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On the free-settling test for estimating activated sludge floc density
War. Res. Vol. 30, No. 3, pp. 541-550, 1996
Pergamon
0043-1354(95)00229-4
Copyright © 1996ElsevierScienceLtd Printed in Great Britain.All fights reserved 0043-1354/96 $15.00 + 0.00
ON THE FREE-SETTLING TEST FOR ESTIMATING ACTIVATED SLUDGE FLOC DENSITY D. J. LEE *@, G. W. CHEN, Y. C. LIAO and C. C. HSIEH Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 106, Republic of China (First rece&ed August 1994; accepted in revised f o r m October 1995)
A~tract--The feasibility of using flee-settling test for estimating activated sludge floc density was discussed in the present work. Some usually applied models or correlations, such as for the primary particle density, the drag coefficient, the correction factor for advection flow through the floc and the estimation for floc permeability, are examined. The results show that floc permeability depends strongly on the models or parameter sets applied. However, the effective floc density, and also the fractal dimension, is insensitive to the floc permeability estimation, but is strongly dependent on the drag coefficient expression employed. Possible valid experimental range is proposed. Key words--floc density, free-settling test, permeability, fractal dimension, freeze/thaw treatment
INTRODUCTION Floc size and floc density (porosity) are two of the factors most influence the efficiency of many processes involving flocs. It is generally accepted that these two quantities are not mutually independent, but are relating by some empirical relationship, say a power-law type relationship. Various methods have been proposed for measuring the floc density, e.g. isopycnic centrifugation (Dammel and Schroeder, 1991; Knocke et al., 1993), interference microscopy (Andreadakis, 1993), and free settling test (Tambo and Watanabe, 1979; Mitani et al., 1983; Li and Ganczarczyk, 1987; Li and Ganczarczyk, 1989; Li and Ganczarczyk, 1990; Li and Ganczarczyk, 1992; Huang, 1993; Lee, 1994a). Among these tests, free settling test is the most widely employed method in literature because of its simplicity and the low testing cost. The information obtained in a free settling test is the diameter and the terminal velocity for a single floc. Assume the floc is moving steadily in the medium, the force balance equation is used for estimating floc density (and also floc porosity). Based on the constructed floc size/density relationship, a floc has been proposed as a highly porous fractal-like aggregate made of many primary particles (Li and Ganczarczyk, 1989; Li and Ganczarczyk, 1990; Li and Ganczarczyk, 1992; Jiang and Logan, 1991). Fractal dimension is a quantitative measure of how *Author to whom all correspondence should be addressed [Fax: (886) 2 362 3040].
the primary particles occupying the floc interior space. It is found that aggregates generated in water and wastewater treatment processes exhibit a fractal dimension ranging between 1.4 and 2.8 (Li and Ganczarczyk, 1989). Beside the floc diameter and terminal velocity data, the information about several unknowns are required in the force balance equation, e.g. drag coefficient (Huang, 1993), primary particle density (Lee, 1994b), or the correction factor for advection flow (Logan and Hunt, 1988; Li and Ganczarczyk, 1988). However, will be shown latter, not all assumptions made in literature are strictly valid for all experimental range generally applied. The focus of this report is to examine the validity of several usually made assumptions in a free settling test. Activated sludge flocs, original or treated with a freeze/thaw treatment, are used as testing material. Possible valid experimental range is proposed. The requirement for further researches is highlighted. MEASUREMENT OF FLOC DENSITY Force balance equation
In general, the force balance for a floc moving steadily in an infinite medium can be described as follows (Neale et al., 1973; Li and Ganczarczyk, 1992; Huang, 1993) p f - pw _ 1 -- e = 3pwf2CD ~ Pp -- Pw 4g(pp -- pw)df v"
541
(1)
542
D.J. Lee et al.
where Co = dr = e= g = v= pw = p~ = pf = =
drag coefficient, diameter of floc (m), porosity of floe, gravitational acceleration = 9.8m/s 2, terminal velocity of the floc (m/s), the density of water (kg/mS), the dcnsity of primary particle (kg/m3), floc density (kg/mS), the ratio of the resistance experienced by a floc to that of an equivalent solid sphere.
Except floc diamctcr and terminal velocity data which are available in a free-settling test, four u n k n o w n s exist in equation (1) (pp, f~, CD, and e or pf). T o estimate floc porosity or effcctivc density, pp, f/and CD are required. If~) is given in priori, only the information about CD is needed, as done by Mitani et al. (1983) and T a m b o and W a t a n a b e (1979).
Primary particle density
pp is the density of the primary particles comprising the floc. In most studies, pp is assumed to be equal to p,, the dried solid density (Tambo and Watanabe, 1979; Li and Ganczarczyk, 1987, 1992). However, in sludge with a large amount of internal water, the bound water and the solid phase will move together and behave like a particle (Michaels and Bolger, 1962; Kawasaki et al., 199t; Lee, 1994b). In such a case, the primary particle density is a function of bound water content, which complicates the analysis (Lee, 1994b). Since the definition of bound water is still ambiguous, the standard method for estimating the moisture distribution in a sludge is lack (Vesilind, 1994, 1995). Only a possible range for pp is proposed as follows. Since the floc density cannot be larger than the dried solid density, p~ can serve as an upper limit. Considering the associated bound water as a part of a primary particle, the following equation holds:
1 + WB
(2)
P P - UPs+ WB/p '
Model
where Ws is kg bound water per kg dried solid. Equation (2) provides a lower estimate. Factor
For a highly porous sphere moving steadily through an infinite medium under creeping flow condition, factor f~ is provided by Brinkman (and corrected by Debye) as follows (Neale et al., 1973) f~ =
2fl2[1- (tanhfl)/fl] 2fl2 + 311 - (tanhfl)/fl]
where -
d, 2,/;
(4)
is a dimensionless floc diameter and k = floc permeability (mS). The validity of equation (3) had been experimentally verified by Matsumoto and Suganuma (1977). A direct application of equation (3), nevertheless, requires a knowledge about floc permeability, whose evaluation is usually based on permeability models. Six typical models which are generally accepted in literature are listed in Table I. All equations are in the form of k = ~ × f(e), wheref(e) is a function of floc porosity, and dp is the characteristic length for the primary particles, both are unknowns in a free settling test. Matsumoto et al. (1978) had employed Davies correlation for estimating the floc permeability. Li and Ganczarczyk (1992) had compared the permeabilities calculated from Carman-Kozeny equation and Davies correlation. Large deviation occurs when different model or parameter dp are applied. Huang (1993) employed Brinkman model on permeability estimation and concluded from his data that the calculated fractal dimension will not be affected when the effects of advection flow is considered. Rogak and Flagan (1990) also proposed an expression for permeability based on the fractal nature of floe. Chellam and Wiesner (1993) had examined Rogak and Flagan's model. Beside the
Table 1. Permeabilitymodelsemployedin this work" Primary particle shape Permeability function
Equation
Brinkman
Sphere
k= ~22 x[3+ ~ - c - 3 l ~ 8 - e -3]
Carman-Kozeny
Shere
k
Happel (or cell model)
Sphere
k= ~
x 33 - 4"573++4'5F52' s ,-
Happcl
Fibcrous
k= ~
x [- In~ + ~2 + l ~1
Davies
Fibcrous
k = ~4 x 16~b3/2( 1I+ 56~b3)
(E)
Fiberous
3 ~ k = ]~ x
(F)
Iberall
(3)
ea
5S8(1-- e)2
(A) (B)
2 - lnRep x 4 - lnRe,
3~6
(C)
(D)
'The symbol dp ~ primary particlediameter(m); ~b = I-e = solidfractionof floe;7 ~= ~t/s;So = specific surface area of the primary particle = 6/dp(m-~);Rep = dpp,v/p.e ~ the Reynolds Number based on the primary particleand internalflow velocity.
