1
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(see figure) involves three chemical reactors A, B, and C.
At steady state, the concentrations of a particular species n
in each reactor has the values , , and in units of
tor j (A, B, or C) is denoted as (units of m3/s), then the
mass flow rate of species n from reactor i to reactor j is
(units of mg/s). Since this chemical species is con-
served (i.e., neither produced nor destroyed) conservation of mass (of the species) for each reactor must
hold. For the process shown in the figure, m3/s, m3/s, m3/s,
m3/s, m3/s, mg/s, and mg/s. Write down the mass con-
tinuity equations for each reactor and solve them to find the concentrations , , and in each reactor.
Solution
Conservation of mass yields:
QAin+xBQBA-xAQAC-xAQAB = 0
xAQAB-xBQBC-xBQBA = 0
QCin+xBQBC+xAQAC-xCQCout = 0
which yields:
Solution with MATLAB:
>> A=[-140 60 0; 40 -80 0; 80 20 -150];
A
A
B
C
x
A
Q
AC
m
Ain
x
C
Q
Cout
xA
xB
xC
Qij
xiQij
QAB 40=
QAC 80=
QBA 60=
QBC 20=
QCout 150=
mCin 195=
mAin 1320=
xA
xB
xC
−
−−
Ain
A
BAABAC
Q
x
0QQQ
−
C
2
>> B=[-1320; 0; -195];
>> x=A\B
x =
8.5000e+00
The solution is xA= 12 mg/m3, xB= 6 mg/m3, xB = and 8.5 mg/m3.