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A model for filter cake formation on geotextiles: Experiments
Geotextiles and Geomembranes 31 (2012) 62e68
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Geotextiles and Geomembranes journal homepage: www.elsevier.com/locate/geotexmem
A model for filter cake formation on geotextiles: Experiments J. Richard Weggel a, *, Jacob Dortch b a b
Professor Emeritus, Civil, Architectural & Environmental Engineering, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA Civil Engineer, First Capital Engineering, 48 South Richland Ave. York, PA, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 March 2011 Received in revised form 3 October 2011 Accepted 18 October 2011 Available online 21 November 2011
The results of 34 experiments of flow through and filter cake sediment accumulation on a geotextile are presented to verify a theoretical numerical model presented in a companion paper by Weggel and Ward (in this issue). Two low permittivity geotextiles (j¼0.05 s1) and three sediments were investigated. The three sediments were a well-sorted Ottawa sand, a fine sand and a well-graded, light weight plastic material. The sediments were suspended in a 1.37 m-long Plexiglas tube and allowed to settle on the geotextile. The time variation of the rate of flow through the geotextile/sediment system was measured and compared with the rate predicted by theory. Comparison between the numerical model and experiments is very good. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Large geotextile bags are increasingly being used to dewater dredged material and mine tailings (Weggel, et al., 2010). As the water passes through the geotextile, solids in the slurry being dewatered are retained on the surface of the geotextile and, as the thickness of the accumulating filter cake increases, the dewatering rate decreases. Thus, as time passes, the dewatering efficiency of the system decreases. The rate of flow through the filter cake depends on the permittivity of the geotextile, the permeability of the filter cake and its thickness. At the start of the dewatering process the permittivity of the geotextile can be important; however, as the filter cake’s thickness increases, the permeability of the filter cake controls the dewatering rate. Weggel and Ward (in this issue) presented a numerical model that describes the accumulation of filter cake on a geotextile. The equations were solved numerically to give the discharge through the geotextilefilter cake layers, the decrease in head, the cumulative discharge and the thickness of the filter cake, all as functions of time. In addition, the distribution of sediment grain size at various layers in the filter cake could be determined given the size distribution of the sediment in suspension at the start of the process. The present paper describes a series of experiments to establish the validity of the numerical theory. Thirty-four
* Corresponding author. fax: þ1 (215) 576 6307. E-mail addresses: [email protected] (J.R. Weggel), [email protected] (J. Dortch). 0266-1144/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2011.10.003
experiments were conducted with two geotextiles and three different sediments. The geotextiles used were Propex 135ST (Geotextile A) and Propex 315ST (Geotextile B), both with permittivities reported by the manufacturer as 0.05 s1. The sediments used were a well-sorted Ottawa sand, a fine sand and a well-graded, light weight plastic material (Plasti-grit). Details of the sediment characteristics are given below. The experiments were conducted using a 1.37 m-long Plexiglas tube with the geotextile attached to the bottom of the tube with a stainless steel hose clamp as shown in Fig. 1.
2. Theory Details of the numerical theory are presented in the companion paper by Weggel and Ward (in this issue). For the reader’s convenience a summary of the theory is presented here. The variables are defined on Fig. 2. The initial flow through the system is given by,
q0 ¼
h0 1
z þ 0 J K
y z0 ¼ 0 1 z0 þ J K
(1)
in which q0 ¼ the initial flow rate, h0 ¼ the initial head, y0 is the initial height of the water level above the geotextile, z0 ¼ the initial thickness of the filter cake, J ¼ the permittivity of the geotextile and K ¼ the permeability of the filter cake. Note that the decrease in head is due both to the lowering of the water level and to the increase in thickness of the filter cake. The initial cumulative discharge is,
J.R. Weggel, J. Dortch / Geotextiles and Geomembranes 31 (2012) 62e68
63
Table 1 Hydraulic Properties of Geotextiles.* Property Material Permittivity Water Flow Rate AOS
Test method
Geotextile A
Geotextile B
ASTM D-4491 ASTM D-4491 ASTM D-4751
Polypropylene 0.05 s1 160 l/min/m2 0.6 mm
Polypropylene 0.05 s1 160 l/min/m2 0.425 mm
* Values are MARV (Minimum Average Roll Values) with 97.7% confidence that the actual value will exceed the given MARV value.
(
ao
zn ¼ zn1 þ
Fig. 1. Settling tube.
ε
þ
X ai i
ε
)
X vi ai ðqn1 þ qn Þ Dt þ Dt ε 2 i
(5)
and the discharge through the system by,
qcum0 ¼ 0
(2)
The initial water level in the tube is y0 and the water level one time step, Dt, later is,
yn ¼ yn1 qn1 Dt
(3)
The rate of change of the filter cake thickness is given by,
dz q X ðvi þ qÞai ¼ ao þ ε dt ε i
(4)
or
dz ¼ dt
(
ao ε
þ
X ai i
ε
) qþ
X vi ai i
qnþ1
8 > ðh þ hn Þ< ¼ qn þ nþ1 > 2 :1
9 > =
1 Dt ðznþ1 þ zn Þ> ; þ J 2K
(6)
The final thickness of the filter cake after all i components have accumulated is,
zN ¼ ho
X ai i
ε
þ zo
(7)
The model assumes that the size components comprising the slurry are completely mixed and uniformly distributed throughout the column at the start of the process. The equations were solved numerically using an Excel spreadsheet.
ε
in which ai ¼ the volumetric solids concentration of the ith component in the slurry, ε ¼ the solids fraction of the accumulated filter cake, vi ¼ the settling velocity of the ith component of the slurry material where the slurry is characterized by a discrete number of size components. The thickness of the filter cake Dt later is calculated by,
3. Experiments 3.1. Geotextiles Two woven polypropylene geotextiles (Geotextile A and Geotextile B) were used for the experiments. They were selected for their low permittivities. Their hydraulic characteristics, as reported by the manufacturer, are given in Table 1. 3.2. Sediments Three sediments were used in the experiments: Ottawa Sand, a fine quartz sand and Plasti-grit (Table 2). Plasti-grit is a commercially available plastic material with a specific gravity of 1.17 used for sand blasting. The size distribution for the Ottawa
Table 2 Sediment characteristics.
Fig. 2. Definition of Terms e Filter cake accumulation model.
