import numpy as np
from porespy.tools import make_contiguous
from scipy.stats import rankdata
__all__ = [
'size_to_seq',
'size_to_satn',
'seq_to_satn',
'pc_to_satn',
'pc_to_seq',
'satn_to_seq',
]
[docs]
def size_to_seq(size, im=None, bins=None, mode='drainage'):
r"""
Converts an image of invasion size values into invasion sequence values
Parameters
----------
size : ndarray
The image containing invasion size in each voxel. Values of 0 are
assumed to be solid (if ``im`` is not given) and values of -1 are
assumed to be uninvaded.
im : ndarray, optional
A binary image of the porous media, with ``True`` indicating the
void space and ``False`` indicating the solid phase. If not given
then it is assumed that the solid is identified as ``size == 0``.
bins : array_like or int (optional)
The bins to use when converting sizes to sequence. The default is
to create 1 bin for each unique value in ``size`` (except for -1 and 0).
If an **int** is supplied, it is interpreted as the number of bins between 1
and the maximum value in ``size``. If an array is supplied it is used as
the bins directly.
mode : str
Controls how the sizes are converted to a sequence. The options are:
============= ==============================================================
`mode` Description
============= ==============================================================
'drainage' The sizes are assumed to have been filled from largest to
smallest, ignoring 0's and -1's
'imbibition' The sizes are assumed to have been filled from smallest to
largest, ignoring 0's and -1's
============= ==============================================================
Returns
-------
seq : ndarray
An ndarray the same shape as ``size`` with invasion size values
replaced by the invasion sequence, according to the specified `mode`.
Any uninvaded voxels, indicated by -1 in ``size`` will be indicated by
-1 in ``seq``.
Examples
--------
`Click here
<https://porespy.org/examples/filters/reference/size_to_seq.html>`_
to view online example.
"""
if im is None:
solid = size == 0
else:
solid = im == 0
uninvaded = size == -1
if bins is None:
bins = np.unique(size)
elif isinstance(bins, int):
bins = np.linspace(0, size.max(), bins)
vals = np.digitize(size, bins=bins, right=True)
if mode.startswith('im'):
vals[solid] = 0
vals[uninvaded] = -1
vals = make_contiguous(vals, mode='symmetric')
if mode.startswith('dr'):
vals = make_contiguous(vals, mode='symmetric')
vals = vals.max() + 1 - vals
vals[solid] = 0
vals[uninvaded] = -1
return vals
[docs]
def size_to_satn(size, im=None, bins=None, mode='drainage'):
r"""
Converts an image of invasion size values into non-wetting phase saturations.
Parameters
----------
size : ndarray
The image containing invasion size values in each voxel. Solid
should be indicated as 0's and uninvaded voxels as -1.
im : ndarray, optional
A binary image of the porous media, with ``True`` indicating the
void space and ``False`` indicating the solid phase. If not given
then it is assumed that the solid is identified as ``size == 0``.
bins : array_like or int (optional)
The bins to use when converting sizes to saturation. The default is
to create 1 bin for each unique value in ``size``. If an **int**
is supplied it is interpreted as the number of bins between 0 and the
maximum value in ``size``. If an array is supplied it is used as
the bins directly.
mode : str
Controls how the sizes are converted to saturations. The options are:
============= ==============================================================
`mode` Description
============= ==============================================================
'drainage' The sizes are assumed to have been filled from largest to
smallest, ignoring 0's and -1's
'imbibition' The sizes are assumed to have been filled from smallest to
largest, ignoring 0's and -1's
============= ==============================================================
Returns
-------
satn : ndarray
An ndarray the same shape as ``size`` but with size values replaced
by the fraction of void space invaded at each size, according to the
specified `mode`. Solid voxels and uninvaded voxels are represented by 0
and -1, respectively.
Notes
-----
If any ``-1`` values are present in `size` the maximum saturation will be less
than 1.0 since this means that not all wetting phase was displaced.
Examples
--------
`Click here
<https://porespy.org/examples/filters/reference/size_to_satn.html>`_
to view online example.
