Chapter 13: Unsteady State Nonisothermal Reactor Design

The ARSST: Testing for Runaway Reaction Temperatures


The Advanced Reactive System Screening Tool (ARSST) is a batch reaction used to identify potential safety hazards.  It consists of a well instrumented batch reaction that is heated in such a manor so as to raise the temperature at a uniform rate.  It is primarily used for liquid phase reactions.

For more information, visit www.ARSST.com

Schematic of a stirred tank reactor showing a stirrer, heat input labeled Q', pressure sensor labeled P, and a temperature controller labeled TC.

 

\( A + B \rightarrow C \)

A batch reactor is heated by an external heater at a rate of 0.2 C/min. Plot T vs. t and find the ignition temperature.

 

Solution

For

\( \Delta \hat{C}_P = 0 \)

\( \frac{dT}{dt} = \frac{Q + (r_A V)(\Delta H_{RX})}{N_A C_{P_A} + N_B C_{P_B} + N_C C_{P_C}} \)

\( = \frac{Q}{N_A C_{P_A} + N_B C_{P_B} + N_C C_{P_C}} + \frac{(r_A V)(\Delta H_{RX})}{N_A C_{P_A} + N_B C_{P_B} + N_C C_{P_C}} \)

dividing by V,

\( \frac{dT}{dt} = \dot{Q}' + \frac{(r_A V)(\Delta H_{RX})}{C_A C_{P_A} + C_B C_{P_B} + C_C C_{P_C}} \)

\( r_A = -k C_A C_B \)

\( k = k_0 \exp \left[ \frac{E}{R} \left( \frac{1}{T_0} - \frac{1}{T} \right) \right] \)

\( \frac{dC_A}{dt} = r_A \)

\( \frac{dC_B}{dt} = r_B = r_A \)

\( \frac{dC_C}{dt} = r_C = -r_A \)

\( \dot{Q} = 0.2 \, \text{°C/min} \)

\( k_0 = 0.00001 \, \text{dm}^3/\text{mol} \cdot \text{min} \)

\( E = 25,000 \, \text{cal/mol} \)

\( R = 1.987 \, \text{cal/mol} \cdot \text{K} \)

\( T_0 = 300 \, \text{K} \)

\( \Delta H_{\text{Rx}} = -70,000 \, \text{cal/mol} \)

\( C_P^A = 30 \, \text{cal/mol/K} \)

\( C_P^B = 40 \, \text{cal/mol/K} \)

\( C_P^C = 70 \, \text{cal/mol/K} \)

\( C_{A0} - C_{B0} = 2 \)

\( T_0 = 300 \)
Using Polymath to Solve:
Reaction equations and parameters for a batch reactor simulation. Includes differential equations for Ca, Cb, Cc, and T, heat input Q, heat capacities (Cpa, Cpb, Cpc), activation energy E, rate constant ko, and Arrhenius rate expression. Initial values are Ca=2, Cb=2, Cc=0, T=300, with t0=0 and tf=100.
Table showing time (t) versus temperature (T) values from 0 to 100 units of time. Temperature increases gradually from 300 K to over 1300 K by t = 100.
Graph showing temperature (T) on the Y-axis scaled by 10^3 against time on the X-axis from 0 to 100. The curve remains nearly flat around 0.3 for most of the time before sharply rising near t = 100.
The ignition temperature is approximately 338K.

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