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Sedimentation test of metal hydroxides: hydrodynamics and influence of pH
Colloids and Surfaces A: Physicochemical and Engineering Aspects 157 (1999) 73 – 84 www.elsevier.nl/locate/colsurfa
Sedimentation test of metal hydroxides: hydrodynamics and influence of pH R. Font *, P. Garcı´a, M. Rodriguez Departamento de Ingenierı´a Quı´mica, Uni6ersidad de Alicante, Apartado 99, Alicante, Spain Received 25 February 1998; accepted 19 February 1999
Abstract Experimental data obtained from sedimentation tests of metal hydroxide suspensions have been discussed considering the compression zone surface observed directly and that deduced joining the critical points estimated from some sedimentation runs, when plotting the settling rate of the suspension – supernatant height versus time. Estimations of the aggregate diameter and the aggregate volume/solids volume ratio (by two independent methods) have also been obtained. The influence of the pH on the hydrodynamics, the aggregate diameter and the aggregate volume/solids aggregate ratio has been studied. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Sedimentation; Metal hydroxides; pH; Aggregate diameter
1. Introduction Sedimentation is a common dewatering unit operation. It is known that aggregates or flocs are formed inside the suspension of small and colloid particles. In the Department of Chemical Engineering of the Alicante University (Spain), a program of research about the fundamentals of sedimentation has been carried out, mainly with calcium carbonate suspensions [1 – 4]. Some conclusions obtained have also been applied to metal hydroxide suspensions [5]. The theory of the sedimentation developed with calcium carbonate suspensions is based on the Kynch theory [6], with * Corresponding author. Tel.: +34-6-590-3546; fax: +346-590-3464. E-mail address: [email protected] (R. Font)
important and significant modifications as indicated later, but this modified theory has not been universally accepted. The application of this modified theory is useful for designing continuous thickeners and also for the characterization of the aggregates formed (density and diameter). In the calcium carbonate suspensions studied, the aggregates formed have a high density (around 1100–1200 kg/m3). The density of some aggregates such as those corresponding to metal hydroxides and sewage sludges usually have values very close to those of water. Due to the fact that the modified Kynch theory has been tested with a suspension with dense aggregates, the analysis of this theory with low density aggregate suspensions can be useful for testing the hydrodynamics assumed. This is one of the objectives of this paper.
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In addition to the testing of the modified Kynch theory, another important aspect has been the estimation of the aggregate volume/solids volume ratio by two independent procedures applying some relations proposed in the literature to the data obtained by the modified Kynch theory. The validity of the model proposed can be tested by comparison of the two values of this parameter. From the value of aggregate density, an estimation of the diameter can also be obtained. Finally, the great importance of the precipitation pH on the hydrodynamics and consequently also on the aggregate volume/solids volume ratio and diameter of the aggregates has been tested. The analysis of this influence has also been another aim of this paper.
2. Fundamentals of the modified Kynch theory In accordance with the fundamentals of sedimentation developed by some researchers [6–11], in very dilute suspensions, the particles settle separately, whereas at higher solids concentrations, aggregates are formed and the sedimentation takes place in different ways. At low solids concentration (dilute suspensions), the aggregates descend separately and the solids concentration controls the sedimentation rate. The range of solids concentration with these properties is known as non-compression range or hindered settling range. When the inertial effects of acceleration or deceleration are negligible, the
Kynch [6] theory can be applied inside this range, because the settling rate only depends on solids concentration. At high solids concentration (concentrated suspensions), the aggregates are together and a coherent network of solids is considered. The settling rate depends on the weight of the upper solids and the resistance force due to the upward liquid flow. In this range, called the compression range, Kynch’s theory cannot be applied. In the sedimentation tests of flocculated suspensions with low initial solids concentration, at least two discontinuities of solids concentration can be considered: the upper discontinuity or the supernatant–suspension discontinuity at the top of the suspension, and the compression zone or extended sediment interface, that rises from the bottom of the cylinder. Fig. 1 shows the evolution of the interfaces. Frequently, the solids settle in the upper part, forming stable aggregates, whereas in the sediment, the solids form a network or matrix, with the corresponding channels for upward circulation of the fluid. These two situations correspond to the hindered settling zone or the non-compression zone (when the aggregates or flocs settle separately, although hindering between themselves), and to the compression range or extended sediment. Inside the non-compression zone or hindered settling area shown in Fig. 1, three zones can be considered. In zone ‘a’, the solids concentration is constant and equals the initial one. The characteristic lines (lines of constant solids concentration
Fig. 1. Sedimentation test.
R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
and constant settling rate) arise from the bottom of the vessel in zone ‘b’ (or from the origin at a height–time diagram), whereas in zone ‘c’, the characteristic lines arise from the top surface of the sediment, tangentially to the sediment curve in a height– time diagram. Zones ‘a’ and ‘b’ are separated by the characteristic line rising from the bottom and corresponding to the initial solids concentration that intercepts with the upper discontinuity height ‘Z’ at the point where the absolute value of the slope ‘ −dZ/dt ’ begins to decrease or there is, in some cases, a first break in on the upper discontinuity line. Zones ‘b’ and ‘c’ are separated by the characteristic line that arises from the bottom of the vessel, tangentially to the extended sediment or compression zone in a height – time diagram. The point where the upper discontinuity intercepts to the compression zone height is known as critical point or second break. A wider discussion of the assumptions considered can be found elsewhere [1–3]. With the procedure presented in a previous paper [1] and taking into account the characteristic lines that arise from the bottom of the cylinder tangentially to the compression zone surface in a height–time diagram, the critical volume fraction of solids ‘fFK’ (corresponding to the situation when the aggregates are in touch as in a fixed bed of solid particles) or the critical solids concentration, CFK, can be calculated by the equation [1]: fFK =
CK f .Z = Ko o rK Z*
(1)
where rK is the solids density, fKo is the initial volume fraction of solids (equal to CKo/rK, where CKo is the initial solids concentration) and Z* is the intercept height of the upper discontinuity with the characteristic line that arises from the bottom of cylinder, tangentially to the compression zone (separating zones ‘b’ and ‘c’). In zone ‘a’, the constant settling rate shown in the upper discontinuity corresponds to the initial solids concentration. The solids settle downwards and the decrease in the solids mass due to the decreasing supernatant – suspension discontinuity is compensated by the increasing solids concen-
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tration of the low layers above the bottom, corresponding to the sediment. In zone ‘a’, the solids concentration equals the initial one, and the aggregates have a constant settling rate as a consequence of the constant solids concentration. In zones ‘b’ and ‘c’ (see Fig. 1), the relationships between the settling rate, calculated as ‘− dZ/dt’, and the volume fraction of solids are calculated, respectively, by the equations [1,6,7,10,12]: fK =
CK fKo.Zo = rK Zi
fK =
CK fKo.Zo = exp − rK Z12 − L1
dZ V = − 2 dt2
V = −
&
t1
0
dZ dt
(2)
dt1 t2 − t1
(3)
where the significance of Zi, Z12, L1, t1 and t2 are shown in Fig. 1. Drawing different characteristic lines, it is possible to obtain values of the settling rate (determined by the settling rate of the upper discontinuity ‘− dZ/dt’ or −dZ2/dt2 at the top of the characteristic lines) and the corresponding volume fraction of solids ‘fK’ or solids concentration, CK, by Eq. (2) (for zone ‘b’) or Eq. (3) (for zone ‘c’). In this way, a settling rate= f(volume fraction of solids) relation such as those shown later in Figs. 10 and 11 can be obtained. In zones ‘b’ and ‘c’, the aggregates are closer to each other and, consequently, the settling rate is less than that of zone ‘a’. The characteristic lines are the lines in the height–time diagram where the solids concentration and settling rate are constant, and they arise from the bottom of the cylinder (origin of the height–time diagram) in the so-called zone ‘b’ or from the sediment surface in the so-called zone ‘c’. Logically, in zone ‘c’ the aggregates are closer to each other than in zone ‘b’. The characteristic lines have a decreasing slope when they intercept at the supernatant–suspension discontinuity at increasing time as a consequence of the Kynch theorems. Eqs. (2) and (3) can be deduced from a mass balance of solids and they are the result of considering that the characteristic lines arise from the bottom of the cylinder (or from the
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Table 1 Equations concerning the settling rate = f(volume fraction of solids) relation V= Vo(1−CAKfK)n or V 1/n 1/n = V 1/n SA−CAKV SAfK
VSA = g(rA−rW)d 2A/(18h)
(4) when ReB0.2
(7)
CAK =aggregate volume/solids volume Re=rVSAdA/h
(5) VSA = [g(rA−rW)d 2A/(18h)] /(1+0.15Re0.687) when Re B 500 (8) rK+(CAK−1)rW Richardson and Zaki [14]: rA = (9) n = 4.65 when ReB0.2 CAK and 0.2BCAKfKB0.55 Garside and Al-Dibouni [15]: (5.09−n)/(n−2.73) =0.104Re0.877
(6)
when 0.2BCAKfKB0.5
origin in a height – time diagram) or from the sediment surface (tangentially to the sediment curve in a height – time diagram). Inside the sediment, the volume fraction of solids at the upper layer equals fFK, and when the sediment height increases, the solids concentration of the deepest layers also increases. The aggregates disappear and there is a matrix of solids with channels where some units of particle rearrangement can also be present, but different to and smaller than the aggregates that settle separately in the hindered settling zone.
