Geometry Models¶
Contents of this Page
Overview of Submodule¶
This submodule contains pore-scale models that calculate geometrical properties. These models are to be added to a Geometry object.
Detailed Model Documentation¶
Pore size¶
The pore-size models in this sub-module are used to apply desired pore-size distributions to a pore network. Most of the models accept pore seeds, and then look-up pore-sizes from cumuative distribtions functions. There is also a model for finding the largest possible sphere that can be placed on each site.
- equivalent_diameter(target, pore_volume='pore.volume', pore_shape='sphere')[source]¶
Calculates the diameter of a sphere or edge-length of a cube with same volume as the pore.
- Parameters
target (OpenPNM Geometry Object) – The Geometry object which this model is associated with. This controls the length of the calculated array, and also provides access to other necessary geometric properties.
pore_volume (string) – The dictionary key containing the pore volume values
pore_shape (string) – The shape of the pore body to assume when back-calculating from volume. Options are ‘sphere’ (default) or ‘cube’.
- Returns
D – Array containing pore diameter values.
- Return type
NumPy ndarray
- from_neighbor_throats(target, prop, mode='max')[source]¶
Adopt a value from the values found in neighboring throats
- 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.
prop (string) – The dictionary key of the array containing the throat property to be used in the calculation.
mode (string) – Controls how the pore property is calculated. Options are ‘min’, ‘max’ and ‘mean’.
- Returns
value – Array containing customized values based on those of adjacent throats.
- Return type
ND-array
- generic_distribution(target, func, seeds='pore.seed')[source]¶
Accepts an ‘rv_frozen’ object from the Scipy.stats submodule and returns values from the distribution for the given seeds
This uses the
ppf
method of the stats object- 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.
seeds (string, optional) – The dictionary key on the Geometry object containing random seed values (between 0 and 1) to use in the statistical distribution.
func (object) – An ‘rv_frozen’ object from the Scipy.stats library with all of the parameters pre-specified.
- Returns
values – Array containing random numbers based on given ppf.
- Return type
NumPy ndarray
Examples
The following code illustrates the process of obtaining a ‘frozen’ Scipy stats object and adding it as a model:
>>> import scipy >>> import numpy >>> import openpnm as op >>> pn = op.network.Cubic(shape=[3, 3, 3]) >>> geo = op.geometry.GenericGeometry(network=pn, pores=pn.Ps, throats=pn.Ts) >>> geo.add_model(propname='pore.seed', ... model=op.models.geometry.pore_seed.random)
Now retrieve the stats distribution and add to
geo
as a model:>>> stats_obj = scipy.stats.weibull_min(c=2, scale=.0001, loc=0) >>> geo.add_model(propname='pore.size', ... model=op.models.geometry.pore_size.generic_distribution, ... seeds='pore.seed', ... func=stats_obj)
>>> import matplotlib.pyplot as plt >>> fig = plt.hist(stats_obj.ppf(q=numpy.random.rand(1000)), bins=50)
- largest_sphere(target, fixed_diameter='pore.fixed_diameter', iters=5)[source]¶
Finds the maximum diameter pore that can be placed in each location without overlapping any neighbors.
This method iteratively expands pores by increasing their diameter to encompass half of the distance to the nearest neighbor. If the neighbor is not growing because it’s already touching a different neighbor, then the given pore will never quite touch this neighbor. Increating the value of
iters
will get it closer, but it’s case of [Zeno’s paradox](https://en.wikipedia.org/wiki/Zeno%27s_paradoxes) with each step cutting the remaining distance in half- 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.
fixed_diameter (string) – The dictionary key containing the pore diameter values already assigned to network, if any. If not provided a starting value is assumed as half-way to the nearest neighbor.
iters (integer) – The number of iterations to perform when searching for maximum diameter. This function iteratively grows pores until they touch their nearest neighbor, which is also growing, so this parameter limits the maximum number of iterations. The default is 10, but 5 is usally enough.
- Returns
D – Array containing pore diameter values.
