The measurement of porosity for an individual taconite pellet

Powder Technology 204 (2010) 167–172

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The measurement of porosity for an individual taconite pellet Keith B. Lodge ⁎ Department of Chemical Engineering, University of Minnesota Duluth, 1303 Ordean Court, Duluth, Minnesota, 55812-3025, USA

a r t i c l e

i n f o

Article history: Received 18 August 2009 Received in revised form 6 July 2010 Accepted 28 July 2010 Available online 5 August 2010 Keywords: Taconite Pellet Porosity Envelope Skeletal Silhouette

a b s t r a c t The knowledge of the variability in the properties of individual taconite pellets as a function of processing conditions may lead to the improvement of the production of iron. An important property is porosity. Pellets with high porosity are desirable for the reduction to iron in the blast furnace. There is a published work describing the measurement of porosity on collections of pellets. Here I describe a method for the determination of the porosity of an individual pellet. Recent determinations of porosity have used the measurements of the skeletal volume and the envelope volume. Helium pycnometry is the method of choice for the measurement of the skeletal volume, whereas volumetric displacement of dry material is now the preferred method for the envelope volume, requiring collections of pellets. I have adapted a method of silhouettes, developed for single items of fruit, to measure the envelope volume of a single pellet. The porosities of six individual sintered pellets from a facility in North-Eastern Minnesota, USA, range from 33 to 38% with a relative uncertainty of about 1%. Certain pellets have significantly different porosities from each other. The magnitudes are comparable to published porosities on green pellets, ranging from 30 to 36%, and to fired pellets, ranging from 28–38%. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The increasing demands for iron by the rapidly developing economies of countries such as India and China are stimulating renewed technical and scientific interest into the extraction and beneficiation of iron ore. Additional impetus originates from the concurrent increase in the demand for energy. Small beneficial changes in large-scale commercial processes can lead to significant savings and smaller impacts on the environment. The processing of taconite [1] on the Iron Range of North-Eastern Minnesota in the USA leads, for the most part, to pellets that travel by ship from ports on the western end of Lake Superior to blast furnaces to the east on other Great Lakes. The important properties of the pellets include strength and porosity. The latter is important for the reduction of iron oxide in the blast furnace to be rapid; it is a measure of the open space, or pore volume, within the pellet that is accessible to the reducing gases. The reduction is a heterogeneous reaction that requires first the adsorption of the reducing gas, typically carbon monoxide, on the solid surface of the iron oxide. The larger the pellet's porosity the more surface area there is for the initial adsorption step. Many have recognized the importance of the measurement of porosity for pellets. Schultz et al. [2] studied the pore and silicate structure of pellets under simulated blast-furnace conditions; they used mercury porosimetry. Janowski et al. [3] also used this method

⁎ Tel.: + 1 218 726 6164; fax: + 1 218 726 6907. E-mail address: [email protected]. 0032-5910/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2010.07.028

and stereological methods to measure the porosity of reduced hematite. A preferred route to the porosity is to measure the envelope and skeletal volumes because it avoids the use of mercury; this is the approach here. Helium pycnometry is the method of choice for the measurement of the skeletal volume; this is a well-established measurement, there being a number of commercial instruments available [4,5]. The development of a method for the measurement of envelope volumes using the displacement of a dry medium [6] has led to a commercial instrument [7]; this requires a collection of pellets. Forsmo et al. [8] developed procedures for the measurement of the porosity of green pellets using this instrument. They have been able to use these for their studies with green pellets of binding [9], and of oxidation and sintering mechanisms [10]. Potential advantages of measuring porosities on single pellets are the future study of relationships between porosity and other singlepellet properties and the effect of processing conditions on such relationships. Related to this is the shrinkage study of composite pellets during reduction in which Halder and Fruehan [11] essentially estimated the envelope volume of a single pellet by measuring its diameter across diametrically opposite points. Here, I investigate another method for the measurement of the envelope volume of a single pellet, which should take better account of a pellet's irregular shape. I have adapted this from a published method, a method of silhouettes, for single items of fruit [12]. Recently, Turchiuli and Castillo-Castaneda used silhouettes to study the size and structure of dehydrated milk agglomerates [13]. For a single irregular-shaped particle, an optical system records silhouettes at regular angular intervals. Image analysis gives the

