Batch Precipitation

In any batch precipitation scheme, a selection must be made between a high-yield, high-supersaturation (without exceeding the critical supersaturation), short operation, and a longer batch time, low-supersaturation one. Such a decision must weigh both the product properties desired and the cost factor associated with the implementation of either scheme. Often, additional considerations may need to be taken into account. For example, as reported by Yokoyama and Toyokura (1993), different polymorphic forms of precipitate can be obtained by controlling the supersaturation level in a double jet-precipitation. 

Precipitation or reactive crystallization is very common in industrial applications and laboratory practice. A large number of high-value added product and intermediate materials are produced via precipitation. The precipitation process is very complex and the properties of precipitate strongly depend on the kinetics of the component subprocesses and their conditions. All these factors, and also the fact that the typical size of precipitate is in the submicron to 100 fim range, make the precipitation process very unique. Frequently, different theoretical and experimental approaches than those used for typical crystallization are required. 

In the entire chapter, a strong emphasis has been put on sparingly soluble, rapid kinetics crystalline materials because the authors felt that this domain of the reactive crystallization spectrum is the most representative for precipitation as well as distinct from other crystallization processes. 

Also discussed are precipitation specific experimental techniques, such as supersaturation measurements, constant composition (CC) method, instantaneous mixing devices, maximum (critical) growth rate experiments, and sizing. Due to the intrinsic difficulties with the direct supersaturation measurements and the microsecond characteristic time scale of precipitation reaction and nucleation, the CC method is used to study the precipitation kinetics. For the same reasons, the critical growth experiments are used to delineate the domain of the reactant feed rate that assures a renucleation-free process and a unimodal CSD. 

The importance of mixing in precipitation is generally appreciated but not well understood due to its complexity. The concepts of macro-, meso-, and micromixing are presented, with a particular attention devoted to micromixing. 

For a constant supersaturation (i.e., S function of time) and a growth rate that is not a function of size (i.e., g(R) = 0 corresponds to polynuclear and screw dislocation growth), the size distribution at any time is simply a shifted version of the initial size distribution, i) (i ), after the nucleation is completed  

For different values of n in g(R) = if, other kinetic expressions can be developed, if all the nuclei are the same size R. Integration of the growth rate (i.e., dR/dt = K f(STg(Ry) gives  

This equation assumes that all the nuclei are the same size, R. The equation gives an expression for the increase in particle size with time for various growth rate mechanisms. This expression is similar to that used by Nielsen [2] in his chronomal analysis. The only difference is that chronomal analysis uses the fiaction precipitated, cAf), as a variable instead of the mean particle size, R(f). The fraction precipitated is defined as 

Redrawn with permission from Dirksen and Ring [4a], Reprinted from [4a], copsTight 1991, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK 

FIGURE 6.30 Formation of Ce02 particles by the forced hydrolysis of an acidic Ce(S04)s solution at 90. (a-c) Fkrtide formation over a 6 hr period and (d) final product after 48 hr of aging (with permission [102]). 

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Wachi and Jones (1991b) used a gas-liquid flat interface reactor as a semi-batch precipitation cell for the experimental measurement of calcium carbonate precipitation, as shown in Figure 8.15. 

Al-Rashed, M.H. and Jones, A.G., Hannan, M. and Price, C., 1996. CFD Application on a simple geometry of batch precipitation of calcium carbonate. In Industrial Crystallization 96. Ed. B. Biscans, Progep, Toulouse, 16-19 September 1996, pp. 419M24. 

Jones, A.G. and Teodossiev, N.M., 1988. Microcomputer programming of dosage rate during batch precipitation. Crystal Research and Technology, 23, 957-966. 

Noor, P. and Mersmann, A., 1993. Batch precipitation of calcium carbonate. Chemical Engineering Science, 48, 3083-3088. 

Sohnel, O. and Matejckova, E., 1981. Batch precipitation of alkaline earth carbonates. Effect of reaction conditions on filterability of resulting suspensions. Industrial and Engineering Chemistry Process Design and Development, 20, 525-528. 

Sohnel, O., Mullin, J.W. and Jones, A.G., 1988. Nucleation, growth and agglomeration during the batch precipitation of strontium molybdate. Industrial and Engineering Chemistry Research, 27, 1721-1728. 

Yagi, H., 1988. Semi-batch precipitation accompanying gas-liquid precipitation. Chemical Engineering Communications, 65, 109-119. 

This paper is concerned with the study of the reverse reaction, the precipitation of alumina. The effects of varying supersaturation, seed surface area and temperature on secondary nucleation rates were studied in a batch precipitator. 

P.H. Karpinsky, Maneuvering through the Complexities of Batch Precipitation, Proc. Int. Symp. Ind. Cryst., Tokyo, Japan, 1998, pp. 13-22. 

An analytical solution to this integro-partial differential equation is not possible without some simplifying assumptions. In the sections that follow, anal5d ical solutions are presented for particle growth in a CSTR and batch precipitation reactors. For systems in which shear is the dominant collision mechanism and not Brownian difhision, the birth and death functions can be rewritten in terms of the mean shear rate, y, as follows [104]. 

