Ind. Eng. Chem. Res. 1993,32, 1180-1185
1180
Cake Formation in Capillary Suction Apparatus D.J. Lee' Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan, 1061 7, R.O.C.
Y.H. Hsu Department of Chemical Engineering, Yuan-Ze Institute of Technology, Taoyuan, Taiwan, 32026, R.O.C.
The fluid flow through porous media in capillary suction apparatus with cake formation was investigated experimentally and theoretically. Celite, CaCOa, kaolin, and bentonite slurries were used to study the effects of cake formation on the filter paper on capillary suction time (CST). It was found that the liquid saturation under the inner cylinder during experiments would approach a constant value when the wet front radius was large, under which the condition could be taken as a constant-pressure filtration process. The capillary suction pressure versus saturation relation was constructed. A method to estimate the averaged specific resistance from the wet front dynamic data and the liquid invasion volume was proposed. T h e calculation results showed satisfactory agreement with experiments.
Introduction Capillary suction apparatus (CSA) had been widely used since first developed by Gale and Baskerville in 1967 (Wilcox et al., 1987; Dohanyos et al., 1988; Vesilind and Davis, 1988; Lu et al., 1989; King and Forster, 1990). A CSA was composed of two plastic plates, a Whatman No. 17 chromatography paper, a stainless steel cylindrical column, several electrodes serving as the sensors, and a timer. Slurry was poured into the column, and the time the filtrate needed to travel between two concentric circles was called the capillary suction time (CST). Baskerville and Gale (1968) obtained a correlation between the CST and the specific resistance under filtration of slurry and showed that a slurry with a long CST indicated that the cake formed would also have a high specific resistance. In practice, the CSA test was much easier to perform than the conventional filtration process. Therefore, the fluid flow in CSA had attracted some attention in the past. Roughly speaking, there existed two ways of describing the fluid motion in porous media (Nguyen, 1980): the piston-like approach, which treated the liquid invasion as a displacement process, and the diffusion-like approach, which treated the process as a diffusion process with the diffusivity as a saturation-dependent property. For most works appearing in the literature, the analyses were based on the piston-like approach. Nguyen (1980) developed a theory by assuming the liquid moving in the filter paper as a piston-like process. Leu (1981) extended and corrected some errors in the work of Nguyen and proposed the concept of rectangular CSA which was also discussed further in Unno et al. (1983) and Tiller et al. (1990). Ju (1982) studied the effects of particle sedimentation on CST and proposed a two-dimensional analysis to relate the CST and the specific resistance of the filtration cake. Vesilind (1988) used CST as a measure of slurry dewaterability and developed a simple model which showed that the diameter of the watered area depended on W. The parameters of the CSA used by investigators were different from case to case, and the data from various sources were hard to compare (Vesilind and Davis, 1988). Lee and Hsu (1992) studied the fluid flow in CSA using the concept of a diffusion-like approach. By assuming a power law dependence of the diffusivity, the wet front
* To whom correspondence should be addressed.
I 1
1
0 Ro
m , , , 0 Ro
I
r
(0)
I
R(t)
( b)
Figure 1. (a) The slurry was poured into the inner cylinder. The filtrate wet the filter paper andthe liquidsaturationunder the cylinder was SO. (b) When cake formed on the fiiter paper, the SaturationSO would decrease. The saturation profile would be described by the equation in the figure.
radius versus time relation could be described by a cubic algebraicequation which contains no parameters that CSA used. It was shown that when pure liquid was used as the testing substance, the liquid saturation under the inner cylinder SO would be unity; when cake formed on the filter paper, the SO would first decrease and then approach a constant value which was less than unity. Effecta of various liquids and the parameters of CSA were investigated. An expression of a modified CST based on the model was proposed to encounter only the properties of the fluid, which could be used to link the data from various investigations. Though the diffusion-like approach was more realistic than the piston-like approach (Lee and HSU,19921, the method based on the diffusion-like approach to obtain the averaged specific resistance of the cake was lacking. In this paper, a method of using CSA to estimate the specific resistance of a slurry which is based on the diffusion-likeapproach is developed. The capillary suction pressure of the filter paper versus liquid saturation relation is constructed. Various slurries are tested, and the results are compared with the data obtained from the vacuum filtration process.
