import numpy as _np
import openpnm.models.geometry.conduit_lengths as _conduit_lengths
from openpnm.models.geometry import _geodocs
__all__ = [
"spheres_and_cylinders",
"circles_and_rectangles",
"cones_and_cylinders",
"intersecting_cones",
"hybrid_cones_and_cylinders",
"trapezoids_and_rectangles",
"hybrid_trapezoids_and_rectangles",
"intersecting_trapezoids",
"pyramids_and_cuboids",
"intersecting_pyramids",
"hybrid_pyramids_and_cuboids",
"cubes_and_cuboids",
"squares_and_rectangles",
"intersecting_trapezoids",
"ncylinders_in_series"
]
[docs]
@_geodocs
def spheres_and_cylinders(
network,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
):
r"""
Computes diffusive shape coefficient for conduits assuming pores are
spheres and throats are cylinders.
Parameters
----------
%(network)s
%(Dp)s
%(Dt)s
Returns
-------
size_factors : ndarray
Array (Nt by 3) containing conduit values for each element
of the pore-throat-pore conduits. The array is formatted as
``[pore1, throat, pore2]``.
Notes
-----
The diffusive size factor is the geometrical part of the pre-factor in
Fick's law:
.. math::
n_A = \frac{A}{L} \Delta C_A
= S_{diffusive} D_{AB} \Delta C_A
Thus :math:`S_{diffusive}` represents the combined effect of the area and
length of the *conduit*, which consists of a throat and 1/2 of the pore
on each end.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[1]).T
L1, Lt, L2 = _conduit_lengths.spheres_and_cylinders(
network,
pore_diameter=pore_diameter,
throat_diameter=throat_diameter
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = 2 / (D1 * _np.pi) * _np.arctanh(2 * L1 / D1)
F2 = 2 / (D2 * _np.pi) * _np.arctanh(2 * L2 / D2)
Ft = Lt / (_np.pi / 4 * Dt ** 2)
vals = _np.vstack([1/F1, 1/Ft, 1/F2]).T
return vals
[docs]
@_geodocs
def circles_and_rectangles(
network,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
):
r"""
Computes diffusive shape coefficient for conduits assuming pores are
circles and throats are rectangles
Parameters
----------
%(network)s
%(Dp)s
%(Dt)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[1]).T
L1, Lt, L2 = _conduit_lengths.circles_and_rectangles(
network,
pore_diameter=pore_diameter,
throat_diameter=throat_diameter
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = 0.5 * _np.arcsin(2 * L1 / D1)
F2 = 0.5 * _np.arcsin(2 * L2 / D2)
Ft = Lt / Dt
vals = _np.vstack([1/F1, 1/Ft, 1/F2]).T
return vals
[docs]
@_geodocs
def cones_and_cylinders(
network,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
):
r"""
Computes diffusive shape coefficient assuming pores are truncated cones
and throats are cylinders.
Parameters
----------
%(network)s
%(Dp)s
%(Dt)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[1]).T
L1, Lt, L2 = _conduit_lengths.cones_and_cylinders(
network,
pore_diameter=pore_diameter,
throat_diameter=throat_diameter
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = 4 * L1 / (D1 * Dt * _np.pi)
F2 = 4 * L2 / (D2 * Dt * _np.pi)
Ft = Lt / (_np.pi * Dt**2 / 4)
vals = _np.vstack([1/F1, 1/Ft, 1/F2]).T
return vals
[docs]
@_geodocs
def intersecting_cones(
network,
pore_diameter="pore.diameter",
throat_coords="throat.coords"
):
r"""
Computes diffusive shape coefficient assuming pores are intersecting cones.
Parameters
----------
%(network)s
%(Dp)s
%(Tcoords)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[1]).T
L1, Lt, L2 = _conduit_lengths.intersecting_cones(
network,
throat_coords=throat_coords
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = 4 * L1 / (D1 * Dt * _np.pi)
F2 = 4 * L2 / (D2 * Dt * _np.pi)
inv_F_t = _np.full(len(Lt), _np.inf)
vals = _np.vstack([1/F1, inv_F_t, 1/F2]).T
return vals
[docs]
@_geodocs
def hybrid_cones_and_cylinders(
network,
pore_diameter="pore.diameter",
throat_coords="throat.coords"
):
r"""
Computes diffusive shape coefficient assuming pores are truncated cones
and throats are cylinders.