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2. Theory and calculations

envelope volume was time consuming; the repetition of the measurement for one pellet, Pellet 03, gave a SEM and I chose this to represent the measure of the uncertainty in the envelope volume, δVE, for Pellet 03 and I chose its relative uncertainty, δVE ∕ VE, to represent the relative uncertainty for each pellet in Eq. (6). The difference in porosities for pellets i and j, enables the comparison of pellets:

2.1. Definition of terms

Δεij = jεi −εj j:

coordinates of the object's perimeter which allows for the calculation of its volume. Here I present data for six sintered taconite pellets. This is a preliminary study designed to judge the efficacy of the method and to see whether there may be advantage in developing the method into a form that is more convenient for routine use.

The terminology follows that given elsewhere [14]. Here the porosity of a single pellet or particle is the final quantity of interest. The porosity, strictly the single-particle porosity, is the ratio of the volume of the open pores in the particle, VOP, to the total volume of the particle, VE: ε = VOP ∕VE :

ð1Þ

The envelope volume is the more common term for the total volume of the particle; this is the volume that would be obtained by shrinking a film around the particle in order to contain it completely — see Fig. 1. The envelope volume comprises the open-pore volume and the skeletal volume, VSK: VE = VOP + VSK :

ð2Þ

The skeletal volume in turn comprises the volume of the solid material, VS, and the volume of closed pores, VCP, within the particle: VSK = VS + VCP :

ð3Þ

Closed pores are inaccessible non-solid regions within the particle. 2.2. General calculations For a single pellet the measurement of the skeletal and envelope volumes enables the open-pore volume to be calculated from Eq. (2): VOP = VE −VSK :

ð4Þ

The application of Eq. (1) gives the porosity: ε = ðVE −VSK Þ∕VE = 1−VSK ∕VE :

ð5Þ

The corresponding uncertainty in the difference is: δΔεij =

  2 1∕2 2 ðδεi Þ + δεj :

2.3. The envelope volume — basic theory The volume of any object may be calculated [16] from b

V = a ∫ AðzÞdz

ð9Þ

where A(z) is the area of a horizontal slice of the object at a height z — see Fig. 2. The vertical extremities of the object are at z = a and at z = b. The analysis proceeds by dividing the slice into a series of triangular wedges centered in the axis of rotation, which is parallel to the z-axis; the angle of the triangles' apices at the center of rotation is θ, defined by the regular interval at which silhouettes are recorded. The area of a single triangular wedge i is: AΔ;i = 1=2 ·ri ·ri + 1 ·sinθ

ð10Þ

where ri and ri + 1 are successive radii. The approximation for the area of the slice is: AðzÞ≈∑i AΔ;i

ð6Þ

It is possible to make many measurements of the skeletal volume, so the Standard Error of the Mean, SEM, is an appropriate measure of its uncertainty, δVSK. In this exploratory work the measurement of the

Fig. 1. Schematic diagram of a pellet showing the three types of volume.

ð8Þ

The comparison of the uncertainty in the difference and the difference itself enables conclusions to be drawn regarding the distinction between pellets [15]. The examination of the ratio Δεij∕δΔεij is a convenient way to do this; if it is greater than unity then the pellets i and j have different porosities.

A standard result gives the uncertainty in the porosity [15]: n o1∕2 δε = ð∂ε∕∂VSK Þ2 ·ðδVSK Þ2 + ð∂ε∕∂VE Þ2 ·ðδVE Þ2 n o1∕2 = ðVSK ∕VE Þ· ðδVSK ∕VSK Þ2 + ðδVE ∕VE Þ2 :

ð7Þ

Fig. 2. Schematic view of horizontal slices through a solid.

