Journal of Porous Materials

, Volume 18, Issue 6, pp 761–766 | Cite as

Three-dimensional void space structure of activated carbon packed beds

  • M. C. Almazán-Almazán
  • A. Léonard
  • N. Job
  • J. López-Garzón
  • J.--P. Pirard
  • S. Blacher


The three-dimensional void space structure generated by piling active carbon grains has a large impact on the filter operation, through the modification of the transport properties inside the bed. To gain insight into the relation between morphology and transport properties, the three-dimensional void space structure of activated carbon packed beds was studied by X-ray microtomography coupled with image analysis. Image analysis algorithms allowing the determination of the total void fraction, the void size distribution and the radial void fraction profiles were developed. This methodology was used to characterize the void space structure of two filters with the same length but different diameters, 15 and 28 mm. Commercial granular activated carbon with average particle size close to 1 mm was used. The comparison of the void size distributions indicated that void sizes are almost normally distributed around only one maximum for the large filter, while the distribution has a more complex shape in the small filter. The radial void fraction profiles showed an increase of the void fraction from the center of the filter to the wall accompanied with an oscillatory behaviour at the small scale. Power spectrum of radial profiles of the large filter shows a characteristic length matching well with the carbon particle size, indicating that the carbon grains are uniformly packed in the bed. In the small filter, power spectrum suggests an uneven packing of grains. For both filters, the total void fraction measured by image analysis was very close to the value determined ‘physically’ knowing the carbon mass, bulk density and filter dimension.


Activated carbon Adsorption filter X-ray microtomography 3D packed bed structure Void distribution 

1 Introduction

Activated carbon packed bed filters are commonly used to remove contaminants from gas streams, e.g. for flue gas treatment or respiratory protection [1, 2, 3, 4, 5]. When the gas is forced through the filter, the pollutant is adsorbed on the activated carbon. The filter progressively saturates from the top to the bottom until breakthrough occurs, corresponding to the maximum lifetime of the filter. The so-called breakthrough curve is the plot of the vapour/gas concentration at the outlet of the bed, relative to the actual concentration at the inlet, as a function of time [6]. If separation results from physisorption only and if the experiments are performed under constant inlet vapour concentration and superficial velocity, the shape and the width of the obtained breakthrough curve give an indication of the bed efficiency, a sharper curve being an indication of a more efficient removal process. The shape of the breakthrough curve reflects how the concentration front moves through the bed, which depends roughly on two factors: the pore texture of the adsorbent at the nanometric scale and the macroscopic transport process in the bed. The textural characteristics of the adsorbent such as its pore volume, specific surface area and pore size distribution, can be accurately determined, e.g. from the analysis of the nitrogen adsorption isotherms at 77 K.

The size and geometry of the bed and the adsorbent particles, which determine the transport properties within the bed, can be chosen at the time of the filter design. However, once the adsorbent is selected in function of its pore texture and the filter is designed, other factors can influence the progression concentration front, making it more dispersive (i.e. a less sharp breakthrough curve). Indeed, when adsorbent particles are randomly packed in a bed, their spatial distribution and the resulting bed void fraction, which are determining factors for the transport properties, can only be calculated in an approximate way [7]. Moreover, wall effects can lead to a maldistribution of adsorbent particles [8, 9, 10] which can greatly modify the shape of the concentration front inside the bed. Hence, the possibility to characterize the 3D structure of activated carbon beds by X-ray microtomography coupled with image analysis will greatly help in understanding the macroscopic transport mechanisms, in order to the develop more efficient devices for vapour/gas separation by adsorption processes.

In this work, X-ray microtomography coupled to image analysis was used to determine the void fraction and the void size distribution in the two beds as well as the radial void size profiles. This technique was recently used to determine axial and radial concentration profiles during dynamic adsorption experiments [11, 12].

2 Materials and methods

2.1 Activated carbon filters

Two sets of plastic canisters with the same height H (33 mm) and different diameters were used in this study: FG (diameter D = 28 mm) and fp (diameter D = 15 mm). They were filled (M = 6.899 g for FG and M = 2.080 g for fp) with a commercial granular activated carbon, Chemviron Carbon BPL, which is an essentially a microporous adsorbent with an average particle diameter dp = 1 mm. The carbon bulk density ρ is equal to 0.53 g/cm³ [13].

