7.10: Untitled Page 155

Chapter 7

Turning our attention to the oxygen balance, we note that the mole fractions in Streams #1 and #2 are specified, thus we can represent Eq. 19

in the form

O :

( M

)

 R

 0 001

.

M

 0 . 21 M

(24)

2

O2 3

O2

1

2

Use of Eq. 7 provides the simplified version of the oxygen balance given by

O :

( M

)

 R

 0 509

.

M

(25)

2

O2 3

O2

1

In order to determine the molar flow rates of oxygen, carbon dioxide and water in the flue gas, we need to determine the global net rates of production of O , CO and H O . From Axiom II, in the form given by 2

2

2

Eqs. 11, and with the use of Eqs. 14, 15 and 16, we can express the global net rates of production of the three pivot species as

 0 . 004 M

 R

 R

 2

1

CO

R

2

H2O

O2

 0 . 528 M

  2 R

 3R

 4 R

(26)

1

CO

H O

O

2

2

2

 0 . 383 M

  2 R

 R

 2

1

CO

H O

RO

2

2

2

The solution of these three equations is given by

R

 0 . 387 M,

R

 0 . 536 M,

R

 

0 . 463 M (27)

CO2

1

H2O

1

O2

1

and these results can be used with Eqs. 20, 21 and 25 to provide the species molar flow rates for the flue gas, Stream #3.

( M

N )

1 94

.

M ,

( M

)

0 046

.

M

2 3

1

O2 3

1

(28)

( M

CO )

0 442

.

M ,

( M

)

0 5

. 36 M

2 3

1

H2O 3

1

One should keep in mind that the solution for the species molar flow rates in the flue gas should be based on three steps. Application of Axiom I and Axiom II represent two of those steps while the third step, a degree‐of-freedom analysis, was omitted.

Material Balances for Complex Systems

287

7.3 Recycle Systems

In the previous section we studied systems in which there were incomplete chemical reactions, such as combustion reactions that yielded both carbon dioxide and carbon monoxide. We must always consider the consequences of a desirable, but incomplete, chemical reaction. Do we simply discard the unused reactants? And if we do, where do we discard them? Can we afford to release carbon monoxide to the atmosphere without recovering the energy available in the oxidation of CO to produce CO ? What is the impact on the environment of 2

carbon monoxide? Even if we can achieve complete combustion of the carbon monoxide ( CO ) , what do we do with the carbon dioxide ( CO ) ?

2

Incomplete chemical reactions demand the use of recycle streams because we cannot afford to release the unused reactants into our ecological system, both for environmental and economic reasons. A typical reaction might involve combining two species, A and B, to form a desirable product C. The product stream from the reactor will contain all three molecular species and we must separate the product C from this mixture and recycle the reactants as indicted in Figure 7‐4. In a problem of this type, one would want to know the composition of the product stream and the magnitude of the recycle stream. The molar flow rate of the recycle stream depends on the degree of completion of the reaction in the catalytic reactor and the degree of separation achieved by the separator. The actual design of these units is the subject of subsequent courses on reactor design and mass transfer, and we will introduce students to a part of the reactor design process in Chapter 9. For the present we will concern ourselves only with the analysis of systems for which the operating characteristics are known or can be determined from the information that is given.

The analysis of systems containing recycle streams is more complex than the systems we have studied previously, because recycle streams create loops in the flow of information. In a typical recycle configuration, a stream generated far downstream in the process is brought back to the front end of the process and mixed with an incoming feed. This is indicated in Figure 7‐4 where we have illustrated a unit called a mixer that combines the feed stream with the recycle stream.

In addition to mixers, systems with recycle streams often contain splitters that produce recycle streams and purge streams. In Figure 7‐5 we have illustrated a unit called an “ammonia converter” in which the feed consists of a mixture of nitrogen and hydrogen containing a small amount of argon. The ammonia produced in the reactor is removed as a liquid in a condenser, and the

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