ð11Þ

K.B. Lodge / Powder Technology 204 (2010) 167–172

where the summation runs over the numbers of wedges (equal to 360°∕θ) in the slice. The capture of silhouettes in the x–z plane leads to the values of ri: ri = xi −xrot

ð12Þ

where xi and xrot are the coordinates of the perimeter and rotation axis, respectively. With the VGA resolution used in this work, 640 pixels in the x-direction and 480 pixels in the z-direction represent the silhouette's image, so the x-coordinate (z-coordinate) of a point on the image corresponds to the pixel number in the x-direction (zdirection). The approximation of the integral in Eq. (9) by a summation leads to the volume: V≈∑j Aðzj Þ·Δzj

ð13Þ

where Δzj is the vertical distance between slices; it is natural to choose: Δzj = Δz = 1pixel:

ð14Þ

2.4. Envelope volume — summary of programming logic Programs were written as Mathcad [17] worksheets; these are part of a technical report [18]. Mathcad was chosen because of the relative ease with which images may be handled; it represents the image as a matrix in which each element represents a single pixel. Worksheet 1 manipulates a single silhouette to extract the coordinates of the silhouette's perimeter. It contains the following steps: 1. The silhouette's image is “binarized”. That is, pixels in light areas (outside the silhouette) are assigned the value 1 and those in dark areas (inside the silhouette) are assigned the value 0. This requires a “threshold” to be set; this is done by inspection and this threshold can change depending on the quality of the image. 2. The pixels that sit on the perimeter of the silhouette are identified by examination of the Mathcad matrix; the row in which the pixel is gives the z-coordinate and the column in which the pixel is gives the x-coordinate. The following logic is used for both searches in the z- (vertical) and x- (horizontal) directions: if the pixel is light and the neighboring pixel is dark, or if the pixel is dark and the neighboring pixel is light, the light pixel is chosen as the pixel on the perimeter. Pixels on the perimeter at the vertical and horizontal extremities of the object may be missed if searches are not done separately in the z- and x- directions.

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3. The results of the two searches are combined and duplicate perimeter pixels are removed. Some extraneous pixels remote from the pellet are removed at this stage; these arise because of imperfections in the optics and the illumination of the pellet. 4. The process leads to pixels with the same z-coordinate but with different x-coordinates that are quite close, being on the same side of the silhouette; these can arise because of irregular shapes. These x-coordinates are averaged so that on the same side of the silhouette the perimeter is defined by a single x-coordinate for a given z-coordinate. The side is defined as being either to the left or right of the rotation axis; this axis is chosen approximately at this stage — the choice is later refined, but the choice at this stage does not affect this calculation. Worksheet 1 is run separately for each silhouette; for the 5-degree interval there are 36 silhouettes. The inspection of the perimeter data for all silhouettes separately is done in Worksheet 2; this is made easier by creating a movie using the animation feature of Mathcad. Sometimes the original silhouette file requires more editing when recalcitrant extraneous pixels and a lack of continuity are apparent at this stage. All the perimeter data are assembled into a single file in Worksheet 3. Horizontal slices, the perimeters in the x–y plane, are plotted; the origin of the plot sits on the rotation axis. At this stage the rotation axis is fixed by inspecting a horizontal slice near the middle of the pellet. This is done by using the following criterion: the perimeter coordinates for silhouette at − 90° should be the same as those for the silhouette at + 90°. If the incorrect rotation axis is chosen, the perimeter coordinates are different; this is demonstrated in Fig. 3. A movie is created showing these slices; this is useful for the visual inspection of the perimeter data for each slice. In the body of the pellet the number of x–y coordinates for a horizontal slice, nxy, is constant, being equal to the number of silhouettes plus two (the silhouettes at −90° and +90° are the same); for a 5-degree interval this number is 74. However, at the top and bottom of the pellet this number decreases to zero outside the pellet; the values of z at which nxy just becomes constant searching from the top, zmax, and searching from the bottom, zmin, are found so they can be used in the calculation of the volume. The volume using horizontal slices from zmin to zmax is calculated in Worksheet 4 using Eqs. (10)–(14). Subsidiary programs were written to extract data from 5-degree-interval data set for the following intervals: 10, 15, 20, 30 and 45 degrees. The corresponding volumes were calculated and plotted against the angular interval; the extrapolation to the interval of zero gives the final envelope volume.

