7.4: Untitled Page 149

Chapter 7

EXAMPLE 7.1: Production of ethylene

Ethylene ( C H ) is one of the most useful molecules in the 2

4

petrochemical industry (see Figure 1‐7) since it is the building block for poly‐ethylene, ethylene glycol, and many other chemical compounds used in the production of polymers. Ethylene can be produced by catalytic dehydrogenation of ethane ( C H ) as shown in Figure 7.1. There we 2

6

have indicated that the stream leaving the reactor contains the desired product, ethylene ( C H ) in addition to hydrogen ( H ) , methane ( CH ) , 2

4

2

4

propylene ( C H ) and some un‐reacted ethane ( C H ) . As in every 3

6

2

6

example of this type, the reader needs to consider the principle of stoichiometric skepticism that is discussed in Sec. 6.1.1 since small amounts of unidentified molecular species are always present in the output of a reactor.

Figure 7.1 Catalytic production of ethylene

The experiment illustrated in Figure 7.1 has been performed in which the molar flow rate entering the reactor (Stream #1) is 100 mol/s of ethane.

From measurements of the effluent stream (Stream #2), the following information regarding the conversion of ethane, the selectivity of ethylene relative to propylene, and the yield of ethylene is available:

 RC H

2

6

C  Conversion of C H



 0 . 2

(1)

2

6

( M



)

C2H6 1

RC H

S  Selectivity of C H /C H



 5

(2)

2

4

3

6 

2

4

RC3H6

RC H

Y  Yield of C

/C H



 0 7

. 5

(3)

2H4

2

6 

2

4

 RC2H6

Material Balances for Complex Systems

275

The global net rates of production of individual species are constrained by the stoichiometry of the system that can be expressed in terms of Axiom II.

The atomic matrix for this system is given by

Molecular Species  H

CH

C H

C H

C H

2

4

2

6

2

4

3

6

carbon

 0

1

2

2

3 

(4)

hydrogen





 2

4

6

4

6 

and the elements of this matrix are the entrees in  N 

 JA  that can be

expressed as

0 1 2 2 3

 N  

(5)

JA









2 4 6 4 6

Use of this atomic matrix with Axiom II as given by Eq. 6‐22 leads to

 R



H2





 R



CH4

0 1 2 2 3 



0

Axiom II:



 R

 

C H

 

(6)

2

6

2 4 6 4 6

0







RC H 

2

4





RC





3 H6 

At this point the atomic matrix can be expressed in row reduced echelon form leading to the global pivot theorem given by Eq. 6‐81. We express this result in the form





RC

 R





2 H6 

H

 1

2

3 

Global Pivot Theorem:

2



 







 R

(7)

C H

R









2

4

 2

2

3  



CH



4 

R



C



3 H6 

and we carry out the matrix multiplication to obtain

R

 R

 2 R

 3R

(8)

H2

C2H6

C2H4

C3H6

R

  2 R

 2 R

 3R

(9)

CH

C2H6

C H4

C3H

4

2

6

The five net rates of production that appear in Eqs. 6 though 9 are represented in the degree of freedom analysis given in Table 7.1. There we see that there are zero degrees of freedom and we have a solvable problem.

276