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Comparisons between experimental data and design equation predictions
Appendix E: Comparisons between experimental data and design
equation predictions In Figures E.1-E.8 various experimental data are compared with theoretical predictions of filtration, expression (consolidation), washing and deliquoring performance. Many of the data were obtained using the experimental apparatus described in Chapter 4, while others were measured directly on process scale plant. The models used for predictions are those presented in Chapters 6 and 7 for each of the cycle phases. Following the usual convention, experimental data are represented on the graphs by symbols and the theoretical predictions are shown as solid lines. For the interested reader further comparisons of experimental data and theoretical predictions are available in Carleton and Mehta (1983), Carleton and Salway (1993), Condie et al (1996), Tarleton and Hancock (1997), Tarleton (1998a,b), Tarleton and Hadley (2003), Wakeman and Tarleton (2005a). Figure E.1 shows cumulative volume of filtrate vs. time data for constant pressure filtrations involving nearly incompressible (calcite) and moderately compressible (talc) cake formations. Both particulate feeds have a mean particle size of --~10 pm in aqueous suspension, however, the calcite exhibits a compressibility index (n) less than 0.2 while the talc shows a compressibility index (dependent on the solution environment) in the region of 0.5. The data show that calcite suspensions filter more easily than corresponding talc suspensions (i.e. lower average specific cake resistance) and filtration rates increase as expected with pressure. Also shown on Figure E.1 are theoretical predictions made using equations (6.4)-(6.7) and (6.12). The excellence of the predictions is indicative of the accuracy of these process design equations. The data are particularly significant as the values for the empirical scale-up constants n, c~0, Co and/~ were determined on a separate (automated) apparatus to the one used to generate the experimental data.
Appendix E • Comparisons between experimental data and design 435 .
.
.
.
.
0.0030 ~E'v 0.0025 d~
0.0020 "5 0.0015
• o.oo~o
"~
talc at Apf 50 kPa
-~ 0.0005 ~
calcite at Apf 600 kPa
0.0000
0
2000
4000
6000
8000
Filtration time (s) FTgure E/] An example of comparisons between theoretical volume of filtrate vs. time and experimental data for the constant pressure filtration of suspensions forming nearly incompressible (calcite) and moderately compressible (talc) filter cakes.
As a consequence of using suitable transducers inside a filter cell, it is possible to evaluate transient cake thickness during a filtration. Figure E.2 shows some cake thickness v s . time data, again for calcite and talc, at different 10 8
E 6 ¢-
.o_ 4 calcite at Apf = 100 kPa calcite at Apf 300 kPa A calciteat Apf = 600 kPa <> talcat Apf = 600 kPa
a3
o
2 0,,, 0
|
|
|
250
500
750
1000
Filtration time (s)
FTgure E,2 An example of comparisons between theoretical cake thickness vs. time and experimental data for the constant pressure filtration of suspensions forming nearly incompressible {calcite) and moderately compressible {talc) filter cakes.
436 Solid/Liquid Separation" Equipment Selection and Process Design constant filtration pressures. As would be expected, the calcite cakes formed more rapidly than talc cakes under similar process conditions. Theoretical predictions of cake growth using equations (6.4)-(6.8) and (6.12) show good agreement with the experimental data and confirm the practical application of the equations proposed for modelling cake formation. Many industrial filtrations are performed under variable rather than constant pressure conditions and Chapter 4 describes how sequences of constant pressure experiments can be used to provide scale-up constants that are valid for other pressure/flow regimes. Figure E.3 shows some experimental data for constant rate calcite filtrations where the pressure changes and flow measurements for the filtration have been provided by a software controlled pressure regulator and an electronic balance, respectively. In accordance with theory, a near linear relation is shown between pressure and time. The theoretical predictions also shown on Figure E.3 were produced using
me/ -- #l~avCq2 t/ + #~Rq
A}
(E.1)
A/
and equations (6.4)-(6.7); the scale-up constants required to evaluate (~av and c were determined using a separate apparatus from which sequences of
500 []
~- 400 13_
-~ 300 c
0
200
o j S
-.~
i,..
o-
m .m
nn/o~'O
u.. 100
,,.x/~ 0 0
0
0 []
q=3xlO -6 m3s -1 q = 4x10-6 m 3 s -1
|
|
|
|
|
100
200
300
400
500
600
Filtration time (s) Figure E~3 An example of comparisons between theoretical filtration pressure vs. time and experimental data for the constant rate filtration of suspensions forming nearly incompressible (calcite) filter cakes.