- Return type
NumPy ndarray
Notes
This model looks into all pores in the network when finding the diameter. This means that when multiple Geometry objects are defined, it will consider the diameter of pores on adjacent Geometries. If no diameters have been assigned to these neighboring pores it will assume 0. If diameter value are assigned to the neighboring pores AFTER this model is run, the pores will overlap. This can be remedied by running this model again.
- normal(target, scale, loc, seeds='pore.seed')[source]¶
Produces values from a Weibull distribution given a set of random numbers.
- Parameters
target (OpenPNM Object) – The object with which this function as associated. This argument is required to (1) set number of values to generate (geom.Np or geom.Nt) and (2) provide access to other necessary values (i.e. geom[‘pore.seed’]).
seeds (string, optional) – The dictionary key on the Geometry object containing random seed values (between 0 and 1) to use in the statistical distribution.
scale (float) – The standard deviation of the Normal distribution
loc (float) – The mean of the Normal distribution
- Returns
values – Array containing normally distributed random numbers.
- Return type
NumPy ndarray
Examples
The following code illustrates the inner workings of this function, which uses the ‘norm’ method of the scipy.stats module. This can be used to find suitable values of ‘scale’ and ‘loc’.
>>> import scipy >>> import numpy >>> func = scipy.stats.norm(scale=.0001, loc=0.001) >>> import matplotlib.pyplot as plt >>> fig = plt.hist(func.ppf(q=numpy.random.rand(10000)), bins=50)
- random(target, seed=None, num_range=[0, 1])[source]¶
Create an array of random numbers of a specified size.
- 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.
seed (int) – The starting seed value to send to Scipy’s random number generator. The default is None, which means different distribution is returned each time the model is run.
num_range (list) – A two element list indicating the low and high end of the returned numbers.
- Returns
values – Array containing uniformly-distributed random numbers.
- Return type
NumPy ndarray
- weibull(target, shape, scale, loc, seeds='pore.seed')[source]¶
Produces values from a Weibull distribution given a set of random numbers.
- 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.
seeds (string, optional) – The dictionary key on the Geometry object containing random seed values (between 0 and 1) to use in the statistical distribution.
shape (float) – This controls the skewness of the distribution, with ‘shape’ < 1 giving values clustered on the low end of the range with a long tail, and ‘shape’ > 1 giving a more symmetrical distribution.
scale (float) – This controls the width of the distribution with most of values falling below this number.
loc (float) – Applies an offset to the distribution such that the smallest values are above this number.
- Returns
values – Array containing random numbers based on Weibull distribution.
- Return type
NumPy ndarray
Examples
The following code illustrates the inner workings of this function, which uses the ‘weibull_min’ method of the scipy.stats module. This can be used to find suitable values of ‘shape’, ‘scale’` and ‘loc’. Note that ‘shape’ is represented by ‘c’ in the actual function call.
>>> import scipy >>> import numpy >>> func = scipy.stats.weibull_min(c=1.5, scale=0.0001, loc=0) >>> import matplotlib.pyplot as plt >>> fig = plt.hist(func.ppf(q=numpy.random.rand(10000)), bins=50)
Pore volume¶
These models calculate pore volumes depending on the specified shape
- circle(target, pore_diameter='pore.diameter')[source]¶
Calculate pore volume from diameter assuming a spherical pore body
- 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 geometric properties.
pore_diameter (string) – The dictionary key of the pore diameter values
- cone(target, pore_diameter='pore.diameter')[source]¶
Calculates pore volume from diameter assuming a conical pore body.
- 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 geometric properties.
pore_diameter (string) – The dictionary key of the pore diameter values
- Returns
value – Array containing pore volume values.
- Return type
NumPy ndarray
- cube(target, pore_diameter='pore.diameter')[source]¶
Calculate pore volume from diameter assuming a cubic pore body
- 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 geometric properties.
pore_diameter (string) – The dictionary key of the pore diameter values
- Returns
value – Array containing pore volume values.
- Return type
NumPy ndarray
- cylinder(target, pore_diameter='pore.diameter')[source]¶
Calculate pore volume from diameter assuming a cylindrical pore body with a height equal to its diameter.
- 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 geometric properties.
pore_diameter (string) – The dictionary key of the pore diameter values
- Returns
value – Array containing pore volume values.