"""
if bins is None:
bins = np.unique(size[size > 0])
elif isinstance(bins, int):
bins = np.linspace(0, size.max(), bins)
if im is None:
im = ~(size == 0)
void_vol = im.sum()
satn = -np.ones_like(size, dtype=float)
if mode.startswith('im'):
for r in bins:
hits = (size <= r) * (size > 0)
temp = hits.sum()/void_vol
satn[hits * (satn == -1)] = temp
elif mode.startswith('dr'):
for r in bins[-1::-1]:
hits = (size >= r) * (size > 0)
temp = hits.sum()/void_vol
satn[hits * (satn == -1)] = temp
satn *= (im > 0)
return satn
[docs]
def seq_to_satn(seq, im=None, mode='drainage'):
r"""
Converts an image of invasion sequence values to non-wetting phase saturation
values.
Parameters
----------
seq : ndarray
The image containing invasion sequence values in each voxel. Solid
should be indicated as 0's and uninvaded voxels as -1.
im : ndarray, optional
A binary image of the porous media, with ``True`` indicating the
void space and ``False`` indicating the solid phase. If not given
then it is assumed that the solid is identified as ``seq == 0``.
mode : str
Controls how the sequences are converted to saturations. The options are:
============= ==============================================================
`mode` Description
============= ==============================================================
'drainage' The saturation is assumed to increase with increasing sequence
'imbibition' The saturation is assumed to decrease with increasing sequence
============= ==============================================================
Returns
-------
satn : ndarray
An ndarray the same shape as ``seq`` but with sequence values replaced
by the fraction of void space invaded at the sequence number, accounting
for the specified `mode`. Solid voxels and uninvaded voxels are represented
by 0 and -1, respectively.
Notes
-----
If any ``-1`` values are present in `seq` the maximum saturation will be less
than 1.0 since this means that not all wetting phase was displaced.
Examples
--------
`Click here
<https://porespy.org/examples/filters/reference/seq_to_satn.html>`_
to view online example.
"""
seq = np.copy(seq).astype(int)
if im is None:
solid_mask = seq == 0
else:
solid_mask = im == 0
uninvaded_mask = seq == -1 # Store uninvaded locations
seq[seq <= 0] = 0 # Set uninvaded to solid for next steps
if mode.startswith('im'):
seq = seq.max() - seq + 1
seq[solid_mask] = 0
seq[uninvaded_mask] = 0
seq = rankdata(seq, method='dense') - 1
b = np.bincount(seq)
if (solid_mask.sum(dtype=np.int64) > 0) or \
(uninvaded_mask.sum(dtype=np.int64) > 0):
b[0] = 0
c = np.cumsum(b)
seq = np.reshape(seq, solid_mask.shape)
satn = c[seq]/(seq.size - solid_mask.sum(dtype=np.int64))
satn[solid_mask] = 0
satn[uninvaded_mask] = -1
return satn
def pc_to_seq(pc, im, mode='drainage'):
r"""
Converts an image of capillary entry pressures to invasion sequence values
Parameters
----------
pc : ndarray
A Numpy array with the value in each voxel indicating the capillary
pressure at which it was invaded. In order to accommodate the
possibility of both positive and negative capillary pressure values,
uninvaded voxels should be indicated by ``+inf`` and residual phase
by ``-inf``. Solid vs void phase is defined by ``im`` which is
mandatory.
im : ndarray
A Numpy array with ``True`` values indicating the void space
mode : str
Controls how the pressures are converted to sequence. The options are:
============= ==============================================================
`mode` Description
============= ==============================================================
'drainage' The pressures are assumed to have been filled from smallest to
largest. Voxels with -np.inf are treated as though they are
invaded by non-wetting fluid at the start of the process, and
voxels with +np.inf are treated as though they are never
invaded.
'imbibition' The pressures are assumed to have been filled from largest to
smallest. Voxels with -np.inf are treated as though they are
already occupied by non-wetting fluid at the start of the
process, and voxels with +np.inf are treated as though they
are filled with wetting phase.
============= ==============================================================
Returns
-------
seq : ndarray
A Numpy array the same shape as `pc`, with each voxel value indicating
the sequence at which it was invaded, according to the specified `mode`.
