SCIENCE Filtration
Approach to determine Particle Density for Modelling Purposes in Water Treatment and Supply Irene Slavik, Andreas Korrenz, Klaus Ripl and Wolfgang Uhl Filtration, drinking water, particle counting, particle size distribution, particle sizing, sedimentation, water treatment
In this study a standardised evaluation routine was developed to determine real particle density in form of a particle density distribution from sedimentation analysis. Sedimentation analysis was performed to determine particle settling velocity as a function of settled distance over time by monitoring the settling particles in a sedimentation apparatus with a particle counter. This means that the change in particle number concentration was monitored over time. Since settling velocity could not be determined directly from the experiment but particle number concentration, an approach to determine settling velocity was developed. This included (i) the use of a mean particle size of the particles of one particle size class, (ii) the definition of a mean sedimentation distance, and (iii) the determination of a mean sedimentation time from the function of the change in particle number concentration over time in relation to the initial particle number concentration. Finally, the mean settling velocity was used in the Stokes’ law equation for density calculations. The sedimentation experiments resulted in a particle density distribution for each particle size class present in a suspension. The experimentally determined particle density distributions can be mathematically described by regression analysis. These functions of particle density distribution can then be used for modelling purposes in water treatment and supply as for example to describe particle transport in drinking water distribution systems.
1. Problem definition and objectives Particle properties like size, structure, volume and density are of special importance for modelling purposes in water treatment and supply. This is because these particle charac teristics directly affect their removability in water treatment as well as their behaviour in water supply systems. The latter includes transport, sedimentation and mobilization. Since particle size is the parameter which is incorporated in the calculation of volume, density and strength, particle charac terisation is mainly based on size measurement. Sizing techniques include microscopy, photography and image analysis, light scattering methods, methods being based on transmitted light measurement, and individual particle sen sors. In contrast, a direct measurement of particle density is not possible. Density data have to be derived from other data obtained from direct measurement, mostly involving some form of sedimentation procedure [1], i. e. the deter mination of the settling velocity. The settling velocity of a spherical particle (as long as the mass of the particle is not too big and the particle settles under laminar conditions) can be determined by applying Stokes’ law, as described for example in [2]. Due to an irregular shape and the porosity
18
of particles present in water treatment and supply systems, shape factors as well as drag coefficient corrections are usually used to extend the basic Stokes’ law equation [2, 3, 4, 5]. Tian et al. [6] described a method for the determination of the settling velocity and the size of fractal aggregates in consideration of the permeating flow. Consequently, using modified Stokes’ equations, it will be possible to calculate particle density from measured data, i. e. from the settling velocity, the particle cross section, the particle hydraulic permeability and the kinetic viscosity of water. However, no study on the determination of an absolute particle density can be found in the literature. As relevant properties rather the following density related parameters were considered so far: a material/true density, a relative den sity [7, 8], a particle/floc effective density [5] and a buoyant density [1, 3]. These density properties were used to discuss the nature of particle density depending on particle size, the impact of treatment process conditions, the composition of raw waters to be treated as well as to characterise corrosion products in water supply systems. Investigations considering the role of particle/floc density in solid-liquid separation processes are mostly based on theoretical approaches [1, 3, 9].
gwf-Wasser | Abwasser
International Issue 2/2015
Filtration
Consequently, the main objective of this research was to develop a method for the determination of a real particle density, including the water filled pores, from settling velocity which was determined using sedimentation analysis.