- Return type
NumPy ndarray
- effective(target, pore_volume='pore.volume', throat_volume='throat.volume')[source]¶
Calculate the effective pore volume for optional use in transient simulations. The effective pore volume is calculated by adding half the volume of all neighbouring throats to the pore volume.
- 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 geometric properties.
pore_volume (string) – The dictionary key of the pore volume values
throat_volume (string) – The dictionary key of the throat volume values
- Returns
value – Array containing pore volume values.
- Return type
NumPy ndarray
- pyramid(target, pore_diameter='pore.diameter')[source]¶
Calculates pore volume from diameter assuming a truncated pyramid pore body.
- 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 geometric properties.
pore_diameter (string) – The dictionary key of the pore diameter values
- Returns
value – Array containing pore volume values.
- Return type
NumPy ndarray
- sphere(target, pore_diameter='pore.diameter')[source]¶
Calculate pore volume from diameter assuming a spherical pore body
- 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 geometric properties.
pore_diameter (string) – The dictionary key of the pore diameter values
- Returns
value – Array containing pore volume values.
- Return type
NumPy ndarray
- square(target, pore_diameter='pore.diameter')[source]¶
Calculate pore volume from diameter assuming a cubic pore body
- 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 geometric properties.
pore_diameter (string) – The dictionary key of the pore diameter values
- trapezoid(target, pore_diameter='pore.diameter')[source]¶
Calculates pore volume from diameter assuming a trapezoidal pore body.
- 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 geometric properties.
pore_diameter (string) – The dictionary key of the pore diameter values
- Returns
value – Array containing pore volume values.
- Return type
NumPy ndarray
Pore seed¶
Pore seed models are use to calculate random numbers for each pore, which can subsequently be used in statistical distributions to calculate actual pore sizes.
- random(target, seed=None, num_range=[0, 1])[source]¶
Create an array of random numbers of a specified size.
- 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.
seed (int) – The starting seed value to send to Scipy’s random number generator. The default is None, which means different distribution is returned each time the model is run.
num_range (list) – A two element list indicating the low and high end of the returned numbers.
- Returns
values – Array containing uniformly-distributed random numbers.
- Return type
NumPy ndarray
Generates pore seeds that are spatailly correlated with their neighbors.
- 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.
weights (list of ints, optional) – The [Nx,Ny,Nz] distances (in number of pores) in each direction that should be correlated.
strel (array_like, optional (in place of weights)) –
The option allows full control over the spatial correlation pattern by specifying the structuring element to be used in the convolution.
The array should be a 3D array containing the strength of correlations in each direction. Nonzero values indicate the strength, direction and extent of correlations. The following would achieve a basic correlation in the z-direction:
:: –
- strel = np.array([[[0, 0, 0], [0, 0, 0], [0, 0, 0]],
[[0, 0, 0], [1, 1, 1], [0, 0, 0]], [[0, 0, 0], [0, 0, 0], [0, 0, 0]]])
- Returns
values – Array containing pore seed values.
- Return type
NumPy ndarray
Notes
This approach uses image convolution to replace each pore seed in the geoemtry with a weighted average of those around it. It then converts the new seeds back to a random distribution by assuming they new seeds are normally distributed.
Because is uses image analysis tools, it only works on Cubic networks.
This is the appproached used by Gostick et al 2 to create an anistropic gas diffusion layer for fuel cell electrodes.
References
- 2
J. Gostick et al, Pore network modeling of fibrous gas diffusion layers for polymer electrolyte membrane fuel cells. J Power Sources v173, pp277–290 (2007)
Examples
>>> import openpnm as op >>> pn = op.network.Cubic(shape=[10, 10, 10]) >>> Ps, Ts = pn.Ps, pn.Ts >>> geom = op.geometry.GenericGeometry(network=pn, pores=Ps, throats=Ts) >>> mod = op.models.geometry.pore_seed.spatially_correlated >>> geom.add_model(propname='pore.seed', model=mod, weights=[2, 2, 2])
Pore surface area¶
- circle(target, pore_diameter='pore.diameter', throat_cross_sectional_area='throat.cross_sectional_area')[source]¶
Calculates internal surface area of pore bodies assuming they are circular then subtracts the area of the neighboring throats in a crude way, by simply considering the throat cross-sectional area, thus not accounting for the actual curvature of the intersection.
