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Filtration experiments with compressible filter cakes in centrifugal fields with superimposed static pressure
Int. J. Miner. Process. 73 (2004) 261 – 267 www.elsevier.com/locate/ijminpro
Filtration experiments with compressible filter cakes in centrifugal fields with superimposed static pressure Thomas Friedmann a, Christoph Lustenberger b,*, Erich J. Windhab b a
DuPont Central Research and Development, Particle Science and Technology, Experimental Station, Wilmington, DE 19880, USA b Department of Food Science, Laboratory of Food Engineering, ETH Zurich, Switzerland Received 29 October 2002; received in revised form 6 November 2002; accepted 2 May 2003
Abstract Combined application of centrifugal and static pressure field has shown improved results for filtration rate and dewatering performance in various applications. Especially for compressible filter cakes, hyperbaric centrifugal filtration promises better results than separation in conventional filter centrifuges. In a beaker centrifuge filtration experiments were carried out up to C-values of 3000. A static pressure field with a maximum pressure up to 5 bar was superimposed in the centrifuge (hyperbaric centrifugal filtration). Visualisation techniques allowed the observation of the filter cake compression during the filtration experiment. Under various C-value and static pressure conditions filtration experiments have been carried out using suspension systems with solids of distinct compressibility. The filtrate flow versus time was monitored. Complementary, the mechanical filter cake properties and filter cake structures were analysed under different process conditions. Relationships between filtrate flow rate and filter cake properties (mechanical behaviour, structure) are described. D 2004 Elsevier B.V. All rights reserved. Keywords: solid – liquid separation; centrifugal filtration; compressible porous media; beaker centrifuge; filter cake structure
1. Introduction Efficient solid – liquid separation can be achieved in filter centrifuges. However, the centrifugal mass forces enhancing desaturation also lead to an additional compression of the filter cake. The principle of hyperbaric centrifugal filtration allows the superposition of a static pressure field to the centrifugal field. This combination of centrifugal and static pressure field was developed at the University of Karlsruhe. * Corresponding author. Fax: +41-1-632-11-55. E-mail address: [email protected] (C. Lustenberger). 0301-7516/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/S0301-7516(03)00078-4
Stadager (1995) investigated the dewatering performance using this new technology. The hyperbaric centrifugal filtration also promises an acceleration of the flow rate through compressible filter cakes. An increased knowledge on the factors influencing flow behaviour through compressible porous media is of major importance to be able to optimise and further develop existing separation processes. 1.1. Cake filtration The fundamental relationship between pressure ˙ through a difference Dp and volumetric flow rate V porous medium was first mentioned by Darcy (1856).
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T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267
Fig. 1. Parameters in cake filtration.
˙ is According to Eq. (1) the volumetric flow rate V directly proportional to the filter area A, to the pressure difference Dp, to the fluid viscosity g and to the total resistance. The total resistance contains the filter cake resistance RC, the height of the packed bed hC and the filter medium resistance RM (Fig. 1). ˙ ¼ V
A Dp gðRC hC þ RM Þ
ð1Þ
For Newtonian fluid properties the desired effect of ˙ to the proportionate increase of volumetric flow rate V increase of pressure difference Dp is found only for rigid particles forming an incompressible filter cake. From experimental data it is known that flow rate increases only slightly for compressible filter cakes. 1.2. Compressible filter cake Considerable work on filtration with compressible filter cakes has been effected by Tiller et al. (Tiller and
Huang, 1961; Tiller and Hsyung, 1993). Many authors have followed their general approaches in various modifications. Absolute values of the compressibility constants may vary depending on the equipment used to measure compressibility. This makes it difficult to compare data from different experiments. Considering the amount of literature available on the subject of compressible filter cakes, there is little about behaviour of such filter cakes in the centrifugal field (Fig. 2). Under a given pressure almost all filter cakes are compressed. At the same time the structure (pore size, porosity) is altered and therefore influences the permeability of the porous medium. Hooke’s law states that if a compressive strain e is applied to an ideal solid, the compressive stress r within the material is directly proportional to the strain. However, this ideal elastic behaviour does not apply for a packed bed of particles, even if the particles are ideal elastic. This non-linearity of the compression modulus G (Eq. (2)) has been shown for various materials and has been also found for soil samples under compression (Krizek, 1971). G¼
dr de
ð2Þ
2. Experimental setup To determine the influence of material and process parameters on flow behaviour, experimental investigations with model systems were carried out. EPDM elastomer particles (ethylene-propylene-diene-polymethylene elastomers) were used as model
Fig. 2. Relation of compressibility exponent d to permeability (Tiller and Hsyung, 1993).
