Chapter 13: Unsteady State Nonisothermal Reactor Design

Questions related to Problem 13-2

1.   Let’s revisit the explosion in Example 13-2. Suppose that the heating had not failed 55 minutes after startup, but instead at 1 hour and 55 minutes, would the reactor have exploded for a down time of 10 minutes? What if the reactor only had a down time of 5 minutes 30 minutes  after start up, would the reactor have exploded? Which of the following figures relates the down tine, td, to time after startup that the heat exchanger failed, ts, for which the reactor would not explode?

Five graphs labeled A to E show different relationships between t_s (x-axis) and t_d (y-axis). Plot A: t_d remains constant as t_s increases, forming a horizontal line. Plot B: t_d increases linearly with t_s, forming a diagonal upward line. Plot C: t_d decreases linearly with t_s, forming a diagonal downward line. Plot D: t_d increases with t_s, peaks at the midpoint, then decreases, forming a symmetric hump-shaped curve. Plot E: t_d increases rapidly with t_s, then levels off, forming a saturation-like curve.

 

Solution#1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.   Suppose inerts are added to the system in Example 13-2. The dashed line represents the relationship after the inerts were added. Which figure represents how the relationship between ts and td would change? The solid line represents the case without inerts?

 

Four plots (A–D) comparing t_d vs t_s before and after a change. A and B show shifts, C shows a directional change, D shows no change.

Solution#2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SOLUTION

1)  The answer is B.

Plot B showing a linear relationship between t_s and t_d.

After longer times, ts, the rate will be slower because reactant will have been consumed.  Therefore, longer down times will be possible. 

 

Question#2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SOLUTION

2) The answer is B. (solid line represents case without inerts)

Plot B showing two lines with positive slopes. Dashed line is above the solid line, indicating increased t_d for the same t_s.

\( \frac{dT}{dt} = Q_g - Q_r = \frac{Q_g - Q_r}{\sum N_i C_{P_i}} = \frac{Q_g - Q_r}{N_A C_{P_A} + N_B C_{P_B} + N_C C_{P_C} + N_I C_{P_I}} \)

We see the rate of temperature increase, dT/dt, decreases as the amount of inert, NI  increases.  Therefore, the temperature will not rise as rapidly during the adiabatic period (down time, td) and we can have longer down times without having an explosion.


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