- Parameters
target (GenericGeometry) – The Geometry object for which these values are being calculated. This controls the length of the calculated array, and also provides access to other necessary thermofluid properties.
pore_diameter (str) – The dictionary key to the pore diameter array.
throat_cross_sectional_area (str) – The dictionary key to the throat cross sectional area array. Throat areas are needed since their insection with the pore are removed from the computation.
- Returns
value – Array containing pore surface area values.
- Return type
NumPy ndarray
- cube(target, pore_diameter='pore.diameter', throat_cross_sectional_area='throat.cross_sectional_area')[source]¶
Calculates internal surface area of pore bodies assuming they are cubes then subtracts the area of the neighboring throats.
- Parameters
target (GenericGeometry) – The Geometry object for which these values are being calculated. This controls the length of the calculated array, and also provides access to other necessary thermofluid properties.
pore_diameter (string) – The dictionary key to the pore diameter array.
throat_cross_sectional_area (str) – The dictionary key to the throat cross sectional area array. Throat areas are needed since their insection with the pore are removed from the computation.
- Returns
value – Array containing pore surface area values.
- Return type
NumPy ndarray
- sphere(target, pore_diameter='pore.diameter', throat_cross_sectional_area='throat.cross_sectional_area')[source]¶
Calculates internal surface area of pore bodies assuming they are spherical then subtracts the area of the neighboring throats in a crude way, by simply considering the throat cross-sectional area, thus not accounting for the actual curvature of the intersection.
- Parameters
target (GenericGeometry) – The Geometry object for which these values are being calculated. This controls the length of the calculated array, and also provides access to other necessary thermofluid properties.
pore_diameter (str) – The dictionary key to the pore diameter array.
throat_cross_sectional_area (str) – The dictionary key to the throat cross sectional area array. Throat areas are needed since their insection with the pore are removed from the computation.
- Returns
value – Array containing pore surface area values.
- Return type
NumPy ndarray
- square(target, pore_diameter='pore.diameter', throat_cross_sectional_area='throat.cross_sectional_area')[source]¶
Calculates internal surface area of pore bodies assuming they are squares then subtracts the area of the neighboring throats.
- Parameters
target (GenericGeometry) – The Geometry object for which these values are being calculated. This controls the length of the calculated array, and also provides access to other necessary thermofluid properties.
pore_diameter (str) – The dictionary key to the pore diameter array.
throat_cross_sectional_area (str) – The dictionary key to the throat cross sectional area array. Throat areas are needed since their insection with the pore are removed from the computation.
- Returns
value – Array containing pore surface area values.
- Return type
NumPy ndarray
Throat cross sectional area¶
- cuboid(target, throat_diameter='throat.diameter')[source]¶
Calculate throat cross-sectional area for a cuboid throat
- 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_diameter (string) – Dictionary key of the throat diameter values
- Returns
value – Array containing throat cross-sectional area values.
- Return type
NumPy ndarray
- cylinder(target, throat_diameter='throat.diameter')[source]¶
Calculate throat cross-sectional area for a cylindrical throat
- 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_diameter (string) – Dictionary key of the throat diameter values
- Returns
value – Array containing throat cross-sectional area values.
- Return type
NumPy ndarray
- rectangle(target, throat_diameter='throat.diameter')[source]¶
Calculate throat cross-sectional area for a rectangular throat
- 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_diameter (string) – Dictionary key of the throat diameter values
Throat size¶
- equivalent_diameter(target, throat_area='throat.area', throat_shape='circle')[source]¶
Calculates the diameter of a cirlce or edge-length of a sqaure with same area as the throat.
- 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.
thorat_area (string) – The dictionary key to the throat area values
throat_shape (string) – The shape cross-sectional shape of the throat to assume when back-calculating from the area. Options are ‘circle’ (default) or ‘square’.
- Returns
value – Array containing throat equivalent diameter.
