Introduction to Chemical Engineering Institute of Process Engineering

Exercise 1: Reactors
Date of distribution: February 27, 2017
Due Date: March 6, 2017
(If you choose to hand in the exercise, please write down name and legi number!)

1.1 Reactor Selection

Hydrolysis of acetic anhydride takes place in the liquid phase at 50◦ C (acetic anhydride is consumed during
the reaction). At this temperature, the rate of reaction is given by r = kc with

k = 3.86 × 10−3 s−1 (1)

where c is the concentration of acetic anhydride in mol L-1 .

(a) Consider a batch reactor with an initial concentration of acetic anhydride of c0 = 0.8 mol L-1 . How
long will it take for the concentration of acetic anhydride to reach a value of 0.08 mol L-1 ?
(b) Consider the five different process configurations of ideal reactors listed below. In all cases the con-
tinuous volume flow is Q = 2 L s-1 with a feed concentration c0 = 0.8 mol L-1 . All reactors shall be
considered to be at steady state and with a constant volume.
What concentration of acetic anhydride should be expected at the outlet of each process configuration?
Which would you choose to maximize conversion?
• Single CSTR (V = 1.2 m3 ).
• 2 CSTR’s (V = 0.8 m3 each) in series (one behind each other).
• 2 CSTR’s (V = 0.8 m3 each) in parallel.
• Single PFR (V = 1.2 m3 ).
• Single CSTR (V = 0.8 m3 ) with a downstream PFR (V = 0.6 m3 ).
Introduction to Chemical Engineering Institute of Process Engineering

1.2 Previous exam question: CSTR with first order reaction

Consider the following liquid-phase first-order irreversible reaction (e.g. a decomposition reaction)

A −→ B + C (2)

Its rate of reaction is r = kc (r in mol L−1 s−1 ), where c [mol L−1 ] is the concentration of the reactant A,
and k [s−1 ] is the reaction rate constant (the reaction rate constant is a function of temperature, whose
value doubles when the temperature increases from 40◦ C to 70◦ C). The reaction is carried out in a CSTR
(Continuous Stirred Tank Reactor) of volume V [L], which is kept at the desired operating temperature.
The system is operated at steady state, with an inlet and outlet volumetric flow rate Q [L s−1 ].

a) Please, write the material balance equation that describes the behavior of the system, by defining the
proper inlet and outlet conditions.
b) Please, write the outlet concentration, c, as a function of the inlet concentration, cin , and of the other
parameters characterizing the system and its operation.
c) Consider cin = 10 mol/L, V =100 L and Q=10 L/s, and an operating temperature T = 40◦ C where k
= 0.1 s−1 . Please, calculate the outlet concentration, c, under these conditions.
d) Assume that production has to be doubled, i.e. Q becomes 20 L/s. Under the constraint that the
outlet concentration must remain the same as calculated at point c), what can one do to cope with
this new production demand without building a second production line and a second reactor? More
specifically, how can one change the operating conditions in the CSTR so as to treat 20 L/s and attain
the same outlet concentration, c?

1.3 Previous exam question: 2nd order reaction

The following reaction
2 A −−→ P + R (3)

is carried out in an isothermal batch reactor.

a) Derive an expression for the concentration of the reactant, c, as a function of time (Hint about
integration: x dx = −x−1 + C).
R −2

b) Consider the time required for the concentration c to become 50% (t1/2 ) and 25% (t1/4 ), respectively, of
the initial value c0 . The different values of k correspond to different temperatures. Fill in the following
table (note that case 6 shows a way to estimate the rate constant using the values of measureable
quantities).

k Lmol−1 s−1
 
case V c0 t1/2 t1/4
1 2 × 10−3 0.5 2
2 2 × 10−3 0.5 1000
3 2 × 10−3 2 2
4 3 × 10−3 2 1
5 3 × 10−3 2 2000
6 0.5 1 250
Introduction to Chemical Engineering Institute of Process Engineering

1.4 Previous exam question: Consecutive reactions in a batch reactor

We would like to produce compound R. However, R reacts further to form compound S, which is not
desired. All reactions that occur in this system are of order one and irreversible. Thus, we are considering
the reaction system in the liquid phase:

A −−→ R r1 =k1 cA desired

R −−→ S r2 =k2 cR undesired

where k1 > k2 ; the units of r1 and r2 are [mol/(L·s)] and cA , cR and cS are volumetric concentrations, in
units of [mol/L].

a) Please formulate the material balances for the components A, R and S in a batch reactor.
b) Please solve the material balance for compound A first. Use this expression to solve the material
balance for compound R to obtain an expression for the time evolution of the concentration of R, that
is cR (t). The initial conditions are cA (t = 0) = c0A and cR (t = 0) = cS (t = 0) = 0.
Hint: For the particular solution of cR use the ansatz, cpa R (t) = α exp (−k1 t), where α is a constant
that is determined by inserting cpaR into the material balance of R.
c) Find the optimal reaction time, topt , at which the maximum amount of R is obtained.
Hint: If you didn’t get a result in b), you may use the following expression for cR :

cR (t) = c0A exp −k12 t − exp −k22 t

to solve this part.

d) Draw the evolution of the concentrations of A, R and S qualitatively in the diagram shown in Figure
1. Make sure that the curves of cA , cR and cS fulfill the limits at t = 0 and t → ∞ quantitatively.
Please label clearly which curve belongs to which compound.
Hint: Note that:
cA + cR + cS = c0A

c0A
concentration / Konzentration ci

0
0 time / Zeit t

Figure 1: Concentration-time diagram.

Introduction to Chemical Engineering Institute of Process Engineering

1.5 Previous exam question: Chemical reactor design

Consider the following irreversible liquid-phase reaction of A producing B:

A −−→ B

For this first order reaction the rate constant at a temperature of 300 K is k = 2 × 10−3 s−1 .

a) Consider a batch reactor kept at a constant temperature of 300 K with an initial concentration of A
c0A = 1 mol · L−1 :
I) Write an expression for the concentration of A as a function of time.
II) What is the concentration of A after 800 s?
−1
In parts b) and c), consider a feed with a concentration of A of cin
A = 1 mol · L and a flow rate of
−1
Q = 0.5 L · s .

b) For an isothermal plug flow reactor at a temperature of 300 K:

I) Write an expression for the concentration of A as a function of the reactor volume.
II) What reactor volume would be necessary to achieve a concentration of A of cA = 0.1 mol · L−1 ?
c) For a single isothermal CSTR at a temperature of 300 K:
I) Write an expression for the concentration of A as a function of the reactor volume.
II) What reactor volume would be necessary to achieve a concentration of A of cA = 0.1 mol · L−1 ?

1 0
a b
0.9
−0.4
0.8
0.7 −0.8
0.6
exp (x)

ln (x)

0.5 −1.2
0.4
−1.6
0.3
0.2 −2
0.1
−2.4
0
−2.4 −2 −1.6 −1.2 −0.8 −0.4 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x x

Figure 2: Auxiliary plots for the estimation of (a) exp (x) and (b) ln (x).