A review of crystallization theory applied to the draft tube baffle crystallizer

Thanassi E. Fakatselis

Abstract

The Draft Tube Baffle (DTB) Crystallizer, used in applications requiring narrow crystal distribution, and larger average crystal size, has been examined widely in crystallisation theory. This paper brings together a design foundation comprising the most important equations that describe the DTB in terms of the crystal size distribution expected, the destruction and classified product removal features that characterise it, and its characteristic population balance plot. A brief description of the DTB's working principles is given.

Introduction

Draft Tube Baffle (DTB) Crystallizer (fig. 1)
Draft Tube Baffle (DTB) Crystallizer (figure 1)

The basic choices of the type of crystallizer for continuous operation are few: the design engineer has to choose between a mixed tank, a fluidised bed (also known as "Growth" type or OSLO) crystallizer, and a Draft Tube Baffle (DTB) crystallizer (fig. 1). The nature of a mixed tank is self-explanatory, and needs no further elaboration. It is the workhorse of crystallisation processes, and is best understood, because its simple nature lends itself to practical modelling and experimentation. The bulk of batch and continuous crystallisation theory is based on work done with this type of crystallizer, the Mixed Suspension, Mixed Particle Removal (MSMPR) unit.

The OSLO crystallizer has been in use for most of this century, and has been employed in cases where a large crystal size is required. It features a crystal bed, which is fluidised by a supersaturated solution. This allows for crystal growth without any mechanical mixing, and can generate very large and well-defined crystals. It is very difficult to model this type of unit in smaller scale, because of geometric limitations; also, its nature is such that basic design parameters must be based on assumptions that are difficult or impossible to verify in the field. As a result, theoretical work on the OSLO is limited, and this raises a severe handicap in scale-up or troubleshooting operations of such units. The understanding of an OSLO, therefore, is case-specific and based on empirical evidence.

The third option, the DTB, is a combination of an MSMPR crystallizer and a classifier. It has been in use for about the last forty years, more or alternative to the OSLO in fulfilling large-crystal requirements. Although the DTB has been marketed by very few crystallisation designers, it has been studied well both by its creators and by Academia. While it also suffers the disadvantage of not being easily reproduced in small scale, for the same reasons as the OSLO, the design parameters are easy to define and control accurately. As a result, its understanding is based on well-proven theoretical work, and this makes the DTB easy to apply to new crystallisation systems, troubleshoot, and optimise.

This paper summarises the most common theoretical work on the DTB, and suggests simple methods of applying this theoretical work to understand and enhance the operation of such a crystallizer.

Brief Description of the DTB

The simplest DTB crystallizer comprises two distinct functions and two distinct regimes (fig. 2): the regime in which crystallisation occurs, and the regime in which clarification is achieved. The crystallisation zone can be viewed as an MSMPR, in broad terms of crystallisation kinetics. The clarification zone is employed to remove particles of a given size from the crystallizer vessel. This is achieved by an overflow from this zone which is set to carry with it particles of the desired size, against gravitational settling, while allowing particles of larger sizes to remain in the crystallisation zone. The disposition of the overflow leaving the DTB is critical to the crystallizer's operation. In some cases, the overflow is simply removed from the crystallisation operation, functioning only as a means to increase the crystallizer's magma density. In other cases, the overflow is recycled to the DTB crystallizer, after it has been thermally or chemically modified. The most common objective of such modifications is the "destruction" (i.e. dissolution) of the crystals in the overflow. The modified overflow is returned to the DTB's crystallisation zone, where it participates in the precipitation process, through its increased supersaturation. This has a marked effect on the crystal size and the size distribution of the product crystals: it produces larger crystals, and narrows their size distribution.

The simplest DTB crystallizer comprises two distinct functions and two distinct regimes (fig. 2): the regime in which crystallisation occurs, and the regime in which clarification is achieved.

The simplest DTB crystallizer comprises two distinct functions and two distinct regimes (fig. 2): the regime in which crystallisation occurs, and the regime in which clarification is achieved.

