THICKENING OF CALCIUM CARBONATE SLURRIES Comparison of Data with Results for Rigid Spheres K E I T H J. SCOTT
Chemical Engineerin! Group, S. A . Council /or Scient@ and Industrial Research, Pretoria, South A/rica
A means of correlating the sedimentation behavior of three different calcium carbonate slurries based upon the reduced flux curve for rigid spheres is presented and used to explain various sedimentation and thickening phenomena which have been reported. The effective solids (aggregate) volume fraction is shown to have an important bearing upon both the mode of settling and the concentration zones which form in a continuous thickener. Three regimes are postulated: dilute, in which the behavior is “ideal;“ intermediate, in which channel formation gives rise to abnormally high static batch settling rates; and concentrated, in which the aggregates are in mechanical compression. Observed deviations from the flux theory are explained, and the doubly humped flux curve is discussed.
Comings (1 940) carried out fairly extensive thickening tests on calcium carbonate and other slurries (Comings et al., 1954), his published data cannot be compared, other than qualitatively, with the predictions of the flux theory (Shannon and Tory, 1965a) because of the lack of sufficient data to construct an experimental flux plot. Tory (1961) obtained extensive batch settling rate data on a calcium carbonate slurry but his slurry differed considerably from the one used by Comings. A similar problem occurs when carrying out extended continuous thickening runs on flocculated slurries whose settling characteristics vary with time, especially when the effects of altering an operating variable are small compared with that due to the change in sedimentation behavior. A means of overcoming this problem has, however, been developed and found to be applicable also to calcium carbonate slurries, so that in spite of differing settling rates, a single flux curve can be drawn. The technique thus provides a basis for the direct comparison of the sedimentation and thickening data of different workers and affords a rational explanation for the shape and properties of the experimental flux plot. This plot proves to be similar to that for rigid spheres (Shannon et al., 1963) in two respects, but it exhibits several important deviations, the understanding of which are essential in interpreting the observed thickening behavior of real slurries. ALTHOUGH
Solids Flux for Rigid Spheres
I t is accepted (Shannon et a/., 1963) that the reduced velocity for rigid spheres is given by Richardson and Zaki’s (1954) equation
!
=
€4.65
UO
where u = measured velocity of slurry interface a t a porosity of E , cm. per minute; u o = Stokes velocity of average particle, cm. per minute; and E = effective porosity expressed as a volume fraction [(l - E ) = effective solids volume fraction]. This equation implies that a positive settling velocity will be observed for all concentrations up to (1 - e) = 1, but as the ultimate concentration observed for spheres is (1 - E ) = 0.64 484
I&EC FUNDAMENTALS
(Shannon et al., 1963), no movement of particles relative to the walls can occur above this concentration. Buchanan (1965) considers that because of the possibility of an upward flow of fluid through the fixed bed, settling velocities above this concentration should be regarded as positive but unreal. Shannon and Tory (1365b), however, point out that to use the flux curve to interpret the rate of rise of discontinuities in batch settling and hence slurry behavior in continuous thickening, the settling velocity at the ultimate solids concentration must be accepted as zero. The only question is whether the approach to zero occurs continuously or abruptly and on this point hangs the validity of the truly doubly humped flux plot (Tory, 1961). In the absence of conclusive experimental evidence, it will be accepted that the settling velocity falls abruptly to zero at the ultimate solids concentration, the value of which requires independent verification. The product of the reduced velocity and the solids volume fraction which, for want of a better term, is called the reduced solids flux, is therefore given as Reduced solids flux =
5 (1 - e)
= e4,65(l
uo
- e)
(2)
The curve of the dimensionless reduced flux against (1 - E ) derived according to Equation 2 is shown in Figure 1. T h e maximum in the curve occurs at (1 - E) = 0.177, and this value may be obtained directly by differentiating Equation 2 and setting the derivative to zero. Solids Flux for Calcium Carbonate Slurries
Flux plots for calcium carbonate by Shannon and Tory (1965a) and Hassett (1964-65) show maximum values a t a dry solids volume fraction of betiveen 0.005 and 0.01, and both well below the theoretical approach zero at a value of 0.08, values of 0.177 and 0.64, respectively, noted above. Furthermore, the particle size distribution of the material used by Hassett indicates that the bulk of the particles lays between 1.5 and 6 microns with a 50% cut at 2.5 microns and as the Stokes cm. per settling velocity for such a particle is only 3.5 x minute, his observed settling rates for dilute suspensions exceeded this by a factor of about 50.
