Fogler^2 describes a safety accident in which a batch reactor was used to produce nitroaniline from ammonia and o-nitro chlorobenzene. On the day of the accident, the feed composition was changed from the normal operating value. Using the material/energy balances and data provided by Fogler, show

Question

Fogler [latex]^{2}[/latex] describes a safety accident in which a batch reactor was used to produce nitroaniline from ammonia and o-nitro chlorobenzene. On the day of the accident, the feed composition was changed from the normal operating value. Using the material/energy balances and data provided by Fogler, show that the maximum cooling rate will not be sufficient to prevent a temperature runaway under conditions of the new feed composition. Use a simulator to solve the model equations.

Accepted Answer

Material balance:

[latex]\left(-r_{A} ight)=-\frac{d C_{A}}{d t}=k C_{A 0}^{2}(1-X)\left(\Theta_{B}-2 X ight)[/latex]

Since

[latex]C_{A}=C_{A 0}(1-X)[/latex]

then

[latex]\frac{d X}{d t}=-\frac{1}{C_{A 0}} \frac{d C_{A}}{d t}[/latex]

Therefore

[latex]\frac{d X}{d t}=k C_{A 0}(1-X)\left(\Theta_{B}-2 X ight)[/latex] (1)

Energy balance:

[latex]\frac{d T}{d t}=\frac{Q_{g}-Q_{r}}{N C_{p}}[/latex] (2)

where

[latex]\begin{aligned}&Q_{g}=k C_{A O}^{2}(1-X)\left(\Theta_{B}-2 X ight) V\left(\Delta H_{R X} ight) \&Q_{r}=U A(T-298)\end{aligned}[/latex]

Eqs. 1 and 2 constitute a differential equation system. By using MATLAB, this system can be solved as long as the initial conditions are specified. Command "ode45" is suggested.

A.- ISOTHERMAL OPERATION UP TO 45 MINUTES

We will first carry out the reaction isothermally at [latex]175^{\circ} C[/latex] up to the time the cooling was turned off at [latex]45 min[/latex].

Initial conditions: [latex]X(0)=0[/latex] and [latex]T(0)=448 K[/latex]

Figure S22.12a shows the isothermal behavior for these first 45 minutes.

B.- ADIABATIC OPERATION FOR 10 MINUTES

The cooling is turned off for 45 to [latex]55 min[/latex]. We will now use the conditions at the end of the period of isothermal operation as our initial conditions for adiabatic operation period between 45 and 55 minutes.

[latex]t=45 \min \quad X=0.033 \quad T=448[/latex]

C.- BATCH OPERATION WITH HEAT EXCHANGE

Return of the cooling occurs at [latex]55 min[/latex]. The values at the end of the period of adiabatic operation are:

[latex]t=55 \quad T=468 K \quad X=0.0423[/latex]

As shown in Fig. S22.12c, the temperature runaway is finally unavoidable under new conditions:

Feed composition [latex]=9.044 kmol[/latex] of [latex]ONCB , 33.0 kmol[/latex] of [latex]NH _{3}[/latex], and [latex]103.7[/latex] [latex]kmol[/latex] of [latex]H _{2} O[/latex]

. Shut off cooling to the reactor at 45 minutes and resume cooling reactor at 55 minutes.

[latex]{ }^{2}[/latex] Essentials of Chemical Reaction Engineering, Prentice Hall, Upper Saddle River, NJ, 2011, p. 608 .

Question 22.12: Fogler^2 describes a safety accident in which a batch reacto...

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