2.2 X-ray microtomograph

Each filter was scanned in the X-ray microtomograph in order to determine their packing three-dimensional structure. The X-ray microtomographic device used was a “Skyscan-1074 X-ray scanner” (Skyscan, Kontich, Belgium). The cone-beam source operated at 40 kV and 1 mA. The detector was a 2D, 768 pixels × 576 pixels, 8-bit X-ray camera producing images with a pixel size of 41 μm. The rotation step was fixed at the minimum, 0.9°, in order to improve image quality, giving total acquisition times close to 10 min. For each filter, a Feldkamp-type algorithm [14] was used to reconstruct about 500 cross sections images separated by 41 μm (Fig. 1a, b). The 3D images were built by stacking the cross section images. This is illustrated in Fig. 1c showing the reconstruction of upper part of the small filter, along 12 mm height.
Fig. 1

Typical transversal sections of: a fp, b FG virgin beds, c 3D reconstruction of the upper part of fp virgin bed

2.3 Image analysis

X-ray microtomography provides a set of grey tone cross section images of the bed in which each grey tone is determined by the X-ray attenuation coefficient of the various points of the structure. The 3D image of a bed is formed by two phases: the carbon grains at low grey levels (dark voxels) and the void space between the grains at high grey levels (bright voxels). To determine the void fraction and the size distribution of voids, the 3D image of the bed must first be segmented. This operation allows determining which phase each voxel of the 3D image belongs to.

Before segmentation, images must be processed in order to improve the contrast between the grains and the background. Indeed, Fig. 1a,b present a non-homogeneous lighting in which the carbon grains placed near the walls of the bed are brighter than those placed nearest the centre. To correct this wall effect a “white-top-hat” (WTH) operator was applied to the 3D image [15]. This operator extracts “white” structures smaller than a given size, i.e., structures that do not contain a specified structuring element (SE) which in our case was a sphere (approximated by an octahedron) with a size of 10 voxels.

Processed images were afterwards binarised by assigning a value of 1 to all voxels with intensity below a given threshold (carbon grains) and a value of 0 to the others (background). Practically, the optimum threshold was easily determined manually using the histogram of grey levels of the image.

From the 3D processed binary images, the void fraction (δimage), defined as the fraction of voxels of the image that belongs to the voids between the carbon grains, was measured first. As the carbon beds present a continuous and rather disordered void structure, a standard granulometric measurement could not be applied. Then, to quantify the void size distribution, the opening size distribution [15] was calculated. This method allows assigning a size to both continuous and individual particles: when an opening transformation is performed on a binary image with a SE of size λ, the image is replaced by the envelope of all SEs inscribed in its objects. For the sake of simplicity, spheres of increasing radius λ (approximated by an octahedron) were used. When an image was opened by a sphere whose diameter was smaller than the smallest features of its objects, it remained unchanged. As the size of the sphere increased, larger parts of the objects were removed by the opening transformation. Therefore, opening could be considered as equivalent to a physical sieving process.

Radial profiles were determined using layers, each layer being defined as the volume in-between successive cylinders constructed from the periphery to the centre of the filter. The radius of the successive cylinders was decreased by steps of 82 μm, starting from the canister wall. In each layer located at a distance r of the centre of the sample, the sum of the grey-level intensity of all voxels was normalized by the number of voxels in the layer. These average intensities were then drawn in function of r. For this kind of measurements the shape of the layers must be chosen in function of the structure of the sample. Radial profiles were built (i) considering the raw grey level of voids and (ii) by assigning to them a grey level value equal to 0.

3 Results

Activated carbon grains of dp = 1 mm average diameter were randomly packed in fp (D = 15 mm) and FG (D = 28 mm) filters. The void fraction measured by image analysis was εimage = 0.35 and 0.30, respectively. These values are very close and agree well with the void fractions εp = 0.33 and 0.36 determined physically using the following expression
$$ \varepsilon_{\rm p} = \,1 - {\frac{\rm M}{\rho \cdot {\rm V}}} $$
where M is the weight of carbon in the bed, ρ is the BPL carbon bulk density, and V is the volume of the cylindrical packed bed.
A simple observation of the 2D cross sections (Fig. 1a, b) suggests that voids distribute differently in the two beds. Indeed, grains seem better dispersed in the case of the large filter. This is confirmed by the void size distributions obtained from the segmented 3D images. Fig. 2 indicates that for FG, void sizes are almost normally distributed around only one maximum (FG average void size = 0.38 ± 0.09 mm) whereas for fp the distribution is broader (fp average void size = 0.50 ± 0.12 mm). This indicates that, in the case of fp, the local variations of interparticle spaces detected will certainly affect the gas flow through the bed.
Fig. 2