Free-settling test measuring floc density information about the primary particles themselves, the way these particles occupying the floc space is also required in their model. Due to too many quantities unavailable, Rogak and Flagan's model is not examined in the present work. D r a g coefficient
Drag coefficient is a function of Reynolds number and floc sphericity (Tambo and Watanabe, 1979; Namer and Ganczarczyk, 1993). The effect of particle shape on Co can be found in Pattyjohn and Christiansen (1948) and Ganser (1993). A modified Stokes' law taking floc shape into account is expressed as follows
cD =
K Re
(5)
where K is a constant depending on floc sphericity. Tambo and Watanabe (1979) assumed ~ = 1 and K = 45 in equation (5), equation (1) then reads Apf = p f -
34#w V
pw -
gd~f
(6)
where /z, is water viscosity. Various studies had applied equation (6) or its equivalent form for constructing floc size/density relationship. A good review can be found in Huang (1993). Equation (5) might fail in high Reynolds number regime (e.g. Re > 1). For an impermeable sphere moving steadily with Reynolds number ranging from 1 to 1000, the following expression is suggested by Concha and Almerdra (1979) 9.06 ~2
CD = 0.28(1 + ~
j.
(7)
The only available correlation to the authors for a permeable sphere moving under high Reynolds number regime is proposed by Masliyah and Polikar (1980). With/~ ranging from 15 to 33 and Reynolds number from 0.2 to 120, the following equations based on experimental data were proposed 240 CD = ~ e [1 + 0.1315Re ~°.2-°°5~]
543
The application of equation (7) to floc system in high Reynolds number range is also challenged by Masliyah and Polikar's experiment. However, due to the small fl range been investigated in Masliyah and Polikar's work (Masliyah and Polikar, 1980), the general correlations for CD, and also fL for a permeable floc under high Reynolds number regime is actually lack. EXPERIMENTALSECTIONS Activated sludge samples were taken from wastewater treatment plant in Neili Bread Plant, President Enterprise Co., Taoyuan, Taiwan, and were tested within 2 h after sampling. The dried solid density was measured using a pycnometer. The results were all approx. 1450 kg/m3. A glass cylinder (6 cm in dia. and 50 cm in height), sectioned on a side with an attaching plane view glass, was used for free-settling test. Before testing, the sludge was stirred for 10 rain by a mechanical stirrer with a rotational speed of 250 r.p.m, to release most of the memory effects. A JVC camera equipped with a close-up lens was used to record the floc diameter (normal to the vertical direction) and the terminal velocity data. When floc diameter is larger than 1 mm, the maximum error for diameter or velocity measurement is 0.1 mm or 0.2 mm/s, respectively. When floc is less than 100 #m, the error for diameter measurement is smaller than 10 #m. The freeze/thaw treatment was conducted by placing sludge samples into a freezer (-15°C). After 12 h of freezing, the frozen samples were thawed for another 12 h under room temperature. The raw and treated sludges were referred to as the "original sludges" and the "frozen sludges", respectively. Drying test was employed for measuring bound water contents in sludges (Tsang and Vesilind, 1990; Lee, 1994a). The drying temperature was kept at 42°C and an electronic balance connecting to a personal computer was automatically recording the sample weight during an experiment. A typical test time was 24 h for the system to attain equilibrium state. The residue water content remained in the cake was determined by further drying the cake at 102°C. The samples utilised in a drying test was prepared by first vacuum filtering the sludges into a wet cake to remove most of the free moisture, and then the wet cake was shaped into a fixed disk with thickness 1 mm and area 10-2 m2. The sample weight was kept approx. 11 g. RESULTS AND DISCUSSION
(8a) General
for 0.1 < Re < 7 240 CD = ~ [1 + 0.0853Re o°93- 0~05~.)]
(8b)
for7
A total of 1385 floes are examined. The terminal velocity vs floc diameter data are summarised in Fig. 1. The solid and open symbols represent respectively the data for original and frozen sludges. Floc diameter ranges from 30 #m to about 1.2 era. The corresponding Reynolds number ranges from 0.0112 to 115 for the original sludges, and from 0.0114 to 188 for the frozen sludges. The upper limit of floe diameter (and also the Reynolds number) studied is much larger than most previous investigations. The data in Fig. 1 approximately exhibit a powerlaw relationship as v oc d °.7-°,s over the whole data range. The exponent for an impermeable sphere
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Fig. 1. Floc terminal velocity vs diameter data. Close symbols are for original sludges; open symbols are for frozen sludges. is 2.0 in Stokes' regime, gradually decreases with increasing Reynolds number, and approaches 0.5 in Newtonian regime. The smaller-than-two exponent in Fig. 1 for flocs in Stokes' regime (dr < 1 mm) is an index for the fractal nature of the flocs (Li and Ganczarczyk, 1989). The near-constant exponent for larger flocs is abnormal, which will be discussed in details in latter sections. Bound water measured by drying test is around 5 ~ 7 kg/kg dried solid for original sludges, and 3 ~ 4 kg/kg for frozen sludges. Visual and optical observations demonstrate that the frozen sludge floc possesses a more compact structure and a better settleability, which is consistent with Lee and Hsu (1994). In the following sections, the analyses considering the flocs as impermeable (f~ = 1) or permeable (Q < 1) spheres are discussed separately. I m p e r m e a b l e cases (f2 = 1)
Assume the floc is an impermeable sphere, f~ can hence be taken as unity. The effective density vs floc diameter data can be constructed if the expression for drag coefficient is known. Calculation results with CD given by Stokes' law [(equation (5) with K = 24] in Re < 1 region and equation (7) in Re > 1 region are shown in Fig. 2. Clearly floc density decreases with increasing floc diameter, which is a typical feature for a fractal object (Feder, 1988; Li and Ganczarczyk, 1989). The straight lines in Fig. 2 are the best-fitted lines for data with Reynolds number less or larger than unity. The slopes of these straight lines give a measure of the fractal dimension of the flocs (Lee and Hsu,
1994). The best-fitted fractal dimensions are listed in Tables 2-4. Three points are noticeable. First, based on the same floc diameter, after a freeze/thaw treatment, floc density increases by about 2-5 times. Second, when floc Reynolds number is less than unity, the fractal dimension for original sludge (1.27) is less than the frozen sludge (1.69), indicating a more compact structure for the frozen sludge flocs; when Reynolds number is larger than unity, the condition is reversed (1.94 and 2.24) and is opposite to the experimental observations. Third, the fractal dimensions thus determined for both the original and frozen sludges depend on the range of data taken into regression. Take all data into regression analysis gives a fractal dimension of 2.18 for original sludge and 2.04 for frozen sludge. The "two-stage" behaviour in Fig. 2 will be discussed in latter sections. In some previous investigations, equation (5) is assumed a valid correlation for drag coefficient regardless the Reynolds number range employed (Tambo and Watanabe, 1979; Lee and Hsu, 1994). The effective density vs floc diameter plot based on such an assumption is shown in Fig. 3. Roughly speaking, all data can be fitted by a single straight line. No obvious "two-stage" behaviour as shown in Fig. 2 exists. P e r m e a b l e cases (f2 < 1)
Since the dried solid density data are all approx. 1450 kg/m ~, with help of the measured bound water contents, the primary particle density can be estimated as ranging from 1450 kg/m ~ to about
Free-settling test measuring floc density
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[(equation (2)] 1045 kg/m 3 for original sludges or 1070 kg/m 3 for frozen sludges. Another parameter dp is the diameter of primary particles, which is usually not an available quantity for activated sludges. Li and Ganczarczyk (1992) had arbitrarily taken dp as between 1 and 10 #m. In the present work, a range of 1-20/~m is studied to cover most possible range of interest. A program is installed in a PC486 to solve Equation 1 numerically. Not all calculations are converged when various models or parameter sets are assumed, especially when dp is large. Only the convergent results are discussed further. With (pp, dp) = (1450 kg/m 3, 1/~m), the mean floc permeability of frozen sludges calculated by the six models in Table 1 is demonstrated in Fig. 4. Clearly,
floc permeability increases rapidly with increasing floc diameter when floc is small. Within the floc diameter range studied, permeability might change from 10 -17 to 10 -8 m 2. For a specific floc, the k values calculated from various models usually vary within a range of two to three orders of magnitudes. For models assuming a spherical primary particle shape [equations (A), (B) and (C)], Carman-Kozeny model usually gives the highest estimate [which is consistent with Li and Ganczarczyk (1992)], and also the largest data scattering. The permeabilities from Happel or Brinkman model are lower. The results based on the three fibrous models [equation (D), (E) and (F)] are close and are usually located between the three spherical models.
