Three-dimensional void space structure of activated carbon packed beds
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.
KeywordsActivated carbon Adsorption filter X-ray microtomography 3D packed bed structure Void distribution
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 . 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 . 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 .
2.2 X-ray microtomograph
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 . 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  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.
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 . 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 . On the one hand, Scott and Kilgour  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 ( 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).
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.
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