3D void size distributions

Radial profiles (Fig. 3) give information about the spatial distribution of the carbon grains in the two beds. Intensities (y-axis) are given in arbitrary units as the variation of the grey tone intensity of images as a function of the radius of the beds is the only relevant parameter for our study. These radial profiles show two main characteristics: (i) the grey level intensity decreases from the external wall to the centre of the bed; (ii) this decrease is accompanied by an oscillatory behaviour at a small scale. The first characteristic is directly linked to the presence of the wall and indicates that the carbon grain concentration increases towards the centre of the bed; higher porosities near the wall are well known to induce preferential channelling [16, 17, 18, 19, 20, 21]. The second one has been described by several authors [8, 21, 22, 23, 24, 25, 26]: in a packed bed of monodisperse particles, the radial void distribution undergoes damped oscillations reaching a constant value after a distance close to 5 particle diameters [25, 27].
Fig. 3

Intensity radial distributions

To quantify the influence of the filter diameter on this wall effect, radial measurements were fitted according to a monotonic exponential, Eq. 2. The assumption of an exponential decay of the average void size has been often used, as reviewed recently in reference [28]. Idecay is the fitted grey level intensity; β is the decay constant which depends on the tube-to-particle diameter ratio, D/dp; A and B are parameters depending on the attenuation coefficient of the carbon grains, μ; r is the radial distance, varying between 0 and D/2.
$$ {\rm I}_{\rm decay} ({\rm r},\mu ) = {\rm A}(\mu ) + {\rm B}(\mu )e^{{\left( { - \beta \,{\rm r}} \right)}} $$
The measured and the fitted radial profiles as well as the obtained β values are shown in Fig. 3. As observed in other works [21], the model overestimates the intensity value, related to local void fraction, near the wall in the case of the large filter. This can be due to the presence of small particles, according to the fact that the BPL carbon grain sizes are distributed between 0.6 and 1.7 mm [11]. However, in both cases the correlation coefficient was higher than 0.98. For the activated carbon used in this study, the fitting of Eq. 2 gave A = 0.062 and B = 0.016. The larger decay constant for fp (β = 0.44) than for FG (β 0.14) indicates that, in the smaller canister, carbon grains are less uniformly distributed with a larger concentration gradient from the walls to the centre of the bed. The fraction of the canister influenced by the presence of the wall is higher for decreasing D/dp ratios.
Fig. 4

Intensity oscillations for FG and fp

To analyse the oscillating behaviour Iosc (r), the fitted radial profiles Idecay (r) were subtracted from the measured ones I (r), as shown in Fig. 4, according to
$$ {\rm I}_{\rm osc} ({\rm r}) = {\rm I}({\rm r}) - {\rm I}_{{\rm decay}} ({\rm r}) $$
This figure shows that, for FG, oscillations are almost periodic, with valleys and peaks. This is confirmed by the power spectrum of Iosc (Fig. 5) which presents a main peak at the frequency ω = 7.12 mm−1, and its harmonics, i.e. its whole multiples. This value is related to the characteristic length λ = 2π/ω = 0.8 mm, which matches well with the diameter of a carbon grain, dp = 1 mm. This result confirms that carbon grains are uniformly packed layer by layer in the bed. On the contrary, oscillations are not periodic in the case of fp, suggesting an uneven packing of grains. Moreover, in this case it is not relevant to calculate a characteristic length from a power spectrum because Iosc is a short set with too few oscillations to detect a clear periodicity.
Fig. 5

Power spectrum of Iosc for FG

4 Discussion

The void fraction and its distribution in a packed bed have a direct impact on the fluid/particles hydrodynamic interactions. The efficiency of catalytic fixed-bed reactors or adsorbers can be greatly affected by the transport properties. The knowledge of the void distribution inside a bed is very important to set up models allowing the simulation of local velocity profiles, for example.

However, its experimental determination was difficult until the development of non-destructive investigating methods such as magnetic resonance imaging [24, 29] and X-ray tomography [30]. This latter technique, coupled with image analysis enabled to visualise the structure of the adsorbent bed and to determine the spatial void distribution from the analysis of 3D microtomograms.

In the present work, two beds with different diameters randomly filled with a commercial active carbon were scanned by X-ray microtomography. Each reconstructed 3D image was processed to determine the total void fraction and the void size distribution. Taking into account that each 3D image is formed by piling up approximately 500 2D images, it must be pointed out that image processing and measurements require powerful computer resources to avoid time consuming calculations. In order to discriminate between pixels belonging to the carbon grains and to the voids, images were first pre-processed to enhance the contrast.

