Each OpenPNM object is a Python dictionary which allows data to be stored and accessed by name, with a syntax like
network['pore.diameter']. Inside each dictionary or dict are stored numerous Numpy arrays containing pore or throat data corresponding to the key (i.e.
Numpy arrays are enforced, such that any data written into one of the OpenPNM object dicionaries is converted to a Numpy array. This is done to ensure that all mathematically operations throughout the code can be consistently done using vectorization. Note that any subclasses of Numpy arrays, such as Dask arrays or Unyt arrays are also acceptable.
Several rules have been implemented to control the integrity of the data:
- All array names must begin with either ‘pore.’ or ‘throat.’ which serves to identify the type of information they contain.
- For the sake of consistency only arrays of length Np or Nt are allowed in the dictionary. Assigning a scalar value to a dictionary results in the creation of a full length vector, either Np or Nt long, depending on the name of the array.. This effectively applies the scalar value to all locations in the network.
- Any Boolean data will be treated as a label while all other numerical data is treated as a property. The difference between these is outlined below.
All pore and throat data are stored in arrays of either Np or Nt length representing the number of pores and throats on the object, respectively. This means that each pore (or throat) has a number or index that is implicitly indicated by it’s location in the arrays. All properties for pore i or throat j are stored in the array at the element i or j. Thus, the diameter for pore 15 is stored in the
'pore.diameter' array in element 15, and the length of throat 32 is stored in the
'throat.length' array at element 32. This array-based approach is ideal when using the Numpy and Scipy libraries which are designed for elementwise, vectorized programming. For instance, the volume of each throats can be found simultaneously using
T_vol = 3.1415*(network['throat.radius']**2) * network['throat.length'].
T_vol will be an Nt-long array of values, because
'throat.radius' were also Nt-long.
The physical details about pores and throats are referred to as properties, which includes information such as pore volume and throat length. Properties are accessed using Python dictionary syntax to access the array of choice, then Numpy array indexing to access the pore or throat locations of choice:
>>> import openpnm as op >>> import scipy as sp >>> import numpy as np >>> pn = op.network.Cubic(shape=[3, 3, 3]) >>> pn['pore.coords'] array([0.5, 0.5, 1.5])
pn['pore.coords'] retrieves the Numpy array from the dictionary, while the
 retrieves the value in element 1 of the Numpy array.
Writing data is straightforward:
>>> pn['pore.foo'] = 1.0 >>> pn['pore.foo'] 1.0 >>> pn['pore.foo'] = 2.0 >>> pn['pore.foo'] 2.0 >>> pn['pore.foo'] 1.0
The above lines illustrate how a scalar value is converted to a vector (Np-long), and how specific pore values can be assigned. It is also possible to assign an entire array in one step:
>>> pn['pore.bar'] = np.random.rand(27) # pn has 27 pores (3*3*3)
Attempts to write an array of the wrong size will result in an error:
pn['pore.baz'] = [2, 3, 4]
To quickly see a complete list properties on an object use the
props method. You can specify whether only pore or throat properties should be returned, but the default is both:
>>> pn.props() ['pore.bar', 'pore.coords', 'pore.foo', 'throat.conns'] >>> pn.props('throat') ['throat.conns']
You can also view a nicely formatted list of
Labels are a means of dynamically creating groups of pores and throats so they can be quickly accessed by the user. For instance, is helpful to know which pores are on the ‘top’ surface. This label is automatically added by the Cubic network generator, so a list of all pores on the ‘top’ can be retrieved by simply querying which pores possess the label ‘top’ using the
>>> pn.pores('top') array([ 2, 5, 8, 11, 14, 17, 20, 23, 26])
The only distinction between labels and properties is that labels are Boolean masks of True/False. Thus a
True in element 10 of the array
'pore.top' means that the label ‘top’ has been applied to pore 10. Adding and removing existing labels to pores and throats is simply a matter of setting the element to
False. For instance, to remove the label ‘top’ from pore 2:
>>> pn['pore.top'] = False >>> list(np.where(pn['pore.top'])) [5, 8, 11, 14, 17, 20, 23, 26] >>> pn['pore.top'] = True # Re-apply label to pore 2
Creating a new label array occurs automatically if a Boolean array is stored on an object:
>>> pn['pore.dummy_1'] = np.random.rand(27) < 0.5
A complication arises if you have a list of pore numbers you wish to label, such as [3, 4, 5]. You must first create the label array with all
False values, then assign
True to the desired locations:
>>> pn['pore.dummy_2'] = False # Automatically assigns False to every pore >>> pn['pore.dummy_2'][[3, 4, 5]] = True >>> list(pn.pores('dummy_2')) [3, 4, 5]
The label functionality uses Scipy’s
where method to return a list of locations where the array is
>>> list(np.where(pn['pore.dummy_2'])) [3, 4, 5]
throats methods offer several useful enhancements to this approach. For instance, several labels can be queried at once:
>>> list(pn.pores(['top', 'dummy_2'])) [2, 3, 4, 5, 8, 11, 14, 17, 20, 23, 26]
And there is also a
mode argument which can be used to apply set theory logic to the returned list:
>>> list(pn.pores(['top', 'dummy_2'], mode='intersection')) 
This set logic basically retrieves a list of all pores with the label
'top' and a second list of pores with the label
dummy_2, and returns the
'intersection' of these lists, or only pores that appear in both lists.
