Delivered at the Crystal Engineering to Crystal Growth: Design and Function Symposium, ACS 223rd National Meeting, Orlando, Florida, April 7-11, 2002
CRYSTAL GROWTH & DESIGN 2002 VOL. 2, NO. 5 375-379
Residence Time Optimization in Continuous Crystallizers Thanassi E. Fakatselis* Messo Inc., 563 North Oak, Hinsdale, Illinois 60521 Received April 16, 2002
ABSTRACT: The production rate of a given crystallizer is defined, in part, by the residence time provided by the crystallizer vessel. Typically, this parameter is based on small-scale tests, which exaggerate the effects of secondary nucleation. Scale-up of crystallization equipment should allow for lower secondary nucleation, and this may, on occasion, allow for lower residence time than that used in pilot testing. In scale-up, the attrition rate decreases with the square of the vessel size increase, at constant specific energy input, and crystal-crystal contact is more dependent on crystal size, than crystal number. To determine the results of increasing production (lowering the crystal residence time), one needs to consider specific characteristics of the crystal shape, hardness, brittleness, sources of attrition, stresses on the crystal structure, supersaturation, and type of equipment in use. A reduction in residence time is not necessarily going to bring about poorer crystal quality. Introduction One of the primary design parameters of a crystallizer is the crystal residence time. This parameter impacts on the product size to be obtained, embodies the crystal growth rate and the effective nucleation rate, and is usually determined by experimentation. The residence time is a deciding factor in defining the crystallizer geometric size, and as a result it has direct bearing on the economics of a given crystallization system. Short residence times will define a smaller (less expensive) unit, but also one that may fail to produce crystals of sufficient size. As engineers, by nature, will err on the safe side, many operating crystallizers may be oversized, and their productivity may be increased under certain conditions. If the specific application is examined closely, with a view to how the residence time is affected by crystal characteristics and hardware configuration, it may be possible to improve the unit’s productivity with little penalty on crystal quality. Figure 1 shows that the residence time of a crystallizer is, at least, dependent on certain macro effects of the suspension fluid mechanics. The efficiency of mixing, whether in terms of proper suspension, good distribution of the solids, and good mixing, will all affect the real residence time of a crystallizer. The implication here is that in a case of perfect mixing, the residence time is at some minimum value. This value is then increased in practice, to account for mixing inefficiencies. The common concern, however, in increasing the production in an existing crystallizer is that because of shorter residence time, it will bring about higher su* Author correspondence. Tel: 708-672-1068. E-mail: t.fakatselis@ messo.net.
Figure 1. Suspension fluid mechanics effects on kinetic processes in a crystallizer, categorized by scale (after ref 8). RTD is residence time distribution.
persaturation, which in turn will reduce the average particle size. Sometimes, to avoid decreasing the residence time, the magma density of the crystallizer will be increased, but this holds the danger of increased attrition, which will also result in a smaller product. The general expectation in connection with these or related actions is that the secondary nucleation rate will increase, while the effective growth rate of the crystals will be reduced. Therefore, the general belief is that in increasing production (or providing shorter residence times for a new crystallizer) the average crystal purity or size will decline. In the following sections, we will review each of the parameters affected by increased production or shorter residence time in a continuous crystallizer, and how they might actually affect crystal quality.
10.1021/cg020014b CCC: $22.00 © 2002 American Chemical Society Published on Web 07/25/2002
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Fakatselis
Figure 2. Dependence of overall growth rate constant on prevailing supersaturation for two different crystallizer volumes, 300 and 3850 mL (after ref 2).
Figure 3. Dependence of average crystal size on ratio of feed supersaturation to mixing intensity in reaction crystallization (after ref 3).