Particle growth in a batdi environment is more difficult to predict because the steady state assumption previously used for the CSTR case is no loiter applicable. For a batch precipitator, the simplified population balance becomes... 

Supercritical carbon dioxide is a very good solvent for small molecules, but a poor solvent for most high molecular weight polymers at mild conditions (T<100 °C, P<350 bar). Amorphous fluoropolymers and silicones are the only polymers known to be soluble in CO2 at mild conditions [6]. This difference in solubilities is an advantage for C02-based polymerizations, as it can be used to reduce the energy requirements necessary to separate and purify a polymer after synthesis. Consider, for example, a batch precipitation polymerization in... 

The objective of the work is to present an experiment-founded adsorption model for precipitate flotation. Batch precipitate flotation of CufOH) with dodecylbenzene sulphonate (DBS) as collector, was carried out both with dissolved (DAF) and dispersed (DIS) air. The processes were considered as a succession of the dynamic equilibria taking place at the gasliquid and solidliquid interfaces. Both flotation processes were expressed quantitatively in terms of surface concentrations of Cu(OH)2 and DBS per unit surface area of the air buble, as well as the ratio of the numbers of air bubbles and solid particles (B /P ). Also the maximal concentrations of both DBS and Cu(OH)2, recoverable under the given conditions were calculated. All these values were determined by following the Cu(OH)2 and DBS recovery. The 2 flotation techniques were compared in regard to their efficiency and mechanism. Finally, the results obtained were discussed in terms of the other models for the colloid particle adsorption at the air-water interface. 

Batch precipitate flotation with dispersed [10, 11] and dissolved [12 ]air has been carried out on a conventional laboratory set-up microflotation, adopting the procedures described earlier. The air flow rate in the flotation with dispersed air was 3 dm /h... 

R.W. Thompson and MJ. Huber, Analysis of the Growth of Molecular-Sieve Zeolite Naa in a Batch Precipitation System. J. Cryst. Growth, 1982, 56, 711-722. 

Phillips, R., S. Rohani, and J. Baldgya (1999). Micromixing in a single-feed semi-batch precipitation process. AIChE J. 45, 82-92. 

The topics presented in this paper include a description of the bench-scale system, the experimental approach, and the results of degradation testing. Also included are the results of batch precipitation experiments designed to study coprecipitation of adipic acid in scrubber waste solids. 

In order to further characterize this mechanism for adipic acid loss, two series of batch precipitation experiments were performed. The tests were designed to study ... 

Solids from the batch precipitation tests were also examined by scanning electron microscopy. In tests where no adipic acid was added, the calcium sulfite solids formed a single platelet crystal. However, upon addition of 3,000 ppm adipic acid prior to solids precipitation, the calcium sulfite crystals formed as platelet clusters or rosettes. As the concentration of adipic acid was increased the crystals became smaller and less plate-like until at 10,000 ppm adipic acid in the slurry solution the crystals were submicron in size and resembled popcorn shaped spheres (5). These results suggest that adipic acid effects the nuclea-tion rate of calcium sulfite and certainly can drastically change the particle size distribution and crystal morphology of precipitated solids. 

The batch precipitation tests show dramatic effects of adipic acid slurry concentration and solid phase oxidation fraction on coprecipitation of adipic acid in scrubber solids. Real world scrubbers would probably never operate at adipic acid concentrations as high as those tested and would also not likely ever produce pure phase calcium sulfite hemihydrate. Therefore, the magnitude of the results observed is somewhat a product of the laboratory test conditions. The results do, however, establish the potential importance of adipic acid coprecipitation and, hence, the need for analysis of scrubber solids for adipic acid when determining adipic acid chemical degradation rates by a mass balance calculation approach. 

Figure 6.9 Effect of feed configuration—see Figure 6.8—on supersaturation profile in semi-batch precipitation of BaS04 (after Baldyga et al. 1995). Configuration I—after 1/3 feed added configuration II—for initial period of feeding.

Semi-Batch Precipitator. Assuming constant feed rate and no outflow, in addition to the assumptions made for the MSMPR precipitator, the PBE for a semi-batch precipitator is as follows (Kim and Tarbell 1991)... 

Based on the approaches proposed for batch crystallization— which employed cooling/evaporation rates to control supersaturation, and on the specifics of the batch precipitation process—the reactant addition rate was chosen as the controlling variable. 

The simplified overall (total, integral) material balance of the batch precipitation states that the mass increase due to the growth of precipitate crystals of the molecular weight M from the initial size Lo to an arbitrary size L, in an arbitrary time t, is equal to the mass of the solute of volume V delivered by the equimolar doublejet whose molar concentration Cr... 

Equation (6.56) is parabolic in t. For a nonzero initial size it does not reduce to 0 = 0 at t = 0. This is quite understandable, since the initial crystals whose size is Lq are able to accept the growth material, incoming at the volumetric rate equal to that given by Eq. (6.54). The latter equation determines the magnitude of the allowable initial reactant addition rate for the first moment of the growth stage of batch precipitation. 

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