Isothermal reactors CSTRs

In previous studies, the main tool for process improvement was the tubular reactor. This small version of an industrial reactor tube had to be operated at less severe conditions than the industrial-size reactor. Even then, isothermal conditions could never be achieved and kinetic interpretation was ambiguous. Obviously, better tools and techniques were needed for every part of the project. In particular, a better experimental reactor had to be developed that could produce more precise results at well defined conditions. By that time many home-built recycle reactors (RRs), spinning basket reactors and other laboratory continuous stirred tank reactors (CSTRs) were in use and the subject of publications. Most of these served the original author and his reaction well but few could generate the mass velocities used in actual production units. 

The general rule is that combinations of isothermal reactors provide intermediate levels of performance compared with single reactors that have the same total volume and flow rate. The second general rule is that a single, piston flow reactor will give higher conversion and better selectivity than a CSTR. Autocatalytic reactions provide the exception to both these statements. 

Example 14.1 shows how an isothermal CSTR with first-order reaction responds to an abrupt change in inlet concentration. The outlet concentration moves from an initial steady state to a final steady state in a gradual fashion. If the inlet concentration is returned to its original value, the outlet concentration returns to its original value. If the time period for an input disturbance is small, the outlet response is small. The magnitude of the outlet disturbance will never be larger than the magnitude of the inlet disturbance. The system is stable. Indeed, it is open-loop stable, which means that steady-state operation can be achieved without resort to a feedback control system. This is the usual but not inevitable case for isothermal reactors. 

Consecutive reactions, isothermal reactor cmi < cw2, otai = asi = 0. The course of reaction is shown in Fig. 5.4-71. Regardless the mode of operation, the final product after infinite time is always the undesired product S. Maximum yields of the desired product exist for non-complete conversion. A batch reactor or a plug-flow reactor performs better than a CSTR Ysbr.wux = 0.63, Ycstriiuix = 0.445 for kt/ki = 4). If continuous operation and intense mixing are needed (e.g. because a large inteifacial surface area or a high rate of heat transfer are required) a cascade of CSTRs is recommended. 

In the previous section we indicated how various mathematical models may be used to simulate the performance of a reactor in which the flow patterns do not fit the ideal CSTR or PFR conditions. The models treated represent only a small fraction of the large number that have been proposed by various authors. However, they are among the simplest and most widely used models, and they permit one to bracket the expected performance of an isothermal reactor. However, small variations in temperature can lead to much more significant changes in the reactor performance than do reasonably large deviations inflow patterns from idealized conditions. Because the rate constant depends exponentially on temperature, uncertainties in this parameter can lead to design uncertainties that will make any quantitative analysis of performance in terms of the residence time distribution function little more than an academic exercise. Nonetheless, there are many situations where such analyses are useful. 

Isothermal Reactor with Complex Reaction 265 Continuous Stirred-Tanks, Tracer Experiment 273 Deactivating Catalyst in a CSTR 268 Distribution of an Insecticide in an Aquatic Ecosystem 581... 

We took the 4- sign on the square root term for second-order kinetics because the other root would give a negative concentration, which is physically unreasonable. This is true for any reaction with nth-order kinetics in an isothermal reactor There is only one real root of the isothermal CSTR mass-balance polynomial in the physically reasonable range of compositions. We will later find solutions of similar equations where multiple roots are found in physically possible compositions. These are true multiple steady states that have important consequences, especially for stirred reactors. However, for the nth-order reaction in an isothermal CSTR there is only one physically significant root (0 < Ca < Cao) to the CSTR equation for a given T. ... 

Thus it is evident that a PFTR is always the reactor of choice (smaller for greater than zero-order kinetics in an isothermal reactor. The CSTR may stUl be favored for n > 0 for cost reasons as long as the conversion is not too high, but the isothermal PFTR is much superior at high conversions whenever n > 0. 

For a single reaction in an isothermal reactor the design principles involved primarily the reactor configuration for niinimum residence time. This generally favors the PFTR over the CSTR for positive-order kinetics. However, the CSTR frequently is less costly and easier to maintain, and one or more CSTRs can frequently be preferred over a PFTR. 

Thus we see that for nonisothermal reactors this 1/r versus Cao Ca curve is not always an increasing function of conversion as it was for isothermal reactors even with positive-order kinetics. Since the 1/r curve can have a rninimum for the nonisothermal reactor, we confirm the possibility that the CSTR requires a smaller volume than the PFTR for positive-order kinetics. This is hue even before the multiple steady-state possibilities are accounted for, which we will discuss in the next chapter. This is evident from our 1 /r plot for the PFTR and CSTR and will occur whenever r has a sufficiently large maximum that the area under the rectangle is less than the area under the curve of 1/r versus Cao Ca-... 

In the previous chapter we showed how nonisothermal reactors can exhibit much more complex behavior than isothermal reactors. This occurs basically because k(T) is strongly temperature dependent Only a single steacfy state is possible in the PFTR, but the CSTR, although (or because) it is described by algebraic equations, can exhibit even more interesting (and potentially even more dangerous) behavior. 

