Study on the influence of solids volume fraction on filter cake structures using micro tomography

doi:10.1016/j.powtec.2019.12.054

Powder Technology

Volume 363, 1 March 2020, Pages 286-299

https://doi.org/10.1016/j.powtec.2019.12.054 Get rights and content

Highlights

•
A downscale of lab nutsch according to VDI 2762 allows in-situ x-ray measurements.
•
Particle properties along the filter cake height are analysed by micro tomography.
•
Sedimentation effect in filtration is detected by top layer formation.
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Further increase in feed solid fraction reduces particle property deviation.
•
Feed solid fraction influences cake structure and so filter cake resistance.

Abstract

Prediction of micro processes, filter cake build-up and porous media flow is a key challenge to describe macroscopic parameters like filter cake resistance. This is based on a precise description, not only of the disperse solid fraction, but the distributed properties of the voids between the particles. Lab-experiments are carried out with alumina and limestone, which differ in particle size distribution (PSD) and resulting filter cake structure. Filter cakes of both materials are characterized by standardized lab tests and additionally, alumina cakes are measured with X-ray microscopy (XRM). Focusing on distributed process key parameters, the data gives a deeper understanding of the laboratory experiments.

The solid volume fraction inside the feed strongly influences the particle sedimentation and leads typically to a top layer formation of fine particles in the final filter cake, which has a negative influence on subsequent process steps. The top layers seal the filter cake for washing liquid and increase the capillary entry pressure for gas differential pressure de-watering. The influence on cake structure can be seen in a change of porosity, particle size and shape distribution over the height of the filter cake. In all measurements, homogenous filter cake structures could only be achieved by increasing the solid volume fraction inside the suspension above a certain percentage, at which particle size related sedimentation effects could be neglected and only zone sedimentation occurred. XRM offers the chance to quantify these effects, which previously could only be described qualitatively.

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, x_50.3 = 102 μm, σ₃ = ln(x_84.3/x_50.3) = 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. $x (EQPS) = \sqrt[3]{\frac{6}{π} V}$

Even a solid volume fraction of c_V = 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 c_V = 0.10 to 0.40: All solid feed fractions are measured once, except c_V = 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. $f^{2} = f_{A}^{2} + f_{P}^{2}$

With f² as total error, combining the errors f_A² for sampling and f_P² 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 c_V = 0.25, superimposed separation of size and shape of the particles as a function of the filter cake height occurred. Only when c_V 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)
A_P	projection area (m²)
A_S	surface area (m²)
B	permeability (m²)
c_v	solid volume fraction (m³/m³)
d	diameter (m)
f	total error (-)
f_p	error value of sampling (-)
f_a	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 (-)
r_C	specific filter cake resistance (1/m²)
U_P	Projection perimeter (m)
u_L	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.

References (74)

J. Van Brakel
Pore space models for transport phenomena in porous media review and evaluation with special emphasis on capillary liquid transport
Powder Technol.
(1975)
C. Tien et al.
Can filter cake porosity be estimated based on the Kozeny-Carman equation?
Powder Technol.
(2013)
E. Höfgen et al.
A comparison of filtration characterisation devices for compressible suspensions using conventional filtration theory and compressional rheology
Powder Technol.
(2019)
J. Comiti et al.
A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles
Chem. Eng. Sci.
(1989)
P. Maarten Biesheuvel
Particle segregation during pressure filtration for cast formation
Chem. Eng. Sci.
(2000)
J.D. Miller et al.
Liberation-limited grade/recovery curves from X-ray micro CT analysis of feed material for the evaluation of separation efficiency
Int. J. Miner. Proces.
(2009)
C.L. Lin et al.
Advanced three-dimensional multiphase flow simulation in porous media reconstructed from X-ray microtomography using the he-Chen-Zhang lattice Boltzmann model
Flow Meas. Instrum.
(2010)
C.L. Lin et al.
Cone beam X-ray microtomography for three-dimensional liberation analysis in the 21st century
Int. J. Miner. Proces.
(1996)
C.L. Lin et al.
3D characterization and analysis of particle shape using X-ray microtomography (XMT)
Powder Technol.
(2005)
C.L. Lin et al.
Pore structure and network analysis of filter cake
Chem. Eng. J.
(2000)

A.N. Houston et al.

Quantification of the pore size distribution of soils: assessment of existing software using tomographic and synthetic 3D images

Geoderma

(2017)

E.M.A. Hussein et al.

Calibration-free quantification of interior properties of porous media with x-ray computed tomography

Appl. Radiat. Isot.

(2015)

Y. Wang et al.

Improved 3D image segmentation for X-ray tomographic analysis of packed particle beds

Miner. Eng.

(2015)

B.C. Roberts et al.

Application of the digital volume correlation technique for the measurement of displacement and strain fields in bone: a literature review

J. Biomech.

(2014)

R. Ditscherlein et al.

Preparation techniques for micron-sized particulate samples in X-ray microtomography

Powder Technol.

(2020)

E. Vigneau et al.

Number of particles for the determination of size distribution from microscopic images

Powder Technol.

