2.3.1. Study of Operation Parameters and Process Evaluation

Altogether, seven experiments were planned and carried out for 8 h in this first attempt to systematically investigate the influence of the operation conditions on the process performance. In continuation of the previous study [14], a saturation temperature of 35 ◦C was chosen for most of the experiments (Tsat, Table 1). The first three processes (Exps. 1–3, Table 1) were used to determine the operation window of the process with respect to the crystallization temperature (Tcrys, Table 1).


**Table 1.** Process conditions and objectives of all experiments.

The data of Exp. 2 were additionally utilized to determine the required time to reach steady-state operation. It was found that after two product withdrawals (process time approximately 2 h) all process characteristics became constant. Hence, some of the later experiments were split into two periods, where two sets of process parameters (compared, for example, to the volume flow of Exp. 4) were tested for 4 h each, to enhance the time efficiency of the investigation. Exps. 4 and 5 were carried out to evaluate stepwise the influence of the volume flow rate (F, Table 1) between 10 and 14 L/h. In

Exp. 6, the supersaturation was kept constant but the saturation and crystallization temperature were reduced by approximately 10 K to investigate the influence of reduced crystallization kinetics. In Exp. 7 the central test point was run again, Tsat = 35 ◦C, Tcrys = 30 ◦C, and F = 12 L/h, to evaluate the standard deviation of all process characteristics for a longer time period.

Every reached operation point was evaluated based on the normalized volume related product crystal size distributions, q3 (Equation (3)), their mean sizes, L3 (Equation (4)), and their respective standard deviation, sL3 (Equation (5)), as well as the achieved yields, Y, and productivities, Pr (Equations (6) and (7), respectively) calculated from the product masses and the time window between two withdrawals.

$$\mathbf{q}\_3(\mathbf{z}\_k) = \frac{\mu\_\mathbf{k}}{\Delta \mathbf{z}\_\mathbf{k}} \tag{3}$$

$$\overline{\mathbf{L}\_3} = \sum\_{\mathbf{k}=1}^{N} \mathbf{z}\_{\mathbf{k}} \cdot \boldsymbol{\mu}\_{\mathbf{k}} \tag{4}$$

$$\mathbf{s}\_{\rm L3} = \sqrt{\sum\_{\mathbf{k}=1}^{N} \left(\mathbf{z}\_{\mathbf{k}} - \overline{\mathbf{L}\_3}\right)^2 \cdot \mu\_{\mathbf{k}}} \tag{5}$$

where

μ<sup>k</sup> = mass fraction of sieve class k [-] zk = characteristic length of sieve class k [μm]

Δzk = width of sieve class k [μm]

$$\mathcal{Y} = \frac{\mathbf{m}\_{\text{prod}}}{\mathbf{m}\_{\text{theo}}} \tag{6}$$

$$\text{Pr} = \frac{\text{m}\_{\text{prod}}}{\Delta \text{t} \cdot \text{V}\_{\text{tot}}} \tag{7}$$

where

mprod = mass of withdrawn product crystals [g] mtheo = theoretical maximum of product mass [g] Δt = time window between two withdrawals [h] Vtot = total volume of tubular crystallizer [L] (C1 = 0.478 L, C2 = 0.511 L)