T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267 Table 1 Compressible particles used for model filter cake
G62.0005 G62.0515 G62.1030
Particle diameter dp [Am]
Packed bed porosity eV [ – ]
250 – 500 500 – 1500 1500 – 3000
0.747 0.648 0.611
system for a compressible filter cake that contains particles that are deformable. Three different particle size distributions were used for the investigations (Table 1). The density of EPDM is 1.57 kg/dm3. The elastomers were supplied by Gezolan, CH-6252 Dagmersellen, Switzerland. Suspensions of the mentioned particles were prepared with Newtonian aqueous polyethylene glycol solutions (PEG35000 from Hoechst, Germany). PEG solutions showed Newtonian flow behaviour over a wide shear rate range (0.1 – 2000 1/s). 2.1. Filter cake mechanics In the present work, the mechanical response of the material to an applied stress was investigated by means of DMTA (dynamic mechanical thermal analysis) with the objective to establish relationships between structural parameters of the porous medium and the characteristics of filtration processes. Experiments were performed in a Rheometrics Solids Analyzer RSA II. The test geometry used was a cylinderplate compression tool as shown schematically in Fig. 3. Elastomer particles were filled into the cylin-
Fig. 3. Rheometrics Solids Analyzer RSA II-test geometry.
263
der, where they were compressed with a strain rate of 0.002 1/s. The actual sample deformation e is calculated according to Eq. (3) where DL is the tool displacement and Ke is the strain constant. Ke is given by Eq. (4), where L is the sample height. e ¼ Ke DL Ke ¼
1 L
ð3Þ ð4Þ
2.2. Compression in centrifugal field The deformation of a packed bed under centrifugal force was visualised in an optical laboratory centrifuge using stroboscopic techniques (Fig. 4). The centrifuge beaker containing the sample gives an impulse to a photoelectric reflection sensor. The signal controls the connected strobe thus the flash frequency equals the centrifuge frequency at all times during the process. The ‘frozen’ image is recorded with a CCDcamera and is subjected to image analysis where the cake height was determined. To determine the compression degree during centrifugal filtration visualisation experiments were carried out in the hyperbaric beaker filter centrifuge (Section 2.3), which allows observation of the filter cake during process.
Fig. 4. Experimental set-up for visualisation of packed bed in the centrifugal field; (a) centrifuge rotor, (b) sample in centrifuge beaker, (c) strobe, (d) CCD-camera, (e) photoelectric reflection sensor.
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T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267
Fig. 5. Schematic drawing of the hyperbaric beaker filter centrifuge HB600; (a) fluid vessel, (b) beaker filter centrifuge, (c) flow meter, (d) pressure sensor, (e) balance.
2.3. Flow through compressible porous media Flow behaviour through compressible filter cakes in the centrifugal field was investigated with a hyperbaric beaker filter centrifuge (Fig. 5). The filter centrifuge HB600 was developed by Heinkel AG, D-74321 Bietigheim-Bissingen, Germany, on the basis of a beaker filter centrifuge used by Mayer (1986). The HB600 can be loaded during rotation with suspension into the two opposite beakers. Through the same conduct, wash liquid can be added after cake built-up. Optional static pressure can be superimposed through the axial inlet. This operation is called hyperbaric centrifugation. Further specifications and experimental set-up are described by Friedmann (1999).
rheology also influences strongly the filtrate flow rate. The experiments presented here were performed with a Newtonian fluid. 3.1. Filter cake deformation Compressive load cycles are shown in Fig. 6 for the three samples G62.0005, G62.0515 and G62.1030. Particle size distributions have a marked effect on
3. Results and discussion Flow-through experiments under various process conditions with compressible filter cakes were carried out. The deformation behaviour of the same filter cake material was analysed to find relationships between filtrate flow rate and filter cake properties. The fluid
Fig. 6. Compressibility function for different packed beds of elastomer particles.