In chapters 2-5 two models of oscillatory reaction in closed vessels were considered one based on chemical feedback (autocatalysis), the other on thermal coupling under non-isothermal reaction conditions. To begin this chapter, we again return to non-isothermal systems, now in a well-stirred flow reactor (CSTR) such as that considered in chapter 6. 

It is useful to examine the consequences of a closed ion source on kinetics measurements. We approach this with a simple mathematical model from which it is possible to make quantitative estimates of the distortion of concentration-time curves due to the ion source residence time. The ion source pressure is normally low enough that flow through it is in the Knudsen regime where all collisions are with the walls, backmixing is complete, and the source can be treated as a continuous stirred tank reactor (CSTR). The isothermal mole balance with a first-order reaction occurring in the source can be written as... 

In the following we attempt to describe the acetylcholinesterase/choline acetyltransferase enzyme system inside the neural synaptic cleft in a simple fashion see Figure 4.49. The complete neurocycle of the acetylcholine as a neurotransmitter is simulated in our model as a simple two-enzymes/two-compartments model. Each compartment is described as a constant-flow, constant-volume, isothermal, continuous stirred tank reactor (CSTR). The two compartments (I) and (II) are separated by a nonselective permeable membrane as shown in Figure 4.50. 

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. 

Let us consider one of the simplest recycle processes imaginable a continuous stirred tank reactor (CSTR) and a distillation column. As shown in Figure 2.5. a fresh reactant stream is fed into the reactor. Inside the reactor, a first-order isothermal irreversible reaction of component A to produce component B occurs A -> B. The specific reaction rate is k (h1) and the reactor holdup is VR (moles). The fresh feed flowrate is Fs (moles/h) and its composition is z0 (mole fraction component A). The system is binary with only two components reactant A and product B. The composition in the reactor is z (mole fraction A). Reactor effluent, with flowrate F (moles/h) is fed into a distillation column that separates unreacted A from product B. 

The principal advantage of continuous reaction vessels is that they operate (after an initial transient period) under steady-state conditions that are conducive to the formation of a highly uniform and well-regulated product. In this section, we shall confine the discussion to continuous stirred-tank reactors (CSTRs). These reactors are characterized by isothermal, spatially uniform operation. 

Tests were run on a small ejtperimental reactor used for decomposing nitrogen oxides in an automobile exhaust stream. In one series of tests, a nitrogen stream containing various concentrations of NOj was fed to a reactor and the kinetic data obtained are shown in Figure P5-11. Each point represents one complete run. The reactor operates essentially as an isothermal backmix reactor (CSTR). What can you deduce abmit the apparent order of the reaction over the temperature range studied ... 

Design Stmcture for Isothermal Reactors 125 Scale-up of Liquid-Phase Batch Reactor Data to the Design of a CSTR 129... 

In this work we consider a benehmark eontrol problem of the isothermal operation of a eontinuous stirred tank reactor (CSTR) where the Van de Vusse reaetions take place [12, 13] (i.e. A B -> C and 2A -> D). The performance index is defined as the weighted sum of squares of errors between the setpoint and the estimated model output predieted for the time step in the future with witk) = D.D for all w(t< ) = 10,000foj- k=Mp The... 

Calculate the reactor size requirements for one continuously stirred tank reactor (CSTR). Also calculate the volume requirements for a cascade composed of two identical CSTRs. Assume isothermal operation at 25°C where the reaction rate constant is equal to 9.92m /(kgmol ks). Reactant concentrations in the feed are each equal to 0.08kgmol/m, and the liquid feed rate is equal to 0.278 m /ks. The desired degree of conversion is 87.5%. 

In continuous stirred-tank reactors (CSTRs), complex kinetics may give rise to multiple steady states even in isothermal operation, especially in heterogeneous catalysis. However, to unravel the causes may be difficult. Here, Feinberg s network theory can help [3]. It operates with a deficiency index that is a readily calculated zero or positive integer. The most useful result of the theory is ... 

Numerical simulations and analyses were performed for both the continuous stirred-tank reactor (CSTR) and the plug-flow reactor (PER). A comparison between the microkinetic model predictions for an isothermal PFR and the experimental results [13], is presented in Fig. 2 for the following conditions commercial low temperature shift Cu catalyst loading of 0.14 g/cm total feed flow rate of 236 cm (STP) min residence time r = 1.8 s feed composition of H20(10%), CO(10%), C02(0%), H2(0%) and N2(balance). As can be seen, the model can satisfactorily reproduce the main features of the WGSR on Cu LTS catalyst without any further fine-tuning, e.g., coverage dependence of the activation energy, etc, which is remarkable and provides proof of the adequacy of the... 

Consider an isothermal continuous stirred tank reactor (CSTR). Analyse its dynamic behaviour in the case of a first-order irreversible reaction. 

EXAM PLE 2.5. The component balance equation for an irreversible /)th-order. non-isothermal reaction occurring in a constant-volume, variable-throughput continuous stirred-tank reactor (CSTR) is... 

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