This is part one of a two-part feature that examines the fundamentals and discuss equipment selection and process design. Part 2, which appeared in December 2003 Chemical Processing, addresses scaleup, simulation and new technologies
Crystallization combines particle formation and purification in a single operation, and is used to make a wide variety of products, from commodity chemicals to chiral pharmaceuticals. Crystallization is often more energy efficient than distillation, since the heat of crystallization is usually 1/5th ," 1/10th of the heat of evaporation. In addition, the growing crystal surface can be extremely selective, allowing crystallization to be used in challenging separations such as ultrapure powders or heat sensitive materials.
Part 1 will focus on the basics, providing guidance for process design and equipment selection.
Purification and crystal growth
To optimize purification, the desired solute must be incorporated into the crystal surface as the rate-limiting step for growth. The driving force for crystallization is the level of supersaturation during crystallization. Supersaturation must be maintained at a low level, while providing enough mass transfer from the bulk solution to the growing surface. If supersaturation is too high, impurities can be incorporated and remain within the lattice, leading to problems that include caking and product instability.
Nucleation, or formation of a new crystal, can be either primary or secondary. Primary nucleation occurs in the absence of product crystals and usually at high levels of supersaturation. Solute entities cluster together in solution to achieve an orderly arrangement with minimum free energy. If the clusters exceed a minimum size, they survive and grow. If not, they dissolve. This mechanism often is the major nuclei source for precipitations created by reaction, salting-out or pH adjustment since they often have high levels of supersaturation and a low percent solids slurry density. Typically, a thick mass of small crystals will suddenly appear as the system "crashes out."
In contrast, secondary nucleation requires that product crystals exist in the slurry. Usually the dominant nucleation force in a mixed-suspension crystallizer operating at low supersaturations, it occurs through contact, fluid shear on semiordered surface layers or attrition or breakage. The mechanism depends on the level of supersaturation, percent solids, circulation rate, type of agitator, tip speed and power input/unit slurry volume. Contact nucleation is the predominant type and results from collisions between crystals, or between crystals and walls or agitators.
The basic engineering equation for secondary nucleation is:
B Degrees = kNSbMTJA1 (1)
B Degrees = the nucleation rate; number of nuclei/unit volume/unit time.
kN = the nucleation rate constant, which depends on temperature.
S = the supersaturation
MT = the slurry density such as grams solids per liter
A = a measure of the degree of agitation such as rpm and power per unit slurry volume.
b, j, l are exponents that can be experimentally determined, with j often close to 1.0.
Crystal growth involves the diffusion of solute to the crystal surface, followed by a surface reaction. One of these mechanisms will control the rate. As with nucleation, growth is driven by supersaturation and can be described by a simple empirical equation:
G = kg Sg = dL/dt (2)
G = the growth rate in, for example, mm/min.
kg = the growth rate constant dependent on temperature, agitation and solution composition.
g = the exponential relating supersaturation to growth
L = a characteristic dimension such as an average screen opening
t = time
Since both Equations 1 and 2 contain the supersaturation term, a value difficult to measure, one can combine them to obtain a new expression for nucleation:
B Degrees =k'NGiMTjAl (3)
Where i = b/g, and i is normally greater than 1.0, indicating that nucleation has a higher order of dependence on supersaturation than on growth.
Supersaturation results from cooling and evaporation. It can also stem from chemical reaction, salting-out and pH adjustment, techniques that are common for precipitations that can yield high levels of supersaturation. In these cases, mixing can have a great influence on product characteristics. Equilibrium relationships for crystallization systems are expressed as solubility data, which are plotted as phase diagrams or solubility curves. Solubility data are usually stated as parts by weight of anhydrous material per hundred parts of solvent or solution, or weight percent anhydrous material. If hydrates are present, they are indicated as a separate phase.
The concentration is normally plotted as a function of temperature. If there are two components in solution, concentrations can be plotted on the x and y axes, and solubilities represented by isotherms. With three or more compounds, two- and three-dimensional models can be used . Generally, the solubility curve for a given crystallization will determine which method to use for crystallization. Figure 1 shows a typical curve for an unseeded batch cooling crystallization.