Fig. 3. Horizontal slices through a pellet with correct and incorrect rotation axes. ■ Perimeter points. A shows the slice with the correct axis, and B shows the slice with an incorrect axis.

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3. Experimental 3.1. Samples

6.

The sintered taconite pellets are part of the sample produced by a manufacturing facility in North-Eastern Minnesota, USA; they were collected by R. Visness in 1999.

7.

3.2. The skeletal volume The measurements were done with a Quantachrome Autopycnometer, the UltaPyc 1000, using helium. The daily operations included calibration following the manufacturer's procedures. Before and after measurements on pellets, measurements were made on a stainless steel ball, Micromeritics Part No. 131/25607/00, for which the volume is known accurately [19]; these data are used to assess the performance of the autopycnometer. 3.3. The envelope volume by the method of the silhouettes The silhouettes were recorded at 5-degree intervals using a custom-built apparatus, shown in Fig. 4. The apparatus comprised, moving from left to right in Fig. 4: 1. A small screen illuminated by an optical fiber, a fiber-optic backlight (Edmund Optics A54-228 and A38-944); this was fed with a tungsten-filament white-light source (Edmund Optics A55-718). 2. A rotary optical mount calibrated in degrees (− 90 to + 90°, Edmund Optics A53-027). 3. A custom-built 3-pin mount upon which the pellet sat; this mount was placed on the rotation axis of the rotary optical mount. 4. A digital camera (DSP MS-980 N) with a focusable lens (Edmund Optics A53-027); the camera was connected to a video monitor (Toshiba CM1310A), which in turn was connected to the USB port of a personal computer using an adapter (Belkin F5U208). 5. Items 1–4 were mounted on an optical bench (Edmund Optics Part No. A54-402) with suitable slides and mounting posts. The general procedure was as follows: 1. The light source was switched on and imaging software was opened to view the 3-pin mount. 2. The horizontal alignment of the 3-pin mount was checked, and adjusted, using a small microscope slide atop and viewing its image over the full range of rotation. 3. The selected pellet was placed on the 3-pin mount, generally with its longest dimension aligned approximately in the vertical direction. The mount was rotated through its full range to check that all the silhouettes would fall comfortably into the imagingcapture window of the software. 4. The camera was focused and this lens position was kept unchanged throughout the experiment for a single pellet. 5. The silhouettes were captured at 5-degree intervals using imaging software [20] in the public domain. The size of the images is

Fig. 4. The apparatus for recording silhouettes. A fiber-optic white backlight creates the silhouette of the pellet, sitting on a rotary mount. A digital camera records the image of the silhouette, which is then captured on a personal computer.

8.

9.

640 × 480 pixels; they were saved as JPEG files in a folder created for the pellet. The 3-pin mount was removed by editing with the imaging software from each image; each edited image was saved under a different filename. The edited images were then run through the series of Mathcad worksheets to calculate an initial value of the envelope volume. The programs were run at this stage to see if the image files could be processed satisfactorily. If not, the unsatisfactory images were then re-recorded after making any necessary adjustments. The pixels, for the vertical and horizontal directions, in the images were calibrated by fixing a graticule, containing a 1-mm grid with 0.01 mm divisions (Edmund Optics AA005), in place of the pellet. The final envelope volume was calculated using the calibration.

The measurements of the skeletal and envelope volumes were made on 6 pellets taken at random from the available sample. The envelope volume of Pellet 03 was measured at two randomly selected orientations. In addition, the envelope volume of a stainless steel ball was measured using this silhouette method and a pair of vernier calipers (General Tools No. 143).

