Page 114 - Chemical process engineering design and economics

98 Chapter 3

First, prime all the known variables, as shown in Table 3.1.1. Then list all the un-
knowns and calculate the degrees of freedom as shown. Because there is one de-
gree of freedom, no solution is possible. We must specify another variable.
To calculate the purging time from Equation 3.1.4, we must specify the final
oxygen concentration. When filling the tank with methane, it must be certain that
the methane concentration will never be within the flammability limits. The trian-
gular diagram in Figure 3.1.3 shows the flammability or ignition limits for mix-
tures of oxygen, nitrogen, and methane. Ignition could occur for any mixture of
the three gases within the flamability curve shown in Figure 3.1.3. Before filling
the tank with methane, reduce the oxygen content in the tank to avoid creating a
flammable mixture. In Figure 3.1.3, the sides and base of the triangle represent
two component mixtures. The base represents mixtures of oxygen and nitrogen,
the left side, mixtures of oxygen and methane, and the right side, mixtures of ni-
trogen and methane. If we do not purge the tank with nitrogen before filling with
methane, the concentration of the three component mixture will pass through the
flammability range. The mixing line in Figure 3.1.3 shows the mixing of methane
with air. The mixing line begins at the base of the triangle at 21% oxygen and ends
at the apex of the triangle, which represents 100% methane and 0% nitrogen. By
reducing the oxygen concentration to about 12% by adding nitrogen, the mixing
line will be tangent to the flammability curve when adding methane, as shown in
Figure 3.1.3. To be safe, however, reduce the oxygen concentration to 1% in the
nitrogen-oxygen mixture. The base of the triangle represents the mixing of nitro-
gen with air. After the oxygen concentration reaches 1%, then stop the nitrogen
flow. When filling the storage tank with methane initially, the methane will con-
tain an excessive amount of nitrogen. The storage facility will have to be designed
to dispose of the gases until the concentration of methane in the storage tank
reaches an acceptable level of purity. Essentially, the nitrogen-oxygen mixture is
now being purged with methane.
Now that we have specified the final oxygen concentration, the degrees of
freedom are zero, and we can solve the set of equations in Table 3.1.1. The next
step is to outline a solution procedure, i.e., to determine the order we will solve the
equations. In this case, the procedure is simple, and we can arrive at a suitable
order by inspection. When the number of equations increases, a greater effort will
be required to set up an efficient solution procedure.
After integrating Equation 3.1.4, the oxygen concentration in the tank at any
time becomes

y 2 j l =Kexp(-m 2 t/N) (3.1.13)

where K is a constant of integration. Using the initial condition that at t = 0, y 2,\ =
0.21 in Equation 3.1.13, we obtain K = 0.21.
Thus, Equation 3.1.13 becomes
y 2>! =0.21exp(-m 2 t/N) (3.1.14)

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