CSTR Simulation

The method has been demonstrated on a continuous stirred tank reactor (CSTR) simulation to identify an abnormal inlet concentration disturbance [340]. The jacketed CSTR, in which an exothermic reaction takes place, is under level and temperature control. An important process variable is the coolant flow rate through the jacket, that is related to the amount of heat produced in the CSTR, and it indirectly characterizes the state of the process. This variable will be monitored in this classification scheme. 

The trend analysis strategy will be shown to be able to differentiate between normal and abnormal responses of the coolant flow rate and is similar to the example used in the paper by Whiteley and Davis [325]. Here, three categories of classification are considered normal, intermediate and abnormal. An intermediate class represents a window of data that can move into the normal or abnormal classes in the next window and no definitive decision between normal and abnormal can be made during that specific time period. For normal operation, the system is able to handle a 5% 

In half of the simulations, a step increase of 5% in the inlet feed temperature was introduced this change is deemed to be normal and can be easily handled by the feedback control system. In the remaining 25 simulations, this step change was used in addition to a 5% increase in the feed concentration, resulting in an abnormal process trend that cannot be handled by the control system and leading to off-specification product. 

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Figure 6.4.2 Table of error-free kinetic data from CSTR simulation.

Fig. 6. Influence of the cycling strategy on the enhancement factor in a CSTR simulation at 723 K, ts = 0.1 s. Curves (1) S02 and 02 concentration varied 180° out of phase, (2) only S02 concentration varied, (3) S02 and 02 concentration varied in phase, (4) SO3 present in the feed so that Jts02 + so = 0.1 and (x02 + so3)/2 = 0.1 and Xso3 = 0.09, (5) as in (4) but with jcS03 = 0.096. (Figure taken from Strots et al, 1992, with permission, 1992 Elsevier Science Publishers.)...

Atrazine o3, o3/H2o2 CSTR simulation. Kinetic modeling. C 3x10 8 M 126... 

Prom the results above, one can conclude that the MHMT method for trend analysis correctly classifies the different process operating conditions. There are a few ambiguities in the transient region, which result from the similar responses of manipulated variables to different process events. In other words, the information contained in two variables is not enough to immediately discern the transient part of the process. To eliminate such ambiguities, additional variables may be needed in the HMT model. Sun et al. [286] have shown the extension of the method to the multivariate case for the CSTR simulation example. 

A similar situation crops up in many chemical engineering problems, such as, for instance, the calculation of chemical equilibria and CSTR simulations. 

Figure 6.4.3 Data for kinetic analysis. Simulated CSTR results with random error added to UCKRON-I.

Of these three, two must be measured experimentally to calculate the stability criteria. In recycle reactors that operate as CSTRs, rates are measured directly. Baloo and Berty (1989) simulated experiments in a CSTR for the measurement of reaction rate derivatives with the UCKRON test problem. To develop the derivatives of the rates, one must measure at somewhat higher and lower values of the argument. From these the calculated finite differences are an approximation of the derivative, e.g. ... 

This result was checked by simulation of both CSTR measurements and calculations of tubular reactor incipient runaways. It should be noted that the predicted AT at inflection from CSTR experiments agrees well with measures in tubular simulation. At hotspot the AT to the AT at inflection is between 1.4 and 1.8. Using a multiplier of 1.4 as recommended by Nelson (1974) is safe. 

This program helps calculate the rate of methanol formation in mol/m s at any specified temperature, and at different hydrogen, carbon monoxide and methanol concentrations. This simulates the working of a perfectly mixed CSTR specified at discharge condition, which is the same as these conditions are inside the reactor at steady-state operation. Corresponding feed compositions and volumetric rates can be calculated from simple material balances. 

Yu (13) simulated a periodically operated CSTR for the thermal polymerization of styrene and found the MWD to increase at low frequencies but all effects were damped out at higher frequencies because of the limited heat transfer which occurs relative to the thermal capacity of industrial scale reactors. 

The most comprehensive simulation of a free radical polymerization process in a CSTR is that of Konopnicki and Kuester (15). For a mechanism which includes transfer to both monomer and solvent as well as termination by combination and disproportionation they examined the influence of non-isothermal operation, viscosity effects as well as induced sinuoidal and square-wave forcing functions on initiator feed and jacket temperature on the MWD of the polymer produced. 

The method of false transients converts a steady-state problem into a time-dependent problem. Equations (4.1) govern the steady-state performance of a CSTR. How does a reactor reach the steady state There must be a startup transient that eventually evolves into the steady state, and a simulation of... 

The ODEs governing the unsteady CSTR are obtained by adding accumulation terms to Equations (4.1). The simulation holds the volume constant, and... 

These can be solved by classical methods (i.e., eliminate Sout to obtain a second-order ODE in Cout), by Laplace transformation techniques, or by numerical integration. The initial conditions for the washout experiment are that the entire system is full of tracer at unit concentration, Cout = Sout = L Figure 15.7 shows the result of a numerical simulation. The difference between the model curve and that for a normal CSTR is subtle, and would not normally be detected by a washout experiment. The semilog plot in Figure 15.8 clearly shows the two time constants for the system, but the second one emerges at such low values of W t) that it would be missed using experiments of ordinary accuracy. 