T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267 Table 2 Compressibility factors C1 and C2 determined by DMTA G62.0005 G62.0515 G62.1030
C1
C2
1350 8396 24 109
8.277 9.736 10.564
compressibility of the packed bed. As shown, the smallest particles were found to be the most compressible ones. However, the higher compressibility was not only attributed to particle size but also to the packed bed porosity. The particle shape of the G62.0005 resulted in a higher porosity. The loose structure of the G62.0005 packed bed favoured rearrangement of the particles to denser packing. The highly non-linear compressibility of packed beds and filter cakes was described by modifying Hooke’s law according to Eq. (5) and Eq. (6), where C1 and C2 are the compressibility factors determined by DMTA measurements (Table 2). r ¼ GðeÞe
ð5Þ
GðeÞ ¼ C1 eC2 e
ð6Þ
3.2. Compression in centrifugal field The compression in the centrifugal field was investigated experimentally for various packed beds. Fig. 7 illustrates the deformation of a packed bed of elastomer particles (G62.0515) at various centrifuge speeds.
265
Fig. 8 shows deformation e versus C-value for packed beds of elastomer particles G62.0005, G62.0515 and G62.1030 saturated with water. The Cvalue is the dimensionless centrifugal acceleration defined according to Eq. (7), where r is the radial distance from the axis, x is the angular velocity and g is the gravitational constant. The C-value is, therefore, a measure of the relative centrifugal force with respect to the earth’s gravitational force. C¼
rx2 g
ð7Þ
For all packed beds investigated, similar non-linear compression behavior was observed similar to the DMTA measurements. Calculated values (lines) based on the analytical results from the DMTA were in good agreement with the experimental results (symbols) for compaction of a packed bed in the centrifugal field. In another experiment series the relationship between initial cake height hC(0) and deformation at a certain C-value was investigated. For this purpose, packed beds of various initial heights (hC(0) = 10, 20 and 40 mm) were tested. As expected the largest deformations were found for the packed bed with maximum initial height. Since the centrifugal force acts on the mass of the particles and is added up over the cake height, a packed bed with larger hC(0) consequently generates a higher total compression force acting on the lower particle layers in the packed bed.
Fig. 7. Packed bed of elastomer particles (G62.0515) deformed in an optical centrifuge setup at different centrifuge speeds; (a) 475 rpm (C = 50), (b) 815 rpm (C = 149), (c) 2090 rpm (C = 977).
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T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267
In pressure filtration the compression of the packed bed is due to viscous drag forces. 3.3. Flow through compressible porous media
Fig. 8. Deformation versus C-value for packed bed of elastomer particles (G62.0005, G62.0515 and G62.1030); calculated values from Friedmann (1999).
A compressible porous material is also deformed due to fluid flow. This deformation is due to shear stress transmitted to the solids phase by the fluid. Visualisation experiments during centrifugal filtration were performed with elastomer particles (G62.0005) and a PEG 10% w/w solution (Newtonian). After cake build-up at 208 rpm, the centrifuge speed was increased and/or hyperbaric pressure was superimposed (see Section 3.3). The results show that the packed bed compression is significantly higher at increased rotational speed compared to the hyperbaric pressure. The deformation of a packed bed in the centrifuge can be estimated from the centrifugal force acting on the solid particles.