bY mtons
2
v
,
I
I
02
0
I
7
04 Vduml
h-,
I
06 hcllon
101148
08
IO
I1.E)
Figure 1. Reduced flux curve for rigid spheres
I
c,
T h e slurry therefore cannot consist of the individually dispersed calcium carbonate particles, but if the particles are assumed to be aggregated into sedimentation units with properties similar to flocs, the above discrepancies can be removed. Michaels and Bolger (1962) have shown that such units effectively immobilize a relatively large volume of water thus reducing the apparent porosity and, if the total volume of the aggregates is assumed to be proportional to the weight of dry solids: e =
(1
- kc)
Figure 2. Relationship between ~ ‘ ’ 4 . ~and ~ concentration o f calcium carbonate for sedimentation data of various authors
(3)
where e = effective porosity; c = calcium carbonate concentration, grams per cc. of slurry; k = volume of aggregates, cc. per gram of contained calcium carbonate; kc = effective solids volume fraction (1 - E) = aggregate volume fraction. Inserting this value of E into Equation 1 gives - - (1
- kc)4.66
QlCP
(4)
110
Because of the aggregation, the values of u o and k are unknown and they, with the validity of Equation 3, must be experimentally verified. Using the mean values of u and c obtained from Tory’s thesis (1961), a plot of u1/*.65 against c should yield a straight line, and the actual results (Figure 2) confirm that this is so between c = 0.01 and c = 0.035. Using the intercept values of this line, the unknown constants of Equation 4 are: uo = 6.2 cm. per minute and k = 10.8 cc. per gram. One may now estimate the reduced flux curve for this material using the appropriate values of (1 - E) = 10.8 c and u o = 6.2 cm. per minute in Equation 2. T h e reduced flux is thus equal to u ’ c 10.8/6.2, where u is the mean of the maximum batch settling rates a t a concentration of c grams per cc. taken from Tory (1 961). A plot of the reduced flux against the effective solids volume fraction (10.8~) is shown in Figure 3. The experimental points are shown together with the corresponding curve for rigid spheres (Equation 2). The results indicate that the correlation is excellent up to a “solids” volume fraction of 0.4, but that above this value the reduced flux for calcium carbonate is in excess of that for rigid spheres. Differences between Calcium Carbonate Slurry and Rigid Spheres
T h e value of 0.64 solids volume fraction represents the maximum packing density for rigid spheres. If the calcium carbonate aggregates behaved in a similar manner the complete sedimentation curve for the most dilute slurry in Figure 3 (point A 0.0099 gram per cc.) should follow the lines DEF in Figure 4, where DE represents the descent of the
k c . (I-€)
Figure 3. Comparison of experimental data of Tory (1961) for calcium carbonate with reduced flux curve for rigid spheres
Run 28 (Tory, 19611 5- 0
0099 g l c o
Ho*140.0cm
f 2
.g
06
0.41
\ Tima
lmin)
Figure 4. Reduced sedimentation curve for a dilute slurry
interface during free settling; OE represents the rise of the fixed bed consisting of aggregates a t a 0.64 volume packing (c = 0.64/10.8 = 0.054 gram per cc.), and EF represents the state of the interface if no compression were possible. The actual curve (Tory, 1961) followed the path DGHJ, indicating several important differences. First, H J lies below EF and therefore the “maximum” settled density is in excess of 0.64 aggregate volume fraction and corresponds more closely to about 0.92 a t t = 0 (tangent construction a t point K ) . Furthermore, slope H J indicates that the density of the bed increases steadily with time so that this “maximum” value has VOL. 7
NO. 3 A U G U S T 1 9 6 %
485
r
Table 1. Classification of Calcium Carbonate Slurries Group Designation (7 - E ) Mode of Settling I Dilute 0-0.4 Free settling of individual
I1
Intermediate
I11
Concentrated