Analysis The process is schematically shown in Figure 1. When the slurry was injected into the inner cylinder, filtrate would first wet the filter paper under the cylinder and
0888-588519312632-1180$04.00/0 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 1181
V = 7rR; &(1 + 2y + y2)
then spread out. During the process, the cake would form continuously on the paper and the amount of the cake was proportional to the volume of filtrate if no sedimentation occurred. Since the liquid invasion velocity in CSA experiments was relatively slow, pseudo-steady-state approximation could be assumed. It was proposed previously that the liquid saturation profile in the filter paper could be described by the function shown in Figure l b (Lee and HSU,1992). Since the index n was larger than unity (3.6), the shape of the profile would be concave downward and dropped to zero when r R. Therefore, the filter paper outside the wet front would be completely dry, which was consistent with the experimental observations. When fluid was flowing steadily through a porous media (the cake), the pressure drop could be stated as
Y = (R/Ro)- 1 (7) and 6 and e were the thickness and the porosity of the wet filter paper, respectively. It was clear that the liquid volume predicted from eq 6 would only depend on y; i.e., if the wet front radii of two experiments were the same, the liquid invasion volumes would also be the same. In the diffusion-like approach, the liquid invasion volume was (Lee and Hsu, 1992)
Ucde = (l/A)kaavCoVu (1) where aav, V, and p were the averaged specific resistance for the cake, the filtrate volume, and the liquid viscosity, respectively. Other parameters were defined as follows (Leu, 1981):
where
-
and 1 dV u =-(2b) A dt When liquid invaded a porous media, the capillary suction pressure of the media would decrease as the liquid saturation increased. The P, versus s relation could be described as
Pc = f(s) (3) Though the form of f(s) might be very complicated and was not easy to obtain, we could still assume that f(1) = Po
where
V = SoR&27rrsdr
The liquid volume described by eq 8 would depend on both the wet front radius and the liquid saturation SO. Therefore, the wet front radius versus time data alone, which were the only information the conventional CSA tests could provide, were not sufficient to determine the liquid invasion volume. Equation 8 could be used to calculate the liquid saturation so if V and y at fixed time intervals were available. Therefore, besides the wet front dynamic data, the liquid invasion volume was also needed to measure in the CSA experiments. To obtain the superficialvelocity,eq 8 was differentiated with respect to time as 1 dV u = -A dt
(4a)
and
u = d(s,
f(0) = Pcd (4b) where P c d and POwere the capillary suction pressure at s = 0 and 1, respectively. For the water/Whatman No. 17 fiiter paper combination, the Pd was shown fromregressing the experimental data with piston-like flow model to be 14 853 Pa (Leu, 1981). Assuming that the saturation of the filter paper under the inner cylinder was SO and the distribution of the liquid saturation in this portion of paper was uniform, the capillary suction pressure of the filter paper under the inner cylinder could be taken as a constant f(s0). Since the pressure drop needed to drive the liquid through the cake should be provided by the capillary suction pressure of the filter paper under the inner cylinder and the liquid head, the pressure drop across the cake could be stated as (5)
where h was the liquid height in the inner cylinder. Usually, the liquid head was small when compared with the capillary suction pressure and could be neglected safely in the analysis (Lee and Hsu, 1992). In such a case, the pressure drop across the cake would be equal to the capillary suction pressure of the filter paper under the inner cylinder. In the piston-like approach, the liquid invasion volume was equal to the wet filter paper volume times the porosity, i.e.,
(6)
+ G(y)
2)
which was a function of so and the wet front radius, y. The dG(y)/dt in eq 11 could be obtained from conventional CSA experiments, but the rate of change of so, which was also necessary to determine the superficial velocity, was lacking. Lee and Hsu (1992) had shown that when using kaolin slurry in CSA experiments, the liquid saturation SO would first decrease and then approach a constant value. In the region where SO was a constant, dsoldt would vanish and the superficial velocity could be calculated from the wet front radius versus time data alone. When the liquid saturation was kept unchanged, the capillary suction pressure under the cylinder would also remain unchanged. Therefore, by neglecting the liquid head in the inner cylinder, the pressure drop across the cake would be a constant and the condition would be actually a constant-pressure filtration process (Lee and HSU,1992). If the specific resistance was the function of applied pressure difference only,the v2’s should be a linear function of time under constant-pressure filtration. In such a case, if CO did not change significantly during experiments, eq 1 could be integrated as
where C1 was the integration constant.