In centrifugal filtration both components, centrifugal forces and drag forces due to fluid flow, act simultaneously. Deformation of the filter cake results from a combination of both compressive components. Since the hyperbaric filter centrifuge permits combination of centrifugal force and superposition of hydrostatic pressure, the effects on compression of the filter cake could be observed. At 208 rpm an average cake height of hC = 24.0 mm was determined. With increasing rotational speed up to 1100 rpm a noticeable decrease of the cake height was observed. Keeping the rotational speed at 208 rpm and imposing a hyperbaric pressure (up to 2 bar) no significant decrease of the cake height could be observed. It has to be noted that at this point the cake is already compressed and therefore the compression modulus of the packed bed has increased. The increase of the driving pressure difference by superposition of the hydrostatic pressure however had a marked effect on the filtrate flow rate. Deformation of the pores leads to an increase of filter cake resistance, which is responsible for the nonlinear relationship of volumetric flow rate and driving pressure difference. This effect of pressure on the permeability of compactible systems is commonly described in the literature by an exponential function (Tiller and Huang, 1961). It is often assumed that with
Fig. 9. Volumetric flux J versus hyperbaric pressure phyp at constant C-values in the centrifuge for filter cakes of elastomer particles (G62.0005) flown through with PEG solution (10% w/w).
T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267
a higher pressure difference, higher or at least equal volumetric flow rates will result. It has been shown within this work that there are compressible porous systems that exhibit an optimum pressure range for maximum flow rate. An increase of driving fluid pressure difference Dpfl by means of centrifugal acceleration is coupled with a substantial increase of the compressive pressure on the pore network, thus leading to a marked flow rate reduction. Superimposed static pressure improves volumetric flow rate because Dpfl is raised without strongly contributing to the filter cake compression to the same amount as centrifugal acceleration does. In Fig. 9 the evolution of volumetric flow rate as a function of superimposed (hyperbaric) pressure phyp is shown for elastomer filter cakes (G62.0005). Centrifugal acceleration was kept constant at C = 15 and C = 406, respectively. A marked increase of flow rate was observed in comparison to volumetric flow rates attained under pure centrifugal force ( phyp = 0). Furthermore, the typical trend of flow rate as a function of compressive pressure for compressible filter cakes was found again in these experiments. The efficiency of a volumetric flow rate increase by superimposed pressure, however, was found to strongly depend on the actual centrifugal acceleration.
4. Conclusions It was shown that DMTA can be used for the characterisation of the deformation behaviour of porous media. The deformation behaviour of packed beds (filter cakes) was found to be highly non-linear. The deformation of a packed bed or filter cake under centrifugal force was visualised in an optical laboratory centrifuge using stroboscopic techniques. The analytical results from the DMTA were in good agreement with the experimental results for compaction of a packed bed in the centrifugal field. In conclusion it can be said that hyperbaric centrifugation is able to provide better results in solid– liquid separation for highly compressible materials. However, process parameters have to be chosen adequately. Low C-values and a superimposed static pressure optimised for the particular product yielded the best results with respect to flow rate. The mentioned phenomena (flow rate increase due to C-value
267
and/or superimposed pressure phyp) were found to be even more effective for non-Newtonian (shear thinning) fluids. This is evident, since filter cake structure determines flow behaviour. The structure of a compressible filter cake, though, was shown to be influenced by the main process parameters of hyperbaric centrifugation, namely C-value and superimposed pressure phyp. The aim of analytical models is to describe complex processes and the underlying physical phenomena. The interactions of the centrifugal field and the sumperimposed static pressure and their combined effect on pore structure and related fluid behaviour are ongoing subjects of research interest. Such an analytical model has been presented by Friedmann (1999). Combined use of theoretical models and experimental knowledge is regarded as the most promising approach for the scale-up of centrifugal processes.
Acknowledgements Authors are grateful to Heinkel (Germany) for the financial support. The authors also recognize the technical support from the Laboratory of Food Process Engineering at the ETH Zurich.