Parameters
----------
%(network)s
%(Dp)s
%(Tcoords)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[1]).T
L1, Lt, L2 = _conduit_lengths.hybrid_cones_and_cylinders(
network,
pore_diameter=pore_diameter,
throat_coords=throat_coords
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = 4 * L1 / (D1 * Dt * _np.pi)
F2 = 4 * L2 / (D2 * Dt * _np.pi)
Ft = Lt / (_np.pi * Dt**2 / 4)
mask = Lt == 0.0
if mask.any():
inv_F_t = _np.zeros(len(Ft))
inv_F_t[~mask] = 1/Ft[~mask]
inv_F_t[mask] = _np.inf
else:
inv_F_t = 1/Ft
vals = _np.vstack([1/F1, inv_F_t, 1/F2]).T
return vals
[docs]
@_geodocs
def trapezoids_and_rectangles(
network,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
):
r"""
Compute diffusive shape coefficient for conduits assuming pores are
trapezoids and throats are rectangles.
Parameters
----------
%(network)s
%(Dp)s
%(Dt)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[-1]).T
L1, Lt, L2 = _conduit_lengths.trapezoids_and_rectangles(
network,
pore_diameter=pore_diameter,
throat_diameter=throat_diameter
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = L1 * _np.log(Dt / D1) / (Dt - D1)
F2 = L2 * _np.log(Dt / D2) / (Dt - D2)
Ft = Lt / Dt
# Edge case where Di = Dt
mask = _np.isclose(D1, Dt)
F1[mask] = (L1 / D1)[mask]
mask = _np.isclose(D2, Dt)
F2[mask] = (L2 / D2)[mask]
vals = _np.vstack([1/F1, 1/Ft, 1/F2]).T
return vals
[docs]
@_geodocs
def intersecting_trapezoids(
network,
pore_diameter="pore.diameter",
throat_coords="throat.coords"
):
r"""
Computes diffusive shape coefficient for conduits of intersecting
trapezoids.
Parameters
----------
%(network)s
%(Dp)s
%(Tcoords)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[-1]).T
L1, Lt, L2 = _conduit_lengths.intersecting_trapezoids(
network,
throat_coords=throat_coords
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = L1 * _np.log(Dt / D1) / (Dt - D1)
F2 = L2 * _np.log(Dt / D2) / (Dt - D2)
# Edge case where Di = Dt
mask = _np.isclose(D1, Dt)
F1[mask] = (L1 / D1)[mask]
mask = _np.isclose(D2, Dt)
F2[mask] = (L2 / D2)[mask]
inv_F_t = _np.full(len(Lt), _np.inf)
vals = _np.vstack([1/F1, inv_F_t, 1/F2]).T
return vals
[docs]
@_geodocs
def hybrid_trapezoids_and_rectangles(
network,
pore_diameter="pore.diameter",
throat_coords="throat.coords"
):
r"""
Compute diffusive shape coefficient for conduits assuming pores are
trapezoids and throats are rectangles.
Parameters
----------
%(network)s
%(Dp)s
%(Tcoords)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[-1]).T
L1, Lt, L2 = _conduit_lengths.hybrid_trapezoids_and_rectangles(
network,
pore_diameter=pore_diameter,
throat_coords=throat_coords
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = L1 * _np.log(Dt / D1) / (Dt - D1)
F2 = L2 * _np.log(Dt / D2) / (Dt - D2)
Ft = Lt / Dt
# Edge case where Di = Dt
mask = _np.isclose(D1, Dt)
F1[mask] = (L1 / D1)[mask]
mask = _np.isclose(D2, Dt)
F2[mask] = (L2 / D2)[mask]
mask = Lt == 0.0
if mask.any():
inv_F_t = _np.zeros(len(Ft))
inv_F_t[~mask] = 1/Ft[~mask]
inv_F_t[mask] = _np.inf
else:
inv_F_t = 1/Ft
vals = _np.vstack([1/F1, inv_F_t, 1/F2]).T
return vals
[docs]
@_geodocs
def pyramids_and_cuboids(
network,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
):
r"""
Computes diffusive size factor for conduits of truncated pyramids and
cuboids.
Parameters
----------
%(network)s
%(Dp)s
%(Dt)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[-1]).T
L1, Lt, L2 = _conduit_lengths.pyramids_and_cuboids(
network,
pore_diameter=pore_diameter,
throat_diameter=throat_diameter
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = L1 / (D1 * Dt)
F2 = L2 / (D2 * Dt)
Ft = Lt / Dt**2
vals = _np.vstack([1/F1, 1/Ft, 1/F2]).T
return vals
[docs]
@_geodocs
def hybrid_pyramids_and_cuboids(
network,
pore_diameter="pore.diameter",
throat_coords="throat.coords"
):
r"""
Computes diffusive size factor for conduits of truncated pyramids and
cuboids.
