def conduit_lengths(target, throat_endpoints='throat.endpoints',
throat_length='throat.length'):
r"""
Calculate conduit lengths. A conduit is defined as half pore + throat
+ half pore.
Parameters
----------
target : OpenPNM Object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
throat_endpoints : string
Dictionary key of the throat endpoint values.
throat_diameter : string
Dictionary key of the throat length values.
throat_length : string (optional)
Dictionary key of the throat length values. If not given then the
direct distance bewteen the two throat end points is used.
Returns
-------
Dictionary containing conduit lengths, which can be accessed via the dict
keys 'pore1', 'pore2', and 'throat'.
"""
_np.warnings.filterwarnings('ignore', category=RuntimeWarning)
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
cn = network['throat.conns'][throats]
# Get pore coordinates
C1 = network['pore.coords'][cn[:, 0]]
C2 = network['pore.coords'][cn[:, 1]]
# Get throat endpoints and length
EP1 = network[throat_endpoints + '.head'][throats]
EP2 = network[throat_endpoints + '.tail'][throats]
try:
# Look up throat length if given
Lt = network[throat_length][throats]
except KeyError:
# Calculate throat length otherwise
Lt = _sqrt(((EP1 - EP2)**2).sum(axis=1))
# Calculate conduit lengths
L1 = _sqrt(((C1 - EP1)**2).sum(axis=1))
L2 = _sqrt(((C2 - EP2)**2).sum(axis=1))
_np.warnings.filterwarnings('default', category=RuntimeWarning)
return {'pore1': L1, 'throat': Lt, 'pore2': L2}
def piecewise(target, throat_endpoints='throat.endpoints',
throat_centroid='throat.centroid'):
r"""
Calculate throat length from end points and optionally a centroid
Parameters
----------
target : OpenPNM Object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
throat_endpoints : string
Dictionary key of the throat endpoint values.
throat_centroid : string
Dictionary key of the throat centroid values, optional.
Returns
-------
Lt : ndarray
Array containing throat lengths for the given geometry.
Notes
-----
(1) By default, the model assumes that the centroids of pores and the
connecting throat in each conduit are colinear.
(2) If `throat_centroid` is passed, the model accounts for the extra
length. This could be useful for Voronoi or extracted networks.
"""
_np.warnings.filterwarnings('ignore', category=RuntimeWarning)
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
# Get throat endpoints
EP1 = network[throat_endpoints + '.head'][throats]
EP2 = network[throat_endpoints + '.tail'][throats]
# Calculate throat length
Lt = _sqrt(((EP1 - EP2)**2).sum(axis=1))
# Handle the case where pores & throat centroids are not colinear
try:
Ct = network[throat_centroid][throats]
Lt = _sqrt(((Ct - EP1)**2).sum(axis=1)) + \
_sqrt(((Ct - EP2)**2).sum(axis=1))
except KeyError:
pass
_np.warnings.filterwarnings('default', category=RuntimeWarning)
return Lt
def conduit_lengths(target, throat_endpoints='throat.endpoints',
throat_length='throat.length'):
r"""
Calculate conduit lengths. A conduit is defined as half pore + throat
+ half pore.
Parameters
----------
target : OpenPNM Object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
throat_endpoints : string
Dictionary key of the throat endpoint values.
throat_diameter : string
Dictionary key of the throat length values.
throat_length : string (optional)
Dictionary key of the throat length values. If not given then the
direct distance bewteen the two throat end points is used.
Returns
-------
Dictionary containing conduit lengths, which can be accessed via the dict
keys 'pore1', 'pore2', and 'throat'.