Figure 1. Operating Curve for Unseeded Batch Cooling
The process follows a path. First, unsaturated feed (A) is cooled through the solubility curve (B), the metastable zone (C) and into the labile zone (D). Rapid nucleation occurs in the labile zone. The concentration then falls out of the labile zone (E), and growth occurs within the metastable zone during the reamainder of the cooling (F). The metastable zone is where growth occurs in the absence of primary nucleation.
Solubility and Phase Diagrams
Figure 2. Phase Diagram Typical for Compounds with Waters of Hydration
This phase diagram for the MgSO4H2O system is typical of compounds that display waters of hydration.
Phase diagrams can be utilized to determine yield of crystallization. Usually the mother liquor is essentially a saturated solution at the final temperature. If evaporation is employed, solvent removal must be taken into account. If hydrates are formed, the solvent used for hydration must be included. The following examples serve to demonstrate calculation techniques for the MgSO4 system.
A 10,000 lb batch of 35% MgSO4 at 170 Degrees F is cooled without appreciable evaporation to 70 Degrees F. What hydrate of MgSO4 is formed and what weight of crystals is produced?
From the solubility diagram in Fig. 2 at 70 Degrees F, the hydrate produced is MgSO47H2O (point C), with a saturated mother liquor of 26.3% at point A. The molecular weight of MgSO4 is 120.38 and that of MgSO47H2O is 246.49. The hydrate is 48.8% anhydrous MgSO4. For hydrated salts, it is convenient to perform the calculations based on the hydrate and "free water:"
0.35 x 246.94/120.38 = 0.718 MgSO47H2O/unit feed
0.263 x 246.94/120.38 = 0.540 MgSO4 7H2O/unit mother liquor
The free water is constant and the final soluble hydrate can be determined by the 0.540/0.460 ratio.
Conditions are the same as Example 1 except that 500 lb of H2O are evaporated
An engineering formula that can be used is as follows:(4)
P = weight of crystals, lb
R = MW hydrate/MW anhydrous
S = anhydrous solubility in ML, lb/100 lb solvent
Wo = weight of anhydrous solute in initial batch
Ho = weight of solvent in initial batch
E = evaporation, lb
For Example 1,
For Example 2, P = 4,406 lb. Differences are due to rounding.
Table 1 provides a basic checklist of crystallizer design specifications.
Batch crystallization, as an unsteady-state process, often requires provision for seed addition to achieve an acceptable purity, crystal size distribution (CSD), production rate and on-stream time. It is necessary to maintain a reasonable and constant supersaturation .
Indirect cooling crystallization requires slow cooling of the batch after seeding, followed by an accelerated temperature drop vs. time. The coolant should also have a programmed drop in temperature over time. Low log mean temperature differences (LMTDs), often as low as 1-5 Degrees F, are required to stay within the metastable zone. Likewise, a batch evaporative crystallization requires low evaporation at the start followed by a programmed accelerating evaporation profile. The evaporation rate from start to finish may vary by two orders of magnitude and the heat transfer surfaces for both the crystallizer and condenser must be adequate to handle this variation.
There are also a number of continuous configurations . Other than the simple stirred tank, the most common and least-expensive method is the forced-circulation (FC) unit shown in Figure 3.
Figure 3. Forced-Circulation Crystallizer Allows Continuous Operation
In the forced-circulation unit, shown here, a low-head, low-shear axial flow pump is used to reduce secondary nucleation. Slurry velocities are about 7 fps, and the evaporative unit must be submerged to prevent material from salting out on the tubes, and to stop undesired nucleation. Applications include citric acid, sodium and lithium chloride and sodium sulfate production, generating a CSD in the 35-140 U.S. mesh range.
CSD and morphology can have a huge impact on downstream processing steps, so it is essential that the crystallization system operate at design conditions to assure the expected feed to downstream processing.
Mixing can dramatically affect the performance of a crystallizer and the resultant product [6, 7]. Each crystallizer requires the specification of blending characteristics, flow patterns, circulation times, tank shape and baffles plus impeller selection, placement and D/T ratio, where D is the agitator diameter and T is the tank diameter.
Three forms of mixing can be considered: macromixing, micromixing and mesomixing. The latter can have a large impact on fast chemical reactions and precipitations taking place at the reactant or anti-solvent feed point. An improperly designed feed can result in variable and high local levels of supersaturation, producing high nucleation rates and a small CSD.
