Stirred tank heat transfer

Having considered PID controllers in Chapter 8, we now consider the other components of the feedback control loop. As an illustrative example, consider the stirred-tank heating system in Fig. 9.1. A thermocouple measures the liquid temperature and converts it to a millivolt-level electrical signal. This signal is then amplified to a voltage level and transmitted to the electronic controller. The feedback controller performs the control calculations and sends the calculated value as an output signal to the final control element, an electrical heater that adjusts the rate of heat transfer to the liquid. This example illustrates the three important functions of a feedback control loop (1) measurement of the controlled variable (CV), (2) adjustment of the manipulated variable (MV), and (3) signal transmission between components. 

Figure 2.5 Heat transfer to and from stirred tanks.

Some modes of heat transfer to stirred tank reacdors are shown in Fig. 23-1 and to packed bed reactors in Fig. 23-2. Temperature and composition profiles of some processes are shown in Fig. 23-3. Operating data, catalysts, and reaction times are stated for a number of industrial reaction processes in Table 23-1. 

FIG. 23-1 Heat transfer to stirred tank reactors, a) Jacket, (h) Internal coils, (c) Internal tubes, (d) External heat exchanger, (e) External reflux condenser. if) Fired heater. (Walas, Reaction Kinetics for Chemical Engineers, McGraw-Hill, 1959). 

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. 

A basic stirred tank design is shown in Fig. 23-30. Height to diameter ratio is H/D = 2 to 3. Heat transfer may be provided through a jacket or internal coils. Baffles prevent movement of the mass as a whole. A draft tube enhances vertical circulation. The vapor space is about 20 percent of the total volume. A hollow shaft and impeller increase gas circulation (as in Fig. 23-31). A splasher can be attached to the shaft at the hquid surface to improve entrainment of gas. A variety of impellers is in use. The pitched propeller moves the liquid axially, the flat blade moves it radially, and inclined blades move it both axially and radially. The anchor and some other designs are suited to viscous hquids. 

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. 

A common process task involves heating a slurry by pumping it through a well-stirred tank. It is useful to know the temperature profile of the slurry in the agitated vessel. This information can be used to optimize the heat transfer process by performing simple sensitivity studies with the formulas presented below. Defining the inlet temperature of the slurry as T, and the temperature of the outer surface of the steam coil as U then by a macroscopic mass and energy balance for the system, a simplified calculation method is developed. 

A continuous flow stirred tank reactor (CFSTR) differs from the batch reactor in that the feed mixture continuously enters and the outlet mixture is continuously withdrawn. There is intense mixing in the reactor to destroy any concentration and temperature differences. Heat transfer must be extremely efficient to keep the temperature of the reaction mixture equal to the temperature of the heat transfer medium. The CFSTR can either be used alone or as part of a series of battery CFSTRs as shown in Figure 4-5. If several vessels are used in series, the net effect is partial backmixing. 

In many eases, the heat flow (Q) to the reaetor is given in terms of the overall heat transfer eoeffieient U, the heat exehange area A, and the differenee between the ambient temperature, T, and the reaetion temperature, T. For a eontinuous flow stirred tank reaetor (CFSTR) in whieh both fluid temperatures (i.e., inside and outside the exehanger) are eonstant (e.g., eondensing steam), Q is expressed as... 

An endothermie reaetion A —> R is performed in three-stage, eon-tinuous flow stirred tank reaetors (CFSTRs). An overall eonversion of 95% of A is required, and the desired produetion rate is 0.95 x 10 kmol/see of R. All three reaetors, whieh must be of equal volume, are operated at 50°C. The reaetion is first order, and the value of the rate eonstant at 50°C is 4 x 10 see The eoneentration of A in the feed is 1 kmol/m and the feed is available at 75°C. The eontents of all three reaetors are heated by steam eondensing at 100°C inside the eoils. The overall heat transfer eoeffieient for the heat-exehange system is 1,500 J/m see °C, and the heat of reaetion is -1-1.5 x 10 J/kmol of A reaeted. 

The advantages of continuous tubular reactors are well known. They include the elimination of batch to batch variations, a large heat transfer area and minimal handling of chemical products. Despite these advantages there are no reported commercial instances of emulsion polymerizations done in a tubular reactor instead the continuous emulsion process has been realized in series-connected stirred tank reactors (1, . ... 

Power input to a homogeneous reaction stirred tank is 0.5-1.5 HP/1000 gal, but three times this amount when heat is to be transferred. 

Recycling of partially reacted feed streams is usually carried out after the product is separated and recovered. Unreacted feedstock can be separated and recycled to (ultimate) extinction. Figure 4.2 shows a different situation. It is a loop reactor where some of the reaction mass is returned to the inlet without separation. Internal recycle exists in every stirred tank reactor. An external recycle loop as shown in Figure 4.2 is less common, but is used, particularly in large plants where a conventional stirred tank would have heat transfer limitations. The net throughput for the system is Q = but an amount q is recycled back to the reactor inlet so that the flow through the reactor is Qin + q- Performance of this loop reactor system depends on the recycle ratio qlQin and on the type of reactor that is in the loop. Fast external recycle has... 

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. 

Example 5.8 Suppose that, to achieve a desired molecular weight, the styrene polymerization must be conducted at 413 K. Use external heat transfer to achieve this temperature as the single steady state in a stirred tank. 

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... 

Therefore, many traditional designs, such as stirred tank reactors, incorporate heat transfer in the process (jacket, external or internal coil, etc.). However, in these devices, there is a significant distance between the heat transfer site and the site of the chemical reaction where heat is released. As a consequence semibatch mode is implemented while batch mode and/or systems are diluted. 

Four mmoles of malononitrile and benzaldehyde were introduced in a batch stirred tank reactor at 323 K with toluene as solvent (30 ml). Then 0.05 g of aluminophosphate oxynitride was added. Samples were analysed by gas chromatography (Intersmat Delsi DI200) using a capillary column (CPSilSCB-25 m). Care was taken to avoid mass or heat transfer limitations. Before the reaction no specific catalyst pretreatment was done. 

Fig. 5.4-23 shows a sketch drawing of a BSC (Brogli et al., 1981). The stirred-tank reactor made of glass (a metal version is also available) is surrounded by a jacket through which a heat-transfer fluid flows at a very high rate the jacket is not insulated. The temperature of the circulation loop is regulated by a cascaded controller so that the heat evolution in the reactor is equilibrated by heat transfer through the reactor wall. The temperature in the loop is adjusted by injection of thermostatted hot or cold fluid. 

Liquid is fed continuously to a stirred tank, which is heated by internal steam coils (Fig. 1.21). The tank operates at constant volume conditions. The system is therefore modelled by means of a dynamic heat balance equation, combined with an expression for the rate of heat transfer from the coils to the tank liquid. 

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... 

Figure 3.2. Model representation of a stirred-tank reactor with heat transfer to or from the jacket.

Chapter 3 concerns the dynamic characteristics of stagewise types of equipment, based on the concept of the well-stirred tank. In this, the various types of stirred-tank chemical reactor operation are considered, together with allowance for heat effects, non-ideal flow, control and safety. Also included is the modelling of stagewise mass transfer applications, based on liquid-liquid extraction, gas absorption and distillation. 

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