2. Materials and methods To determine particle density from settling velocity, ex periments were performed using a settling column ap paratus as shown in Figure 1. The column was a sealed plexiglas pipe with an inner diameter of 150 mm which could be filled with a particle-containing suspension up to a height of 950 mm. To guarantee complete mixing or, put differently, to prevent the demixing of the solid and liquid phases of the suspensions to be investigated, the settling column was filled from the bottom by pumping. Sampling was performed via a polyethylene pipe with an inner dia meter of 6 mm and the opening being 500 mm below the water level at the beginning of an experimental run. The column was jacketed with polyethylene foam mats for temperature control to avoid thermal currents that could possibly disturb the particle settlement process. Particle settling velocity was determined as a function of settled distance over time by monitoring the settling particles in the sedimentation apparatus with a particle counter Abakus Mobile Fluid (Co. Klotz, Germany). This means that the change in particle number concentration was monitored over time. For this, samples of 30 mL were abstracted from the column during each sampling cycle including 10 mL for the analysis and 20 mL for flushing purposes in the particle counting instrument. Consequently, sampling resulted in a water level drawdown. Knowing the initial water level s0, the inner diameter of the column D, and the volume abstracted due to sampling as flow rate Q, the maximum possible number of samples nsamples can be calculated according to Eq. (1). 1000⋅ Δs⋅ π ⋅D 2 nsamples ( Δs) = [m]; 0 ≤ Δs ≤ s0 4⋅Q
The particle counting instrument offers sampling intervals between 1 min and 1 h, the cycle times applied in this study 105 s, 180 s, 360 s, 800 s, and 1200 s. were = V0 −Q ⋅t sed analyses VSedimentation = A⋅ s0 −Q ⋅ Δtperformed = ssed ⋅ A using suspensions tsed were obtained from pipe flushing in a drinking water distribution system. To yield particle concentrations that lie within the measuring range of the particle counting instrument, the
flushing suspensions # & diluted with drinking water Q were s sed =was ssed previously / 2 = % s0 − filtered ⋅t sed ( through / 2 which a 0.2 µm cartridge filter $ ' A (Co. Pall). The experiments were run at room temperature (23 °C ± 1 °C). To ensure high measurement data quality, outlier tests Δt carried out. For this statistical analysis, mean by tGrubbs were sed ,i = t i − 3 values and standard deviations were determined for nine
gwf-Wasser | Abwasser International Issue 2/2015 Ai =
Δt ⋅ Δhi
consecutive measurement values. The error probability applied was 10 %. Moreover, measurement data were processed by taking the particle number concentration of the dilution water into account. Since settling velocity could not be determined directly from the experiment but particle number concentration, an approach to determine settling velocity was developed. At first, a mean particle size of the particles of one particle size class was used. Furthermore, a mean sedimentation distance s-sed was defined. The determination of a mean sedimentation distance s-sed was based on the22 assumption that the sample ⋅D 1000⋅ΔΔs⋅s⋅ππ⋅D 1000⋅ Δss))=particle = [m]; nnsamples [m]; 00≤≤ΔΔsiss≤≤constant. ss00 flow Q of((Δ the measuring device Due to samples 4⋅Q 4⋅Q the sampling, the volume V of the sedimentation column is decreasing over time. Consequently, the volume at the t-sed is time
−Q⋅t⋅tsedsed==A⋅ A⋅ss00−Q −Q⋅⋅ΔΔtt==sssedsed⋅⋅AA (2) VVtsed ==VV00−Q tsed
with A being the column area, and the mean sedimentation distance s-sed becomes
## QQ && sssedsed==sssedsed//22==%%ss00−− ⋅t⋅tsedsed((//22 (3) $$ AA '' a mean sedimentation time t- was determined from Finally, sed
the function of the change in particle number concentration ΔΔtt in relation to the initial particle number over time c(t) ttsedsed,i ,i==tti i−− concentration 33 c0. For this, following characteristic values were determined: ■■ The number i of density classes for one particle size class ■■ The mean sedimentation time for each of these density classes t-Δsed,i ΔΔtt⋅⋅Δ hhi i A = i i = mean sedimentation time for one particle size ■■ A The 2 2 class t sed
= sed = ttsed
(1)
SCIENCE
∑((AA ⋅t⋅t )) ∑ ∑AA ∑ ii
sed,i,i sed
ii
18⋅vsedsed⋅⋅ηηfluid 18⋅v fluid = ρρparticle ++ρρfluid particle= fluid 22 g⋅dparticle g⋅d particle
