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Simulation of a semi-industrial pilot plant thickener using CFD approach
International Journal of Mining Science and Technology 23 (2013) 63–68
Contents lists available at SciVerse ScienceDirect
International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Simulation of a semi-industrial pilot plant thickener using CFD approach Majid Ebrahimzadeh Gheshlaghi, Ataallah Soltani Goharrizi ⇑, Alireza Aghajani Shahrivar Department of Chemical Engineering, College of Engineering, Shahid Bahonar University of Kerman, Kerman 76169-133, Iran
a r t i c l e
i n f o
Article history: Received 14 May 2012 Received in revised form 26 June 2012 Accepted 28 July 2012 Available online 10 February 2013 Keywords: Thickener CFD Modeling Flocculation Feedwell Population balance
a b s t r a c t Thickeners are important units for water recovery in various industries. In this study, a semi-industrial pilot plant thickener similar to the tailing thickener of the Sarcheshmeh Copper Mine was simulated by CFD modeling. The population balance was used to describe the particle aggregation and breakup. In this population balance, 15 particle sizes categories were considered. The Eulerian–Eulerian approach with standard k–e turbulence model was applied to describe two phases of slurry flow in the thickener under steady-state condition. The simulation results have been compared with the experimental measurements to validate the accuracy of the CFD modeling. After checking the numerical results, the effect of important parameters such as, feed flow rate, solid percentage in the feed, and solid particle size on the thickener performance was studied. The thickener residence time distribution were obtained by the modeling and also compared with the experimental data. Finally, the effects of feedwell feeding on the average diameter of aggregate and turbulent intensity were evaluated. Ó 2013 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
1. Introduction Sedimentation of a solid in a fluid by gravitational force is one of the most common methods of solid–liquid separation. This method mainly attributes in mineral and chemical industries. A common way to separate solids from liquids in high volumes is using the sedimentation under gravity within vessels called washers, thickeners, and clarifiers [1]. Solid–liquid separation by gravitational settling has long been used in many applications. Gravity thickeners enable the treatment of vast volumes of dilute slurry that pass through a central feedwell, with the intention of dissipating much of the incoming stream’s kinetic energy and gently discharging this stream into the main tank volume. The solids settle to form a bed, with solids concentration increasing towards the underflow at the base. This is why it is called thickener. Clarified liquor is collected at the peripheral overflow, while a centrally driven rake promotes consolidation and assists sediment transport to the underflow discharge [2]. Using synthetic polymer flocculants in thickeners leads to high and fast aggregation between solids that cause large and fast sedimentation. Also, the effect of the flocculants results in having more inlet load for a specified thickener or using smaller thickeners for a specified inlet load. Optimizing the flocculation process was not the issue in many huge conventional thickeners. Gunthert investigated the effect of blade velocity and blade height on the rake blade performance; by carrying out experiments on five fullscale thickeners, increasing the blade height and velocity improved the sludge collection [3].
Wood et al. concluded that flocculant consumption, underflow density and some other operational parameters are related to the mixing conditions during flocculation process [4]. Burger et al. used the CFD modeling to predict the feedwell performance for a range of designs, and determined the effect of the solid concentration, turbulence levels, flocculent type and dosage on the flocculation kinetics in a pipe reactor. Population balance (PB) is a method to mathematically describe the kinetics of the aggregate growth and breakup [5,6]. Several researchers studied the applicability of the PB to describe flocculation over a range of conditions [7,8]. They used a pipe reactor with different mineral feeds. Sutalo et al. presented dye visualization results in a small scale thickener and studied the velocity field in the thickener [9]. Peloquin et al. applied conventional CFD modeling for a bauxite residue feedwell and thickener to show the effect of the mean particle size, feed flow rate and feedwell diameter on the flow patterns [10]. Owen et al. investigated the effect of different ways of flocculant addition and location on the performance of feedwell [11]. In this research, a semi-industrial pilot plant thickener was simulated based on CFD method to investigate the effect of operational parameters on the thickener performance. The Eulerian–Eulerian approach was applied to describe the two phases of slurry flow in the thickener. In the simulation, the population balance was used to describe the particle aggregation and breakage. The model performance has been compared with the experimental measurement data and the effect of operating parameters on the sedimentation in the thickener has been evaluated.
⇑ Corresponding author. Tel.: +98 341 211 8298. E-mail address: [email protected] (A. Soltani Goharrizi). 2095-2686/$ - see front matter Ó 2013 Published by Elsevier B.V. on behalf of China University of Mining & Technology. http://dx.doi.org/10.1016/j.ijmst.2013.01.010
64
M. Ebrahimzadeh Gheshlaghi et al. / International Journal of Mining Science and Technology 23 (2013) 63–68
At k–e model, turbulent viscosity (lt) depends on the turbulent kinetic energy (k) and turbulent dissipation rate of turbulence (e).