References Darcy, H.P.G., 1856. Appendice D—Filtrage: e´xperiences concernant la loi de l’e´coulement de l’eau a` travers les sables, et des conside´rations ge´ne´erales relatives aux sources. Les Fontaines publiques de la ville de Dijon, Paris, Victor Dalmont, pp. 559 – 603. Friedmann, T., 1999. Flow of non-Newtonian Fluids Through Compressible Porous Media in Centrifugal Filtration Processing. PhD Thesis, ETH Zurich, Switzerland. Krizek, R.J., 1971. Rheologic behaviour of cohesionless soils subjected to dynamic loads. Journal of Rheology 15 (3), 491 – 540. Mayer, G., 1986. Die Beschreibung des Entfeuchtungsverhaltens von ko¨rnigen Haufwerken im Fliehkraftfeld. PhD Thesis, TU Karlsruhe, Germany. Stadager, C., 1995. Die Entfeuchtung von Filterkuchen durch die Kombination von Zentrifugal-und Gasdruckkraft. PhD Thesis, TU Karlsruhe, Germany. Tiller, F.M., Hsyung, N.B., 1993. Unifying the theory of thickening, filtration and centrifugation. Water Science Technology 28 (1), 1 – 9. Tiller, F.M., Huang, C.J., 1961. Theory on filtration equipment. Industrial and Engineering Chemistry 53 (7), 529 – 537.
Filtration experiments with compressible filter cakes in centrifugal fields with superimposed static pressure Thomas Friedmann a, Christoph Lustenberger b,*, Erich J. Windhab b a
DuPont Central Research and Development, Particle Science and Technology, Experimental Station, Wilmington, DE 19880, USA b Department of Food Science, Laboratory of Food Engineering, ETH Zurich, Switzerland Received 29 October 2002; received in revised form 6 November 2002; accepted 2 May 2003
Abstract Combined application of centrifugal and static pressure field has shown improved results for filtration rate and dewatering performance in various applications. Especially for compressible filter cakes, hyperbaric centrifugal filtration promises better results than separation in conventional filter centrifuges. In a beaker centrifuge filtration experiments were carried out up to C-values of 3000. A static pressure field with a maximum pressure up to 5 bar was superimposed in the centrifuge (hyperbaric centrifugal filtration). Visualisation techniques allowed the observation of the filter cake compression during the filtration experiment. Under various C-value and static pressure conditions filtration experiments have been carried out using suspension systems with solids of distinct compressibility. The filtrate flow versus time was monitored. Complementary, the mechanical filter cake properties and filter cake structures were analysed under different process conditions. Relationships between filtrate flow rate and filter cake properties (mechanical behaviour, structure) are described. D 2004 Elsevier B.V. All rights reserved. Keywords: solid – liquid separation; centrifugal filtration; compressible porous media; beaker centrifuge; filter cake structure
1. Introduction Efficient solid – liquid separation can be achieved in filter centrifuges. However, the centrifugal mass forces enhancing desaturation also lead to an additional compression of the filter cake. The principle of hyperbaric centrifugal filtration allows the superposition of a static pressure field to the centrifugal field. This combination of centrifugal and static pressure field was developed at the University of Karlsruhe. * Corresponding author. Fax: +41-1-632-11-55. E-mail address: [email protected] (C. Lustenberger). 0301-7516/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/S0301-7516(03)00078-4
Stadager (1995) investigated the dewatering performance using this new technology. The hyperbaric centrifugal filtration also promises an acceleration of the flow rate through compressible filter cakes. An increased knowledge on the factors influencing flow behaviour through compressible porous media is of major importance to be able to optimise and further develop existing separation processes. 1.1. Cake filtration The fundamental relationship between pressure ˙ through a difference Dp and volumetric flow rate V porous medium was first mentioned by Darcy (1856).
262
T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267
Fig. 1. Parameters in cake filtration.