It is recognized that there are many applications where the desired crystal product is not the largest possible, that sometimes, small crystals are required expressly, and that on occasion, agglomerated solids is the desired form. In the author’s opinion, however, the majority of industrial crystallizers is called upon to produce as large a product as possible, within the unit’s design limitations, and it is for this reason, that in this paper the concept of “better” crystals is often used interchangeably with “larger” crystals.
comes a critical parameter. In such cases, the crystallizer requires more intense mixing to counter the increase in ∆c, and to avoid the occurrence of excessive primary nucleation. As an example, Torbacke3 found that the average crystal size in reacting hydrochloric acid with sodium benzoate increased with increased circulation and increased feed point mixing intensity (Figure 3). The above illustrate that a higher ∆c in an operating crystallizer, or a higher ∆c allowed in a new design (as opposed to previous practice) does not necessarily imply a requirement for increased mixing, to compensate for the resultant supersaturation. A well-defined MZW and a better understanding of the crystallization kinetics of a given process may allow for such an increase in the ∆c with no discernible penalty.
Increased Supersaturation A crystallizer is usually provided with some mixing mechanism to control the supersaturation (∆c) generated by the crystallization process. The supersaturation limit is usually described by the metastable zone width (MZW); after that limit has been surpassed, primary nucleation, with detrimental effects on crystal size, is expected to occur. The mixing, therefore, provides a means to maintain the local supersaturation to some optimum level, and definitely, to a level below the limit set by the MZW. For a given operating crystallizer, increases in production mean an increase in the ∆c value within which the crystallizer operates, given that the mixing rate does not change. The optimum level of supersaturation is not known in most cases, because it is not a parameter that can be easily quantified: tests are usually carried out in small scale (lab) units, which do not correspond well to the dynamic system of the equivalent industrial crystallizer. As a result, an increase in ∆c is considered dangerous, because there is little actual knowledge of how far into the MZW the unit may already be operating. The fear exists that the higher ∆c value might exceed the MZW. However, there are several exceptions to this line of reasoning. Increasing supersaturation might result in larger crystals, due to agglomeration,1 given, of course, that the intensity of mixing will be such that such agglomerates will not be broken up. In some cases, such as in drowning-out precipitation or cooling crystallization of potassium sulfate,2 the growth rate can be independent of crystallizer volume size, crystallizer geometry, and mode of agitation (Figure 2). In certain fast-rate crystallization reactions, as production increases in the crystallizer, micro- or meso-mixing be-
Crystal Characteristics The need to dissipate a higher level of supersaturation normally leads to increasing the crystallizer’s mixing rate or intensity. A more esoteric approach to reducing the ∆c is to increase the magma density in the crystallizer, so that the available crystal surface area compensates for the increase in supersaturation. Increasing agitation intensity or magma density is thought to increase the attrition rate of the crystal, and thus lead to reduced overall crystal size. While this is generally true, the degree to which these phenomena are experienced in a specific system is not the same, and may not be as severe as one might expect. Ploss4 found that crystals break when a certain stress threshold is exceeded, and not (as generally thought) as a function of energy input to the slurry by the mixing device. Further, in industrial-size crystallizers, the contribution to the overall nucleation rate by crystalcrystal collisions, rather than propeller collisions, is the deciding factor, and crystal shape is an important criterion on how stresses will be distributed within the lattice of a given crystal. It follows that in larger crystallizers, estimating crystal breakage involves some understanding of the hardness and brittleness of the crystal, rather than the effect of the energy input by the mixing device. The effect of mixing energy input on nucleation is, in any case, diminished as the crystallizer size increases, simply due to the larger volume of the slurry being mixed.
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Figure 5. Effect of scale-up factor on overall attrition rate (ref 7).
Figure 4. Relationship between relative speed (crystal and propeller); propeller characteristic length T ) B[sin(β - R)], a function of blade width B, blade angle [β], and crystal path incident angle [R]; crystal size; and probability of contact (after ref 6).
