Stable Operating Conditions in Stirred Tank Reactors

6 STABLE OPERATING CONDITIONS IN STIRRED TANK REACTORS 

When a reactor is operating at steady state, the rate of energy release by chemical reaction must be equal to the sum of the rates of energy loss by convective flow and heat transfer to the surroundings. This statement was expressed in algebraic form in equations (10.3.4) and (10.4.6) for the CSTR and PFR, respectively. This statement can serve as the physical basis for examination of the stability of various operating points. 

Let Qg represent the rate at which thermal energy is released by an exothermic chemical reaction in a CSTR. If (2g is plotted versus the temperature of the reactor contents for a fixed feed rate and feed composition, there are several curves that may result, depending on the nature of the 

If there is no volume change because of reaction, the design equation for a CSTR indicates that 

The rate at which energy is removed from the system, Q, is equal to the rate at which it is being lost by heat transfer processes plus the mass flow rate times the gain in sensible heat per unit mass. Thus, 

5-4 Stable Operating Conditions in Stirred-tank Reactors  

In Example 5-3 the temperature and conversion leaving the reactor were obtained by simultaneous solution of the mass and energy balances. The results for each temperature in Table 5-7 represented such a solution and corresponded to a diiferent reactor, i.e., a different reactor volume. However, the numerical trial-and-error solution required for this multiple-reaction system hid important features of reactor behavior. Let us therefore reconsider the performance of a stirred-tank reactor for a simple single-reaction system. 

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 

The energy balance [Eq. (3-6)] for adiabatic operation and zero conversion in the feed is 

Since the heat of reaction usually varies little with temperature, Eq. (5-18) shows a linear relationship between T — Tq and conversion and is represented by the straight line in Fig. 5-9. 

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SECTldN 5-4 STABLE OPERATING CONDITIONS IN STIRRED-TANK REACTORS... 

This set of first-order ODEs is easier to solve than the algebraic equations where all the time derivatives are zero. The initial conditions are that a ut = no, bout = bo,... at t = 0. The long-time solution to these ODEs will satisfy Equations (4.1) provided that a steady-state solution exists and is accessible from the assumed initial conditions. There may be no steady state. Recall the chemical oscillators of Chapter 2. Stirred tank reactors can also exhibit oscillations or more complex behavior known as chaos. It is also possible that the reactor has multiple steady states, some of which are unstable. Multiple steady states are fairly common in stirred tank reactors when the reaction exotherm is large. The method of false transients will go to a steady state that is stable but may not be desirable. Stirred tank reactors sometimes have one steady state where there is no reaction and another steady state where the reaction runs away. Think of the reaction A B —> C. The stable steady states may give all A or all C, and a control system is needed to stabilize operation at a middle steady state that gives reasonable amounts of B. This situation arises mainly in nonisothermal systems and is discussed in Chapter 5. 

The shape of the curve in Fig. 5-IZ introduces the possibility of multiple, stable operating conditions for exothermic reactions in stirred-tank reactors. This is discussed in Sec. 5-4. 

Equating Q and Qr -slI steady state determines 7 — 7], in terms of AH, the rate parameters A and E for the.reaction, h, and the unknown surface concentration Q. The requirement that Qr = Q introduces interesting questions about stable operating conditions. The problem is very similar to the stability situation in stirred-tank reactors, discussed in Sec. 5-4. We consider this problem and the evaluation of E — E, for two cases negligible and finite external-diffusion resistance. 

One of the advantages of the continuous stirred-tank reactor is the fact that it is ideally suited to autothermal operation. Feed-back of the reaction heat from products to reactants is indeed a feature inherent in the operation of a continuous stirred-tank reactor consisting of a single tank only, because fresh reactants are mixed directly into the products. An important, but less obvious, point about autothermal operation is the existence of two possible stable operating conditions. 

Consider an exothermic irreversible reaction with first order kinetics in an adiabatic continuous flow stirred tank reactor. It is possible to determine the stable operating temperatures and conversions by combining both the mass and energy balance equations. For the mass balance equation at constant density and steady state condition,... 

Detailed work undertaken for the first time on this technique, which is mainly described in patents and therefore little known, has focused on special reaction conditions and special measures (even within extreme limits) which are based on the biphasic character of the conversion such as pH values, addition of C02, salt effects and solution ionic strengths, catalyst modifiers, spectator effects, or ultrasonic devices, etc. [35]. The measures mentioned allowed a considerably simplified process to be used compared with other oxo processes (basically consisting of a stirred tank reactor and a decanter), this being a consequence of the biphasic concept of RCH/RP. These relationships ensure a smooth, stable operation yielding high selectivities to n-butyraldehyde (cf. Section 6.1.3.1). The specific load of the system may be altered very unequivocally by varying the temperature, pressure, partial pressures, and concentrations (catalyst, ligands, and salts). 

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