- Return type
NumPy ndarray
- from_neighbor_pores(target, prop='pore.diameter', mode='min')[source]¶
Adopt a value based on the values in neighboring pores
- 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.
prop (string) – The dictionary key to the array containing the pore property to be used in the calculation.
mode (string) – Controls how the throat property is calculated. Options are ‘min’, ‘max’ and ‘mean’.
ignore_nans (boolean (default is
True
)) – IfTrue
the result will ignorenans
in the neighbors
- Returns
value – Array containing customized values based on those of adjacent pores.
- Return type
ND-array
- generic_distribution(target, func, seeds='throat.seed')[source]¶
Accepts an ‘rv_frozen’ object from the Scipy.stats submodule and returns values from the distribution for the given seeds
This uses the
ppf
method of the stats object- 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.
seeds (string, optional) – The dictionary key on the Geometry object containing random seed values (between 0 and 1) to use in the statistical distribution.
func (object) – An ‘rv_frozen’ object from the Scipy.stats library with all of the parameters pre-specified.
- Returns
values – Array containing random numbers based on given ppf.
- Return type
NumPy ndarray
Examples
The following code illustrates the process of obtaining a ‘frozen’ Scipy stats object and adding it as a model:
>>> import scipy >>> import numpy >>> import openpnm as op >>> pn = op.network.Cubic(shape=[3, 3, 3]) >>> geo = op.geometry.GenericGeometry(network=pn, pores=pn.Ps, throats=pn.Ts) >>> geo.add_model(propname='pore.seed', ... model=op.models.geometry.pore_seed.random)
Now retrieve the stats distribution and add to
geo
as a model:>>> stats_obj = scipy.stats.weibull_min(c=2, scale=.0001, loc=0) >>> geo.add_model(propname='pore.size', ... model=op.models.geometry.pore_size.generic_distribution, ... seeds='pore.seed', ... func=stats_obj)
>>> import matplotlib.pyplot as plt >>> fig = plt.hist(stats_obj.ppf(q=numpy.random.rand(1000)), bins=50)
- normal(target, scale, loc, seeds='throat.seed')[source]¶
Produces values from a Weibull distribution given a set of random numbers.
- Parameters
target (OpenPNM Object) – The object with which this function as associated. This argument is required to (1) set number of values to generate (geom.Np or geom.Nt) and (2) provide access to other necessary values (i.e. geom[‘pore.seed’]).
seeds (string, optional) – The dictionary key on the Geometry object containing random seed values (between 0 and 1) to use in the statistical distribution.
scale (float) – The standard deviation of the Normal distribution
loc (float) – The mean of the Normal distribution
- Returns
values – Array containing normally distributed random numbers.
- Return type
NumPy ndarray
Examples
The following code illustrates the inner workings of this function, which uses the ‘norm’ method of the scipy.stats module. This can be used to find suitable values of ‘scale’ and ‘loc’.
>>> import scipy >>> import numpy >>> func = scipy.stats.norm(scale=.0001, loc=0.001) >>> import matplotlib.pyplot as plt >>> fig = plt.hist(func.ppf(q=numpy.random.rand(10000)), bins=50)
- random(target, seed=None, num_range=[0, 1])[source]¶
Create an array of random numbers of a specified size.
- 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.
seed (int) – The starting seed value to send to Scipy’s random number generator. The default is None, which means different distribution is returned each time the model is run.
num_range (list) – A two element list indicating the low and high end of the returned numbers.
- Returns
values – Array containing uniformly-distributed random numbers.
- Return type
NumPy ndarray
- weibull(target, shape, scale, loc, seeds='throat.seed')[source]¶
Produces values from a Weibull distribution given a set of random numbers.
- 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.
seeds (string, optional) – The dictionary key on the Geometry object containing random seed values (between 0 and 1) to use in the statistical distribution.
shape (float) – This controls the skewness of the distribution, with ‘shape’ < 1 giving values clustered on the low end of the range with a long tail, and ‘shape’ > 1 giving a more symmetrical distribution.
scale (float) – This controls the width of the distribution with most of values falling below this number.
loc (float) – Applies an offset to the distribution such that the smallest values are above this number.
- Returns
values – Array containing random numbers based on Weibull distribution.
