In stirred tanks

In this equation, represents the rate of energy dissipation per unit mass of fluid. In pulsed and reciprocating plate columns the dimensionless proportionahty constant K in equation 38 is on the order of 0.3. In stirred tanks, the proportionaUty constant has been reported as 0.024(1 + 2.5 h) in the holdup range 0 to 0.35 (67). The increase of drop si2e with holdup is attributed to the increasing tendency for coalescence between drops as the concentration of drops increases. A detailed survey of drop si2e correlations is given by the Hterature (65). 

F. A. Holland and F. S. Chapman, EiquidMixing and Processing in Stirred Tanks, Van Nostrand Reinhold, New York, 1966. 

FIG. 6-40 Dimensionless power number in stirred tanks. (Reptinted with petTwssion from Bates, Fondy, and Cotpstein, Ind. Eng. Gbem. Process Design Develop., 2, 310 [1.963].)... 

The profiles of temperature and composition shown in Fig. 23-3 are not of homogeneous liqmd reactions, but are perhaps representative of all lands of reactions. Only in stirred tanks and some fluidized beds are nearly isothermal conditions practically attainable. 

Polymerization processes are characterized by extremes. Industrial products are mixtures with molecular weights of lO" to 10. In a particular polymerization of styrene the viscosity increased by a fac tor of lO " as conversion went from 0 to 60 percent. The adiabatic reaction temperature for complete polymerization of ethylene is 1,800 K (3,240 R). Heat transfer coefficients in stirred tanks with high viscosities can be as low as 25 W/(m °C) (16.2 Btu/[h fH °F]). Reaction times for butadiene-styrene rubbers are 8 to 12 h polyethylene molecules continue to grow lor 30 min whereas ethyl acrylate in 20% emulsion reacts in less than 1 min, so monomer must be added gradually to keep the temperature within hmits. Initiators of the chain reactions have concentration of 10" g mol/L so they are highly sensitive to poisons and impurities. 

In order to allow integration of countercurrent relations like Eq. (23-93), point values of the mass-transfer coefficients and eqiiilibrium data are needed, over ranges of partial pressure and liquid-phase compositions. The same data are needed for the design of stirred tank performance. Then the conditions vary with time instead of position. Because of limited solubihty, gas/liquid reactions in stirred tanks usually are operated in semibatch fashion, with the liquid phase charged at once, then the gas phase introduced gradually over a period of time. CSTR operation rarely is feasible with such systems. 

TABLE 23-12 Correlations of Mass-Transfer Coefficients in Stirred Tanks... 

TIME-DEPENDENT TURBULENT MIXING AND CHEMICAL REACTION IN STIRRED TANKS ... 

The objeetive of the following model is to investigate the extent to whieh Computational Fluid Mixing (CFM) models ean be used as a tool in the design of industrial reaetors. The eommereially available program. Fluent , is used to ealeulate the flow pattern and the transport and reaetion of ehemieal speeies in stirred tanks. The blend time predietions are eompared with a literature eonelation for blend time. The produet distribution for a pair of eompeting ehemieal reaetions is eompared with experimental data from the literature. 

In these model equations it is assumed that turbulence is isotropic, i.e. it has no favoured direction. The k-e model frequently offers a good compromise between computational economy and accuracy of the solution. It has been used successfully to model stirred tanks under turbulent conditions (Ranade, 1997). Manninen and Syrjanen (1998) modelled turbulent flow in stirred tanks and tested and compared different turbulence models. They found that the standard k-e model predicted the experimentally measured flow pattern best. 

Baldyga, J. and Bourne, J.R., 1992. Interactions between mixing on various scales in stirred tank reactors. Chemical Engineering Science, 47, 1839-1848. 

Bourne, J.R. and Dell Ava, P., 1987. Micro- and macromixing in stirred tank reactors of different sizes. Chemical Engineering Research and Design, 65, 180-186. 

Bourne, J.R. and Yu, S., 1994. Investigation of micromixing in stirred tank reactors using parallel reactions. Industrial and Engineering Chemistry Research, 33, 41-55. 

Geisler, R., Mersmann, A. and Voit, H., 1991. Macro- and micromixing in stirred tanks. International Chemical Engineering, 31, 642-653. 

Holland, F.A. and Chapman, F.S., 1966. Liquid mixing and processing in stirred tanks. New York Reinhold. 

Manninen, M. and Syrjanen, I., 1998. Modelling turbulent flow in stirred tanks. CFX Update, 16, 10-11. 

Kinetics c/c0 in piston flow reactor Si, Sc o c/c0 in stirred tank reactor St,... 

Batch reactions are conducted in stirred tanks for small daily production rates or when the reaction times are long or when some condition such as feed rate or temperature must be programmed in some way. 

This chapter develops the techniques needed to analyze multiple and complex reactions in stirred tank reactors. Physical properties may be variable. Also treated is the common industrial practice of using reactor combinations, such as a stirred tank in series with a tubular reactor, to accomplish the overall reaction. 

This set of first-order ODEs is easier to solve than the algebraic equations where all the time derivatives are zero. The initial conditions are that a ut = no, bout = bo,... at t = 0. The long-time solution to these ODEs will satisfy Equations (4.1) provided that a steady-state solution exists and is accessible from the assumed initial conditions. There may be no steady state. Recall the chemical oscillators of Chapter 2. Stirred tank reactors can also exhibit oscillations or more complex behavior known as chaos. It is also possible that the reactor has multiple steady states, some of which are unstable. Multiple steady states are fairly common in stirred tank reactors when the reaction exotherm is large. The method of false transients will go to a steady state that is stable but may not be desirable. Stirred tank reactors sometimes have one steady state where there is no reaction and another steady state where the reaction runs away. Think of the reaction A B —> C. The stable steady states may give all A or all C, and a control system is needed to stabilize operation at a middle steady state that gives reasonable amounts of B. This situation arises mainly in nonisothermal systems and is discussed in Chapter 5. 

The existence of three steady states, two stable and one metastable, is common for exothermic reactions in stirred tanks. Also common is the existence of only one steady state. For the styrene polymerization example, three steady states exist for a limited range of the process variables. For example, if Ti is sufficiently low, no reaction occurs, and only the lower steady state is possible. If Tin is sufficiently high, only the upper, runaway condition can be realized. The external heat transfer term, UAextiTout — Text in Equation (5.28) can also be used to vary the location and number of steady states. 

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