4. Results Table 1 contains the final skeletal and envelope volumes, and the resulting pore volumes and porosities for the pellets; it also contains the volumes for the stainless steel ball. For Pellet 03, the envelope volume was determined twice at different positions on the 3-point mount. Table 2 shows the ratios of the difference in porosities between pellets to the corresponding uncertainty in the differences. Fig. 5 contains a graph, using the data for Pellet 01 and 06, showing an example of the extrapolation of the envelope volume as a function of angular interval to zero angular interval. The extrapolation using a cubic or quartic polynomial gives a square of the correlation coefficient greater than 0.9998, and the maximum difference between the extrapolated value and the value for an angular interval of 5 degrees is 0.003 mL.

5. Discussion The results obtained for the stainless steel ball allow for the assessment, in part, of the degree to which the method of silhouettes measures the envelope volume accurately. The envelope volume measured by the method of silhouettes, 1.485 ± 0.009 mL, is in good agreement with that measured with a standard pair of vernier calipers, 1.490 ± 0.006 mL. A more rigorous and realistic test would be to apply the method to an object of approximately the same size and irregular shape for which the envelope volume had been determined by another method. There are other possible methods for doing this in future work. The envelope volume of single items of densified biomass was measured by Igathinathane et al. [21] with a commercial 3D laser scanner [22]. Dummer et al. [23] describe another method using pressure equalization of gas chambers, one of which contains the sample; however, there does not seem to be any published data on its application to particular samples, or a commercial instrument available that exploits this method. The magnitudes of the measured porosities for the pellets seem reasonable. For example, published studies report values for green pellets in the following ranges: for untreated green pellets 30–33% [8]; for green pellets with various additions of bentonite, 30–36% [9]; and for green pellets, 31–32% [10]. The range measured here for sintered pellets is 33–38%. Schultz et al. [2] studied the pore and silicate structure of pellets under simulated blast-furnace conditions; they measured porosities in the range 28–38%.

K.B. Lodge / Powder Technology 204 (2010) 167–172

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Table 1 Measured volumes and porosities for the six sintered taconite pellets. Envelope

Skeletal volumeb/mL

Pore

Porositye

Sample

Mass/g

volumea/mL

Value

Uncertaintyc

volumed/mL

Value

Uncertaintyf

Pellet 01 Pellet 02 Pellet 03 Duplicate Mean Standard Error of the Mean Pellet 04 Pellet 05 Pellet 06 Stainless steel ball Method of silhouettesg Using calipersh

3.392 2.415 2.981 –

1.110 0.806 0.943 0.932 0.938 0.006 1.094 1.045 0.784

0.714 0.5005 0.595 –

0.002 0.0004 0.001 –

0.396 0.305 0.349 0.337 0.343

0.357 0.379 0.369 0.362 0.365

0.004 0.004

0.004

0.369 0.345 0.264

0.337 0.330 0.336

0.004 0.004 0.004

3.424 3.334 2.496

0.725 0.701 0.5200

0.001 0.001 0.0004

1.485 ± 0.009 1.490 ± 0.006

a

Envelope volumes for pellets were determined by the method of silhouettes. Skeletal volumes were determined by autopycnometry. c Uncertainties are Standard Errors of the Mean (SEM). d Pore volume = Envelope volume − Skeletal volume. e Porosity = Pore volume / Envelope volume. f Uncertainties were calculated using Eq. (6). SEMs were used for the uncertainties for the skeletal volumes and the SEM for Pellet 03 for the uncertainty of its envelope volume. The relative uncertainty for the envelope volume of Pellet 03 was used for all pellets. g Uncertainty is calculated from the relative SEM for Pellet 03. h General tools No. 143, resolution 0.01 cm. The uncertainty is the SEM. b