Table 2. Calculated fractal dimension under various conditions for all data Model for k
Equation Equation Equation Equation Equation Equation Equation Equation Equation Equation Equation Equation
(A) (A) (B) (B) (C) (C) (D) (D) (E) (E) (F) (F)
Original sludges
Frozen sludges
App(kg/m~)
dp(izm)
Model for f~
D
R 2b
D
R 2b
450 45 or 70~ 450 45 or 70~ 450 45 or 70i 450 45 or 70~ 450 45 or 70~ 450 45 or 70"
20 l 20 1 20 1 20 I 20 1 20 1
f2 = 1 Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3)
2.25 2.32 2.36 2.35 2.36 2.31 2.36 2.26 2.36 2.66 2.36 2.54 2.36
0.65 0.56 0,58 0.11 0.58 0.57 0.58 0.64 0.58 0.04 0.58 0.25 0.58
2.12 2.16 2.16 2.21 2.16 2.16 2.16 2.14 2.16 2.19 2.16 2,29 2.16
0.87 0.85 0.84 0.55 0.84 0.85 0.84 0.87 0.84 0,81 0.84 0.75 0.84
"App = 45 kg/m 3 for original sludges and App = 70 kg/m 3 for frozen sludges. N2orrelation coefficient (squared).
546
D. J. Lee et al.
Table 3. Calculated fractal dimension under various conditions when Re > 1 Model for k Original sludges Frozen sludges App(kg/m3) dp(/tm) Model for fl D R2b D R2b f~ = 1 1.31 0.8 1.74 0.69 Equation (A) 450 20 Equation (3) 1.29 0.73 1.78 0.65 Equation (A) 45 or 70" 1 Equation (3) 1.42 0.66 1.92 0.53 Equation (B) 450 20 Equation (3) 0.64 0.22 1.48 0.18 Equation (B) 45 or 701 Equation (3) 1.42 0.66 1.92 0.53 Equation (C) 450 20 Equation (3) 1.29 0.74 1.78 0.66 Equation (C) 45 or 70~ 1 Equation (3) 1.42 0.66 1.92 0.53 Equation (D) 450 20 Equation (3) 1.33 0.79 1.79 0.69 Equation (D) 45 or 701 Equation (3) 1.42 0.66 1.92 0.53 Equation (E) 450 20 Equation (3) 0.7 0.21 1.75 0.55 Equation (E) 45 or 70~ 1 Equation (3) 1.42 0.66 1.92 0.53 Equation (F) 450 20 Equation (3) 1.71 0.28 2.35 0.18 Equation (F) 45 or 70" 1 Equation (3) 1.42 0.66 1.93 0.53 "App= 45 kg/m3 for original sludges and App= 70 kg/m3 for frozen sludges, bCorrelation coefficient (squared).
Permeabilities for original sludges calculated by B r i n k m a n model with various p a r a m e t e r sets are s h o w n in Fig. 5. T h e results f r o m o t h e r models are all similar a n d are n o t s h o w n here for brevity. As expected, floc permeability increases with increasing p r i m a r y particle density a n d / o r diameter. Calculations also d e m o n s t r a t e d t h a t based o n the same parameters, a freeze/thaw t r e a t m e n t m i g h t reduce permeability to a b o u t 5-10 times (not s h o w n in the figure). Since the real situation m a y lie o n somewhere o f the p a r a m e t e r space studied, possible e r r o r for floc permeability estimation m i g h t be as high as 1000 times. C a u t i o n m u s t be paid, therefore, to any conclusion d r a w n f r o m the floc permeability inform a t i o n thus obtained. A m o r e direct a n d reliable m e a s u r e m e n t technique is required. W i t h the calculated floc permeability, fl values are d e m o n s t r a t e d in Fig. 6. T h o u g h scattering greatly, still exhibits a clear descending trend w h e n floc diameter is less t h a n a b o u t 0.5 mm. A b o v e this diameter, fl increases with floe diameter. Based o n the same parameters, fl value is raised after a freeze/thaw treatment. However, as stated before, large uncertainty exists due to the possible error in permeability estimation. Li a n d G a n c z a r c z y k (1992) defined a critical value o f 10.9, below w h i c h the floc can be viewed as a permeable floc. In Fig. 6, with (9p, d p ) = (1450 kg/ m 3, 20 # m ) , a b o u t 27.5% for original or 15.2% for
frozen sludge flocs are permeable, which are close to t h a t reported by Li a n d G a n c z a r c z y k (1992) based o n C a r m a n - K o z e n y model. However, w h e n other p a r a m e t e r sets are employed, all flocs become impermeable. T h e calculations show t h a t a large floc ( > 1 m m ) is n o t always more permeable t h a n a small floc. Except for (pp, d p ) = (1450 kg/m 3, 20/~m), all p a r a m e t e r sets give a near-unity f~. W h e n floc becomes larger, or w h e n the floc is treated by a freeze/thaw treatment, f~ increases accordingly. The effective floc density against diameter plot can hence be constructed according to E q u a t i o n 1, as s h o w n in Fig. 7. It is n o t surprised to find t h a t the o b t a i n e d floc density is insensitive to the permeability model or the p a r a m e t e r set applied, due to the high fl (or near-unity W ) values of all flocs examined. The " t w o - s t a g e " b e h a v i o u r observed in Fig. 2 still exists in Fig. 7. The results from o t h e r permeability models are all alike. The best-fitted fractal dimensions are also s u m m a r i s e d in Tables 2-3. N o t e the low regression coefficients o b t a i n e d in equations (B), (E) a n d (F) w h e n d p = 2 0 / l m . Some calculations h a d t a k e n floc shape into considerations. T h o u g h with some d a t a shift, nevertheless, all basic characteristics stated above are the same. Therefore, the a b n o r m a l l y high fractal dimensions o b t a i n e d for large flocs in Fig. 2 c a n n o t
Table 4. Calculated fractal dimension under various conditions when Re > 1
Original sludges Frozen sludges D R 2b D R2b dp(um) Model for tq 2.42 0.39 2.09 0.76 f~= 1 2.46 0.34 2.11 0.74 Equation (A) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (A) 45 or 70' Equation (3) 2.62 0.02 2.12 0.63 Equation (B) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (B) 45 or 70Equation (3) 2.46 0.34 2.11 0.75 Equation (C) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (C) 45 or 70Equation (3) 2.42 0.39 2.l 0.76 Equation (D) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (D) 45 or 70" Equation (3) 2.66 0.06 2.12 0.72 Equation (E) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (E) 45 or 70' Equation (3) 2.52 0.27 2.14 0.73 Equation (F) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (F) 45 or 70" Equation (3) 'App = 45 kg/rn3 for original sludges and App ~ 70 kg/m~ for frozen sludges. ~orrelation coeflieiem (squared). Model for k App(kg/mO
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constant # value (and also a constant floc permeability) was obtained regardless of the floc diameter. From Fig. 6, if only a narrow diameter range is considered, a constant # value can be used to approximate the real situation. This approximation fails, however, when the floc diameter range considered is large.