Ottawa Sand, SG ¼ 2.65, r ¼ 2650 kg/m3 Geometric mean (mm) % 0.7140 97 Fine Sand, SG ¼ 2.62, r ¼ 2620 kg/m3 Geometric mean (mm) % 0.1057 20.2 0.1930 76.0 0.2725 3.0 0.3532 0.6 Plasti-grit, SG ¼ 1.17, r ¼ 1170 kg/m3 Geometric mean (mm) % 0.0690 10.8 0.2470 26.7 0.3615 35.8 0.5288 20.5 0.7736 3.2
Settling velocity (cm/s) 7.875 Settling velocity (cm/s) 0.0834 2.2440 3.4753 4.5424 Settling velocity (cm/s) 0.00119 0.00151 0.03219 0.06767 0.13780
64
J.R. Weggel, J. Dortch / Geotextiles and Geomembranes 31 (2012) 62e68
SIZE DISTRIBUTION - OTTAWA SAND
HISTOGRAM - FINE SAND 80
100
70
PERCENT WITHIN SIZE CLASS
90 80
60 50 40 30
50 40 30 20 10
20
0.1
1
10
1.2969
0.5943
0.3532
0.1057
0
0.2725
0
10
0.1930
% PASSING
70
60
GEOMETRIC MEAN DIAMETER (mm)
DIAMETER (mm)
Fig. 6. Four-Component histogram for fine sand size distribution. Fig. 3. Size distribution of Ottawa sand.
HISTOGRAM - OTTAWA SAND
SIZE DISTRIBUTION - PLASTI-GRIT
100
100 90
90
80
PERCENT WITHIN SIZE CLASS
80
70
% FINER
70 60
60 50 40 30
50
20
40
10 0 0.01
30
0.10
1.00
10 .0 0
DIAMETER (mm)
20 Fig. 7. Size distribution for Plasti-grit.
10
Sand is given in Fig. 3. It was characterized by a single median size as shown in the histogram in Fig. 4. The size distribution for the fine sand is given in Fig. 5 and the four sizes used to characterize it are shown in the histogram of Fig. 6. The Plasti-grit size distribution is given in Fig. 7 and the five sizes used to characterize it are shown in the histogram of Fig. 8. The size characteristics of the
0.714
1.001
0
GEOMETRIC MEAN DIAMETER (mm) Fig. 4. One-Component histogram for Ottawa sand size distribution.
SIZE DISTRIBUTION - FINE SAND 100
FIVE COMPONENT SIZE DISTRIBUTION - PLASTI-GRIT
90
40
80
35
% WITHIN SIZE CLASS
60 50 40 30
30 25 20 15 10
20 5
10
DIAMETER (mm)
Fig. 5. Size distribution of fine sand.
0.7736
0.5288
1.00
0.3615
0
0 .1 0
0.2470
0 0.01
0.0690
% PASSING
70
GEOMETRIC MEAN DIAMETER (mm)
Fig. 8. Five-Component histogram for Plasti-grit size distribution.
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65
Table 3 Summary of experimental values of found for J, Ksys, z and K.
J (s1)
Ksys (cm/s)
z (cm)
K (cm/s)
only only only only
0.05430 0.05320 0.05850 0.05820 0.05605
NA NA NA NA
NA NA NA NA
NA NA NA NA
only only only only only
0.15890 0.16130 0.16010 0.15710 0.15730 0.15894
NA NA NA NA NA
NA NA NA NA NA
NA NA NA NA NA
sand sand sand sand
0.15894 0.15894 0.15894 0.15894
0.6081 0.5648 0.6398 0.6425
7.1110 6.6041 7.1110 7.1110
1.3161 1.2195 1.4740 1.4886
sand sand sand sand sand
0.05605 0.05605 0.05605 0.05605 0.05605
0.4846 0.5242 0.5416 0.5121 0.5297
7.6200 7.6200 7.8730 7.6200 7.8730
0.4846 0.5242 0.5416 0.4521 0.5297
Plasti-grit Plasti-grit Plasti-grit Plasti-grit Plasti-grit
0.05605 0.05605 0.05605 0.05605 0.05605
0.03258 0.03563 0.03164 0.04176 0.03292
8.1290 8.8910 8.0010 9.9060 7.8638
0.03505 0.03840 0.03413 0.04511 0.03566
135ST 135ST
none/water only none/water only Average¼
0.07750 0.07940 0.07845
NA NA
NA NA
NA NA
21 22 22A
135ST 135ST 135ST
Ottawa sand Ottawa sand Ottawa sand
0.07845 0.07845 0.07845
0.56971 0.45720 0.39258
7.2390 7.1119 6.0960
0.5697 2.5322 2.1921
23 23A 24 24A
135ST 135ST 135ST 135ST
Fine Fine Fine Fine
sand sand sand sand
0.07845 0.07845 0.07845 0.07845
0.031089 0.027858 0.023256 0.020757
7.2390 6.4770 7.1120 6.3499
0.03292 0.02957 0.02438 0.02164
25 25A 26
135ST 135ST 135ST
Plasti-grit Plasti-grit Fine sand/ Plasti-grit Mix
0.07845 0.07845 0.07845
0.013624 0.010698 0.038709
3.5561 2.7941 4.5720
0.01433 0.01128 0.04328
27 28
315ST 315ST
none/water only none/water only Average¼
0.22010 0.22500 0.22255
NA NA
NA NA
NA NA
29 30 30A
315ST 315ST 315ST
Ottawa Sand Ottawa Sand Ottawa Sand
0.22255 0.22255 0.22255
0.77907 0.69799 0.74706
7.8730 7.1110 7.6200
1.40269 1.24877 1.33532
31 31A 31B 31C 32
315ST 315ST 315ST 315ST 315ST
Fine Fine Fine Fine Fine
sand sand sand sand sand
0.22255 0.22255 0.22255 0.22255 0.22255
0.045201 0.045201 0.045201 0.045201 0.153314
8.8910 8.3820 8.1290 7.6200 8.6350
0.04602 0.04633 0.04480 0.04206 0.16673
33 34
315ST 315ST
Plasti-grit Plasti-grit
0.22255 0.22255
0.054205 0.045110
5.0810 4.9530
0.05699 0.04694
Test #
Geotextile
Sediment
1 2 3 4
135ST 135ST 135ST 135ST
none/water none/water none/water none/water Average¼
5 6 7 8 9
315ST 315ST 315ST 315ST 315ST
none/water none/water none/water none/water none/water Average¼
10 10A 11 12
315ST 315ST 315ST 315ST
Ottawa Ottawa Ottawa Ottawa
13 14 14A 15 15A
135ST 135ST 135ST 135ST 135ST
Ottawa Ottawa Ottawa Ottawa Ottawa
16 16A 17 18 18A
135ST 135ST 135ST 135ST 135ST
19 20
three sediments are given in Table 2 along with the settling velocities as determined from the Rubey (1933) equation,
3.3. Experiment Protocol
8sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 =qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi < 2 36n2 36n2 gdi ðrS =r 1Þ vi ¼ þ 3 : 3 gd ðrS =r 1Þ gd3i ðrS =r 1Þ; i
Experiments were conducted using a 4.46 cm (1.756-inch) inside diameter Plexiglas settling tube approximately 1.37 m (4.5 feet) long. A scale graduated in inches was taped to the side of the tube. The geotextile was fastened to the bottom of the tube with a hose clamp. See Figs. 1 and 9. Initial experiments were conducted without sediment in order to determine the permittivity of the geotextile. The bottom of the tube was placed on the floor on a large
(8)
in which vi ¼ the settling velocity, di ¼ the particle diameter, rS ¼ the density of the sediment, r ¼ the fluid density and g ¼ the acceleration of gravity.
