Exothermic CSTR

THERMFF - Feedforward Control of an Exothermic CSTR System... 

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... 

Eq.(30) is a straight line and Eq.(27) is an S shaped curve as shown in Eigure 2. This plot shows the curve of heat generated and the line of heat removed versus temperature in an exothermic CSTR. The three steady-states are the points of intersection Pi, P2, P3, of the curve Qg and the line Qr-... 

A. Cinar, K. Rigoponlos, S.M. Meerkov, and X. Shu. Vibrational Control of an exothermic CSTR. In American Control Conference (ACC), pages 593-598, Seattle, WA, 1986. 

In the present chapter, steady state, self-oscillating and chaotic behavior of an exothermic CSTR without control and with PI control is considered. The mathematical models have been explained in part one, so it is possible to use a simplified model and a more complex model taking into account the presence of inert. When the reactor works without any control system, and with a simple first order irreversible reaction, it will be shown that there are intervals of the inlet flow temperature and concentration from which a small region or lobe can appears. This lobe is not a basin of attraction or a strange attractor. It represents a zone in the parameters-plane inlet stream flow temperature-concentration where the reactor has self-oscillating behavior, without any periodic external disturbance. 

Figure 4.7 Exothermic CSTR with single steady-state condition.

Figure 14.2. Stable and unstable steady states in an exothermic CSTR (schematic).

The nonlinear nature of the energy and material balances can lead to multiple steady-state solutions. Steady-state solutions may be unstable, and the reactor can exhibit sustained oscillations. These reactor behaviors were illustrated with exothermic CSTRs and autotherma tubular reactors. 

Since Luyben identified the snowball effect (Luyben, 1994), the sensitivity of reactor-separator-recycle processes to external disturbances has been the subject of several studies (e.g., Wu and Yn, 1996 Skogestad, 2002). Recent work by Bildea and co-workers (Bildea et al., 2000 and Kiss et aL, 2002) has shown that a critical reaction rate can be defined for each reactor-separator-recycle process using the Damkohler number. Da (dimensionless rate of reaction, proportional to the reaction rate constant and the reactor hold-up). When the Damkohler number is below a critical value, Bildea et al. show that the conventional unit-by-unit approach in Figure 20.15 leads to the loss of control. Furthermore, they show that controllability problems associated with exothermic CSTRs and PFRs are resolved often by controlling the total flow rate of the reactor feed stream. 

In cases where a large reactor operates similarly to a CSTR, fluid dynamics sometimes can be estabflshed in a smaller reactor by external recycle of product. For example, the extent of soflds back-mixing and Hquid recirculation increases with reactor diameter in a gas—Hquid—soflds reactor. Consequently, if gas and Hquid velocities are maintained constant when scaling and the same space velocities are used, then the smaller pilot unit should be of the same overall height. The net result is that the large-diameter reactor is well mixed and no temperature gradients occur even with a highly exothermic reaction. 

Use Scalable Heat Transfer. The feed flow rate scales as S and a cold feed stream removes heat from the reaction in direct proportion to the flow rate. If the energy needed to heat the feed from to Tout can absorb the reaction exotherm, the heat balance for the reactor can be scaled indefinitely. Cooling costs may be an issue, but there are large-volume industrial processes that have Tin —40°C and Tout 200°C. Obviously, cold feed to a PFR will not work since the reaction will not start at low temperatures. Injection of cold reactants at intermediate points along the reactor is a possibility. In the limiting case of many injections, this will degrade reactor performance toward that of a CSTR. See Section 3.3 on transpired-wall reactors. 

Consider a continuous-stirred-tank reactor (CSTR) with cooling jacket where a first order exothermic reaction takes place. It is required to derive a model relating the extent of the reaction with the flowrate of the heat... 

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. 

CSTR WITH EXOTHERMIC REACTION AND JACKET COOLING Dynamic solution for phase-plane plots Located steady-states with THERMPLO and use same parameters. 

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... 