Parameters
----------
%(network)s
%(Dp)s
%(Tcoords)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[-1]).T
L1, Lt, L2 = _conduit_lengths.hybrid_pyramids_and_cuboids(
network,
pore_diameter=pore_diameter,
throat_coords=throat_coords
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = L1 / (D1 * Dt)
F2 = L2 / (D2 * Dt)
Ft = Lt / Dt**2
mask = Lt == 0.0
if mask.any():
inv_F_t = _np.zeros(len(Ft))
inv_F_t[~mask] = 1/Ft[~mask]
inv_F_t[mask] = _np.inf
else:
inv_F_t = 1/Ft
vals = _np.vstack([1/F1, inv_F_t, 1/F2]).T
return vals
[docs]
@_geodocs
def intersecting_pyramids(
network,
pore_diameter="pore.diameter",
throat_coords="throat.coords"
):
r"""
Computes diffusive size factor for conduits of pores with intersecting pyramids.
Parameters
----------
%(network)s
%(Dp)s
%(Tcoords)s
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[-1]).T
L1, Lt, L2 = _conduit_lengths.intersecting_pyramids(
network,
throat_coords=throat_coords
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = L1 / (D1 * Dt)
F2 = L2 / (D2 * Dt)
inv_F_t = _np.full(len(Lt), _np.inf)
vals = _np.vstack([1/F1, inv_F_t, 1/F2]).T
return vals
[docs]
@_geodocs
def cubes_and_cuboids(
network,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
pore_aspect=[1, 1, 1],
throat_aspect=[1, 1, 1],
):
r"""
Computes diffusive shape coefficient for conduits assuming pores are
cubes and throats are cuboids.
Parameters
----------
%(network)s
%(Dp)s
%(Dt)s
pore_aspect : list
Aspect ratio of the pores
throat_aspect : list
Aspect ratio of the throats
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[-1]).T
L1, Lt, L2 = _conduit_lengths.cubes_and_cuboids(
network,
pore_diameter=pore_diameter,
throat_diameter=throat_diameter
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = L1 / D1**2
F2 = L2 / D2**2
Ft = Lt / Dt**2
vals = _np.vstack([1/F1, 1/Ft, 1/F2]).T
return vals
[docs]
@_geodocs
def squares_and_rectangles(
network,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
pore_aspect=[1, 1],
throat_aspect=[1, 1],
):
r"""
Computes diffusive size factor for conduits assuming pores are squares
and throats are rectangles.
Parameters
----------
%(network)s
%(Dp)s
%(Dt)s
pore_aspect : list
Aspect ratio of the pores
throat_aspect : list
Aspect ratio of the throats
Returns
-------
Notes
-----
This model should only be used for true 2D networks, i.e. with planar
symmetry.
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[-1]).T
L1, Lt, L2 = _conduit_lengths.squares_and_rectangles(
network,
pore_diameter=pore_diameter,
throat_diameter=throat_diameter
).T
# Fi is the integral of (1/A) dx, x = [0, Li]
F1 = L1 / D1
F2 = L2 / D2
Ft = Lt / Dt
vals = _np.vstack([1/F1, 1/Ft, 1/F2]).T
return vals
[docs]
@_geodocs
def ncylinders_in_series(
network,
pore_diameter="pore.diameter",
throat_diameter="throat.diameter",
n=5
):
r"""
Computes diffusive size factors for conduits of spheres and cylinders
with the spheres approximated as N cylinders in series.
Parameters
----------
%(network)s
%(Dp)s
%(Dt)s
n : int
Number of cylindrical divisions for each pore and throat
Returns
-------
Notes
-----
"""
D1, Dt, D2 = network.get_conduit_data(pore_diameter.split('.', 1)[-1]).T
# Ensure throats are never bigger than connected pores
Dt = _np.minimum(Dt, 0.99 * _np.minimum(D1, D2))
L1, Lt, L2 = _conduit_lengths.spheres_and_cylinders(
network,
pore_diameter=pore_diameter,
throat_diameter=throat_diameter
).T
dL1 = _np.linspace(0, L1, num=n)
dL2 = _np.linspace(0, L2, num=n)
r1 = D1 / 2 * _np.sin(_np.arccos(dL1 / (D1 / 2)))
r2 = D2 / 2 * _np.sin(_np.arccos(dL2 / (D2 / 2)))
gtemp = (_np.pi * r1**2 / (L1 / n)).T
F1 = 1 / _np.sum(1 / gtemp, axis=1)
gtemp = (_np.pi * r2 ** 2 / (L2 / n)).T
F2 = 1 / _np.sum(1 / gtemp, axis=1)
Ft = (_np.pi * (Dt / 2)**2 / (Lt)).T
vals = _np.vstack([F1, Ft, F2]).T
return vals