Macromixing refers to the overall mixing performance and involves bulk fluid movement and blending. It is dictated by the type of agitator, agitator speed and vessel geometry. Macromixing is generally measured as the overall circulation, residence-time distribution (RTD), turnovers and degree of solid suspension. For turbulent flow, the macromixing time increases with vessel diameter and decreases with average power per unit volume, (P/V)avg, with P/V defined as the energy dissipation rate.
For a given agitator design and vessel geometry, (P/V)avg is a key measure of the degree of macromixing, which determines the relative flow rates and blending efficiency. Macromixing reduces local differences in temperature, concentration, supersaturation, suspended solids density and other parameters.
Micromixing, or turbulent mixing at the molecular level, can have a significant impact on precipitations resulting from fast chemical reactions or anti-solvent addition. It can dictate the level of supersaturation, influencing the nucleation and growth rate of particles.
The local P/V will affect the degree of micromixing, and values can vary by more than two orders of magnitude at different locations within a crystallizer. With (P/V)avg defined as the overall power input from the agitator divided by the total slurry volume, the local P/V equals about 70 (P/V)avg at the mixer impeller swept volume, 3.5 (P/V)avg in the discharge stream and 20 (P/V)avg in the overall impeller region but only one-fifth of that value at the liquid surface, baffles and corners. As a result of this hundred-fold difference, the relative importance of micromixing and reaction rates for precipitation can vary greatly within a vessel. One must take these variations into account when specifying feed-point location, vessel design and the type of agitator.
Generally, to be effective in crystallization, an agitator must be capable of the following:
Full crystal off-bottom suspension to maintain growth.
Sufficient mixing and solids availability to eliminate local excessive levels of supersaturation at feed points, cooling surfaces and evaporation surfaces
Adequate heat transfer, allowing for operation within the metastable zone.
Product removal via isokinetic discharge.
Acceptable levels of secondary nucleation and breakage, yielding desired CSD and shape.
Table 2 presents turbulent-flow parameters for five typical agitators. (Q/P)R is the ratio of flow for that particular agitator design for the same power input and diameter vs. the PBT as the standard. NQ, defined as the agitator flow number, varies less among mixer types than does the agitator power number, NP.
* 2,000 gallon glass lined vessel, diameter @ 44" and NRe>2.4 x 106
**2,000 gallon glass lined vessel, diameter @ 33" and NRe>2.4 x 106
These values are for turbulent flow and specific geometric configurations. They are independent of scale, assuming geometric similarity. For a given power input, the hydrofoil produces 51 percent more flow than the PBT, while the radial flow Rushton turbine produces only 18 percent of the flow generated by the standard PBT. Note that, for the same flow, the hydrofoil requires about 34 percent less power than the PBT while the radial, high-shear 90 Degrees pitch Rushton requires approximately 450 percent more power than the PBT. The increased power and shear can have a negative impact on secondary nucleation and crystal breakage.
Using the agitator parameters in Table 2, one can calculate the primary impeller pumping capacity and power draw as follows:
Q=NQND3x7.48 (in gpm) (5)
Where N is rotational speed in rpm , D is impeller diameter in feet, and Q is the flow just off the blade.
Where D is impeller diameter in inches and sg is specific gravity.
The Rushton turbine, due to its high power number, is a high-torque impeller requiring a relatively low speed for a given power and size. Torque is defined as power divided by speed. Low Np agitators such as a hydrofoil, when operated at the same power and diameter as the Rushton, run at higher speed. Thus, they require less torque and are cheaper to install since they have smaller shaft diameters, seals and gear boxes. Due to their favorable flow-vs.-power characteristics, hydrofoil impellers are often used for solids suspension.
Note that the values of NP and NQ for glass-lined agitators are measured at different configurations than those employed for metal agitators. For example, the baffling and the impeller-to-tank diameter ratio is different for the GL vessel. Thus, a direct comparison between the performances of these agitators would not be entirely accurate.
Wayne Genck, principal of Genck International, is an industrial consultant in the field of crystallization and precipitation. He can be reached at (708) 748-7200.