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CHARACTERIZATION OF POROSITY IN COKES BY IMAGE ANALYSIS
Stein Rrvik1, Harald A. ye2, Morten Srlie3
1 SINTEF Applied Chemistry, Inorganic Chemistry, Trondheim N-7465 Norway2
Norwegian University of Science and Technology, Department of Chemistry, Trondheim N-7491 Norway3 Elkem ASA Research, Kristiansand N-4675 Norway
ABSTRACT
A fully automatic method for image analysis of porosity of cokes
has been developed. The method outputs a continuous pore size
distribution from 1 m to 10 mm, and will therefore cover a larger
range than mercury porosimetry. The method measures only pores
inside the coke grains; voids between coke grains in the sample
are ignored. A selection of calcined commercial cokes in different
fraction sizes has been analysed. There are considerable
differences in the pore size distributions of the different cokes.
INTRODUCTION
A fully automatic method for image analysis of porosity in carbon
materials has been developed within the frame of the Expomat /
Prosmat research program during the last years. The method is
based on computerised image analysis and optical microscopy,
and is capable of analysing large sample areas (several cm2). It
provides a logarithmic size distribution of pores in the range of 1
m to 10 mm pore radius. In addition to this size distribution, a
relative measure of pore surface area and pore connectivity is
given.
The main aspects of this image analysis method have been
published earlier [1], as a method to analyse porosity in anodes.
This paper describes how the previous method has been modified
to be suitable for analysis of coke grains.The main problem to resolve with respect to porosity analysis of
cokes is how to separate pores inside coke grains from the voids
between grains. Vibrated bulk density (VBD) of a narrow coke
fraction is a common measure of macroporosity in cokes. VBD
includes all voids between grains, and the result will then be
dependent on grain size and shape. Mercury porosimetry ignores
voids between grains (provided that the coke particle size is not
too small) at the same time as it fills large pores inside the coke
grains. Hence, both these methods have disadvantages. This paper
shows how image analysis can be used to ignore voids between
grains and include all pores inside grains. Comparison with VBD
and mercury porosity will be given. The analysed cokes presented
in this paper are petroleum cokes used for anodes in the
aluminium industry, made by six different producers.
METHOD DESCRIPTION
A brief summary of the previously published method [1] follows
here:
1. Coke grains are sieved to different fraction sizes and
impregnated with a fluorescent epoxy1 under vacuum. The
sample surfaces are ground and polished after curing of the
epoxy. Pores filled with fluorescent epoxy light up brightly if
viewed with ultraviolet light in a microscope. This reduces
the error of creating false pores when cuttingand polishing
the samples.
2. The samples are examined using a standard inverted reflected
light metallurgical microscope (Leica MeF3A), equipped
with a motorised XY- stage and focus controller. The stage
movement and focus is controlled directly by the computer
image analysis software. Digital images are acquired using
an electronic 3-chip CCD2 video camera (Sony DCX 930P)
and a frame-grabber card.
1 The epoxy is two-component and consists o f Bisphenol-A-Diglycidyl-Ether and Tri-Ethylene-Tetramin with Sodium-Fluorescein added as fluorescent dye. Product trade
names are Epofix and Epodye; both made by Struers, Denmark.
2 CCD is an abbreviation for Charge Coupled Device. These cameras use a chip withan array of sensors that accumulates an electrical charge proportional to the amount of
light exposed onto them.
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3. A grid of adjacent images, sufficiently large to cover most of
the sample is acquired automatically by the computer and
stored on disk. The images are then analysed in batch. When
the adjacent frames are analysed, the pores entirely inside each
frame are measured while the pores cut by the image edges are
not. These pores are saved and measured after four frames have
been analysed and merged. This process continues recursively,
allowing arbitrarily large pores to be measured. There is no
upper limit to the measured pore size. The advantage of thismethod is obvious: Mercury porosimetry does not give reliable
values above 40-50 m, while the pore size that can be
analysed by the image analysis method is only limited by the
movement of the stage, which is 50 mm. The disadvantage
with the image analysis method is that it does not include
microporosity below 1 m pore radius.
