# 7.5: Untitled Page 150

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## Chapter 7

*Table 7.1*. Degrees‐of‐freedom for production of ethylene from ethane Stream & Net Rate of Production Variables

compositions (5 species & 2 streams)

*N* x *M* = 5 x 2 = 10

flow rates (2 streams)

*M* = 2

net rates of production (5 species)

*N* = 5

**Generic Degrees of Freedom**** (A)**

**17**

Number of Independent Balance Equations

mass/mole balance equations (5 species)

*N* = 5

Number of Constraints for Compositions (2 streams)

*M* = 2

Number of Constraints for Reactions (2 atomic species)

*T* = 2

**Generic Specifications and Constraints**** (B)**

**9**

Specified Stream Variables

compositions

4

Stream #1

flow rates

1

Stream #1

Constraints for Compositions

0

Auxiliary Constraints

3

Eqs. 1, 2 and 3

**Particular Specifications and Constraints**** (C) **

**8**

**Degrees of Freedom**** (A ‐ B ‐ C) **

**0**

At this point we direct our attention to Eq. 8 and make use of the information provided in Eqs. 1, 2, and 3 in order to express the net molar rate of production of hydrogen as

Y

R

1 2Y 3

C ( *M*

)

(10)

H

2

C

S

2

H6 1

Moving on to Eq. 9 we again utilize Eqs. 1, 2, and 3 in order to obtain

3Y

R

2 2Y

C ( *M*

)

(11)

CH

4

C

S

2H

1

6

Given the experimental values of the conversion, yield and selectivity indicated by Eqs. 1 through 3, along with the molar flow rate of Stream #1

( *M*

)

100 mol/s

(13)

C2H6 1

*Material Balances for Complex Systems *

277

we can solve Eqs. 10 and 11 to determine the global rates of production for methane and hydrogen.

R

19 *. * 0 mol/s *, *

R

1.0 mol/s

(14)

H2

CH4

Given these global rates of production for (CH ) and (H ) , the values for 4

2

the global rates of production of the other species can be easily calculated and this is left as an exercise for the student.

**7.2 Combustion Reactions**

Computation of the rate of production or consumption of chemical species during combustion is an important part of chemical engineering practice.

Efficient use of irreplaceable fossil energy resources is ecologically responsible and economically sound. Fuels are burned in combustion chambers using air as the source of oxygen ( O ) as illustrated in Figure 7‐3.. The fuel enters the 2

*Figure 7‐3*. Combustion process

combustion chamber at Stream #1 and air is supplied via Stream #2. Since air is 79% nitrogen ( N ) , and nitrogen can form NOX as part of the combustion 2

reaction, it is good practice to use only the amount of air that is needed for the reaction. On the other hand, the need to burn the fuels completely requires

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