permeability measurement by tomographic analysis

8/4/2019 Permeability Measurement by Tomographic Analysis

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PermeabilityMeasurement by

Tomographic Analysis

Muhammad Bilal AhmedSchool of Petroleum & MiningEngineering

University of Alberta


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Overview

Image Acquisition and Image Processing

Generating Link and Node files

Theory behind Porenet.exe Software

Calculating Petro-physical Propertiesusing Software Simulation


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Image Acquisition and ImageProcessing

CroppingTo obtain the desired sub-section of the whole

image, the plug-in of TransformJ is used tocrop the data in 3D with user defined

dimensions. In our case the raw image wasalready cropped so this step was omitted.


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The original 32 bit image is converted to 16bit to save the memory usage and hard diskstorage

Segmentation

To transform the gray scale into black andwhite image (pore space and solid phase), go toImage->Adjust->Threshold. A threshold value isselected automatically by Image based on anisodata algorithm (Ridler and Calvard, 1978)


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Normalization

Since the desired input data for porenet.exe(the program to extract a network from anygeneric 3D images) consists only 0s (pore space)and 1s (solid phase), we give the pores a value of

0 and the remaining solids the value of 1. We dothis by using the following link in Image J visitingProcess->Math->Max, and setting the maximumvalue at 1.


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Network Extraction

We use the software Porenet to extract thenetwork.

Data type: Binary

File name: .dat

Program: Porenet.exe input_file


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Finally after running the Porenet.exe we areleft with 4 files two of them are Link files

and the other two are Node files.These arelater used in other softwares as input files


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Theory behind Porenet.exe

Two processes are basically being carried outin this software.

1. We use a Running Length Encoding (RLE)algorithm to compress the data to save theirmemory occupation during the calculation

2. We use Maximal balls algorithm to extractpore network


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Running Length Encoding (RLE)algorithmRun-length encoding (RLE) is a very simple form

of data compression in which runs of data (thatis, sequences in which the same data valueoccurs in many consecutive data elements) arestored as a single data value and count, rather

than as the original run Let us take a hypothetical single scan line, with

B representing a black pixel and W representingwhite:

WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWWWWWWWWWWWWWWWWWWWBWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBWWWWWWWWWWWWWW


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If we apply the run-length encoding (RLE) datacompression algorithm to the above

hypothetical scan line, we get the following:12W1B12W3B24W1B30W36B16W

This is to be interpreted as twelve W's, one B,twelve W's, three B's, etc. The run-length coderepresents the original 67 characters in only18.


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Maximal Ball Algorithm

Analysing porous structures statisticallyrequires a division of the porous structure intoseparate entities. Essentially it is important todistinguish between two different types of

entities, the pore bodies and the throats ornecks between the pore bodies

Pores are the larger bodies in the porousmedia with the main function of storing liquid

whereas the throats are referred to as thesmaller 3- dimensional bodies formingconnections between pores


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In the 3D image, from a voxel in the void space (0),the radius is increase by one step until the ball hits

a solid phase voxel(1). We call the ball a maximalball at voxel


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Building the hierarchyAfter finding all the maximal balls, we compare

them to build the hierarchy. If two balls areoverlapped, the bigger one is the smallers master,and recognize the smaller a slave.

If a ball has no master, it is a super master anddefined as the pore body; if a ball has no slaves, itis a super slave and gives information forminimum radius of the throat.


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The allocation of pore bodies and throats is startedby considering the largest master sphere which has

no other masters connections as a principalsphere for pore body.

This sphere will consists of all the informationabout the entire pore body entity which has cluster

sphere or a slave sphere connected to it and theircoordinates centre is used to identify thecoordinates of the entire pore body entity.


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The throat length lt is defined by subtractingthe two pore lengths (li andlj) from the totalthroat length lij (the distance from pore i

center to pore j center).

lt = lij-li-lj

The pore length li and lj are defined by

lj = ltj (1-0.6 rt/rj)

li= lti (1-0.6 rt/ri)

where ri, r and rt are the radii of ore i, ore


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Real pores and throats have complex and highirregular geometrical profiles. We approximate

them as cylindrical capillaries with a constantbut arbitrary cross section with adimensionless factor shape G

where As is the surface area of the pore orthroat block this is found by counting thenumber of surfaces between void and solid ineach element; V is block volume; and L is theblock length.


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Calculating Petro-physicalProperties using SoftwareSimulationWe basically use 2 softwares developed by the

people at Imperial College London namelyProfessor Martin Blunt and Xavier Lopez.

Non-Newtonian Code v 1.0

Non-Newt 3


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Theory Behind the Softwares

Darcy Law

permeability measurement by tomographic analysis

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