Stirred vessels scale

Turbulent Flow in Stirred Vessels Turbulence parameters such as intensity and scale of turbulence, correlation coefficients, and... 

The vertical vibratoiy mill has good wear values and a low-noise output. It has an unfavorable residence-time distribution, since in continuous operation it behaves like a well-stirred vessel. Tube mills are better for continuous operation. The mill volume of the vertical mill cannot be arbitrarily scaled up because the static load of the upper media, especially with steel beads, prevents thorough energy introduction into the lower layers. Larger throughputs can therefore only be obtained by using more mill troughs, as in tube mills. 

In the case of stirred vessels the values A/riL can be calculated by the following equation using the geometry parameter d/D, H/D, the Newton number Ne, the Reynolds number Re = nd /v, the energy dissipation ratio e/e and the related macro scale A/d. For standard turbines e.g. Mockel [24] found the value A/d = 0.08 close to the impeller. Corresponding to this the maximum of the dissipation ratio ,/ has to be used which can be estimated by Eq. (20). 

Figure 1.14 Schematic representation of a stirred vessel (left) and a T-shaped micro reactor (right). Both devices can be used for liquid/liquid and for gas/liquid reactions. The length scales indicate typical physical dimensions.

Worz et al. give a numerical example to illustrate the much better heat transfer in micro reactors [110-112]. Their treatment referred to the increase in surface area per unit volume, i.e. the specific surface area, which was accompanied by miniaturization. The specific surface area drops by a factor of 30 on changing from a 11 laboratory reactor to a 30 m stirred vessel (Table 1.7). In contrast, this quantity increases by a factor of 3000 if a 30 pm micro channel is used instead. The change in specific surface area is 100 times higher compared with the first example, which refers to a typical change of scale from laboratory to production. 

Finally, yield improvements were also reported for industrial process developments. For the Merck Grignard process, a yield of 95% was obtained by a micro mixer-based process, while the industrial batch process (6 m stirred vessel) had only a 72% yield (5 h, at -20 °C) [11]. The laboratory-scale batch process (0.5 1 flask ... 

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

First of all, the increased computer power makes it possible to switch to transient simulations and to increase spatial resolution. One no longer has to be content with steady flow simulations on relatively coarse grids comprising 104-105 nodes. Full-scale Large Eddy Simulations (LES) on fine grids of 106—107 nodes currently belong to the possibilities and deliver realistic reproductions of transient flow and transport phenomena. Comparisons with quantitative experimental data have increased the confidence in LES. The present review stresses that this does not only apply to the hydrodynamics but relates to the physical operations and chemical processes carried out in stirred vessels as well. Examples of LES-based simulations of such operations and processes are due to Flollander et al. (2001a,b, 2003), Venneker et al. (2002), Van Vliet et al. (2005, 2006), and Flartmann et al. (2006). 

Even nowadays, a DNS of the turbulent flow in, e.g., a lab-scale stirred vessel at a low Reynolds number (Re = 8,000) still takes approximately 3 months on 8 processors and more than 17 GB of memory (Sommerfeld and Decker, 2004). Hence, the turbulent flows in such applications are usually simulated with the help of the Reynolds Averaged Navier- Stokes (RANS) equations (see, e.g., Tennekes and Lumley, 1972) which deliver an averaged representation of the flow only. This may lead, however, to poor results as to small-scale phenomena, since many of the latter are nonlinearly dependent on the flow field (Rielly and Marquis, 2001). 

Even when the number of grid cells in a LB LES simulation of a stirred vessel 1.1 m3 in size amounts to some 36 x 106 grid cells, this implies a cell size, or grid spacing, of 5 mm only. Even a cell size of just a few millimeters makes clear that substantial parts of the transport of heat and species as well as all chemical reactions take place at scales smaller than those resolved by the flow simulation. In other words concentrations of species and temperature still vary and fluctuate within a cell size. The description of chemical reactions and the transport of heat and species therefore ask for subtle approaches to these SGS fluctuations. 

Furthermore, the physics of the interaction between turbulence and bubbles in the complex flow of a stirred vessel, with its implications for coalescence and break-up of bubbles and drops, is still far from being understood. Up to now, simple correlations are available for scale-up of industrial processes generally, these correlations have been derived in experimental investigations focusing on the eventual mean drop diameter and the drop size distributions as brought... 

Colenbrander, G. W., Experimental Findings on the Scale-Up Behaviour of the Drop Size Distribution of Liquid-Liquid Dispersions in Stirred Vessels . Proceedings of the 10th European Conference on Mixing, Delft, Netherlands, 173-180 (2000). 

Coupons of the materials were exposed to various acid compositions and temperatures in stirred vessels. The acid compositions used in the tests reflected various average annual acid compositions likely to be encountered in the pilot-scale distillation system HNO3 - 10 to 60 wtZ H2SO4 - 0 to 60 wtZ HF - 0 to 0.2 wtZ. The coupons were suspended in six stirred vessels containing mixed acid solutions for tests at ambient temperatures. One set of coupons was placed in a round-bottomed flask containing acid with the reference composition (Case II in Table 2) and maintained at a temperature of 100 C. 

The first example for small-scale reactors is a stirred vessel for a maximum pressure of 32.5 MPa and 350°C (Fig. 4.3-25). It has a volume of 0.4 1 and can be used batchwise or in continuous operation, preferably for gas-liquid reactions, without- or with soluble or suspended catalysts. 

A further unfortunate characteristic of the stirred vessel is that its mixing capability is also a strong function of its size. Scale-up usually proceeds on the basis of a constant impeller tip speed, and since the mean circulation speed in the vortices is broadly proportional to the tip speed chosen, the circulation time is proportional to the vessel diameter. Thus the turnover time of the vessel contents increases at the larger scale and the macro mixing performance deteriorates. 

Frequently, weakly basic amines, such as negatively substituted 4-nitroandines or aminoheterocycles, must be diazotized. These reactions require concentrated sulfuric acid, phosphoric acid (85 wt %), glacial acetic acid, propionic acid, or mixtures of thereof as the reaction medium, with nitrosylsulfuric acid as the reagent. On an industrial scale, this reaction is conducted preferably in enameled, stirred vessels. Whenever the stability of the amine or the diazonium salt permits, diazotization is carried out in concentrated sulfuric acid at slightly elevated temperature (10-40 °C). With regard to safety, factors such as temperature and concentration must be controlled carefully to avoid explosion [42],... 

Challenge 4.3. Reliability of traditional scale-up rule of a stirred vessel n 13-18 19... 

---