Appendix E. Comparisons between experimental data and design 437 constant pressure tests were performed. It is clear from Figure E.3, and many other similar data, that the equations and modelling procedures proposed for variable pressure filtration are sufficiently accurate for practical design calculations. Figure E.4 illustrates some comparisons between experimental data obtained from the expression of agar-agar gel suspensions and theoretical predictions made using equations (6.36)-(6.38). Although there are some deviations between the experiments and theory these data and many other sets obtained with, for instance, mineral suspensions, illustrate the predictive qualities of Shirato's models for expression and cake consolidation (Shirato et al, 1986).
0.020 Initial suspension concentration = 2.3 %w/w E
v
-~ 0.015 E
._o ffl E
Q..
O 0.010 rl
"-.I
O
O
O
E-- 0.005
Pc = 48 kPa
.i
-1r-l~ 0.000 0
Pc ~11020 kPa
i
i
|
i
i
100
200
300
400
500
600
(Time) o.s (s°S)
Figure E~4 Typical comparisons between experimental data and theoretical predictions for the expression of gels (data extracted from Sambuichi et al, 1994).
In Figure E.5 an example is given of the manner in which equilibrium cake moisture content varies with the deliquoring pressure. As expected, cake moisture falls as the deliquoring pressure is increased and theoretical predictions using, for instance, equations (6.68) and (6.69) and the associated design chart (Figure 6.8) show sufficient agreement for design calculations. These findings are in general agreement with the data of independent researchers (e.g. Figure E.6 and Carleton, 1993), which show good predictions of both laboratory and larger scale deliquoring operations when Wakeman's model is used. Figure E.7 shows example data for both calcite and talc cakes washed at a pressure of 400 kPa. It is clear that the higher specific resistance of the talc
438 Solid/Liquid Separation- Equipment Selection and Process Design 50
40 ~
o
~ 30 E
o 20 E
0
oB .Q ..-
"5 10 0" I.u
0
i
i
i
i
i
i
100
200
300
400
500
600
700
Deliquoring pressure (kPa)
Figure E 5 Equilibrium moisture contents of calcite cakes for increasing deliquoring pressure.
70
60 DO
CZc
5O ,B
O
F
40
c-
t-
30
O O
E
i_
"
._~
20
O
O
Predictions from design charts Leaf tests
B
10
[]
'
'
'
'
I
10
'
'
'
'
I
20
'
'
'
'
I
30
'
'
'
'
I
40
'
'
'
'
I
50
'
'
'
'
I
'
60
'
'
'
70
Moisture content (leaf test and predictions) % Figure E.6 Comparison of cake moisture contents from full scale filters with leaf test data and with predictions from design charts, e.g. Figure 6.8 (Carleton and Mehta, 1983). (A - sand, 50 mm cake, ~av = 5.9 x 106 m kg -1, table filter; B - sand, 70 mm cake, ~av = 1.4 x 107 m kg -1, table filter; C - gypsum in phosphoric acid, 30-46 mm cake, ~ov = 1.9 x 109 m kg-1, belt filter; D - ' i m purity', 46 mm cake, ~ov = 5.5 x 109 m kg -1, drum filter; E - chalk, 5 mm cake, ~av = 2.1 x 1011 m kg -1, drum filter; F - pigment, 4 mm cake, ~av = 2.1 x 1011 m kg -1, drum filter; G - pigment, <1 mm cake, ~av = 2.7 x 1011 m kg -1, drum filter.)
Appendix E. Comparisons between experimental data and design 439 1.2 ,7" 1.0
~ m n D D D D D D D D
0.8
[]
"5 0.6 "~ 0.4 0
~
o.2
O []
0.0 0
,
,
2000
4000
6000
8000
calcite talc 10000
12000
Filtration time (s) F i g u r e E,7 Example predictions of washing performance using the dispersion model and experimental data for the displacement washing of calcite and talc cakes at a constant pressure of 400 kPa.
cake leads to significantly longer washing times and thus slower recovery of solute. The theoretical predictions using equations (6.49) and (6.54)-(6.57) and the associated design chart in Figure 6.7 indicate reasonable agreement with the experimental data. It is difficult to represent on a single graph the results of sequential filtration, washing and deliquoring phases in a filter cycle. Perhaps the best method is 0.006 m"" 0.005
E
(1)
0.004 O
E
0.003
O
•
0.002
E --, 0.001 O 0.000
O [] 0
. 1 000
.
. 2000
Apf = 100 kPa Apf=600 kPa
. 3000
4000
5000
Filtration time (s)
Figure Eo8
Comparisons of theory and experimental data for constant pressure filter cycles
involving filtration, washing and dewatering of 10o/o v/v calcite suspensions.
