Oxidation of Naphthalene to Phthalic Anhydride

The oxidation is to be carried out in a packed bed reactor with cooling. The ambient temperature is constant along the length of the reactor. The pressure is 1 atm and the partial pressure of naphthalene is varied between 0.01 atm and 0.02 atm. The entering temperature is varied between 600 and 675.

a) Starting
with the nomenclature and the mole balances in the text, write the mole balances
in the form given by VanWelseneare and Froment [*CES*
**25** p1503 (1970)].

b) Starting with the nomenclature and the energy balances given in the text, write the energy balance in the form given by VanWelseneare and Froment.

c) For each of the conditions in part (b), make a phase plane plot to include the critical trajectories for

1) Locus of maximum concentrations C_{Am} vs. T

2) Locus of inflection point concentrations C_{Ai}(1)
and C_{Ai}(2)
vs. T

d) Plot the partial pressure and temperature profile for

1) T_{0}
= 600 , T_{a}
= 600 , P_{i0}
= 0.017 atm

2) T_{0}
= 625 , T_{a}
= 625 , P_{i0}
= 0.017 atm

3) T_{0}
= 625 , T_{a}
= 625 , P_{i0}
= 0.01825 atm

4) T_{0}
= 625 , T_{a}
= 625 , P_{i0}
= 0.0185 atm

a) Put the mole balance equation in form used by VanWelseneare, i.e.

Starting with the Mole Balance

The rate law is

Combine rate law and mole balance

b) Put the energy balance in the form used by VanWelseneare

Starting
from the basic energy balance

Parameter Values

Gas density:

Catalyst bulk density:

Entering gas velocity:

Specific reaction rate:

Overall heat transfer coefficients:

Radius of pipe:

Entering partial pressure of O_{2} (B) [X.S.O_{2}]:

**Evaluating
the parameters A, B, and C.
**

c) Calculate the locus of the maximum,

At the maximum, T_{m}

at max P_{A} = P_{m}

At the inflection point
at T = T_{i},
P_{A}
= P_{i
}

The equations for the inflection points are

The equations for the inflection points are

Table R8.2-1. Finding P_{m}, P_{1}, and P_{2} as a Function of
Temperature

The Polymath program to calculate the trajectories is shown in Table R8.2-2.

Table R8.2-2. Trajectories for Runaway

Inflection Points

P_{1}=P_{i1}

Inflection Points

P_{1}=P_{i1}

P_{2}=P_{i2}

d) We will now increase P_{A0} from a stable 0.017 atm to 0.0185 atm where runaway will occur.

Criteria 1 is not exceeded.

Reaction Conditions: T_{0} = T_{w} = 600K , P_{A} = 0.017
atm

We are far from runaway. The intersection of the P_{A} vs. T trajectory with P_{m} vs.
T_{m} is no where near the maximum. Very little conversion at these conditions _{}. Now increase the temperature to 625°K.

Runaway Criteria 1 exceeded, but Criteria 2 is not exceeded.

Reaction Conditions: T_{0} = T_{w} = 625K , P_{A0} = 0.018 atm

Here we are at (approximately) criteria 1 the P_{A} vs. T trajectory intersects the P_{m} vs.
T_{m} curve near the maximum.

At P_{A0}=0.01825 atm we are at the oneset of Runaway.

Reaction Conditions: T_{0} = T_{w} = 625K , P = 0.01825 atm

One notes that we are at the onset of runaway. The P_{A} vs. T trajectory is tangent to the inflection
point curve (criteria 2).

Runaway has occured.

Reaction Conditions: T_{0} = T_{w} = 625K , P = 0.0185 atm

Runaway occurs when we increased the entering partial pressure ever so slightly from 0.01.

Back to Runaway Reactions in PFRs