2. Experimental The thickener with a cylindrical tank made of iron sheet with a 0.7 m height and 0.75 m diameter was used in all experiments. The effect of flocculant and its injection to the system had a vital role on the thickener performance. In thickener, flocculant injection system was considered that the flocculant could be injected in different parts of the pipeline. Also, the height of feedwell was variable to investigate the thickener performance. A schematic view of the thickener setup for the experimental study is shown in Fig. 1. 3. Governing equations 3.1. Mass and momentum equations The Eulerian–Eulerian approach was used for modeling the slurry flow in the thickener. This model considers better interaction phases than the Lagrangian model and when the volume of the solid phase is high, the Eulerian–Eulerian model is more suitable than Lagrangian model. Continuity and momentum equations for the continuous phase (c) and dispersed (d) can be constructed. Continuity equations express the mass conservation and momentum equations are used for expression of the momentum conservation. The energy equations are not considered in the thickeners, because the thickeners do not have thermal transfer. Continuity equations:
3.2. Population balance model (PB) A population balance is a mathematical model used to describe changes in a particle-size distribution through time. Population balance models have been used to describe a wide range of practical systems, for example: coagulation or flocculation, crystallization, size reduction in grinding mills, and droplet coalescence in solvent extraction or flotation columns [12]. Smoluchowski proposed the population balance approach to the flocculation kinetics modeling, and considered three possible mechanisms for the particle collision: differential settling, Brownian motion and fluid shear [12]. Population balance modeling basically provides a size distribution by defining the size range of particles into discrete categories. The result of the model, in fact, is a system of differential equations that describe the accumulation or loss of value or number of particles in each size category [13]. Population balance models may include a term of aggregation, breakage, or both. In this study, the Luo model was used for aggregation kernel, and The Luo and Lehr models are integrated kernels, encompassing both the breakage frequency and the PDF (probability density function) of breaking particles.
3.3. Method of solution
@ ac þ r:ðac U c Þ ¼ 0 @t @ ad qd þ r:ðad U d Þ ¼ 0 @t
qc
ð1Þ ð2Þ
where q, a, t and U are the density, volume fraction, time and velocity vector, respectively. Momentum equations:
@ðac U c Þ þ r:ðac U c U c Þ ¼ Iac rP þ lc r2 ðac U c Þ þ SMc @t @ðad U d Þ þ r:ðad U d U d Þ ¼ Iad rP þ ld r2 ðad U d Þ þ SMd qd @t
qc
ð3Þ ð4Þ
where l, P and SM are the dynamic viscosity, pressure and body force source term, respectively. The k–e model is the most important turbulent model in engineering applications which was used in the modeling procedure.
The thickener process was studied in the steady state condition. The governing mass and momentum equations were solved by using commercial Ansys Fluent 12.0 CFD package. The package numerical kernel uses the element based finite volume method (EBFVM) to treat generalized unstructured meshes in Cartesian coordinates. No-slip boundary conditions at the walls were applied. The SIMPLEC algorithm was used for velocity and pressure relationship. Moreover, the boundary conditions at the inlet and the lower outlet were the mass flow rate boundary conditions. Particle size distribution at inlet feed is shown in Fig. 2. The grid independency test was carried out with three different threedimensional meshes, which contained 8000, 20,000 and 35,000 cells for the feedwell, and 50,000, 170,000 and 300,000 cells for the main body of the thickener respectively. Comparison between simulation results and experimental data showed that at least 20,000 cells for the feedwell and 170,000 cells for the main body of the thickener were needed to produce the grid-independent solution. The computational mesh is shown in Fig. 3.
Feed pipe 0.3775 m 35
0.075 m 0.15-0.25 m
30
0.045 m
0.6 m Thickener
Frequency
25
0.075 m Feedwell
20 14.8
15 10
Gy Gz Gx
6.2 0.07 m
Rake
29.9
0.05 m 0.05 m Under flowpipe
Fig. 1. Schematic view of the thickener setup.
5
7.2
8.4 6.2
8
6.8
6.2
3.8
1.4 1.1 0 -4 -4 -5 1.10×10-5 2.30×10-5 4.40×10-5 7.40×10 1.49×10 2.97×10 Particle size (m) Fig. 2. Particle size distribution in the thickener feed.
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Output solid percentage (%)
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55 50 45 40 35 Modeling result Experimental data
30 25 20
5
10
15
20 25 Q (L/min)
30
35
Fig. 4. Comparison between the experimental data and modeling results for output solid percent at inlet solid percentage of 22.5%.
Fig. 3. Computational mesh for pilot plant thickener.