440 Solid/Liquid Separation" Equipment Selection and Process Design shown in Figure E.8 where the volumes of liquids extracted during a filter cycle are plotted against time at two different constant pressures. The theoretical predictions represent combinations of the process model equations for the three individual phases as shown in Chapter 6 and these again show reasonable agreements with the experimental data.
equation predictions In Figures E.1-E.8 various experimental data are compared with theoretical predictions of filtration, expression (consolidation), washing and deliquoring performance. Many of the data were obtained using the experimental apparatus described in Chapter 4, while others were measured directly on process scale plant. The models used for predictions are those presented in Chapters 6 and 7 for each of the cycle phases. Following the usual convention, experimental data are represented on the graphs by symbols and the theoretical predictions are shown as solid lines. For the interested reader further comparisons of experimental data and theoretical predictions are available in Carleton and Mehta (1983), Carleton and Salway (1993), Condie et al (1996), Tarleton and Hancock (1997), Tarleton (1998a,b), Tarleton and Hadley (2003), Wakeman and Tarleton (2005a). Figure E.1 shows cumulative volume of filtrate vs. time data for constant pressure filtrations involving nearly incompressible (calcite) and moderately compressible (talc) cake formations. Both particulate feeds have a mean particle size of --~10 pm in aqueous suspension, however, the calcite exhibits a compressibility index (n) less than 0.2 while the talc shows a compressibility index (dependent on the solution environment) in the region of 0.5. The data show that calcite suspensions filter more easily than corresponding talc suspensions (i.e. lower average specific cake resistance) and filtration rates increase as expected with pressure. Also shown on Figure E.1 are theoretical predictions made using equations (6.4)-(6.7) and (6.12). The excellence of the predictions is indicative of the accuracy of these process design equations. The data are particularly significant as the values for the empirical scale-up constants n, c~0, Co and/~ were determined on a separate (automated) apparatus to the one used to generate the experimental data.
Appendix E • Comparisons between experimental data and design 435 .
.
.
.
.
0.0030 ~E'v 0.0025 d~
0.0020 "5 0.0015
• o.oo~o
"~
talc at Apf 50 kPa
-~ 0.0005 ~
calcite at Apf 600 kPa
0.0000
0
2000
4000
6000
8000
Filtration time (s) FTgure E/] An example of comparisons between theoretical volume of filtrate vs. time and experimental data for the constant pressure filtration of suspensions forming nearly incompressible (calcite) and moderately compressible (talc) filter cakes.
As a consequence of using suitable transducers inside a filter cell, it is possible to evaluate transient cake thickness during a filtration. Figure E.2 shows some cake thickness v s . time data, again for calcite and talc, at different 10 8
E 6 ¢-
.o_ 4 calcite at Apf = 100 kPa calcite at Apf 300 kPa A calciteat Apf = 600 kPa <> talcat Apf = 600 kPa
a3
o
2 0,,, 0
|
|
|
250
500
750
1000
Filtration time (s)
FTgure E,2 An example of comparisons between theoretical cake thickness vs. time and experimental data for the constant pressure filtration of suspensions forming nearly incompressible {calcite) and moderately compressible {talc) filter cakes.
436 Solid/Liquid Separation" Equipment Selection and Process Design constant filtration pressures. As would be expected, the calcite cakes formed more rapidly than talc cakes under similar process conditions. Theoretical predictions of cake growth using equations (6.4)-(6.8) and (6.12) show good agreement with the experimental data and confirm the practical application of the equations proposed for modelling cake formation. Many industrial filtrations are performed under variable rather than constant pressure conditions and Chapter 4 describes how sequences of constant pressure experiments can be used to provide scale-up constants that are valid for other pressure/flow regimes. Figure E.3 shows some experimental data for constant rate calcite filtrations where the pressure changes and flow measurements for the filtration have been provided by a software controlled pressure regulator and an electronic balance, respectively. In accordance with theory, a near linear relation is shown between pressure and time. The theoretical predictions also shown on Figure E.3 were produced using
me/ -- #l~avCq2 t/ + #~Rq
A}
(E.1)
A/
and equations (6.4)-(6.7); the scale-up constants required to evaluate (~av and c were determined using a separate apparatus from which sequences of
500 []
~- 400 13_
-~ 300 c
0
200
o j S
-.~
i,..
o-
m .m
nn/o~'O
u.. 100
,,.x/~ 0 0
0
0 []
q=3xlO -6 m3s -1 q = 4x10-6 m 3 s -1
|
|
|
|
|
100
200
300
400
500
600
Filtration time (s) Figure E~3 An example of comparisons between theoretical filtration pressure vs. time and experimental data for the constant rate filtration of suspensions forming nearly incompressible (calcite) filter cakes.