1182 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993
Therefore, the specificresistance could be obtained from the slope of linear regression oft vs v2 data, which should be more accurate and reproducible than direct differentiation. However,when the specificresistance was affected by the cake clogging and particle migration, direct differentiation was necessary. By combining eqs 3,5, and 12, the following expression could be obtained:
0.7
0.6 0.5
~
-8 where the subscript indicates that the condition was under the constant liquid saturation region. Since the wet front dynamic data and the liquid invasion volume could be obtained in CSA experiments, the remaining problem was to determine the functional form off(s). Direct determination of the dependence of capillary suction pressure on liquid saturation was not an easy task. However, in this work, an alternative approach was used. Since eq 13was valid when liquid saturation s~ was kept unchanged, using slurry with a known specific resistance and concentration in CSA experiments could get the f ( s ) values under various SO'S. If the range of SO'S was wide enough to cover the region of interest, empirical correlation could be used to serve as the working equation. After f(s) was determined, the standard procedure of estimating the specific resistance was as follows. The liquid invasion volume and the wet front dynamic data were recorded simultaneously with the CST. The liquid saturation SO at fixed time intervals was then calculated from eq 8. When the saturation had attained the constant region, the slope of t vs v2 data could be obtained by linear regression. Finally, the specific resistance could be calculated by eq 13 if the specific resistance was the function of pressure difference only. Experimental Section Details of the CSA, the data acquisition system, and the experimental procedures can be found elsewhere (Lee and , I" 1992). A stainless steel cylinder with a radius of 0.535cm was used in this study. Electrodes were installed at locations along and across the grain to serve as sensors. After the device was cleaned and dried, the inner cylinder and the Whatman No. 17 filter paper were positioned and assembled. By injecting a fixed amount of slurry into the cylindrical column, the contact of the liquid with the inner cylinder triggered the timer in the computer. For checking purposes, a JVC V8 camera was used to record the wet front radius and the CST simultaneously. By replaying the tape, the wet front dynamic data could be obtained. The errors in measuring the time and the front radius were estimated to be within 0.01 s and0.5 mm, respectively. The inner cylinder was calibrated and labeled, and the data of time for a fixed amount of water invading the paper were recorded in experiments. The error in measuring the liquid volume was estimated to less than 3 %. A vacuum filtration system was installed. The weight of the filtrate was recorded by an electronic balance, and the data were continuously and automatically sent to a personal computer. The filtration time was also recorded by a timer in the computer. Standard procedures were applied to determine the specific resistance of the cake (Leu, 1981). The vacuum filtration pressure difference used in this study was fixed to be 62 cmHg if not otherwise mentioned. The slurry was prepared by adding a fixed amount of celite, CaC03, kaolin, or bentonite particles into deionized
0.4
0.3 0.2
t
o
O.l nb
I
I
I
0
1
2
3
"
kao5 benl benl bend
a
i
,Cu(OHh
1
5
4
log CST
Figure 2. Experimental results. Ro = 0.535 cm. Celite, 2.85 wt % celite slurry; Cal, 0.74 wt % CaCOs slurry; Ca2,1.75 wt % CaCOs slurry; Ca3,2.71 wt % CaCOs slurry; Ca4,3.32 wt % CaCOa slurry; Ca5,11.62 wt % CaCOs slurry; Ca6,1&86 wt % CaCOs slurry; kaol, 1.6 wt % kaolin slurry; kao2,3.21 wt % kaolin slurry; kao3,3.76 wt 5% kaolin slurry; kao4, 6.46 wt % kaolin slurry; ka05, 14.4 wt % kaolin slurry; benl, 1.26 wt % bentonite slurry; ben2, 1.37 wt % bentonite slurry; ben3,3.12 wt % bentonite slurry; Cu(OH)z, 1.99wt % CU(OH)~ slurry. Table I. Characteristice of the Slurriee Ueed in This