"""
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
cn = network['throat.conns'][throats]
# Get pore coordinates
C1 = network['pore.coords'][cn[:, 0]]
C2 = network['pore.coords'][cn[:, 1]]
# Get throat endpoints and length
EP1 = network[throat_endpoints + '.head'][throats]
EP2 = network[throat_endpoints + '.tail'][throats]
try:
# Look up throat length if given
Lt = network[throat_length][throats]
except KeyError:
# Calculate throat length otherwise
Lt = _sqrt(((EP1 - EP2)**2).sum(axis=1))
# Calculate conduit lengths
L1 = _sqrt(((C1 - EP1)**2).sum(axis=1))
L2 = _sqrt(((C2 - EP2)**2).sum(axis=1))
return {'pore1': L1, 'throat': Lt, 'pore2': L2}
def ctc(target):
r"""
Calculate throat length assuming point-like pores, i.e. center-to-center
distance between pores. Also, this model assumes that pores and throat
centroids are colinear.
Parameters
----------
target : OpenPNM Object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
Returns
-------
value : NumPy ndarray
Array containing throat length values.
"""
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
cn = network['throat.conns'][throats]
C1 = network['pore.coords'][cn[:, 0]]
C2 = network['pore.coords'][cn[:, 1]]
value = _sqrt(((C1 - C2)**2).sum(axis=1))
return value
def ctc(target, pore_diameter='pore.diameter'):
r"""
Calculate throat length assuming point-like pores, i.e. center-to-center
distance between pores. Also, this models assumes that pores and throat
centroids are colinear.
Parameters
----------
target : OpenPNM Object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
pore_diameter : string
Dictionary key of the pore diameter values
"""
_np.warnings.filterwarnings('ignore', category=RuntimeWarning)
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
cn = network['throat.conns'][throats]
C1 = network['pore.coords'][cn[:, 0]]
C2 = network['pore.coords'][cn[:, 1]]
value = _sqrt(((C1 - C2)**2).sum(axis=1))
_np.warnings.filterwarnings('default', category=RuntimeWarning)
return value
def ctc(target):
r"""
Calculate throat length assuming point-like pores, i.e. center-to-center
distance between pores. Also, this model assumes that pores and throat
centroids are colinear.
Parameters
----------
target : OpenPNM Object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
Returns
-------
value : NumPy ndarray
Array containing throat length values.
"""
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
cn = network['throat.conns'][throats]
C1 = network['pore.coords'][cn[:, 0]]
C2 = network['pore.coords'][cn[:, 1]]
value = _sqrt(((C1 - C2)**2).sum(axis=1))
return value
def piecewise(target, throat_endpoints='throat.endpoints',
throat_centroid='throat.centroid'):
r"""
Calculate throat length from end points and optionally a centroid
Parameters
----------
target : OpenPNM Object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
throat_endpoints : string
Dictionary key of the throat endpoint values.
throat_centroid : string
Dictionary key of the throat centroid values, optional.
Returns
-------
Lt : ndarray
Array containing throat lengths for the given geometry.
Notes
-----
(1) By default, the model assumes that the centroids of pores and the
connecting throat in each conduit are colinear.
(2) If `throat_centroid` is passed, the model accounts for the extra
length. This could be useful for Voronoi or extracted networks.
"""
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
# Get throat endpoints
EP1 = network[throat_endpoints + '.head'][throats]
EP2 = network[throat_endpoints + '.tail'][throats]
# Calculate throat length
Lt = _sqrt(((EP1 - EP2)**2).sum(axis=1))
# Handle the case where pores & throat centroids are not colinear
try:
Ct = network[throat_centroid][throats]
Lt = _sqrt(((Ct - EP1)**2).sum(axis=1)) + \
_sqrt(((Ct - EP2)**2).sum(axis=1))
except KeyError:
pass
return Lt
def classic(target, pore_diameter='pore.diameter'):
r"""
Find throat length as the pore-to-pore center distance, less the radii of
each pore.