The duplicate measurements on Pellet 03 indicate that random errors give rise to relative uncertainties of about 0.6% in the envelope volume. There are two possible sources of systematic error: 1. Contributions to the envelope volume from slices of the pellet with incomplete data at the top and the bottom were ignored (z N zmax, z b zmin), because the general programming for these slices is difficult for a small reward, and so these contributions were omitted at this stage. It is estimated that missing contributions [18] to the volume of the stainless steel ball amount to about 0.002 mL. 2. The potentially more serious source of systematic error arises for those pellets that have significant “dimples”. This is not a problem for the spherical stainless steel ball. The effect of this is shown schematically in Fig. 6. Related to the latter source of systematic error, others [24] have noted that there is a degree of uncertainty in the definition of the envelope volume itself; this arises from the extent to which a film would shrink over open pores, the uncertainty being more pronounced as the size of the openings of the pores increases. The definition of the envelope volume is a practical one in which the method of measurement essentially defines it. The key question is: are the porosities of the individual pellets significantly different from one another? The ratios in Table 2 indicate an affirmative answer for certain cases in which the ratios are greater than unity. For example, the porosity of Pellet 03 is significantly different from those of Pellets 02, 04, 05 and 06, but not so when compared with that of Pellet 01. The expression for the relative uncertainty in the porosity, Eq. (6), leads to possible improvements in the methodology. For the data

reported here, the relative uncertainty in the skeletal volume has the range: δVSK ∕VSK e 0:0007–0:0030: The relative uncertainty in the envelope volume is: δVE ∕VE = 0:006: There is little control over the relative uncertainty in the skeletal volume; this is essentially dictated by the properties of the commercial instrument and the properties of the material under test. However, it is possible to improve the relative uncertainty in the envelope volume. The present apparatus captures the silhouette in an image that contains 630 × 480 pixels or picture elements; this corresponds to VGA resolution. A single pixel fixes the inherent resolution, and in this work 1 pixel corresponds to 36 μm approximately. The resolution of the vernier calipers used to measure the stainless steel ball is 0.1 mm or 100 μm. The use of a high-resolution camera and associated optics would improve the inherent resolution of the silhouette method. For example, if the image contained 1920 × 1200 pixels (WUXGA resolution) the inherent resolution

Table 2 Ratios of the difference in porosities to the corresponding uncertainty in the differences.

Pellet Pellet Pellet Pellet Pellet Pellet

01 02 03 04 05 06

Pellet 01

Pellet 02

Pellet 03

Pellet 04

Pellet 05

Pellet 06

0

4 0

1 2 0

3 7 5 0

4 9 6 1 0

3 7 5 0 1 0

Ratio = Δεij∕δΔεij. Ratios that are greater than unity are emboldened.

Fig. 5. Envelope volumes for Pellets 01 and 06 determined at various angular intervals plotted against the angular interval. ○ data for pellet 01 ─────────────────────────── fit with 3rd degree polynomial. ◊ data for pellet 06 ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ fit with 4th degree polynomial.

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Acknowledgements I am indebted to the Natural Resources Research Institute of the University of Minnesota Duluth for funding. I wish to thank R. Davis for useful discussions and D. Long for technical assistance. References

Fig. 6. Schematic two-dimensional view of a horizontal slice through an irregular object. The silhouette is obtained from a direction parallel to the y-axis. For this angle, the true perimeter should be represented by points A and B. However, dimples would cause the silhouette to give rise to points A′ and B′ as the perimeter points.

would be about 13 μm. The 3D laser scanner used for determining the envelope volumes of densified biomass [21] is expected at best to have a resolution of about 50 μm [22]. This work was exploratory with the apparatus being assembled from readily-available components; the measurements, the development of computer programs and the treatment of data were time consuming. More automation in the silhouette method is possible; this was indeed the case in the method developed for fruit [12] where a commercial imaging and software system [25] was used. Other differences between the methods developed here and those described earlier for fruit are found in: (1) the methods for searching for the perimeter pixels, (2) the locating of the rotation axis and the methods of calibration, and (3) the use of angular intervals and extrapolation to obtain the final envelope volume. The observation that there are significant differences in the porosities provides stimulus for further development. With a greater ease of obtaining individual envelope volumes, thorough statistical treatments for (1) the comparison of individual pellets' porosities, and (2) the relationships between porosities and various other singlepellet properties would be feasible.

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