Adiabatic CSTR

We first consider the adiabatic reactor for which Q = 0 and therefore = 0. The left-hand side or heat removal R(T) is 

We solved this example for the first-order irreversible reaction A B because it is easy to solve. If the reactor is not adiabatic, the R(T) curve has a different slope and intercept, but it is still a straight line. If the kinetics are not first order but are stiU irreversible. 

X(T) still has the same qualitative shape, and if the reaction is reversible and exothermic, X(T) decreases at sufficiently high temperature as the equihhrium X decreases. We can generalize therefore to say that multiple steady states may exist in ary exothermic reaction in a nonisothermal CSTR. 

The existence and properties of these steady states and their impHcations in the design of CSTRs is the major subject of this chapter. 

Without jacket cooling, only three terms remain in the heat balance the accumulation, the heat release rate of the reaction, and the sensible heat due to the temperature difference between the feed and the reactor contents. Thus, we obtain 

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A graphical explanation for the constant flow and variable feed temperature controlled adiabatic CSTR is given in Figure 9.6.6. 

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. 

P4.07-11. TWO STAGE ADIABATIC CSTR. SECOND ORDER REACTION. 

Figure 5-7 Ca and T versus t in an adiabatic CSTR. The unusual shapes of these curves will require considerable examination in this Chapter and in Chapter 6. Residence time is in minutes.

This is a straight line whose slope is IJ and which intersects the T axis at X = 0 where Tq (Figure 6-3). It is evident that there may be one or three intersections of these curves (the large dots in the figure), and these represent one or three-steady states in the adiabatic CSTR. 

Figure 63 Dimensionless heat removal curve R(T) versus T for the adiabatic reactor plotted along with the heat generation curve X(T). There can be one or three intersections corresponding to one or three possible temperatures in the adiabatic CSTR, depending on Tq.

Figure 6-6 Adiabatic CSTR in which feed temperature To is varied.

To in an adiabatic CSTR. The arrows indicate discontinuous jumps in reactor temperature T. The points marked are from Figure 6-7 with points 4 and 8 tangents of the heat gaieration and removal curves. 

Figure 6-12 Transients in the adiabatic CSTR for the irreversibe reaction of the previous example. The upper panels show X(t) and T(t), while the lower panel displays X(T) for the same curves shown in the upper panel. The system converges on one of the stable steady states but never on the middle unstable steady state.

Figure 6-14 Plot of possible conversions (Xj -1 X2) versus reactor temperature T in an adiabatic CSTR with series exothermic reactions /I B C. Up to five steady state intersections are possible for this situation.

For the exothermic reactions, 4 -> B —> C in an adiabatic CSTR the total conversion (Xi +X2) versus T curves might look as shown in Figure 6-14. 

The proeess produces only ethylene in a reaction that goes to completion with a feed of 5 mole % C2H6 in air in an adiabatic CSTR operated at a pressure of 2 atm with r = 10 min. We find that the reaetion rate is given approximately by the expression... 

Consider the preceding reaction system to be run in two adiabatic CSTRs operated in series... 

Figure 6-1 1 shows the steady states in an adiabatic CSTR for several different values of Cao for the example worked previously with T = 300 K. 

Before we proceed, note that these equations look identical in form to the adiabatic CSTR equations of Chapter 6,... 

An example of such a system is the first-order decomposition of the organic compound di-tertiarybutyl peroxide which has been studied experimentally in a non-adiabatic CSTR. 

Fig. 7.2. Thermal or flow diagram for the first-order non-isothermal reaction (FON1) in a non-adiabatic CSTR the rate curve R and the flow line L both depend on the dimensionless residence time, but their intersections still correspond to stationary-state solutions—and tangen-cies to points of ignition or extinction. Note that R has a non-zero value at zero conversion. Exact numerical values correspond to 0ai = 10, t, = tn = A ...

We now turn to the non-isothermal reaction system in a non-adiabatic CSTR, as studied in 7.2.4—6. We begin with the simplified model with exponential approximation to the Arrhenius law, and to systems for which the inflow and ambient temperatures are the same (y = 0 and gc = 0), This system has two unfolding parameters gad and rN. The stationary-state equation and its various derivatives are... 

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