4. Results and discussion 4.1. Validation modeling data 4.1.1. Effect of feed flow rate The effect of feed flow rate on the outlet solid percent at constant underflow rate is shown in Fig. 4. The inlet solid percent and flocculant dosage were 22.5% and 3.5 g/ton, respectively. The modeling results had a good match with the experimental data. As it can be seen in Fig. 4, with increasing the feed flow rate and because of the input solid enhancement to the thickener, the underflow solid percent increases. Therefore, at constant underflow rate, the solid percent of the underflow in the thickener will be increased. Classical theories have been established about the sediment region with an ideal flow pattern. In these theories, it is assumed that the solid particles move vertically downwards and displaced liquid moves vertically upwards. The flow pattern is achieved ideally in the experiments with the settlement cylinder. But for the thickeners in the laboratory observations, it becomes clear that the flow inside the cone has not one dimensional pattern and the developed compression/infiltration theories could possibly describe the behavior of the sedimentation. The solid particles in the settling region move first vertically and then horizontally along a spiral path to the center of output way. The spiral-like movements of the particles are influenced from several parameters such as feed flow rate, flocculation process, the design of blades rake, rotation speed and the properties of the slurry flow. The liquid displaced from doping solids, moves mainly in the vertical direction upwards until it reaches to the interface of the clear/compact zone, then cross the interface to reach the spiral clear liquid. In this investigation, two regions were considered in which the sediment mud and the spiral dilute slurry zone are formed. Although, there was not a distinct interface between these two zones. The solid volume fraction for various feed flow rate are demonstrated in Fig. 5. With increasing the feed flow rate, the input solid to the thickener increases and then the bed height increases. Also, at low feed flow rate, the region between the mud zone and clear water become small, but with increasing the feed flow rate, this region will be increased. The comparison between the experimental data and modeling results for the height of the mud zone and spiral slurry zone are shown in Fig. 6a. 4.1.2. Effect of inlet solid percent The effect of the inlet solid percent on the height of sediment mud and slurry spiral zone is illustrated in Fig. 6b. It can be seen
that with increasing the inlet solid percent, the height of mud and spiral slurry flow increase. In fact, at low inlet solid percent, the flocculation process occurs very well. Then the larger flocs and consequently a denser sediment mud are formed and as a results, the height of the above mentioned two zones reaches to the lower levels. At 17% as the inlet solid percent, the height of two zones increases faster. At this point, the flocculent dosage is not efficient to generate the large flocs, and then the small particle remains in the water and causes the higher height of these zones. 4.1.3. Residence time distribution (RTD) The comparison between residence time distribution obtained from the experimental tests and modeling results are shown in Fig. 7. These curves show the response of the system to a pulse feeding of a salt solution. As results show, the maximum point of the RTD curve occurs in initial times and the curve has rapid changes at low flow rates. Due to low flow rate, the height of the sediment mud zone is low; therefore, resistance time for passing of the water is low. By increasing the flow rate and due to increasing the mud height, the curve becomes wider and changes gradually. 4.2. Change effect’s parameters 4.2.1. Effect of particle size Effect the faster settling process happens in the thickeners for the bigger size particles. Also the flocculation process is occurred better in this situation. To check the effect of inlet particle size on the thickener performance, an average particle diameter was assumed in the tests. A constant rate of the solid flow and flocculant dosage were considered to investigate the effect of inlet particle size on the thickener efficiency. The effect of particle size on the outlet solid percent and the height of sediment mud are shown in Fig. 8. The underflow concentration (p) is related directly to the density and concentration of the bottom and coning parts of the thickener. To achieve high concentration at the bottom of the thickener, dense sediment formation is required. Increasing the particles size causes a rapid formation of sediment and a higher concentration will be formed at the bottom of the thickener. A larger aggregate formation depends on the primary particles, flocculant, flocculation process, and even the geometry of the feedwell. The effect of particle size on the sedimentation process revealed that increasing the particles diameter causes enhancement of the bottom concentration and consequently the height of the sediment mud can be effectively reduced. 4.2.2. Different methods for thickener feeding Two different kinds of methods were considered for feeding the thickener. It can be seen from Fig. 9a, in the first method (Type 1),
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(a)
(c)
4.85e-01 4.61e-01 4.37e-01 4.12e-01 3.88e-01 3.64e-01 3.40e-01 3.15e-01 2.91e-01 2.67e-01 2.43e-01 2.18e-01 1.94e-01 1.70e-01 1.46e-01 1.21e-01 9.70e-02 7.28e-02 y 4.85e-02 2.43e-02 z x 0
(b)
4.56e-01 4.33e-01 4.10e-01 3.88e-01 3.65e-01 3.42e-01 3.19e-01 2.96e-01 2.74e-01 2.51e-01 2.28e-01 2.05e-01 1.82e-01 1.60e-01 1.37e-01 1.14e-01 9.12e-02 6.84e-02 y 4.56e-02 2.28e-02 z x 0
(d)
4.95e-01 4.70e-01 4.45e-01 4.20e-01 3.96e-01 3.71e-01 3.46e-01 3.22e-01 2.97e-01 2.72e-01 2.47e-01 2.23e-01 1.98e-01 1.73e-01 1.48e-01 1.24e-01 9.89e-02 7.42e-02 4.95e-02 2.47e-02 0
z
5.18e-01 4.92e-01 4.66e-01 4.40e-01 4.14e-01 3.88e-01 3.62e-01 3.37e-01 3.11e-01 2.85e-01 2.59e-01 2.33e-01 2.07e-01 1.81e-01 1.55e-01 1.29e-01 1.04e-01 7.77e-02 5.18e-02 2.59e-02 0
z
y x
y x
Fig. 5. Height of the sediment bed in the thickener at various feed flow rate ((a) 18.7 L/min; (b) 14.7 L/min; (c) 23.3 L/min; (d) 6.6 L/min).
40 35 25
Height of sediment mud (modeling) Height of spiral moving slurry (modeling) Height of spiral moving slurry (experimental) Height of sediment mud (experimental)
20 15 10 5 0
5
10 15 20 25 Feed flow rate (L/min)
30
Height (cm)
Height (cm)
30
35
20 18 16 14 12 10 8 6 4 2 0
5
8
11 14 17 20 Input solid percent (%)
(a) Feed flow rate
23
26
(b) Input solid percent
Fig. 6. Comparison between the experimental data and modeling results for height of the sediment zone as a function of feed flow rate and input solid percent.
Modeling result Experimental data
5 4 3 2 1 0
6
12 18 24 30 36 Time (min)
42 48
(a) Flow rate of 8 L/min
4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0
3.5 Concentration (g/L)
6
Concentration (g/L)
Concentration (g/L)
7
6
12 18 24 30 36 Time (min)
42 48
(b) Flow rate of 16 L/min Fig. 7. RTD curve for the flow rates.
