Transient Continuous Stirred Tank Reactors

Step 1 You can use the following MATLAB m-file along with the fsolve command (available in the Optimization Toolbox)  

Step 2 Test the m-file with the following commands  

Step 3 Then in the command window, issue the following commands  

Reactors do not always run at steady state. In fact, many pharmaceuticals are made in a batch mode. Such problems are easily solved using the same techniques presented above because the plug flow reactor equations are identical to the batch reactor equations. Even CSTRs can be run in a transient mode, and it may be necessary to model a time-dependent CSTR to study the stability of steady solutions. When there is more than one solution, one or more of them will be unstable. Thus, this section considers a time-dependent CSTR as described by Eq. (8.51)  

The parameter Le is a Lewis number, and it includes the heat capacity of the system. The Da is a Damkdhler number and includes the rate of reaction. The parameters are taken as 

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Transient continuous stirred tank reactors Chapter 8, p. 137. 

X H kJ/mol. Since the sticking coefficient of H2 on Cu( 111) is not known, the prefactor for the sticking and the activation energy of the Cu(l 10) surface was used as areliable approximation. From the kinetic gas theory, a preexponential factor Aads = 9.2 x 10 (torr-s) was derived for our model. In our calculation we assumed 132 /xmol/gr active sites based on theexperimental results of Muhler et al. [6] for the Cu/Zn0/Al203 based on a H/ = H (2 Cu) = 1 1 stoichiometry. Under the conditons of perfect mixing gas phase condition is uniform throughout the bed. The reactor mass balance for a transient continuous stirred tank reactor was used in the form... 

For steady-state operation of a continuous stirred-tank reactor or continuous stirred-tank reactor cascade, there is no change in conditions with respect to time, and therefore the accumulation term is zero. Under transient conditions, the full form of the equation, involving all four terms, must be employed. 

The chemical reactor is the unif in which chemical reactions occur. Reactors can be operated in batch (no mass flow into or out of the reactor) or flow modes. Flow reactors operate between hmits of completely unmixed contents (the plug-flow tubular reactor or PFTR) and completely mixed contents (the continuous stirred tank reactor or CSTR). A flow reactor may be operated in steady state (no variables vary with time) or transient modes. The properties of continuous flow reactors wiU be the main subject of this course, and an alternate title of this book could be Continuous Chemical Reactors. The next two chapters will deal with the characteristics of these reactors operated isothermaUy. We can categorize chemical reactors as shown in Figure 2-8. 

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. 

In an ideal continuous stirred tank reactor, composition and temperature are uniform throughout just as in the ideal batch reactor. But this reactor also has a continuous feed of reactants and a continuous withdrawal of products and unconverted reactants, and the effluent composition and temperature are the same as those in the tank (Fig. 7-fb). A CSTR can be operated under transient conditions (due to variation in feed composition, temperature, cooling rate, etc., with time), or it can be operated under steady-state conditions. In this section we limit the discussion to isothermal conditions. This eliminates the need to consider energy balance equations, and due to the uniform composition the component material balances are simple ordinary differential equations with time as the independent variable ... 

Using the thus built kinetic model, both the dynamic and steady state cases of a continuous stirred tank reactor were simulated. We show here the simulation results concerning transient effects. The case considered is the switching of feeds with different H2S concentrations. The shapes of the trajectories and the variations of activities are generally comparable to the experiment results (20,21), although the latter were obtained under low pressure (fig. 2). It is known that the addition of H2S depresses the HDS activity. Simulation results refine the conclusion. They confirm the experimentally found phenomenon in (22) that, for catalysts with different compositions, the depression... 

Miro, E.E., D.R. Ardiles, E.A. Lombardo, and J.O. Petunchi, "Continuous-Stirred Tank Reactor (CSTR) Transient Studies in Heterogeneous Catalysts", J. Catal., 97,43,1986... 