3. Relationships between the solids concentration and the settling rate in the non-compression range Table 1 shows a diagram of the equations used in this paper based on some relations proposed in literature. Eq. (4) relates the decrease of the settling rate as a function of the porosity interaggregates (1− CAKfK) in accordance with the Michaels and Bolger [13] equation. The parameter CAK is the m3 aggregate/m3 solids ratio in an aggregate, thus ‘CAKfK’ is the volume fraction of aggregates fA.
The parameter ‘n’ can be considered to be 4.65 in accordance with the Richardson and Zaki [14] equation or calculated with the relation proposed by Garside and Al-Dibouni [15], depending on the value of the Reynolds number Re, considering the aggregate diameter, dA, the settling velocity, VSA, of solids at infinite dilution, and the liquid viscosity, h. The settling rate VSA of the aggregates at infinite dilution is related to the liquid density, rW, solids density, rK, gravity acceleration, g, and aggregate diameter, dA, by Eqs. (7) and (8). In some suspensions, the initial aggregates grow during the first few minutes of the sedimentation run after previously stirring and, consequently, the settling velocity of solids increases during the first period of the sedimentation test. In other suspensions, the initial settling rate of solids is higher than after a few minutes, and this can be explained admitting that the layer of fluid surrounding the aggregates can be very thin at the beginning and fluid can circulate upwards easier than later on [3]. The V 1/n versus fK plot can be used for analysing the experimental data, deducing if there is there is a flocculation process during the first few minutes of the sedimentation test and if the parameter CAK is or is not constant, calculating its value, and estimating also the diameter of the aggregates by the previous equations shown in Table 1.
4. Experimental procedure A suspension of metal hydroxides was obtained dissolving NiSO4·6H2O, ZnSO4·7H2O and CuSO4·5H2O in water, stirring slowly and gradually adding a suspension formed by water (50% wt) and solids (50% wt), the solids being a mixture of Ca(OH)2 (70% wt)+Mg(OH)2 (30% wt). The contents (ppm) of Ni2 + , Zn2 + and Cu2 + were similar. In this way, adding the basic suspension instead of the solids directly to the aqueous solution, uniform aggregates were formed. After adding the basic suspension, the pH value increased slowly to a stable final value after 24 h. Using the same procedure, and controlling the value of pH, the results were reproducible. After
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the period of 24 h, it was observed that the pH value varied slowly decreasing around 0.2 units in 2 months. The suspensions with different values of pH precipitation and pH at 24 h presented different hydrodynamics of the suspension (this aspect is discussed in the following sections). The density of the precipitated solids was 2837 kg/m3. This value was determined by boiling a suspension with a known amount of solids, cooling afterwards and transferring the suspension to a flask with a known volume. In this way, water filled the internal porous of the solids and the real density of the solids could be determined. The precipitated solids have a specific surface area around 3.9 g/m2, determined by the application of the BET equation to the 273 K carbon dioxide adsorption isotherm (Quantachrome Autosorb 6 sorption apparatus). This small value indicates that the internal porosity of the solids is very small. The diameter of the particles precipitated at pH 12 was measured by Fraunhouffer diffraction of a laser, obtaining a mean volume diameter of 35 mm when the particles were not deflocculated and a mean volume diameter of 12 mm when the suspension was deflocculated (3 g of solids in 25 cm3 with 0.4 g of sodium carbonate and 1.8 g of sodium hexametaphosphate). The supernatant obtained at pH 11.7 was analyzed showing concentrations of Ni, Cu and Zn, each one less than 1 ppm, coinciding with the values determined and presented in another paper [5]. Sedimentation tests were carried out in graduated glass cylinders of 6 cm internal diameter and 1 m height at 28 – 30°C. The verticality of the cylinders was controlled in all the runs. The runs were carried out as follows. The prepared suspension was introduced into the cylinders and then stirred slowly for 4 min. Afterwards, the test began and the height values of the upper discontinuity and the compression zone discontinuity (observed with difficulty) were measured at different times. The upper discontinuity was measured clearly after the first 7–8 min; the compression zone discontinuity was considered in the level where a significant change of porosity could be observed. Above the level con-
77
sidered, the porous structure corresponding to the hindered settling zone could be observed, whereas below the level considered, only some thin channels could be observed.
5. Experimental results
5.1. Runs at the same initial solids concentration and the same precipitation pH A series with six sedimentation runs, at CKo equal to 11.6 kg/m3 and precipitation pH 11.9, was carried out at different initial heights from 0.861 to 0.358 m. Fig. 2 shows the variation of the heights corresponding to the upper discontinuities and to the compression zones. The similarity of the initial upper interface descending with the same velocity corresponding to the initial solids concentration, and then a similar variation, can logically be observed. Considering the compression zone points shown in Fig. 2, it can be observed that these variations coincide from the bottom to the corresponding critical point. This coincidence can be explained taking into account the Kynch theory applied to the non-compression zone (which is the zone where only the assumptions considered in the Kynch theory are approximately correct). Considering the settling flux density–volume frac-
Fig. 2. Sedimentation tests with constant solids concentration and different initial heights (CKo =11.6 kg/m3).
