Superpixels_PNM

Superpixels pore network extraction for geological tomography images

The present repository is to support the paper Superpixels pore network extraction for geological tomography images which proposes a new method of extraction of pore networks from 3D images of porous material. Superpixels, a classic method of image segmentation, has been employed as a part of the proposed algorithm to analyze 3D micro-structures and construct a pore network model that is representative of the hydraulic and electrical behavior of the studied porous mediums. In addition, an effective throat radius is introduced to compensate for over-segmentation issues in pore network extraction. In the corresponded paper, pore network models obtained from superpixels were extensively compared with those from watershed segmentation in terms of network statistics, morphology, permeability, and formation factor. It is found that despite differences in network morphology due to over-segmentation, macroscopic properties of the samples can be still modeled with the same level of accuracy as watershed networks. Superpixels proved to be exponentially faster but linearly more memory intensive than the watershed, which makes the superpixels a significant option to analyze large-size tomography images due to better scalability.

How to use?

Simply copy "spnm" into your working directory in MATLAB and run a demo in the same forlder. If you can convert your tomography image into a 3D binary MATLAB variable "A" in which 0 is pore space and 1 is the solid space, everything is set and ready to go. Just call "[NW,NM]=spnm.netext2(A,Res,'super');" and then the rest of analysis as you can see in Demo 1. "NW" gives back the extracted network and "NM" gives back the node map in which every pore is labeled with a unique integer. The results can be exported into several fromats: (1) txt, (2) csv summary, and (3) vtk which can be visulized using ParaView (https://www.paraview.org/).

Demo 1

% Demo 1
clear; close all; 
% Setting spatial resolution which simply says how large is one pixel in 
% the image
Res=5; %micron/pixel

% Making a random Gaussain geometry to play with, 0 is void sapce and 1 is 
% solid space, here we set an arbitrary porosity of 22%
A=imgaussfilt3(rand([100,100,100]),2); A=A>quantile(A,.22);

% Extracting the pore network via superpixels method
[NW,NM]=spnm.netext2(A,Res,'super');

% Correcting the effective area in the transmiscibility term to compensate 
% for possible over-segmentation
[NW]=spnm.ThroatAreaCorrection(NW,Res);

% Calculating the directional absolute permeability and formation factors
NW=spnm.absperm(NW);
NW=spnm.formfact(NW); 

% Exporting the network and its information in text, csv and vtk formats
spnm.net2txt(NW,2,1,'Network');
spnm.net2csv(NW,'Network');
spnm.net2vtk(NW,'Network',...
    NW.Pres(1).Pore,'Pore_Pressure_Pa_X',...
    NW.Pres(2).Pore,'Pore_Pressure_Pa_Y',...
    NW.Pres(3).Pore,'Pore_Pressure_Pa_Z',...
    NW.Flow(1).Throat,'Flow_rate_mic3/s',...
    NW.Flow(2).Throat,'Flow_rate_mic3/s',...
    NW.Flow(3).Throat,'Flow_rate_mic3/s');

% Printing results
disp(['Porosity: ' num2str(NW.Poro) ])
disp(['Average pore size: ' num2str(mean(NW.R)) ' Micron'])
disp(['Average absolute permeability: ' num2str(mean(NW.perm)) ' Darcy'])
disp(['Average formation factor: ' num2str(mean(NW.formfact))])

spnm.section(A); title('Original geometry'); saveas(gcf, 'Original geometry.png');
if numel(NW.R)<4000
spnm.netview(NW,'Pore size'); title('Pore Network structure'); saveas(gcf, 'Pore Network structure.png');
spnm.netview(NW,'Pore pressure',0,NW.Pres(1).Pore); title('Pore pressure'); saveas(gcf, 'Pore pressure.png');
end

And as a result the code will visulize and save cross-section of the 1) original geometry, 2) pore network structure color labeled for different pore sizes and 3) Pore pressure distribution in steady state incompressible flow in X direction.

The network metrics are exported as text format in two files of "Network_Pores.txt" and "Network_Throats.txt" like this:

An then finally, all the information including network metrics, structure, fluid flow rate and pressure distribution are exported into a vtk file that can be read in Paraview for all sorts of visulizations. Check the example below:

Demo 2

This demo shows how to use a sequence of images as input to form the 3D structure as a matlab binary variable and run the pore network extraction.

% Demo 2
clear; close all; 
% Setting spatial resolution which simply says how large is one pixel in 
% the image
Res=5; %micron/pixel

% Reading data from image sequence
% unzipping the folder
try; unzip('Image Seq.zip'); catch; end
% reading the image sequence
A=spnm.seq2mat('Image Seq/*.png');
% binarizing the image
A=imbinarize(A); 

% And then doing the rest of your analysis such as 
% Extracting the pore network via superpixels method
[NW,NM]=spnm.netext2(A,Res,'super');

% Printing results
disp(['Porosity: ' num2str(NW.Poro) ])
disp(['Average pore size: ' num2str(mean(NW.R)) ' Micron'])

Note: An example image sequence is provided that is being unzipped in the code. If you have yours ready, just remove the 'unzip' line.

Demo 3

In this code, we run a snesitivity analysis on the relationship between porosity, absolute permability and formation factor of some Gaussian porous structures.

% Demo 3
clear; close all; 
% Setting spatial resolution which simply says how large is one pixel in 
% the image
Res=5; %micron/pixel
% assuming a list of porosity 
PoroList=[0.1,0.15,0.2,0.25,0.3,0.4];
% initializing some arrays
Permeability=[];FormationFactor=[];
for Poro=PoroList

% Making a random Gaussain geometry with specific porosity
A=imgaussfilt3(rand([100,100,100]),2); A=A>quantile(A,Poro);

% Extracting the pore network via superpixels method
[NW,NM]=spnm.netext2(A,Res,'super');

% Correcting the effective area in the transmiscibility term to compensate 
% for possible over-segmentation
[NW]=spnm.ThroatAreaCorrection(NW,Res);

% Calculating the directional absolute permeability and formation factors
NW=spnm.absperm(NW);
NW=spnm.formfact(NW); 

Permeability(end+1)=mean(NW.perm);
FormationFactor(end+1)=mean(NW.formfact);
end
% plotting 
figure; subplot(1,2,1); plot(PoroList,Permeability,'o-'); xlabel('Porosity'); ylabel('Permeability (D)'); axis square; 
subplot(1,2,2); plot(PoroList,FormationFactor,'o-'); xlabel('Porosity'); ylabel('Formation factor'); axis square; 
saveas(gcf, 'Sensitivity analysis.png');

And the result will like this:

Citation

If you are using this work in your research please cite:

Arash Rabbani (2023), Superpixels pore network extraction for geological tomography images, Journal of Advances in Water Resources, Vol. 182, 104582.