˙ is According to Eq. (1) the volumetric flow rate V directly proportional to the filter area A, to the pressure difference Dp, to the fluid viscosity g and to the total resistance. The total resistance contains the filter cake resistance RC, the height of the packed bed hC and the filter medium resistance RM (Fig. 1). ˙ ¼ V
A Dp gðRC hC þ RM Þ
ð1Þ
For Newtonian fluid properties the desired effect of ˙ to the proportionate increase of volumetric flow rate V increase of pressure difference Dp is found only for rigid particles forming an incompressible filter cake. From experimental data it is known that flow rate increases only slightly for compressible filter cakes. 1.2. Compressible filter cake Considerable work on filtration with compressible filter cakes has been effected by Tiller et al. (Tiller and
Huang, 1961; Tiller and Hsyung, 1993). Many authors have followed their general approaches in various modifications. Absolute values of the compressibility constants may vary depending on the equipment used to measure compressibility. This makes it difficult to compare data from different experiments. Considering the amount of literature available on the subject of compressible filter cakes, there is little about behaviour of such filter cakes in the centrifugal field (Fig. 2). Under a given pressure almost all filter cakes are compressed. At the same time the structure (pore size, porosity) is altered and therefore influences the permeability of the porous medium. Hooke’s law states that if a compressive strain e is applied to an ideal solid, the compressive stress r within the material is directly proportional to the strain. However, this ideal elastic behaviour does not apply for a packed bed of particles, even if the particles are ideal elastic. This non-linearity of the compression modulus G (Eq. (2)) has been shown for various materials and has been also found for soil samples under compression (Krizek, 1971). G¼
dr de
ð2Þ
2. Experimental setup To determine the influence of material and process parameters on flow behaviour, experimental investigations with model systems were carried out. EPDM elastomer particles (ethylene-propylene-diene-polymethylene elastomers) were used as model
Fig. 2. Relation of compressibility exponent d to permeability (Tiller and Hsyung, 1993).
T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267 Table 1 Compressible particles used for model filter cake
G62.0005 G62.0515 G62.1030
Particle diameter dp [Am]
Packed bed porosity eV [ – ]
250 – 500 500 – 1500 1500 – 3000
0.747 0.648 0.611
system for a compressible filter cake that contains particles that are deformable. Three different particle size distributions were used for the investigations (Table 1). The density of EPDM is 1.57 kg/dm3. The elastomers were supplied by Gezolan, CH-6252 Dagmersellen, Switzerland. Suspensions of the mentioned particles were prepared with Newtonian aqueous polyethylene glycol solutions (PEG35000 from Hoechst, Germany). PEG solutions showed Newtonian flow behaviour over a wide shear rate range (0.1 – 2000 1/s). 2.1. Filter cake mechanics In the present work, the mechanical response of the material to an applied stress was investigated by means of DMTA (dynamic mechanical thermal analysis) with the objective to establish relationships between structural parameters of the porous medium and the characteristics of filtration processes. Experiments were performed in a Rheometrics Solids Analyzer RSA II. The test geometry used was a cylinderplate compression tool as shown schematically in Fig. 3. Elastomer particles were filled into the cylin-
Fig. 3. Rheometrics Solids Analyzer RSA II-test geometry.
263
der, where they were compressed with a strain rate of 0.002 1/s. The actual sample deformation e is calculated according to Eq. (3) where DL is the tool displacement and Ke is the strain constant. Ke is given by Eq. (4), where L is the sample height. e ¼ Ke DL Ke ¼
1 L
ð3Þ ð4Þ
2.2. Compression in centrifugal field The deformation of a packed bed under centrifugal force was visualised in an optical laboratory centrifuge using stroboscopic techniques (Fig. 4). The centrifuge beaker containing the sample gives an impulse to a photoelectric reflection sensor. The signal controls the connected strobe thus the flash frequency equals the centrifuge frequency at all times during the process. The ‘frozen’ image is recorded with a CCDcamera and is subjected to image analysis where the cake height was determined. To determine the compression degree during centrifugal filtration visualisation experiments were carried out in the hyperbaric beaker filter centrifuge (Section 2.3), which allows observation of the filter cake during process.
Fig. 4. Experimental set-up for visualisation of packed bed in the centrifugal field; (a) centrifuge rotor, (b) sample in centrifuge beaker, (c) strobe, (d) CCD-camera, (e) photoelectric reflection sensor.
264
T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267
Fig. 5. Schematic drawing of the hyperbaric beaker filter centrifuge HB600; (a) fluid vessel, (b) beaker filter centrifuge, (c) flow meter, (d) pressure sensor, (e) balance.