x)==cc++ee(b(b0 +b0 +b1⋅x1⋅x) ) ff((x)
Figure 1: Experimental set-up of the settling column with particle counting device
19
s sed = ssed / 2 =#% s0 −Q ⋅t sed&( / 2 A &' #$ ss sed sed = ssed / 2 = % s0 − Q ⋅t sed ( / 2 = ssed / 2 = %$ s0 − A ⋅t sed (' / 2 $ ' A
SCIENCE Filtration
The procedure for the determination of these characteris tic values is represented in Figure 2 and Figure 3. Figure 2 2 shows the general approach a standardised suspension 1000⋅ Δs⋅ π ⋅Dfor nsamples ( Δs) = [m]; 0 ≤ Δs ≤ s containing particles of one particle size class0 featuring five 4⋅Q different densities. The mean sedimentation time of par ticles of the density i t-sed,i is determined from the centroid of the area determined by the function of the change in particle number concentration over time c(t), the change Vtsed = V0 −Q ⋅t sed = A⋅ s0 −Q ⋅ Δt = ssed ⋅ A in sedimentation time ∆t and the respective percentage of particles of the density i of the entity of particles hi. share In case the suspension is not standardised, meaning that it contains not only five different densities but a density distribution, then classes need to be defined. As # density & Q s sed = s / 2 = % s0 − ⋅t sed ( / 2 shown insedFigure were divided into five $ 3, the ' A particles density classes. The mean sedimentation time of a density class i t-sed,i can then be calculated according to Eq. (4)
Δt t sed ,i = t i − (4) 3
t sed =
0 0
∑( A ⋅t ) ∑A sed ,i
i
i
ρ particle =
18⋅v sed ⋅ ηfluid + ρfluid 2 g⋅d particle
Figure 2: Approach for the determination of the mean sedimentation time of particles. Suspension includes particles of one particle size class and five different densities
f ( x) = c + e (b0 +b1⋅x )
Figure 3: Approach for the determination of the mean sedimentation time of particles. Suspension includes particles of one particle size class and five different density classes
20
particle
particle particle
0
Δt ⋅ Δhi Ai = 2
t sed ,i = t − Δt i Δ3t sed ,i = t i − Δt tt sed ,i = t i − 33 as derived from the centroid of the area Ai which was determined by Δs⋅ π ⋅D 2 nA = Δ(tΔ⋅sΔ)h=i 1000⋅ [m]; 0 ≤ Δs ≤ s0 i samples Δtt ⋅⋅ 2Δ Δhhi 4⋅Q Δ A = i Ai = 2 (5) 2 i The mean sedimentation time of all particles of one particle class t-sed results from Eq. (6) size Vtsed = V0 −Q ,i )⋅ Δt = ssed ⋅ A 0 −Q ∑⋅t(sedA=i A⋅⋅tssed t sed = ∑( A Ai ⋅t ⋅t sed ,i ) t sed = ∑(∑ i Ased ,i ) (6) i t sed = Ai ∑ A ∑ i Knowing s-sed and t-sed , the mean settling velocity v-sed can # & Q = % sused ⋅t sed 2 law equation for d sed = ssed / 2and be s calculated in the ensity ( /Stokes’ 0 − $ ' A calculations as given in Eq. (7) ρ = 18⋅v sed ⋅ηfluid + ρ particle 18⋅v sed 2⋅η fluid (7) fluid g⋅d sed ⋅ ηfluid ρ particle = = 18⋅v +ρ ρfluid Δ t 2 ρ + fluid g⋅d 2 t sedparticle ,i = t − g⋅d ρparticlei being 3 the particle density, ηfluid being the d with ynamic viscosity of the liquid phase of the suspension, dparticle being the diameter of a particle (particle size) and ρfluid being the density of the liquid phase of the suspension. Af ( =x)Δ=tc⋅ Δ+he(bi(b+b +b⋅x⋅x) ) i x) = c + e (b +b ⋅x ) ff (( x) = c 2+ e 3. Results The sedimentation experiments resulted in a particle density distribution for each particle size class present in a suspension. This is exemplarily shown in Figure 4 where ⋅t sed ,i ) of the particle size classes the particle∑ density ( Ai distributions t sed =
1
1 1
ranging from 0.9 to 19.8 µm are represented. Ai Based on the results, certain relationships between particle size and particle density could be identified. It was shown that there was a higher share of high densities small particles size classes (red coloured in Figure 4) within in comparison to larger particles (blue coloured in Figure 4). This is consistent ⋅ ηfluidfindings from the literature according 18⋅v sedwith ρ particle = + ρ 2 particlesfluid to which smaller are more compact and charac g⋅d particle terised by a higher density, thus [1, 3, 5, 10, 11]. The experimentally determined particle density distri butions can be mathematically described by regression analysis in form of Eq. (8)
∑
f ( x) = c + e (b0 +b1⋅x )
(8)
with c, b0 and b1 being the regression coefficients. These functions of particle density distribution can then be used for modelling purposes in water treatment and supply as for example to describe particle transport in drinking water distribution systems.