aggregates 0.4-1 . 0 Channeling between aggregates >1 . O Structural collapse of aggregates
, 50
I
IW
150
Tima
1
2W
lminl
DlCD
Figure 6. Sedimentation curve of intermediate slurry
so
100 lima
150
Iminl
Figure 5. Variation of solids concentration at the 16.4-cm. level with time
little practical significance. More important, two distinct breaks occur, a t points G and H, representing a buildup zone of intermediate concentration. This is unexpected if the maximum aggregate fraction is 0.64, but readily predictable from Figure 3, provided the maximum aggregate fraction is in excess of 0.84 (tangent .4BC, Figure 3). T h e predicted aggregate fraction of this intermediate buildup zone ( B ) is 0.42 from Figure 3, and this is confirmed by the experimental value of 0.41, determined by the y-ray density measurements in Tory’s run 28 (1961). T h e settling curve of Figure 4 is therefore consistent with a “maximum” aggregate volume fraction in excess of 0.84, and hence it appears that the aggregates, unlike glass spheres, can deform readily to fill the voids and hence produce relatively higher packing densities. T h e extent to \vhich the voids may be filled can be tested experimentally. Starting with a slurry of uniform solids concentration in excess of 0.45 aggregate fraction-i.e., c > 0.45/10.8 = 0.042 gram per cc.-a buildup zone of the “maximum” density should be propagated upward from the base of the vessel and, according to Figure 3, no intermediate concentrations should appear. Tory’s run 11 (1961), with a n initial concentration of 0.055 gram per cc., satisfies this condition, and Figure 5 shows that a sudden concentration increase occurred a t the 16.4-cm. level 70 minutes after commencement of the test. The concentration increased from c = 0.055 to c = 0.105 gram per CC. over 20 minutes and thereafter sho\ved a further gradual increase a t the same level until finally a value of c = 0.172 gram per cc. was recorded. The aggregate volume “fraction” corresponding to G = 0.10 gram per cc. (70 minutes) is 1.08, which suggests that a n aggregate volume fraction of 1.00 can be readily attained by gravity sedimentation and that the calcium carbonate aggregates must therefore easily deform to fill entirely the effective free voidage. Although this value of (1 - e) = 1.00 may be regarded as the “maximum” value obtainable by free settling, rather than 0.64, it clearly does not represent the practical 486
l&EC FUNDAMENTALS
maximum, and hence some mechanism whereby the deformed aggregates can now reduce their volume and release excess water must come into play. Higher concentrations are formed as a result of increasing the weight of overlying solid (Shannon and Tory, 1965a), and hence it seems reasonable to suppose that when the yield strength of the aggregates is exceeded structural collapse occurs as a result of shearing the particleparticle bonds, and the water within the aggregates is thereby released. Tentative Classification of Slurries
For purposes of further discussion, slurries with a n aggregate volume fraction of less than 1.0(c 1. @ / k )will be regarded as being free settling. Such suspensions settle readily to form a concentration c = 1.0/k gram per cc. by a process involving sedimentation and deformation (change of shape) but not a change in volume of the contained aggregates. Concentrations in excess of c = 1.0/k gram per cc. are attainable only by reduction in the initial volume of the aggregates, and the author postulates that this is brought about by an increased weight of solids per unit area. The latter process is hence termed compressive settling. The “free settling” suspensions may be divided into two groups according to whether or not they follow the settling behavior of spheres (Figure 3). Free settling slurries with an effective solids volume fraction in excess of 0.4 are termed intermediate slurries. These groups are collected in Table I.