(2000)

G.-H. Xiao et al.

Effect of filter layer thickness on the filtration characteristics of dual layer granular beds

Powder Technol.

(2018)

J.F. Richardson et al.

The sedimentation of a suspension of uniform spheres under conditions of viscous flow

Chem. Eng. Sci.

(1954)

N. Paul et al.

Influence of shape and surface charge on the sedimentation of spheroidal, cubic and rectangular cuboid particles

Powder Technol.

(2017)

R. Cepuritis et al.

Comparison of 2-D and 3-D shape analysis of concrete aggregate fines from VSI crushing

Powder Technol.

(2017)

J. Linsong et al.

Pore-scale simulation of flow and turbulence characteristics in three-dimensional randomly packed beds

Powder Technol.

(2018)

P.M. Heertjes et al.

On the instability and inhomogeneity of filter-cakes

Chem. Eng. Sci.

(1957)

R. Font et al.

Numerical modelling of filtration with and without sedimentation runs

Powder Technol.

(2007)

T. Benesch et al.

Modelling filtration with superimposed sedimentation

Sep. Purif. Technol.

(2004)

K.J. Dong et al.

DEM simulation of cake formation in sedimentation and filtration

Miner. Eng.

(2009)

Y. Li et al.

Filtration and dewatering of the mixture of quartz and kaolinite in different proportions

J. Colloid Interface Sci.

(2019)

R. Wakeman

The influence of particle properties on filtration

Sep. Purif. Technol.

(2007)

R.J. Wakeman et al.

Removal of filtrate and soluble material from compressible filter cakes

Filtr Sep, 13

(1976)

R.D. Wyckoff et al.

The flow of gas-liquid mixtures through unconsolidated sands

J. Appl. Phys.

(1936)

F.M. Tiller et al.

The role of porosity in filtration: part V. porosity variation in filter cakes

AICHE J.

(1962)

F.M. Tiller et al.

The role of porosity in filtration VII effect of side-wall friction in compression-permeability cells

AICHE J.

(1972)

C.M. Alles et al.

Efficient process strategies for compressible cake filtration

Chemie-Ingenieur-Technik

(2003)

C. Bothe et al.

Experimentelle und theoretische Untersuchungen zur Filtration mit überlagerter Sedimentation in Drucknutschen

Chemie-Ingenieur-Technik

(1997)

P.C. Carman

Some physical aspects of water flow in porous media

Discuss. Faraday Soc.

(1948)

H. Darcy

Les fontaines publiques de la ville de Dijon. Exposition et application des principes à suivre et des formules à employer dans les questions de distribution d'eau: ouvrage terminé par un appendice relatif aux fournitures d'eau de plusieurs villes au filtrage des eaux et à la fabrication des tuyaux de fonte, de plomb, de tole et de bitume

Dalmont

(1856)

J.D. Miller et al.

Three-dimensional analysis of particulates in mineral processing systems by cone beam X-ray microtomography

Miner. Metall. Process.

(2004)

J.D. Miller et al.

A review of X-ray computed tomography and its applications in mineral processing

Miner. Process. Extr. Metall. Rev.

(1990)

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Study on the influence of solids volume fraction on filter cake structures using micro tomography

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Material characterization

Experimental set-up

Sample preparation and tomography measurements

Workflow for image processing

Detailed insight into filter cake structure

Discussion and comparison

Conclusions

Notation

Acknowledgement

Declaration of Competing Interest

Powder Technol.

Powder Technol.

Powder Technol.

Chem. Eng. Sci.

Chem. Eng. Sci.

Int. J. Miner. Proces.

Flow Meas. Instrum.

Int. J. Miner. Proces.

Powder Technol.

Chem. Eng. J.

Geoderma

Appl. Radiat. Isot.

Miner. Eng.

J. Biomech.

Powder Technol.

Powder Technol.

Powder Technol.

Chem. Eng. Sci.

Powder Technol.

Powder Technol.

Powder Technol.

Chem. Eng. Sci.

Powder Technol.

Sep. Purif. Technol.

Miner. Eng.

J. Colloid Interface Sci.

Sep. Purif. Technol.

Removal of filtrate and soluble material from compressible filter cakes

Filtr Sep, 13

The flow of gas-liquid mixtures through unconsolidated sands

J. Appl. Phys.

The role of porosity in filtration: part V. porosity variation in filter cakes

AICHE J.

The role of porosity in filtration VII effect of side-wall friction in compression-permeability cells

AICHE J.

Efficient process strategies for compressible cake filtration

Chemie-Ingenieur-Technik

Experimentelle und theoretische Untersuchungen zur Filtration mit überlagerter Sedimentation in Drucknutschen

Chemie-Ingenieur-Technik

Some physical aspects of water flow in porous media

Discuss. Faraday Soc.

Dalmont

Three-dimensional analysis of particulates in mineral processing systems by cone beam X-ray microtomography

Miner. Metall. Process.

A review of X-ray computed tomography and its applications in mineral processing

Miner. Process. Extr. Metall. Rev.