4. The resulting data is merged using Microsoft Excel macros
and presented using templates (Figure 1). The image analysis
outputs the porosity values as thesum of the areas pores with a
specified inscribed radius cover, as a percentage of total
analysed sample area. The sum of all porosity values is thus
equivalent to the total porosity. The overview image in Figure
1 shows pores greater than about 50 m radius and gives useful
visual information such as the apparent homogeneity of thecoke grains.
5. The image analysis procedure is fully automated, it only
requires an operator to place the sample on the microscope and
start the procedure using the desired parameters. With
sufficient storage space, images of a series of cokes can be
acquired during daytime and be analysed in batch by the
computer during the night. At medium magnification (80x)
16x24 = 384 frames are required to cover a 30 mm sample. It
takes about half an hour to acquire these frames and 2 hours to
analyse them. See Figure 2 for an overview of how the sample
is covered by the adjacent frames.
The computer software used was the general image analysis
Macintosh application NIH image, developed by Wayne Rasbandat the National Institute of Health in the US. This software is
available in the public domain, and can be downloaded freely from
ftp://rsbweb.nih.gov/pub/nih-image/3. The source code has been
customised by adding support for the microscope hardware and
some extra image analysis procedures. The NIH image software has
a Pascal-like macro language, which was used to control the
analysis. A proper macro programming language is essential for this
kind of work.
3Alternate sources for NIH image are from Library 9 of the MacApp forum
on CompuServe, and on floppy disk from NTIS, 5285 Port Royal
Rd.,Springfield, VA 22161, part number PB93-504868.
Porosit (smoothed) [%]
1 0.0000
1.26 0.0000
1.58 0.0000
2 0.0000
2.51 0.0637
3.16 0.1275
3.98 0.0637
5.01 0.0764
6.31 0.1826
7.94 0.2121
10 0.2687
12.59 0.3484
15.85 0.416119.95 0.5255
25.12 0.6604
31.62 0.8309
39.81 0.9369
50.12 0.9147
63.1 0.9182
79.43 0.9522
100 0.9512
125.89 0.9672
158.49 1.1726
199.53 1.5764
251.19 1.7463
316.23 1.5828
398.11 1.5538
501.19 1.4824
630.96 1.2417
794.33 0.9543
1000 0.3751
1258.93 0.0000
1584.89 0.0000
1995.26 0.0000
2511.89 0.0000
3162.28 0.0000
3981.07 0.0000
5011.87 0.00006309.57 0.0000
7943.28 0.0000
Sum 21.1016
SF pores 0.07639
SF carbon 0.02336
Porosity 21.10
Connectivity 0.10
SampleName 17.7.1
Figure 1: Standard diagram for pore size analysis of a single
sample, created by a Microsoft Excel template.
Figure 2: Schematic view of the order the images are acquired at
80x magnification, with the sizes involved for a 30 mm sample.
Sample - Coke
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
10
Pore Radius [m]
Porosity[%]
Porosity [%]
Porosity (sm) [%]
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PORES VS. VOIDS BETWEEN GRAINS
As explained in the introduction, the main problem with measuring
porosity in cokes is to distinguish between pores inside grains and
voids between grains. Figure 3 shows an example image with coke
grains (from the 1.0-2.0 mm fraction) embedded in epoxy. The
carbon in the coke appears grey in this image, while the epoxy with
the fluorescent dye is black. The grains were embedded in epoxyunder vacuum. The epoxy wets the carbon well, so the epoxy fills
the pores almost completely. The fraction of closed pores is less
than a percent and these pores are usually smaller than 5 m. Closed
pores will be ignored by the image analysis.