Significant Equations

A very useful tool in understanding the operation of a DTB is the graphical depiction of its population balance, commonly being a plot of the natural log of the number of crystals of each discreet crystal size. In these coordinates, the MSMPR crystallizer should produce a straight line, assuming that the crystal growth rate is independent of crystal size. There are several variations of this relationship, depending on controlling situations in the crystallizer (agglomeration, size-dependent less as t growth, breakage, etc.) and these have been covered adequately in the literature (for example, Canning, 1976).

The DTB does not alter the kinetic characteristics of a particular crystallisation process. These characteristics are the linear growth rate G (m/s) and nucleation rate Bo (1/m3-s), as well as the effects that secondary nucleation, supersaturation, magma density, etc will have on these parameters. This means that an MSMPR model can be used with reasonable accuracy to obtain these values.

The DTB's ability to operate at magma densities higher than the "natural" level (the density resulting from the crystallisation operation only, i.e. by concentration or cooling), by utilising its thickening feature, allows the engineer to exploit any positive influence this action may provide on crystal growth and nucleation rates. As a result, small-scale experiments can easily determine the relationship of MT to G, and Bo, and the DTB can be designed to achieve this specific condition. In purely theoretical terms, the gravitational clarification function of the DTB might be considered equivalent to a hydrocyclone, which removes the clarified liquor overflow, while it returns the heavy slurry underflow to the MSMPR. However, this arrangement would present serious practical difficulties: a large volume of slurry would need to be recycled from the MSMPR unit through the hydrocyclone, at considerable energy input. This would degrade the crystal size through breakage of the recycled crystals and increased secondary nucleation. Since crystal attrition is very difficult to quantify beforehand, such a design would be unpredictable, until operated at its full scale. At any rate, the knowledge missing in the design phase would not be whether a hydrocyclone-and-mixedtank arrangement would produce smaller crystals than a DTB, but how much smaller such a system's crystal would be.

The DTB has a characteristic Crystal Size Distribution (CSD), which includes information on the clarification performance of the Baffle. Compared to the MSMPR CSD, the DTB shows a characteristically different distribution, with a clear indication of the maximum particle size (LF) removed by the baffle overflow.

Since a simple crystal size distribution of a slurry sample from the DTB will give us this information, the baffle can be characterised directly in terms of effectiveness (LF) and in terms of clarity (amount of crystals present in the overflow). One may also estimate the effect of varying the overflow rate on the population balance of the DTB, or, inversely, one may estimate the actual overflow rate of an operating unit from the population balance.

The population balance, as represented in the ln(n) vs. L plot, also provides information on the nucleation rate, the growth rate, and the number of new nuclei formed at size L ~ 0 (Fig. 4).

Given the above information, one can now calculate the theoretical crystal size distribution, for a variety of operating conditions: a change in the upward velocity of the "clear" liquor in the baffle will change the LF; a change in the amount of mother liquor withdrawn from the crystallizer via the baffle will change the tF. Both of these variables will in turn affect the crystal size (Randolph et al, 1973):

In the above equations, we are dealing with the so-called R-z system (in this case, a DTB which not only thickens, but also classifies the product crystals, prior to their discharge from the crystallizer); at steady state, {yi} is the dimensionless population density, n/no, and {x} is the dimensionless size, L/Gt. For reasons of simplicity, we will deal with the classified discharge feature of the crystallizer a bit later.

These equations, combined with the magma density, can provide the weight fraction of size L in a DTB (Bennett, 1993):

It is now possible to use this information, and to estimate the expected performance of a DTB, as the recycle {R} is changed. Using Stoke's Law, we can estimate LF as follows (Nývlt, 1992):

The DTB offers further crystal size control by means of classification of the discharge from the crystallizer. A combination of fines destruction, where the crystals contained in the flow removed from the baffle are destroyed (typically by heating this stream, to increase its saturation point), and classified product discharge, where the smaller crystals are returned to the DTB so that they may grow to a larger size, can produce impressive results. In the familiar population density plot, the classified product discharge is indicated as shown on fig. 5.