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R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
Fig. 3. Solids flux density versus volume fraction of solids.
tion of solids plot shown in Fig. 3, for the runs with the initial concentration fKo, the rising of the sediment at t =0 corresponds to the slope AB. Later, when the compression zone thickness increases and the slope of the compression zone decreases as a consequence of its compression, the solids at the sediment surface have a small value of settling rate, and the slope of the compression zone equals A%B%, and later A%%B%%, etc. Consequently, the first portion of the rising compression zone does not depend on the initial height and logically must be common for all the tests, as occurs experimentally. The maximum height of the critical point logically depends on the amount of solids and therefore on the initial height. On way of analysing batch testing is by the Tory plots, where the variation of the supernatant–suspension discontinuity (− dZ/dt) is plotted versus the suspension height Z or versus the ratio of the suspension height to the initial suspension height (Z/Zo). The values of − dZ/dt have been calculated correlating the point considered, the previous one and the posterior point to a second-order relation Z = a +bt + ct 2, differentiating the corresponding function and calculating its value at the intermediate point. Fig. 4 shows this plot for one run. Fig. 5 shows the lower part corresponding to the variation of − dZ/dt versus Z for the same run and the estimated location of the critical point. The critical points are those located at the end of the lower straight lineal variation in accordance with the Roberts’ equa-
Fig. 4. Values − dZ/dt versus Z for the test CKo =11.6 kg/m3, pH 12 and Zo =0.660 m.
tion [16] and the discussion carried out by Fitch [9]. Fig. 6 presents all the correlations together, showing a similar variation. In order to compare the estimated critical points with the sediment location, Fig. 7 shows the variations of the sediment heights versus time and the critical points, deducing their coincidence, and corroborating that the criteria for estimating the location of the sediment (when a change of porous structure to a nearly continuous structure) was correct.
Fig. 5. Values − dZ/dt versus Z and location of the critical point for the test CKo =11.6 kg/m3, pH 12 and Zo =0.660 m.
R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
Fig. 6. Values −dZ/dt versus Z for all the runs with CKo 11.6 kg/m3 and pH 12.
5.2. Runs at different initial concentration and different pH 6alues
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Fig. 8. Sedimentation test with different initial solids concentration for two runs: (a) CKo =20.0 kg/m3, pH 12.0; (b) CKo =4.80 kg/m3, pH 11.3.
A series of five experiments was carried out at different solids concentration between 20.0 and 4.80 kg/m3, and with similar initial height around 0.84 m.. The value of pH stabilized after 24 h varies from one experiment to other, so this value was measured in each run. Fig. 8 shows the variation of the upper discontinuity and the estimated sediment surface for two runs. Similar
variations were observed for the other runs, although there is no coincidence of the discontinuities when all the runs are plotted together. Fig. 9 shows the Tory plots for all the runs, showing the similar tendencies observed in the previous series of runs. The estimated critical points, at the intersection of the two discontinuity curves, coincide approximately with the end of the straight line drawn at the bottom of the Tory plots, corroborating the estimation of the compression zone surface.
Fig. 7. Compression zone height versus time and location of the critical points.
Fig. 9. Values −dZ/dt versus Z for all the runs with different initial solids concentration.
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Table 2 Values of critical solids concentration for different operating conditions CKo (kg/m3) Runs at same concentration 1 11.7 2 11.7 3 11.7 4 11.7 5 11.7 6 11.7 Runs at different concentrations 1 20.0 2 14.6 3 10.8 4 8.56 5 4.80
fKo
pH at 24 h
Zo (m)
Z* (m)
CFK (kg/m3)
fFK
0.00411 0.00411 0.00411 0.00411 0.00411 0.00411
11.9 11.9 11.9 11.9 11.9 11.9
0.861 0.764 0.660 0.556 0.458 0.358
0.241 0.207 0.186 0.150 0.125 0.104
41.5 43.0 41.3 43.2 42.6 40.1
0.0146 0.0151 0.0145 0.0152 0.0150 0.0141
0.00705 0.00516 0.00381 0.00302 0.00169
12.0 12.0 11.7 11.7 11.3
0.858 0.835 0.880 0.888 0.835
0.445 0.317 0.391 0.296 0.220
38.6 38.6 24.4 25.7 18.2
0.0136 0.0136 0.0086 0.0090 0.0064
5.3. Determination of the critical solids concentration Determining Z* (intercept height between the upper discontinuity and the tangent to the compression zone at the origin) in accordance with Fig. 1, and applying Eq. (1), the values of the critical solids concentration were obtained for all the runs. Polynomial correlations of Z = Z(t) and L=L(t) were obtained for determining the slope dL/dt at t=0 and the intersection of the tangent to the compression zone at the bottom with the upper discontinuity. The values obtained were close to those deduced graphically from the figures. Table 2 shows the values obtained of the critical solids concentration for the different operating conditions. It can be observed that the suspensions with similar pH at 24 h have similar values of critical solids concentration. It can also be deduced that the precipitation at pH 12.0 leads to higher values of critical solids concentration than at pH 11.3 and 11.7.
5.4. Determination of the relation between the settling rate and the solids concentration in the hindered settling zone An important relation for the design of continuous thickeners is the relationship between the settling rate and the solids concentration. The equations, proposed by different researchers and
presented in Table 1, have been used to obtain this relationship and also to test the different hypotheses: Kynch theory, with the modifications introduced as a consequence of the sediment curvature in a Z–t diagram (zones b and c in Fig. 1), and the models of Richardson and Zaki [14] and Garside and Al-Dibouni [15] have been used. Considering the Z–t diagram of Figs. 2 and 8, the following variations of the upper discontinuity can be observed: a nearly constant variation of − dZ/dt corresponding to zone ‘a’ (zone of constant solids concentration equal to the initial one), a variation of − dZ/dt corresponding to zone ‘b’ and where Eq. (2) can be applied, and zone ‘c’ where Eq. (3) must be used. Considering different points in the curve Z= f(t) and determining the corresponding parameters, Zi for zone ‘b’ and Z12, L1 and tt211/(t2 − t1) dt1 for zone ‘c’, several values of V (settling rate) and the corresponding values of solids concentration were obtained for the different runs. Figs. 10 and 11 show the variation of the experimental values of V 1/4.65 versus the solids concentration in accordance with the Richardson and Zaki [14] equations for the runs with constant solids concentration and different solids concentration, respectively. A coincidence of the linear variation for the runs carried out with the same pH at 24 h can be observed. There is an initial portion that deviates from linearity, corresponding to the initial period of the batch testing after
R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
Fig. 10. Variation of V 1/4.65 versus fK for the runs with the same initial solids concentration.
the stirring of the suspension (this effect was also observed with calcium carbonate suspensions; this can be explained admitting that with the stirring, the water layer that surrounds the aggregates is thin and so the interaggregate porosity can be greater than afterwards without stirring, causing an initial great settling velocity). One interesting aspect that can be deduced is the great influence of the pH on the settling rate of solids for the same concentration. It is known that Mg(OH)2 causes the formation of large crys-
Fig. 11. Variation of V 1/4.65 versus fK for the runs with different initial solids concentration.
