12.6.2 Parallel Reactions in a PFR

We will now give three examples of multiple reactions with heat effects: Example 12-5 discusses parallel reactions, Example 12-6 discusses series reactions, and Example 12-7 discusses complex reactions.

Example 12-5. Parallel Reactions in a PFR with Heat Effects

The following gas-phase reactions occur in a PFR:

E12-5.1

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E12-5.2

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Pure A is fed at a rate of 100 mol/s, a temperature of 150°C, and a concentration of 0.1 mol/dm3. Determine the temperature and molar flow rate profiles down the reactor.

Additional information

ΔHRx1A = –20,000 J/(mol of A reacted in reaction 1)

ΔHRx2A = –60,000 J/(mol of A reacted in reaction 2)

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Solution

The PFR energy balance becomes [cf. Equation (12-35)]

E12-5.3

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Mole balances:

E12-5.4

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E12-5.5

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E12-5.6

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Rates:

Rate laws

E12-5.1

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E12-5.2

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Relative rates

Reaction 1: image

Reaction 2: image

Net rates:

E12-5.7

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E12-5.8

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E12-5.9

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Stoichiometry (gas phase ΔP = 0):

E12-5.10

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E12-5.11

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E12-5.12

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image

E12-5.13

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Energy balance:

E12-5.14

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The Polymath program and its graphical outputs are shown in Table E12-5.1 and Figures E12-5.1 and E12-5.2.

Table E12-5.1. Polymath Program

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Why does the temperature go through a maximum value?

Figure E12-5.1. Temperature profile.

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Figure E12-5.2. Profile of molar flow rates FA, FB, and FC.

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Analysis: The reactant is virtually consumed by the time it reaches a reactor volume V = 0.45 dm3 and beyond this point Qr > Qg and the reactor temperature begins to drop. In addition, the selectivity image remains constant after this point. If a high selectivity is required, then the reactor should be shortened to V = 0.3 dm3, at which point the selectivity is image.

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