Stirred vessels, example

Suspensions of fine sohds may have pseudoplastic or plastic-flow properties. When they are in laminar flow in a stirred vessel, motion in remote parts of the vessel where shear rates are low may become negligible or cease completely. To compensate for this behavior of slurries, large-diameter impellers or paddles are used, with (D /Df) > 0.6, where Df is the tank diameter. In some cases, for example, with some anchors, > 0.95 Df. Two or more paddles may be used in deep tanks to avoid stagnant regions in slurries. 

The most common heterogeneous catalytic reaction is hydrogenation. Most laboratory hydrogenations are done on liquid or solid substrates and usually in solution with a slurried catalyst. Therefore the most common batch reactor is a stirred vessel, usually a stirred autoclave (see Figure 2.1.1 for a typical example). In this system a gaseous compound, like hydrogen, must react at elevated pressure to accelerate the process. 

Stirred vessel, heat transfer rales, example 498... 

The experimental results for hybridoma and protozoa cells given as examples in Fig. 25 indicate that much higher stress (4 to 30 times) is required under laminar flow conditions of viscosimeters than in stirred vessels to achieve the same death rate k. Here the death rate k is defined as first order deactivation constant k = 1/t In (Nq/N), where N, is the initial and N the time-dependent number of living cells in special deactivation experiments under otherwise optimal living conditions. The stress in Fig. 25 was calculated with Eq. (28) for stirred vessels and with Eq. (1) for the viscosimeter. Our own results for hybri-... 

The uncertainty involved in the calculation of the energy dissipation rate makes it difficult to compare experimental results reported by different researchers. For the same reasons, so far it has proved difficult to assess flow induced effects in different items of process equipment using the common basis of equal energy dissipation rate. For example. Fig. 14 shows the biological response of (SF-9) insect cells as a function of the energy dissipation rates in a capillary tube and in a mechanically stirred vessel [99]. In these plots the calcula-... 

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. 

This simple example illustrates two important features of stirred tanks (1) the concentration of dissolved species is uniform throughout the tank, and (2) the concentration of these species in the exit stream is identical to their concentration in the tank. Note that a consequence of the well-stirred behavior of this model is that there is a step change in solute concentration from the inlet to the tank, as shown in the concentration profile in Figure 2. Such idealized behavior cannot be achieved in real stirred vessels even the most enthusiastically stirred will not display this step change, but rather a smoother transition from inlet to tank concentration. It should also be noted that stirred tank models can be used when chemical reactions occur within the tank, as might occur in a flow-through reaction vessel, although these do not occur in the simple dye dilution example. 

While the simple stirred tank and plug flow models are adequate to describe convective transport in many cases, a more complete description of fluid flow is sometimes needed. For example, an accurate description of tablet dissolution in a stirred vessel may require information about the changing fluid velocity near the tablet surface. Neither the stirred tank nor the plug flow models can address these velocity changes, since both assume that velocity is independent of position and time. In such cases, a more detailed description of fluid flow can be developed using the Navier-Stokes equations, which describe the effects of pressure, viscos-... 

Flow in stirred vessels was also investigated by Holmes et al. (H5), who simulated mass transfer in a diaphragm diffusion cell stirred by magnetic stirrer bars. This is a good example of a simple model study with a direct practical purpose. A minimum stirring speed in such cells is necessary to avoid appreciable errors in the cell constant. The experiment permits this stirring speed to be related to the solution properties. 

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). 

An example rather than linking average bubble size to just or essentially the (overall) power input of a particular vessel-impeller combination, dedicated CFD (preferably DNS and LES) allows for studying ( tracking ) the response of bubble size to local and spatial variations in the turbulence levels in a stirred vessel. In this way, the validity of certain modeling assumptions may be affirmed or disproved. Particularly, effects of spatial variations in e which... 

The microreactor shown in Fig. 1 can be regarded as a continuous-flow reactor equivalent to the common batch reactor flask. The microreactor has a mixer section that provides more precise mixing characteristics than those typically achievable in a stirred vessel. For example, in the... 

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. 