Most image analysis programs have a function to discard pores
touching the edge of an image. Figure 4 shows the effect of this
function. Pores connected to the image edge (the surrounding epoxy
will always cross the image edge) are here rendered in grey, while
unconnected pores are black. The large pore inside the grain on the
right is connected to the surrounding epoxy through some cracks.
This is very typical. Most cracks in the coke grains are connected to
the outside. It is obvious that regular image analysis of such images
will give a too low porosity. The larger the pores, the lower the total
porosity will be.
A common way to resolve the problem with connected pores is by a
technique called watershed segmentation [3]. This technique is
based on an erosion of features until one point is left, and then a
conditional iterative growth that avoids joining features. The effect
of this segmentation is that white lines will be drawn across all parts
of features that are narrower than the neighbourhood. Figure 5
shows the result of applying watershed segmentation to Figure 4.
The black areas show the features that will be disconnected from the
edge and analysed. In this case, far too many pores will be analysed.
All areas between the coke grains will be measured as pores.
As Figure 5 shows, regular watershed segmentation will not give
the desired result. The implementation was therefore changed with a
condition that does not create separation lines longer than aspecified width. The value of this variable was called
MaxDisconnect (MD). This is in some applications called limited
watershed erosion. Figure 6 shows the result of the modified
watershed segmentation, using a value of 200 m in MD. Some of
the areas between grains will now not be included, but there is still
too much intergrain porosity measured.
Figure 7 shows the result of the modified watershed segmentation
with a value of MD decreased to 50 m. Most of the intergrain
porosity is now ignored, except the area in the middle of the image.
The grains are in this case closer than 50 m. Decreasing the value
of MD further will cause the cracks inside the coke to be ignored as
well, which is not desired. A different approach to the problem is
therefore needed.
Some condition must be added that will separate the areas based on
maximum size, in addition to the maximum separation width.
Simply setting a limit to the maximum size of the pores that will be
measured has been shown not to work very well. Especially with
sponge-like coke grains, the size of the pores inside the grains are
sometimes as large or larger than the size of the voids between the
grains. Because of this, the implementation was changed to includea condition based on relative size rather than absolute size.
Separation lines will only be drawn between features where the
smallest feature has a maximum inscribed circle radius smaller than
a specified percent below the largest features radius. This
percentage was called RelativeSizeDifference (RSD). A RSD value
of 0% means that the condition has no effect; all features will be
disconnected as usual. 100% means that no features will be
disconnected. 33% means that features will be separated if the
smaller feature has a size less than 2/3 of the larger feature. Tests
have shown that values between 10% and 40% work well. Figure 8
shows the result of the modified watershed segmentation with a MD
value of 50 m and a RSD value of 20%. Now the large area
between the coke grains is excluded from the measurement, because
its maximum radius is about the same as the maximum radius of the
other areas between grains. The crack inside the grain on the left is
measured, because its maximum radius is much smaller than the
areas between the grains. Some small short segments between flat
edges of adjacent grains will still be included, but that is difficult to
avoid without setting the limits too tight.
The value of the MaxDisconnect variable must be increased at
increasing grain size. Larger grains have larger pores and cracks
along edges that should be included in the measurement, but also a
larger distance between the particles. The larger distance between
particles appears because the surface examined is a plane cutting the
coke grains at random sections. For spherical grains, the intersected
area will be a sinus function of the maximum diameter. The average
distance between grains in an intersection will therefore be roughly
proportional to the grain size.
In this work, a MD value of 25 m was used for measurements of
the 0.5-1.0 mm fraction; 50 m was used for the 1.0-2.0 mm
fraction and 75 m was used for the 2.0-4.0 mm fraction. These
values gave a satisfactory separation between pores inside grains
and voids between grains.