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tals in the 9.5–12 pH range due to the slow rate of precipitation [17], but this effect cannot explain the great influence of the pH. The correlations between V 1/4.65 and CK were obtained without considering the initial points with unusual high settling rate as a consequence of the agitation for obtaining a uniform suspension. From the slope and intercept to the y axis, and in accordance with Eq. (4), the values of CAK and VSA have been obtained for all the runs. Considering that the aggregate density can be calculated by Eq. (9), the aggregate diameter was calculated by Eqs. (7) and (8). Table 3 shows the parameters deduced of CAK, aggregate diameter and the Reynolds number using the Richardson and Zaki [14] equation with n =4.65. In accordance with the Al-Dibouni and Garside equation, value n in Eq. (4) is around 5. In order to test the incidence of considering 5 instead of 4.65, the procedure was duplicated but considering n= 5. Similar variations to those observed in Figs. 10 and 11 were obtained. The values of CAK (aggregate volume/solids volume ratio), aggregate diameter and Reynolds number were also obtained and are shown in Table 3. It can be observed that the values of aggregate diameter and CAK are very similar when considering n= 4.65 or n= 5. On the other hand, values CAK can be calculated from the relationship, taking into account that at the critical solids concentration, the interaggregate porosity, which equals CAKfFK, can be close to that of a fixed bed of spheres ‘0.65’ [18].Table 3 also shows these values. Some interesting conclusions can be obtained from Table 3. 1. The values of CAK obtained by two different methods, both considering the Kynch theory with some modifications and the equations presented in Table 1, are very close indicating once again that the sedimentation model can roughly represent the real phenomena that take place. 2. There is a variation of the CAK and the aggregate diameter with the pH as observed in Figs. 12 and 13. On the other hand, when the values of CAK decrease, the aggregate diameters also decrease following the general tendency shown in other cases [19,20].
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Table 3 Values of CAK (aggregate volume/solids volume ratio) and aggregate diameter dA fKo
pH
n =4.65 dA (m)×104
CAK*
dA (m)×104
44.0 44.0 44.0 44.0 44.0 44.0
2.09 2.09 2.09 2.09 2.09 2.09
42.4 42.4 42.4 42.4 42.4 42.4
2.10 2.10 2.10 2.10 2.10 2.10
44.4 42.9 44.5 42.7 43.2 45.9
41.1 42.8 71.1 71.2 105
1.73 1.80 2.27 2.49 2.77
30.0 39.4 68.0 68.2 99.2
1.44 1.72 2.26 2.47 2.77
47.7 47.7 75.5 71.7 101
CAK* Runs at the same initial solids concentration 1 0.0411 11.9 2 0.0411 11.9 3 0.0411 11.9 4 0.0411 11.9 5 0.0411 11.9 6 0.0411 11.9 Runs at different solids concentration 1 0.00705 12.0 2 0.00515 12.0 3 0.00379 11.7 4 0.00302 11.6 5 0.00169 11.3
CAK**
n =5
* From Figs. 10 and 11 by Eq. (4). ** From 0.65/fFK.
Note that the aggregate diameter is between 144 and 210 mm, that are values greater than the mean diameter particle around 12 mm, corroborating the flocculent character of the suspension. It can also be observed that when the CAK increases, the aggregate diameter also increases, in accordance with that observed in other research [5].
Fig. 12. Variation of the aggregate volume/solids volume ratio versus pH.
In order to discuss the influence of the pH, some suspensions were prepared at different pH values. Table 4 shows the variation of conductivity and ions Ca2 + , Mg2 + and SO24 − versus the pH. From these values, it is observed that there is an increase of the conductivity with the increase of the pH, as a consequence of the ions OH, Ca2 + , Mg2 + and SO24 − . This increase in the concentration of ions
Fig. 13. Variation of the aggregate diameter versus pH.
R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
83
Table 4 Variation of the conductivity versus pH pH
Ca2+ (ppm)
Mg2+ (ppm)
SO2− (ppm) 4
Conductivity (mS/cm)
7.0 8.7 11.8 12.3
527 433 365 949
33 13 B1 B1
1650 1590 1490 1780
2.3 2.3 2.7 4.3
probably causes the formation of dense flocs or aggregates, in accordance with the flocculation theory. This effect can also be related with the electrokinetic effect observed by Agerbæk and Keiding [21], where an increase is observed in the conductivity of the liquid causing a decrease in the flow resistance in a cake filtration.
CKo CK dA L1
n Re t t1
6. Conclusions The modified Kynch theory considering the two zones of solids concentration, hindered settling zone and compression zone, is useful for discussing the experimental results of chemical sludges. Tory plots (subsidence rate of the upper discontinuity versus the ratio of upper discontinuity height to the initial suspension height) can also be considered useful for identifying the critical points in the batch tests. The similar values of aggregate volume/solids volume ratio obtained in two independent ways, considering some relationships proposed in the literature, confirms that the sedimentation model with these relationships can satisfactorily interpret the sedimentation process. The great influence of the pH precipitation on the aggregate diameter and the average volume index has been deduced.
t2
V VSA
Z0 Zi
Z12 Appendix A. Notation CAK
CFK
ratio between aggregate volume and solids volume in an aggregate, dimensionless final solids concentration corresponding to the critical solids concentration, kg/m3
Z2 Z*
initial solids concentration, kg/m3 solids concentration, kg/m3 aggregate diameter, m height of the compression zone or extended sediment at time t1, m exponent in Eq. (4) Reynolds number time, s time at which the characteristic line of zone ‘c’ arises tangently from the compression zone surface, s time at the intersection of the characteristic line of zone ‘c’ with the suspension–supernatant interface, s absolute value of the settling velocity of solids, m/s absolute value of the settling velocity at dilution infinity, m/s initial height of suspension, m intercept of the tangent to the suspension–supernatant interface on the x axis in zone ‘b’, m intersection height of the tangent at (t2, Z2) with the vertical line at t1, m suspension height at time t2, m intercept height of the tangent to compression zone at the origin with the suspension–supernatant height, m
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Greek letters h r rA rK fA fFK fK fKo
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liquid viscosity, kg/(m s) liquid density, kg/m3 aggregate density, kg/m3 solids density, kg/m3 volume fraction of aggregates, dimensionless critical volume fraction of solids, dimensionless volume fraction of solids, dimensionless initial volume fraction of solids, dimensionless
References [1] [2] [3] [4]
R. Font, AIChE J. 34 (1988) 229. R. Font, AIChE J. 36 (1990) 3. R. Font, Chem. Eng. Sci. 46 (1991) 2473. R. Font, M. Perez, C. Pastor, Ind. Eng. Chem. Res. 33 (1994) 2859. [5] R. Font, A. Marcilla, C. Zoffmann, Powder Technol. 71 (1992) 217.
.
[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
G.J. Kynch, Trans. Faraday Soc. 48 (1952) 166. B. Fitch, AIChE J. 25 (1979) 913. B. Fitch, AIChE J. 29 (6) (1983) 940. B. Fitch, AIChE J. 39 (1993) 27. F.M. Tiller, AIChE J. 27 (1981) 823. F.M. Tiller, Z. Khatib, J. Colloid Interface Sci. 100 (1984) 55. T.h.F. Tadros, Solid/liquid dispersions, Academic Press, London, 1987. A.S. Michaels, J.C. Bolger, Ind. Eng. Chem. Fundam. 1 (1962) 24. J.F. Richardson, W.N. Zaki, Trans. Inst. Chem. Eng. 32 (1954) 35. J. Garside, M.R. Al-Dibouni, Ind. Eng. Chem. Proc. Des. Dev. 16 (1977) 206. E.J. Roberts, Mining Eng. 1 (1949) 61. J. Tering, Plat. Surf. Finish. 11 (1986) 34. P.T. Shannon, R.D. Dehaas, E.P. Stroupe, E.M. Tory, Ind. Eng. Chem. Fundam. 3 (1964) 250. R.V. Stephenson, J.M. Montgomery, E.R. Baumann, Partic. Sci. Technol. 4 (1986) 237. N. Tambio, Y. Watanabe, Water Res. 13 (1979) 409. M.L. Agerbæk, K. Keiding, J. Colloid Interface Sci. 169 (1995) 342.