3.0 2.5 2.0 1.5 1.0 0.5 0
6
12 18 24 30 36 42 48 Time (min) (c) Flow rate of 20 L/min
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Height of sediment mud (cm)
Output solid percent (%)
54 51 48 45 42 39 36 33 30
0
0.02 0.04 0.06 0.08 Average particle diameter (m)
0.10
40 35 30 25 20 15 10 5 0
(a) On the outlet solid percent
0.02 0.04 0.06 0.08 Average particle diameter (m)
0.10
(b) On the height of the sediment mud
Fig. 8. Effect of the particle size on the two above places.
Gy
Gy Gx
Gz
Gx
Gz
(a) Type 1
(b) Type 2
240 220 200 180
Method 1
160
Method 2
140 120
5
7
9 11 13 15 17 19 21 23 25 Feed flow rate (L/s) (a) Mean aggregates size
70
Mean aggregate diameter (µm)
280 260
Mean turbulence intensity (%)
Mean aggregate diameter (µm)
Fig. 9. Feedwell geometry.
65 60 55 50 45 40 35 30
5
7
9 11 13 15 17 19 21 23 25 Feed flow rate (L/s) (b) Mean aggregates size
800 700 600 500 400 300 200 100
5
7
9 11 13 15 17 19 21 23 25 Feed flow rate (L/s)
(c) Maximum aggregate diameter
Fig. 10. Mean aggregates size, mean turbulence intensity and maximum aggregate diameter vs. feed flow rate.
the feed enters to the feedwell from two entrance pipes with 2.54 cm diameter. In the second one (Type 2), as shown in Fig. 9b, the feed enters from the peripheral wall of the feedwell with an angle 45° toward to the origin. The mean average aggregate diameters in the thickener for these two feeding methods are shown in Fig. 10a. It is concluded that the mean diameter increases with increasing the feed flow rate, and the mean diameter is obtained higher in the first method. By increasing the feed flow rate, the fluid velocity and turbulency increases. Due to the positive effect of turbulency on the aggregation process, the aggregate diameter increases in the higher turbulency. The mean turbulent intensity for the two methods at various feed flow rate are presented in Fig. 10b. This figure shows that the higher turbulent
intensity is achieved for the first method. Generally, turbulency causes enhancement of particle collision rate and consequently aggregates formation increases. But, at higher turbulency, the aggregate will break up, and its effect will be opposite. As it can be concluded in Fig. 10a, because of higher turbulency in the first method, the aggregate diameter is obtained higher than the second one. The maximum aggregate diameter at various feed flow rates is presented in Fig. 10c. It is obvious that at low flow rate and due to increase the turbulency with feed flow rate, the maximum average diameter increases. But increasing the feed flow rate higher than 19 L/min causes the maximum aggregate diameter to decrease. In this condition, the turbulency is very high and it causes that aggregate break up to lower diameter. The mean aggregate
280 260 240 220 Free surface Feed inlet 6 cm under the surface 12 cm under the surface Output
200 180 160 140 120
5
7
9
11 13 15 17 19 Feed flow rate (L/s)
21
23
25
Mean aggregate diameter (µm)
M. Ebrahimzadeh Gheshlaghi et al. / International Journal of Mining Science and Technology 23 (2013) 63–68
Mean aggregate diameter (µm)
68
270 240 210 180 150 120 90 60 30
5
(a) Method 1
7
9
11 13 15 17 19 Feed flow rate (L/s)
21
23
25
(b) Method 2
Fig. 11. Mean aggregate size vs. the feed flow rate at different part of the feedwell.
diameter for these two methods at various part of the feedwell is shown in Fig. 11. Due to the effect of flocculation process, the aggregates diameter at the bottom part of the feedwell is higher. Also the aggregate size for the first method is higher because of the turbulency effect. 5. Conclusions A dilute feed is effective on the performance of the thickener and extends its capacity due to a better flocculant impact on the solids. As a result of high feed flow rate, great amount of water will be recycled. Adjustment of the feed dilution can be done by using recycled water coming from the thickener. Increasing the feed flow rate causes outlet concentration and consequently the height of sedimentation to increase. Residence time increases with the increase in the feed flow rate. In fact, the system works close to the perfect mixing. Also with increasing particle size, settling process is done effectively and outlet concentration increases. One of the key variables affecting the flocculation process is the fluid stress. Higher stress levels increase the amount of mixed flocculants, absorption, particle collision (aggregate growth) and aggregate breakage. By increasing the feed flow rate, the stress in the pulp increases and more non-uniform distribution in the feedwell occur. Increased residence time can be effective on the flocculant absorption and aggregate growth. The feedwell geometry is also one of the effective parameters which can influence the creation of tension. In this study, a good matching between the experimental results and modeling using computational fluid dynamics (CFD) and population balance model was achieved which was applied to
investigate the tailing thickener performance in the Sarcheshmeh Copper Mine. References [1] Rudman M, Paterson DA, Simic K. Efficiency of raking in gravity thickeners. Int J Miner Process 2010;95:30–9. [2] Svarovsky L. Gravity clarification and thickening, solid–liquid separation. Oxford: Butterworth-Heinemann; 2000. [3] Gunthert FW. Thickening zone and sludge removal in circular final settling tanks. Water Sci Technol 1984;16:303–16. [4] Wood MG, Greenfield PF, Howes T, Johns MR, Keller J. Computational fluid dynamics modeling of wastewater ponds to improve design. Water Sci Technol 1995;3:111–8. [5] Burger R, Bustos MC, Concha F. Settling velocities of particulate system, phenomenological theory of sedimentation processes: numerical simulation of the transient behavior of flocculated suspensions in an ideal batch or continuous thickener. Int J Miner Process 1999;55:267–82. [6] Farrow JB, Johnston RRM, Simic K, Swift JD. Consolidation and aggregate densification during gravity thickening. Chem Eng J 2000;80:141–8. [7] Kahane RB, Schwarz MP, Johnston RRM. Residue thickener modeling at Worsley Alumina. Appl Math Modell 2002;26:281–96. [8] White RB, Sutalo ID, Nguyen T. Fluid flow in thickener feedwell models. Miner Eng 2003;16:145–50. [9] Sutalo ID, Paterson DA, Rudman M. Flow visualization and computational prediction in thickener rake models. Miner Eng 2003;16:93–102. [10] Ma LQ, Zhang DS, Jing SG. Numerical simulation analysis by solid-liquid coupling with 3DEC of dynamic water crannies in overlying strata. J China Univ Mining Technol 2008;18(3):347–52. [11] Owen AT, Nguyen TV, Fawell PD. The effect of flocculant solution transport and addition conditions on feedwell performance in gravity thickener. Int J Miner Process 2009;93:115–27. [12] Heath AR, Bahri PA, Fawell PD, Farrow JB. Polymer flocculation of calcite: population balance mode. AIChE J 2006;52:1641–53. [13] Ramakrishna D, Mahoney AW. Population balances modeling. Chem Eng Sci 2002;57:595–606.