2.3. Flow through compressible porous media Flow behaviour through compressible filter cakes in the centrifugal field was investigated with a hyperbaric beaker filter centrifuge (Fig. 5). The filter centrifuge HB600 was developed by Heinkel AG, D-74321 Bietigheim-Bissingen, Germany, on the basis of a beaker filter centrifuge used by Mayer (1986). The HB600 can be loaded during rotation with suspension into the two opposite beakers. Through the same conduct, wash liquid can be added after cake built-up. Optional static pressure can be superimposed through the axial inlet. This operation is called hyperbaric centrifugation. Further specifications and experimental set-up are described by Friedmann (1999).
rheology also influences strongly the filtrate flow rate. The experiments presented here were performed with a Newtonian fluid. 3.1. Filter cake deformation Compressive load cycles are shown in Fig. 6 for the three samples G62.0005, G62.0515 and G62.1030. Particle size distributions have a marked effect on
3. Results and discussion Flow-through experiments under various process conditions with compressible filter cakes were carried out. The deformation behaviour of the same filter cake material was analysed to find relationships between filtrate flow rate and filter cake properties. The fluid
Fig. 6. Compressibility function for different packed beds of elastomer particles.
T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267 Table 2 Compressibility factors C1 and C2 determined by DMTA G62.0005 G62.0515 G62.1030
C1
C2
1350 8396 24 109
8.277 9.736 10.564
compressibility of the packed bed. As shown, the smallest particles were found to be the most compressible ones. However, the higher compressibility was not only attributed to particle size but also to the packed bed porosity. The particle shape of the G62.0005 resulted in a higher porosity. The loose structure of the G62.0005 packed bed favoured rearrangement of the particles to denser packing. The highly non-linear compressibility of packed beds and filter cakes was described by modifying Hooke’s law according to Eq. (5) and Eq. (6), where C1 and C2 are the compressibility factors determined by DMTA measurements (Table 2). r ¼ GðeÞe
ð5Þ
GðeÞ ¼ C1 eC2 e
ð6Þ
3.2. Compression in centrifugal field The compression in the centrifugal field was investigated experimentally for various packed beds. Fig. 7 illustrates the deformation of a packed bed of elastomer particles (G62.0515) at various centrifuge speeds.
265
Fig. 8 shows deformation e versus C-value for packed beds of elastomer particles G62.0005, G62.0515 and G62.1030 saturated with water. The Cvalue is the dimensionless centrifugal acceleration defined according to Eq. (7), where r is the radial distance from the axis, x is the angular velocity and g is the gravitational constant. The C-value is, therefore, a measure of the relative centrifugal force with respect to the earth’s gravitational force. C¼
rx2 g
ð7Þ
For all packed beds investigated, similar non-linear compression behavior was observed similar to the DMTA measurements. Calculated values (lines) based on the analytical results from the DMTA were in good agreement with the experimental results (symbols) for compaction of a packed bed in the centrifugal field. In another experiment series the relationship between initial cake height hC(0) and deformation at a certain C-value was investigated. For this purpose, packed beds of various initial heights (hC(0) = 10, 20 and 40 mm) were tested. As expected the largest deformations were found for the packed bed with maximum initial height. Since the centrifugal force acts on the mass of the particles and is added up over the cake height, a packed bed with larger hC(0) consequently generates a higher total compression force acting on the lower particle layers in the packed bed.
Fig. 7. Packed bed of elastomer particles (G62.0515) deformed in an optical centrifuge setup at different centrifuge speeds; (a) 475 rpm (C = 50), (b) 815 rpm (C = 149), (c) 2090 rpm (C = 977).
266
T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267
In pressure filtration the compression of the packed bed is due to viscous drag forces. 3.3. Flow through compressible porous media
Fig. 8. Deformation versus C-value for packed bed of elastomer particles (G62.0005, G62.0515 and G62.1030); calculated values from Friedmann (1999).
A compressible porous material is also deformed due to fluid flow. This deformation is due to shear stress transmitted to the solids phase by the fluid. Visualisation experiments during centrifugal filtration were performed with elastomer particles (G62.0005) and a PEG 10% w/w solution (Newtonian). After cake build-up at 208 rpm, the centrifuge speed was increased and/or hyperbaric pressure was superimposed (see Section 3.3). The results show that the packed bed compression is significantly higher at increased rotational speed compared to the hyperbaric pressure. The deformation of a packed bed in the centrifuge can be estimated from the centrifugal force acting on the solid particles.