Sedimentation test of metal hydroxides: hydrodynamics and influence of pH R. Font *, P. Garcı´a, M. Rodriguez Departamento de Ingenierı´a Quı´mica, Uni6ersidad de Alicante, Apartado 99, Alicante, Spain Received 25 February 1998; accepted 19 February 1999
Abstract Experimental data obtained from sedimentation tests of metal hydroxide suspensions have been discussed considering the compression zone surface observed directly and that deduced joining the critical points estimated from some sedimentation runs, when plotting the settling rate of the suspension – supernatant height versus time. Estimations of the aggregate diameter and the aggregate volume/solids volume ratio (by two independent methods) have also been obtained. The influence of the pH on the hydrodynamics, the aggregate diameter and the aggregate volume/solids aggregate ratio has been studied. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Sedimentation; Metal hydroxides; pH; Aggregate diameter
1. Introduction Sedimentation is a common dewatering unit operation. It is known that aggregates or flocs are formed inside the suspension of small and colloid particles. In the Department of Chemical Engineering of the Alicante University (Spain), a program of research about the fundamentals of sedimentation has been carried out, mainly with calcium carbonate suspensions [1 – 4]. Some conclusions obtained have also been applied to metal hydroxide suspensions [5]. The theory of the sedimentation developed with calcium carbonate suspensions is based on the Kynch theory [6], with * Corresponding author. Tel.: +34-6-590-3546; fax: +346-590-3464. E-mail address: [email protected] (R. Font)
important and significant modifications as indicated later, but this modified theory has not been universally accepted. The application of this modified theory is useful for designing continuous thickeners and also for the characterization of the aggregates formed (density and diameter). In the calcium carbonate suspensions studied, the aggregates formed have a high density (around 1100–1200 kg/m3). The density of some aggregates such as those corresponding to metal hydroxides and sewage sludges usually have values very close to those of water. Due to the fact that the modified Kynch theory has been tested with a suspension with dense aggregates, the analysis of this theory with low density aggregate suspensions can be useful for testing the hydrodynamics assumed. This is one of the objectives of this paper.
0927-7757/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 9 9 ) 0 0 0 9 1 - 6
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In addition to the testing of the modified Kynch theory, another important aspect has been the estimation of the aggregate volume/solids volume ratio by two independent procedures applying some relations proposed in the literature to the data obtained by the modified Kynch theory. The validity of the model proposed can be tested by comparison of the two values of this parameter. From the value of aggregate density, an estimation of the diameter can also be obtained. Finally, the great importance of the precipitation pH on the hydrodynamics and consequently also on the aggregate volume/solids volume ratio and diameter of the aggregates has been tested. The analysis of this influence has also been another aim of this paper.
2. Fundamentals of the modified Kynch theory In accordance with the fundamentals of sedimentation developed by some researchers [6–11], in very dilute suspensions, the particles settle separately, whereas at higher solids concentrations, aggregates are formed and the sedimentation takes place in different ways. At low solids concentration (dilute suspensions), the aggregates descend separately and the solids concentration controls the sedimentation rate. The range of solids concentration with these properties is known as non-compression range or hindered settling range. When the inertial effects of acceleration or deceleration are negligible, the
Kynch [6] theory can be applied inside this range, because the settling rate only depends on solids concentration. At high solids concentration (concentrated suspensions), the aggregates are together and a coherent network of solids is considered. The settling rate depends on the weight of the upper solids and the resistance force due to the upward liquid flow. In this range, called the compression range, Kynch’s theory cannot be applied. In the sedimentation tests of flocculated suspensions with low initial solids concentration, at least two discontinuities of solids concentration can be considered: the upper discontinuity or the supernatant–suspension discontinuity at the top of the suspension, and the compression zone or extended sediment interface, that rises from the bottom of the cylinder. Fig. 1 shows the evolution of the interfaces. Frequently, the solids settle in the upper part, forming stable aggregates, whereas in the sediment, the solids form a network or matrix, with the corresponding channels for upward circulation of the fluid. These two situations correspond to the hindered settling zone or the non-compression zone (when the aggregates or flocs settle separately, although hindering between themselves), and to the compression range or extended sediment. Inside the non-compression zone or hindered settling area shown in Fig. 1, three zones can be considered. In zone ‘a’, the solids concentration is constant and equals the initial one. The characteristic lines (lines of constant solids concentration
Fig. 1. Sedimentation test.
R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
and constant settling rate) arise from the bottom of the vessel in zone ‘b’ (or from the origin at a height–time diagram), whereas in zone ‘c’, the characteristic lines arise from the top surface of the sediment, tangentially to the sediment curve in a height– time diagram. Zones ‘a’ and ‘b’ are separated by the characteristic line rising from the bottom and corresponding to the initial solids concentration that intercepts with the upper discontinuity height ‘Z’ at the point where the absolute value of the slope ‘ −dZ/dt ’ begins to decrease or there is, in some cases, a first break in on the upper discontinuity line. Zones ‘b’ and ‘c’ are separated by the characteristic line that arises from the bottom of the vessel, tangentially to the extended sediment or compression zone in a height – time diagram. The point where the upper discontinuity intercepts to the compression zone height is known as critical point or second break. A wider discussion of the assumptions considered can be found elsewhere [1–3]. With the procedure presented in a previous paper [1] and taking into account the characteristic lines that arise from the bottom of the cylinder tangentially to the compression zone surface in a height–time diagram, the critical volume fraction of solids ‘fFK’ (corresponding to the situation when the aggregates are in touch as in a fixed bed of solid particles) or the critical solids concentration, CFK, can be calculated by the equation [1]: fFK =
CK f .Z = Ko o rK Z*
(1)
where rK is the solids density, fKo is the initial volume fraction of solids (equal to CKo/rK, where CKo is the initial solids concentration) and Z* is the intercept height of the upper discontinuity with the characteristic line that arises from the bottom of cylinder, tangentially to the compression zone (separating zones ‘b’ and ‘c’). In zone ‘a’, the constant settling rate shown in the upper discontinuity corresponds to the initial solids concentration. The solids settle downwards and the decrease in the solids mass due to the decreasing supernatant – suspension discontinuity is compensated by the increasing solids concen-
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tration of the low layers above the bottom, corresponding to the sediment. In zone ‘a’, the solids concentration equals the initial one, and the aggregates have a constant settling rate as a consequence of the constant solids concentration. In zones ‘b’ and ‘c’ (see Fig. 1), the relationships between the settling rate, calculated as ‘− dZ/dt’, and the volume fraction of solids are calculated, respectively, by the equations [1,6,7,10,12]: fK =
CK fKo.Zo = rK Zi
fK =
CK fKo.Zo = exp − rK Z12 − L1
dZ V = − 2 dt2
V = −
&
t1
0
dZ dt
(2)
dt1 t2 − t1
(3)
where the significance of Zi, Z12, L1, t1 and t2 are shown in Fig. 1. Drawing different characteristic lines, it is possible to obtain values of the settling rate (determined by the settling rate of the upper discontinuity ‘− dZ/dt’ or −dZ2/dt2 at the top of the characteristic lines) and the corresponding volume fraction of solids ‘fK’ or solids concentration, CK, by Eq. (2) (for zone ‘b’) or Eq. (3) (for zone ‘c’). In this way, a settling rate= f(volume fraction of solids) relation such as those shown later in Figs. 10 and 11 can be obtained. In zones ‘b’ and ‘c’, the aggregates are closer to each other and, consequently, the settling rate is less than that of zone ‘a’. The characteristic lines are the lines in the height–time diagram where the solids concentration and settling rate are constant, and they arise from the bottom of the cylinder (origin of the height–time diagram) in the so-called zone ‘b’ or from the sediment surface in the so-called zone ‘c’. Logically, in zone ‘c’ the aggregates are closer to each other than in zone ‘b’. The characteristic lines have a decreasing slope when they intercept at the supernatant–suspension discontinuity at increasing time as a consequence of the Kynch theorems. Eqs. (2) and (3) can be deduced from a mass balance of solids and they are the result of considering that the characteristic lines arise from the bottom of the cylinder (or from the
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Table 1 Equations concerning the settling rate = f(volume fraction of solids) relation V= Vo(1−CAKfK)n or V 1/n 1/n = V 1/n SA−CAKV SAfK
VSA = g(rA−rW)d 2A/(18h)
(4) when ReB0.2
(7)
CAK =aggregate volume/solids volume Re=rVSAdA/h
(5) VSA = [g(rA−rW)d 2A/(18h)] /(1+0.15Re0.687) when Re B 500 (8) rK+(CAK−1)rW Richardson and Zaki [14]: rA = (9) n = 4.65 when ReB0.2 CAK and 0.2BCAKfKB0.55 Garside and Al-Dibouni [15]: (5.09−n)/(n−2.73) =0.104Re0.877
(6)
when 0.2BCAKfKB0.5
origin in a height – time diagram) or from the sediment surface (tangentially to the sediment curve in a height – time diagram). Inside the sediment, the volume fraction of solids at the upper layer equals fFK, and when the sediment height increases, the solids concentration of the deepest layers also increases. The aggregates disappear and there is a matrix of solids with channels where some units of particle rearrangement can also be present, but different to and smaller than the aggregates that settle separately in the hindered settling zone.