labels method can be used to obtain a list of all defined labels. This method optionally accepts a list of pores or throats as an argument and returns only the labels that have been applied to the specified locations.
>>> pn.labels() ['pore.all', 'pore.back', 'pore.bottom', 'pore.dummy_1', 'pore.dummy_2', 'pore.front', 'pore.internal', 'pore.left', 'pore.right', 'pore.surface', 'pore.top', 'throat.all', 'throat.internal', 'throat.surface']
This results can also be viewed with
The Importance of the ‘all’ Label
All objects are instantiated with a
'throat.all' label. These arrays are essential to the framework since they are used to define how long the ‘pore’ and ‘throat’ data arrays must be. In other words, the
__setitem__ method checks to make sure that any ‘pore’ array it receives has the same length as
One of the features in OpenPNM is the ability to model heterogeneous materials by applying different pore-scale models to different regions. This is done by (a) creating a unique Geometry object for each region (i.e. small pores vs big pores) and (b) creating unique Physics object for each region as well (i.e. Knudsen diffusion vs Fickian diffusion). One consequence of this segregation of properties is that a single array containing values for all locations in the domain does not exist. OpenPNM offers a shortcut for this, known as
interleave_data, which happens automatically, and makes it possible to query Geometry properties via the Network object, and Physics properties from the associated Phase object:
Let’s demonstrate this by creating a network and assigning two separate geometries to each half of the network:
>>> import openpnm as op >>> pn = op.network.Cubic([5, 5, 5]) >>> geo1 = op.geometry.GenericGeometry(network=pn, pores=range(0, 75), ... throats=range(0, 150)) >>> geo2 = op.geometry.GenericGeometry(network=pn, pores=range(75, 125), ... throats=range(150, 300)) >>> geo1['pore.diameter'] = 1.0 >>> geo2['pore.diameter'] = 0.1
Each of the Geometry objects has a ‘pore.diameter’ array with different values. To obtain a single array of ‘pore.diameter’ with values in the correct locations, we can use the Network as follows:
>>> Dp = pn['pore.diameter'] >>> print(Dp[70:80]) [1. 1. 1. 1. 1. 0.1 0.1 0.1 0.1 0.1]
As can be seen, the ‘pore.diameter’ array contains values from both Geometry objects, and they are in their correction locations in terms of the domain number system. This is referred to as
interleave_data. It also works to obtain Physics values via their associated Phase object.
Interleaving of data also works in the reverse direction, so that data only present on the network can be accessed via the Geometry objects:
>>> coords = geo1['pore.coords'] >>> print(coords[0:3]) [[0.5 0.5 0.5] [0.5 0.5 1.5] [0.5 0.5 2.5]]
interleave_data works between Subdomain objects of the same type, so that if ‘pore.volume’ is present on one but not another Geometry object, you will get an array of NaNs when asking for it on the object that does not have it:
>>> geo1['pore.volume'] = 3.0 >>> print(geo2['pore.volume'][:5]) [nan nan nan nan nan]
Points to Note
- Data cannot be written in this way, so that you cannot write ‘pore.diameter’ values from the Network (e.g. pn[‘pore.diameter’] = 2.0 will result in an error)
- Interleaving data occurs automatically if the requested key is not found. For instance, when you request
pn['pore.diameter']it is not found, so a search is made of the associated Geometry objects and if found an array is built.
- If an array named ‘pore.foo’ is already present on the Network or Phase, it cannot be created on a Geometry or Physics, resepctively, since this would break the automated
interleave_datamechanism, which searches for arrays called ‘pore.foo’ on all associated objects