Contents lists available at SciVerse ScienceDirect
International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Simulation of a semi-industrial pilot plant thickener using CFD approach Majid Ebrahimzadeh Gheshlaghi, Ataallah Soltani Goharrizi ⇑, Alireza Aghajani Shahrivar Department of Chemical Engineering, College of Engineering, Shahid Bahonar University of Kerman, Kerman 76169-133, Iran
a r t i c l e
i n f o
Article history: Received 14 May 2012 Received in revised form 26 June 2012 Accepted 28 July 2012 Available online 10 February 2013 Keywords: Thickener CFD Modeling Flocculation Feedwell Population balance
a b s t r a c t Thickeners are important units for water recovery in various industries. In this study, a semi-industrial pilot plant thickener similar to the tailing thickener of the Sarcheshmeh Copper Mine was simulated by CFD modeling. The population balance was used to describe the particle aggregation and breakup. In this population balance, 15 particle sizes categories were considered. The Eulerian–Eulerian approach with standard k–e turbulence model was applied to describe two phases of slurry flow in the thickener under steady-state condition. The simulation results have been compared with the experimental measurements to validate the accuracy of the CFD modeling. After checking the numerical results, the effect of important parameters such as, feed flow rate, solid percentage in the feed, and solid particle size on the thickener performance was studied. The thickener residence time distribution were obtained by the modeling and also compared with the experimental data. Finally, the effects of feedwell feeding on the average diameter of aggregate and turbulent intensity were evaluated. Ó 2013 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
1. Introduction Sedimentation of a solid in a fluid by gravitational force is one of the most common methods of solid–liquid separation. This method mainly attributes in mineral and chemical industries. A common way to separate solids from liquids in high volumes is using the sedimentation under gravity within vessels called washers, thickeners, and clarifiers [1]. Solid–liquid separation by gravitational settling has long been used in many applications. Gravity thickeners enable the treatment of vast volumes of dilute slurry that pass through a central feedwell, with the intention of dissipating much of the incoming stream’s kinetic energy and gently discharging this stream into the main tank volume. The solids settle to form a bed, with solids concentration increasing towards the underflow at the base. This is why it is called thickener. Clarified liquor is collected at the peripheral overflow, while a centrally driven rake promotes consolidation and assists sediment transport to the underflow discharge [2]. Using synthetic polymer flocculants in thickeners leads to high and fast aggregation between solids that cause large and fast sedimentation. Also, the effect of the flocculants results in having more inlet load for a specified thickener or using smaller thickeners for a specified inlet load. Optimizing the flocculation process was not the issue in many huge conventional thickeners. Gunthert investigated the effect of blade velocity and blade height on the rake blade performance; by carrying out experiments on five fullscale thickeners, increasing the blade height and velocity improved the sludge collection [3].
Wood et al. concluded that flocculant consumption, underflow density and some other operational parameters are related to the mixing conditions during flocculation process [4]. Burger et al. used the CFD modeling to predict the feedwell performance for a range of designs, and determined the effect of the solid concentration, turbulence levels, flocculent type and dosage on the flocculation kinetics in a pipe reactor. Population balance (PB) is a method to mathematically describe the kinetics of the aggregate growth and breakup [5,6]. Several researchers studied the applicability of the PB to describe flocculation over a range of conditions [7,8]. They used a pipe reactor with different mineral feeds. Sutalo et al. presented dye visualization results in a small scale thickener and studied the velocity field in the thickener [9]. Peloquin et al. applied conventional CFD modeling for a bauxite residue feedwell and thickener to show the effect of the mean particle size, feed flow rate and feedwell diameter on the flow patterns [10]. Owen et al. investigated the effect of different ways of flocculant addition and location on the performance of feedwell [11]. In this research, a semi-industrial pilot plant thickener was simulated based on CFD method to investigate the effect of operational parameters on the thickener performance. The Eulerian–Eulerian approach was applied to describe the two phases of slurry flow in the thickener. In the simulation, the population balance was used to describe the particle aggregation and breakage. The model performance has been compared with the experimental measurement data and the effect of operating parameters on the sedimentation in the thickener has been evaluated.