Acknowledgements This paper is based on the keynote lecture with the same title delivered by the author at, and included in electronic proceedings of, the Filtech 2015 in Cologne, February 24–26, 2015.
gwf-Wasser | Abwasser
International Issue 2/2015
Filtration
SCIENCE
Figure 4: Particle density distributions. Particle size classes: 0.9 to 19.8 µm
References [1]
Gregory, J.: The role of floc density in solid-liquid separation. Filtration & Separation 35 (4), 1998, p. 367–371.
[2]
Parsons, S. A. et al.: Treatment of Waters with Elevated Organic Content. AWWA Research Foundation, 2007.
[3]
Gregory, J.: The density of particle aggregates. Water Sci. Technol. 36 (4), 1997, p. 1–13.
[4]
Johnson, C. P., Li, X. and Logan, B. E.: Settling Velocities of Fractal Aggregates. Environ. Sci. Technol. 30 (1996), p. 1911–1918.
[5]
Tambo, N. and Watanabe, Y.: Physical Characteristics of Flocs – I. The Floc Density Function and Aluminium Floc. Water Res. 13 (1979), p. 409–419.
[6]
Tian, W. J., Nakayama, T., Huang, J. P. and Yu, K. W.: Scaling be haviours in settling process of fractal aggregates in water. EPL 78, 46001, 2007.
[7]
Boller, M. and Blaser, S.: Particles under stress. Water Sci. Technol. 37 (10), 1998, p. 9–29.
[8]
Spicer, P. T. et al.: Effect of shear schedule on particle size, density, and structure during flocculation in stirred tanks. Powder Technol. 97 (1), 1998, p. 26–34.
[9]
Bache, D. H. and Gregory, R.: Flocs and separation processes in drinking water treatment: a review. J. Water Supply: Res. Technol.– AQUA 59 (1), 2010, p. 16–30.
[10] Boller, M. A. and Kavanaugh, M. C.: Particle characteristics and headloss increase in granular media filtration. Water Res. 29 (4), 1995, p. 1139–1149. [11] Klimpel, R. C., Dirican, C. and Hogg, R.: Measurement of agglomerate density in flocculated fine particle suspensions. Particulate Science and Technology 4 (1986), p. 45–59.
gwf-Wasser | Abwasser International Issue 2/2015
Authors Dr.-Ing. Irene Slavik
[email protected] | Wahnbachtalsperrenverband | Siegelsknippen | 53721 Siegburg | Germany | (Formerly: Technische Universität Dresden, Chair of Water Supply Engineering) B. Sc. Andreas Korrenz und Dipl.-Ing. Klaus Ripl Technische Universität Dresden | Institute of Urban Water Management | Chair of Water Supply Engineering | 01062 Dresden | Germany Prof. Dr.-Ing. Wolfgang Uhl
[email protected] | Norwegian Institute for Water Research (NIVA) | Gaustadalléen 21 | 0349 Oslo | Norway | (Formerly: Technische Universität Dresden, Chair of Water Supply Engineering)
21