The development of practical methods [56] for the systematic design of new oscillating reactions in continuous stirred tank reactors (CSTR) lead to the discovery of several dozens of different isothermal oscillating systems, including the CIMA reaction [57]. This reaction is one of the very few to also exhibit transient oscillatory behavior in batch conditions. This and the fact that it does not exhibit marked excitability character like the well-known Belousov-Zhabotinsky reaction [5], lead us to select the CIMA reaction for systematic research on stationary spatial structures in open spatial reactors [14]. 

An attractive property of monolithic reactors is their flexibility of application in multiphase reactions. These can be classified according to operation in (semi)batch or continuous mode and as plug-flow or stirred-tank reactor or, according to the contacting mode, as co-, counter-, and crosscurrent. In view of the relatively high flow rates and fast responses in the monolith, transient operations also are among the possibilities. 

In Chapter 3, the analytical method of solving kinetic schemes in a batch system was considered. Generally, industrial realistic schemes are complex and obtaining analytical solutions can be very difficult. Because this is often the case for such systems as isothermal, constant volume batch reactors and semibatch systems, the designer must review an alternative to the analytical technique, namely a numerical method, to obtain a solution. For systems such as the batch, semibatch, and plug flow reactors, sets of simultaneous, first order ordinary differential equations are often necessary to obtain the required solutions. Transient situations often arise in the case of continuous flow stirred tank reactors, and the use of numerical techniques is the most convenient and appropriate method. 

Various laboratory reactors have been described in the literature [3, 11-13]. The most simple one is the packed bed tubular reactor where an amount of catalyst is held between plugs of quartz wool or wire mesh screens which the reactants pass through, preferably in plug flow . For low conversions this reactor is operated in the differential mode, for high conversions over the catalyst bed in the integral mode. By recirculation of the reactor exit flow one can approach a well mixed reactor system, the continuous flow stirred tank reactor (CSTR). This can be done either externally or internally [11, 12]. Without inlet and outlet feed, this reactor becomes a batch reactor, where the composition changes as a function of time (transient operation), in contrast with the steady state operation of the continuous flow reactors. 

Steady State Multiplicity, Stability, and Complex Transients. This subject is too large to do any real justice here. Ever since the pioneering works of Liljenroth (41), van Heerden (42), and Amundson (43) with continuous-flow stirred tank reactors, showing that multiple steady states — among them, some stable to perturbations, while others unstable — can arise, this topic has... 

In the analysis of batch reactors, the two flow terms in equation (8.0.1) are omitted. For continuous flow reactors operating at steady state, the accumulation term is omitted. However, for the analysis of continuous flow reactors under transient conditions and for semibatch reactors, it may be necessary to retain all four terms. For ideal well-stirred reactors, the composition and temperature are uniform throughout the reactor and all volume elements are identical. Hence, the material balance may be written over the entire reactor in the analysis of an individual stirred tank. For tubular flow reactors the composition is not independent of position and the balance must be written on a differential element of reactor volume and then integrated over the entire reactor using appropriate flow conditions and concentration and temperature profiles. When non-steady-state conditions are involved, it will be necessary to integrate over time as well as over volume to determine the performance characteristics of the reactor. 

Kinetics in a Continuously Stirred Photochemical Tank Reactor. Gregoire, F. Lavabre, D. Micheau, 1. C. Gimenez, M. Laplante, J.P. (Lab. Interact. Mol. React. Chim. Photochim., Univ. Paul Sabatier, F-31062 Toulouse, Fr.). J. Photochem. 1985, 28 (2), 261-71 (Eng.). The continuously stirred photochem. tank reactor (REPAC) is a new semiautomatic app. for photochem. measurements. From the kinetic anal, of steady-state regimes, this open system allows detn. of the quantum yields, the thermal-return rate consts. and the spectra of photoproducts. Moreover, the kinetic anal, of transient regimes affords further information on the mechanism of the photochem. process. The possibUities of the REPAC are shown using various photochromic compds. Theor. anal, of the kinetic rate equations in the REPAC shows that quite unusual behavior, such as unstable steady states or photochem. oscillations, can be exhibited. Nonhnear photochem. reaction schemes are likely to show such behavior. 

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