Study
celite CaCOs CaCOa CaCOS CaCOs CaCOa kaolin kaolin kaolin kaolin kaolin bentonite bentonite bentonite
2.85 1.75 2.71 3.32 11.62 13.86 1.60 3.21 3.76 6.46 14.4 1.26 1.37 3.12
30.8 17.9 28.2 34.8 139.3 181.4 16.5 34.4 41.0 76.2 209.8 13.4 14.6 36.5
0.99 0.85 1.00 0.88 1.03 1.08 0.86 0.88 1.08 1.04 1.02 0.94 1.06 0.97
0.48 3.90 1.44 0.67 0.51 0.55 5.20 1.87 3.16 2.75 3.46 3800 4680 3400
6.60 1.56 0.88 0.45 0.57 5.32 2.56 3.14 2.38 2.67 3720 4490 3580
water stirred vigorously with a magnetic stirrer. To prevent particle sedimentation which might distort the experimental resulta (Ju, 1982),the slurry was filtered by a coarse filter plate to remove the large particles. The mass fraction of the resultingfiltrate was then determined by sampling and drying. Since the bentonite slurry was highly compressible, the porosity of the cake was determined from a variable-area filtration cell similar to that described in Murase et al. (1987) and Jen (1991). The porosity under 60 cmHg pressure difference was shown to be around 0.75 and was used as such. The characteristics of slurries used in this study are listed in Table I. Results and Discussion General. Figure 2 shows the experimental results. The data for pure water are also shown in the figure for comparison. It is clear that when cake formed on the filter paper, the time needed for the wet front to travel a fixed distance increased. It is also shown that when more particles were added into the slurry and/or the average specific resistance of the cake increased, the capillary suction time was larger. All the data shown in the log-log
Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 1183 I Cal A Ca2 L, Ca4 benl a bcnl bcn3
I
I
o water
'
o celite @ kaol 0kao2 Q kao3 0 kao4
20
0 1
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3
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Solid line, calculation result for pistonlike approach (eq 6); dashed lines, calculation results for diffusionlike approach(eq 8) for various sovalues. Celite, 2.85%celite slurry; Cal, 0.74wt % CaCOa slurry;Ca2,1.75w t % CaCOs slurry;Ca4,3.32 wt % CaCOS slurry; kaol, 1.6 w t % kaolin slurry; kao2,3.21 w t % kaolin slurry; kao3,3.76w t % kaolin slurry; kao4,6.46w t % kaolin slurry; benl, 1.26 w t % bentonite slurry; ben2,1.37 wt % bentonite slurry; ben3,3.12 w t % bentonite slurry. Figure 3. V/uR026c va y.
Slurry
e
e
e
--
-
a
-
- @ kaol 0
kao2
0 .
- P kao3 0
- a
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kao4 benl bene a ben3 CU(OH~~ 1
a '
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I
plot appear to be straight lines and the intercepts of these lines shifts downward when the specific resistance and/or slurry concentration increases. Take the time needed for the wet front to travel from R = 1.5 cm to R = 2.5 cm as example. The CST data for water, celite (2.85wt %), CaC03 (0.76%),kaolin (3.37%), and bentonite (3.12%) slurries were 20, 21, 27, 47, and 5300 s, respectively, which indicated that the specific resistance of the bentonite slurry was much larger than other slurries. The data for celite slurry were very close to the pure water test, which indicated that the slurry was easy to filter and the specific resistance was low (4.82 X 1010 m/kg). To use the CSA with slurries of still lower specific resistance and slurry concentration would be impractical. It was also clear that for slurry which was
more difficult to filter than the bentonite slurry would be very time-consuming and the CSA lost its superiority. Validity of Diffusion-like Approach. To check the validity of the diffusion-likeapproach, the liquid invasion volume and the correspondingy data are plotted in Figure 3. The dot-dash line is the calculation results for the piston-like approach (eq 6), and the solid lines are the calculation results for the diffusion-like approach (eq 8) with various SO values. It is clear that the results from the piston-like approach seriously overestimated the liquid invasion volume (and also the superficial velocity). The deviation was about 30% when compared with the pure water