966
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 966-970
Mixing experiments were carried out by using two columns (0.816 and 0.0102 m3) and two air tanks (0.03 and 0.0542 m3). Experimental results did not appear to substantiate theoretical predictions (2) and (3). This may be partly due to the fact that the required air quantity varied only discretely according to the number of air injections. From an operational viewpoint, the above predictions can be justified. Transient air pressures inside of a column and an air tank were measured, in which measurements were then used to calculate the entropy generation and work. The calculated values were different from theoretical predictions by approximately 5% in terms of entropy generation and 10% in terms of work. Thus, conclusions (l),(2), and (3) (those based on a quasi-steady-state assumption) were proven to be valid in theory. Acknowledgment We are grateful to one of the referees (of the previous work) who suggested the calculation of entropy generation. Nomenclature A , = cross-sectionalarea at the conical apex, m2 A , = cross-sectionalarea of the nozzle, m2 d = pipe diameter, m G = mass velocity, kg/s L = pipe length, m m = molecular weight, kg M = u/cro, degree of mixing Mal,Ma2= Mach number, m/s n = number of sampling points N = number of air injections N , = work performed by air with one air injection, J N, = work performed by the jetting air stream, J Nt = "1, J Po P4 = pressure, Pa APi = Pi - Po, Pa APf = Pf - Po, Pa Pat= atmospheric pressure, Pa R = gas constant, J/(K.mol) Re = d W / P s = specific entropy, J/(K kg) S,, S,, = entropy generation, J/K
-
t = time, s t o = time span during which mixing effectively occurred, s u,u ( t ) = air velocity from the nozzle, m/s = characteristic velocity (eq 22) V = V , or V,, m3 V , = volume of column minus particles, m3 V , = volume of air tank, m3 w = Nw,,kg w 1 = air quantity with one air injection, kg W = total particle weight, kg x = volume fraction of smaller particles x , = x when perfect mixing is achieved 3 = average value of x for the five sampling points Y = defined by eq 5 Greek Letters = air density, kg/m3 = variance defined by eq 21
p u
uo =
variance before mixing
-
Subscripts 0 4 = position in the flow system (Figure 1) i = initial f = final
Literature Cited Akiyama, T.; Peters, L. K.; Kageyama, S.; Hosoi, M.; Yokota, I.; Kono, M. Ind. Eng. Chem. Process Des. Dev. 1981, 21, 664. Akiyama, t.; Kano, T.; Matsubara, K.: Kono, M.; Melo, J. Huntakog8ku 1983, 20. 141. Akiyama, T.; Tada, I. Ind. Eng. Chem. Process Des. Dev. 1984 in press. Bejan, A. "Entropy Generation Through Heat and Fluid Flow"; Wlley: New York, 1982; Chapter 2. Cheremlsinoff, N. P.; Cheremislnoff, P. N. "Hydrodynamics of Gas-Solids Fluidization"; Gulf Publishing Co.: Houston, 1984; Chapter 11. Davklson, J. F.; Harrlson, D. "Fluidization";Academlc Press: London, 1971; Chapter 2. Davklson, J. F.; Keairns, D. L. "Fluidization"; Cambridge Unlverslty Press: New York, 1978; Chapter 6 . Lapple. C. E. Trans. Am. Inst. &em. Eng. 1843. 3 9 , 385. Levenspiel, 0. A I C M J . 1977, 23, 402. Mathur, K. 8.; EDsteln, N. "S~outedBed"; Academic Press: New York. 1974 Chapte; 4. Shapko, A. "Compressible Fluid Flow"; Ronald Press: New York, 1953: Vol. 1, Chapter 6.
Received for review April 16, 1984 Revised manuscript received November 13, 1984 Accepted December 5 , 1984
Buoyant-Particle-Promoted Settling of I ndustrial Suspensions S. Venkataraman and Ralph H. Welland' Depafiment of Chemlcal Engfneerlng, Clarkson Universlv, Potsdam, New York 13676
Enhanced sedlmentatlon of industrial self-flocculatlng suspensions by the addition of rigid buoyant particles is demonstrated for calcium carbonate suspensions. Sedimentation rates were increased by up to a factor of 4. Some of the calcium carbonate was entrained with the buoyant particles, but this is shown to be more an artifact of batch settling rather than a potentially serious problem in continuous sedimentation.