66
J.R. Weggel, J. Dortch / Geotextiles and Geomembranes 31 (2012) 62e68 DIMENSIONAL PLOT - TEST 13 - OTTAWA SAND y (m) - THEORY
1.6
0.16
y (m) - DATA qcum (m) - THEORY
1.4
0.14
qcum (m) - DATA q (m/sec) - THEORY
1.2
0.12
0.10
0.8
0.08
0.6
0.06
0.4
0.04
0.2
0.02
z (m) - THEORY
0.0 0
10
20
30
40
50
60
70
80
90
q (m/s), z (m)
(m)
1.0
y (m), q
q (m/sec) - DATA
0.00 100
t (s)
Fig. 11. Typical experimental results for Ottawa sand (J ¼ 0.07 s1, K ¼ 0.0061 m/s, z0 ¼ 0.1579 m, z ¼ 0.0762 m, y0 ¼ 1.164 m, geotextile A).
Fig. 9. Experimental Setup.
diameter rubber stopper and filled with water. (The stopper diameter was larger than the outside diameter of the tube.) The stopper and tube were picked up and placed over a receiving basin, the stopper was removed and the time for the water surface to pass various levels on the graduated scale recorded. In effect, the system was a falling head permeameter. (Note that this is not a standardized test for determining permittivity; however, it was deemed appropriate to determine the permittivity in situ rather than in a separate test.)
Essentially the same procedure was used in subsequent experiments with sediment; however, an additional stopper with a hole was inserted into the top of the tube. The bottom of the tube was placed on the large stopper; a measured quantity of sediment placed in the tube and water added to fill the tube. The tube and stoppers were picked up and the system shaken until the sediment appeared to be evenly distributed throughout the water column. (It was difficult to achieve a uniform distribution of sediment for the Ottawa sand because of its high settling velocity. It was also difficult for the fine sand but the distribution was observed to be more uniform than for the Ottawa sand. A uniform distribution was achievable with the Plasti-grit.) The tube was placed over the receiving basin, the bottom stopper removed and the time for the water surface to pass various levels on the graduated scale measured. After water stopped draining from the system, the weight of water released was recorded and the thickness of the sediment in the bottom of the tube measured to the nearest 0.25 cm (0.1 inch). The thickness of the accumulated sediment filter layer was sensitive to any subsequent agitation of the tube. If, following a test, the tube was disturbed, the sediment consolidated and its thickness decreased; consequently, for some tests, several sediment thicknesses were recorded. The basic data obtained from each test was: the water level as a function of time, the weight of the sediment introduced, the weight of the water released and the
DIMENSIONAL PLOT - TEST 24 - FINE SAND
FALLING HEAD TESTS FOR 135ST 10.0000
0.14
1.2
0.12
TEST #1
TEST #3 TEST #4
1.0
Expon. (TEST #1)
(m)
y = 1.2749e R = 0.9947
Expon. (TEST #4)
Expon. (TEST #2)
1.0000
y (m) q
Expon. (TEST #3)
y = 1.332e R = 0.9912
y (m) - DATA
0.8
0.08
qcum (m) - THEORY qcum - DATA
0.6
0.06
q (m/sec) - THEORY q (m/sec) - DATA
0.4
y = 1.3423e R = 0.9897
0.10
y (m) - THEORY
0.04
z (m) - THEORY
0.2
0.02
0.0 0
0.1000 0
5
10
15
20
25
30
35
40
45
Time (s)
Fig. 10. Typical permittivity Determination from head vs. Time data, geotextile A.
q (m/s), z (m)
y = 49.423e R = 0.9979
TEST #2
HEAD (meters)
1.4
100
200
300
400
500
600
700
800
900
0.00 1000
t (s)
Fig. 12. Typical experimental results for fine sand (J ¼ 0.05 s1, K ¼ 0.000228 m/s, z0 ¼ 0.0091 m, z ¼ 0.0711 m, y0 ¼ 1.289 m, geotextile A).
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67
DIMENSIONAL PLOT - TEST 18 - PLASTI-GRIT y (m) - THEORY
1.4
0.07
y (m) - DATA qcum (m) - THEORY
1.2
0.06
qcum (m) - DATA q (m/sec) - THEORY
1.0
0.05
z (m) - THEORY
0.8
0.04
0.6
0.03
0.4
0.02
0.2
0.01
0.0 0
50
100
150
200
q (m/s), z (m)
y (m) q
(m)
q (m/sec) - DATA
0.00 300
250
t (s)
Fig. 13. Typical experimental results for Plasti-grit (J ¼ 0.05 s1, K ¼ 0.000152 m/s, z0 ¼ 0.0213 m, z ¼ 0.099 m, y0 ¼ 1.25 m, geotextile A).
Table 4 Parameter values used to Reconcile data with theory.
DIMENSIONAL PLOT - TEST 10 - OTTAWA SAND
0.9
y (m), q
(m)
0.8
0.50
y (m) - THEORY
y (m) - DATA
qcum (m) - THEORY
qcum (m) - DATA
q (m/sec) - THEORY
q (m/sec) - DATA
0.45 0.40
z (m) - THEORY
0.7
0.35
0.6
0.30
0.5
0.25
0.4
0.20
0.3
0.15
0.2
0.10
0.1
0.05
0.0
q (m/sec), z (m)
1.0
0.00 0
5
10
15
20
25
30
35
40
Fig. 16. Typical experimental results for Plasti-grit (J ¼ 0.05 s1, K ¼ 0.00035 m/s, z0 ¼ 0.0183 m, z ¼ 0.0418 m, y0 ¼ 1.250 m, geotextile B).
45
50
t (s)
Fig. 14. Typical experimental results for Ottawa sand (J ¼ 0.08 s1, K ¼ 0.0137 m/s, z0 ¼ 0.0737 m, z ¼ 0.0737 m, y0 ¼ 0.890 m, geotextile B).
