label=s)

s_prof2 = ps.metrics.satn_profile(satn=inv.im_satn, s=0.6, mode='tile')
plt.plot(s_prof2.position, s_prof2.saturation, 'r-o', label=s)

plt.xlabel("distance from injection face")
plt.ylabel("non-wetting phase saturation")
plt.legend();
../../../_images/3ecc0eac1db85bceeb36eeb7484659089484f64bdb5478cc1486e6fd4e09e60f.png

axis

The direction along with the averaging window moves. This can be perpendicular to the axis where the injection occurred to give additional insights into the saturation distribution:

s_prof1 = ps.metrics.satn_profile(satn=inv.im_satn, s=0.6, axis=0)
plt.plot(s_prof1.position, s_prof1.saturation, 'b-o', label=0)

s_prof2 = ps.metrics.satn_profile(satn=inv.im_satn, s=0.6, axis=1)
plt.plot(s_prof2.position, s_prof2.saturation, 'r-o', label=1)

plt.xlabel("distance from injection face")
plt.ylabel("non-wetting phase saturation")
plt.legend();
../../../_images/83e31253c48bb8af25f058a383ac9d0bb6ab8ba4791be15ecc88d8bf876f7784.png