The separation of solids suspended in a liquid constitutes an important step in a large variety of industrial processes. One of the simplest and most common methods of achieving such a separation is by gravity settling; however, gravity is a rather weak force when the particles are small or they have a specific gravity only slightly greater than the suspending fluid. Among the techniques in current use to enhance settling rates are the use of flocculating agents which increase the particle size and the 0196-4305/85/ 1 124-0966$0 1.50/0
insertion of inclined plates inb the settler, thereby creating huge surface areas for particle deposition. Another lesswell-known means of improving sedimentation rates, and one that is still in the experimental stages, is through the addition of substantial quantities of buoyant particles to the suspension before settling commences. Motivated by some early observations of Whitmore (1955) that the presence of neutrally buoyant particles could sometimes promote-settling, Weiland and McPherson (1979) further 0 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 967
developed the notion by extending it to include the addition of positively buoyant particles. Their study and those of Fessas (1983) and Fessas and Weiland (1981,1982, 1984) all dealt with the buoyant-particle-enhanced sedimentation of so-called model suspensions of nearly spherical particles, mostly of single sizes, which did not flocculate; nevertheless, all these studies indicated that sedimentation rates could be increased by factors of 20 times or more. All tests were done in the batch mode, and it was found that the most difficult-to-settle suspensions were the very ones whose settling rates could be most improved by the addition of buoyant particles. The presence of buoyant particles destabilizes uniform settling and drives the heavy particles to separate from the buoyant ones in the lateral direction. A state is quickly reached in which the particulate species present in the smallest volumetric concentration segregates into streams which flow through a continuum suspension of particles of the other kind. The streams and the continuum have quite different densities, mainly as a result of the particles they contain being of different density, and gravity drives a large-scale convective flow of the streams through the surrounding continuum. This convection is superimposed on normal hindered settling velocities, and it is this that is responsible for the large increases in overall rates of separation. A more detailed description of the evolutionary process has been presented by Weiland et al. (1984) who also report that similar convective flows result even when the particles are both more dense than the fluid-all that is needed is for there to be present two types of particles distinguishable by size or density and in sufficient concentration. Model suspensions have usually been observed to separate quite cleanly in that the resulting sediments were free of particles of the opposite kind unless extremely high concentrations were being used or the settling vessel was too shallow. Early tests of this technique on the settling of flocculating industrial suspensions (Vilambi, 1982), however, indicated that the bed of buoyant material which collects at the top of a batch settling vessel was often contaminated by varying quantities of the heavy solids phase. His experiments included tests on suspensions of calcium carbonate, tailings from a Minnesota taconite mill, and fine coal-all these materials are self-flocculating. On the other hand, his experiments also showed enormous improvements to the settling rates of these slurries. If three-phase settling is to be used industrially in the continuous mode to improve sedimentation rates, contamination of either suspension by particles of the opposite density cannot be tolerated. Slight contamination of thickener overflow, i.e., the slurry of buoyant particles, could be handled by recycle since the buoyant phase would be recycled in any case; slight contamination of the underflow would represent a small loss of the buoyant promoter which could be made up; gross contamination, however, is another matter. Vilambi found that up to 30% by weight of the heavy solids could end up in the bed of buoyant particles which, in commercial operation, would seriously reduce the effectiveness of using buoyant particles. The present work is motivated by his observations, and it seeks to answer the question as to whether contamination is an artifact of the batch mode of settling. The second purpose is to present data on the efficacy of using buoyant particles to promote the settling of industrial suspensions. Experimental Section The heavy suspension used in this study consisted of self-flocculating calcium carbonate particles of material
specific gravity 2.649 in water. The buoyant particles were hollow ceramic microballoons (Emerson and Cumming, Inc.) which, as received, varied in specific gravity from 0.44 to 1.0 and covered a wide spectrum of sizes. Two batches of material having specific gravities in the ranges 0.66-0.81 and 0.81-1.0 were obtained by successively sink-floating the original mixture in water, ethanol, and n-hexane. These fractions were then dry-screened by using an air-jet sieve into size fractions -180+150, -150+125, -125+106, and -106+90 pm. Experiments were done to determine (i) the primary particle size and the floc size, (ii) the way in which the calcium carbonate is distributed within the bed of buoyant ceramic particles that collects at the top of the sedimentation vessel, and (iii) the degree of enhancement to sedimentation that results from the addition of buoyant particles. Floc characteristics were estimated from settling rate measurements by following a procedure similar to one used by Thomas (1963). In the sedimentation of flocculating suspensions, there is a critical concentration above which the flocs no longer settle as individuals but instead they begin interacting rather strongly with each other and, as a result, they settle as networks. Below the critical concentration, the settling rate can be related to the concentration and to the settling rate at infinite dilution by the relationship ln Uf = In Ufo - 5.94f = In Ufo - 5.9 (1 + a14 (1) where a is the volume ratio of fluid to solids within the floc and