Uninvaded voxels are set to -1.
Notes
-----
Voxels with `+inf` are treated as though they were never invaded so are given a
sequence value of -1. Voxels with `-inf` are treated as though they were
invaded by non-wetting phase at the start of the simulation so are given a
sequence number of 1 for both mode `drainage` and `imbibition`.
Examples
--------
`Click here
<https://porespy.org/examples/filters/reference/pc_to_seq.html>`_
to view online example.
"""
inf = pc == np.inf # save for later
if mode == 'drainage':
bins = np.unique(pc)
elif mode == 'imbibition':
pc[pc == -np.inf] = np.inf
bins = np.unique(pc)[-1::-1]
a = np.digitize(pc, bins=bins)
a[~im] = 0
a[np.where(inf)] = -1
a = make_contiguous(a, mode='symmetric')
return a
[docs]
def pc_to_satn(pc, im, mode='drainage'):
r"""
Converts an image of capillary entry pressures to saturation values
Parameters
----------
pc : ndarray
A Numpy array with the value in each voxel indicating the capillary
pressure at which it was invaded. In order to accommodate the
possibility of both positive and negative capillary pressure values,
uninvaded voxels should be indicated by ``+inf`` and residual phase
by ``-inf``. Solid vs void phase is defined by ``im`` which is
mandatory.
im : ndarray
A Numpy array with ``True`` values indicating the void space
mode : str
Controls how the pressures are converted to sequence. The options are:
============= ==============================================================
`mode` Description
============= ==============================================================
'drainage' The pressures are assumed to have been filled from smallest to
largest.
'imbibition' The pressures are assumed to have been filled from largest to
smallest
============= ==============================================================
Returns
-------
satn : ndarray
A Numpy array the same shape as `pc`, with each voxel value indicating
the global saturation at which it was invaded, according to the specified
`mode`. Voxels with `-inf` are treated as though they were invaded
at the start of the simulation so are given a sequence number of 1 for both
mode `drainage` and `imbibition`.
Notes
-----
If any ``+inf`` values are present the maximum saturation will be less than
1.0 since not all wetting phase was displaced.
Examples
--------
`Click here
<https://porespy.org/examples/filters/reference/pc_to_satn.html>`_
to view online example.
"""
a = np.digitize(pc, bins=np.unique(pc))
a[~im] = 0
a[np.where(pc == np.inf)] = -1
satn = seq_to_satn(seq=a, im=im, mode=mode)
return satn
[docs]
def satn_to_seq(satn, im=None, mode='drainage'):
r"""
Converts an image of nonwetting phase saturations to invasion sequence
values
Parameters
----------
satn : ndarray
A Numpy array with the value in each voxel indicating the global
saturation at the point it was invaded. -1 indicates a voxel that
not invaded, and 0 indicates solid phase.
im : ndarray
A Numpy array with ``True`` values indicating the void space.
mode : str
Controls how the saturations are converted to sequence. The options are:
============= ==============================================================
`mode` Description
============= ==============================================================
'drainage' The pressures are assumed to have been filled from smallest to
largest, ignoring 0's and -1's
'imbibition' The sizes are assumed to have been filled from largest to
smallest, ignoring 0's and -1's
============= ==============================================================
Returns
-------
seq : ndarray
A Numpy array the same shape as `satn` with each voxel value indicating
the sequence in which it was invaded, according to the specified `mode`.
Solid voxels are indicated by 0 and uninvaded by -1.
Examples
--------
`Click here
<https://porespy.org/examples/filters/reference/satn_to_seq.html>`_
to view online example.
"""
if im is None:
im = satn > 0
uninvaded = satn == -1
values = np.unique(satn)
seq = np.digitize(satn, bins=values)
# Set uninvaded by to -1
seq[satn == -1] = -1
# Set solids back to 0
seq[~im] = 0
# Ensure values are contiguous while keeping -1 and 0
seq = make_contiguous(im=seq, mode='symmetric')
if mode.startswith('im'):
seq = (seq.max() + 1) - seq
seq[~im] = 0
seq[uninvaded] = -1
return seq