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Use of free-settling test on floc density estimation A close examination of Fig. 2 and Fig. 3 and 7 (and also the outputs from other permeability models) shows that the drag coefficient expression employed might be the most influencing factor affecting the
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Free-settling test measuring floc density
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floe diameter (m) Fig. 7. Effective floc density vs floc diameter. Brinkman model. Equation (5) with K = 24 for Re < 1 and equation (7) for Re > 1 region. Close symbols and solid lines are for original sludges; open symbols and dashed lines are for frozen sludges. associated f~ value) for permeable sphere under high Reynolds number are actually lack in literature, no conclusive results can be hence obtained from the free-settling test on large flocs. The studies for the drag coefficients, the associated correction factor f~ for nonspherical permeable object in high Reynolds number region are needful. On the other hand, no direct proof against the validity of the free-settling test on flocs with Reynolds number less than unity is found. Since the correlations of drag coefficient and f~ value for a permeable sphere under creeping flow condition have a sound theoretical base, the free-settling test for smaller flocs provides a at least qualitatively valid floc density estimation. Since the density calculations are insensitive to the permeability models applied, due to better convergence character and less data scattering, the Brinkman [model (A)] or Happel's cell models [equations (C) and (D)] with small dp is recommended in floc density estimation. Carman-Kozeny equation is not suggested by the present authors for the much larger data scattering obtained. If the structure for flocs over the whole diameter range does exhibit the same fractal character, the log-log plot for effective density vs floc diameter data should locate on a straight line. Compared with Fig. 2 or 3, the result in Fig. 3, which uses the equations valid only for Stokes' regime to the whole data regime, is a surprising good description warrants some discussions. For an impermeable sphere moving through a medium, boundary layer separation occurs and wake
forms covering the entire rear hemisphere as the Reynolds number is increased beyond the creeping flow condition (McCabe et al., 1985). More energy dissipation results and t h e drag coefficient then departs from the Stokes' law. For a highly porous sphere, however, due to the existence of advection flow, no serious distortion of the streamlines occurs (Chellam and Wiesner, 1993). Boundary layer separation and the after-sphere wake might not happen when Reynolds number exceeds unity, as that for an impermeable sphere. Therefore, the combined Stokes' law and Brinkman correction factor [equation (3)] might be possibly still a valid description for permeable floe moving under higher Reynolds number regime, which results in the straight-line behaviour in Fig. 3. CONCLUSIONS The feasibility of using free-settling test for activated sludge floc density estimation was discussed in the present work. The terminal velocity and diameter data for a total of 1385 flocs, original or treated by a freeze/thaw treatment, were found experimentally. Some usually employed models or correlations for the primary particle density, the drag coefficient, and the correction factor for advection flow through the floc (and also the floc permeability) were examined. The results showed that the floc permeability is a strong function of the permeability model and the parameter set used. Based on the same parameters,
550
D.J. Lee et al.
the permeability increased with increasing floc diameter, or increased after a freeze/thaw treatment. However, large uncertainty existed in such an estimation. The effective floc density, and also the fractal dimension, nevertheless, was insensitive to the floc permeability estimation. The free-settling test for flocs with Reynolds n u m b e r less than unity is believed, to the first approximation, valid for floc density estimation. The abnormal "two-stage" effective floc density vs diameter relationship is caused by the drag coefficient correlations applied. Further studies for drag coefficient and correction factor for a permeable sphere moving under high Reynolds n u m b e r regime are required. A direct and reliable method for permeability measurement is also needful.
Acknowledgements--The authors are grateful to Neili Bread plant, President Enterprise Co., Taoyuan, Taiwan for providing activated sludge samples. This work is supported by National Science Council, R.O.C.
REFERENCES
Andreadakis A. D. (1993) Physical and chemical properties of activated sludge floc. Wat. Res. 27, 1707-1714. Chellam S. and Wiesner M. R. (1993) Fluid mechanics and fractal aggregates. Wat. Res. 27, 1943-1946. Concha F. and Almerdra E. R. (1979) Settling velocities of particulate system, 1. Settling velocities of individual spherical particles. Int. J. Min. Process. 5, 349-367. Dammel E. E. and Schroeder, E. D. (1991) Density of activated sludge solids. Wat. Res. 25, 841-846. Feder J. (1988) Fractals, Chap. 3. Plenum Press, New York. Ganser G. H. (1993) A rational approach to drag prediction of spherical and nonspherical particles. Powder Technol. 77, 143-152. Huang H. (1993) Porosity-size relationship of drilling mud flocs: fractal structure. Clay Clay Miner. 41, 373-379. Jiang Q. and Logan E. B. (1991) Fractal dimensions of aggregates determined from steady-state size distribution. Environ. Sci. Technol. 25, 2031-2038. Kawasaki K., Matsuda A. and Mizukawa Y. (1991) Compression characteristics of excess activated sludges treated by freeze-and-thawing process. 24, 743-748. Knocke W. R., Dishman C. M. and Miller G. F. (1993) Measurement of chemical sludge floc density and implications related to sludge dewatering. Wat, environ. Res. 65, 735-743. Lee D. J. (1994a) Floc structure and bound water content in excess activated sludges. J. Ch. I. Ch. E. 25, 201-207. Lee D. J. (1994b) Measurement of bound water in waste activated sludges: use of the centrifugal settling method. J. Chem. Tech. Biotechnol. 61, 139-144.
Lee D. J. and Hsu Y. H. (1994) Fast freeze/thaw treatment on activated sludge: floc structure and sludge dewaterability. Environ. Sei. Technol. 28, l~a~ 1449. Lee D. J. and Hsu Y. H. (1995) Measurement of Bound water in sludges: a comparative study. Wat. environ, Res. 67, 310-317. Li D. H. and Ganczarczyk J. J. (1987) Stroboscopic determination of settling velocity, size and porosity of activated sludge flocs. War. Res. 21, 257-262. Li D. H. and Ganczarczyk J. J. (1988) Flow through activated sludge flocs. War. Res. 22, 789-792. Li D. H. and Ganczarczyk J. J. (1989) Fractal geometry of particle aggregates generated in water and wastewater treatment process. Environ. Sci. Technol. 23, 1385-1389. Li D, H. and Ganczarczyk J. J. (1990) Structure of activated sludge flocs. Biotechnol. Bioengng 35, 57~5. Li D. H. and Ganczarczyk J. J. (1992) Advective transport in activated sludge flocs, Wat. environ. Res. 64, 236-240. Logan B. E. and Hunt J. R. (1988) Biofloccuation as microbial response to substrate limitation. Biotechnol. Bioengng 31, 92-101. Masliyah J. H. and Polikar M. (1980) Terminal velocities of porous spheres. Can. J. Chem. Engng 58, 299-302. Matsumoto K. and Mori Y. (1975) Settling velocity of floc--new measurement method of floe density. J. Chem. Engng Jap. 8, 143-147. Matsumoto K. and Suganuma A. (1977) Settling velocity of a permeable model floc. Chem. Engng Sci. 32, 445-447. Matsumoto K., Suganuma A. and Kunii D. (1978) Effect of permeability on the settling velocity of an actual floc. Chem. Engng Sci. 33, 1554-1556. Matsumoto K., Suganuma A. and Kunii D. (1980) The effect of cationic polymer on the settling characteristics of activated sludge. Powder Technol. 25, 1-10. McCabe W. L., Smith J. C. and Harriot, P. (1985) Unit Operations of Chemical Engineering, Chap. 7, 4th edn. McGraw-Hill, New York. Michaels A. S. and Bolger J. C. (1962) Settling rates and sediment volumes of focculated kaolin suspensions. Ind. Engng Chem. Fundam. 1, 24-33. Mitani T., Unno H. and Akekata I". (1983) A structure model for activated sludge flocs. Jap. Wat. Res. 6, 65-79 Namer J. and Ganczarczyk J. J. (1993) Settling properties of digested sludge particle aggregates. Wat. Res. 27, 1285-1294. Neale G., Epstein N. and Nader W. (1973) Creeping flow relative to permeable spheres. Chem. Engng Sci. 28, 1865-1874. Pattyjohn E. A. and Christiansen E. B. (1948) Effect of particle-shape on free settling rates of isometric particles. Chem. Engng Prog. 44, 157-172. Rogak S. N. and Flagan R. C. (1990) Stokes drag on self-similar clusters of spheres. J. Coll. Interf. Sci. 134, 206-218. Tambo N. and Watanabe Y. (1979) Physical characteristics of flocs--I. The floc density function and aluminum floc. Wat. Res. 13, 409-419. Tsang K. R. and Vesilind P. A. (1990) Moisture distribution in sludges. War. Sci. Technol. 22, 135-142. Vesilind P. A. (1994) The role of water in sludge dewatering. Wat. environ. Res. 66, 4-11.