The void fractions of fp and FG measured by image analysis were εimage = 0.35 and 0.30 (packing density of 0.65 and 0.70), respectively. This values are very close and agree well with the void fractions εp = 0.33 and 0.36 determined physically.

The state of dispersion of particles is crucially influenced by two factors: the accuracy of the random packing and the wall canister effects. Random close packing is usually defined as the maximum particle density that a large, random collection of spheres can attain and which is a universal quantity. However, reaching this value is not straightforward as packing density frequently depends on the protocol employed to produce it [31]. On the one hand, Scott and Kilgour [32] showed that into a tower (300 mm height and 100 mm diameter) filled with 80,000 balls of 3 mm diameter, it is necessary to vibrate vertically the system for sufficiently long times to achieve maximum densification and obtain a packing density of 0.637, corresponding to a void fraction of 0.363. On the other hand, numerical simulations performed with different algorithms lead to packing density values between 0.60 and 0.70 ([31] and references therein) which agree well with the results obtained from microtomographic investigation in the present work.

Radial profiles (Fig. 3) showed that the void fraction of the bed is characterized by an oscillating behaviour. This periodic behaviour is characteristic of randomly packed beds in which walls exert a confinement effect on the particle localization; this effect tends to organise the particles in more ordered layers near the wall [8, 27]. Oscillations are superimposed to an exponential decay of the grey level intensity when going from the wall to the centre of the tube. This indicates that carbon grains tend to assemble in the centre of the bed. The extent of this wall effect depends on the D/dp ratio and on the size distribution of carbon grains [9, 25]. A comparison between radial profiles of the two studied packed beds (Fig. 3), showed that, as one could expect, wall effects are less marked in the broad canister, which presents a smaller void fraction, a narrow void size distribution and a more ordered spatial distribution of grains. Indeed, for the FG canister, the decay coefficient in Eq. 2, which depends on D/dp only, is smaller than for fp. This results in a flatter radial profile. Moreover, the power spectrum (Fig. 5) of the periodic component highlights a characteristic length which agrees with the average diameter of a carbon grain (~1 mm).

5 Conclusions

X-ray microtomography coupled with image analysis was used to characterize the 3D void structure of BPL active carbon beds. It was shown that this methodology is a powerful tool to determine the void fraction and its distribution in a non-destructive way. The results confirmed the influence of the tube-to-particle ratio on the structural properties of activated carbon beds. In further works, other parameters such as tortuosity and connectivity will be analysed. The characteristics of the bed microstructure will be linked with the motion of an adsorbate concentration front in the carbon filter.



M.C. Almazan Almazan acknowledges financial support of Ministerio de Educación y Ciencia (MEC) and Fundación Española para la Ciencia y la Tecnología (FCYT) as a postdoctoral contract. The authors also acknowledge the Interuniversity Attraction Pole (IAP-P6/17) for financial support. A. Léonard and N. Job thanks the FRS-FNRS (Fund for Scientific Research) for their Research Associate and Postdoctoral Researcher positions, respectively.


