Question
Transcribed Text
Assignment 2: Mass balances in chemical reactors (5 marks)
Background. A chemical constituent flows between three reactors as depicted in
Fig. 1. Steady-state mass balances can be written for a substance that reacts with
first-order kinetics. For example, the mass balance for reactor 1 is
- - -
(1)
where Q1,1n = the volumetric inflow to reactor 150 (L/min), C1,1n= the inflow
concentration to reactor 10 (g/L), Qu = the flow from reactor ito
Cs = the concentration of reactor i(g/L), k = a first-order decay rate (/min), and V1=
the volume of reactor i (mp).
02,in = 12 =
C2,in = 220
V2 = 50
Q2,1 = 22
03.2 = 5
01.2 = 5
V1 = 100
V3 = 150
Q1.in = 150
Q1.3 = 117
Q3,out = 112
C1,in = 10
Figure 1: Flow diagram for 3 chemical reactors.
Assignment
a) If k = 0.2/min, write the mass balances for all three reactors as a system of
linear algebraic equations.
b) Compute the LU decomposition for this system.
c) Use the LU decomposition to compute the matrix inverse.
d) Use the matrix inverse to answer the following questions: (i) What are the
steady-state concentrations for the thrce reactors? (ii) What fractions of this
concentration come from reactor 1 and reactor 27 (iii) If the inflow
concentration to the second reactor is set to zero, what is the resulting
reduction in concentration of reactor 17 (iv) If the in- flow concentration to
reactor 1 is doubled, and the inflow concentration to reactor 2 is halved, what
is
the concentration of reactor 3?
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