The apparent size of the primary particles is related to the effective floc size by (1 + C Y ) ~ D = ,Df
(4)
In these expressions, f refers to flocs, p refers to primary particles, and unsubscripted variables refer to the fluid. The quantity 4 is the volume fraction solids in the fluid, and 4f is the volume fraction flocs in the fluid; these are related by
4f = (1+ a14
(5)
Thus, experiments were done to measure the settling velocity, Uf, as a function of the solids concentration, 4, and from a plot of In Uf against 4 one can determine a. Then, floc density can be found from eq 3 and the effective floc size from eq 2. Finally, the primary particle size can be calculated from eq 4. Michaels and Bolger (1962) in their experiments with flocculated kaolin suspensions observed a small intermediate concentration regime at which the transition from rapid-settling flocs to slow-settling networks occurred. In the dilute regime, they related the settling velocity U, to the free-settling velocity U,O by the relationship
Uf = UfO(1-&)4.65
(6)
The apparatus used for the measurements of floc characteristics consisted of a Plexiglas tube 50.8 mm i.d. by 600 mm long mounted vertically with the aid of a theodolite. The tube was graduated with a millimeter scale, and it contained several sampling ports at regular intervals of 50 mm. Experiments were done by starting with the most concentrated slurry (4.3% by volume),
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Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
400
t
-
4
t
20
40
80
Time,
80
100
120
minutes
Figure 2. Set of typical settling curves for calcium carbonate promoted by buoyant particles of size 125-150 fim and density 660-810 kg/m3. Calcium carbonate concentration is 100 kg/m3, and numbers on lines are weight ratios of microballoons to calcium carbonate.
important parameter in determining the size of buoyant particles to be used. For example, Fessas (1983) has found that for buoyant particles whose density differs from the fluid by about the same amount as the heavy particles, the buoyant particle size should not exceed about 4 times that of the heavy particles. The values of the floc characteristics estimated by using the correlation suggested by Michaels and Bolger are in close agreement with the values determined by Thomas's correlation except that the relationship (6) predicts a lower free-settling velocity compared to the correlation (1)and hence a lower floc size of 165 pm. A typical set of settling curves for a 100 kg/m3 calcium carbonate slurry is shown in Figure 2 for various weight ratios of microballoons to calcium carbonate. From these plots, it is evident that even though the addition of buoyant particles results in a greater initial height of mixed suspension, it also enhances the settling rate tremendously. In the case of buoyant particles being added in the weight ratio of 2:1, the settling velocity increases from 1.25 to 16 mm/min, a factor of a nearly 13 times increase. Even though the initial slurry depth was some 90 mm greater than in the absence of buoyant particles, at the expiration of only 12 min the suspension has settled 110 mm when it would have taken 90 min to settle that distance unaided. In partical terms, this represents a factor of 7 improvement. This degree of enhancement is even more striking when it is realized that a 100 kg/m3 concentration is equivalent to nearly 3.8% by volume, at which concentration the flocs are settling as networks, not as discrete individuals; nevertheless, the buoyant particles have no difficulty in causing their rapid segregation into streams. The bend in the curves in Figure 2 occurs at the point when the buoyant and heavy particles separate from each other vertically, Le., at the so-called disengagement point. Beyond this point, settling rates return pretty much to what they would have been without buoyant particles. This suggests that the concentration of the carbonate suspension formed after disengagement is unaffected by the presence or absence of buoyant particles; however, settling velocity is a relatively weak function of concentration in this range so the settling curves cannot be expected to depart much from parallel in any case. If one is interested in the formation of sediments, then an enhancement ratio can be conveniently defined as the rate of sediment formation (weight per unit time) during the accelerated rate period divided by the sediment for-
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 969 4
I
I
I
I
I
O
'
O
e
8
~i 00
t 1
I
0.0
0.5
1
I
I
1 .o
1.5
I
I
1
2.0
2.5
Weight Ratio (Buoyant : Heavy) Figure 3. Effect of heavy and buoyant particle concentrations on the enhancement to the rate of sediment formation. Calcium carbonate concentrations are 50 (A),75 ( O ) , and 100 kg/m3 ( O ) , and buoyant particle density is 660-810 kg/m3. Points are averages for the four particle size ranges.
