Study on the influence of solids volume fraction on filter cake structures using micro tomography
Graphical abstract
Introduction
By cake filtration, highly concentrated suspensions with solid volume fraction of around 20 to 25 vol.-% are lead through the filter medium, where the particles are retained and form a water filled voids structure, mainly described by the void to total volume fraction, the porosity.
As an important step, filter cake de-watering can only sufficiently be described by understanding the interconnected pore network. Results in [1,2] are usually based on homogenous filter cakes with constant porosity and therefore globally estimated permeability related to Darcy's law and the established channel model. These estimations only include one-dimensional liquid flow through an incompressible filter cake. In reality, particle properties like shape, size, and wetting behaviour are distributed and they highly influence the porous network build-up with possible local deviation in vertical or horizontal alignment. Contrary, in practice on the macroscopic scale only integral properties are used – understanding of microscopic effects becomes very difficult. Wakeman [3] proved that the consolidation of filter cakes is both, a time and a pressure function. The velocity of consolidation depends on particle size and shape distribution. The balance between particle and liquid pressure reaches the equilibrium state for complete consolidation [4]. Wyckoff and Botset [5] detected a fluctuating liquid flow rate through sand, if it was not completely saturated. A restructuring of the layers took place due to increasing or decreasing saturation. Tiller and Cooper [6] observed differences in pressure at different locations within the bed, Comiti [7] traced it back to the fact of a strong wall effect. Tiller [8] and Alles [9] give proof of an instability by showing the influence of the cake pressure on the filter cake resistance. For differential pressure filtration, Bothe et al. [10] found that due to a widely distributed particle size distribution, segregation occurred within the feed, which subsequently negatively influenced the filter cake structure for subsequent dewatering. Hwang found similar results for filtration in the centrifugal field and attributed this to a heterogeneous cake structure. The results were all the worse when mixtures of several particle systems were used [11].
In contrast to the findings above, in filtration dominated theory and in simplified models for apparatus design, homogenous structures are assume and preferred, e.g. described in the established Kozeny-Carman equation [12] and Darcy's law [13]. Therefore, the combined development of experimental and theoretical techniques is essential to develop a better understanding of cake filtration and prove the findings of several authors above. By combining an in-situ XRM filtration setup with validation of experiments at laboratory scale, it becomes possible to gain an insight into network structure after filtration. Structure analysis with an achievable resolution of 5 μm enables to visualize porous network structures enhanced by single particle analysis.
In the area of the measuring method and the field of micro tomography, the reader is referred to the work of Miller et al. [[14], [15], [16]] and Lin et al. [[17], [18], [19], [20], [21]] for particulate systems. In the field of analysis of micro-tomography measurements of porous media, many works have emerged in recent years [18,[22], [23], [24], [25], [26]]. The authors deal with the permeability and pore size distributions on which many modeling approaches are based.
Section snippets
Material characterization
For all filtration experiments, crushed and classified α-Al2O3 particles (T60/64, Almatis, Germany, ρ = 3.82 g/cm3) in the size range of 55 to 200 μm are used. The particle system can be described with a lognormal distribution function, defined as the first derivation of the cumulative particle size distribution (PSD, x50.3 = 102 μm, σ3 = ln(x84.3/x50.3) = 0.43, laser diffraction, cf. Fig. 1).
As reference for laser diffraction (LD, Sympatec HELOS) the PSD was also measured by dynamic image
Experimental set-up
The filtration experiments are carried out at 0.3 bar in a lab-scale pressure nutsch filter set-up (cf. Fig. 2) according to VDI 2762–1 with an internal diameter of 5 cm and an effective filter area of A = 20 cm2. The filtration tests stop at complete saturation of the filter cakes. The filter cakes are subsequently dried at 40 °C for 48 h, so that rearrangement of particles can be neglected due to drying effects as seen from micro tomography scans before and after drying. The two datasets were
Sample preparation and tomography measurements
Tomography measurements offer the possibility to gain an insight into the differences of the packing structure without destroying the filter cake matrix. Compared to a conventional tomographic set-up, an XRM has a microscopy optic that allows an additional magnification by the factor of 10. Due to the non-destructive nature of X-ray tomography, the sample can be reused for other measuring principles besides X-ray tomography. Considering the internal dimensions of the XRM and the projected
Workflow for image processing
The reconstruction is done by using the filtered back projection algorithm implemented in the ZEISS Xradia reconstruction software (Xradia XMReconstructor 10.7). This includes an automatic centre shift and beam hardening correction with a factor of 0.05. A gauss filter with a kernel of 0.7 for smoothing is applied already at the raw data. The image data has to be further processed because of artefacts due to the XRM-measurement, low contrast and image noise. Filtering in ImageJ (Fiji 1.51n)
Detailed insight into filter cake structure
Comparing the PSD measured by image analysis from XRM, different size distributions over the whole height of filter cake are detected, proven by the cumulative PSD in Fig. 7, in which the distributions are calculated by the equivalent sphere diameter (EQPS, eq. (4)). Based on the binary image stack, the porosity as number of void voxels can be also determined along the depth of the built cake.
Even a solid volume fraction of cV = 0.25 within the suspension does not prevent
Discussion and comparison
In Table 1 the number of analysed particles of each scan offers an overview about the statistics behind each data point for cV = 0.10 to 0.40: All solid feed fractions are measured once, except cV = 0.25, for which three different experiments are carried out. The work of Koglin et al. [41] proved that with increasing number of particles the possible error related to the analysis can be neglected due to.
With f2 as total error, combining the errors fA2 for sampling and fP2 of the
Conclusions
With the obtained data from XRM measurements, many properties of both, the disperse particle system and filter cake characteristics can be determined by one single tomogram. By varying the solids volume fraction, it was found that with conventionally suggested volume fraction of cV = 0.25, superimposed separation of size and shape of the particles as a function of the filter cake height occurred. Only when cV was increased to >0.3, it was possible to prevent the formation of a top layer of fine
Notation
Symbol/abbr. Meaning (Unit) A filter area (m2) AP projection area (m2) AS surface area (m2) B permeability (m2) cv solid volume fraction (m3/m3) d diameter (m) f total error (-) fp error value of sampling (-) fa error value of analysis (-) h filter cake height (m) n number of particles (-) P(t) tolerable error rate due to t-distribution (-) p pressure (Pa) Q3 sum distribution (-) rC specific filter cake resistance (1/m2) UP Projection perimeter (m) uL velocity of the liquid (m/s) V particle volume (m3) x particle
Acknowledgement
We express our gratitude to the Deutsche Forschungsgemeinschaft (DFG), which supported this research, project number 1160/23-1. Additionally, we would like to thank Vietnam International Education Development (VIED) – Ministry of Education and Training for financial support through the 911 Project. Further, thanks to DAAD and WUS for their support in Germany. The Authors would like to thank colleagues in the department of Mechanical Process Engineering and Mineral Processing, TU Bergakademie
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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