- Return type
NumPy ndarray
Examples
The following code illustrates the inner workings of this function, which uses the ‘weibull_min’ method of the scipy.stats module. This can be used to find suitable values of ‘shape’, ‘scale’` and ‘loc’. Note that ‘shape’ is represented by ‘c’ in the actual function call.
>>> import scipy >>> import numpy >>> func = scipy.stats.weibull_min(c=1.5, scale=0.0001, loc=0) >>> import matplotlib.pyplot as plt >>> fig = plt.hist(func.ppf(q=numpy.random.rand(10000)), bins=50)
Throat length¶
- circles_and_rectangles(target, pore_diameter='pore.diameter', throat_diameter='throat.diameter')[source]¶
Finds throat length assuming pores are circles and throats are rectangles.
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the pore diameter values.
throat_diameter (str) – Dictionary key of the throat diameter values.
- Returns
Array containing throat length values.
- Return type
ndarray
- classic(target, pore_diameter='pore.diameter')[source]¶
Finds throat length as the pore-to-pore center distance, less the radii of each pore.
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the pore diameter values
- conduit_lengths(target, throat_endpoints='throat.endpoints', throat_length='throat.length', throat_centroid='throat.centroid')[source]¶
Calculates conduit lengths. A conduit is defined as half pore + throat + half pore.
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the throat endpoint values.
throat_diameter (str) – 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’.
- cones_and_cylinders(target, pore_diameter='pore.diameter', throat_diameter='throat.diameter')[source]¶
Finds throat length assuming pores are cones and throats are cylinders.
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the pore diameter values.
throat_diameter (str) – Dictionary key of the throat diameter values.
- Returns
Array containing throat length values.
- Return type
ndarray
- ctc(target)[source]¶
Calculates 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 (GenericGeometry) – Geometry 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 – Array containing throat length values.
- Return type
ndarray
- cubes_and_cuboids(target, pore_diameter='pore.diameter', throat_diameter='throat.diameter')[source]¶
Finds throat length assuming pores are cubes and throats are cuboids.
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the pore diameter values.
throat_diameter (str) – Dictionary key of the throat diameter values.
- Returns
Array containing throat length values.
- Return type
ndarray
- piecewise(target, throat_endpoints='throat.endpoints', throat_centroid='throat.centroid')[source]¶
Calculates throat length from end points and optionally a centroid
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the throat endpoint values.
throat_centroid (str) – Dictionary key of the throat centroid values, optional.
- Returns
Lt – Array containing throat lengths for the given geometry.
- Return type
ndarray
Notes
By default, the model assumes that the centroids of pores and the connecting throat in each conduit are colinear.
If throat_centroid is passed, the model accounts for the extra length. This could be useful for Voronoi or extracted networks.
- pyramids_and_cuboids(target, pore_diameter='pore.diameter', throat_diameter='throat.diameter')[source]¶
Finds throat length assuming pores are pyramids and throats are cuboids.
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the pore diameter values.
throat_diameter (str) – Dictionary key of the throat diameter values.
- Returns
Array containing throat length values.
- Return type
ndarray
- spheres_and_cylinders(target, pore_diameter='pore.diameter', throat_diameter='throat.diameter')[source]¶
Finds throat length assuming pores are spheres and throats are cylinders.
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the pore diameter values.
throat_diameter (str) – Dictionary key of the throat diameter values.
- Returns
Array containing throat length values.
- Return type
ndarray
- squares_and_rectangles(target, pore_diameter='pore.diameter', throat_diameter='throat.diameter')[source]¶
Finds throat length assuming pores are squares and throats are rectangles.
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the pore diameter values.
throat_diameter (str) – Dictionary key of the throat diameter values.
- Returns
Array containing throat length values.
- Return type
ndarray
- trapezoids_and_rectangles(target, pore_diameter='pore.diameter', throat_diameter='throat.diameter')[source]¶
Finds throat length assuming pores are trapezoids and throats are rectangles.
- Parameters
target (GenericGeometry) – Geometry 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 (str) – Dictionary key of the pore diameter values.
throat_diameter (str) – Dictionary key of the throat diameter values.
- Returns
Array containing throat length values.
