The adiabatic stirred tank

We have already obtained the basic design equations for the stirred tank [Eqs. (7.3.1) and (7.3.2)] and these will represent an adiabatic operation if we set Q = 0. Thus in the steady state 

We shall assume that J does not vary appreciably—a reasonable assumption which allows the general picture of adiabatic operation to emerge without too much clutter. This means that the product state (, T) lies on a line of slope through the feed state (0, as shown in Fig. 8.2. The point F represents the feed states and the locus of product states is the line FG whose equation is Eq. (8.2.3). The equilibrium state for adiabatic operation is at point G and there the reaction rate is zero. However, it is clearly possible 

2 Variation of an exothermic reaction rate in adiabatic reaction. 

This provides an equation for calculating the locus F m, though unfortunately not as manageable an equation as that for F. The derivative with respect to f along an adiabatic path is djd. If we were to plot the reciprocal of the reaction rate along a particular adiabatic path, we would have a curve as in Fig. 8.3 the corresponding points are marked. 

Production rate specified. The production rate of any product of the reaction will be proportional to, and if this is specified, either f or can be chosen and the other will be fixed. If q = P, the volume required of the reactor is 

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This is the classical argument introduced by van Heerden in 1953 for the adiabatic stirred tank. It is a most important one to grasp firmly for it can be used in more complicated situations to get some insight into the stability of a system. However, its limitations must be also thoroughly understood. In particular, it can be used to establish instability, but it does not count conclusively for stability because of several reasons. First, we should be suspicious of a single condition for a system in which there are two variables. Second, the diagram for the heat generation was drawn in a rather special way, for the steady state-mass balance equation, f 7), was first... 

We have already considered the stability of the adiabatic stirred tank (Sec. 7.5) and have observed that since M = 1, the slope condition L> N suffices to ensure stability. Now recalling the definitions of L and N this is... 

While the adiabatic batch reactor is important and presents many control issues in its own right, we are concerned here primarily with continuous systems. We consider in detail two distinct reactor types the continuous stirred tank reactor (CSTRj and the plug-flow reactor. They differ fundamentally in the way the reactants and the products... 

Exercise 8,3.1. Show how contours of constant i r i, T) in the f, T plane might be used to calculate the holding time required of an adiabatic stirred tank. Sketch them carefully. 

Suppose an exothermic irreversible reaction with first-order kinetics is carried out in an adiabatic stirred-tank reactor, as shown in Fig. 5-9. The... 

We have simulated the complete (stirred tank and tube) reactor system combining our model for the cascade reactor, with only one stirred tank, with the model for the adiabatic ideal tubular reactor. An example of the excellent fit between simulated and eiq)eriinentally found resiUts is given in fig. 3. ... 

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. 

There are a variety of limiting forms of equation 8.0.3 that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular flow reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resultant differential equation must then be solved in conjunction with the differential equation describing the material balance on the differential element. 

The reactor system may consist of a number of reactors which can be continuous stirred tank reactors, plug flow reactors, or any representation between the two above extremes, and they may operate isothermally, adiabatically or nonisothermally. The separation system depending on the reactor system effluent may involve only liquid separation, only vapor separation or both liquid and vapor separation schemes. The liquid separation scheme may include flash units, distillation columns or trains of distillation columns, extraction units, or crystallization units. If distillation is employed, then we may have simple sharp columns, nonsharp columns, or even single complex distillation columns and complex column sequences. Also, depending on the reactor effluent characteristics, extractive distillation, azeotropic distillation, or reactive distillation may be employed. The vapor separation scheme may involve absorption columns, adsorption units,... 

One of the simplest practical examples is the homogeneous nonisothermal and adiabatic continuous stirred tank reactor (CSTR), whose steady state is described by nonlinear transcendental equations and whose unsteady state is described by nonlinear ordinary differential equations. 

Continuous Stirred Tank Reactor The Adiabatic Case... 