⇑ Corresponding author. Tel.: +98 341 211 8298. E-mail address: [email protected] (A. Soltani Goharrizi). 2095-2686/$ - see front matter Ó 2013 Published by Elsevier B.V. on behalf of China University of Mining & Technology. http://dx.doi.org/10.1016/j.ijmst.2013.01.010
64
M. Ebrahimzadeh Gheshlaghi et al. / International Journal of Mining Science and Technology 23 (2013) 63–68
At k–e model, turbulent viscosity (lt) depends on the turbulent kinetic energy (k) and turbulent dissipation rate of turbulence (e).
2. Experimental The thickener with a cylindrical tank made of iron sheet with a 0.7 m height and 0.75 m diameter was used in all experiments. The effect of flocculant and its injection to the system had a vital role on the thickener performance. In thickener, flocculant injection system was considered that the flocculant could be injected in different parts of the pipeline. Also, the height of feedwell was variable to investigate the thickener performance. A schematic view of the thickener setup for the experimental study is shown in Fig. 1. 3. Governing equations 3.1. Mass and momentum equations The Eulerian–Eulerian approach was used for modeling the slurry flow in the thickener. This model considers better interaction phases than the Lagrangian model and when the volume of the solid phase is high, the Eulerian–Eulerian model is more suitable than Lagrangian model. Continuity and momentum equations for the continuous phase (c) and dispersed (d) can be constructed. Continuity equations express the mass conservation and momentum equations are used for expression of the momentum conservation. The energy equations are not considered in the thickeners, because the thickeners do not have thermal transfer. Continuity equations:
3.2. Population balance model (PB) A population balance is a mathematical model used to describe changes in a particle-size distribution through time. Population balance models have been used to describe a wide range of practical systems, for example: coagulation or flocculation, crystallization, size reduction in grinding mills, and droplet coalescence in solvent extraction or flotation columns [12]. Smoluchowski proposed the population balance approach to the flocculation kinetics modeling, and considered three possible mechanisms for the particle collision: differential settling, Brownian motion and fluid shear [12]. Population balance modeling basically provides a size distribution by defining the size range of particles into discrete categories. The result of the model, in fact, is a system of differential equations that describe the accumulation or loss of value or number of particles in each size category [13]. Population balance models may include a term of aggregation, breakage, or both. In this study, the Luo model was used for aggregation kernel, and The Luo and Lehr models are integrated kernels, encompassing both the breakage frequency and the PDF (probability density function) of breaking particles.
3.3. Method of solution
@ ac þ r:ðac U c Þ ¼ 0 @t @ ad qd þ r:ðad U d Þ ¼ 0 @t
qc
ð1Þ ð2Þ
where q, a, t and U are the density, volume fraction, time and velocity vector, respectively. Momentum equations:
@ðac U c Þ þ r:ðac U c U c Þ ¼ Iac rP þ lc r2 ðac U c Þ þ SMc @t @ðad U d Þ þ r:ðad U d U d Þ ¼ Iad rP þ ld r2 ðad U d Þ þ SMd qd @t
qc
ð3Þ ð4Þ
where l, P and SM are the dynamic viscosity, pressure and body force source term, respectively. The k–e model is the most important turbulent model in engineering applications which was used in the modeling procedure.
The thickener process was studied in the steady state condition. The governing mass and momentum equations were solved by using commercial Ansys Fluent 12.0 CFD package. The package numerical kernel uses the element based finite volume method (EBFVM) to treat generalized unstructured meshes in Cartesian coordinates. No-slip boundary conditions at the walls were applied. The SIMPLEC algorithm was used for velocity and pressure relationship. Moreover, the boundary conditions at the inlet and the lower outlet were the mass flow rate boundary conditions. Particle size distribution at inlet feed is shown in Fig. 2. The grid independency test was carried out with three different threedimensional meshes, which contained 8000, 20,000 and 35,000 cells for the feedwell, and 50,000, 170,000 and 300,000 cells for the main body of the thickener respectively. Comparison between simulation results and experimental data showed that at least 20,000 cells for the feedwell and 170,000 cells for the main body of the thickener were needed to produce the grid-independent solution. The computational mesh is shown in Fig. 3.
Feed pipe 0.3775 m 35
0.075 m 0.15-0.25 m
30
0.045 m
0.6 m Thickener
Frequency
25
0.075 m Feedwell
20 14.8
15 10
Gy Gz Gx
6.2 0.07 m
Rake
29.9
0.05 m 0.05 m Under flowpipe
Fig. 1. Schematic view of the thickener setup.
5
7.2
8.4 6.2
8
6.8
6.2
3.8
1.4 1.1 0 -4 -4 -5 1.10×10-5 2.30×10-5 4.40×10-5 7.40×10 1.49×10 2.97×10 Particle size (m) Fig. 2. Particle size distribution in the thickener feed.
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Output solid percentage (%)
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55 50 45 40 35 Modeling result Experimental data
30 25 20
5
10
15
20 25 Q (L/min)
30
35
Fig. 4. Comparison between the experimental data and modeling results for output solid percent at inlet solid percentage of 22.5%.
Fig. 3. Computational mesh for pilot plant thickener.