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Figure 3: Coke grains embedded in epoxy
Figure 4: Pores connected to surrounding epoxy (grey)
Figure 5: Pores split by regular watershed segmentation (black)
Figure 6: Modified watershed segmentation, MD=200
Figure 7: Modified watershed segmentation, MD=50
Figure 8: Modified watershed segm., MD=50, RSD=20%
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0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1 10 100 1000
Radius [m]
Porosity[%]
Coke A, 2.0-4.0 mm
Coke A, 1.0-2.0 mm
Coke A, 0.5-1.0 mm
Figure 9: Pore size distributions for fractions of coke A
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1 10 100 1000
Radius [m]
Porosity[%]
Coke B, 2.0-4.0 mm
Coke B, 1.0-2.0 mm
Coke B, 0.5-1.0 mm
Figure 10: Pore size distributions for fractions of coke B
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1 10 100 1000
Radius [m]
Porosity[%]
Coke C, 2.0-4.0 mm
Coke C, 1.0-2.0 mm
Coke C, 0.5-1.0 mm
Figure 11: Pore size distributions for fractions of coke C
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1 10 100 1000
Radius [m]
Porosity[%]
Coke D, 2.0-4.0 mm
Coke D, 1.0-2.0 mm
Coke D, 0.5-1.0 mm
Figure 12: Pore size distributions for fractions of coke D
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1 10 100 1000
Radius [m]
Porosity[%]
Coke E, 2.0-4.0 mm
Coke E, 1.0-2.0 mm
Coke E, 0.5-1.0 mm
Figure 13: Pore size distributions for fractions of coke E
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1 10 100 1000
Radius [m]
Porosity[%]
Coke F, 2.0-4.0 mm
Coke F, 1.0-2.0 mm
Coke F, 0.5-1.0 mm
Figure 14: Pore size distributions for fractions of coke F
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RESULTS AND DISCUSSION
Figure 9 to Figure 14 show the pore size distributions for 6
different cokes. Three different fraction sizes were analysed: 0.5 to
1.0 mm, 1.0 to 2.0 mm and 2.0 to 4.0 mm. As expected, the porosity
decreases with decreasing fraction size. The difference is larger
between the 0.5-1.0 and the 1.0-2.0 fraction than the 1.0-2.0 and
2.0-4.0 mm fraction. Most cokes have a similar size distribution up
to 10 m, where the smallest fraction starts to decrease in porosity.
The two larger fractions decrease in porosity from 20 to 50 m
radius, and then increase again up to 100 m. This two peak
distribution is typical for calcined cokes. The largest diameter peak
is due to large, round gas entrapment pores that are present in the
green coke. The smallest diameter peak is due to the slit-like pores
and cracks that evolve during the calcination process.
One of the cokes, B, has a much different distribution compared to
the other cokes (Figure 10). The 0.5-1.0 mm fraction is similar to
the other cokes, but the two coarser fractions have a much lower
porosity and only one peak, around 30 m. The 2.0-4.0 mm fraction
has a lower porosity than the 1.0-2.0 mm fraction up to 50 m.
Coke B is known to have a higher content of shot coke than the
other cokes. The shot grains, which have a lower porosity than the
other grains, partially survive the crushing and get concentrated in
the coarser fractions.
Figure 15 compares mercury and image analysis porosity for the
middle fraction. It is seen here that coke B does not have lower
porosity than the other cokes as measured with mercury porosity,
but the difference in macro-porosity is easily seen with image
analysis. Coke B also has the largest difference between porosity as
measured by mercury porosimetry and by image analysis.
coke 1.0-2.0 mm
0
2
4
6
8
10
12
1416
18
20
Coke
A
Coke
B
Coke
C
Coke
D
Coke
E
Coke
F
Porosity[%]
Total Porosity, Hg [%]
Total Porosity, IA [%]
Figure 15: Comparison of total porosity measured by image
analysis (IA) and mercury porosity (Hg)
Figure 16 and Figure 17 shows a 12.5 x 12.5 mm overview area of
the 1.0-2.0 mm fraction of coke A and B, respectively. The black
areas are pores that have been measured, while the grey areas are
ignored. It is evident from these images that the technique described
above is quite successful in separating pores inside coke grains and
voids between grains.