In centrifugal filtration both components, centrifugal forces and drag forces due to fluid flow, act simultaneously. Deformation of the filter cake results from a combination of both compressive components. Since the hyperbaric filter centrifuge permits combination of centrifugal force and superposition of hydrostatic pressure, the effects on compression of the filter cake could be observed. At 208 rpm an average cake height of hC = 24.0 mm was determined. With increasing rotational speed up to 1100 rpm a noticeable decrease of the cake height was observed. Keeping the rotational speed at 208 rpm and imposing a hyperbaric pressure (up to 2 bar) no significant decrease of the cake height could be observed. It has to be noted that at this point the cake is already compressed and therefore the compression modulus of the packed bed has increased. The increase of the driving pressure difference by superposition of the hydrostatic pressure however had a marked effect on the filtrate flow rate. Deformation of the pores leads to an increase of filter cake resistance, which is responsible for the nonlinear relationship of volumetric flow rate and driving pressure difference. This effect of pressure on the permeability of compactible systems is commonly described in the literature by an exponential function (Tiller and Huang, 1961). It is often assumed that with
Fig. 9. Volumetric flux J versus hyperbaric pressure phyp at constant C-values in the centrifuge for filter cakes of elastomer particles (G62.0005) flown through with PEG solution (10% w/w).
T. Friedmann et al. / Int. J. Miner. Process. 73 (2004) 261–267
a higher pressure difference, higher or at least equal volumetric flow rates will result. It has been shown within this work that there are compressible porous systems that exhibit an optimum pressure range for maximum flow rate. An increase of driving fluid pressure difference Dpfl by means of centrifugal acceleration is coupled with a substantial increase of the compressive pressure on the pore network, thus leading to a marked flow rate reduction. Superimposed static pressure improves volumetric flow rate because Dpfl is raised without strongly contributing to the filter cake compression to the same amount as centrifugal acceleration does. In Fig. 9 the evolution of volumetric flow rate as a function of superimposed (hyperbaric) pressure phyp is shown for elastomer filter cakes (G62.0005). Centrifugal acceleration was kept constant at C = 15 and C = 406, respectively. A marked increase of flow rate was observed in comparison to volumetric flow rates attained under pure centrifugal force ( phyp = 0). Furthermore, the typical trend of flow rate as a function of compressive pressure for compressible filter cakes was found again in these experiments. The efficiency of a volumetric flow rate increase by superimposed pressure, however, was found to strongly depend on the actual centrifugal acceleration.
4. Conclusions It was shown that DMTA can be used for the characterisation of the deformation behaviour of porous media. The deformation behaviour of packed beds (filter cakes) was found to be highly non-linear. The deformation of a packed bed or filter cake under centrifugal force was visualised in an optical laboratory centrifuge using stroboscopic techniques. The analytical results from the DMTA were in good agreement with the experimental results for compaction of a packed bed in the centrifugal field. In conclusion it can be said that hyperbaric centrifugation is able to provide better results in solid– liquid separation for highly compressible materials. However, process parameters have to be chosen adequately. Low C-values and a superimposed static pressure optimised for the particular product yielded the best results with respect to flow rate. The mentioned phenomena (flow rate increase due to C-value
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and/or superimposed pressure phyp) were found to be even more effective for non-Newtonian (shear thinning) fluids. This is evident, since filter cake structure determines flow behaviour. The structure of a compressible filter cake, though, was shown to be influenced by the main process parameters of hyperbaric centrifugation, namely C-value and superimposed pressure phyp. The aim of analytical models is to describe complex processes and the underlying physical phenomena. The interactions of the centrifugal field and the sumperimposed static pressure and their combined effect on pore structure and related fluid behaviour are ongoing subjects of research interest. Such an analytical model has been presented by Friedmann (1999). Combined use of theoretical models and experimental knowledge is regarded as the most promising approach for the scale-up of centrifugal processes.
Acknowledgements Authors are grateful to Heinkel (Germany) for the financial support. The authors also recognize the technical support from the Laboratory of Food Process Engineering at the ETH Zurich.
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