Test #
Sediment
Geotextile
J (s1)
K (m/s)
z0 (m)
z (m)
y0 (m)
10 11 12 13 14 15 16 17 18 23 24 25 29 30 31 32 33 34
Ottawa Ottawa Ottawa Ottawa Ottawa Ottawa Plasti-grit Plasti-grit Plasti-grit Fine sand Fine sand Plasti-grit Ottawa Ottawa Fine sand Fine sand Plasti-grit Plasti-grit
315ST 315ST 315ST 135ST 135ST 135ST 135ST 135ST 135ST 135ST 135ST 135ST 315ST 315ST 315ST 315ST 315ST 315ST
0.080 0.070 0.070 0.070 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.058 0.055 0.050 0.050 0.050 0.050
0.0137 0.0305 0.0213 0.00609 0.01219 0.01067 0.00018 0.00011 0.00015 0.00026 0.00023 0.00006 0.15240 0.03353 0.00029 0.00030 0.00035 0.00030
0.0738 0.0710 0.0710 0.0579 0.0610 0.0610 0.0335 0.0061 0.0213 0.0722 0.0091 0.0085 0.0786 0.0064 0.0152 0.0107 0.0183 0.0244
0.0738 0.0710 0.0710 0.0762 0.0786 0.0786 0.0890 0.0689 0.0990 0.0722 0.0710 0.0357 0.0786 0.0710 0.0890 0.0863 0.0418 0.0497
0.8900 1.0881 1.2039 1.1643 1.1887 1.1643 1.2497 1.3411 1.2496 1.2832 1.2893 1.3015 0.9693 1.1796 1.1796 1.2009 1.0973 1.1918
4. Experimental results final thickness of the sediment layer. (Note that some small amount of water was retained in the pores of the accumulated sediment at the end of a test; however, the amount of water remaining in the filter cake was small relative to the amount in the initial water column.)
Thirty-four experiments were conducted, 18 with Geotextile A and 16 with Geotextile B. Of these, 13 were conducted with only water to determine the permittivity of the geotextile while 21 were conducted with sediment. Table 3 presents a summary of the experiments. 4.1. Permittivity Geotextile permittivities were determined from the tests conducted with only water. Permittivity was determined using the settling tube as described above and plotting water level against time with water level on a logarithmic scale. An exponential curve was fitted to the data with the permittivity found from the exponent. Fig. 10 presents a typical plot for Geotextile A for Tests 1 through 4. Permittivity values thus found for Geotextile A ranged from J ¼ 0.0532 to 0.0585 s1. (Similar analyses for Tests 5 through 9 for Geotextile B yield permittivities ranging from J ¼ 0.1571 to 0.1613 s1.) The permeability of the accumulating filter cake sediment was determined from the final permeability of the geotextile/ filter cake system and the permittivity of the geotextile from the equation,
z z 1 Ksys J
K ¼ 1
Fig. 15. Typical experimental results for fine sand (J ¼ 0.07 s , K ¼ 0.0061 m/s, z0 ¼ 0.0579 m, z ¼ 0.0762 m, y0 ¼ 1.1643 m, geotextile B).
(9)
68
J.R. Weggel, J. Dortch / Geotextiles and Geomembranes 31 (2012) 62e68
where K ¼ the permeability of the filter cake alone, z ¼ the thickness of the filter cake and Ksys ¼ the permeability of the combined filter cake/geotextile system. Ksys was determined from the rate of water level decline near the end of a test after all of the sediment had accumulated. Eq. (9) is very sensitive to the value of J and yields negative values of K when J is too small, particularly if Ksys is relatively large such as for Ottawa sand. Table 3 presents the values of J, Ksys, z and K found using Eq. (9). Some tests report two values, one for each of two values of z observed. Some of the K values for Ottawa sand in the table are indicated only as being greater than the value of Ksys since Eq. (9) yields negative values. This is due to the sensitivity of Eq. (9) to the value of J relative to Ksys. Larger values of J or smaller values of Ksys would yield positive values. Fig. 11 though 16 present typical experimental results compared with the theory for six tests. Figs. 11e13 are for Geotextile A with Ottawa sand, fine sand and Plasti-grit, respectively. Figs. 14e16 are for Geotextile B. The figures show the variation with time of y ¼ the water level in the tube, q ¼ the flow through the system, qcum ¼ the cumulative volume of flow through the system and z ¼ the thickness of the accumulating filter cake. (Only theoretical values for z are given on the plots since only the final thickness of the filter cake was measured.) In general, agreement between theory and experiment is very good; however, the agreement for Ottawa sand is not as good as for the fine sand and Plasti-grit. This is due to the speed at which the Ottawa sand settled during the experiments. Initially, comparisons were made assuming that the initial sediment thickness was zero; however, the rapidity with which the Ottawa sand settled and the likelihood that it was not completely mixed throughout the water column at the start of the experiment made it necessary to assume an initial sediment thickness for comparison with theory. (The Ottawa sand settled so quickly that a significant amount of sediment accumulated during the first timing interval e in some cases the entire amount in suspension. The fine sand also accumulated relatively quickly while the Plasti-grit accumulated slowest.) In plotting the data and theory, several variables had to be adjusted to give the observed fit: the permittivity of the geotextile (although it was close to the value reported by the manufacturer), the permeability of the filter cake and the initial thickness of the filter cake. The values of the variables that gave the best fit were not necessarily those found in Table 3 by the analysis described above. The values used for plotting the experimental data and theory are
presented in Table 4. Except for the Ottawa sand tests, the results were fairly insensitive to the permittivity of the geotextile. (In adjusting the model to fit the Ottawa sand data, changing the value of J resulted in changes in the theoretical solution). For the fine sand and Plasti-grit changing the value of J did not change the solution, that is, the solution was insensitive to the geotextile’s permittivity while the permeability of the filter cake dominated the process. When the permeability of the filter cake was relatively large, as it was for the Ottawa sand, the solution was sensitive to permittivity. For most of the tests, the permittivity giving the best fit was close to the 0.05 s1 reported by the manufacturer. 5. Discussion & conclusion Agreement between the numerical theory and the experiments is very good and indicates the success of the theory and numerical model for describing filter cake accumulation on geotextiles. The experiments also indicate that for fine sediments, such as those usually dewatered using geotextile tubes, the model gives excellent results and indicates that the permittivity of the geotextile is normally of secondary importance; the permeability of the accumulating filter cake dominates the process. For coarse, rapidly settling, highly permeable sediments such as Ottawa sand, the permittivity of the geotextile plays a more significant role, at least at the beginning of the process. Following initial settlement of the Ottawa sand the process is essentially dewatering by gravity and there is no further increase in its thickness and the reduction in head is due only to the decreasing water level. In the present experiments, the Plasti-grit most closely approximates the type of sediment dewatered because of its relatively slow setting velocity; however, additional experiments should be performed using finer, more slowly settling sediments to confirm the theory’s validity for them.
References Rubey, W.W., 1933. Settling velocities of gravel, sand and silt particles. American Journal of Science, 5th Series 25, 325e338. Weggel, J.R., Dortch, J., Gaffney, D., 2010. Analysis of fluid discharge from a hanging geotextile bag. Geotextiles and Geomembranes 29, 65e73. Weggel, J.R., & Ward, N.D., 2011. A model for filter cake Formation on Geotextiles: theory, Geotextiles & Geomembranes, in this issue.