We have used CO oxidation on Pt to illustrate the evolution of models applied to interpret critical effects in catalytic oxidation reactions. All the above models use concepts concerning the complex detailed mechanism. But, as has been shown previously, critical. effects in oxidation reactions were studied as early as the 1930s. For their interpretation primary attention is paid to the interaction of kinetic dependences with the heat-and-mass transfer law [146], It is likely that in these cases there is still more variety in dynamic behaviour than when we deal with purely kinetic factors. A theory for the non-isothermal continuous stirred tank reactor for first-order reactions was suggested in refs. 152-155. The dynamics of CO oxidation in non-isothermal, in particular adiabatic, reactors has been studied [77-80, 155]. A sufficiently complex dynamic behaviour is also observed in isothermal reactors for CO oxidation by taking into account the diffusion both in pores [71, 147-149] and on the surfaces of catalyst [201, 202]. The simplest model accounting for the combination of kinetic and transport processes is an isothermal continuously stirred tank reactor (CSTR). It was Matsuura and Kato [157] who first showed that if the kinetic curve has a maximum peak (this curve is also obtained for CO oxidation [158]), then the isothermal CSTR can have several steady states (see also ref. 203). Recently several authors [3, 76, 118, 156, 159, 160] have applied CSTR models corresponding to the detailed mechanism of catalytic reactions. 

Knowledge of these types of reactors is important because some industrial reactors approach the idealized types or may be simulated by a number of ideal reactors. In this chapter, we will review the above reactors and their applications in the chemical process industries. Additionally, multiphase reactors such as the fixed and fluidized beds are reviewed. In Chapter 5, the numerical method of analysis will be used to model the concentration-time profiles of various reactions in a batch reactor, and provide sizing of the batch, semi-batch, continuous flow stirred tank, and plug flow reactors for both isothermal and adiabatic conditions. 

Examples of stirred tank reactors with heat transfer are shown in Fig. 19-1. If the heat of reaction is not significant, an adiabatic reactor may be used. For modest heat addition (removal), a jacketed stirred tank is adequate (Fig. 19-la). As the heat exchange requirements... 

We have a first-order homogeneous reaction, taking place in an ideal stirred tank reactor. The volume of the reactor is 20 X 10 3 m3. The reaction takes place in the liquid phase. The concentration of the reactant in the feed flow is 3.1 kmol/m3 and the volumetric flow rate of the feed is 58 X 10 m3/s. The density and specific heat of the reaction mixture are constant at 1000 kg/m3 and 4.184kJ/(kg K). The reactor operates at adiabatic conditions. If the feed flow is at 298 K, investigate the possibility of multiple solutions for conversion at various temperatures in the product stream. The heat of reaction and the rate of reaction are... 

More quantitative measurements are attainable by using an accelerated rate calorimeter (ARC), which is an adiabatic (sealed) calorimeter used to study runaway reactions.The data generated can be directly applied for plant scale-up, e.g., for calculating whether the cooling system for scale-up can safely accommodate the reaction exotherm. Sealed calorimeters show a decreasing boiling point associated with a change in the volatile reaction components [2]. Stirred tank calorimetry can also be used to accurately calculate the heat of reaction [3]. 

Vejtasa, S.A. Schmitz, R.A. An experimental study of steady state multiplicity and stability in an adiabatic stirred reactor. AIChE J. 1970,16, 410 19. Schmitz, R.A. Multiplicity, stability, and sensitivity of states in chemically reacting systems - a review. Adv. Chem. Ser. 1975, 148, 156-211. Razon, L.F. Schmitz, R.-A. Multiplicities and instabilities in chemically reacting systems - a review. Chem. Eng. Sci. 1987, 42, 1005-1047. Uppal, A. Ray, W.H. Poore, A.B. On the dynamic behavior of continuous stirred tank reactors. Chem. Eng. Sci. 1974, 29, 967-985. 

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