3. Relationships between the solids concentration and the settling rate in the non-compression range Table 1 shows a diagram of the equations used in this paper based on some relations proposed in literature. Eq. (4) relates the decrease of the settling rate as a function of the porosity interaggregates (1− CAKfK) in accordance with the Michaels and Bolger [13] equation. The parameter CAK is the m3 aggregate/m3 solids ratio in an aggregate, thus ‘CAKfK’ is the volume fraction of aggregates fA.
The parameter ‘n’ can be considered to be 4.65 in accordance with the Richardson and Zaki [14] equation or calculated with the relation proposed by Garside and Al-Dibouni [15], depending on the value of the Reynolds number Re, considering the aggregate diameter, dA, the settling velocity, VSA, of solids at infinite dilution, and the liquid viscosity, h. The settling rate VSA of the aggregates at infinite dilution is related to the liquid density, rW, solids density, rK, gravity acceleration, g, and aggregate diameter, dA, by Eqs. (7) and (8). In some suspensions, the initial aggregates grow during the first few minutes of the sedimentation run after previously stirring and, consequently, the settling velocity of solids increases during the first period of the sedimentation test. In other suspensions, the initial settling rate of solids is higher than after a few minutes, and this can be explained admitting that the layer of fluid surrounding the aggregates can be very thin at the beginning and fluid can circulate upwards easier than later on [3]. The V 1/n versus fK plot can be used for analysing the experimental data, deducing if there is there is a flocculation process during the first few minutes of the sedimentation test and if the parameter CAK is or is not constant, calculating its value, and estimating also the diameter of the aggregates by the previous equations shown in Table 1.
4. Experimental procedure A suspension of metal hydroxides was obtained dissolving NiSO4·6H2O, ZnSO4·7H2O and CuSO4·5H2O in water, stirring slowly and gradually adding a suspension formed by water (50% wt) and solids (50% wt), the solids being a mixture of Ca(OH)2 (70% wt)+Mg(OH)2 (30% wt). The contents (ppm) of Ni2 + , Zn2 + and Cu2 + were similar. In this way, adding the basic suspension instead of the solids directly to the aqueous solution, uniform aggregates were formed. After adding the basic suspension, the pH value increased slowly to a stable final value after 24 h. Using the same procedure, and controlling the value of pH, the results were reproducible. After
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the period of 24 h, it was observed that the pH value varied slowly decreasing around 0.2 units in 2 months. The suspensions with different values of pH precipitation and pH at 24 h presented different hydrodynamics of the suspension (this aspect is discussed in the following sections). The density of the precipitated solids was 2837 kg/m3. This value was determined by boiling a suspension with a known amount of solids, cooling afterwards and transferring the suspension to a flask with a known volume. In this way, water filled the internal porous of the solids and the real density of the solids could be determined. The precipitated solids have a specific surface area around 3.9 g/m2, determined by the application of the BET equation to the 273 K carbon dioxide adsorption isotherm (Quantachrome Autosorb 6 sorption apparatus). This small value indicates that the internal porosity of the solids is very small. The diameter of the particles precipitated at pH 12 was measured by Fraunhouffer diffraction of a laser, obtaining a mean volume diameter of 35 mm when the particles were not deflocculated and a mean volume diameter of 12 mm when the suspension was deflocculated (3 g of solids in 25 cm3 with 0.4 g of sodium carbonate and 1.8 g of sodium hexametaphosphate). The supernatant obtained at pH 11.7 was analyzed showing concentrations of Ni, Cu and Zn, each one less than 1 ppm, coinciding with the values determined and presented in another paper [5]. Sedimentation tests were carried out in graduated glass cylinders of 6 cm internal diameter and 1 m height at 28 – 30°C. The verticality of the cylinders was controlled in all the runs. The runs were carried out as follows. The prepared suspension was introduced into the cylinders and then stirred slowly for 4 min. Afterwards, the test began and the height values of the upper discontinuity and the compression zone discontinuity (observed with difficulty) were measured at different times. The upper discontinuity was measured clearly after the first 7–8 min; the compression zone discontinuity was considered in the level where a significant change of porosity could be observed. Above the level con-
77
sidered, the porous structure corresponding to the hindered settling zone could be observed, whereas below the level considered, only some thin channels could be observed.
5. Experimental results
5.1. Runs at the same initial solids concentration and the same precipitation pH A series with six sedimentation runs, at CKo equal to 11.6 kg/m3 and precipitation pH 11.9, was carried out at different initial heights from 0.861 to 0.358 m. Fig. 2 shows the variation of the heights corresponding to the upper discontinuities and to the compression zones. The similarity of the initial upper interface descending with the same velocity corresponding to the initial solids concentration, and then a similar variation, can logically be observed. Considering the compression zone points shown in Fig. 2, it can be observed that these variations coincide from the bottom to the corresponding critical point. This coincidence can be explained taking into account the Kynch theory applied to the non-compression zone (which is the zone where only the assumptions considered in the Kynch theory are approximately correct). Considering the settling flux density–volume frac-
Fig. 2. Sedimentation tests with constant solids concentration and different initial heights (CKo =11.6 kg/m3).