tests, and was as high as 500% when compared with the bentonite slurries. Taking they = 4 case as an example, the liquid volume calculated from the piston-like approach was 2.25 mL; the experimental results for pure water, celite (2.85 wt %), CaC03 (0.74 w t %), kaolin (3.76 wt %), and bentonite slurry (3.12 wt %) were about 1.65, 1.40, 1.45, 1.20, and 0.45 mL, respectively. The degree of overestimation increased when the specific resistance and/or the slurry concentration increased. However, the data could be well described by the diffusion-likeapproach. The data for pure water test fitted well with the line of SO = 1, which was the upper bound of the liquid invasion volume for a fixed wet front radius. The data of shmy tests could also be fitted well by eq 8 if the SO value (lessthan unity) was properly chosen. Figure 4 shows the calculation results. As shown in the figure, the saturation for incompressible (or slightly compressible)cakes (celite,CaC03, and kaolin) all first decrease and then approach a constant SO, However, for the compressible bentonite cakes, the saturation SO first increases and then approaches a constant value. The SO,..% for celite, CaC03, kaolin, and bentonite slurrieswere 1.0-0.85,0.85-0.75,0.70-0.60, and about 0.30, respectively. The slurry concentration had only a secondary effect on the value. Since the bentonite slurry was the most difficult one to filter among slurries used in this work, it was reasonable that the liquid saturation was also the lowest one among these slurries. It was therefore concluded that the diffusion-like approach was adequate in describing the flow process in CSA. The analysis based on the piston-like approach might overestimate the pressure drop across the cake, and the condition became worse when the slurry concentration and/or the specific resistance of the cake increased. Capillary Suction Pressure-Saturation Curve. In this section, the capillary suction pressure versus liquid saturation relation (P,-s curve) for water/ Whatman No. 17 filter paper is constructed. Figure 5 shows some of the t versus v2 data for kaolin slurries. It is clear that when y is large, all data can be represented by straight lines. The correlation coefficienb of all testa are above 0.99, and for some cases,the coefficient can be as high as 0.999. From the slope data, the slurry concentration, and the specific resistance of the cake, the capillary suction pressure could be calculated from eq 13. The results are shown in Figure 6. From the figure, it is shown that when the liquid saturation decreases from 0.8 to about 0.3, the capillary suction pressure increases from 3000 to around 33 OOO Pa. Various forms of the P,-sorelation could be used to correlate these data. For the sake of simplicity, a simple power form was assumed and the best-fitted result is
.
f(s) = P,(1 - S11.M (14) where Pd was estimated to be 62 200 Pa. The correlation
1184 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993
1
t
5t
.-----.?
,
2
1
Slurry
1
1
0
I
I
I
I
2
3
4
5
2
-12
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2
\
2 -
0
.5
r
eq.1141
5 AP
rn
Slurry
\
3 -
*O
a!
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0
6
Figure 5. t vs v2. kaol, 1.6 w t % kaolin slurry; kao2, 3.21 wt % kaolin slurry; kao3, 3.76 wt % kaolin slurry; kao4,6.46 wt % kaolin slurry; Cu(OH)2, 1.99 wt % Cu(0H)z slurry.
I
0
Q e b 0
a
a
,lo'
9
Pa
Figure 7. Averaged specificreaistancevsapplied pressure difference. 1.99 wt % Cu(0H)z slurry. Solid symbols, vacuum filtration tests; open symbol, CSA test.
I
kaol kao2 kao3 kao4 ka05 benl ben2 ben3
1.0
S Figure 6. Capillary suction pressure vs liquid saturation. Whatman No. 17 chromatographic paper. Ca2,1.75 wt 5% CaCOs slurry; Ca3, 2.71 w t % CaC03 slurry; Ca4, 3.32 w t % CaC03 slurry; Ca5, 11.62 w t % CaCOs slurry; Ca6,13.86 w t % CaCOs slurry; kaol, 1.6 w t % kaolin slurry; kao2,3.21 wt % kaolin slurry; kao3,3.76 wt % kaolin slurry; kao4,6.46 wt % kaolin slurry; kao5,14.4 wt % kaolin slurry; benl, 1.26 wt % bentonite slurry; ben2,1.37 wt % bentonite slurry; ben3, 3.12 w t % bentonite slurry.
