**4. Discussion**

A variety of the literature deal with the heat and mass balance of industrial crystallization processes [13,16,20,21].

Figure 10 shows a schematic and simplified mass balance for an evaporative continuous crystallization process with an exemplary concentration factor of 10. Both the yield of the process as well as the purity of the product are a function of the concentration factor α. For the chosen example, the dependencies of the process yield and product purity are shown in Figure 11. Depending on the requirements defined by a producer or the market, only a certain working range for α is acceptable because, otherwise, the yield would be too low (α < αcritical) on the one hand, or the purity would be to low (α > αcritical) on the other.

**Figure 10.** Simplified block balance of an evaporative crystallization process (concentration factor of 10).

From the results of the multi-stage discontinuous tests, it can be clearly seen that the concentration factor would need to be limited to maximum α = 4 to avoid endangering the requested purity of 99.3% (on a dry basis). However, due to the strong effect on crystal shape (needle-like shape), it was decided that we would keep the concentration factor α even lower, below 2.5.

This limits the process yield for single-stage processes, which was not crucial for the case study presented here, as the client could recycle the purge from crystallization into an upstream process outside of the battery limit of the crystallization.

When there is no overlap for the concentration factor with regards to yield and purity, and intensive cake washing within solid–liquid separation is not enough to achieve a critical yield, there are, nevertheless, various concepts to achieve such a critical yield.

Two major concepts should be introduced here: the so-called first crop–second crop concept and the re-crystallization concept [21].

For the first crop–second crop concept, the product is crystallized to a certain concentration factor in the first crop crystallization, respecting the critical value of α with regards to purity. In order to increase the yield of the overall process, the mother liquor of the first crop crystallization is further concentrated, and an out-of-specification product is generated in the second crop crystallization step. This impure product is dissolved in the feed solution (if undersaturated) or by the addition of a solvent, and is recycled for the first crop crystallization. The final overall process purge is taken from the second crop crystallization.

For the re-crystallization concept, an out-of-specification product (raw product) is produced by an initial crystallization step, applying high concentration factors. The product is subsequently totally dissolved in the solvent and completely re-crystallized in a second crystallization step, producing a product with the requested purity (pure product). The purge is taken from the first raw crystallization step.

From plant manufacturing or engineering companies' perspectives, the concentration factor α is the most crucial factor for continuous evaporative crystallization processes, as it enables the balance of the outer process. .

$$
\dot{m}\_{\text{Fard}} = \dot{m}\_{\text{Product}} + \dot{m}\_{\text{Condensate}} + \dot{m}\_{\text{Pur}\_{\text{Fect}}} \tag{2}
$$

The concentration factor, as one possible dimensionless characterization of the grade of concentration, is defined between one, standing for no evaporation and therefore no crystallization occurrence, and infinity, standing for a complete evaporation of all solvents, leaving a dry and solid product next to the solvent removed by evaporation.

By increasing the concentration factor, the concentration of impurities increases in the mother liquor of the crystallization, which causes several effects in relation to our case study:


It must be highlighted here that all parts of the study were carried out to gain specific required knowledge on the relevant process and product parameters that will enable an engineering company to scale up this process to an industrial plant. Neither a complete parameter study, nor repetitions satisfying statistical approaches, could be performed.
