Solution Found!
Three stirred-tanks in series are used in a reactor train
Chapter 3, Problem 3.20(choose chapter or problem)
Three stirred-tanks in series are used in a reactor train (see Fig. E3.20). The flow rate into the system of some inert species is maintained constant while tracer test are conducted. Assuming that mixing in each tank is perfect and volumes are constant:
(a) Derive model expressions for the concentration of tracer leaving each tank, \(c_i\) is the concentration of tracer entering the first tank.
(b) If \(c_i\) has been constant and equal to zero for a long time and an operator suddenly injects a large amount of tracer material in the inlet to tank 1 , what will be the form of \(c_3(t)\) (i.e., what kind of time functions will be involved) if
1. \(V_1=V_2=V_3\)
2. \(V_1 \ne V_2 \ne V_3\)
(c) If the amount of tracer injected is unknown, is it possible to back-calculate the amount from experimental data? How?
Questions & Answers
QUESTION:
Three stirred-tanks in series are used in a reactor train (see Fig. E3.20). The flow rate into the system of some inert species is maintained constant while tracer test are conducted. Assuming that mixing in each tank is perfect and volumes are constant:
(a) Derive model expressions for the concentration of tracer leaving each tank, \(c_i\) is the concentration of tracer entering the first tank.
(b) If \(c_i\) has been constant and equal to zero for a long time and an operator suddenly injects a large amount of tracer material in the inlet to tank 1 , what will be the form of \(c_3(t)\) (i.e., what kind of time functions will be involved) if
1. \(V_1=V_2=V_3\)
2. \(V_1 \ne V_2 \ne V_3\)
(c) If the amount of tracer injected is unknown, is it possible to back-calculate the amount from experimental data? How?
ANSWER:
Step 1 of 19
(a) Consider, three stirred-tanks are connected in series, and used in a reactor train. The flow rate of inert species into the system is constant.
Refer to Figure E3.20 in the textbook.
\(V_{1}\) is the volume of the first tank.
\(V_{2}\) is volume of the second tank.
\(V_{3}\) is volume of the third tank.
\(q\) is flow rate of inert species, which is maintained constant.
\(c_{i}\) is the concentration of tracer entering the first tank.
\(c_{1}\) is the concentration of tracer entering the second tank.
\(c_{2}\) is the concentration of tracer entering the third tank.
\(c_{3}\) is the concentration of tracer leaving the third tank.