- Return type
ndarray
Throat perimeter¶
- cuboid(target, throat_diameter='throat.diameter')[source]¶
Calcuate the throat perimeter assuming a square cross-section
- 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_diameter (string) – The dictionary key of the array containing the throat diameter values.
- Returns
value – Array containing throat perimeter values.
- Return type
NumPy ndarray
- cylinder(target, throat_diameter='throat.diameter')[source]¶
Calcuate the throat perimeter assuming a circular cross-section
- 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_diameter (string) – The dictionary key of the array containing the throat diameter values
- Returns
value – Array containing throat perimeter values.
- Return type
NumPy ndarray
- rectangle(target, throat_diameter='throat.diameter')[source]¶
Calcuate the throat perimeter assuming a rectangular cross-section (2D)
- 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_diameter (string) – The dictionary key of the array containing the throat diameter values
- Returns
value – Array containing throat perimeter values.
- Return type
NumPy ndarray
Throat surface area¶
- cuboid(target, throat_diameter='throat.diameter', throat_length='throat.length')[source]¶
Calculate surface area for a cuboid throat
- 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_diameter (string) – Dictionary key to the throat diameter array. Default is ‘throat.diameter’.
throat_length (string) – Dictionary key to the throat length array. Default is ‘throat.length’.
- Returns
value – Array containing throat surface area values.
- Return type
NumPy ndarray
- cylinder(target, throat_diameter='throat.diameter', throat_length='throat.length')[source]¶
Calculate surface area for a cylindrical throat
- 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_diameter (string) – Dictionary key to the throat diameter array. Default is ‘throat.diameter’.
throat_length (string) – Dictionary key to the throat length array. Default is ‘throat.length’.
- Returns
value – Array containing throat surface area values.
- Return type
NumPy ndarray
- extrusion(target, throat_perimeter='throat.perimeter', throat_length='throat.length')[source]¶
Calculate surface area for an arbitrary shaped throat give the perimeter and length.
- 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_perimeter (string) – Dictionary key to the throat perimeter array. Default is ‘throat.perimeter’.
throat_length (string) – Dictionary key to the throat length array. Default is ‘throat.length’.
- Returns
value – Array containing throat surface area values.
- Return type
NumPy ndarray
- rectangle(target, throat_length='throat.length')[source]¶
Calculate surface area for a rectangular throat
Only suitable for true 2D simulations
- 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_length (string) – Dictionary key to the throat length array. Default is ‘throat.length’.
Throat vector¶
- pore_to_pore(target)[source]¶
Calculates throat vector as straight path between connected pores.
- Parameters
target (OpenPNM object) – The object containing the geometrical properties of the throats
- Returns
unit_vec – Array containing pore-to-pore unit vectors
- Return type
NumPy ndarray, shape = (N, 3)
Notes
There is an important impicit assumption here: the positive direction is taken as the direction from the pore with the lower index to the higher. This corresponds to the pores in the 1st and 2nd columns of the ‘throat.conns’ array as stored on the etwork.
Throat volume¶
- cuboid(target, throat_length='throat.length', throat_diameter='throat.diameter')[source]¶
Calculate throat volume assuing a square cross-section
- 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.
and throat_diameter (throat_length) – The dictionary keys containing the arrays with the throat diameter and length values.
- Returns
value – Array containing throat volume values.
- Return type
NumPy ndarray
Notes
At present this models does NOT account for the volume reprsented by the intersection of the throat with a spherical pore body.
- cylinder(target, throat_length='throat.length', throat_diameter='throat.diameter')[source]¶
Calculate throat volume assuing a cylindrical shape
- 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.
and throat_diameter (throat_length) – The dictionary keys containing the arrays with the throat diameter and length values.
- Returns
value – Array containing throat volume values.
- Return type
NumPy ndarray
Notes
At present this models does NOT account for the volume reprsented by the intersection of the throat with a spherical pore body.
- extrusion(target, throat_length='throat.length', throat_area='throat.area')[source]¶
Calculate throat volume from the throat area and the throat length. This method is useful for abnormal shaped throats.
- 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.
and throat_area (throat_length) – The dictionary keys containing the arrays with the throat area and length values.