Pergamon
0043-1354(95)00229-4
Copyright © 1996ElsevierScienceLtd Printed in Great Britain.All fights reserved 0043-1354/96 $15.00 + 0.00
ON THE FREE-SETTLING TEST FOR ESTIMATING ACTIVATED SLUDGE FLOC DENSITY D. J. LEE *@, G. W. CHEN, Y. C. LIAO and C. C. HSIEH Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 106, Republic of China (First rece&ed August 1994; accepted in revised f o r m October 1995)
A~tract--The feasibility of using flee-settling test for estimating activated sludge floc density was discussed in the present work. Some usually applied models or correlations, such as for the primary particle density, the drag coefficient, the correction factor for advection flow through the floc and the estimation for floc permeability, are examined. The results show that floc permeability depends strongly on the models or parameter sets applied. However, the effective floc density, and also the fractal dimension, is insensitive to the floc permeability estimation, but is strongly dependent on the drag coefficient expression employed. Possible valid experimental range is proposed. Key words--floc density, free-settling test, permeability, fractal dimension, freeze/thaw treatment
INTRODUCTION Floc size and floc density (porosity) are two of the factors most influence the efficiency of many processes involving flocs. It is generally accepted that these two quantities are not mutually independent, but are relating by some empirical relationship, say a power-law type relationship. Various methods have been proposed for measuring the floc density, e.g. isopycnic centrifugation (Dammel and Schroeder, 1991; Knocke et al., 1993), interference microscopy (Andreadakis, 1993), and free settling test (Tambo and Watanabe, 1979; Mitani et al., 1983; Li and Ganczarczyk, 1987; Li and Ganczarczyk, 1989; Li and Ganczarczyk, 1990; Li and Ganczarczyk, 1992; Huang, 1993; Lee, 1994a). Among these tests, free settling test is the most widely employed method in literature because of its simplicity and the low testing cost. The information obtained in a free settling test is the diameter and the terminal velocity for a single floc. Assume the floc is moving steadily in the medium, the force balance equation is used for estimating floc density (and also floc porosity). Based on the constructed floc size/density relationship, a floc has been proposed as a highly porous fractal-like aggregate made of many primary particles (Li and Ganczarczyk, 1989; Li and Ganczarczyk, 1990; Li and Ganczarczyk, 1992; Jiang and Logan, 1991). Fractal dimension is a quantitative measure of how *Author to whom all correspondence should be addressed [Fax: (886) 2 362 3040].
the primary particles occupying the floc interior space. It is found that aggregates generated in water and wastewater treatment processes exhibit a fractal dimension ranging between 1.4 and 2.8 (Li and Ganczarczyk, 1989). Beside the floc diameter and terminal velocity data, the information about several unknowns are required in the force balance equation, e.g. drag coefficient (Huang, 1993), primary particle density (Lee, 1994b), or the correction factor for advection flow (Logan and Hunt, 1988; Li and Ganczarczyk, 1988). However, will be shown latter, not all assumptions made in literature are strictly valid for all experimental range generally applied. The focus of this report is to examine the validity of several usually made assumptions in a free settling test. Activated sludge flocs, original or treated with a freeze/thaw treatment, are used as testing material. Possible valid experimental range is proposed. The requirement for further researches is highlighted. MEASUREMENT OF FLOC DENSITY Force balance equation
In general, the force balance for a floc moving steadily in an infinite medium can be described as follows (Neale et al., 1973; Li and Ganczarczyk, 1992; Huang, 1993) p f - pw _ 1 -- e = 3pwf2CD ~ Pp -- Pw 4g(pp -- pw)df v"
541
(1)
542
D.J. Lee et al.
where Co = dr = e= g = v= pw = p~ = pf = =
drag coefficient, diameter of floc (m), porosity of floe, gravitational acceleration = 9.8m/s 2, terminal velocity of the floc (m/s), the density of water (kg/mS), the dcnsity of primary particle (kg/m3), floc density (kg/mS), the ratio of the resistance experienced by a floc to that of an equivalent solid sphere.
Except floc diamctcr and terminal velocity data which are available in a free-settling test, four u n k n o w n s exist in equation (1) (pp, f~, CD, and e or pf). T o estimate floc porosity or effcctivc density, pp, f/and CD are required. If~) is given in priori, only the information about CD is needed, as done by Mitani et al. (1983) and T a m b o and W a t a n a b e (1979).
Primary particle density
pp is the density of the primary particles comprising the floc. In most studies, pp is assumed to be equal to p,, the dried solid density (Tambo and Watanabe, 1979; Li and Ganczarczyk, 1987, 1992). However, in sludge with a large amount of internal water, the bound water and the solid phase will move together and behave like a particle (Michaels and Bolger, 1962; Kawasaki et al., 199t; Lee, 1994b). In such a case, the primary particle density is a function of bound water content, which complicates the analysis (Lee, 1994b). Since the definition of bound water is still ambiguous, the standard method for estimating the moisture distribution in a sludge is lack (Vesilind, 1994, 1995). Only a possible range for pp is proposed as follows. Since the floc density cannot be larger than the dried solid density, p~ can serve as an upper limit. Considering the associated bound water as a part of a primary particle, the following equation holds:
1 + WB
(2)
P P - UPs+ WB/p '
Model
where Ws is kg bound water per kg dried solid. Equation (2) provides a lower estimate. Factor
For a highly porous sphere moving steadily through an infinite medium under creeping flow condition, factor f~ is provided by Brinkman (and corrected by Debye) as follows (Neale et al., 1973) f~ =
2fl2[1- (tanhfl)/fl] 2fl2 + 311 - (tanhfl)/fl]
where -
d, 2,/;
(4)
is a dimensionless floc diameter and k = floc permeability (mS). The validity of equation (3) had been experimentally verified by Matsumoto and Suganuma (1977). A direct application of equation (3), nevertheless, requires a knowledge about floc permeability, whose evaluation is usually based on permeability models. Six typical models which are generally accepted in literature are listed in Table I. All equations are in the form of k = ~ × f(e), wheref(e) is a function of floc porosity, and dp is the characteristic length for the primary particles, both are unknowns in a free settling test. Matsumoto et al. (1978) had employed Davies correlation for estimating the floc permeability. Li and Ganczarczyk (1992) had compared the permeabilities calculated from Carman-Kozeny equation and Davies correlation. Large deviation occurs when different model or parameter dp are applied. Huang (1993) employed Brinkman model on permeability estimation and concluded from his data that the calculated fractal dimension will not be affected when the effects of advection flow is considered. Rogak and Flagan (1990) also proposed an expression for permeability based on the fractal nature of floe. Chellam and Wiesner (1993) had examined Rogak and Flagan's model. Beside the
Table 1. Permeabilitymodelsemployedin this work" Primary particle shape Permeability function
Equation
Brinkman
Sphere
k= ~22 x[3+ ~ - c - 3 l ~ 8 - e -3]
Carman-Kozeny
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k
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k= ~
x 33 - 4"573++4'5F52' s ,-
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(E)
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ea
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2 - lnRep x 4 - lnRe,
3~6
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'The symbol dp ~ primary particlediameter(m); ~b = I-e = solidfractionof floe;7 ~= ~t/s;So = specific surface area of the primary particle = 6/dp(m-~);Rep = dpp,v/p.e ~ the Reynolds Number based on the primary particleand internalflow velocity.
Free-settling test measuring floc density information about the primary particles themselves, the way these particles occupying the floc space is also required in their model. Due to too many quantities unavailable, Rogak and Flagan's model is not examined in the present work. D r a g coefficient
Drag coefficient is a function of Reynolds number and floc sphericity (Tambo and Watanabe, 1979; Namer and Ganczarczyk, 1993). The effect of particle shape on Co can be found in Pattyjohn and Christiansen (1948) and Ganser (1993). A modified Stokes' law taking floc shape into account is expressed as follows
cD =
K Re
(5)
where K is a constant depending on floc sphericity. Tambo and Watanabe (1979) assumed ~ = 1 and K = 45 in equation (5), equation (1) then reads Apf = p f -
34#w V
pw -
gd~f
(6)
where /z, is water viscosity. Various studies had applied equation (6) or its equivalent form for constructing floc size/density relationship. A good review can be found in Huang (1993). Equation (5) might fail in high Reynolds number regime (e.g. Re > 1). For an impermeable sphere moving steadily with Reynolds number ranging from 1 to 1000, the following expression is suggested by Concha and Almerdra (1979) 9.06 ~2
CD = 0.28(1 + ~
j.