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R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
Fig. 3. Solids flux density versus volume fraction of solids.
tion of solids plot shown in Fig. 3, for the runs with the initial concentration fKo, the rising of the sediment at t =0 corresponds to the slope AB. Later, when the compression zone thickness increases and the slope of the compression zone decreases as a consequence of its compression, the solids at the sediment surface have a small value of settling rate, and the slope of the compression zone equals A%B%, and later A%%B%%, etc. Consequently, the first portion of the rising compression zone does not depend on the initial height and logically must be common for all the tests, as occurs experimentally. The maximum height of the critical point logically depends on the amount of solids and therefore on the initial height. On way of analysing batch testing is by the Tory plots, where the variation of the supernatant–suspension discontinuity (− dZ/dt) is plotted versus the suspension height Z or versus the ratio of the suspension height to the initial suspension height (Z/Zo). The values of − dZ/dt have been calculated correlating the point considered, the previous one and the posterior point to a second-order relation Z = a +bt + ct 2, differentiating the corresponding function and calculating its value at the intermediate point. Fig. 4 shows this plot for one run. Fig. 5 shows the lower part corresponding to the variation of − dZ/dt versus Z for the same run and the estimated location of the critical point. The critical points are those located at the end of the lower straight lineal variation in accordance with the Roberts’ equa-
Fig. 4. Values − dZ/dt versus Z for the test CKo =11.6 kg/m3, pH 12 and Zo =0.660 m.
tion [16] and the discussion carried out by Fitch [9]. Fig. 6 presents all the correlations together, showing a similar variation. In order to compare the estimated critical points with the sediment location, Fig. 7 shows the variations of the sediment heights versus time and the critical points, deducing their coincidence, and corroborating that the criteria for estimating the location of the sediment (when a change of porous structure to a nearly continuous structure) was correct.
Fig. 5. Values − dZ/dt versus Z and location of the critical point for the test CKo =11.6 kg/m3, pH 12 and Zo =0.660 m.
R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
Fig. 6. Values −dZ/dt versus Z for all the runs with CKo 11.6 kg/m3 and pH 12.
5.2. Runs at different initial concentration and different pH 6alues
79
Fig. 8. Sedimentation test with different initial solids concentration for two runs: (a) CKo =20.0 kg/m3, pH 12.0; (b) CKo =4.80 kg/m3, pH 11.3.
A series of five experiments was carried out at different solids concentration between 20.0 and 4.80 kg/m3, and with similar initial height around 0.84 m.. The value of pH stabilized after 24 h varies from one experiment to other, so this value was measured in each run. Fig. 8 shows the variation of the upper discontinuity and the estimated sediment surface for two runs. Similar
variations were observed for the other runs, although there is no coincidence of the discontinuities when all the runs are plotted together. Fig. 9 shows the Tory plots for all the runs, showing the similar tendencies observed in the previous series of runs. The estimated critical points, at the intersection of the two discontinuity curves, coincide approximately with the end of the straight line drawn at the bottom of the Tory plots, corroborating the estimation of the compression zone surface.
Fig. 7. Compression zone height versus time and location of the critical points.
Fig. 9. Values −dZ/dt versus Z for all the runs with different initial solids concentration.
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R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
Table 2 Values of critical solids concentration for different operating conditions CKo (kg/m3) Runs at same concentration 1 11.7 2 11.7 3 11.7 4 11.7 5 11.7 6 11.7 Runs at different concentrations 1 20.0 2 14.6 3 10.8 4 8.56 5 4.80
fKo
pH at 24 h
Zo (m)
Z* (m)
CFK (kg/m3)
fFK
0.00411 0.00411 0.00411 0.00411 0.00411 0.00411
11.9 11.9 11.9 11.9 11.9 11.9
0.861 0.764 0.660 0.556 0.458 0.358
0.241 0.207 0.186 0.150 0.125 0.104
41.5 43.0 41.3 43.2 42.6 40.1
0.0146 0.0151 0.0145 0.0152 0.0150 0.0141
0.00705 0.00516 0.00381 0.00302 0.00169
12.0 12.0 11.7 11.7 11.3
0.858 0.835 0.880 0.888 0.835
0.445 0.317 0.391 0.296 0.220
38.6 38.6 24.4 25.7 18.2
0.0136 0.0136 0.0086 0.0090 0.0064
5.3. Determination of the critical solids concentration Determining Z* (intercept height between the upper discontinuity and the tangent to the compression zone at the origin) in accordance with Fig. 1, and applying Eq. (1), the values of the critical solids concentration were obtained for all the runs. Polynomial correlations of Z = Z(t) and L=L(t) were obtained for determining the slope dL/dt at t=0 and the intersection of the tangent to the compression zone at the bottom with the upper discontinuity. The values obtained were close to those deduced graphically from the figures. Table 2 shows the values obtained of the critical solids concentration for the different operating conditions. It can be observed that the suspensions with similar pH at 24 h have similar values of critical solids concentration. It can also be deduced that the precipitation at pH 12.0 leads to higher values of critical solids concentration than at pH 11.3 and 11.7.
5.4. Determination of the relation between the settling rate and the solids concentration in the hindered settling zone An important relation for the design of continuous thickeners is the relationship between the settling rate and the solids concentration. The equations, proposed by different researchers and
presented in Table 1, have been used to obtain this relationship and also to test the different hypotheses: Kynch theory, with the modifications introduced as a consequence of the sediment curvature in a Z–t diagram (zones b and c in Fig. 1), and the models of Richardson and Zaki [14] and Garside and Al-Dibouni [15] have been used. Considering the Z–t diagram of Figs. 2 and 8, the following variations of the upper discontinuity can be observed: a nearly constant variation of − dZ/dt corresponding to zone ‘a’ (zone of constant solids concentration equal to the initial one), a variation of − dZ/dt corresponding to zone ‘b’ and where Eq. (2) can be applied, and zone ‘c’ where Eq. (3) must be used. Considering different points in the curve Z= f(t) and determining the corresponding parameters, Zi for zone ‘b’ and Z12, L1 and tt211/(t2 − t1) dt1 for zone ‘c’, several values of V (settling rate) and the corresponding values of solids concentration were obtained for the different runs. Figs. 10 and 11 show the variation of the experimental values of V 1/4.65 versus the solids concentration in accordance with the Richardson and Zaki [14] equations for the runs with constant solids concentration and different solids concentration, respectively. A coincidence of the linear variation for the runs carried out with the same pH at 24 h can be observed. There is an initial portion that deviates from linearity, corresponding to the initial period of the batch testing after
R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
Fig. 10. Variation of V 1/4.65 versus fK for the runs with the same initial solids concentration.
the stirring of the suspension (this effect was also observed with calcium carbonate suspensions; this can be explained admitting that with the stirring, the water layer that surrounds the aggregates is thin and so the interaggregate porosity can be greater than afterwards without stirring, causing an initial great settling velocity). One interesting aspect that can be deduced is the great influence of the pH on the settling rate of solids for the same concentration. It is known that Mg(OH)2 causes the formation of large crys-
Fig. 11. Variation of V 1/4.65 versus fK for the runs with different initial solids concentration.