A combination of high mixing rate and high magma density is generally thought to produce conditions similar to those in a crystal grinder, as the probability of a crystal being hit by the mixer increases in time and in intensity. However, Crawley5 found that crystals do not necessarily break into progressively smaller and smaller parts as they are subjected to continuous agitation; many fines reattach themselves to larger crystals, others agglomerate into larger particles, and the resulting effective secondary nucleation is much lower than theoretically expected. In combination, Gahn6 notes that as crystal size increases, the probability that a crystal will contact the impeller decreases, because the inertia of a larger mass will allow the crystal to follow flow-lines, rather than be caught in mid-flight by the mixer blade (Figure 4). This means that larger crystals are actually subjected less frequently to impact forces, and the result is erosion, rather than attrition. This explains well the fact that the typical shape of most large crystals made in continuous crystallizers is spheroid. The above illustrate that increasing the agitation rate is not necessarily a detrimental action in maintaining a given crystal size, while increasing crystallizer production. Such parameters as the crystal physical properties (hardness, shape, elasticity, etc.), as well as the actual crystal size distribution should be considered in deciding whether to increase the mixing intensity in the crystallizer. Scale-Up Under the best-hoped-for conditions, the average crystallizer unit has been designed on the basis of smallscale (1- to 6-L) test units. Typically, the residence time used in the scale-up is very close to that found as optimum in the testwork. Optimum residence time is thought to be that at which crystal growth is maximized, while attrition, erosion, and generally, secondary nucleation is minimized, to produce a large crystal. However, it is well-known that small-scale equipment provides higher levels of secondary nucleation, than the same system in its scaled-up version.
Figure 6. Nucleation rate vs growth rate for 50 µm K2SO4 crystals, cooling crystallization (after ref 2).
Several methods for scale-up from a laboratory crystallizer to an industrial-size unit have been proposed, and are used, on the basis of what the designer might consider important attributes of a particular crystallization operation. In short, these methods address mostly physical or fluid-dynamic variables as power input, mixing intensity, turbulence, geometric similarity, etc. There is, by the nature of the problem, very little known on the scale-up characteristics for residence time, growth and nucleation rate for a particular system. Synowiec7 shows that while the attrition due to turbulent forces caused by fluid motion is independent of vessel size, the maximum contribution to the total number of fragments would be in the 30-40% range. He further elaborated that at constant power input per unit volume, as a unit’s volume is scaled up, the relative attrition rate (the ratio of attrition in the larger unit to that of the pilot unit) drops exponentially as the scaleup factor increases (Figure 5). Jones2 found lower nucleation rates for larger crystallizer volumes of the same crystallization system while no effect of crystallizer size was noted on growth rate (Figure 6). Finally, working with stirred tanks, Rielly8 confirmed that the frequency with which a crystal is hit by the propeller is a function of the crystal size. He found that crystal size distributions for generally smaller crystals reflect higher rates of breakage by the propeller, due to the higher probability that the propeller will hit most crystals in such a system. However, when the same compound is crystallized in a larger volume, it will produce a somewhat larger average particle (because
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nucleation in the larger unit is generally lower), the larger particle, in turn, will be less prone to be damaged by the propeller. He concluded that stirred tanks are not to be considered well mixed, and that using that model to predict MSMPR crystallization kinetics is “fraught with difficulties”, because average values are used, which are not reproducible in other systems. The above (as well as other) work leads to the conclusion that in most industrial crystallizers the residence time used in the vessel’s original design is very likely a conservative estimate, and a certain amount of production increase may be possible without any penalty in crystal quality. It is important to consider, however, the actual contributors to the unit’s effective nucleation rate, and the type of geometric configuration employed. This approach would safeguard against an overly optimistic approach to the safety factor inherent in a crystallizer’s residence time. Attrition There are three serious sources of attrition in an industrial crystallizer: attrition due to crystals hit by the propeller of the mixer, attrition from one crystal striking another, and attrition from a crystal striking crystallizer parts (vessel walls, vanes, supports, etc.). The two first are the most important contributors to overall crystal attrition, and each will be addressed separately. Attrition: Crystal-Impeller. As discussed earlier, a common concern to increasing the production rate of a crystallizer is the effect that higher supersaturation will have on nucleation rate and scaling tendency within the crystallizer vessel. The usual solution to problems stemming from high supersaturation is to increase the agitation in the crystallizer. However, there is fear that in increasing the mixing intensity