Appendix E. Comparisons between experimental data and design 437 constant pressure tests were performed. It is clear from Figure E.3, and many other similar data, that the equations and modelling procedures proposed for variable pressure filtration are sufficiently accurate for practical design calculations. Figure E.4 illustrates some comparisons between experimental data obtained from the expression of agar-agar gel suspensions and theoretical predictions made using equations (6.36)-(6.38). Although there are some deviations between the experiments and theory these data and many other sets obtained with, for instance, mineral suspensions, illustrate the predictive qualities of Shirato's models for expression and cake consolidation (Shirato et al, 1986).
0.020 Initial suspension concentration = 2.3 %w/w E
v
-~ 0.015 E
._o ffl E
Q..
O 0.010 rl
"-.I
O
O
O
E-- 0.005
Pc = 48 kPa
.i
-1r-l~ 0.000 0
Pc ~11020 kPa
i
i
|
i
i
100
200
300
400
500
600
(Time) o.s (s°S)
Figure E~4 Typical comparisons between experimental data and theoretical predictions for the expression of gels (data extracted from Sambuichi et al, 1994).
In Figure E.5 an example is given of the manner in which equilibrium cake moisture content varies with the deliquoring pressure. As expected, cake moisture falls as the deliquoring pressure is increased and theoretical predictions using, for instance, equations (6.68) and (6.69) and the associated design chart (Figure 6.8) show sufficient agreement for design calculations. These findings are in general agreement with the data of independent researchers (e.g. Figure E.6 and Carleton, 1993), which show good predictions of both laboratory and larger scale deliquoring operations when Wakeman's model is used. Figure E.7 shows example data for both calcite and talc cakes washed at a pressure of 400 kPa. It is clear that the higher specific resistance of the talc
438 Solid/Liquid Separation- Equipment Selection and Process Design 50
40 ~
o
~ 30 E
o 20 E
0
oB .Q ..-
"5 10 0" I.u
0
i
i
i
i
i
i
100
200
300
400
500
600
700
Deliquoring pressure (kPa)
Figure E 5 Equilibrium moisture contents of calcite cakes for increasing deliquoring pressure.
70
60 DO
CZc
5O ,B
O
F
40
c-
t-
30
O O
E
i_
"
._~
20
O
O
Predictions from design charts Leaf tests
B
10
[]
'
'
'
'
I
10
'
'
'
'
I
20
'
'
'
'
I
30
'
'
'
'
I
40
'
'
'
'
I
50
'
'
'
'
I
'
60
'
'
'
70
Moisture content (leaf test and predictions) % Figure E.6 Comparison of cake moisture contents from full scale filters with leaf test data and with predictions from design charts, e.g. Figure 6.8 (Carleton and Mehta, 1983). (A - sand, 50 mm cake, ~av = 5.9 x 106 m kg -1, table filter; B - sand, 70 mm cake, ~av = 1.4 x 107 m kg -1, table filter; C - gypsum in phosphoric acid, 30-46 mm cake, ~ov = 1.9 x 109 m kg-1, belt filter; D - ' i m purity', 46 mm cake, ~ov = 5.5 x 109 m kg -1, drum filter; E - chalk, 5 mm cake, ~av = 2.1 x 1011 m kg -1, drum filter; F - pigment, 4 mm cake, ~av = 2.1 x 1011 m kg -1, drum filter; G - pigment, <1 mm cake, ~av = 2.7 x 1011 m kg -1, drum filter.)
Appendix E. Comparisons between experimental data and design 439 1.2 ,7" 1.0
~ m n D D D D D D D D
0.8
[]
"5 0.6 "~ 0.4 0
~
o.2
O []
0.0 0
,
,
2000
4000
6000
8000
calcite talc 10000
12000
Filtration time (s) F i g u r e E,7 Example predictions of washing performance using the dispersion model and experimental data for the displacement washing of calcite and talc cakes at a constant pressure of 400 kPa.
cake leads to significantly longer washing times and thus slower recovery of solute. The theoretical predictions using equations (6.49) and (6.54)-(6.57) and the associated design chart in Figure 6.7 indicate reasonable agreement with the experimental data. It is difficult to represent on a single graph the results of sequential filtration, washing and deliquoring phases in a filter cycle. Perhaps the best method is 0.006 m"" 0.005
E
(1)
0.004 O
E
0.003
O
•
0.002
E --, 0.001 O 0.000
O [] 0
. 1 000
.
. 2000
Apf = 100 kPa Apf=600 kPa
. 3000
4000
5000
Filtration time (s)
Figure Eo8
Comparisons of theory and experimental data for constant pressure filter cycles
involving filtration, washing and dewatering of 10o/o v/v calcite suspensions.
440 Solid/Liquid Separation" Equipment Selection and Process Design shown in Figure E.8 where the volumes of liquids extracted during a filter cycle are plotted against time at two different constant pressures. The theoretical predictions represent combinations of the process model equations for the three individual phases as shown in Chapter 6 and these again show reasonable agreements with the experimental data.