(7)
The only available correlation to the authors for a permeable sphere moving under high Reynolds number regime is proposed by Masliyah and Polikar (1980). With/~ ranging from 15 to 33 and Reynolds number from 0.2 to 120, the following equations based on experimental data were proposed 240 CD = ~ e [1 + 0.1315Re ~°.2-°°5~]
543
The application of equation (7) to floc system in high Reynolds number range is also challenged by Masliyah and Polikar's experiment. However, due to the small fl range been investigated in Masliyah and Polikar's work (Masliyah and Polikar, 1980), the general correlations for CD, and also fL for a permeable floc under high Reynolds number regime is actually lack. EXPERIMENTALSECTIONS Activated sludge samples were taken from wastewater treatment plant in Neili Bread Plant, President Enterprise Co., Taoyuan, Taiwan, and were tested within 2 h after sampling. The dried solid density was measured using a pycnometer. The results were all approx. 1450 kg/m3. A glass cylinder (6 cm in dia. and 50 cm in height), sectioned on a side with an attaching plane view glass, was used for free-settling test. Before testing, the sludge was stirred for 10 rain by a mechanical stirrer with a rotational speed of 250 r.p.m, to release most of the memory effects. A JVC camera equipped with a close-up lens was used to record the floc diameter (normal to the vertical direction) and the terminal velocity data. When floc diameter is larger than 1 mm, the maximum error for diameter or velocity measurement is 0.1 mm or 0.2 mm/s, respectively. When floc is less than 100 #m, the error for diameter measurement is smaller than 10 #m. The freeze/thaw treatment was conducted by placing sludge samples into a freezer (-15°C). After 12 h of freezing, the frozen samples were thawed for another 12 h under room temperature. The raw and treated sludges were referred to as the "original sludges" and the "frozen sludges", respectively. Drying test was employed for measuring bound water contents in sludges (Tsang and Vesilind, 1990; Lee, 1994a). The drying temperature was kept at 42°C and an electronic balance connecting to a personal computer was automatically recording the sample weight during an experiment. A typical test time was 24 h for the system to attain equilibrium state. The residue water content remained in the cake was determined by further drying the cake at 102°C. The samples utilised in a drying test was prepared by first vacuum filtering the sludges into a wet cake to remove most of the free moisture, and then the wet cake was shaped into a fixed disk with thickness 1 mm and area 10-2 m2. The sample weight was kept approx. 11 g. RESULTS AND DISCUSSION
(8a) General
for 0.1 < Re < 7 240 CD = ~ [1 + 0.0853Re o°93- 0~05~.)]
(8b)
for7
A total of 1385 floes are examined. The terminal velocity vs floc diameter data are summarised in Fig. 1. The solid and open symbols represent respectively the data for original and frozen sludges. Floc diameter ranges from 30 #m to about 1.2 era. The corresponding Reynolds number ranges from 0.0112 to 115 for the original sludges, and from 0.0114 to 188 for the frozen sludges. The upper limit of floe diameter (and also the Reynolds number) studied is much larger than most previous investigations. The data in Fig. 1 approximately exhibit a powerlaw relationship as v oc d °.7-°,s over the whole data range. The exponent for an impermeable sphere
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Assume the floc is an impermeable sphere, f~ can hence be taken as unity. The effective density vs floc diameter data can be constructed if the expression for drag coefficient is known. Calculation results with CD given by Stokes' law [(equation (5) with K = 24] in Re < 1 region and equation (7) in Re > 1 region are shown in Fig. 2. Clearly floc density decreases with increasing floc diameter, which is a typical feature for a fractal object (Feder, 1988; Li and Ganczarczyk, 1989). The straight lines in Fig. 2 are the best-fitted lines for data with Reynolds number less or larger than unity. The slopes of these straight lines give a measure of the fractal dimension of the flocs (Lee and Hsu,
1994). The best-fitted fractal dimensions are listed in Tables 2-4. Three points are noticeable. First, based on the same floc diameter, after a freeze/thaw treatment, floc density increases by about 2-5 times. Second, when floc Reynolds number is less than unity, the fractal dimension for original sludge (1.27) is less than the frozen sludge (1.69), indicating a more compact structure for the frozen sludge flocs; when Reynolds number is larger than unity, the condition is reversed (1.94 and 2.24) and is opposite to the experimental observations. Third, the fractal dimensions thus determined for both the original and frozen sludges depend on the range of data taken into regression. Take all data into regression analysis gives a fractal dimension of 2.18 for original sludge and 2.04 for frozen sludge. The "two-stage" behaviour in Fig. 2 will be discussed in latter sections. In some previous investigations, equation (5) is assumed a valid correlation for drag coefficient regardless the Reynolds number range employed (Tambo and Watanabe, 1979; Lee and Hsu, 1994). The effective density vs floc diameter plot based on such an assumption is shown in Fig. 3. Roughly speaking, all data can be fitted by a single straight line. No obvious "two-stage" behaviour as shown in Fig. 2 exists. P e r m e a b l e cases (f2 < 1)
Since the dried solid density data are all approx. 1450 kg/m ~, with help of the measured bound water contents, the primary particle density can be estimated as ranging from 1450 kg/m ~ to about
Free-settling test measuring floc density
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df (m) Fig. 2. Effective floc density vs floc diameter. ~ -- 1, equation (5) with K = 24 for Re< 1 and equation (7) for Re > 1 region. Closed symbols and solid lines are for original sludges; open symbols and dashed lines are for frozen sludges.
[(equation (2)] 1045 kg/m 3 for original sludges or 1070 kg/m 3 for frozen sludges. Another parameter dp is the diameter of primary particles, which is usually not an available quantity for activated sludges. Li and Ganczarczyk (1992) had arbitrarily taken dp as between 1 and 10 #m. In the present work, a range of 1-20/~m is studied to cover most possible range of interest. A program is installed in a PC486 to solve Equation 1 numerically. Not all calculations are converged when various models or parameter sets are assumed, especially when dp is large. Only the convergent results are discussed further. With (pp, dp) = (1450 kg/m 3, 1/~m), the mean floc permeability of frozen sludges calculated by the six models in Table 1 is demonstrated in Fig. 4. Clearly,
floc permeability increases rapidly with increasing floc diameter when floc is small. Within the floc diameter range studied, permeability might change from 10 -17 to 10 -8 m 2. For a specific floc, the k values calculated from various models usually vary within a range of two to three orders of magnitudes. For models assuming a spherical primary particle shape [equations (A), (B) and (C)], Carman-Kozeny model usually gives the highest estimate [which is consistent with Li and Ganczarczyk (1992)], and also the largest data scattering. The permeabilities from Happel or Brinkman model are lower. The results based on the three fibrous models [equation (D), (E) and (F)] are close and are usually located between the three spherical models.
Table 2. Calculated fractal dimension under various conditions for all data Model for k
Equation Equation Equation Equation Equation Equation Equation Equation Equation Equation Equation Equation
(A) (A) (B) (B) (C) (C) (D) (D) (E) (E) (F) (F)
Original sludges
Frozen sludges
App(kg/m~)
dp(izm)
Model for f~
D
R 2b
D
R 2b
450 45 or 70~ 450 45 or 70~ 450 45 or 70i 450 45 or 70~ 450 45 or 70~ 450 45 or 70"
20 l 20 1 20 1 20 I 20 1 20 1
f2 = 1 Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3) Equation (3)
2.25 2.32 2.36 2.35 2.36 2.31 2.36 2.26 2.36 2.66 2.36 2.54 2.36
0.65 0.56 0,58 0.11 0.58 0.57 0.58 0.64 0.58 0.04 0.58 0.25 0.58
2.12 2.16 2.16 2.21 2.16 2.16 2.16 2.14 2.16 2.19 2.16 2,29 2.16
0.87 0.85 0.84 0.55 0.84 0.85 0.84 0.87 0.84 0,81 0.84 0.75 0.84
"App = 45 kg/m 3 for original sludges and App = 70 kg/m 3 for frozen sludges. N2orrelation coefficient (squared).