Contents lists available at SciVerse ScienceDirect
Geotextiles and Geomembranes journal homepage: www.elsevier.com/locate/geotexmem
A model for filter cake formation on geotextiles: Experiments J. Richard Weggel a, *, Jacob Dortch b a b
Professor Emeritus, Civil, Architectural & Environmental Engineering, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA Civil Engineer, First Capital Engineering, 48 South Richland Ave. York, PA, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 March 2011 Received in revised form 3 October 2011 Accepted 18 October 2011 Available online 21 November 2011
The results of 34 experiments of flow through and filter cake sediment accumulation on a geotextile are presented to verify a theoretical numerical model presented in a companion paper by Weggel and Ward (in this issue). Two low permittivity geotextiles (j¼0.05 s1) and three sediments were investigated. The three sediments were a well-sorted Ottawa sand, a fine sand and a well-graded, light weight plastic material. The sediments were suspended in a 1.37 m-long Plexiglas tube and allowed to settle on the geotextile. The time variation of the rate of flow through the geotextile/sediment system was measured and compared with the rate predicted by theory. Comparison between the numerical model and experiments is very good. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Large geotextile bags are increasingly being used to dewater dredged material and mine tailings (Weggel, et al., 2010). As the water passes through the geotextile, solids in the slurry being dewatered are retained on the surface of the geotextile and, as the thickness of the accumulating filter cake increases, the dewatering rate decreases. Thus, as time passes, the dewatering efficiency of the system decreases. The rate of flow through the filter cake depends on the permittivity of the geotextile, the permeability of the filter cake and its thickness. At the start of the dewatering process the permittivity of the geotextile can be important; however, as the filter cake’s thickness increases, the permeability of the filter cake controls the dewatering rate. Weggel and Ward (in this issue) presented a numerical model that describes the accumulation of filter cake on a geotextile. The equations were solved numerically to give the discharge through the geotextilefilter cake layers, the decrease in head, the cumulative discharge and the thickness of the filter cake, all as functions of time. In addition, the distribution of sediment grain size at various layers in the filter cake could be determined given the size distribution of the sediment in suspension at the start of the process. The present paper describes a series of experiments to establish the validity of the numerical theory. Thirty-four
* Corresponding author. fax: þ1 (215) 576 6307. E-mail addresses: [email protected] (J.R. Weggel), [email protected] (J. Dortch). 0266-1144/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2011.10.003
experiments were conducted with two geotextiles and three different sediments. The geotextiles used were Propex 135ST (Geotextile A) and Propex 315ST (Geotextile B), both with permittivities reported by the manufacturer as 0.05 s1. The sediments used were a well-sorted Ottawa sand, a fine sand and a well-graded, light weight plastic material (Plasti-grit). Details of the sediment characteristics are given below. The experiments were conducted using a 1.37 m-long Plexiglas tube with the geotextile attached to the bottom of the tube with a stainless steel hose clamp as shown in Fig. 1.
2. Theory Details of the numerical theory are presented in the companion paper by Weggel and Ward (in this issue). For the reader’s convenience a summary of the theory is presented here. The variables are defined on Fig. 2. The initial flow through the system is given by,
q0 ¼
h0 1
z þ 0 J K
y z0 ¼ 0 1 z0 þ J K
(1)
in which q0 ¼ the initial flow rate, h0 ¼ the initial head, y0 is the initial height of the water level above the geotextile, z0 ¼ the initial thickness of the filter cake, J ¼ the permittivity of the geotextile and K ¼ the permeability of the filter cake. Note that the decrease in head is due both to the lowering of the water level and to the increase in thickness of the filter cake. The initial cumulative discharge is,
J.R. Weggel, J. Dortch / Geotextiles and Geomembranes 31 (2012) 62e68
63
Table 1 Hydraulic Properties of Geotextiles.* Property Material Permittivity Water Flow Rate AOS
Test method
Geotextile A
Geotextile B
ASTM D-4491 ASTM D-4491 ASTM D-4751
Polypropylene 0.05 s1 160 l/min/m2 0.6 mm
Polypropylene 0.05 s1 160 l/min/m2 0.425 mm
* Values are MARV (Minimum Average Roll Values) with 97.7% confidence that the actual value will exceed the given MARV value.
(
ao
zn ¼ zn1 þ
Fig. 1. Settling tube.
ε
þ
X ai i
ε
)
X vi ai ðqn1 þ qn Þ Dt þ Dt ε 2 i
(5)
and the discharge through the system by,
qcum0 ¼ 0
(2)
The initial water level in the tube is y0 and the water level one time step, Dt, later is,
yn ¼ yn1 qn1 Dt
(3)
The rate of change of the filter cake thickness is given by,
dz q X ðvi þ qÞai ¼ ao þ ε dt ε i
(4)
or
dz ¼ dt
(
ao ε
þ
X ai i
ε
) qþ
X vi ai i
qnþ1
8 > ðh þ hn Þ< ¼ qn þ nþ1 > 2 :1
9 > =
1 Dt ðznþ1 þ zn Þ> ; þ J 2K
(6)
The final thickness of the filter cake after all i components have accumulated is,
zN ¼ ho
X ai i
ε
þ zo
(7)
The model assumes that the size components comprising the slurry are completely mixed and uniformly distributed throughout the column at the start of the process. The equations were solved numerically using an Excel spreadsheet.
ε
in which ai ¼ the volumetric solids concentration of the ith component in the slurry, ε ¼ the solids fraction of the accumulated filter cake, vi ¼ the settling velocity of the ith component of the slurry material where the slurry is characterized by a discrete number of size components. The thickness of the filter cake Dt later is calculated by,
3. Experiments 3.1. Geotextiles Two woven polypropylene geotextiles (Geotextile A and Geotextile B) were used for the experiments. They were selected for their low permittivities. Their hydraulic characteristics, as reported by the manufacturer, are given in Table 1. 3.2. Sediments Three sediments were used in the experiments: Ottawa Sand, a fine quartz sand and Plasti-grit (Table 2). Plasti-grit is a commercially available plastic material with a specific gravity of 1.17 used for sand blasting. The size distribution for the Ottawa
Table 2 Sediment characteristics.
Fig. 2. Definition of Terms e Filter cake accumulation model.