mation rate in the absence of buoyant particles. In this way, one can also take into account the fact that, at least in the batch mode, some of the calcium carbonate gets entrained into the buoyant particle bed. It was found that the buoyant particles of higher density produced relatively poor enhancement ratios (1.2 to 1.8), whereas, enhancement ratios of up to 4 were obtained by using the lower density particles. Statistical analysis of the data showed that buoyant particle size did not have a significant effect on the enhanced rate of sediment formation. The enhancement ratio was found to increase with increasing concentrations of both the heavy and the buoyant particles until it reached a maximum and thereafter dropped off. This is shown in Figure 3 and is quite similar to what has been observed by using model suspensions of spherical nonflocculating materials (Fessas, 1983). However, model suspensions containing less than about 10% by volume of heavy particles often exhibit retardation to the settling rate from buoyant particle addition; in the present work, 50 and 100 kg/m3 suspensions correspond to only 1.9% and 3.8%, respectively, of primary particles by volume so retardation might be expected on the basis of observations in model systems. But in terms of volume fractions of flocs, even the 50 kg/m3 suspension corresponds to over 50% flocs. (This assumes that floc density is independent of particle concentration, an obvious fallacy in this case at high-enough concentrations). Thus, in all cases in the present work, we are dealing with very concentrated suspensions in terms of floc volume fraction; so in that sense acceleration would be expected. One of the major difficulties encountered by Vilambi (1982) in trying to enhance the settling of industrial suspensions by using buoyant particles was that the separated bed of buoyant particles invariably was contaminated to some extent by particles of the opposite kind, although the settled sediment of heavy particles was always free of buoyant ones. In an effort to understand this phenomenon, the beds of buoyant particles were cut into thin horizontal slices and the calcium carbonate content of each slice was determined titrimetrically. This resulted in profiles of carbonate concentration as a function of depth into the bed, a typical set of which is shown in Figure 4. Here, X measures the
'
'
"
1
50
~
'
"
~
100
'
'
'
160
'
~
'
'
ZOO
'
x, m m
Figure 4. Contamination profile of the calcium carbonate content of the packed bed of buoyant particles. Calcium carbonate concentration is 100 kg/m3, and buoyant particle density and size are 660-810 kg/m3 and 150-180 pm. Numbers on the lines are weight ratios of buoyant particles to calcium carbonate.
distance from the top of the bed, larger values of X corresponding to later formed sediments. Evidently, the first-formed sediments are very highly contaminated with calcium carbonate, and the extent of contamination drops off rapidly as fresh sediment deposits. There are two major possible causes for contamination: either the two types of particles are coflocculated or in some sense physically bound, or contamination arises from hydrodynamic interaction. If physical binding were the cause, then one would expect the degree of contamination to be independent from the time the sediment was deposited. Such is not the case; rather, the longer the time available for separation, the less contamination there is. This suggests that rather weak hydrodynamic forces are responsible for the buoyant particles dragging along heavy ones with them and, of greter practical importance, that contamination is unlikely to be a serious problem in continuous thickening. The high degree of contamination seen in this study is truly an artifact of the batch mode of making the tests. On first setting the mixed suspension to rest, there is just not sufficient time for the two types of particles to separate before some of the buoyant ones have already formed a thin layer of sediment and have entrapped heavy particles. That contamination is a result of hydrodynamic interaction is further supported by the fact that the lower density, large buoyant particles entrain less of the heavy material, presumably because their rise velocity is higher. In continuous settlers, it is likely that fluid motion will be strong enough to dislodge most of the heavy material before the buoyant particles reach the top of the suspension.
Concluding Remarks These are the first reported experiments demonstrating that the addition of buoyant particles to industrial flocculating suspensions results in marked improvement to sedimentation rates. Although the separation of buoyant from heavy particles is not perfectly sharp, this is more likely an artifact of the batch mode of these tests, and it is doubtful that contaminationwill be serious in continuous settling. Acknowledgment This work was supported by the National Science Foundation under Grants CPE-8023185 and CPE8305011. The assistance of Dorr-Oliver, Inc., is gratefully acknowledged.
