Supersaturation Profile

Although the experimental and simulation time scales differ, the CFD simulation (Figure 8.29(a),(c),(e)) for the zeroth moment (Mq) indicates that once the particles reach the observable size, they will appear approximately in the experimentally observed regions (Figure 8.29 (b),(d),(f)). Predicted velocity vectors are superimposed on supersaturation profiles in Figure 8.30. 

The supersaturation profile for unagitated batch operation is also... 

In the direct design approach, a desired supersaturation profile that falls between the solubility curve and the metastable limit of the system is followed based on feedback control of the concentration measurement. This is in contrast to the traditional first-principles approach, where a desired temperature profile or antisolvent addition rate profile is followed over time such as shown in Fig. 14. For a cooling crystallization, the direct design approach follows a setpoint profile that is solution concentration vs. temperature (or solvent-antisolvent ratio) as opposed to temperature (or addition rate) vs. time. Because the desired crystallizer temperature is determined from an in-situ solution concentration measurement, the batch time is not fixed. 

Fig. 15 shows an example of the direct design approach implemented for the isothermal antisolvent crystallization of acetaminophen (paracetamol) from acetone-water mixture. A constant relative supersaturation (Ac/c ) setpoint profile was followed. The flow rate setpoint of the antisolvent was calculated every minute based on the solution concentration measured using the IR spectra so that a setpoint supersaturation profile was followed. The change in solution concentration and antisolvent flow rate during the batch is shown in Fig. 16. After an initial start-up...

Batch crystallization process control using the first-principles and direct design approaches were discussed. The first-principles approach utilizes crystallization process models, which require the associated determination of crystallization kinetics. The optimal seed characteristics and/or supersaturation profile to obtain the desired product characteristics are then computed. The direct design approach involves feedback control of a state measurement, in this case the solution... 

For crystallization by cooling, the following factors can affect the supersaturation profile either locally or globally ... 

Mixing may affect crystallization by cooling in all of the ways outlined in Chapter 6. In particular, wall film thickness and the resultant heat transfer rate are most affected, along with local supersaturation profiles at the cooling surface. 

Figure 9-4 Solubility and supersaturation profiles for the linear and optimum addition rates. During the linear addition period, the supersaturation is not maintained at a constant level and will reach a maximum which may exceed the upper metastable zone boundary. For optimum addition, the supersaturation is maintained below a certain level and should approach the solubility limit.

Figure 16 Supersaturation profiles during precipitation of acetaminophen by means of a two-component mixing nozzle at (a) Re = 1000 and (b) Re = 30,000. Pressure is 20 MPa, temperature 323.1 K. The volumetric flow ratio between CO2 and the ethanol solution is constant at 0/Qa 100.

Figure 17 Comparison of experimental data with model predictions for mean particle size of acetaminophen crystals obtained by jet mixing, from direct CFD calculations of macromixing and supersaturation profile in Figure 16 and from mechanistic modeling (44-46), which allows for inclusion of the effects of molecular viscosity and diffusivity on rate of mixing on molecular scale (important for low Re).

The first factor to be considered for particle size reduction is the supersaturation profile. For very low concentrations of the nonvolatile solutes in antisolvent crystallization, supersaturation during the initial precipitation stage is characterized by the maximum attainable supersaturation, a. This... 

The solvent system selected may be an important factor influencing the supersaturation profile, product yield, size, and morphology of the particles produced. Thus in the experiments with SX, methanol, acetone, and tetra-hydrofuran solvents were tested. Although all these solvents are suitable for antisolvent precipitation, methanol was selected for further studies because of its high yield ( > 95%) and suitable particle size distribution for respiratory delivery ( v < 5 pm) achieved. 

The solubility of the reactants and products are shown in Figure 1.20. Again in this type of process mixing is crucial in obtaining a homogenous supersaturation profile. Precipitation is important in the manufacture of a variety of materials. TPA, which is an organic commodity chemical used in the manufacture of polymers, is made from the oxidation of p-xylene in an acetic acid water mixture. The product has a very low solubility in the solvent system and rapidly precipitates out. Control of the supersaturation in a precipitation process is difficult because it involves control of the mixing of the reactants and or the reaction rate. 