An exothermic reaction with the stoichiometry A 2B takes place in organic solution. It is to be carried out in a cascade of two CSTR s in series. In order to equalize the heat load on each of the reactors it will be necessary to operate them at different temperatures. The reaction rates in each reactor will be the same, however. In order to minimize solvent losses by evaporation it will be necessary to operate the second reactor at 120 °C where the reaction rate constant is equal to 1.5 m3/kmole-ksec. If the effluent from the second reactor corresponds to 90% conversion and if the molal feed rate to the cascade is equal to 28 moles/ksec when the feed concentration is equal to 1.0 kmole/m3, how large must the reactors be If the activation energy for the reaction is 84 kJ/mole, at what temperature should the first reactor be operated ... 

Let Qg represent the rate at which thermal energy is released by an exothermic chemical reaction in a CSTR. If Qg is plotted versus the temperature of the reactor contents for a fixed... 

Rate of energy release by reaction versus temperature for an irreversible exothermic reaction carried out in a CSTR. 

Energy release and energy loss curves for reversible exothermic reaction in a CSTR. 

ILLUSTRATION 10.8 DETERMINATION OF OPTIMUM TEMPERATURE FOR OPERATION OF A SINGLE CSTR IN WHICH A REVERSIBLE EXOTHERMIC REACTION IS BEING CARRIEb OUT... 

An unusual feature of a CSTR is the possibility of multiple stationary states for a reaction with certain nonlinear kinetics (rate law) in operation at a specified T, or for an exothermic reaction which produces a difference in temperature between the inlet and outlet of the reactor, including adiabatic operation. We treat these in turn in the next two sections. 

If feed at a specified rate and T0 enters a CSTR, the steady-state values of the operating temperature T and the fractional conversion fA (for A —> products) are not known a priori. In such a case, the material and energy balances must be solved simultaneously for T and fA. This can give rise to multiple stationary states for an exothermic reaction, but not for an endothermic reaction. 

For exothermic, reversible reactions, the existence of a locus of maximum rates, as shown in Section 5.3.4, and illustrated in Figures 5.2(a) and 18.3, introduces the opportunity to optimize (minimize) the reactor volume or mean residence time for a specified throughput and fractional conversion of reactant. This is done by choice of an appropriate T (for a CSTR) or T profile (for a PFR) so that the rate is a maximum at each point. The mode of operation (e.g., adiabatic operation for a PFR) may not allow a faithful interpretation of this requirement. For illustration, we consider the optimization of both a CSTR and a PFR for the model reaction... 

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 process is run in a CSTR without solvent at 50 °C. The reaction is highly exothermic and heat is removed via external circulation. To ensure high... 

Example 2.6. The CSTR system of Example 2.3 will be considered again, this time with a cooling coil inside the tank that can remove the exothermic heat of reaction 2 (Btu/lb. mol of A reacted or cal/g mol of A reacted). We use the normal convention that 2 is negative for an exothermic reaction and positive for an endothermic reaction. The rate of heat generation (energy per time) due to reaction is the rate of consumption of A times 2. 

Write the energy equation for the CSTR of Example 2.6 in which consecutive first order reactions occur with exothermic heats of reaction A, and Aj. 

In the reactors studied so far, we have shown the effects of variable holdups, variable densities, and higher-order kinetics on the total and component continuity equations. Energy equations were not needed because we assumed isothermal operations. Let us now consider a system in which temperature can change with time. An irreversible, exothermic reaction is carried out in a single perfectly mixed CSTR as shown in Fig. 3.3. 

There are several control problems in chemical reactors. One of the most commonly studied is the temperature stabilization in exothermic monomolec-ular irreversible reaction A B in a cooled continuous-stirred tank reactor, CSTR. Main theoretical questions in control of chemical reactors address the design of control functions such that, for instance (i) feedback compensates the nonlinear nature of the chemical process to induce linear stable behavior (ii) stabilization is attained in spite of constrains in input control (e.g., bounded control or anti-reset windup) (iii) temperature is regulated in spite of uncertain kinetic model (parametric or kinetics type) or (iv) stabilization is achieved in presence of recycle streams. In addition, reactor stabilization should be achieved for set of physically realizable initial conditions, (i.e., global... 

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