546
D. J. Lee et al.
Table 3. Calculated fractal dimension under various conditions when Re > 1 Model for k Original sludges Frozen sludges App(kg/m3) dp(/tm) Model for fl D R2b D R2b f~ = 1 1.31 0.8 1.74 0.69 Equation (A) 450 20 Equation (3) 1.29 0.73 1.78 0.65 Equation (A) 45 or 70" 1 Equation (3) 1.42 0.66 1.92 0.53 Equation (B) 450 20 Equation (3) 0.64 0.22 1.48 0.18 Equation (B) 45 or 701 Equation (3) 1.42 0.66 1.92 0.53 Equation (C) 450 20 Equation (3) 1.29 0.74 1.78 0.66 Equation (C) 45 or 70~ 1 Equation (3) 1.42 0.66 1.92 0.53 Equation (D) 450 20 Equation (3) 1.33 0.79 1.79 0.69 Equation (D) 45 or 701 Equation (3) 1.42 0.66 1.92 0.53 Equation (E) 450 20 Equation (3) 0.7 0.21 1.75 0.55 Equation (E) 45 or 70~ 1 Equation (3) 1.42 0.66 1.92 0.53 Equation (F) 450 20 Equation (3) 1.71 0.28 2.35 0.18 Equation (F) 45 or 70" 1 Equation (3) 1.42 0.66 1.93 0.53 "App= 45 kg/m3 for original sludges and App= 70 kg/m3 for frozen sludges, bCorrelation coefficient (squared).
Permeabilities for original sludges calculated by B r i n k m a n model with various p a r a m e t e r sets are s h o w n in Fig. 5. T h e results f r o m o t h e r models are all similar a n d are n o t s h o w n here for brevity. As expected, floc permeability increases with increasing p r i m a r y particle density a n d / o r diameter. Calculations also d e m o n s t r a t e d t h a t based o n the same parameters, a freeze/thaw t r e a t m e n t m i g h t reduce permeability to a b o u t 5-10 times (not s h o w n in the figure). Since the real situation m a y lie o n somewhere o f the p a r a m e t e r space studied, possible e r r o r for floc permeability estimation m i g h t be as high as 1000 times. C a u t i o n m u s t be paid, therefore, to any conclusion d r a w n f r o m the floc permeability inform a t i o n thus obtained. A m o r e direct a n d reliable m e a s u r e m e n t technique is required. W i t h the calculated floc permeability, fl values are d e m o n s t r a t e d in Fig. 6. T h o u g h scattering greatly, still exhibits a clear descending trend w h e n floc diameter is less t h a n a b o u t 0.5 mm. A b o v e this diameter, fl increases with floe diameter. Based o n the same parameters, fl value is raised after a freeze/thaw treatment. However, as stated before, large uncertainty exists due to the possible error in permeability estimation. Li a n d G a n c z a r c z y k (1992) defined a critical value o f 10.9, below w h i c h the floc can be viewed as a permeable floc. In Fig. 6, with (9p, d p ) = (1450 kg/ m 3, 20 # m ) , a b o u t 27.5% for original or 15.2% for
frozen sludge flocs are permeable, which are close to t h a t reported by Li a n d G a n c z a r c z y k (1992) based o n C a r m a n - K o z e n y model. However, w h e n other p a r a m e t e r sets are employed, all flocs become impermeable. T h e calculations show t h a t a large floc ( > 1 m m ) is n o t always more permeable t h a n a small floc. Except for (pp, d p ) = (1450 kg/m 3, 20/~m), all p a r a m e t e r sets give a near-unity f~. W h e n floc becomes larger, or w h e n the floc is treated by a freeze/thaw treatment, f~ increases accordingly. The effective floc density against diameter plot can hence be constructed according to E q u a t i o n 1, as s h o w n in Fig. 7. It is n o t surprised to find t h a t the o b t a i n e d floc density is insensitive to the permeability model or the p a r a m e t e r set applied, due to the high fl (or near-unity W ) values of all flocs examined. The " t w o - s t a g e " b e h a v i o u r observed in Fig. 2 still exists in Fig. 7. The results from o t h e r permeability models are all alike. The best-fitted fractal dimensions are also s u m m a r i s e d in Tables 2-3. N o t e the low regression coefficients o b t a i n e d in equations (B), (E) a n d (F) w h e n d p = 2 0 / l m . Some calculations h a d t a k e n floc shape into considerations. T h o u g h with some d a t a shift, nevertheless, all basic characteristics stated above are the same. Therefore, the a b n o r m a l l y high fractal dimensions o b t a i n e d for large flocs in Fig. 2 c a n n o t
Table 4. Calculated fractal dimension under various conditions when Re > 1
Original sludges Frozen sludges D R 2b D R2b dp(um) Model for tq 2.42 0.39 2.09 0.76 f~= 1 2.46 0.34 2.11 0.74 Equation (A) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (A) 45 or 70' Equation (3) 2.62 0.02 2.12 0.63 Equation (B) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (B) 45 or 70Equation (3) 2.46 0.34 2.11 0.75 Equation (C) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (C) 45 or 70Equation (3) 2.42 0.39 2.l 0.76 Equation (D) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (D) 45 or 70" Equation (3) 2.66 0.06 2.12 0.72 Equation (E) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (E) 45 or 70' Equation (3) 2.52 0.27 2.14 0.73 Equation (F) 450 20 Equation (3) 2.44 0.38 2.09 0.76 Equation (F) 45 or 70" Equation (3) 'App = 45 kg/rn3 for original sludges and App ~ 70 kg/m~ for frozen sludges. ~orrelation coeflieiem (squared). Model for k App(kg/mO
Free-settling test measuring floc density
547
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o
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•
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°
o
8o~ • o
lOO.O
~..~a o~ ;.;.
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•
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1.0
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o
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0.1
° I
[
I
1 .e-4
1 .e-3
1 .e-2
df (m)
Fig. 3. Effective floc density vs floc diameter, f~ = 1, equation (5) with K = 24 for all data range. Closed symbols and solid line are for original sludges; open symbols and dashed line are for frozen sludges. be explained by the effects of advection flow or of the floc shape. An expression between the floc settling velocity, floe density and diameter had been proposed in Matsumoto and Mori (1975) and had been employed in Matsumoto et al. (1980). Since the diameter range studied in their work was narrow (0.5-2.0 mm), a
constant # value (and also a constant floc permeability) was obtained regardless of the floc diameter. From Fig. 6, if only a narrow diameter range is considered, a constant # value can be used to approximate the real situation. This approximation fails, however, when the floc diameter range considered is large.
1 .e-8 /
1 .e-9
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J
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/
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E _~ 1.e-12~
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equation (A) equation (B)
~- 1 . e - 1 4 .
--
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--
equation (C) . . . . . . equation (13) . . . . . . . . . . . . . . .
1.e-151.e-16-
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. . . . . . . .
equation (F)
. . . . . . . .
1.e-17 I
I
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1 .e-4
1 .e-3
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df (m) Fig. 4. Floc permeability vs floc diameter (p. dp) = (1450 kg/m3, 1 mm). Frozen sludges. WR
30/3---E
548
D.J. Lee et al. I
1 .e-7
I
I
•
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1
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1 .e-18 1 .e-4
1 .e-3
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Fig. 5. Floc permeability vs floc diameter. Brinkman model. Closed symbols are for original sludges; open symbols are for frozen sludges. size-density relationship. From equation (2) and data shown in Fig. 1, if Q is close to unity, effective floc density is approximately proportional to CD • ~.~.6. The log-log plot for effective density against floc diameter is therefore strongly dependent on the shape of CD. Since the drag coefficient expression (and the
Use of free-settling test on floc density estimation A close examination of Fig. 2 and Fig. 3 and 7 (and also the outputs from other permeability models) shows that the drag coefficient expression employed might be the most influencing factor affecting the
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Fig. 6. Dimensionless group fl vs floc diameter. Briakman model. Critical fl value is set as 10.9. Closed symbols are for original sludges; open symbols are for frozen sludges.
Free-settling test measuring floc density
549
1000.0
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~ o°
.o ~ .oO~ ! • 100.0
~o o ~ ' o~ o
oo o
•
Original sludges Re>l
•
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o
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o
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, I
oo
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~
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.
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.