4. Results and discussion 4.1. Validation modeling data 4.1.1. Effect of feed flow rate The effect of feed flow rate on the outlet solid percent at constant underflow rate is shown in Fig. 4. The inlet solid percent and flocculant dosage were 22.5% and 3.5 g/ton, respectively. The modeling results had a good match with the experimental data. As it can be seen in Fig. 4, with increasing the feed flow rate and because of the input solid enhancement to the thickener, the underflow solid percent increases. Therefore, at constant underflow rate, the solid percent of the underflow in the thickener will be increased. Classical theories have been established about the sediment region with an ideal flow pattern. In these theories, it is assumed that the solid particles move vertically downwards and displaced liquid moves vertically upwards. The flow pattern is achieved ideally in the experiments with the settlement cylinder. But for the thickeners in the laboratory observations, it becomes clear that the flow inside the cone has not one dimensional pattern and the developed compression/infiltration theories could possibly describe the behavior of the sedimentation. The solid particles in the settling region move first vertically and then horizontally along a spiral path to the center of output way. The spiral-like movements of the particles are influenced from several parameters such as feed flow rate, flocculation process, the design of blades rake, rotation speed and the properties of the slurry flow. The liquid displaced from doping solids, moves mainly in the vertical direction upwards until it reaches to the interface of the clear/compact zone, then cross the interface to reach the spiral clear liquid. In this investigation, two regions were considered in which the sediment mud and the spiral dilute slurry zone are formed. Although, there was not a distinct interface between these two zones. The solid volume fraction for various feed flow rate are demonstrated in Fig. 5. With increasing the feed flow rate, the input solid to the thickener increases and then the bed height increases. Also, at low feed flow rate, the region between the mud zone and clear water become small, but with increasing the feed flow rate, this region will be increased. The comparison between the experimental data and modeling results for the height of the mud zone and spiral slurry zone are shown in Fig. 6a. 4.1.2. Effect of inlet solid percent The effect of the inlet solid percent on the height of sediment mud and slurry spiral zone is illustrated in Fig. 6b. It can be seen
that with increasing the inlet solid percent, the height of mud and spiral slurry flow increase. In fact, at low inlet solid percent, the flocculation process occurs very well. Then the larger flocs and consequently a denser sediment mud are formed and as a results, the height of the above mentioned two zones reaches to the lower levels. At 17% as the inlet solid percent, the height of two zones increases faster. At this point, the flocculent dosage is not efficient to generate the large flocs, and then the small particle remains in the water and causes the higher height of these zones. 4.1.3. Residence time distribution (RTD) The comparison between residence time distribution obtained from the experimental tests and modeling results are shown in Fig. 7. These curves show the response of the system to a pulse feeding of a salt solution. As results show, the maximum point of the RTD curve occurs in initial times and the curve has rapid changes at low flow rates. Due to low flow rate, the height of the sediment mud zone is low; therefore, resistance time for passing of the water is low. By increasing the flow rate and due to increasing the mud height, the curve becomes wider and changes gradually. 4.2. Change effect’s parameters 4.2.1. Effect of particle size Effect the faster settling process happens in the thickeners for the bigger size particles. Also the flocculation process is occurred better in this situation. To check the effect of inlet particle size on the thickener performance, an average particle diameter was assumed in the tests. A constant rate of the solid flow and flocculant dosage were considered to investigate the effect of inlet particle size on the thickener efficiency. The effect of particle size on the outlet solid percent and the height of sediment mud are shown in Fig. 8. The underflow concentration (p) is related directly to the density and concentration of the bottom and coning parts of the thickener. To achieve high concentration at the bottom of the thickener, dense sediment formation is required. Increasing the particles size causes a rapid formation of sediment and a higher concentration will be formed at the bottom of the thickener. A larger aggregate formation depends on the primary particles, flocculant, flocculation process, and even the geometry of the feedwell. The effect of particle size on the sedimentation process revealed that increasing the particles diameter causes enhancement of the bottom concentration and consequently the height of the sediment mud can be effectively reduced. 4.2.2. Different methods for thickener feeding Two different kinds of methods were considered for feeding the thickener. It can be seen from Fig. 9a, in the first method (Type 1),
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(a)
(c)
4.85e-01 4.61e-01 4.37e-01 4.12e-01 3.88e-01 3.64e-01 3.40e-01 3.15e-01 2.91e-01 2.67e-01 2.43e-01 2.18e-01 1.94e-01 1.70e-01 1.46e-01 1.21e-01 9.70e-02 7.28e-02 y 4.85e-02 2.43e-02 z x 0
(b)
4.56e-01 4.33e-01 4.10e-01 3.88e-01 3.65e-01 3.42e-01 3.19e-01 2.96e-01 2.74e-01 2.51e-01 2.28e-01 2.05e-01 1.82e-01 1.60e-01 1.37e-01 1.14e-01 9.12e-02 6.84e-02 y 4.56e-02 2.28e-02 z x 0
(d)
4.95e-01 4.70e-01 4.45e-01 4.20e-01 3.96e-01 3.71e-01 3.46e-01 3.22e-01 2.97e-01 2.72e-01 2.47e-01 2.23e-01 1.98e-01 1.73e-01 1.48e-01 1.24e-01 9.89e-02 7.42e-02 4.95e-02 2.47e-02 0
z
5.18e-01 4.92e-01 4.66e-01 4.40e-01 4.14e-01 3.88e-01 3.62e-01 3.37e-01 3.11e-01 2.85e-01 2.59e-01 2.33e-01 2.07e-01 1.81e-01 1.55e-01 1.29e-01 1.04e-01 7.77e-02 5.18e-02 2.59e-02 0
z
y x
y x
Fig. 5. Height of the sediment bed in the thickener at various feed flow rate ((a) 18.7 L/min; (b) 14.7 L/min; (c) 23.3 L/min; (d) 6.6 L/min).