- Returns
value – Array containing throat volume values.
- Return type
NumPy ndarray
Notes
At present this models does NOT account for the volume reprsented by the intersection of the throat with a spherical pore body.
- lens(target, throat_diameter='throat.diameter', pore_diameter='pore.diameter')[source]¶
Calculates the volume residing the hemispherical caps formed by the intersection between cylindrical throats and spherical pores.
This volume should be subtracted from throat volumes if the throat lengths were found using throat end points.
- Parameters
throat_diameter (string) – The dictionary keys containing the array with the throat diameter values.
pore_diameter (string) – The dictionary keys containing the array with the pore diameter values.
- Returns
volume – The volume that should be subtracted from each throat volume to prevent double counting the volume of overlapping area.
- Return type
ND-array
Notes
This model does NOT consider the possibility that multiple throats might overlap in the same location which could happen if throats are large and connectivity is random.
See also
- pendular_ring(target, throat_diameter='throat.diameter', pore_diameter='pore.diameter')[source]¶
Calculates the volume of the pendular rings residing between the end of a cylindrical throat and spherical pores that are in contact but not overlapping.
This volume should be added to the throat volume if the throat length was found as the center-to-center distance less the pore radii.
- Parameters
throat_diameter (string) – The dictionary keys containing the array with the throat diameter values.
pore_diameter (string) – The dictionary keys containing the array with the pore diameter values.
- Returns
volume – The volume that should be added to each throat volume to account for under-represented void volume at the pore-throat junctions.
- Return type
ND-array
Notes
This model does NOT consider the possibility that multiple throats might overlap in the same location which could happen if throats are large and connectivity is random.
See also
- rectangle(target, throat_length='throat.length', throat_diameter='throat.diameter')[source]¶
Calculate throat volume assuing a rectangular shape
- 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.
and throat_diameter (throat_length) – The dictionary keys containing the arrays with the throat diameter and length values.
Notes
At present this models does NOT account for the volume reprsented by the intersection of the throat with a spherical pore body.
Throat capillary shape factor¶
- compactness(target, throat_perimeter='throat.perimeter', throat_area='throat.area')[source]¶
Mortensen et al. have shown that the Hagen-Poiseuille hydraluic resistance is linearly dependent on the compactness. Defined as perimeter^2/area. The dependence is not universal as shapes with sharp corners provide more resistance than those that are more elliptical. Count the number of vertices and apply the right correction.
- 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_perimeter (string) – The dictionary key of the array containing the throat perimeter values.
throat_area (string) – The dictionary key of the array containing the throat area values.
- Returns
alpha – Array containing throat compactness values.
- Return type
NumPy ndarray
References
Mortensen N.A, Okkels F., and Bruus H. Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels. Physical Review E, v.71, pp.057301 (2005).
- jenkins_rao(target, throat_perimeter='throat.perimeter', throat_area='throat.area', throat_diameter='throat.indiameter')[source]¶
Jenkins and Rao relate the capillary pressure in an eliptical throat to the aspect ratio
- 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_perimeter (string) – The dictionary key of the array containing the throat perimeter values.
throat_area (string) – The dictionary key of the array containing the throat area values.
throat_diameter (string) – The dictionary key of the array containing the throat diameter values.
- Returns
value – Array containing throat capillary pressure values.
- Return type
NumPy ndarray
References
Jenkins, R.G. and Rao, M.B., The effect of elliptical pores on mercury porosimetry results. Powder technology, 38(2), pp.177-180. (1984)
- mason_morrow(target, throat_perimeter='throat.perimeter', throat_area='throat.area')[source]¶
Mason and Morrow relate the capillary pressure to the shaped factor in a similar way to Mortensen but for triangles.
- 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_perimeter (string) – The dictionary key of the array containing the throat perimeter values.
throat_area (string) – The dictionary key of the array containing the throat area values.
- Returns
value – Array containing throat shape factor values.
- Return type
NumPy ndarray
References
Mason, G. and Morrow, N.R.. Capillary behavior of a perfectly wetting liquid in irregular triangular tubes. Journal of Colloid and Interface Science, 141(1), pp.262-274 (1991).