coefficient was above 0.97. Other correlation equations had been tested and showed no significant improvement when the complexity of the correlation form increased. The data for celite slurries are not included in Figure 6, since serious sedimentation usually occurred and the specific resistance data scattered greatly for both CSA and vacuum filtration experiments. The Pc-s curve is concave upward, which might introduce a larger error in determining the pressure drop when the liquid saturation was close to unity. In practice, it was better to keep the SO,- value less than about 0.8. The capillary suction pressure at s = 0 obtained in this work was different from that in Leu (1981). The result was not surprising since these two values were obtained from two totally different approaches. Specific Resistance. By combining eqs 13and 14,the average specific resistance of the cake could be stated as
The specific resistances of the slurries used in this study were calculated by eq 15 and are listed in the last column of Table I. It was shown that the calculation results agreed well with the specificresistance obtained from the vacuum Titration process. The mean relative error was about l o % , which was close to the error caused from the individual quality variation between filter papers (Lee and Hsu, 1992). Therefore, if the liquid invasion volume was recorded simultaneously with the CST data, the liquid saturation and the slope could be calculated from eq 8and from linear regression, and the specific resistance could be obtained from eq 15. Compressible Cake. In order to demonstrate the feasibility of using eq 15to calculate the specificresistance of highly compressible cakes, a test with Cu(OH)2 slurry was investigated. The slurry was prepared by adding 50 g of CuSO4 and 18 g of NaOH into deionized water and stirring vigorously for 30 min. The volume of the slurry was adjusted to 1L. To prevent the possible aging effect, fresh slurries were used in this work. The slurry was vacuum filtered with a pressure difference ranging from 17 to 60 cmHg, and the averaged specific resistance was determined according to the method proposed in Leu and Lee (1991). The results are shown in Figure 7. It was shown clearly that the Cu(0H)zslurry was highly compressible and the specific resistance was a strong function of applied pressure difference. The data could be correlated as = aoP" (16) where a0 and m were 8.83 X loBand 0.361, respectively. The unit of P in eq 16 was Pa. The data for using Cu(OH12 slurry in the CSA experiments are shown as the solid symbols in Figure 2. The liquid saturation SO'S calculated by eq 8 are also shown in Figure 4. For the bentonite slurry, the saturation first increased and then approached a constant value (0.58). Therefore, the capillary suction pressure was estimated to be 15 000 Pa. The t versus v2 data are shown in Figure 5. The specific resistance could then be calculated from eq 15 as about 2.7 X lo1' m/kg. The result is shown as the open symbol in Figure 7. It is clear that the specific aav
Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 1186 resistance fitted well with the correlation equation from filtration experiments.
Conclusions The fluid flow process in the capillary suction apparatus with cake formation was studied experimentally and theoretically. Using celite, CaC03, kaolin, and bentonite slurries, the wet front dynamic data and the liquid invasion volume were measured simultaneously. The following conclusions were obtained in this study: 1. Capillary suction time would increase when cake formed in CSA. For fixed sampling locations, CST increased as the increase of slurry concentration and/or the specific resistance of the cake. 2. The liquid invasion volume obtained from the pistonlike approach was overestimated. The deviation was about 30% for pure water testa, and was as high as 500% for bentonite slurrytests. It was found that the liquid invasion volume could be described by the diffusion-like approach with properly chosen liquid saturation under the inner cylinder. 