in an existing crystallizer, or using a higher mixing intensity in a new design, one might bring about higher rates of crystal breakage. There are, however, several situations where this fear may be groundless. Nienow9 showed that the impact efficiency (the probability of a given crystal hitting the impeller) drops dramatically with increasing vessel size. Therefore, although one might expect some effect from increased agitation in a large-scale crystallizer, it is likely that it will not be as severe as theory might predict. The overall effect of increased agitation on crystals is small, according to Synowiec7 who developed equations showing that while crystal-impeller contacts are a strong function of crystal size (fifth order dependence), they are only linearly dependent on magma density and power input. Further, Synowiec developed data that indicated a significant reduction in the number of fragments generated by the impeller, if the impeller surface hardness were to be reduced. Combining the above, one might conclude that increasing mixing rate in a crystallizer, while at the same time changing the mixer surface material, may result in only small increases in secondary nucleation. Zwietering10 shows that given geometric similarity, the specific energy input (kW/kg of crystal) from a mixer decreases exponentially with increasing scale-up ratios. Therefore, the breakage detected in pilot plant work is
Fakatselis
Figure 7. Normalized shear rate (shear rate/rotation rate) vs local Reynolds number for disks (diameters of 80-160 mm) and impeller (160 mm diameter), after ref 11.
most likely far greater than what will be experienced in a larger unit. Combining this finding with Synowiec’s work we may state that increasing mixing intensity in a crystallizer, as we also increase the crystallizer’s size, should result in little or no adverse effects on crystal size. Increasing mixing intensity in an existing crystallizer can be achieved by speeding up the existing stirrer, by increasing the stirrer’s diameter, or changing its pumping efficiency (changing the impeller type). The second choice may be the optimum: Wichterle11 found that the shear rate of a centrifugal pump impeller (and thus the secondary nucleation produced by it) is directly related to impeller speed (Figure 7). Figure 7 illustrates that the same turbulence (Reynolds number) can be obtained at several combinations of shear rates and impeller speeds. As a result, a carefully chosen impeller (larger diameter will produce the same flow at lower speed) may avoid excessive nucleation at higher pumping rates. Naturally, changing the impeller type (improving the pumping efficiency) is an even better solution, which, however, is usually not feasible because of mechanical limitations of the stirrer in use. On the basis of the above sampling of published work, it may be seen that increasing mixing intensity at higher production rates should be seriously considered, as it may be more beneficial than generally expected. Attrition: Crystal-Crystal. A typical way to increase production, while maintaining a constant (before and after the production increase) residence time, is to increase the magma density (kg of crystals/m3 of slurry) in the crystallizer. Conventional theory indicates that, in such case, the secondary nucleation should increase, because of increased probability of crystal-crystal collisions. Further, there are limitations to the level of such an increase, due to suspension limitations by the crystallizer stirrer. In scale-up, however, at constant specific energy input, the attrition rate decreases with the square of the vessel size increase; crystal-crystal contact is eighth-order dependent on crystal size, and only secondorder dependent on crystal number, according to the work of Synowiec.7 Therefore, increasing magma density to compensate for residence time lost to an increase in production may be acceptable in cases where the crystal size is small, and the stirrer has the capability of maintaining suspension of the crystals in a heavier magma density.
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Figure 8. Mass transfer in a flat-bottom agitated tank as a function of Reynolds number, for benzoic acid, salt, barium chloride, naphthalene, in aqueous, or methanol, or other solutions (after ref 12).
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tion crystallizers is less than the ideal 50% because of poor mixing. Improving the mixing in an forced circulation crystallizer would thus utilize crystallizer volume that was, hereto, idle, and thus the crystallizer would gain production capability without a penalty in crystal quality. (iv) Gahn6 determined that, for a DTB (on potassium nitrate production), an increase in magma density had little effect on crystal size, after a certain threshold is passed (Figure 9). From field experience, we have found this to be true for other compounds as well. (v) Gahn,6 Synowiec,7 and others have over time suggested that the agitator or pump impeller may be designed in such a way that one may reduce the probability of crystal to impeller impact. Such designs have begun to be industrially available, and can be used in operation upgrades. (vi) Increasing the capacity of an OSLO crystallizer can be made with some geometric changes, to improve its clarification capabilities at higher throughput rates. However, as such improvements have physical limitations, OSLO units that are pushed very hard will tend to operate as FCs, with the attendant effects on crystal size (smaller crystals). Conclusions
Figure 9. Potassium nitrate in a DTB crystallizer, residence time of 2.2 h, specific energy input of 1 W/kg (after ref 6).