Ottawa Sand, SG ¼ 2.65, r ¼ 2650 kg/m3 Geometric mean (mm) % 0.7140 97 Fine Sand, SG ¼ 2.62, r ¼ 2620 kg/m3 Geometric mean (mm) % 0.1057 20.2 0.1930 76.0 0.2725 3.0 0.3532 0.6 Plasti-grit, SG ¼ 1.17, r ¼ 1170 kg/m3 Geometric mean (mm) % 0.0690 10.8 0.2470 26.7 0.3615 35.8 0.5288 20.5 0.7736 3.2
Settling velocity (cm/s) 7.875 Settling velocity (cm/s) 0.0834 2.2440 3.4753 4.5424 Settling velocity (cm/s) 0.00119 0.00151 0.03219 0.06767 0.13780
64
J.R. Weggel, J. Dortch / Geotextiles and Geomembranes 31 (2012) 62e68
SIZE DISTRIBUTION - OTTAWA SAND
HISTOGRAM - FINE SAND 80
100
70
PERCENT WITHIN SIZE CLASS
90 80
60 50 40 30
50 40 30 20 10
20
0.1
1
10
1.2969
0.5943
0.3532
0.1057
0
0.2725
0
10
0.1930
% PASSING
70
60
GEOMETRIC MEAN DIAMETER (mm)
DIAMETER (mm)
Fig. 6. Four-Component histogram for fine sand size distribution. Fig. 3. Size distribution of Ottawa sand.
HISTOGRAM - OTTAWA SAND
SIZE DISTRIBUTION - PLASTI-GRIT
100
100 90
90
80
PERCENT WITHIN SIZE CLASS
80
70
% FINER
70 60
60 50 40 30
50
20
40
10 0 0.01
30
0.10
1.00
10 .0 0
DIAMETER (mm)
20 Fig. 7. Size distribution for Plasti-grit.
10
Sand is given in Fig. 3. It was characterized by a single median size as shown in the histogram in Fig. 4. The size distribution for the fine sand is given in Fig. 5 and the four sizes used to characterize it are shown in the histogram of Fig. 6. The Plasti-grit size distribution is given in Fig. 7 and the five sizes used to characterize it are shown in the histogram of Fig. 8. The size characteristics of the
0.714
1.001
0
GEOMETRIC MEAN DIAMETER (mm) Fig. 4. One-Component histogram for Ottawa sand size distribution.
SIZE DISTRIBUTION - FINE SAND 100
FIVE COMPONENT SIZE DISTRIBUTION - PLASTI-GRIT
90
40
80
35
% WITHIN SIZE CLASS
60 50 40 30
30 25 20 15 10
20 5
10
DIAMETER (mm)
Fig. 5. Size distribution of fine sand.
0.7736
0.5288
1.00
0.3615
0
0 .1 0
0.2470
0 0.01
0.0690
% PASSING
70
GEOMETRIC MEAN DIAMETER (mm)
Fig. 8. Five-Component histogram for Plasti-grit size distribution.
J.R. Weggel, J. Dortch / Geotextiles and Geomembranes 31 (2012) 62e68
65
Table 3 Summary of experimental values of found for J, Ksys, z and K.
J (s1)
Ksys (cm/s)
z (cm)
K (cm/s)
only only only only
0.05430 0.05320 0.05850 0.05820 0.05605
NA NA NA NA
NA NA NA NA
NA NA NA NA
only only only only only
0.15890 0.16130 0.16010 0.15710 0.15730 0.15894
NA NA NA NA NA
NA NA NA NA NA
NA NA NA NA NA
sand sand sand sand
0.15894 0.15894 0.15894 0.15894
0.6081 0.5648 0.6398 0.6425
7.1110 6.6041 7.1110 7.1110
1.3161 1.2195 1.4740 1.4886
sand sand sand sand sand
0.05605 0.05605 0.05605 0.05605 0.05605
0.4846 0.5242 0.5416 0.5121 0.5297
7.6200 7.6200 7.8730 7.6200 7.8730
0.4846 0.5242 0.5416 0.4521 0.5297
Plasti-grit Plasti-grit Plasti-grit Plasti-grit Plasti-grit
0.05605 0.05605 0.05605 0.05605 0.05605
0.03258 0.03563 0.03164 0.04176 0.03292
8.1290 8.8910 8.0010 9.9060 7.8638
0.03505 0.03840 0.03413 0.04511 0.03566
135ST 135ST
none/water only none/water only Average¼
0.07750 0.07940 0.07845
NA NA
NA NA
NA NA
21 22 22A
135ST 135ST 135ST
Ottawa sand Ottawa sand Ottawa sand
0.07845 0.07845 0.07845
0.56971 0.45720 0.39258
7.2390 7.1119 6.0960
0.5697 2.5322 2.1921
23 23A 24 24A
135ST 135ST 135ST 135ST
Fine Fine Fine Fine
sand sand sand sand
0.07845 0.07845 0.07845 0.07845
0.031089 0.027858 0.023256 0.020757
7.2390 6.4770 7.1120 6.3499
0.03292 0.02957 0.02438 0.02164
25 25A 26
135ST 135ST 135ST
Plasti-grit Plasti-grit Fine sand/ Plasti-grit Mix
0.07845 0.07845 0.07845
0.013624 0.010698 0.038709
3.5561 2.7941 4.5720
0.01433 0.01128 0.04328
27 28
315ST 315ST
none/water only none/water only Average¼
0.22010 0.22500 0.22255
NA NA
NA NA
NA NA
29 30 30A
315ST 315ST 315ST
Ottawa Sand Ottawa Sand Ottawa Sand
0.22255 0.22255 0.22255
0.77907 0.69799 0.74706
7.8730 7.1110 7.6200
1.40269 1.24877 1.33532
31 31A 31B 31C 32
315ST 315ST 315ST 315ST 315ST
Fine Fine Fine Fine Fine
sand sand sand sand sand
0.22255 0.22255 0.22255 0.22255 0.22255
0.045201 0.045201 0.045201 0.045201 0.153314
8.8910 8.3820 8.1290 7.6200 8.6350
0.04602 0.04633 0.04480 0.04206 0.16673
33 34
315ST 315ST
Plasti-grit Plasti-grit
0.22255 0.22255
0.054205 0.045110
5.0810 4.9530
0.05699 0.04694
Test #
Geotextile
Sediment
1 2 3 4
135ST 135ST 135ST 135ST
none/water none/water none/water none/water Average¼
5 6 7 8 9
315ST 315ST 315ST 315ST 315ST
none/water none/water none/water none/water none/water Average¼
10 10A 11 12
315ST 315ST 315ST 315ST
Ottawa Ottawa Ottawa Ottawa
13 14 14A 15 15A
135ST 135ST 135ST 135ST 135ST
Ottawa Ottawa Ottawa Ottawa Ottawa
16 16A 17 18 18A
135ST 135ST 135ST 135ST 135ST
19 20
three sediments are given in Table 2 along with the settling velocities as determined from the Rubey (1933) equation,
3.3. Experiment Protocol
8sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 =qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi < 2 36n2 36n2 gdi ðrS =r 1Þ vi ¼ þ 3 : 3 gd ðrS =r 1Þ gd3i ðrS =r 1Þ; i
Experiments were conducted using a 4.46 cm (1.756-inch) inside diameter Plexiglas settling tube approximately 1.37 m (4.5 feet) long. A scale graduated in inches was taped to the side of the tube. The geotextile was fastened to the bottom of the tube with a hose clamp. See Figs. 1 and 9. Initial experiments were conducted without sediment in order to determine the permittivity of the geotextile. The bottom of the tube was placed on the floor on a large
(8)
in which vi ¼ the settling velocity, di ¼ the particle diameter, rS ¼ the density of the sediment, r ¼ the fluid density and g ¼ the acceleration of gravity.