'
970
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 ,
Nomenclature D = particle size, m g = acceleration due to gravity, m/s2 U = settling velocity, m/s X = distance from the top of the buoyant sediment, mm Subscripts f = refers to flocs p = refers to primary particles Superscript O = at infinite dilution Greek Letters (Y
p p
= fluid to solid volume ratio in the floc = fluid viscosity, kg/(m s)
970-976
4 = volume fraction solids Registry No. Calcium carbonate, 471-34-1. Literature Cited Fessas, Y. P. Ph.D. Thesis, Clarkson University, Potsdam, NY, 1983. Fessas, Y. P.; Weiland, R. H. AIChE J . 1981, 2 7 , 588. Fessas, Y. P.; Weiland, R. H. Resour. Conserv. 1982, 9 , 87. Fessas, Y. P.; Weiland, R. H. I n t . J. MuMphase Flow 1984, 10, 485. Michaels, A. S.;Bolger, J. C. Ind. Eng. Chem. Fundam. 1962, 1 , 24. Stagle, D. S.;Shah, Y. T.; Klinzing, G. E.; Waiters, J. G. Ind. Eng. Chem. Process D e s . Dev. 1978, 17, 500. Thomas, D. G. AIChE J . 1963, 9 , 310. Vilambi, N. R. K. M.S. Thesis, Clarkson University, Potsdam, NY, 1982. Weiland, R. H.;Fessas. Y. P.; Ramarao. B. V. J . Fluid Mech. 1984, 142, 383. Weiland, R. H.; McPherson, R. R. Ind. Eng. Chem. Fundam. 1979, 18, 45. Whitmore, R. L. Br. J . Appl. Phys. 1955, 6 , 239.
Received for reuiew May 31, 1984 Accepted November 29, 1984
= density (of fluid if not subscripted), kg/m3
Cost Dtagrams and the Quick Screening of Process Alternatives James M. Douglas' Chemical Engineerlng Department, Universm of Massachusetts, Amherst, Massachusetts 0 1003
Duncan C. Woodcock Imperial Chemical Industries, Runcorn. Cheshire WA7 4QE. England
Cost diagrams provide a useful way of summarizing total processing cost information for preliminary process designs. I n addition, they are often useful for checking rules of thumb, for obtaining quick estimates of the economics of process alternatives, and for establishing a hierarchy of optimization variables. Thus, they help to establish priorities for more detailed design studies.
A t the initial stage of designing a new process, it is possible to generate more than 1 million flow sheets (Douglas, 1985) and there are about 10-20 optimizations of the design variables required for each flow sheet (Westerberg, 1981). Heuristics can often be used to eliminate some of the alternate flow sheets and to provide first estimates of some of the design variables, but there are still a very large number of process alternatives and optimizations that need to be considered. Since flow sheets normally are dropped from further consideration based on the total processing costs (safety, operability, and pollution may play a part), it is useful to have a simple and efficient way of summarizing cost information. Cost diagrams can be used for this purpose. In addition, cost diagrams sometimes are useful for checking rules of thumb, for obtaining quick estimates of the economics of process alternatives, and for identifying a hierarchy of optimization problems. Previous Work From an examination of published design case studies (Washington University Design Case Study Series; AIChE Student Problems; Stanford Research Institute Reports; Peters and Timmerhaus, 1980; Happel and Jordan, 1975; Baasel, 1977; Ulrich, 1984), it seems to be common practice to tabulate the manufacturing costs and the capital costs separately. The list of capital costs normally is itemized to correspond to names or tags shown on a flow sheet, but 0196-4305/85/1124-0970$01.50/0
all the steam or cooling water costs usually are added together and reported as a single item. Separate tables of manufacturing and capital costs would then be prepared for each process alternative. Cost Diagrams As an alternate approach to summarizing cost information at the preliminary stages of a process design, we can prepare a cost diagram. The annualized, installed capital cost of each piece of equipment is listed inside of the equipment box on a flow sheet, and the annual operating costs are attached to the stream arrows. Figure 1 shows a cost diagram for the production of acetone by the dehydrogenation of isopropyl alcohol, which is a modified version of the 1948 AIChE Student Contest Problem (McKetta, 1976). The values in Figure 1are reported in terms of thousands of dollars per year. Of course, we could also divide both the annualized capital costa and the annual operating costs by the annual production rate of the process. Then, the cost diagram would indicate the dollars per pound of product that each item on the flow sheet contributed to the final product price. This type of an approach is sometimes used in industry for the design of batch processes. Use of Cost Diagrams To Check Rules of Thumb It is natural to assume that the reflux ratios for the two distillation columns shown in Figure 1 were fixed by the 0 1985 American Chemical Society