,
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r 1 .e-4
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i
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i 1.e-2
floe diameter (m) Fig. 7. Effective floc density vs floc diameter. Brinkman model. Equation (5) with K = 24 for Re < 1 and equation (7) for Re > 1 region. Close symbols and solid lines are for original sludges; open symbols and dashed lines are for frozen sludges. associated f~ value) for permeable sphere under high Reynolds number are actually lack in literature, no conclusive results can be hence obtained from the free-settling test on large flocs. The studies for the drag coefficients, the associated correction factor f~ for nonspherical permeable object in high Reynolds number region are needful. On the other hand, no direct proof against the validity of the free-settling test on flocs with Reynolds number less than unity is found. Since the correlations of drag coefficient and f~ value for a permeable sphere under creeping flow condition have a sound theoretical base, the free-settling test for smaller flocs provides a at least qualitatively valid floc density estimation. Since the density calculations are insensitive to the permeability models applied, due to better convergence character and less data scattering, the Brinkman [model (A)] or Happel's cell models [equations (C) and (D)] with small dp is recommended in floc density estimation. Carman-Kozeny equation is not suggested by the present authors for the much larger data scattering obtained. If the structure for flocs over the whole diameter range does exhibit the same fractal character, the log-log plot for effective density vs floc diameter data should locate on a straight line. Compared with Fig. 2 or 3, the result in Fig. 3, which uses the equations valid only for Stokes' regime to the whole data regime, is a surprising good description warrants some discussions. For an impermeable sphere moving through a medium, boundary layer separation occurs and wake
forms covering the entire rear hemisphere as the Reynolds number is increased beyond the creeping flow condition (McCabe et al., 1985). More energy dissipation results and t h e drag coefficient then departs from the Stokes' law. For a highly porous sphere, however, due to the existence of advection flow, no serious distortion of the streamlines occurs (Chellam and Wiesner, 1993). Boundary layer separation and the after-sphere wake might not happen when Reynolds number exceeds unity, as that for an impermeable sphere. Therefore, the combined Stokes' law and Brinkman correction factor [equation (3)] might be possibly still a valid description for permeable floe moving under higher Reynolds number regime, which results in the straight-line behaviour in Fig. 3. CONCLUSIONS The feasibility of using free-settling test for activated sludge floc density estimation was discussed in the present work. The terminal velocity and diameter data for a total of 1385 flocs, original or treated by a freeze/thaw treatment, were found experimentally. Some usually employed models or correlations for the primary particle density, the drag coefficient, and the correction factor for advection flow through the floc (and also the floc permeability) were examined. The results showed that the floc permeability is a strong function of the permeability model and the parameter set used. Based on the same parameters,
550
D.J. Lee et al.
the permeability increased with increasing floc diameter, or increased after a freeze/thaw treatment. However, large uncertainty existed in such an estimation. The effective floc density, and also the fractal dimension, nevertheless, was insensitive to the floc permeability estimation. The free-settling test for flocs with Reynolds n u m b e r less than unity is believed, to the first approximation, valid for floc density estimation. The abnormal "two-stage" effective floc density vs diameter relationship is caused by the drag coefficient correlations applied. Further studies for drag coefficient and correction factor for a permeable sphere moving under high Reynolds n u m b e r regime are required. A direct and reliable method for permeability measurement is also needful.
Acknowledgements--The authors are grateful to Neili Bread plant, President Enterprise Co., Taoyuan, Taiwan for providing activated sludge samples. This work is supported by National Science Council, R.O.C.
REFERENCES
Andreadakis A. D. (1993) Physical and chemical properties of activated sludge floc. Wat. Res. 27, 1707-1714. Chellam S. and Wiesner M. R. (1993) Fluid mechanics and fractal aggregates. Wat. Res. 27, 1943-1946. Concha F. and Almerdra E. R. (1979) Settling velocities of particulate system, 1. Settling velocities of individual spherical particles. Int. J. Min. Process. 5, 349-367. Dammel E. E. and Schroeder, E. D. (1991) Density of activated sludge solids. Wat. Res. 25, 841-846. Feder J. (1988) Fractals, Chap. 3. Plenum Press, New York. Ganser G. H. (1993) A rational approach to drag prediction of spherical and nonspherical particles. Powder Technol. 77, 143-152. Huang H. (1993) Porosity-size relationship of drilling mud flocs: fractal structure. Clay Clay Miner. 41, 373-379. Jiang Q. and Logan E. B. (1991) Fractal dimensions of aggregates determined from steady-state size distribution. Environ. Sci. Technol. 25, 2031-2038. Kawasaki K., Matsuda A. and Mizukawa Y. (1991) Compression characteristics of excess activated sludges treated by freeze-and-thawing process. 24, 743-748. Knocke W. R., Dishman C. M. and Miller G. F. (1993) Measurement of chemical sludge floc density and implications related to sludge dewatering. Wat, environ. Res. 65, 735-743. Lee D. J. (1994a) Floc structure and bound water content in excess activated sludges. J. Ch. I. Ch. E. 25, 201-207. Lee D. J. (1994b) Measurement of bound water in waste activated sludges: use of the centrifugal settling method. J. Chem. Tech. Biotechnol. 61, 139-144.
Lee D. J. and Hsu Y. H. (1994) Fast freeze/thaw treatment on activated sludge: floc structure and sludge dewaterability. Environ. Sei. Technol. 28, l~a~ 1449. Lee D. J. and Hsu Y. H. (1995) Measurement of Bound water in sludges: a comparative study. Wat. environ, Res. 67, 310-317. Li D. H. and Ganczarczyk J. J. (1987) Stroboscopic determination of settling velocity, size and porosity of activated sludge flocs. War. Res. 21, 257-262. Li D. H. and Ganczarczyk J. J. (1988) Flow through activated sludge flocs. War. Res. 22, 789-792. Li D. H. and Ganczarczyk J. J. (1989) Fractal geometry of particle aggregates generated in water and wastewater treatment process. Environ. Sci. Technol. 23, 1385-1389. Li D, H. and Ganczarczyk J. J. (1990) Structure of activated sludge flocs. Biotechnol. Bioengng 35, 57~5. Li D. H. and Ganczarczyk J. J. (1992) Advective transport in activated sludge flocs, Wat. environ. Res. 64, 236-240. Logan B. E. and Hunt J. R. (1988) Biofloccuation as microbial response to substrate limitation. Biotechnol. Bioengng 31, 92-101. Masliyah J. H. and Polikar M. (1980) Terminal velocities of porous spheres. Can. J. Chem. Engng 58, 299-302. Matsumoto K. and Mori Y. (1975) Settling velocity of floc--new measurement method of floe density. J. Chem. Engng Jap. 8, 143-147. Matsumoto K. and Suganuma A. (1977) Settling velocity of a permeable model floc. Chem. Engng Sci. 32, 445-447. Matsumoto K., Suganuma A. and Kunii D. (1978) Effect of permeability on the settling velocity of an actual floc. Chem. Engng Sci. 33, 1554-1556. Matsumoto K., Suganuma A. and Kunii D. (1980) The effect of cationic polymer on the settling characteristics of activated sludge. Powder Technol. 25, 1-10. McCabe W. L., Smith J. C. and Harriot, P. (1985) Unit Operations of Chemical Engineering, Chap. 7, 4th edn. McGraw-Hill, New York. Michaels A. S. and Bolger J. C. (1962) Settling rates and sediment volumes of focculated kaolin suspensions. Ind. Engng Chem. Fundam. 1, 24-33. Mitani T., Unno H. and Akekata I". (1983) A structure model for activated sludge flocs. Jap. Wat. Res. 6, 65-79 Namer J. and Ganczarczyk J. J. (1993) Settling properties of digested sludge particle aggregates. Wat. Res. 27, 1285-1294. Neale G., Epstein N. and Nader W. (1973) Creeping flow relative to permeable spheres. Chem. Engng Sci. 28, 1865-1874. Pattyjohn E. A. and Christiansen E. B. (1948) Effect of particle-shape on free settling rates of isometric particles. Chem. Engng Prog. 44, 157-172. Rogak S. N. and Flagan R. C. (1990) Stokes drag on self-similar clusters of spheres. J. Coll. Interf. Sci. 134, 206-218. Tambo N. and Watanabe Y. (1979) Physical characteristics of flocs--I. The floc density function and aluminum floc. Wat. Res. 13, 409-419. Tsang K. R. and Vesilind P. A. (1990) Moisture distribution in sludges. War. Sci. Technol. 22, 135-142. Vesilind P. A. (1994) The role of water in sludge dewatering. Wat. environ. Res. 66, 4-11.