66
J.R. Weggel, J. Dortch / Geotextiles and Geomembranes 31 (2012) 62e68 DIMENSIONAL PLOT - TEST 13 - OTTAWA SAND y (m) - THEORY
1.6
0.16
y (m) - DATA qcum (m) - THEORY
1.4
0.14
qcum (m) - DATA q (m/sec) - THEORY
1.2
0.12
0.10
0.8
0.08
0.6
0.06
0.4
0.04
0.2
0.02
z (m) - THEORY
0.0 0
10
20
30
40
50
60
70
80
90
q (m/s), z (m)
(m)
1.0
y (m), q
q (m/sec) - DATA
0.00 100
t (s)
Fig. 11. Typical experimental results for Ottawa sand (J ¼ 0.07 s1, K ¼ 0.0061 m/s, z0 ¼ 0.1579 m, z ¼ 0.0762 m, y0 ¼ 1.164 m, geotextile A).
Fig. 9. Experimental Setup.
diameter rubber stopper and filled with water. (The stopper diameter was larger than the outside diameter of the tube.) The stopper and tube were picked up and placed over a receiving basin, the stopper was removed and the time for the water surface to pass various levels on the graduated scale recorded. In effect, the system was a falling head permeameter. (Note that this is not a standardized test for determining permittivity; however, it was deemed appropriate to determine the permittivity in situ rather than in a separate test.)
Essentially the same procedure was used in subsequent experiments with sediment; however, an additional stopper with a hole was inserted into the top of the tube. The bottom of the tube was placed on the large stopper; a measured quantity of sediment placed in the tube and water added to fill the tube. The tube and stoppers were picked up and the system shaken until the sediment appeared to be evenly distributed throughout the water column. (It was difficult to achieve a uniform distribution of sediment for the Ottawa sand because of its high settling velocity. It was also difficult for the fine sand but the distribution was observed to be more uniform than for the Ottawa sand. A uniform distribution was achievable with the Plasti-grit.) The tube was placed over the receiving basin, the bottom stopper removed and the time for the water surface to pass various levels on the graduated scale measured. After water stopped draining from the system, the weight of water released was recorded and the thickness of the sediment in the bottom of the tube measured to the nearest 0.25 cm (0.1 inch). The thickness of the accumulated sediment filter layer was sensitive to any subsequent agitation of the tube. If, following a test, the tube was disturbed, the sediment consolidated and its thickness decreased; consequently, for some tests, several sediment thicknesses were recorded. The basic data obtained from each test was: the water level as a function of time, the weight of the sediment introduced, the weight of the water released and the
DIMENSIONAL PLOT - TEST 24 - FINE SAND
FALLING HEAD TESTS FOR 135ST 10.0000
0.14
1.2
0.12
TEST #1
TEST #3 TEST #4
1.0
Expon. (TEST #1)
(m)
y = 1.2749e R = 0.9947
Expon. (TEST #4)
Expon. (TEST #2)
1.0000
y (m) q
Expon. (TEST #3)
y = 1.332e R = 0.9912
y (m) - DATA
0.8
0.08
qcum (m) - THEORY qcum - DATA
0.6
0.06
q (m/sec) - THEORY q (m/sec) - DATA
0.4
y = 1.3423e R = 0.9897
0.10
y (m) - THEORY
0.04
z (m) - THEORY
0.2
0.02
0.0 0
0.1000 0
5
10
15
20
25
30
35
40
45
Time (s)
Fig. 10. Typical permittivity Determination from head vs. Time data, geotextile A.
q (m/s), z (m)
y = 49.423e R = 0.9979
TEST #2
HEAD (meters)
1.4
100
200
300
400
500
600
700
800
900
0.00 1000
t (s)
Fig. 12. Typical experimental results for fine sand (J ¼ 0.05 s1, K ¼ 0.000228 m/s, z0 ¼ 0.0091 m, z ¼ 0.0711 m, y0 ¼ 1.289 m, geotextile A).
J.R. Weggel, J. Dortch / Geotextiles and Geomembranes 31 (2012) 62e68
67
DIMENSIONAL PLOT - TEST 18 - PLASTI-GRIT y (m) - THEORY
1.4
0.07
y (m) - DATA qcum (m) - THEORY
1.2
0.06
qcum (m) - DATA q (m/sec) - THEORY
1.0
0.05
z (m) - THEORY
0.8
0.04
0.6
0.03
0.4
0.02
0.2
0.01
0.0 0
50
100
150
200
q (m/s), z (m)
y (m) q
(m)
q (m/sec) - DATA
0.00 300
250
t (s)
Fig. 13. Typical experimental results for Plasti-grit (J ¼ 0.05 s1, K ¼ 0.000152 m/s, z0 ¼ 0.0213 m, z ¼ 0.099 m, y0 ¼ 1.25 m, geotextile A).
Table 4 Parameter values used to Reconcile data with theory.
DIMENSIONAL PLOT - TEST 10 - OTTAWA SAND
0.9
y (m), q
(m)
0.8
0.50
y (m) - THEORY
y (m) - DATA
qcum (m) - THEORY
qcum (m) - DATA
q (m/sec) - THEORY
q (m/sec) - DATA
0.45 0.40
z (m) - THEORY
0.7
0.35
0.6
0.30
0.5
0.25
0.4
0.20
0.3
0.15
0.2
0.10
0.1
0.05
0.0
q (m/sec), z (m)
1.0
0.00 0
5
10
15
20
25
30
35
40
Fig. 16. Typical experimental results for Plasti-grit (J ¼ 0.05 s1, K ¼ 0.00035 m/s, z0 ¼ 0.0183 m, z ¼ 0.0418 m, y0 ¼ 1.250 m, geotextile B).
45
50
t (s)
Fig. 14. Typical experimental results for Ottawa sand (J ¼ 0.08 s1, K ¼ 0.0137 m/s, z0 ¼ 0.0737 m, z ¼ 0.0737 m, y0 ¼ 0.890 m, geotextile B).