81
tals in the 9.5–12 pH range due to the slow rate of precipitation [17], but this effect cannot explain the great influence of the pH. The correlations between V 1/4.65 and CK were obtained without considering the initial points with unusual high settling rate as a consequence of the agitation for obtaining a uniform suspension. From the slope and intercept to the y axis, and in accordance with Eq. (4), the values of CAK and VSA have been obtained for all the runs. Considering that the aggregate density can be calculated by Eq. (9), the aggregate diameter was calculated by Eqs. (7) and (8). Table 3 shows the parameters deduced of CAK, aggregate diameter and the Reynolds number using the Richardson and Zaki [14] equation with n =4.65. In accordance with the Al-Dibouni and Garside equation, value n in Eq. (4) is around 5. In order to test the incidence of considering 5 instead of 4.65, the procedure was duplicated but considering n= 5. Similar variations to those observed in Figs. 10 and 11 were obtained. The values of CAK (aggregate volume/solids volume ratio), aggregate diameter and Reynolds number were also obtained and are shown in Table 3. It can be observed that the values of aggregate diameter and CAK are very similar when considering n= 4.65 or n= 5. On the other hand, values CAK can be calculated from the relationship, taking into account that at the critical solids concentration, the interaggregate porosity, which equals CAKfFK, can be close to that of a fixed bed of spheres ‘0.65’ [18].Table 3 also shows these values. Some interesting conclusions can be obtained from Table 3. 1. The values of CAK obtained by two different methods, both considering the Kynch theory with some modifications and the equations presented in Table 1, are very close indicating once again that the sedimentation model can roughly represent the real phenomena that take place. 2. There is a variation of the CAK and the aggregate diameter with the pH as observed in Figs. 12 and 13. On the other hand, when the values of CAK decrease, the aggregate diameters also decrease following the general tendency shown in other cases [19,20].
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Table 3 Values of CAK (aggregate volume/solids volume ratio) and aggregate diameter dA fKo
pH
n =4.65 dA (m)×104
CAK*
dA (m)×104
44.0 44.0 44.0 44.0 44.0 44.0
2.09 2.09 2.09 2.09 2.09 2.09
42.4 42.4 42.4 42.4 42.4 42.4
2.10 2.10 2.10 2.10 2.10 2.10
44.4 42.9 44.5 42.7 43.2 45.9
41.1 42.8 71.1 71.2 105
1.73 1.80 2.27 2.49 2.77
30.0 39.4 68.0 68.2 99.2
1.44 1.72 2.26 2.47 2.77
47.7 47.7 75.5 71.7 101
CAK* Runs at the same initial solids concentration 1 0.0411 11.9 2 0.0411 11.9 3 0.0411 11.9 4 0.0411 11.9 5 0.0411 11.9 6 0.0411 11.9 Runs at different solids concentration 1 0.00705 12.0 2 0.00515 12.0 3 0.00379 11.7 4 0.00302 11.6 5 0.00169 11.3
CAK**
n =5
* From Figs. 10 and 11 by Eq. (4). ** From 0.65/fFK.
Note that the aggregate diameter is between 144 and 210 mm, that are values greater than the mean diameter particle around 12 mm, corroborating the flocculent character of the suspension. It can also be observed that when the CAK increases, the aggregate diameter also increases, in accordance with that observed in other research [5].
Fig. 12. Variation of the aggregate volume/solids volume ratio versus pH.
In order to discuss the influence of the pH, some suspensions were prepared at different pH values. Table 4 shows the variation of conductivity and ions Ca2 + , Mg2 + and SO24 − versus the pH. From these values, it is observed that there is an increase of the conductivity with the increase of the pH, as a consequence of the ions OH, Ca2 + , Mg2 + and SO24 − . This increase in the concentration of ions
Fig. 13. Variation of the aggregate diameter versus pH.
R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
83
Table 4 Variation of the conductivity versus pH pH
Ca2+ (ppm)
Mg2+ (ppm)
SO2− (ppm) 4
Conductivity (mS/cm)
7.0 8.7 11.8 12.3
527 433 365 949
33 13 B1 B1
1650 1590 1490 1780
2.3 2.3 2.7 4.3
probably causes the formation of dense flocs or aggregates, in accordance with the flocculation theory. This effect can also be related with the electrokinetic effect observed by Agerbæk and Keiding [21], where an increase is observed in the conductivity of the liquid causing a decrease in the flow resistance in a cake filtration.
CKo CK dA L1
n Re t t1
6. Conclusions The modified Kynch theory considering the two zones of solids concentration, hindered settling zone and compression zone, is useful for discussing the experimental results of chemical sludges. Tory plots (subsidence rate of the upper discontinuity versus the ratio of upper discontinuity height to the initial suspension height) can also be considered useful for identifying the critical points in the batch tests. The similar values of aggregate volume/solids volume ratio obtained in two independent ways, considering some relationships proposed in the literature, confirms that the sedimentation model with these relationships can satisfactorily interpret the sedimentation process. The great influence of the pH precipitation on the aggregate diameter and the average volume index has been deduced.
t2
V VSA
Z0 Zi
Z12 Appendix A. Notation CAK
CFK
ratio between aggregate volume and solids volume in an aggregate, dimensionless final solids concentration corresponding to the critical solids concentration, kg/m3
Z2 Z*
initial solids concentration, kg/m3 solids concentration, kg/m3 aggregate diameter, m height of the compression zone or extended sediment at time t1, m exponent in Eq. (4) Reynolds number time, s time at which the characteristic line of zone ‘c’ arises tangently from the compression zone surface, s time at the intersection of the characteristic line of zone ‘c’ with the suspension–supernatant interface, s absolute value of the settling velocity of solids, m/s absolute value of the settling velocity at dilution infinity, m/s initial height of suspension, m intercept of the tangent to the suspension–supernatant interface on the x axis in zone ‘b’, m intersection height of the tangent at (t2, Z2) with the vertical line at t1, m suspension height at time t2, m intercept height of the tangent to compression zone at the origin with the suspension–supernatant height, m
84
Greek letters h r rA rK fA fFK fK fKo
R. Font et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 157 (1999) 73–84
liquid viscosity, kg/(m s) liquid density, kg/m3 aggregate density, kg/m3 solids density, kg/m3 volume fraction of aggregates, dimensionless critical volume fraction of solids, dimensionless volume fraction of solids, dimensionless initial volume fraction of solids, dimensionless
References [1] [2] [3] [4]
R. Font, AIChE J. 34 (1988) 229. R. Font, AIChE J. 36 (1990) 3. R. Font, Chem. Eng. Sci. 46 (1991) 2473. R. Font, M. Perez, C. Pastor, Ind. Eng. Chem. Res. 33 (1994) 2859. [5] R. Font, A. Marcilla, C. Zoffmann, Powder Technol. 71 (1992) 217.
.
[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
G.J. Kynch, Trans. Faraday Soc. 48 (1952) 166. B. Fitch, AIChE J. 25 (1979) 913. B. Fitch, AIChE J. 29 (6) (1983) 940. B. Fitch, AIChE J. 39 (1993) 27. F.M. Tiller, AIChE J. 27 (1981) 823. F.M. Tiller, Z. Khatib, J. Colloid Interface Sci. 100 (1984) 55. T.h.F. Tadros, Solid/liquid dispersions, Academic Press, London, 1987. A.S. Michaels, J.C. Bolger, Ind. Eng. Chem. Fundam. 1 (1962) 24. J.F. Richardson, W.N. Zaki, Trans. Inst. Chem. Eng. 32 (1954) 35. J. Garside, M.R. Al-Dibouni, Ind. Eng. Chem. Proc. Des. Dev. 16 (1977) 206. E.J. Roberts, Mining Eng. 1 (1949) 61. J. Tering, Plat. Surf. Finish. 11 (1986) 34. P.T. Shannon, R.D. Dehaas, E.P. Stroupe, E.M. Tory, Ind. Eng. Chem. Fundam. 3 (1964) 250. R.V. Stephenson, J.M. Montgomery, E.R. Baumann, Partic. Sci. Technol. 4 (1986) 237. N. Tambio, Y. Watanabe, Water Res. 13 (1979) 409. M.L. Agerbæk, K. Keiding, J. Colloid Interface Sci. 169 (1995) 342.