7.16: Untitled Page 161

Chapter 7

 R

C2H6

2 0 2 2

0

 R

HCl

 

6 1 3 4 

 

0

(5)

 

 RC

2H3Cl

0 1 1 2

0

 

RC

2H4Cl2 

Representing  N

JA  in row reduced echelon form leads to

 R

C2H6

1 0 0 0

0

 R

HCl

 

0 1 0 1 

 

0

(6)

 

 RC

2H3Cl

0 0 1 1

0

 

RC

2H4Cl2 

and application of the global pivot theorem (see Sec. 6.4) provides the following constraints on the global net rates of production:

Axiom II:

R

 0 ,

R

  R

,

R

  R

(7)

C2H6

HCl

C2H4Cl2

C2H3Cl

C2H4Cl2

Here we see that ethane acts as an inert, a conclusion that might have been extracted by intuition but has been made rigorous on the basis of Axiom II. The constraints given by Eqs. 7 apply to each control volume that we construct for the system illustrated in Figure 7.5a, and we are now ready to construct those control volumes making use of the rules listed above. On the basis of those rules we make the following five primary cuts:

I. A cut of Stream #1 is made because the composition of Stream #1

is given. NOTE: “The composition of the feed Stream #1 is 98%

dichloroethane and 2% ethane on a molar basis.”

II. A cut of Stream #5 is made because information about the composition is given for that stream. NOTE: “We assume that the separation column produces a sharp separation meaning that all the dichloroethane leaves in the bottom Stream #5, and the remaining components (ethane, hydrochloric acid and vinyl chloride) leave through the distillate Stream #4.”

III. A cut of Stream #4 is made because information about the composition is given for that stream. NOTE: “We assume that the

Material Balances for Complex Systems

299

separation column produces a sharp separation meaning that all the dichloroethane leaves in the bottom Stream #5, and the remaining components (ethane, hydrochloric acid and vinyl chloride) leave through the distillate Stream #4.”

IV. A cut of Stream #2 is required because information about the global net rate of production is given in terms of conditions in Stream #2. NOTE: The statement about the conversion requires that R

  ( M

C

)

C2H4Cl2

C2H4Cl2 2

V. At least one control volume must enclose the reactor since information about the global net rate of production is given.

NOTE: R

  ( M

C

) .

C2H4Cl2

C2H4Cl2 2

The cuts based on Rules I through VI are indicated in Figure 7.5b. Two control volumes can be created that satisfy these rules, and these are Figure 7.5b. Cuts for the construction of control volumes illustrated in Figure 7.5c where we note that there is a single redundant cut of Stream #1. Given this choice of control volumes, our next step is to perform a degree‐of‐freedom analysis as indicated in Table 7.5. There we see that we have a solvable problem.

300