Test #
Sediment
Geotextile
J (s1)
K (m/s)
z0 (m)
z (m)
y0 (m)
10 11 12 13 14 15 16 17 18 23 24 25 29 30 31 32 33 34
Ottawa Ottawa Ottawa Ottawa Ottawa Ottawa Plasti-grit Plasti-grit Plasti-grit Fine sand Fine sand Plasti-grit Ottawa Ottawa Fine sand Fine sand Plasti-grit Plasti-grit
315ST 315ST 315ST 135ST 135ST 135ST 135ST 135ST 135ST 135ST 135ST 135ST 315ST 315ST 315ST 315ST 315ST 315ST
0.080 0.070 0.070 0.070 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.058 0.055 0.050 0.050 0.050 0.050
0.0137 0.0305 0.0213 0.00609 0.01219 0.01067 0.00018 0.00011 0.00015 0.00026 0.00023 0.00006 0.15240 0.03353 0.00029 0.00030 0.00035 0.00030
0.0738 0.0710 0.0710 0.0579 0.0610 0.0610 0.0335 0.0061 0.0213 0.0722 0.0091 0.0085 0.0786 0.0064 0.0152 0.0107 0.0183 0.0244
0.0738 0.0710 0.0710 0.0762 0.0786 0.0786 0.0890 0.0689 0.0990 0.0722 0.0710 0.0357 0.0786 0.0710 0.0890 0.0863 0.0418 0.0497
0.8900 1.0881 1.2039 1.1643 1.1887 1.1643 1.2497 1.3411 1.2496 1.2832 1.2893 1.3015 0.9693 1.1796 1.1796 1.2009 1.0973 1.1918
4. Experimental results final thickness of the sediment layer. (Note that some small amount of water was retained in the pores of the accumulated sediment at the end of a test; however, the amount of water remaining in the filter cake was small relative to the amount in the initial water column.)
Thirty-four experiments were conducted, 18 with Geotextile A and 16 with Geotextile B. Of these, 13 were conducted with only water to determine the permittivity of the geotextile while 21 were conducted with sediment. Table 3 presents a summary of the experiments. 4.1. Permittivity Geotextile permittivities were determined from the tests conducted with only water. Permittivity was determined using the settling tube as described above and plotting water level against time with water level on a logarithmic scale. An exponential curve was fitted to the data with the permittivity found from the exponent. Fig. 10 presents a typical plot for Geotextile A for Tests 1 through 4. Permittivity values thus found for Geotextile A ranged from J ¼ 0.0532 to 0.0585 s1. (Similar analyses for Tests 5 through 9 for Geotextile B yield permittivities ranging from J ¼ 0.1571 to 0.1613 s1.) The permeability of the accumulating filter cake sediment was determined from the final permeability of the geotextile/ filter cake system and the permittivity of the geotextile from the equation,
z z 1 Ksys J
K ¼ 1
Fig. 15. Typical experimental results for fine sand (J ¼ 0.07 s , K ¼ 0.0061 m/s, z0 ¼ 0.0579 m, z ¼ 0.0762 m, y0 ¼ 1.1643 m, geotextile B).
(9)
68
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where K ¼ the permeability of the filter cake alone, z ¼ the thickness of the filter cake and Ksys ¼ the permeability of the combined filter cake/geotextile system. Ksys was determined from the rate of water level decline near the end of a test after all of the sediment had accumulated. Eq. (9) is very sensitive to the value of J and yields negative values of K when J is too small, particularly if Ksys is relatively large such as for Ottawa sand. Table 3 presents the values of J, Ksys, z and K found using Eq. (9). Some tests report two values, one for each of two values of z observed. Some of the K values for Ottawa sand in the table are indicated only as being greater than the value of Ksys since Eq. (9) yields negative values. This is due to the sensitivity of Eq. (9) to the value of J relative to Ksys. Larger values of J or smaller values of Ksys would yield positive values. Fig. 11 though 16 present typical experimental results compared with the theory for six tests. Figs. 11e13 are for Geotextile A with Ottawa sand, fine sand and Plasti-grit, respectively. Figs. 14e16 are for Geotextile B. The figures show the variation with time of y ¼ the water level in the tube, q ¼ the flow through the system, qcum ¼ the cumulative volume of flow through the system and z ¼ the thickness of the accumulating filter cake. (Only theoretical values for z are given on the plots since only the final thickness of the filter cake was measured.) In general, agreement between theory and experiment is very good; however, the agreement for Ottawa sand is not as good as for the fine sand and Plasti-grit. This is due to the speed at which the Ottawa sand settled during the experiments. Initially, comparisons were made assuming that the initial sediment thickness was zero; however, the rapidity with which the Ottawa sand settled and the likelihood that it was not completely mixed throughout the water column at the start of the experiment made it necessary to assume an initial sediment thickness for comparison with theory. (The Ottawa sand settled so quickly that a significant amount of sediment accumulated during the first timing interval e in some cases the entire amount in suspension. The fine sand also accumulated relatively quickly while the Plasti-grit accumulated slowest.) In plotting the data and theory, several variables had to be adjusted to give the observed fit: the permittivity of the geotextile (although it was close to the value reported by the manufacturer), the permeability of the filter cake and the initial thickness of the filter cake. The values of the variables that gave the best fit were not necessarily those found in Table 3 by the analysis described above. The values used for plotting the experimental data and theory are
presented in Table 4. Except for the Ottawa sand tests, the results were fairly insensitive to the permittivity of the geotextile. (In adjusting the model to fit the Ottawa sand data, changing the value of J resulted in changes in the theoretical solution). For the fine sand and Plasti-grit changing the value of J did not change the solution, that is, the solution was insensitive to the geotextile’s permittivity while the permeability of the filter cake dominated the process. When the permeability of the filter cake was relatively large, as it was for the Ottawa sand, the solution was sensitive to permittivity. For most of the tests, the permittivity giving the best fit was close to the 0.05 s1 reported by the manufacturer. 5. Discussion & conclusion Agreement between the numerical theory and the experiments is very good and indicates the success of the theory and numerical model for describing filter cake accumulation on geotextiles. The experiments also indicate that for fine sediments, such as those usually dewatered using geotextile tubes, the model gives excellent results and indicates that the permittivity of the geotextile is normally of secondary importance; the permeability of the accumulating filter cake dominates the process. For coarse, rapidly settling, highly permeable sediments such as Ottawa sand, the permittivity of the geotextile plays a more significant role, at least at the beginning of the process. Following initial settlement of the Ottawa sand the process is essentially dewatering by gravity and there is no further increase in its thickness and the reduction in head is due only to the decreasing water level. In the present experiments, the Plasti-grit most closely approximates the type of sediment dewatered because of its relatively slow setting velocity; however, additional experiments should be performed using finer, more slowly settling sediments to confirm the theory’s validity for them.
References Rubey, W.W., 1933. Settling velocities of gravel, sand and silt particles. American Journal of Science, 5th Series 25, 325e338. Weggel, J.R., Dortch, J., Gaffney, D., 2010. Analysis of fluid discharge from a hanging geotextile bag. Geotextiles and Geomembranes 29, 65e73. Weggel, J.R., & Ward, N.D., 2011. A model for filter cake Formation on Geotextiles: theory, Geotextiles & Geomembranes, in this issue.