  1. 1.
    K. Sutherland, Filters and Filtration Handbook, 5th edn. (Elsevier, Burlington, 2008)Google Scholar
  2. 2.
    M.B. Hochking, Handbook of Chemical Technology and Pollution Control, 3rd edn. (Elsevier, Amsterdarm, 2005)Google Scholar
  3. 3.
    L.K. Wang, N.C. Pereira, Y.-T. Hung (eds.), Air Pollution Control Engineering (Humana Press Inc., Totowa, 2004)Google Scholar
  4. 4.
    R.T. Yang, Gas Separation by Adsorption Processes (Imperial College Press, London, 1997)Google Scholar
  5. 5.
    W.H.B. Revoir, C.T. Respiratory Protection Handbook (CRC Press LLC, Boca Raton, 1997)Google Scholar
  6. 6.
    P.A. Schweitzer, Handbook of Separation Techniques for Chemical Engineers (McGraw-Hill Companies, New York, 1999)Google Scholar
  7. 7.
    A.J. Sederman, M.L. Johns, P. Alexander, L.F. Gladden. Magn Reson Imaging 16, 497 (1998)Google Scholar
  8. 8.
    M. Suzuki, T. Shinmura, K. Iimura, M. Hirota. Study of Wall Effect on Particle Packing Structure using X-ray Micro Computed Tomography, in Proceedings of 5th World Congress on Industrial Process Tomography, ed. by, Bergen, Norway, 2007, pp. 304Google Scholar
  9. 9.
    W. Kwapinski, M. Winterberg, E. Tsotsas, D. Mewes, Chem. Eng. Technol. 27, 1179 (2004)CrossRefGoogle Scholar
  10. 10.
    M. Suzuki, T. Shinmura, K. Iimura, M. Hirota, Adv. Powder Technol. 19, 183 (2008)CrossRefGoogle Scholar
  11. 11.
    A. Leonard, H. Wullens, S. Blacher, P. Marchot, D. Toye, M. Crine, P. Lodewyckx, Sep. Pur. Technol. 64, 127 (2008)CrossRefGoogle Scholar
  12. 12.
    P. Lodewyckx, S. Blacher, A. Leonard, Adsorption 12, 19 (2006)CrossRefGoogle Scholar
  13. 13.
    K.A.M. Gasem, J. Robinson, R.L., L.R. Radovic. Sequestering carbon dioxide in Coalbeds, (Oklahoma State University, 2001)Google Scholar
  14. 14.
    L.A. Feldkamp, L.C. Davis, J.W. Kress, J. Opt. Soc. Am. A. 1, 612 (1984)CrossRefGoogle Scholar
  15. 15.
    P. Soille, Morphological Image Analysis—Principles and Applications (Springer, New York, 1999)Google Scholar
  16. 16.
    M. Winterberg, E. Tsotsas, AICHE J. 46, 1084 (2000)CrossRefGoogle Scholar
  17. 17.
    B. Eisfeld, K. Schnitzlein, Chem. Eng. Sci. 56, 4321 (2001)CrossRefGoogle Scholar
  18. 18.
    S.M. White, C.L. Tien, Heat Mass Transfer 21, 291 (1987)Google Scholar
  19. 19.
    D. Vortmeyer, J. Schuster, Chem. Eng. Sci. 38, 1691 (1983)CrossRefGoogle Scholar
  20. 20.
    L.H.S. Roblee, R.M. Baird, J.W. Tierney, AICHE J. 4, 460 (1958)CrossRefGoogle Scholar
  21. 21.
    C.G. du Toit, Nucl. Eng. Design 238, 3073 (2008)CrossRefGoogle Scholar
  22. 22.
    A.L. Negrini, A. Fuelber, J.T. Freire, J.C. Thomeo, Braz. J. Chem. Eng. 16, 421 (1999)CrossRefGoogle Scholar
  23. 23.
    K. Schnitzlein, Chem. Eng. Sci. 56, 579 (2001)CrossRefGoogle Scholar
  24. 24.
    A.J. Sederman, P. Alexander, L.F. Galdden, Powder Technol. 117, 255 (2001)CrossRefGoogle Scholar
  25. 25.
    J. Theuerkauf, P. Witt, D. Schwesig, Powder Technol. 165, 92 (2006)CrossRefGoogle Scholar
  26. 26.
    R.F. Benenati, C.B. Brosilow, AICHE J. 8, 359 (1962)CrossRefGoogle Scholar
  27. 27.
    K.V. Sita Ram Rao. Wall Effects in Packed Beds, vol. PhD Thesis, Indian Institute of Science, (Bangalore, India, 1994)Google Scholar
  28. 28.
    W. van Antwerpen, C.G. du Toit, P.G. Rousseau, Nucl. Eng. Design 240, 1803 (2010)CrossRefGoogle Scholar
  29. 29.
    A.J. Sederman, M.L. Johns, A.S. Bramley, P. Alexander, L.F. Gladden, Chem. Eng. Sci. 52, 2239 (1997)CrossRefGoogle Scholar
  30. 30.
    D. Toye, P. Marchot, M. Crine, A.M. Pelsser, G. L’Homme, Chem. Eng. Process 37, 511 (1998)CrossRefGoogle Scholar
  31. 31.
    S. Torquato, T.M. Truskett, P.G. Debenedetti, Phys. Rev. Lett. 84, 2064 (2000)CrossRefGoogle Scholar
  32. 32.
    G.D. Scottand, D.M. Kilgour, Brit. J. Appl. Phys. 2, 863 (1969)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • M. C. Almazán-Almazán
    • 1
    • 2
  • A. Léonard
    • 2
  • N. Job
    • 2
  • J. López-Garzón
    • 1
  • J.--P. Pirard
    • 2
  • S. Blacher
    • 2
  1. 1.Department of Inorganic ChemistryUniversity of GranadaGranadaSpain
  2. 2.Laboratory of Chemical EngineeringUniversity of LiègeLiègeBelgium

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