Scale-up of stirred vessels

D Diameter of agitator Dt Diameter of tank ZA Height of agitator from base of tank H Depth of liquid R No. of baffles WB Width of baffles N Speed of agitator P Pitch of agitator 

For similarity in two mixing systems, it is important lo achieve geometric kinematic and dynamic similarity, 

Geometric similarity prevails between two systems of different sizes if all counterpart length dimensions have a constant ratio. Thus the following ratios must be tbe same in 

Kinematic similarity exists in two geometrically similar units when the velocities at corresponding points have a constant ratio. Also, the paths of fluid motion (flow patterns) must be alike. 

Dynamic similarity occurs in two geometrically similar units of different sizes if all corresponding forces at counterpart locations have a constant ratio. It is necessary here lo distinguish between the various types of force inertial, gravitational, viscous, surface tension and other forms, such as normal stresses in the case of viscoelastic non-Newtonian liquids. Some or all of these forms may be significant in a mixing vessel. Considering 

For heat and mass transfer in stirred vessels, additional dimensionless groups which are important include the Nusselt, Sherwood, Prandtl, Schmidt and Grashof munbers. Likewise, in the case of non-Newtonian flitids, an 

Kinematic and dynamic similarities both require geometrical similarity, so the corresponding positions 1 and 2 can be identified in the two systems. Some of the various types of forces that may arise during mixing or agitation will now be formulated. 

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If Xs has reached a minimum value at a mixing rate that can be achieved on scale-up, a stirred vessel can be used to achieve Yexp. At values of Dum < 0.001, mixing is only necessary for blending and heat exchange, and the concerns about feed pipe placement and addition rate are not applicable. Caution must be used in reaching this conclusion, as even small increases in Xs can cause downstream problems in separation. 

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... 

Kataoka T and Nishiki T. Dispersed mean drop sizes of (W/0)/W emulsions in a stirred tank. J Chem Eng Jpn 1986 19 408-412. Nishikawa M, Mori F, and Fujieda S. Average drop size in a liquid-liquid phase mixing vessel. J Chem Eng Jpn 1987 20 82-88. Nishikawa M, Mori F, Fujieda S, and Kayama T. Scale-up of liquid-liquid phase mixing vessel. J Chem Eng Jpn 1987 20 454—459. Berkman PD and Calabrese RV. Dispersion of viscous liquids by turbulent flow in a static mixer. AIChE J 1988 34 602-609. Chatzi EG, Gavrielides AD, and Kiparissides C. Generalized model for prediction of the steady-state drop size distributions in batch stirred vessels. Ind Eng Chem Res 1989 28 1704—1711. 

Mass-Transfer Models Because the mass-transfer coefficient and interfacial area for mass transfer of solute are complex functions of fluid properties and the operational and geometric variables of a stirred-tank extractor or mixer, the approach to design normally involves scale-up of miniplant data. The mass-transfer coefficient and interfacial area are influenced by numerous factors that are difficult to precisely quantify. These include drop coalescence and breakage rates as well as complex flow patterns that exist within the vessel (a function of impeller type, vessel geometry, and power input). Nevertheless, it is instructive to review available mass-transfer coefficient and interfacial area models for the insights they can offer. 

In the case of stirred tank fermenters, heat that must be dissipated includes not only that generated by microbial metabolic activity but also that evolved from agitation power (i.e., 2500Btu/shp-hr) and expansion of sparged gas. This can lead to scale-up problems because vessel volume is proportional to vessel diameter cubed, while heat transfer area is proportional only to vessel diameter squared. 

Table 3 Guidelines for scale-up of liquid-liquid stirred vessels...

Geisler R.K., Buurman C., Mersmann A.B., Scale-up of the necessary power input in stirred vessels... 

Compared to batch processes, continuous processes often show a higher space-time yield. Reaction conditions may be kept within certain limits more easily. For easier scale-up of some enzyme-catalyzed reactions, the Enzyme Membrane Reactor (EMR) has been developed. The principle is shown in Fig. 7-26 A. The difference in size between a biocatalyst and the reactants enables continuous homogeneous catalysis to be achieved while retaining the catalyst in the vessel. For this purpose, commercially available ultrafiltration membranes are used. When continuously operated, the EMR behaves as a continuous stirred tank reactor (CSTR) with complete backmixing. For large-scale membrane reactors, hollow-fiber membranes or stacked flat membranes are used 129. To prevent concentration polarization on the membrane, the reaction mixture is circulated along the membrane surface by a low-shear recirculation pump (Fig. 7-26 B). 

Geisler, R.K., Buurman, C., and Mersmann, A.B. (1993). Scale-Up of the Necessary Power Input in Stirred Vessels with Suspensions, Chem. Engr. J. 51, pp. 29-39. 

Scaling up of bubble columns is generally based on the requirement of keeping kiA constant. Since A is proportional to, this imphes keeping the superflcial gas velocity constant. Some design aspects of bubble reactors will be illustrated in an example following the section on stirred vessel reactors. 

The evolution of chemical processes and process equipment is closely related to the methods and apparatus used in the chemistry laboratory. At the early stage of evolution of chemical industries, process steps in the manufacture of a chemical mimicked the steps used in the chemistry lab in its preparation. Most of these processes were batch processes. Some of these evolved into continuous processes as the production volumes increased. Batch processes occupy the preeminent position, even today, in the pharmaceutical and fine-chemical industries. Some of the process equipment - stirred vessels, packed towers, filters, and so on - are the up-sealed versions of the apparatus used in the chemistry laboratory of yesteryear. Process intensification (PI), which represents a paradigm shift in equipment as well as in process design, takes advantage of advances in reaction engineering and transport phenomena in the design of equipment and processes (as opposed to the mere scale-up of the apparatus of the chemistry lab and mimicking the step in the laboratory preparation). 

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