Propylene glycol is produced in a CSTR in which precautions have been taken to prevent product loss. Propylene oxide (A) is fed to a 413-gal reactor at a rate of 300 lb mol/h at a temperature of 75°F. Water (B) is fed at a rate of 2000 lb mol/h and methanol at a rate of 20 lb mol/h. Determine what happens to a CSTR operating at 172°F and a conversion of 86.4% when there is a drop in feed temperature from 75°F to 68°F.

Solution

We will first look at the steady-state conditions before the upset occurred. The mole balance conversion is:

The energy balance conversion is:

Neglectingand substituting the appropriate values, we have

(CDE13-3.1)




(CDE13-3.2)

If we were to plot X_EB and X_B as a function of temperature, we would we see that there are three steady-state conditions for this set of parameter values (Table CDE13-3.1). Before the drop in feed temperature occurred we operated at the upper steady state (T = 172°F, X = 0.864). The ignition temperature of the feed is 78°F, and the extinction temperature is 61°F .

We will now consider what happens when an upset occurs while operating at the upper steady state. Say that the inlet temperature drops from 75°F to 68°F. Figure CDE13-3.1 shows the corresponding X_EB and X_MB curves after this drop. There are still three steady states (Table CDE13-3.2) for this new inlet temperature, indicating that we have not dropped below the extinction temperature of 61°F.

Figure CDE13-3.1
X_EB and X_MB after T_O perturbation.

Based on a steady-state analysis, it would appear that after the drop in the inlet temperature we should remain at the upper steady state with T = 164.5°F and X = 82.3%. However, using a dynamic simulation (see the development in the equations below) with POLYMATH (Table CDE13-3.3), we will see that with this perturbation in the inlet temperature, the conversion and temperature drop to the lower steady-state values, as shown in Figure CDE13-3.2.


TABLE CDE13-3.3

Unsteady-State Equations After Temperature Perturbation
Although there are slight differences in the densities of the liquid species, we shall assume constant density.

For constant volume, constant heat of reaction, and no work done by the system, when applied to this example becomes

The number of moles N_i in the denominator is just N_i = C_iV.

We see that even though the entering temperature did not drop below the extinction temperature, the perturbation in the entering temperature was large enough to drive the temperature and conversion drop to their lower steady-state values of 89.5°F and 11.6%, respectively. To prevent this problem of moving to an undesired steady state, a control system is usually incorporated into the reactor system.