# 7.17: Untitled Page 162

## Chapter 7

Figure 7.5c. Control volumes for vinyl chloride production unit

Material Balances for Complex Systems

301

Table 7.5. Degrees‐of‐freedom for production of vinyl chloride from dichloroethane

Stream & Net Rate of Production Variables

compositions (4 species & 4 streams)

N x M = 4 x 4 = 16

flow rates (4 streams)

M = 4

net rates of production (4 species)

N = 4

Generic Degrees of Freedom (A)

24

Number of Independent Balance Equations

mass/mole balance equations

4 x 2 = 8

(4 species & two control volumes)

Number of Constraints for Compositions (4 streams)

M = 4

Number of Constraints for Reactions (3 atomic species)

T = 3

Generic Specifications and Constraints (B)

15

Specified Stream Variables

compositions (Streams #1, 4, & 5)

3 + 1 + 3 = 7

flow rates

0

Constraints for Compositions

0

Auxiliary Constraints (conversion)

1

Particular Specifications and Constraints (C)

8

Degrees of Freedom (A ‐ B ‐ C)

1

Here we note that the concentrations of HCl and C H Cl are zero in 2

3

Stream #2 and this information has been ignored in the degree‐of‐freedom analysis. The explanation for this requires a degree‐of‐freedom analysis of the mixer that is left as an exercise for the student. Since there is one degree of freedom, we will need to work in terms of dimensionless molar flow rates.

For the control volumes illustrated in Figure 7.5c we can express Eq. 2 as

M

(

)

( M )

A exit

A entrance R A

Axiom I:

exits

entrances

(8)

A  1 , 2 , 3 , 4

302