In the typical Class II system (where production is not a function of overflow, and the yield is high), the crystal size distribution of the slurry in the classifying section can be calculated (Randolph et al, 1973) in a similar manner as in equations (2) and (3):

The mixing in the DTB is achieved by a slow-turning agitator is a critical component of the unit's ability to grow large crystals. In a very elegant study, Randolph and Sikdar (1976) put together a very convincing case on the theory that most nucleation is secondary, and results from impeller-to crystal, as well as crystal-to-crystal collisions. They proposed that the nucleation rate equation (1) should be modified, to include, essentially, a term expressing the stirrer speed:

This relationship, between the nucleation rate and the stirrer speed has also been expressed in a somewhat different form (Bennett et al 1973), where:

and

Obviously, either equation needs to be empirically adjusted for the crystallisation system being designed. However, this can be achieved through a brief series of simple, bench-scale tests. Once these parameters have been established, the engineer has a firmer control on crystal size, and a tool to possibly change the crystal size in the field, if conditions require it.

When one combines the above features of the DTB, the result is a machine which is poised to make large crystals by reducing secondary nucleation in its MSMPR zone, by destroying a large number of fines through its clarifying section, and, if equipped with classified discharge capability, removing only the larger crystals. This is not success without a price. The price is cycling of the crystal size, and it can happen if one is not aware of the potential kinetic inertia that can build up in a DTB. The cycling tendency of the DTB is very well understood. Over a quarter-century ago, Randolph et al (1976) proposed a stability criterion for the DTB:

They pointed out that the system is stable within acceptable fluctuation at values of xF > 0.3, and very stable at values of xF > 0.8 (i.e. large LF, large removal rates). The basic cause of the cycling tendency of a DTB is the fact that the higher the dissolved mass (through fines destruction), the higher the G; this increase, over time, reaches a point where there is discontinuous change in nucleation (sudden and massive homogeneous nucleation), which multiplies the number of crystals in the smaller sizes. While the crystallizer is slowly destroying the excess fines, the average crystal size is at the lower part of the cycle range. When the excess fines are destroyed, the growth rate increases, driving the crystal size up.

The cycling behavior has been limited in practice, by controlling the supersaturation in the DTB, so as to avoid, or dampen, the fluctuations of the nucleation rate; in addition, as computational capabilities increased, Farrell et al (1995) were successful in constructing a dynamic model of the DTB, to simulate "nucleation bursts". This model can be used to apply feedback control on the fines removal rate, as well as on other parameters that affect nucleation in a crystallizer of this type.

Concluding Remarks

As can be seen from the above brief review of the theoretical modeling of the DTB, this crystallizer type is well understood, and its design parameters are relatively easy to determine experimentally, often with bench scale equipment. This allows the application of this crystallizer type in a wide variety of crystallization systems with minimal risk, even in cases where the unit in question is the first of its kind. Further, the use of easily defined design parameters permits the engineer to troubleshoot and optimize this type of crystallizer operation with relative ease.

Literature Cited

  • Bennett R. C., Fieldelman, H., and Randolph, A. D., Chem. Eng. Prog., 69 (7), 97, 1973.
  • Bennett, R. C., in "Handbook of Industrial Crystallization", Edited by A. S. Myerson, Butterworth-Heinemann, 1993, pp108-109.
  • Canning, T. F. "Interpreting Population Density Data from Crystallizers", Chem. Eng. Prog., Symposium Series, No. 110, Vol. 67.
  • Farrell, R. J., Belokovskiy, A., and Bennett, R. C. "Simulated Oscillations and Control Strategy for Ammonium Sulfate DTB Crystallizer", AIChE Annual Meeting, 1995.
  • Nývlt, J. "Design of Crystallizers", CRS Press, 1992.
  • Randolph, A. D. "CSD Dynamics, Stability, and Control", AIChE Symposium Series, No. 193, Vol.76, 1980.
  • Randolph, A. D. and Sidhar, S. K. "Creation and Survival of Secondary Crystal Nuclei, The Potassium Sulfate-Water System", Ind. Eng. Chem. Fund., Vol. 15, No.1, 1976.
  • Randolph, A. D., and Larson, M. A., "Theory of Particulate Processes", Academic Press, 1971.
  • Randolph, A. D., Beer, G. L., and Keener, J. P. "Stability of the Class II Classified Product Crystallizer with Fines Removal", AIChE Journal (Vol. 19, No. 6) 1973.

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