Nomura and Fujita (12), Dougherty (13-14), and Storti et al. (12). Space does not permit a review of each of these papers. This paper presents the development of a more extensive model in terms of particle formation mechanism, copolymer kinetic mechanism, applicability to intervals I, II and III, and the capability to simulate batch, semibatch, or continuous stirred tank reactors (CSTR). Our aim has been to combine into a single coherent model the best aspects of previous models together with the coagulative nucleation theory of Feeney et al. (8-9) in order to enhance our understanding of... 

The kinetic parameters associated with the synthesis of norbomene are determined by using the experimental data obtained at elevated temperatures and pressures. The reaction orders with respect to cyclopentadiene and ethylene are estimated to be 0.96 and 0.94, respectively. According to the simulation results, the conversion increases with both temperature and pressure but the selectivity to norbomene decreases due to the formation of DMON. Therefore, the optimal reaction conditions must be selected by considering these features. When a CSTR is used, the appropriate reaction conditions are found to be around 320°C and 1200 psig with 4 1 mole ratio of ethylene to DCPD in the feed stream. Also, it is desirable to have a Pe larger than 50 for a dispersed PFR and keep the residence time low for a PFR with recycle stream. 

In this case, three time constants in series, X, %2 and X3, determine the form of the final outlet response C3. As the number of tanks is increased, the response curve increasingly approximates the original, step-change, input signal, as shown in Fig. 2.12. The response curves for three stirred tanks in series, combined with chemical reaction are shown in the simulation example CSTR. 

Thus the respective rate expressions depend upon the particular concentration and temperature levels, that exist within reactor, n. The rate of production of heat by reaction, rg, was defined in Sec. 1.2.5 and includes all occurring reactions. Simulation examples pertaining to stirred tanks in series are CSTR, CASCSEQ and COOL. 

This analysis is limited, since it is based on a steady-state criterion. The linearisation approach, outlined above, also fails in that its analysis is restricted to variations, which are very close to the steady state. While this provides excellent information on the dynamic stability, it cannot predict the actual trajectory of the reaction, once this departs from the near steady state. A full dynamic analysis is, therefore, best considered in terms of the full dynamic model equations and this is easily effected, using digital simulation. The above case of the single CSTR, with a single exothermic reaction, is covered by the simulation examples, THERMPLOT and THERM. Other simulation examples, covering aspects of stirred-tank reactor stability are COOL, OSCIL, REFRIG and STABIL. 

Other model representations of flow mixing cases in chemical reactors are described by Levenspiel (1972), Fogler (1992) and Szekely and Themelis (1971). Simulation tank examples demonstrating non-ideal mixing phenomena are CSTR, NOSTR, TUBMIX, MIXFLO, GASLIQ and SPBEDRTD. 

Study the simple, open-loop (KC = 0) and closed-loop responses (KC = -1 to 5, TSET = TDIM, and 300 to 350 K) and the resulting yields of B. Confirm the oscillatory behaviour and find appropriate values of KC and TSET to give maximum stable and maximum oscillatory yield. For the open-loop response, show that the stability of operation of the CSTR is dependent on the operating variables by carrying out a series of simulations with varying Tq in the range 300 to 350 K. 

The stability of a first-order exothermic reaction A—>B, in a single CSTR with jacket cooling has been studied by Seborg (1971), and the usefulness of simulations for this type of investigation has been emphasised by Luus (1972). The influence of sinusoidal, feed-temperature variations is corrected by simple... 

Keairns and Manning AIChE J., 15 (660), 1969] have used the reaction between sodium thiosulfate and hydrogen peroxide in a well-stirred flow reactor to check a computer simulation of adiabatic CSTR operation. Data on their experimental conditions and the reaction parameters are listed below. The reaction may be considered second-order in sodium thiosulfate. 

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. 

Example 14-7 can also be solved using the E-Z Solve software (file exl4-7.msp). In this simulation, the problem is solved using design equation 2.3-3, which includes the transient (accumulation) term in a CSTR. Thus, it is possible to explore the effect of cAo on transient behavior, and on the ultimate steady-state solution. To examine the stability of each steady-state, solution of the differential equation may be attempted using each of the three steady-state conditions determined above. Normally, if the unsteady-state design equation is used, only stable steady-states can be identified, and unstable... 

We now proceed to demonstrate the application of the NDDR technique using a simulated CSTR with a first-order, exothermic reaction. The example was taken from Liebman et al. (1992). The dynamic model is given by... 

The jacketed exothermic CSTR discussed in Sec. 3.6 provides a good example of the simulation of very nonlinear ODEs. Both flow rates and holdups will be... 

SI. Simulate the nonisotheimal CSTR of Sec 3.3, using Euler and fourth-order Kunge Kutta, and compare maximum step sizes and computation times that give 0.1% accuracy. 

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