3. When the wet front was large, the SO value would attain a constant value. In the region of constant SO, the fluid flow acrossthe cake was similar to a constant-pressure filtration process. The capillary suction pressure versus saturation relation was constructed. The procedure to estimate the specific resistance of the cake from the wet front dynamic data and the liquid invasion volume was proposed. Calculation results agreed well the experiments. Acknowledgment The authors are grateful to the National Science Council, ROC, for supporting Project NSC82-0402-E002-346. Nomenclature A = cross section area, m2 Co = solid concentration, kg/m3 C1 = integration constant, s f ( s ) = function defined in eq 3 G ( y ) = function defined in eq 9 g = gravitation acceleration, m/s2 h = liquid height in the inner cylinder, m L = cake thickness, m m = index in eq 16 n = index P = pressure difference, Pa P, = capillary suction pressure, Pa hPds = pressure drop across the cake, Pa Pd = capillary suction pressure at s = 0, Pa PO= capillary suction pressure at s = 1,Pa Ro = cylinder inner radius, m R = equivalent radius of the front, m s = liquid Saturation SO = liquid saturation under the inner cylinder t = time, s V = liquid invasion volume, m3
u = superficial velocity, mVm2
w = mass fraction of the slurry y==r+-l Greek Letters a, = averaged specific resistance, m/kg
= fitting constant in eq 16 6 = wet filter paper thickness, m B = wet filter paper porosity p = liquid viscosity, Pes p~ = liquid density, kg/m3 pr = ratio of solid density to liquid density a0
Literature Cited Baskerville, R. C.; Gale, R. S., A Simple Automatic Instrument for DeterminingtheFilterability ofthe Sewage Sludges. WaterPollut. Control, 1968,67, 233-241. Dohanyos, M.; Grau, P.; Sedlacek,M. Interpretation of Dewaterability Measurements by Capillary Suction Time (CST). Water Sci. Technol. 1988,20, 266. Gale, R. 5.; Baakerville, R. C. Capillary Suction Method for Determination of the Filtration Properties of a Solid-Liquid Suspension. Chem. Znd. 1967,9,355-366. King, R. 0.;Forster, C. F. Effecta of Sonication on Activated Sludge. Enzyme Microb. Technol. 1990,12,109. Jen, 2. H. Computer-Aided Constant Preseure Filtration Tests. Maater Thesis. NationalTaiwanUniversity,Taipei, Taiwan, 1991. Ju, S. J., A Study on the Batch Gravitational Filtration. Master Thesis, National Taiwan University, Taipei, Taiwan, 1982. Lee, D. J.; HSU,Y. H. Fluid Flow in Capillary Suction Apparatus. Znd. Eng. Chem. Res. 1992,31, 2379-2385. Leu, W. F. Cake Filtration. Ph.D. Dissertation, University of Houston, Houston, TX,1981. Leu, W. F.; Lee, S. W. The Characteristics of the Cu(OH)2 Slurry Dewaterability. Proceedings of the Sympo8ium on Transport Phenomena and Applications; Chinese Institute of Chemical Engineers: Taipei, Taiwan, 1991. Lu, W. M.; Ju, S. J.; Chang, U. J. Using CST to Measure Particle Characteristic Diameter and the SpecificResistance. Proceedings of the Symposium on Transport Phenomena and Applications; Chinese Institute of Chemical Engineers: Taipei, Taiwan, 1989. Murase, T.; Iritani, E.; Cho, J. H. Determination of Filtration Characteristics Due to Sudden Reduction in Filtration Area of Filter Cake Surface. J. Chem. Eng. Jpn. 1987,20,246. Nguyen, C. T. A Model for the Capillary Suction Apparatus. Master Thesis, University of Houston, Houston, TX, 1980. Tiller, F. M.; Shen, Y. L.; Adin, A. Capillary Suction Theory for Rectangular Cells. Res. J. Water Pollut. Control Fed. 1990,62, 130.
Unno, H.; Muraiso, H.; Akehata, T., Theoretical and Experimental Study of Factors Affecting Capillary Suction Time (CST). Water Res. 1983, 17, 149. Vesilind, P.A. Capillary Suction Time as a Fundamental Measure of Sludge Dewaterability, Res. J. Water Pollut. Control Fed. 1988, 60, 215. Vesilind, P. A.; Davis, H. A. Using the Capillary Suction Time Device for Characterizing Sludge Dewaterability. Water Sci. Technol. 1988, 20, 203.
Wilcox, R. D.; Fisk, Jr., J. V.; Corbett, G. E. Filtration Method Characterizes Dispersive Properties of Shales. SPE Drilling Eng. 1987, 2, 149.
Received for review September 9, 1992 Revised manuscript received February 22, 1993 Accepted March 1,1993