The feed configuration II gave similar trends but smaller crystals were produced and the mean crystal size was in this configuration much more sensitive to the operating conditions even at low concentrations. It is important to emphasize that either feed configuration employed resulted in different supersaturation profile, as depicted in Figure 6.9. 

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.

The quality, productivity, and batch-to-batch consistency of the final crystal product can be affected by the conditions of the batch crystallizer. Several factors considered here include batch cycle time, supersaturation profile, external seeding, fouling control, CSD control, growth rate dispersions, and mixing. 

Figure 10.13 Schematic supersaturation profile in a batch crystallization experiment. (Reproduced with permission from Nyvlt et al. 1985.)...

The supersaturation profile in a batch crystallizer has a profound effect on the nucleation and growth processes and the resulting CSD. It can also affect other factors (e.g., batch cycle time) related to the batch crystallization operation. Figure 10.13 shows schematically a supersaturation profile in a batch crystallization experiment (Nyvlt et al. 1985). At / = 0, the batch crystallizer is filled with a just-saturated solution that contains crystals with a negligible surface area. The solution begins to be supersaturated at a constant rate, and the supersaturation increases until it reaches the limit of the metastable zone (Acmoi)- At this point, nucleation... 

The bulk drug pilot plant must execute unusually varied processing with the requisite degree of control over the process variables, as well as have extraordinary means for data capture on-line (directly from sensors or analyzers in the equipment) and off-line (from samples tested in the laboratoiy and by derivation from raw data e.g., the supersaturation profile of a batch crystallization, the performance of a fermentation cell... 

Figure 9.12. Natural, controlled constant nucleation) and size-optimal cooling modes in a batch crystallizer a) temperature profiles, b) supersaturation profiles...

Constmction of a molecular model for HPMCAS is complicated by the complex and varied substitution patterns possible as evident in the representative substructure shown along with the variety of R-substituents that may he found at each of the indicated oxygens (Fig. 13.6). As recently observed by Porter in et al. [60], a limited variety of HPMCAS products are available, and they cover a relatively small subspace of the entire allowed compendial space. In particular, they observed that the ratio of acetyl to succinyl substitution may have a dramatic impact on the ability of HPMCAS to form supersatnrated solutions as measured by areas under the solution concentration versus time profiles (AUCs). Supersaturation profiles are highly dependent on the HPMCAS composition and also very dmg specific. MD simulations may ultimately contribute to understanding of the molecular basis for the relationship between HPMCAS molecular structure and dispersion performance. Clearly, HPMCAS polymer assembly in terms of composition and substitution pattern requires careful attention. 

The exact supersaturation profile depends on the interplay between the dissolution and crystallization rates of the drug. When considering crystallization, there are two potential recrystaUization routes in aqueous media direct solid-solid (same... 

Cooling crystallization is the preferred option for batch crystallizations as the temperature profile in a reactor can be easily controlled giving perfect control of the supersaturation profile. This curve gives information at which temperature the process has to be started in order to have a reasonable solute/solvent ratio and avoid unnecessary high dilution on the other hand, the solubility at low temperatures fixes the yield that can be achieved with this process. 

Figure 9.7 presents the time variations of the supersaturation profiles relatively for the CBZ and CBZ/NCT solid phases. The primary nucleation of CBZ/NCT first occurred at a supersaturation ratio 15% lower than the CBZ supersaturation ratio. A possible explanation lies in the fact that there may be a better affinity with the solvent of the CBZ/NCT nuclei than with that of the CBZ nuclei leading to a higher nucleation frequency of CBZ/NCT than CBZ. Ten minutes later, CBZ primary nucleation occurred. One could assume that the presence of the co-crystal form in suspension may favour a nucleation of CBZ crystals on the surface of CBZ/NCT solid form. 

An interesting kinetic study deals with the solution-mediated phase transformation of COT and COD into the thermodynamically stable COM [50]. The experimental conditions were adjusted so that either COT or mixtures of COD and COM crystallized initially as confirmed by X-ray diffraction powder patterns. The systems were then aged in contact with the mother liquid, and the transformation of COT or COD into COM was followed by monitoring the total crystal volume as a function of time (by Coulter counter) and determining (by thermo-gravimetric analysis) the relative proportion of the crystal hydrates at fixed time intervals. In addition, supersaturation profiles (i.e., activity products) were determined by solution calcium analysis. In all cases the transformation was completed within approximately 80-100 h. 

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