40 35 25
Height of sediment mud (modeling) Height of spiral moving slurry (modeling) Height of spiral moving slurry (experimental) Height of sediment mud (experimental)
20 15 10 5 0
5
10 15 20 25 Feed flow rate (L/min)
30
Height (cm)
Height (cm)
30
35
20 18 16 14 12 10 8 6 4 2 0
5
8
11 14 17 20 Input solid percent (%)
(a) Feed flow rate
23
26
(b) Input solid percent
Fig. 6. Comparison between the experimental data and modeling results for height of the sediment zone as a function of feed flow rate and input solid percent.
Modeling result Experimental data
5 4 3 2 1 0
6
12 18 24 30 36 Time (min)
42 48
(a) Flow rate of 8 L/min
4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0
3.5 Concentration (g/L)
6
Concentration (g/L)
Concentration (g/L)
7
6
12 18 24 30 36 Time (min)
42 48
(b) Flow rate of 16 L/min Fig. 7. RTD curve for the flow rates.
3.0 2.5 2.0 1.5 1.0 0.5 0
6
12 18 24 30 36 42 48 Time (min) (c) Flow rate of 20 L/min
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Height of sediment mud (cm)
Output solid percent (%)
54 51 48 45 42 39 36 33 30
0
0.02 0.04 0.06 0.08 Average particle diameter (m)
0.10
40 35 30 25 20 15 10 5 0
(a) On the outlet solid percent
0.02 0.04 0.06 0.08 Average particle diameter (m)
0.10
(b) On the height of the sediment mud
Fig. 8. Effect of the particle size on the two above places.
Gy
Gy Gx
Gz
Gx
Gz
(a) Type 1
(b) Type 2
240 220 200 180
Method 1
160
Method 2
140 120
5
7
9 11 13 15 17 19 21 23 25 Feed flow rate (L/s) (a) Mean aggregates size
70
Mean aggregate diameter (µm)
280 260
Mean turbulence intensity (%)
Mean aggregate diameter (µm)
Fig. 9. Feedwell geometry.
65 60 55 50 45 40 35 30
5
7
9 11 13 15 17 19 21 23 25 Feed flow rate (L/s) (b) Mean aggregates size
800 700 600 500 400 300 200 100
5
7
9 11 13 15 17 19 21 23 25 Feed flow rate (L/s)
(c) Maximum aggregate diameter
Fig. 10. Mean aggregates size, mean turbulence intensity and maximum aggregate diameter vs. feed flow rate.
the feed enters to the feedwell from two entrance pipes with 2.54 cm diameter. In the second one (Type 2), as shown in Fig. 9b, the feed enters from the peripheral wall of the feedwell with an angle 45° toward to the origin. The mean average aggregate diameters in the thickener for these two feeding methods are shown in Fig. 10a. It is concluded that the mean diameter increases with increasing the feed flow rate, and the mean diameter is obtained higher in the first method. By increasing the feed flow rate, the fluid velocity and turbulency increases. Due to the positive effect of turbulency on the aggregation process, the aggregate diameter increases in the higher turbulency. The mean turbulent intensity for the two methods at various feed flow rate are presented in Fig. 10b. This figure shows that the higher turbulent
intensity is achieved for the first method. Generally, turbulency causes enhancement of particle collision rate and consequently aggregates formation increases. But, at higher turbulency, the aggregate will break up, and its effect will be opposite. As it can be concluded in Fig. 10a, because of higher turbulency in the first method, the aggregate diameter is obtained higher than the second one. The maximum aggregate diameter at various feed flow rates is presented in Fig. 10c. It is obvious that at low flow rate and due to increase the turbulency with feed flow rate, the maximum average diameter increases. But increasing the feed flow rate higher than 19 L/min causes the maximum aggregate diameter to decrease. In this condition, the turbulency is very high and it causes that aggregate break up to lower diameter. The mean aggregate
280 260 240 220 Free surface Feed inlet 6 cm under the surface 12 cm under the surface Output
200 180 160 140 120
5
7
9
11 13 15 17 19 Feed flow rate (L/s)
21
23
25
Mean aggregate diameter (µm)
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Mean aggregate diameter (µm)
68
270 240 210 180 150 120 90 60 30
5
(a) Method 1
7
9
11 13 15 17 19 Feed flow rate (L/s)
21
23
25
(b) Method 2
Fig. 11. Mean aggregate size vs. the feed flow rate at different part of the feedwell.
diameter for these two methods at various part of the feedwell is shown in Fig. 11. Due to the effect of flocculation process, the aggregates diameter at the bottom part of the feedwell is higher. Also the aggregate size for the first method is higher because of the turbulency effect. 5. Conclusions A dilute feed is effective on the performance of the thickener and extends its capacity due to a better flocculant impact on the solids. As a result of high feed flow rate, great amount of water will be recycled. Adjustment of the feed dilution can be done by using recycled water coming from the thickener. Increasing the feed flow rate causes outlet concentration and consequently the height of sedimentation to increase. Residence time increases with the increase in the feed flow rate. In fact, the system works close to the perfect mixing. Also with increasing particle size, settling process is done effectively and outlet concentration increases. One of the key variables affecting the flocculation process is the fluid stress. Higher stress levels increase the amount of mixed flocculants, absorption, particle collision (aggregate growth) and aggregate breakage. By increasing the feed flow rate, the stress in the pulp increases and more non-uniform distribution in the feedwell occur. Increased residence time can be effective on the flocculant absorption and aggregate growth. The feedwell geometry is also one of the effective parameters which can influence the creation of tension. In this study, a good matching between the experimental results and modeling using computational fluid dynamics (CFD) and population balance model was achieved which was applied to
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