Example prices are given in Table 2. As can be seen from the table, the cost of the SDR system is significantly less than that for a stirred vessel with a similar productive capacity. However, cost considerations are likely to be much less significant than the competitive edge that SDR technology is likely to bring in terms of improved selectivity and product quality. 

The techniques that have been used to characterise the mechanical properties of microparticles may be classified as indirect and direct. The former includes measurement of breakage in a "shear" device, for example, a stirred vessel (Poncelet and Neufeld, 1989) or bubble column (Lu et ah, 1992). However, the results from these indirect techniques are rather difficult to use since the mechanical breakage depends not only on the mechanical properties but also the hydrodynamics of the processing equipment, and the latter are still not well understood. To overcome this problem, a cone and plate viscometer that can apply well-defined shear stresses has been used to study breakage of hybridomas (Born et ah, 1992), but this is not a widely applied or applicable technique because the forces are too small to break most cells. 

Stirring vessels. Upon the examination of different stirring operations it was indeed found that the intensively formulated process parameter P/V represented the pertinent scale-up criterion only if the stirring power has to be dissipated in the volume as evenly as possible (micro-mixing, isotropic turbulence). Examples of this are the dispersion of a gas in a liquid or the dispersion of immiscible liquids s. [22]. 

Example 20 Heat transfer characteristic of a stirring vessel... 

Example 37 Mass transfer in stirring vessels in the G/L system (bulk aeration) Effects of coalescence behavior of the material system... 

Example 35 Steady-state heat transfer in bubble columns 149 Example 36 Time course of temperature equalization in a liquid with temperature-dependent viscosity in the case of free convection 153 Example 37 Mass transfer in stirring vessels in the G/L system (bulk aeration) Effects of coalescence behavior of the material system 156 Example 38 Mass transfer in the G/L system in bubble columns with injectors as gas distributors. The effects of coalescence behavior of the material system 160... 

If is obtained from experiments in stirred suspension or microcarrier cultures, as described above, then, it may be possible to estimate from Q- lqu- However, care must be exercised because can be altered by changes in the culture environment. For example, qy for cells immobilized in agarose beads or hollow fibres may be different from qy for the same cells grown in the same medium in a stirred suspension reactor (Shirai et al, 1988 Wohlpart et al, 1991). In addition, qy may change over time due to changes in cell, nutrient and byproduct concentrations. Analysis of cell density and immobilization effects is complicated by the presence of nutrient concentration gradients. However, stirred vessels with cells immobilized... 

The general formula for for batch growth in a stirred vessel is given by Equation 4.2.32, where P is the extracellular product concentration. Frequently, q is relatively constant during batch growth. One example is monoclonal antibody production by hybridoma cells (Renard et al, 1988). If it is assumed that q does not vary with time, then Equation 4.2.32 can be integrated to yield Equation 4.2.45 ... 

A nucleation-dominated process may be chosen in order to produce fine particles for a product attribute such as bioavailability for a pharmaceutical with low water solubility. The reader is referred to Examples 9-5 and 9-6 for discussion of a process for creating fine particles. Nucleation-dominated processes may be difficult to operate in stirred vessels for the reasons outlined in Section 5.2.1 below and may require intense in-line mixing, as presented in the examples. 

Much of this chapter assumes operation in stirred vessels. Several alternative designs (fluidized bed and impinging jet crystallizers) are summarized early (Table 6-1) for comparison with stirred tanks, and are described later in this chapter and in other parts of this book. An alternative feed addition geometry (mixing elbow) is described in Example 7-1. 

These concerns lead to the conclusion, referred to above, that it is often necessary to choose a mixing condition (impeller speed, type, etc.) that may not be optimum for every aspect of the crystallization and may actually not be optimum for any of them. In many cases, however, one end result (i.e., PSD, bulk density, uniformity of suspension, and approach to equilibrium solubihty [yield]) may dictate the choice of mixing conditions. In this case, it becomes essential to determine if the negatively affected aspects can be tolerated. If these problems are occurring in operation in a stirred vessel, a different type of crystallizer, such as a fluidized bed, might be used to promote crystal growth and minimize nucleation. Readers can find more information on fluidized bed crystallizers in Section 6.6.2 and Examples 7-6 and 11-6. 

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