Figure 16: Overview of 1.5 cm2 area of coke A
Figure 17: Overview of 1.5 cm2 area of coke B
The shot coke grains of coke B are easily seen in Figure 17. These
grains do not have the thin calcination pores that can be seen in
coke A. Coke C through F are visually similar to coke A.
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The only coke other than coke B that shows a lower porosity below
30 m for the largest fraction is coke E (Figure 13). This coke is a
mixed source coke. It probably behaves similarly to coke B: Some
grains are less porous than the other grains, so that these stronger
grains get concentrated in the largest fractions.
Another coke that deviates from the other cokes in size distribution
is coke F (Figure 14). This coke is known to be more brittle and to
have a more fibrous structure than the other cokes. (Coke F is
calcined in a rotary hearth calciner, while the rest are calcined inrotary kilns.) This coke has a larger difference in porosity between
the two largest fractions above 100 m. This indicates that the
porous grains do not survive the crushing as well as in the other
cokes.
The pores below 50 m seem to be most important for strength.
Figure 18 compares coke porosity with Hardgrove Grindability
Index (HGI), which can be considered an inverse measure of coke
grain strength. HGI values were not available for coke A to F, so
Figure 18 shows data for a different set of cokes, analysed at a
different laboratory. These cokes are also commercial petroleum
cokes used in the aluminium industry. There is a trend that the HGI
increases with increasing porosity in the 5-50 m interval, while the
other porosity intervals do not have any significant effect.
coke 1.0-2.0 mm
0.0
2.0
4.0
6.0
8.0
10.0
12.0
20 25 30 35 40
HGI (0.60-1.18mm) [%]
Porosity[%]
Porosity [%] 0-5 m
Porosity [%] 5-50 m
Porosity [%] 50-10000 m
Figure 18: Comparison of coke porosity and HGI
Figure 19 shows a comparison of coke porosity and mill time. Mill
time is the time a given fraction of coke (1.0-2.0 mm) requires in a
ball mill to get 70% of the mass below 200 mesh. It is therefore a
measure of grain strength. The trend is that a decreasing amount of
small pores (0-25 m radius) will give a longer time in the mill. The
larger pores (above 25 m radius) do not seem to correlate with mill
time. Both Figure 18 and Figure 19
indicates that the smallest pores are more important for coke
strength than the larger pores.
coke 1.0-2.0 mm
0
2
4
6
8
10
12
4 24 44 64 84
Mill Time 70 % -200# [min]
Porosity[%]
Porosity [%] 0-25 m
Porosity [%] 25-250 m
Porosity [%] 250-10000 m
Figure 19: Comparison of coke porosity and mill time
CONCLUSION
Image analysis is useful for analysing macroporosity in coke grains.
Image analysis can be used for measuring pores up to several mm
size, and is able to separate between pores inside coke grains and
voids between grains. Image analysis has shown to be a good
alternative to mercury porosimetry analysis of anode cokes.
ACKNOWLEDGEMENTS
Financial support from The Research Council of Norway and the
Norwegian aluminium industry (via the EXPOMAT and
PROSMAT research programs) is gratefully acknowledged. Thanks
are also due to Elkem Aluminium ANS and Hydro Aluminium for
providing coke samples and analysis data.
REFERENCES
[1] Stein Rrvik, Harald A. ye:A Method for Characterizationof Anode Pore Structure by Image Analysis. The Minerals,Metals and Materials Society (TMS); Light MetalsProceedings 1996, p. 561-568.
[2] Kjell Kvam, Harald Schreiner, Stein Rrvik, M. Srlie, H.A. ye: Porosity Development in Sderberg Anodes
Laboratory Simulation. Extended Abstract 24th
BiennialConf. on Carbon, Charleston (South Carolina, USA)American Carbon Society 1999.
[3] J.C. Russ: The Image Processing Handbook; CRC Press,USA (1995) ISBN 0-8493-2516-1, page 476-477.
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