Stirred tank heat transfer coefficient

The principles of heat transfer in stirred tanks are discussed in Chapter 14, with a full set of design correlations for heat transfer coefficients. The key heat transfer concepts to keep in mind are as follows ... 

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. 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

This section is concerned with the UA xtiT — Text) term in the energy balance for a stirred tank. The usual and simplest case is heat transfer from a jacket. Then A xt refers to the inside surface area of the tank that is jacketed on the outside and in contact with the fluid on the inside. The temperature difference, T - Text, is between the bulk fluid in the tank and the heat transfer medium in the jacket. The overall heat transfer coefficient includes the usual contributions from wall resistance and jacket-side coefficient, but the inside coefficient is normally limiting. A correlation applicable to turbine, paddle, and propeller agitators is... 

Fig. 3.2 shows the case of a jacketed, stirred-tank reactor, in which either heating by steam or cooling medium can be applied to the jacket. Here V is volume, Cp is specific heat capacity, p is density, Q is the rate of heat transfer, U is the overall heat transfer coefficient, A is the area for heat transfer, T is temperature, H is enthalpy of vapour, h is liquid enthalpy, F is volumetric flow... 

Heat transfer coefficients in stirred tank operations are discussed in Section 17.7. 

A reaction A——>P is to be performed in a PFR. The reaction follows first-order kinetics, and at 50 °C in the batch mode, the conversion reaches 99% in 60 seconds. Pure plug flow behavior is assumed. The flow velocity should be 1 m s"1 and the overall heat transfer coefficient 1000Wm 2 K"1. (Why is it higher than in stirred tank reactors ). The maximum temperature difference with the cooling system is 50 K. 

A 2.5 m3 stainless steel stirred tank reactor is to be used for a reaction with a batch volume of 2 m3 performed at 65 °C. The heat transfer coefficient of the reaction mass is determined in a reaction calorimeter by the Wilson plot as y = 1600Wnr2KA The reactor is equipped with an anchor stirrer operated at 45 rpm. Water, used as a coolant, enters the jacket at 13 °C. With a contents volume of 2 m3, the heat exchange area is 4.6 m2. The internal diameter of the reactor is 1.6 m. The stirrer diameter is 1.53 m. A cooling experiment was carried out in the temperature range around 70 °C, with the vessel containing 2000 kg water. The results are represented in Figure 9.16. 

In many cases, the heat flow (Q) to the reactor is given in terms of the overall heat transfer coefficient U, the heat exchange area A, and the difference between the ambient temperature, Ta, and the reaction temperature, T. For a continuous flow stirred tank reactor (CFSTR) in which both fluid temperatures (i.e., inside and outside the exchanger) are constant (e.g., condensing steam), Q is expressed as... 

An endothermic reaction A — R is performed in three-stage, continuous flow stirred tank reactors (CFSTRs). An overall conversion of 95% of A is required, and the desired production rate is 0.95 x 10 3 kmol/sec of R. All three reactors, which must be of equal volume, are operated at 50°C. The reaction is first order, and the value of the rate constant at 50°C is 4 x 10-3 sec-1. The concentration of A in the feed is 1 kmol/m3 and the feed is available at 75°C. The contents of all three reactors are heated by steam condensing at 100°C inside the coils. The overall heat transfer coefficient for the heat-exchange system is 1,500 J/m2 sec °C, and the heat of reaction is +1.5 x 108 J/kmol of A reacted. 

The hydrodynamic parameters that are required for stirred tank design and analysis include phase holdups (gas, liquid, and solid) volumetric gas-liquid mass-transfer coefficient liquid-solid mass-transfer coefficient liquid, gas, and solid mixing and heat-transfer coefficients. The hydrodynamics are driven primarily by the stirrer power input and the stirrer geometry/type, and not by the gas flow. Hence, additional parameters include the power input of the stirrer and the pumping flow rate of the stirrer. 

Stirred tank reactors are provided with a jacket or immersion coil for heating or cooling the reaction medium. The temperature of the medium inside the tank is generally uniform. The rate of heat transfer depends on the heat transfer area, the difference in the temperature between the reaction medium and heating or cooling fluid and heat transfer coefficient. 

TABLE 17.14. Equations for Heat Transfer Coefficients inside Stirred Tanks ... 

Eq. (32) is used to determine the internal heat transfer coefficient (apw-g) under gassed conditions in a jacketed stirred tank. After appropriate corrections, it can also be used to approximate the process side heat transfer coefficient (ap g) in the presence of an internal heat exchanger. A multiplying correction factor, the ratio of measured heat transfer coefficients under ungassed conditions (ap-ug/ pw-ug), is used as indicated in Eq. (33). In this case, ap g... 

The stirring and the resulting flow pattern inside the tank can be very important for the overall heat transfer resistance, because the performance of the reactor affects the heat transfer coefficient at the process side hg. The other resistances are determined by the materials used and the properties of the cooling/heating media and are thus not influenced by the reactor performance. 

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