1. The elementary irreversible liquid phase reaction A ----> B + C is carried out in a
tubular reactor. The reactor is surrounded by a heat exchanger and the temperature of
the heating medium Ta is constant at 1150K. The inlet temperature is 1035K and pure
A is provided. Plot the conversion and temperature along the length of the reactor.
FA0 = 0.0376 mol/s, υ0 = 0.002 m3/s, V = 5 dm3, Ua = 16,500 J/m3/s/K
HA° (298K) = -216.67 kJ/mol; HB° (298K) = -61.09 kJ/mol; HC° (298K) = -74.81
kJ/mol;
CpA = 163 J/mol·K, CpB = 83 J/mol·K, CpC = 80 J/mol·K;
a. k is a constant at 0.05s-1
b. k is not a constant, at 6exp(-5000/T) s-1,
c. Calculate what size of the reactor you need to have if the conversion ratio has to
reach 50%.
Explain:
dX
 rA / Fa0 ;
dV
2. Rate Law  rA  kCA
3. Stoichiometry: C A  C A0 (1  X ) for liquid
1. Mass balance:
4. Energy balance:
dT U a(Ta  T )  (rA )( H rx )

dV
Fa 0 ( i Cpi  xCp)
Solution:
We need to solve two ode equations:
dX
 k * C A0 * (1  X ) / Fa0
dV
dT U a(Ta  T )  k * C A0 * (1  X ) * (( H B  H C  H A )  (Cpb  Cpc  Cpa) * (T  298)

dV
Fa 0 (Cpa  x(Cpb  Cpc  Cpa))
Two initial conditions:
X=0 if V=0
T=1035 if V=0
In previous Lab 4 and Lab 5, we use the loop to solve these two equations. This class we are
going to use function ode45 to solve these two equations.
Let us work on Part a) first.
We are going to use ode45 function to solve these equations. First, you need to create a m-file
with the file name same as the function name. For example, let’s create a lab5.m file as the
following: we define our function name as lab5. We are having two equations, so we create a dy
vector with two columns, one column y1 as our conversion ratio X at correspondent V, another
column y2 as our temperature T at correspondent V. Here is the function code:
function dy=lab5(v,y)
y1=y(1);
y2=y(2);
dy1=0.05/0.002*(1-y1);
dy2=(16500*(1150-y2)+0.05*0.0376/0.002*(1-y1)*80770)/(0.0376*163);
dy=[dy1;dy2];
We save this function file as a m-file. Remember, the function name should be defined the same
as the file name without extension “.m”.
As long as function is defined, we then can use ode45 to solve the equations. You can search the
help desk in MathWorks to know the detailed meaning of syntax ode45.
Put the following sentence in your command windows:
[v,y]=ode45(@lab5,[0 0.005],[0,1035]);
@lab5 means that you are going to use your defined function named as “lab5”; [0,0.005] means
that your ‘time’ vector (which in this case is the volume of the reactor V) changes from 0 to
0.005; [0, 1035] means two initial conditions for your equations. Hit the enter and the equations
will be solved.
Finally, you can make a plot and compare these plots with your results from previous lab.
Remember, you are putting solutions into a two column vector with the first column as
conversion ratio X and second column as the temperature T. So when you want to make a plot
between volume V and conversion ratio X, you need to write the following command;
plot (v,y(:,1));
If you want to make a plot between volume V and temperature T, write the following sentence:
plot (v,y(:,2));
Lab assignment: Continue working on part b and c by using ode45 to solve your equations. For
your lab assignments to be turned in, you need to provide the programming codes for part a, b c.
For part a and b, provide plot (volume of the reactor, conversion ratio) and plot (volume of the
reactor, temperature) for each conditions. For part c, provide the size of the reactor.