Crystallization Equipment The tolerance for increased agitation, increased magma density, and reduced residence time, resulting from production increases is a function of (among other things) the type of crystallizer being employed. The main types of crystallizers used in the industry for continuous operation are the forced circulation (FC) crystallizer, which is equivalent to a tank with an external circulation loop; the draft tube baffle (DTB) crystallizer, which combines a settler with an MSMPR section (the stirrer is located within a draft tube for improved mixing efficiency); and the OSLO (or growth) crystallizer, which employs a fluidized bed of crystals to eliminate crystal-to-stirrer attrition. What follows are some of the special characteristics of industrial scale continuous crystallizers, in connection to increased productivity: (i) In a draft tube baffle (DTB) crystallizer equipped with fines destruction capability, increased nucleation due to higher magma density, higher circulation rates, or higher supersaturation may go unnoticed if the fines destruction equipment is so large that it will destroy the new (additional) fragments. (ii) Kneule12 found that for MSMPR units (the forced circulation crystallizer is considered to approximate MSMPR operation) the mass transfer (and thus growth rate) may be improved dramatically by increasing the NRE, for certain ranges of operation, and for certain agitator power numbers (Figure 8). (iii) Bennett13 theorized that the coefficient of variation of crystal size distributions of many forced circula-
The increase of production in an existing crystallizer may, under certain conditions, be achieved with minimal impact on the crystal quality. The crystallizer operation should be reviewed in very specific terms for the crystal tolerance to attrition, the mixer type, the flexibility of the crystallizer type in use, the supersaturation involved, and the type of operation (salting out, reaction, evaporative or surface cooling, etc.). On the basis of this paper, one may develop a strategy that could include special propeller types, specific mixing intensity, magma density increase, etc., that would allow in combination the increase in crystal production without an undue penalty on the product crystal size from higher attrition or nucleation rates. References (1) David, R.; Bossoutrot, J.-M. Chem. Eng. Sci. 1996, 51 (21), 4939-4947. (2) Jones, A. G.; Mydlarz, J. Chem. Eng. Res. Des. 1989, 67, 283-293. (3) Torbacke M.; Rasmuson A° . Chem. Eng. Sci. 2001, 56, 24592473. (4) Ploss, R.; Mersmann, A. Chem. Eng. Tech. 1989, 12, 137146. (5) Crawley, G. M.; Gruy, F.; Cournil, M. Chem. Eng. Sci. 1996, 51 (20), 4537-4550. (6) Gahn, C. In Die Festigkeit von Kristallen und ihr Einfluss auf die Kinetik in Suspensionskristallisatoren; University of Mu¨nchen, Thesis, 1997. (7) Synowiec, P.; Jones, A. G.; Ayazi Shamlou, P. Chem. Eng. Sci. 1993, 48, (20), 3485-3495. (8) Rielly, C. D.; Marquis, A. J. Chem. Eng. Sci. 2001, 56, 24752493. (9) Nienow, A. W. Trans. Inst. Chem. Eng. 1976, 54, 205-207. (10) Zwietering, Tr. N. Chem. Eng. Sci. 1958, 8, 244-253. (11) Wichterle, K.; Sobolik, V.; Lutz, M.; Denk, V. Chem. Eng. Sci. 1996, 51 (23), 5227-5228. (12) Kneule, F. Chemie-Ing. Tech. 1956, 3, 221-225. (13) Bennett, R. C. Chem. Eng. Prog. 1962, 58 (9), 76-80.
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