Parameters
----------
target : OpenPNM object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
pore_diameter : string
Dictionary key of the pore diameter values
"""
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
cn = network['throat.conns'][throats]
C1 = network['pore.coords'][cn[:, 0]]
C2 = network['pore.coords'][cn[:, 1]]
D = _sqrt(((C1 - C2)**2).sum(axis=1))
value = D - _np.sum(network[pore_diameter][cn], axis=1)/2
return value
def classic(target, pore_diameter='pore.diameter'):
r"""
Find throat length as the pore-to-pore center distance, less the radii of
each pore.
Parameters
----------
target : OpenPNM object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
pore_diameter : string
Dictionary key of the pore diameter values
"""
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
cn = network['throat.conns'][throats]
C1 = network['pore.coords'][cn[:, 0]]
C2 = network['pore.coords'][cn[:, 1]]
D = _sqrt(((C1 - C2)**2).sum(axis=1))
value = D - _np.sum(network[pore_diameter][cn], axis=1) / 2
return value
def ball_and_stick_2D(target, pore_area='pore.area',
throat_area='throat.area',
pore_diameter='pore.diameter',
throat_diameter='throat.diameter',
conduit_lengths='throat.conduit_lengths'):
r"""
Calculate conduit shape factors for throat conductance associated with
diffusion-like physics (ex. thermal/diffusive/electrical conductance),
assuming pores and throats are circles (balls) and rectangles (sticks).
Parameters
----------
target : OpenPNM Object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
pore_area : string
Dictionary key of the pore area values
throat_area : string
Dictionary key of the throat area values
pore_diameter : string
Dictionary key of the pore diameter values
throat_diameter : string
Dictionary key of the throat diameter values
conduit_lengths : string
Dictionary key of the conduit lengths' values
Returns
-------
SF : dictionary
Dictionary containing conduit shape factors to be used in conductance
models associated with diffusion-like physics. Shape factors are
accessible via the keys: 'pore1', 'pore2' and 'throat'.
Notes
-----
(1) This model accounts for the variable cross-section area in circles.
(2) WARNING: This model could break if `conduit_lengths` does not
correspond to an actual ball and stick! Example: pore length is greater
than pore radius --> :(
"""
_np.warnings.filterwarnings('ignore', category=RuntimeWarning)
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
cn = network['throat.conns'][throats]
# Get pore diameter
D1 = network[pore_diameter][cn[:, 0]]
D2 = network[pore_diameter][cn[:, 1]]
# Get conduit lengths
L1 = network[conduit_lengths + '.pore1'][throats]
L2 = network[conduit_lengths + '.pore2'][throats]
Lt = network[conduit_lengths + '.throat'][throats]
# Get pore/throat baseline areas (the one used in generic conductance)
A1 = network[pore_area][cn[:, 0]]
A2 = network[pore_area][cn[:, 1]]
At = network[throat_area][throats]
# Preallocating F, SF
# F is INTEGRAL(1/A) dx , x : 0 --> L
F1, F2, Ft = _sp.zeros((3, len(Lt)))
SF1, SF2, SFt = _sp.ones((3, len(Lt)))
# Setting SF to 1 when Li = 0 (ex. boundary pores)
# INFO: This is needed since area could also be zero, which confuses NumPy
m1, m2, mt = [Li != 0 for Li in [L1, L2, Lt]]
SF1[~m1] = SF2[~m2] = SFt[~mt] = 1
F1[m1] = (0.5 * _atanh(2*L1/_sqrt(D1**2 - 4*L1**2)))[m1]
F2[m2] = (0.5 * _atanh(2*L2/_sqrt(D2**2 - 4*L2**2)))[m2]
Ft[mt] = (Lt/At)[mt]
# Calculate conduit shape factors
SF1[m1] = (L1 / (A1*F1))[m1]
SF2[m2] = (L2 / (A2*F2))[m2]
SFt[mt] = (Lt / (At*Ft))[mt]
_np.warnings.filterwarnings('default', category=RuntimeWarning)
return {'pore1': SF1, 'throat': SFt, 'pore2': SF2}